Handbook on Radiation Probing Gauging Imaging and Analysis Applications

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HANDBOOK ON RADIATION PROBING, GAUGING, IMAGING AND ANALYSIS

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Handbook on Radiation Probing,

Gauging, Imaging and Analysis

Volume II:

Applications and Design

by

ESAM M.A. HUSSEIN Department of Mechanical Engineering, University of New Brunswick, Fredericton, New Brunswick, Canada

KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

eBook ISBN: Print ISBN:

0-306-48403-X 1-4020-1295-0

©2004 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©2003 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: and Kluwer's eBookstore at:

http://kluweronline.com http://ebooks.kluweronline.com

Dedicated in memory of my Father Mahmoud, my Uncle Roshdi, and my Aunt Alia.


Contents

Preface Acknowledgments

xix xxi

Foreword

xxiii

VOLUME TWO: APPLICATIONS AND DESIGN

441

PART III:

443

APPLICATIONS

10. PROBING, INSPECTION AND MONITORING 10.1 Surface Condition 10.2 Damage and Flaw Detection 10.3 Residual Stresses 10.4 Flow Obstruction 10.5 Monitors 10.5.1 Process Monitoring 10.5.2 Smoke Detectors 10.5.3 Radon 10.5.4 Other Gases 10.6 Hidden Materials 10.6.1 Industrial Materials 10.6.2 Radioactive Materials 10.6.3 Illicit Materials

447 447 454 456 457 458 458 460 460 462 463 463 463 464

11. GAUGING 11.1 Bulk Density 11.1.1 Alpha-Particle Transmission

465 465 466

vii

viii

Radiation Probing, Gauging, Imaging and Analysis

11.2

11.3 11.4 11.5

11.6

11.1.2 Beta-Particle Transmission 11.1.3 Beta-Particle Scattering 11.1.4 Photon-Based Methods Thickness 11.2.1 Charged Particles 11.2.2 Photon Transmission 11.2.3 Photon Scattering 11.2.4 X-ray Emission 11.2.5 Neutrons 11.2.6 Composition-Independent Porosity and Voidage Water (Moisture) Content Measurements in Fluid Flow 11.5.1 Density 11.5.2 Flow-Rate by Radiotracers 11.5.3 Gas Flow-Rate by Ionization 11.5.4 Flow-Rate by Pulsed-Neutron Activation

11.5.5 Level Measurement 11.5.6 Liquid-Liquid Interface 11.5.7 Leak Detection 11.5.8 Volume 11.5.9 Gas Properties 11.5.10 Flow Distribution 11.5.11 Void Fraction 11.5.12 Multiphase Flow 11.5.13 Isotope Hydrology Dating

12. ELEMENTAL AND CONTENT ANALYSIS 12.1 Nucleus-Based Analysis 12.1.1 Activation Analysis 12.1.2 Passive Emission 12.1.3 Resonance Effects 12.1.4 Fast-Neutron Scatteroscopy 12.1.5 Charged-Particle Scatteroscopy 12.2 Atom-Based Analysis 12.2.1 Fluoroscopic Excitation 12.2.2 Composition Indication 12.3 Hydrogen Measurement 12.3.1 Neutron Slowing-Down 12.3.2 Scattering into Resonances 12.3.3 Beta Particles 12.3.4 Compton Scattering 12.3.5 Cold Neutrons

467 468 468 474 475 476 478 479 482 482 483 484 489 490 491 494 494 495 502 503 506 507 510 511 515 517 518 521 522 522 544 549 553 554 556 556 562 571 574 579 582 584 585

Contents

ix

12.4 Material Content Analysis 12.4.1 Alpha Particles 12.4.2 Beta Particles 12.4.3 Photons 12.4.4 Neutrons 12.4.5 X-ray Fluoroscopic Emission 12.4.6 Mössbauer Spectroscopy 12.4.7 Natural Radioactivity 12.4.8 Combined Techniques

585

586

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591

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603

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604

13. IMAGING 13.1 Photon Radiography 13.1.1 Film Radiography 13.1.2 Radioscopy 13.1.3 Flash Radiography 13.1.4 Microfocus Radiography 13.1.5 Megavoltage Radiography 13.1.6 Low-Energy Radiography 13.1.7 Bremsstrahlung Radiography 13.1.8 Laminography 13.1.9 Scatterography 13.1.10 Emission Imaging 13.1.11 Diffraction Imaging 13.2 Neutron Radiography 13.3 Charged-Particle Radiography 13.3.1 Autoradiography 13.4 Tomography 13.4.1 Photon Tomography 13.4.2 Neutron Tomography 13.4.3 Scatter Imaging 13.4.4 Emission Tomography 13.4.5 Proton Tomography 13.5 Imaging for Material Content 13.5.1 Dual-Energy Imaging 13.5.2 Critical-Edge Tomography 13.5.3 Transmission/Scatter Imaging 13.5.4 Photon Coherent-Scatter Imaging 13.5.5 Emission Imaging

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PART IV:

DESIGN

14. PERFORMANCE PARAMETERS AND DESIGN ASPECTS 14.1 Performance Parameters

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653

x


14.2 Statistical Optimization 14.3 Design Objectives 14.4 Source Selection 14.4.1 Radiotracers 14.4.2 Source Generation 14.4.3 Source Energy 14.4.4 Interfering Radiation 14.5 Selection of Technique 14.6 Detection System 14.6.1 Detector Selection 14.6.2 Electronics 14.6.3 Detector Collimation 14.6.4 Filtration

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15. SOURCE MODULATION 15.1 Source Collimation 15.1.1 Design Parameters 15.1.2 Geometry 15.1.3 Beam Profile 15.1.4 Divergence and Alignment 15.1.5 Collimation of Charged-Particles 15.1.6 Photon Collimation 15.1.7 Fast-Neutron Collimation 15.1.8 Collimation of Thermal-Neutrons 15.2 Filtering 15.2.1 X-Rays 15.2.2 Neutrons 15.3 Neutron Moderation 15.3.1 Moderating Materials 15.3.2 Moderating by Containment 15.3.3 Block Moderation 15.3.4 Moderation by Reflection 15.4 Neutron Multiplication

681

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16. DESIGN CALCULATIONS 16.1 Design Parameters 16.2 Monte Carlo Simulation 16.3 Shielding 16.3.1 General 16.3.2 X-Ray Machines 16.3.3 Isotopic Gamma Sources 16.3.4 Neutrons 16.3.5 Computer Codes

719

719

720

728

728

732

734

735

735

Contents

xi

17. EXPERIMENTS 17.1 Experimental Aspects

17.2 Licensing

17.2.1 General

17.2.2 X-Ray Machines

17.2.3 Radioisotopes

17.2.4 Particle Accelerators

17.3 Background Reduction

17.3.1 Definition and Origin of Background

17.3.2 In Transmission

17.3.3 In Scattering

17.3.4 In Emission

17.4 Dynamic Analysis

17.4.1 Expected-Value Analysis

17.4.2 Frequency Analysis

17.4.3 Movement

739 739 742 742 746 748 749 751 751 752 754 756 757 758 759 761

18. FINALIZATION 18.1 Prototyping

18.2 Intellectual Property Protection

763 763 766

A.

Basic Units and Constants

xxvii

B.

List of Elements and Natural Isotopes

xxix

C.

Relativistic Mechanics

xxxv

D.

Quantum Mechanics D.1 Preliminaries D.2 Schrödinger Equation D.3 Concept of Cross-Section D.4 Quantum Electrodynamics

E.

Nuclear/Atomic Parameters for Compounds and Mixtures E.1 Atomic Density E.2 Electron Density E.3 Macroscopic Cross-Section E.4 Effective Mass and Atomic Numbers E.4.1 Electron-Density Based E.4.2 Reaction Cross-Section Based E.4.3 React ion-Ratio Based

F.

Effective Energy F.1 Mean Energy

xxxix xxxix xli xlvi l liii liii liv lv lvii lvii lvii lviii

lxi lxi

xii


F.2 Most Probable Energy F.3 Cross-Section Dependent F.4 Best Match G.

Radiation Counting Statistics G.1 Poisson Statistics G.1.1 Mean and Variance G.1.2 Population Statistics G.2 Gross/Background Count Rates G.2.1 Net Count Rate G.2.2 Number of Measurements and Counting Period G.3 Goodness of Data G.4 Current-Mode Statistics G.5 Elemental Error

References

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lxv lxv

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lxviii

lxviii

lxix

lxx

lxxii

lxxv

lxxvii

About the Author

clxxxvii

Application Index

clxxxix

Index

cxcix

Contents

Preface Acknowledgments

xix

xxi

Foreword

xxiii

VOLUME ONE: BASICS AND TECHNIQUES

1

1. INTRODUCTION 1.1 Why Radiation 1.2 Nondestructive Examination (NDE) 1.3 Conventional NDE Methods 1.4 Elements of NDE 1.5 Intricacy of Radiation Methods

3

3

4

6

9

10

PART I:

15

BASICS

2. RADIATION TYPES AND SOURCES 2.1 Charged Particles 2.1.1 Alpha Particles 2.1.2 Beta Particles 2.1.3 Discrete-Energy Electrons 2.1.4 Positrons 2.1.5 Heavy-Charged Particles 2.2 Photons 2.2.1 X-ray Machines 2.2.2 Low-Energy Photon Sources 2.2.3 Primary Gamma Rays 2.2.4 Indirect Gamma Rays 2.3 Neutrons 2.3.1 Fast Neutrons 2.3.2 Intermediate-Energy Neutrons 2.3.3 Slow Neutrons 2.3.4 Cold Neutrons 2.4 Natural Sources

xiii

19

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xiv


3. MODIFYING PHYSICS 3.1 General 3.2 Cross Sections 3.2.1 Microscopic Cross-Section 3.2.2 Differential Cross-Section 3.2.3 Macroscopic Cross-Section 3.3 Charged Particles 3.3.1 Alpha Particles 3.3.2 Beta Particles 3.4 Photons 3.4.1 Photoelectric Absorption 3.4.2 Incoherent/Inelastic (Compton) Scattering 3.4.3 Coherent/Elastic Scattering 3.4.4 Pair Production 3.4.5 Photo-nuclear Interactions 3.5 Neutrons 3.5.1 Elastic Scattering 3.5.2 Inelastic Interactions 3.5.3 Absorption 3.5.4 Fission and Multiplicity Reactions 3.5.5 Coherent Scattering 3.5.6 Cross Sections 3.6 Radiation Transport 3.6.1 Classical Laws of Conservation 3.6.2 Divergence Law 3.6.3 Attenuation Law 3.6.4 Diffusion Theory 3.6.5 Transport of Charged-Particles 3.7 Radioactive Decay 3.7.1 Kinetics of Decay 3.7.2 Parent / Daughter Decay 3.7.3 Equilibrium 3.7.4 Decay Chains

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4. DETECTION METHODS 4.1 Introduction 4.2 Charged-Particle Detectors 4.2.1 Detection by Chemical Reactions 4.2.2 Detection by Direct Ionization 4.2.3 Detection by Scintillation 4.2.4 Semiconductor Detectors 4.3 Photon Detectors 4.3.1 Gas-Ionization Detectors 4.3.2 Scintillation Detectors 4.3.3 Semiconductor Detectors 4.3.4 Radiographic Films 4.3.5 Electrostatic Plates 4.4 Neutrons Detectors

139

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Contents

xv

4.4.1 4.4.2 4.4.3 Signal 4.5.1 4.5.2 4.5.3 4.5.4 4.5.5 4.5.6 4.5.7

Gas Detectors Scintillation Detectors Other Detection Methods Processing and Analysis Basic Components Pulse-Mode Counting Current-Mode Operation Energy Spectroscopy Timing Measurements Statistics Problems in Pulse Analysis

189

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5. RADIATION SAFETY 5.1 Introduction 5.2 Principles and Definitions 5.3 Principles of Radiation Protection 5.4 Monitoring and Dosimetry

243

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248

4.5

PART II:

TECHNIQUES

253

6. TRANSMISSION METHODS 6.1 Measurement Model 6.2 Pencil-Beam Probing 6.3 Radiography 6.3.1 Film Radiography 6.3.2 Variations of Film Radiography 6.4 Tomography 6.4.1 Problem Formulation 6.4.2 Back-Projection 6.4.3 Successive Approximation 6.4.4 Modal Approximation 6.4.5 Filtered Back-Projection 6.4.6 Image Quality 6.5 Special Methods 6.5.1 Combined with Scattering 6.5.2 Region-of-Interest Imaging 6.5.3 Dual Transmission 6.5.4 Resonance Mapping 6.5.5 Mössbauer Spectrometry 6.6 Charged-Particle Transmission 6.6.1 Alpha Particles 6.6.2 Beta Particles 6.6.3 Electron Radiography

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7. SCATTERING METHODS 7.1 Introduction 7.2 Measurement Model

311

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xvi


7.3

7.4 7.5

7.6 7.7

7.8 7.9 7.10

7.2.1 Model for Compton Scattering 7.2.2 Model for Neutron-Elastic Scattering Point Probing 7.3.1 Neglected Attenuation 7.3.2 Signal Modulation 7.3.3 Attenuation Averaging 7.3.4 Constant-Transmission 7.3.5 Normalized Scattering and Transmission 7.3.6 Single Low-Energy Source Transmission-Assisted 7.3.7 Two-Source Transmission-Assisted 7.3.8 Dual-Energy: Special Case 7.3.9 Dual-Energy: General Case 7.3.10 Coherent-Scatter Probing 7.3.11 Probing with Neutrons Multi-Point Probing and Analysis Scatterometry 7.5.1 Measurement Model 7.5.2 Linear Response 7.5.3 Variable Source-to-Detector Distance Method 7.5.4 Ratio Method 7.5.5 Saturated Scattering 7.5.6 Energy Spectrum 7.5.7 Combined Bulk and Probing Measurements Scatterography Reconstructed Scatter-Imaging 7.7.1 Point-by-Point Scanning 7.7.2 Integration Method 7.7.3 Nonlinear Solution 7.7.4 Coherent-Scatter Imaging X-Ray Diffraction and Refraction 7.8.1 X-Ray Diffraction 7.8.2 Refraction Neutron Diffraction Scattering of Charged-Particles 7.10.1 Scattering of Alpha-Particles 7.10.2 Scattering of Beta-Particles 7.10.3 Scattering of Ions

8. EMISSION METHODS 8.1 Gamma-Ray Emission by Neutron Activation 8.1.1 Measurement Model 8.1.2 Thermal-Neutron Activation 8.1.3 Epithermal-Neutron Activation 8.1.4 Fast-Neutron Activation 8.2 Gamma-Ray Emission by Charged-Particle Activation 8.3 Gamma-Ray Emission by Photon Activation 8.4 Gamma-Ray Emission by Positronium Decay

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Contents

xvii

8.5

399

400

401

8.6

8.7

8.8

Charged-Particles Emission 8.5.1 Charged-Particle Emission by Photon Activation 8.5.2 Charged-Particles Emission by Neutron Activation 8.5.3 Charged-Particle Emission by Charged-Particle

Activation Neutron Emission 8.6.1 Neutron Emission by Gamma-Ray Activation 8.6.2 Neutron Emission by Charged-Particle Activation 8.6.3 Neutron Emission by Neutron Activation X-Ray Emission

8.7.1 Excitation by Isotopic Sources

8.7.2 X-Ray Excitation

8.7.3 Charged-Particle Excitation

Emission from Internal Sources

8.8.1 Radiotracing 8.8.2 Radioactive Materials 8.8.3 Emission Imaging 8.8.4 Gamma Cameras

9. ABSORPTION METHODS

9.1 Absorption of Charged Particles

9.2 Photon Absorption Methods

9.3 Neutron Flux Depression Method

9.4 Decay-Time of Neutrons

402

404

404

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406

407 408 414 415 417 418 420 425 430 433 433 435 436 439

A.

Basic Units and Constants

xxvii

B.

List of Elements and Natural Isotopes

xxix

C.

Relativistic Mechanics

xxxv

D.

Quantum Mechanics D.1 Preliminaries D.2 Schrödinger Equation D.3 Concept of Cross-Section D.4 Quantum Electrodynamics

E.

Nuclear/Atomic Parameters for Compounds and Mixtures E.1 Atomic Density E.2 Electron Density E.3 Macroscopic Cross-Section E.4 Effective Mass and Atomic Numbers E.4.1 Electron-Density Based E.4.2 Reaction Cross-Section Based E.4.3 Reaction-Ratio Based

xxxix xxxix xli xlvi l liii liii liv lv lvii lvii lvii lviii

xviii


F.

Effective Energy F.1 Mean Energy F.2 Most Probable Energy F.3 Cross-Section Dependent F.4 Best Match

G.

Radiation Counting Statistics G.1 Poisson Statistics G.1.1 Mean and Variance G.1.2 Population Statistics G.2 Gross/Background Count Rates G.2.1 Net Count Rate G.2.2 Number of Measurements and Counting Period G.3 Goodness of Data G.4 Current-Mode Statistics G.5 Elemental Error

References

lxi lxi lxii lxii lxii lxv lxv lxvi lxvii lxviii lxviii lxix lxx lxxii lxxv lxxvii

About the Author

clxxxvi

Application Index

clxxxix

Index

cxcix

Preface

The need for this book arose from my teaching, engineering, and research experience in the non-power aspects of nuclear technology. The lack of a comprehensive textbook in industrial applications of radiation frustrated my students, who had to resort to a multitude of textbooks and research publications to familiarize themselves with the fundamental and practical aspects of radiation technology. As an engineer, I had to acquire the design aspects of radiation devices by trial-and-error, and often by accidental reading of a precious publication. As a researcher and a supervisor of graduate students, I found that the needed literature was either hard to find, or too scattered and diverse. More than once, I discovered that what appeared to be an exciting new idea was an old concept that was tried a few decades earlier during the golden era of “Atom for Peace”. I am hoping, therefore, that this book will serve as a single comprehensive reference source in a growing field that I expect will continue to expand. This book is directed to both neophytes and experts, and is written to combine the old and the new, the basic and the advanced, the simple and the complex. It is anticipated that this book will be of help in reviving older concepts, improving and expanding existing techniques and promoting the development of new ones. Hopefully, the consolidation of this material in one book will incite wider use and application of this powerful and useful technology. Therefore, the book is intended to be a single handy source of information for students, instructors, current and potential users of radiation technology, and its design engineers and researchers. The book is divided into four parts to accommodate a wide spectrum of readers. Part I deals with the fundamental aspects of radiation sources, physics and detection, and is particularly helpful for students who are not familiar with nuclear and atomic radiation. Part II is dixix

xx


rected to industrial physicists and engineers, as it provides an exposition of the different ways (techniques) by which radiation can be used to meet industrial measurement needs. Part III presents a large number of specific industrial applications. In order to assist the reader, an application index is given at the end of the book, identifying the areas in which radiation techniques are utilized. Those who would like to design a new device, or improve or alter an existing system, can refer to Part IV. This book can serve both as a reference book and as a textbook. To assist readers in searching and locating specific information, two separate indices are provided, paragraphs are given titles, and wide use is made of cross-referencing. Extensive literature is cited, and references are listed in detail. Three one-semester courses can be based on this book. The first part of the book, along with appendices C, D, E and G, can be used in an introductory course on radiation fundamentals to students with no or little background in atomic and nuclear physics. Part II, introduced by Chapter 1 and supplemented by appendix F, can serve as a course on nondestructive examination and imaging with radiation, assisted by example applications from Part III. A design course can be based on Part IV, with design projects assigned for systems described in Part III. For a set of problems and solutions, instructors can contact the author by e-mail at [email protected]. The author welcomes any comments and suggestions for inclusion in future revisions of this book. ESAM M. A. HUSSEIN

Acknowledgments

Dr. John H. Hubbell has given me the great honor of writing the “Foreword” to the book, and provided viable comments and suggestions. Dr. Hubbell needs no introduction; researchers, practitioners and students of x- and gamma-rays are all familiar with his comprehensive work and tables on photon cross sections. The concept of this work was formulated through discussions with esteemed colleagues: Dr. Ned Kondic (formerly with the US Nuclear Regulatory Commission) in the late 1980’s, and Dr. Richard C. Lanza (Massachusetts Institute of Technology) and Prof. Nares Chankow (Chulalongkorn University, Thailand) in the nineties. Although writing this manuscript was a solo endeavor, it would not have been possible without the effort of all the authors whose work is cited in the book. Mr. P. Jacob Arsenault, Mr. Hassan A. Jama, Dr. Edward J. Waller and Dr. Ilan Yaar, of the Laboratory for Threat Material Detection at University of New Brunswick (UNB), thankfully read some chapters and provided useful suggestions. The prompt and professional response of the staff of the UNB Libraries, particularly at the Engineering Library and the Document Delivery Department, made it possible for me to readily access the based on needed literature. This book was written using platform, with WinTex 2000 as the interfacing editor. Finally a personal note to my wonderful children Mahmoud and Amina: without your love, forbearance, patience and understanding, the completion of this work would not have been possible.

xxi


Foreword

In browsing through a draft copy of this two-volume “how-to” desk reference on virtually all aspects of the use of photon and corpuscular radiations in the interrogation of materials and structures, I found the presentation format to be unique and useful. Although the variety and comprehensiveness is akin to a topical encyclopedia, the presentation reminded me of a thesaurus, in which the subtopics are not sequenced alphabetically, but, similar to in a thesaurus, are sequenced in a logical progression. Then, going “Roget” one better, at the end of the book are found not one, but two alphabetized indexes, first an “application index” and finally a conventional index alphabetically listing key words and their page numbers from throughout the text. In Volume One (Basics and Techniques), following a brief Chapter 1 (Introduction) surveying the unique features of radiation interrogation, often the only available tool for some NDE (nondestructive evaluation) challenges, Part I (Basics) begins this logical progression, in Chapter 2 (Radiation Types and Sources), with the definitions and nature of the various available radiations and how they can be obtained, then progressing in Chapter 3 (Modifying Physics) to the basic underlying physical processes by which these different radiations interact with atoms and with bulk materials. Part I concludes with a virtual Baedeker to the many types of radiation detectors and their underlying principles in Chapter 4 (Detection Methods) and a briefer Chapter 5 (Radiation Safety) addressing both common-sense and mandatory regulatory concerns. In Part II (Techniques) the logical topical progression continues in Chapter 6 (Transmission Methods) with a comprehensive array of topics ranging from time-honored film radiography to the mathematical intricacies of tomography to the esoteric application of Mössbauer spectrometry. Chapters 7 (Scattering Methods), 8 (Emission Methods) and xxiii

xxiv


9 (Absorption Methods) similarly provide encyclopedic coverage of the available methods and techniques in each of these categories. Volume Two (Applications and Design) brings the above wealth of “why?” and “how-to” information “into the real world” beginning in Part III (Applications) with an introductory Chapter 10 (Probing, Inspection and Monitoring) with topics ranging from the function of the alpha-particle sources in most smoke detectors (such as the ones in my home) to monitoring package-filling in opaque containers. This is followed by Chapter 11 (Gauging) listing and exhaustively discussing the otherwise-difficult-or-impossible interrogations of bulk density, thickness, porosity and voidage, moisture content, fluid flow and finally dating including with carbon-14 (geological time scales), tritium (short term, such as for ground waters) and the use of thermoluminescence for TL dating (archeological time scales). Chapter 12 (Elemental and Content Analysis) continues the logical progression of subtopics including nucleus-based analysis (e.g., activation analysis), atom-based analysis (e.g., x-ray fluorescence spectroscopy, XRFS), hydrogen measurement (mostly by neutrons), and material content analysis (e.g., applications of the above-mentioned Mössbauer spectroscopy). Concluding Part III, Chapter 13 (Imaging) catalogs and provides detailed information on the many different kinds of photon radiography, on neutron and charged-particle radiography, on tomography and on imaging for material content such as in dual-energy imaging. Finally, in Part IV (Design) the author shares the experiences and knowledge accumulated in his long and distinguished teaching and research career, much of it involved in synthesizing the above material into the invention, production and putting into practice a significant fraction of the above principles and devices for carrying out NDE tasks. Thus, Chapter 14 (Performance Parameters and Design Aspects) opens Part IV with material on performance parameters, statistical optimization, design objectives, and source, technique, and detection system selections, followed by Chapter 15 (Source Modulation) with collimation considerations, filtration, and for neutrons, both moderation and multiplication. The book’s logical topical progression continues in Chapter 16 (Design Calculations) with subtopics on Monte Carlo simulations, and shielding requirements in the differing cases of x-ray machines, isotopic gamma sources, and for neutron sources. Finally, Chapter 17 (Experiments) treats the important considerations of licensing, background reduction and dynamic analysis to verify that the device will indeed perform its intended function, and the brief Chapter 18 (Finalization) discusses prototyping and intellectual property protection (trade secrets, copyright, trademarks and patents).

xxv

Volume Two closes with several appendices providing valuable information including (A) Basic Units and Constants, (B) List (alphabetically) of Elements and Natural Isotopes, (C) Relativistic Mechanics, (D) Quantum Mechanics, including the Schrödinger equation and the concept of cross-section, (E) Nuclear/Atomic Parameters for Compounds and Mixtures, (F) Effective Energy, and finally (G) Radiation Counting Statistics, including Poisson statistics, mean and variance. Following the appendices is the listing of the 1373 references including full titles and inclusive page numbers, followed in turn by the two indexes mentioned, an Application Index and a conventional Index concluding this monumental and uniquely useful “encyclopedic/thesauric” guide and companion through the thickets of radiation nondestructive probing, gauging, imaging and analysis. John H. Hubbell Ionizing Radiation Division “Emeritus” National Institute of Standards and Technology Gaithersburg, Maryland USA October 31, 2002


VOLUME TWO:

APPLICATIONS AND

DESIGN


PART III: APPLICATIONS


Applications

445

This Part of the book presents examples of industrial applications, classified according to the nature of their indication: probing, inspection, monitoring, gauging, elemental/composition analysis, or imaging. These examination processes, defined in chapter 1, are analogous to those performed by medical physicians when examining patients. A general practitioner “propes” a patient by verbal questioning or by examining certain localized body sites to identify any abnormalities. Since verbal interrogation of objects is not possible, probing in industrial applications refers to the process of searching (on “spot-check basis”) for changes in an object via a series of localized examinations. A physician also attempts to diagnose a disease or a condition via general “inspection” of the patient for signs and symptoms. Patients are also connected to devices to monitor their vital signs. Quantitative measurements (“gauging”) of body parameters, such as blood pressure, body temperature, heart-beat rate, etc. also assist the physician in making a diagnosis. A general practitioner, or a medical specialist, may also order blood tests or bioassay for elemental or composition “analysis”. Medical doctors also acquire radiological, ultrasonic or magnetic-resonance “images” to facilitate the diagnosis process. All these examinations are used to provide proper diagnosis, or for health-monitoring purposes. Industrial examinations aim at the same objectives, assuring the integrity, quality, or condition of an object, material, a part, a structure or a process. To aid readers in findings a particular application in a certain field, or circumstances, an application index is given at the end of the book (page ??). Some applications require a combination of a number of indications and techniques. Therefore, while Part II of this book presented mainly methods based on a single physical indication (e.g. transmission, scattering, emission or absorption), Part III presents some methods that combine more than one indication. Such combination may be required to neutralize the effect of a particular physical parameter, or may be needed to provide supplementary or confirmatory indications.


Chapter 10 PROBING‚ INSPECTION‚ MONITORING

Probing‚ as defined in chapter 1‚ is the investigation of a particular location. Inspection provides an overall assessment that need not be location-specific. Monitoring is a passive process of probing or inspection. The probing process is particularly helpful in detecting discontinuities caused by abnormal changes in the examined material. Unlike gauging and elemental analysis‚ probing and inspection do not necessarily provide quantified information. Therefore‚ probing and inspection can be seen as assessment tools for diagnosing the condition of an industrial object or a process. Therefore‚ the applications in this chapter are classified by the overall nature of the provided diagnostic information.

10.1.

Surface Condition

The surface condition of industrial components can be affected by deposition and erosion. For example‚ corrosion on the inside walls of pipelines and vessels can cause the condition of internal walls to deteriorate‚ creating safety and operational concerns. While deposition causes the addition of undesirable material‚ erosion results in the loss of primary material. Therefore‚ both processes change the apparent thickness and density of affected walls‚ or in other words‚ the areal density (density × thickness). This makes such measurements particularly amenable to the radiation transmission method discussed in section 6.2. Transmission Probing. With a narrow (well-collimated) beam‚ a rapid scan of a wall can be performed to detect changes in the transmission signal‚ which can be an indication of the occurrence of deposition. Gamma-radiation is particularly useful for such applications due to its high penetrability‚ ease of collimation‚ portability (due to the small size 447

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Radiation Probing‚ Gauging‚ Imaging and Analysis

of gamma-sources) and mobility (due to the self-powered nature of isotopic sources). Example applications of gamma-transmission using a source include: the inspection of tubes in the radiant section of a cracker furnace for coke deposits‚ and the deposition of powder in the tubes of a serpentine cooler of hot powdered pigment [286]. Severe corrosion or erosion‚ that can result in wall thinning‚ can also be probed by gamma-ray transmission measurements. For example‚ the transmission of photons emitted from an source was used to “spot-check” for thinning in the tubes of heat exchangers by inserting a source in one tube and a miniature Geiger-Müller tube in an adjacent tube [286]. Scatter Probing. When accessibility to two opposite sides of an object is not possible‚ probing by radiation scattering can be employed. Also while probing with radiation-transmission provides indications along the line connecting a source to a detector‚ scattering probes a volume defined by the intersection of the fields-of-view of the source and the detector‚ as discussed in section 7.7.1. Therefore‚ by source and detector collimation‚ the inspected volume can be confined to a small zone‚ providing point-by-point scanning. On the other hand‚ relaxing the collimation of either the source or the detector or both‚ widens the size of the zone of inspection. Since gamma-rays can be readily collimated and have a good penetration depth‚ they are usually used for probing purposes‚ in the backscattering modality‚ to permit one-side inspection. For example‚ the back scattering of photons was used for detecting the corrosion of cast-iron pipelines (so-called graphitization) [287]. Steel rust buildup under insulation was also measured and quantified with backscattering of 160 kV x-rays [288]. Neutrons. Although neutrons are more difficult to collimate than gamma-rays‚ they are useful for probing hydrogenous materials. Neutron scattering is also used to avoid the collimation process required to define a transmission beam. However‚ the lack of collimation produces a larger inspection volume‚ thus neutrons are useful in probing for bulk changes. For example‚ neutron scattering was used to detect the deposition of heavy hydrocarbons at the bottom of pipelines or storage vessels‚ or the fouling of flarestack by ice deposits under severe cold-weather conditions [289]. Charged-Particle Scattering. The backscattering of low-energy ( 50 MeV), has a half life of 20 ms and decays by emitting high-energy electrons. The bremsstrahlung radiation associated with these electrons may be used to detect nitrogen, say in explosives

12.1.1.3

Charged-Particle Activation

The poor penetrability of charged-particles limits their use to nearsurface analysis. On the other hand, their unique feature of losing energy continuously provides them with the ability to determine the spatial distribution of element concentration, i.e. depth profiling. Some specific applications are discussed below. Charged-Particle In – Charged-Particle Out.

As discussed in

section 8.5.3, the energy of emitted charged-particles, for a given source energy, not only indicates whether a particular reaction has taken place, but also it uniquely determines the direction of emission, hence the location of scattering, Eq. (8.9). Therefore, charged-particle spectrometry has been used to measure the distribution of a number of light elements implanted in a heavier matrix material [257]. This analysis has, however, to be performed in vacuum, so that the detected charged-particles do not lose energy after emission from the inspected object. Table 8.11

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lists some of the useful reactions for this technique. The depth profile of hydrogen, deuterium, or helium implanted in metals, was measured with this reaction. Other depth-profile measurements include those of beryllium in nickel alloys, boron in semiconductor (silicon) wafers and glass, and carbon in tantalum carbide films, thin plastic sheets, and organic materials. The depth profile of nitrogen in glass, silicon wafers, steel, organic materials (such as seeds) and human tooth dentine, was also measured with this reaction. The positrons arising from the decay of (66 s, half-life), with the latter produced by the reaction was used to determine the nitrogen content in diamond [629]. The distribution of oxygen in a metal is determined by the reaction since the proton reaction with is endoergic. (0.20%) is compensated for by the The low natural abundance of reactively high cross-section of the reaction for incident protons of energy in the range of 600 to 800 keV. This method is used to examine the oxygen profile in niobium and in steel exposed to moist carbon dioxide Reference [630] reported the use of this reaction, with labeled with as a tracer, to measure the oxygen profile in rutile and sapphire. Most commonly though, a deuteron beam is used for analysis, either with the (d,p) or the reactions, both are exoergic reactions, but the (d,p) reaction is preferred because of the longer range of protons. Therefore, the (n,p) reaction with was utilized for determining the oxygen distribution in silicon wafers and tooth enamel. The reactions and were also used to study the oxygen profile, in particular in the analysis of pellets exposed to a leachant comparable to thermal granite ground water [630]. The distribution of heavy elements embedded in a matrix of other heavy elements has also been studied with charged-particle spectroscopy. Reference [257] reported the determination of the profiles of silicon in metals, chromium in thin layers on metal substrate, and nickel on substrates of metal (copper), while reference [630] discussed the use of the technique for investigating the carbon content of ceramic substrates utilized in high-performance packaging technology, the sulfur diffusion in bulk CdTe and CdTe/CdSi thin-film hetrojunction solar cells, and the silicon diffusion from a thin Si film into polycrystalline gold foils. The reaction induced by 3 MeV ions, was used to detect carbon impurities introduced in the manufacturing of HgCdMnTe semiconductors; is a positron emitter with a 20.38 min half-life [631]. The reaction also takes place, enabling the detection of the oxygen concentration by the annihilation of the positrons emitted by the decay of with a 109.72 min half-life.

Elemental and Content Analysis

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The superb selectivity and high counting efficiency of coincidence measurement of the two reaction products emitted by charged-particle activation, see section 8.5.3, is particularly useful for detecting trace or small amounts of elements. The method has been used for the determination of trace amounts of hydrogen in aluminum, titanium, uranium and in polyester plastics films [257]. The selectivity of the coincide method makes it also attractive for the isotopic composition determination of lithium and boron [257]. The reaction is utilized in an alpha-proton-x-ray spectrometer (APXs) to analyze in situ the composition of the surface of Mars in the Pathfinder mission [632, 633, 634] and in the Surveyor lunar missions [635], see section 12.1.5. The reactions provided data on light elements (carbon to iron), while the x-rays (produced as a result of atomic excitation by the alpha-source) enables the detection of elements heavier than silicon. Charged-Particle In – Photon Out. This method is often referred to as PIGME, for particle-induced gamma emission. Some elements that can be detected by this technique are given in Table 8.7, and many others are cataloged in reference [257]. The limited range of incident charged-particles makes it possible to confine elemental analysis to near the surface of an object. This makes the technique particularly useful for analyzing small samples, or for studying the distribution of elements implanted in metals to improve their surface quality. The method can monitor either the gamma-rays promptly emitted with the activation reaction or the delayed photons produced as the activation products decay. The former method is known as PIPPS (particle-induced prompt photon spectrometry), as it involves measuring the energy of the emitted gamma-rays to identify the characteristic emission of the elements of interest. The prompt gamma-emission method has been used in many applications [257]. Fluorine was measured in glass, air, cement ores and food samples. Sulfur in coal, magnesium in vegetation, beryllium in air-born dust and in boron carbide, were also measured with the technique. The method was also used for determining the elemental content of chalcogenide glasses (S, As, Ge and Te), and for analyzing archeological artifacts for B, F, Na, Mg, Al, Si, Cu. Geological samples were also analyzed for Li, F, Na, Mg, Al, Ti, Mn and Te. The C, O, Si, Cr, Co, V and Mo content of in steel and the B, Li, F, Na content of niobium was also evaluated. The method was also used for the isotopic analysis of enriched boron. Delayed gamma-emission is mainly used for the detection of light elements (B, C, N and O) in metals and semiconductor materials [255].

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Charged-Particle In – Neutron out. This technique is suitable for measuring light elements: Li, B, C, N, Ca and O. Neutron mission by charged-particle activation has been also used in some applications, in spite of the relatively complex process of measuring the spectrum of neutrons [257]. The technique has been used for the measurement of deuterium concentration in gases (housed in a thin nickel window). Nitrogen in gases and steel, and oxygen in gases and metals, were also measured. The isotopic content of calcium enriched with or were also determined by this method. In the case of oxygen, it can The threshold energy for be measured via the reaction this reaction is only 0.6992 MeV, allowing the use of one of the isotopic sources listed in Table 2.1. Reference [257] reported the utilization of a source for this purpose. Note also that the Be reaction is commonly employed in neutron sources (see section 2.3), because of the low coulomb barrier of beryllium. Therefore, beryllium can be readily detected with the reaction, using either an isotopic source or a ion beam.

12.1.2.

Passive Emission

As indicated in section 8.8.2, radioactive isotopes in a nuclear materials and radioactive waste are identified by their emitted characteristic gamma-rays. Gamma spectroscopy is routinely used for this purpose in nuclear facilities and in nuclear-weapons verification. Radiation emission is also used for detecting tritium in air [636], water [637] and aqueous solutions [638] of nuclear power plants employing heavy water as a coolant, by detecting the beta-rays (18 keV maximum energy) emitted from the decay of (12.3 year, half-life); produced by neutron-absorption by the deuterium of heavy water. Natural emission of radiation is also used in well-logging. Below the surface of the Earth, gamma activity is high in oil-bearing shales, medium for sand, and low for dense carbonates and anhydrites. Naturalradioactivity logs are, therefore, used to locate oil and natural gas. This can be done either by measuring the total radioactivity, including all sources of natural radiation, or by performing gamma-ray spectroscopy to determine the content of U, Th or the U/Th ratio. As indicated in section 8.8.2, the high penetrability of gamma-rays makes them more suited than charged-particles (alpha and beta particles) for use in applications involved large objects, such as the surroundings of a borehole. At any rate, alpha and beta natural emissions are quite weak to be of a practical use in well-logging. The well-logging device for natural emission is simply a photon detector, housed in a steel casing to protect it against hydrostatic pressure.


545

The detector can be hanged by a cable in wireline arrangement, or incorporated into the drill pipe to perform measurements while a well is drilled. In either case, measurements can be stored in a computer chip and sent to the surface through telemetry. Any of the gamma-ray detectors described in chapter 4 can be used for this purpose. However, scintillator detectors have the advantage of high efficiency, which makes it possible to use smaller detectors. In well-logging, a small detector provides a smaller vertical spatial resolution, as it enables the recordings of more measurement points in the log as the tool is driven down a borehole. Geiger-Müller tubes, though less sensitive than scintillators, and have a slower response-time, are inexpensive and simple to operate (as they produce large pulses, and as such require no amplification), but typically large-size tubes are required. Ionization-chambers are large in size and less efficient than scintillation detectors, but are relatively simple since their charge-carriers are collected directly, without the use of fragile photomultiplier tubes as is the case with scintillators. The count rate of a well-logging tool measuring the total natural radioactivity can be modeled as [40]:

where C is the total measurable gamma-radiation signal, is the bulk density of the formation in which the borehole is drilled, is the density of the radioactive mineral or element present in the formation at and is an activity factor characterizing the ravolume fraction dioactivity of mineral or element The model of Eq. (12.1) reflects the fact that the gamma-count rate will depend on the concentration of the radioactive material in the medium, i.e. to the summation of the density of the individual radioactive isotopes However, the density of since the activity per unit each isotope is weighted by the factor, weight of one isotope is different from the others. The factor is typically given relative to the gamma-ray activity per unit weight of where the subscript refers to the element involved. Subsequently, for thorium, [40]. In spite and for uranium of its low relative contribution, contributes significantly (typically about 50%) to the gamma count, as it is more abundant than thorium (28%) and uranium (24%). The bulk density of the formation, is included in the model of Eq. (12.1) to account for the fact that the emitted radiation signal is modified by absorption by the material of the formation. Therefore, a radioactive material present at a certain abundance in a dense formation would give rise to a radiation count lower than that obtained for the same abundance in a lighter formation.

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The measurement model of Eq. (12.1) indicates that, if the total count rate is measured (giving only one piece of information), neither the nature of the active elements nor their relative contribution can be determined. However, the overall level of activity is indicative of shaliness, since shales are the most common radioactive rocks. When the energy spectrum of emitted radiation is measured, typically using a scintillation detector, such NaI(Tl), the intensity of emissions from and the daughters of can be quantified. Since rocks year of age or older are considered to be in secular equilibrium, see section 3.7, the concentration of all members of the decay series of thorium or uranium can be calculated, if the concentration of one of the members of the decay series is measured. Therefore, it is sufficient to measure the at 2.62 MeV concentration of one of the daughters of thorium gamma) and one of the daughters of at 1.76 MeV gamma), see section 8.8.2. Potassium-40 is detected by its unique gamma-emission at 1.46 MeV. Therefore, typically the radiation intensity corresponding to these three energy bins are used to calculate the concentration of the corresponding elements. However, a certain energy bin corresponding to one isotopes is also sensitive to the presence of other isotopes, due to the emission and subsequent scattering within the detector of photons by other daughters isotopes of thorium and uranium. Therefore, the count rate, at an energy bin is generally expressed as [40]:

where and are coefficients for energy bin obtained from calibration. Calibration is initially performed in a special pit containing known concentrations of the three radioactive elements, potassium, thorium and uranium. In the field, a block of material of known concentration of radioactivity (such as monazite) is used to check and adjust the positioning of the energy bins of the spectrum [40]. More than three energy bins can also be monitored, including bins at lower energies (resulting from Compton scattering of higher energy photons within the detector, as well as from lower energy emissions from the daughters of and This also helps reduce the effect of the detector’s escape peaks, resulting from pair-production interactions in the detector (see section 4.3). The use of additional energy bins overdetermines the problem, enabling a least-squares solution that minimizes the effect of statistical variations on the measurements. This is particularly helpful in spectroscopy measurements at lower count rates. Many spectrum measurements can be obtained as a detector is lowered into a borehole. It is then desirable to filter the acquired measurements to reduce the effect of statistical variability on the results, see section 4.5.7.1. Another prob-


547

lem that can degrade the quality of spectral data is detector drifting, due to temperature changes. This is overcome by employing stabilizing electronics, see also section 4.5.7.1. A number of other parameters affect the response of a device monitoring natural activity, whether it is measuring the total count rate or acquiring a spectrum of emitted radiation. The inspection volume, or sphere of influence of a detector depends on the nature of the material surrounding the detector. Therefore, any surrounding fluid, tubing, casing, cement, etc., can affect the value of the count rate recorded by a detector inserted in a borehole. Eccentricity of a detector within the hole can also bias the results, by deviating them from the idealized calibration conditions. Moreover, if the sphere of influence is not completely filled with the formation material, a misleading indication will be obtained. The logging speed, along with the time-constant setting of the detector’s circuitry also affects the readings of the instrument. The faster the logging speed, or the longer the time-constant, the less representative is the recorded log of spatial changes in the bed formation. Reference [40] reported a number of applications of natural overall radioactivity measurement in well-logging. Lithology evaluation for potassium, uranium and thorium-bearing minerals and rocks; was performed using their emissions. The fraction of shales (the most common radioactive rocks) in reservoir rocks; was also estimated. A comparison between wells for shale content is possible by contrasting their natural emissions against each others. Sedimentology indications can be also deduced from the change of gamma emission with depth; the latter information is also used for depth control of drilling and testing equipment. Natural emissions from coal, due to the presence of uranium, thorium and potassium, are indicative of its presence and concentration. The natural gamma-ray activity per unit volume (specific activity) is related to coal concentration, or conversely to the absence of coal (or presence of ash). Natural activity emissions were, therefore, used for measuring the ash content of coal [639], and to discriminate low-ash coal from useless overburden and in-stream sediment [640]. The intensity of natural gamma emission, combined with a density measurement, using the backscattering of photons (see section 7.5) recorded with the same detector, provided an emission-density map from which coal, clay and sand strata were detected from logged drilled holes in a coal mine [641, 642]. The scattering of gamma-rays, introduced by a source, was also used, along with the detection of naturally emitted gamma-rays, to identify three basic components of brown coal formations (coal, clay and sand) [641].

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The 583 keV and 609 keV characteristic gamma-ray associated, respectively, with the decay of (a daughter of and (a daughter of were used to assay the thorium and uranium contents of soil [643]. The same approach was employed for measuring the distribution of natural gamma-emitting radionuclides in soil and water [644], by monitoring, in addition to the above emissions, the 911 keV gamma(a daughter of thorium) and the 1.46 MeV gamma-rays rays of of Airborne surveys are used in mineral exploration, including, in addition to uranium, Ag, Au, Be, Bi, Co, Cu, Hg, Mo, Ni, Pb, Re, Sn, W, Zn and Zr [323]. The 2.6 MeV gamma-rays emitted from the decay of years, half-life) was used for measuring the thorium abundance on the lunar surface [645]. Natural gamma-emission was also used to detect on-stream truckload quantities of shale in sedimentary iron-ore belts [384]. Natural radioactivity from thorium, uranium and their daughters, and from are found in high-grade hematite. The total gamma-activity in the 300400 keV range can be scaled to the alumina concentration of ferruginous scales, hence to the shale content or iron. However, other shale material, such as highly siliceous chert and jaspilite, have low natural radioactivity and, therefore, are not detectable by this method. The use of a large was necessary to enable detecNaI(Tl) detector tion of the small natural radioactivity of the shale. Also, gamma-rays spectroscopic analysis of river sediments collected around phosphate fertilizer plants indicated accumulation of natural radioactivity originating from effluent released from the plants [646]. Another application for natural radioactivity is to use the gamma emissions of from plant contraband materials (such as marijuana and tobacco) to passively detect their presence in cargo containers [647, 648]. Measurement of environmental contamination due to the Chernobyl Nuclear Power Plant accident was done by monitoring the characteristic gamma-rays emitted from the contaminating isotopes, etc. This method is also used for the characterization of nuclear waste, see for example [649]. In addition, contamination with plutonium and americium isotopes was detected by the characteristic x-rays from Pu (17.06 keV) and the 59.6 keV gamma-rays of using a planer HPGe detector [650]. A method for detecting and in contaminated soil, in a nuclear waste site, was reported in reference [651]. The method relies on measuring beta-particles emitted from or (decay daughters of and respectively), at a maximum energy of 2.3 MeV for each isotope. Using flat ribbons composed of numerous square scintillating fibers, and stacked on top of each other, with each connected to a photomultiplier tube, high energy


549

beta-particles will cause scintillation in a number of subsequent layers. On the other hand, lower energy beta-particles, arising from natural daughters, and its daughters and will sources (other only penetrate a layer or two, thus can be discriminated against. Neutrons emitted from plutonium can be used also for monitoring its presence in containers, either by direct counting of the total neutron emission or by coincidence measurement of neutrons emitted by spontaneous fission; the latter is particularly useful when non-plutonium related random neutron emitters are present [600, 601]. References [652] suggested the use of scintillating glass fiber detectors for the detection of plutonium, that may be concealed in freight and vehicles, by its neutron emission. In order to correct for neutron attenuation within the matrix material in which the fissile material is embedded, the transmission and scattering of was measured in some applications [653, 654]. Cosmic-ray interactions with matter produce a “neutron signature” that can be used for verifying the type of nuclear materials within a closed container [655]. When galactic high-energy cosmic radiation interacts with the elements of a planet, they release fast-neutrons. These neutrons are, however, slowed-down in energy by interacting with the nuclei of the regolith, and eventually reach the thermal energy. The neutrons can, therefore, activate the elements of the planet. The gamma-rays emitted from the activated elements can be used to characterize elements such as silicon, oxygen, iron, magnesium, potassium, aluminum, calcium, sulfur, carbon and hydrogen. In addition, water or ice, if present, would affect the is buried beneath a thick (a spectrum of the neutrons, even when refew hundred mm) hydrogen-poor soil [656]. The hydrogen in duces the number of fast and epithermal neutrons, by moderating them, and in turn, tends to increase the thermal-neutron flux [657]. On the other hand, an increase in both the epithermal and thermal-neutron counts was seen as indicative of the presence of a ice cap (frost that precipitates out of the atmosphere) above a hydrogen-rich soil, since the low absorption cross-section of allows more of the epithermal neutrons produced in the soil beneath to reach the atmosphere. This process was used in the analysis of both the Lunar and the Martian surfaces [658, 659, 660].

12.1.3.

Resonance Effects

Energy Spectrum. Resonances exhibited in the neutron total crosssection of some elements, see section 6.5.4, were exploited for elemental analysis by measuring the energy spectrum of transmitted neutrons. With neutrons in the few eV range, the technique was used to measure

550


the isotopic abundance of nuclear reactor fuel elements [172], by measuring the energy of transmitted neutrons using a proportional counter detector. By analyzing the measurements at energies corresponding to the resonances of and the abundance of each isotope can be determined. Moreover, in a spent nuclear fuel, the abundance of and were also evaluated [172]. Resonances in the cross-sections of In, Hf, Au, Gd, Cd, Eu, Dy, Co, Ir, Mn, Rh, Sm, Ag and Ta were also used for measuring the concentration of these elements [343]. Neutron resonances at higher energies, between 1 and 3 MeV, observed in the cross-sections of H, C, N and O, was used to determine the concentration of these elements, using a pulsed beam of fastneutrons [173, 661]. A pulsed source enables the measurement of the energy of transmitted photons using the time-of-flight method, discussed in section 4.25. With a broad-energy beam of neutrons (from 0.5 to 10 MeV, obtained by bombarding a beryllium target with 4.5 MeV deuterons), the resonances in many elements can be measured simultaneously. This technique was, therefore, considered for the detection of explosives and drugs [662, 663, 664, 665]. The prompt gamma-rays that is usually associated with neutron production was also utilized to provide gamma-transmission measurements [666]. With gamma-rays in the energy range where Compton scattering dominates, the electron density, of the material present along the radiation source can be determined, see Eq. (3.40). While neutron transmission provides the atomic-density, N, then is a direct measure of the number of electrons per atom, i.e. the atomic number Z. This combined approach of neutron resonance transmission and gamma transmission improves the elemental discrimination ability of the detection system. The fast-neutron transmission spectroscopy techniques was also source [177], taking advantage of the wellapplied using a characterized and smoothly varying nature of the energy spectrum of this source. The analysis of the spectrum of fast scattered neutrons was also proposed for the detection of landmines [218, 667, 668, 669] and illicit drugs [669]. An empirical fast-neutron scatter/transmission technique was also proposed for bulk detection of explosives [670]; with neutron transmission providing an indication of the attenuating ability of the interrogated material, and the scattered neutrons indicate the mass-number, density and fast-neutrons cross-sections of the materials. The unique resonances in the scattering cross-sections of nitrogen and oxygen (two of the main constituents of nitrogen-based explosives) between 1 and 3 MeV energy provide a strong scattering indication,


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which when mapped against the neutron transmission signal provide a distinguished indication of ammonium-nitrate (an explosive-like material) [670]. Transmission resonance was also utilized for measuring the amount of protein in meat [343]. The concentration of nitrogen is taken as an indication of the protein content. Therefore, by measuring the transmission of monoenergetic neutrons at the 432 keV resonance of nitrogen, its concentration, hence the protein content, can be estimated. Neutron-resonance transmission was also used to measure the isotopic content of fresh and spent nuclear reactor fuel samples, where the content of and in fresh fuel, and the abundances of 11 actinides and 5 fission products in spent fuel, were obtained with neutrons emitted from a 100-MeV electron Linac pulsed neutron source [671]. A similar approach was used to determine the absolute content of and in irradiated fuel, using a fast-chopper time-of-flight spectrometer [672].

Slowing-Down Time Spectrometry. Resonance effects can also be observed using slowing-down-time spectrometry. When a monoenergetic pulse of neutrons is slowed-down in a medium other than hydrogen, it tends to scatter into a narrow energy group, the value of which depends on the mass-number of the slowing-down medium. With such medium, a number of collisions are required to significantly affect the energy of incident neutrons, as evident from Eq. (3.80). However, a significant change in direction takes place and after a sufficiently large number of collisions neutrons “forget” their initial direction and energy, but tend to be “focussed” into a narrow energy band. To understand this focusing effect, let us assume that the total macroscopic scattering cross-section of the medium changes with neutron velocity, as where K and are constants. The average number of collisions per second would be equal to keeping in mind that is equal to mean-freepath of neutrons, see section 3.11. Higher-velocity neutrons will scatter more often, and consequently slow-down at a faster rate than slower Then, the neutron velocity, and in turn energy, will neutrons, if increase with time, after the issuing of the pulse. The energy of the slowed-down neutrons will then be approximately inversely proportional to the square of the slowing-down time [673]. Lead is a suitable element for use in this process, since its scattering cross-section is such that it satisfies the above required behavior of the scattering-cross section, with velocity, hence energy, at most of its energy range. The reader can verify this by plotting the cross-section using the on-line program of reference [27]. Other advantages of lead is that it is readily available,

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not highly absorbing of neutrons, and because of its high mass-number leads to a continuous slowing-down process. This technique, known as lead slowing-down-time spectrometry (LSuses pulses of 14 MeV neutrons, produced by the reaction, since neutron generators based on this reaction are readily available, see section 2.3.1.3. A neutron generator is placed at the center of a large block (a meter or two) of pure lead, with the interrogated object and detectors placed inside the assembly. The scattering of neutrons within the assembly allows the object to be subjected to neutrons at a wide range of energy. The technique has been mainly utilized for the assay of fissile materials, namely and These nuclides, unlike fertile ones such as have strong resonances in the eV range in their fission cross-sections. Therefore, the spectrum of the slowing-down time of neutrons depends on the amount of fissile material present in the interrogated object [674, 675]. DTS),

Gamma-Resonance. Resonance absorption with gamma-rays can also be used for elemental identification, provided that the gamma-rays are sufficiently high in energy to interact with the nucleus. For example, the 9.172 MeV nuclear level of can cause resonant absorption of 9.712 MeV photons, making it possible to determine the concentration of nitrogen, and hence detect explosive materials [676]. Such photons target with 1.75 MeV protons, can be produced by bombarding a to produce an excited nucleus, which then emits the excitation energy in the form of 9.172 MeV photons. The emitted photons can then be directed to the interrogated subject, where they are resonantly absorbed by the nitrogen of the object. From the reduction in the intensity of transmitted radiation, the concentration of nitrogen in the object can be determined. A similar technique can be used for the detection of chlorine-rich narcotics, with the 8.12 MeV gamma-radiation that is resonantly absorbed by175] [175]. Photon-Scatter Resonance. Borehole analysis for copper and nickel using gamma-ray resonance scattering was also reported [677], where gaseous and gamma-sources were used to produce photons with energies that coincide with the critical (resonant) absorption energies of the concerned nuclei, copper and nickel, respectively. For boreholes in rock of constant type and density, the number of resonantly scattered gamma is proportional to the concentration of the wanted element. More information on the use of gamma scattering in the assay of mine boreholes can be found in reference [678].


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Charged-Particle Resonance. Resonance of charged-particle reactions are also exploited for elemental analysis. The backscattering resonance of alpha-particles at 3.045 MeV with was proposed for the analysis of oxygen in high atomic-number compounds, such as metal oxides and cubic zirconia [679] A number of reactions have strong resonances for activation by charged-particles, as listed in Table 8.8. The increased activation yield of these resonances has been used for the detection of carbon contamination under gold-covering of silicon substrates and for depth profiling of hydrogen in glasses, carbon, metal foils and geological samples. Sodium in glass and silicon substrates, aluminum in silicon and its compounds; and helium, nitrogen and fluorine in metals, were also measured with the technique [257]. This activation technique is particularly useful for analysis of fluorine in small quantities, a task that is not achievable by other methods [680]. Also, the resonant reaction was used to determine the lithium concentration in ‘smart glass’ (a glass that changes from clear to dark by applying electrical bias, typically consisting of two electrochromic layers of and [630]. Enhanced resonances activation of charged-particles was also used for the analysis of oxygen in silicon single crystals, in gallium phosphide oxide films on aluminum, and in metal single crystals and oxide flake (scale) [257]. Oxygen was also measured in silicon surface technology. The technique was also utilized to measure boron in silicon wafers, and aluminum in semiconductors. Resonant profiling was also used, with the reaction for examining the kinetics of hydrogen implantation-induced blistering of semiconductors; for measuring the hydrogen content in amorphous solar-cell materials; and for studying the reaction between water and soda-lime glass [630]. The reaction was also used to measure the profile of nitrogen implantation into aluminum, while the resonant reaction was utilized to determine the fluorine content in dielectric films [630]. Backscattering using 7.6 MeV ions was also used to perform depth profiling of oxygen and carbon in heavy matrices of gold, silver and copper [681]. In this process, advantage was taken of the resonances of the elastic scattering cross-sections at 7.3 MeV for O and 7.65 MeV for C.

12.1.4.

Fast-Neutron Scatteroscopy

The energy of a neutron after encountering an elastic scattering with a nucleus of mass-number A, is determined by value of A, as well as by the angle of scattering, see Eq. (3.80). Therefore, by fixing the energy and direction of an incident neutron beam, and monitoring the

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neutrons scattered at a certain angle, one can determine the value of A from the energy of scattered neutrons, and the density of the element of mass-number A from the intensity of the neutrons at that energy. This technique of measuring the energy of scattering to determine elemental information is called here scatteroscopy, and was proposed for measuring and in mixtures containing these the concentration of elements [228]. The technique was also investigated for detecting explosives by resolving the difference in energy loss of neutrons scattered by the four main elements of explosives: hydrogen, carbon, nitrogen and oxygen [682, 683]. The method was also used to detect these elements, in addition to Al, S, Fe and Pb, in samples weighing 0.2 to 0.8 kg [684]. The energy structure of the elastic scattering cross section of C, N and O, weighted by the energy spectrum of a Pu/Be source, was shown to result in characteristic peaks that were also reflected in the spectrum of backscattered neutrons [685, 686]. The relative ratio of these peaks can also be used for identifying materials containing high concentrations of these elements. Reference [687] studied the transmission characteristics of passing through rare earth and boron loaded concrete slabs, enabling the analysis of concrete for such elemental content.

12.1.5.

Charged-Particle Scatteroscopy

The dependence of Rutherford scattering (nuclear elastic) scattering of alpha-particles, or accelerated ions, on the atomic-number (see section 3.3.1.1), has been utilized for composition determination of thin materials. A number of detectors are available for measuring the spectrum of alpha-particles, including proportional counters, scintillation detectors, Frisch-grid ionization chambers and silicon gold surface-barrier detectors [688]. Reference [237] reported a number of applications. The method was used to determine the atomic-number of thick metal backings, and to obtain complete and detailed in situ chemical analysis of surfaces and thin atmospheres of extraterrestrial bodies. The method was utilized to study the structure and composition of mechanically polished and chemically etched surfaces of CdTe single crystals, and for near-surface analysis of oxygen-containing high atomic-number compounds. The concentration of thin films on high atomic-number substrates and high atomic-number bulk oxides was also measured with this method. The concentration of trace and minor elements (Na, S, Cl, K and Ca [689]) in cigarette tobacco was also determined using this technique. The method was also employed for elemental trace analysis of sugar-spirit solution, wheat and well-water samples. Other applications are also presented in reference [242]. Various types of ion beams were used to study the diffusion of a small cobalt surface impurity into


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silicon and to characterize nitride and oxide layers on silicon. Changes in the tribo-surfaces of bearing steel subjected to lubricated sliding wear were also monitored with the technique, to examine the effect of additives to the lubricating oil in reducing wear and preventing seizure [690]. The elemental composition of various types of films and film deposits and coatings was also determined using this method. Reference [691] described a system useful for application of Rutherford scattering in an industrial environment, and summarized its utilization in the analysis of microelectronic materials and polymer and synthetic fibers and the study of catalysis agents such as cage compounds in zeolites. Reference [692] described the use of backscattering and forward scattering of ion beams for depth profiling of solids, and provided some representative applications. Alpha spectrometry has also been used to measure the concentration of various plutonium isotopes in samples, and in the analysis of irradiated nuclear fuel and cladding materials for actinide elements and for the chemical separation of actinides [688]. Alpha-particle backscattering, using a alpha-source, was also used for analyzing the chemical composition of the Lunar surface [693]. According to the kinetic of elastic scattering of alphaparticles, Eq. (3.19), for backscattering (i.e. at a scattering angle of the energy of a scattered alpha-particle, is related to its incident energy by:

where A is the mass-number of the target nucleus, and the value of 4 is equal to the mass of an alpha-particle in atomic-mass-units. Therefore, by measuring the scattering energy, one can determine the mass-number, hence identify, the present element. The intensity of scattered particles provides an estimate of the atomic concentration of the scattering element. Since alpha-particles are not very penetrating, the monitored scattering will emerge mainly from near the surface. But even then, an alpha-particle may scatter more than once before being reflected back to the medium, losing additional energy. However, the emerging scattered particles cannot have an energy greater than that of a particle that encountered only one scattering as determined by Eq. (12.3). Therefore, the energy distribution of the scattered alpha-particles from a thick target is a continuous distribution that extends from zero to a maximum energy, determined by Eq. (12.3), and is characteristic of the scattering element. Therefore, the energy at which the scattering spectrum sharply drops to zero corresponds to the values as determined by Eq. (12.3), from which the value of A can be calculated. A monoenergetic alphasource is needed for this application, in order to be able to make use

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of Eq. (12.3). Although, emits two main alpha energies [12], 6.069 (25%) and 6.112 MeV (74%), the two energies are so close that in practice they can be considered as a single energy. The half-life of the source is also sufficiently long (162.8 days) to be of practical value. This source was employed in the alpha-backscattering technique used by the Surveyor 5, 6, and 7 spacecraft [635]. The Mars Pathfinder mission used this technique in its Alpha-Proton-X-ray Spectrometer (APXS) for chemical elemental analysis of the Martian soil and rocks in situ near the landing site [632]. The APXS technique also employed an source and used the reaction for detecting Na, Mg, Al, Si and S, and the characteristic x-rays produced alpha-particle excitation for measuring heavier elements [633, 634]. The backscattering of beta-particles has also been used for composition indication. For example, the backscattering of beta-particles emitted form a source, and detected with a cadmium telluride solid-state detector, was used for the precise determination of the effective atomic-number of materials of atomic-number ranging from 9 to 30 [694]. Reference [24] reported a number of applications. The technique was also utilized to measure the lead content in glass, glazed and porcelain artifacts, and for determining the composition of bronze mirrors and vessels;. Japanese antiques were investigated with this method. The analysis of Pharmaceuticals for the content of heavy elements (Pb, Bi, Cu, Zn, Ca, Au, Sb, I, Hg, and Br) was also performed using this ions was utilized to study the stoichiomethod. The scattering of metric variation in semiconductor layers [695].

12.2. Atom-Based Analysis 12.2.1. Fluoroscopic Excitation Fluoroscopic emissions produced by photon or charged-particle excitation of atomic electrons plays a vital role in elemental analysis. The technique is discussed in section 8.7, and some of its applications are given here. Note that due to the limited penetrability of both the incident and emitted radiation, the method is useful for surface analysis and for examining small samples. The applications of the method can be classified into four categories: qualitative, relative, quantitative and trace analysis. Qualitative Analysis. The objective of this analysis is identify present elements without necessary determining their concentration. Qualitative analysis can also be viewed as a “probing” process for the quick assay of materials to determine whether certain elements are


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present or not in a sample. This process can be useful, for instance, in detecting a certain contaminant in food produces or a pollutant in an environmental sample. Relative Analysis. This process aims at not only confirming that certain elements are present in an examined material, but also to determine their relative concentration, as done in the content analysis discussed in section 12.4. Signature analysis is used for this purpose, where the presence of main features (characteristic energy peaks) is ascertained as a finger print of the element(s) that ought to be present in a certain material. The intensity of these peaks in the detected signal can then be used to determine the relative content of the elements of interest. This process is useful in metal sorting steel by alloy type analysis of forensic samples and authentication of artifacts and currency [269], with the used isotope given in brackets. Quantitative Analysis. This is the process of calculating the concentration of all elements from their emission spectra. For this process to be accurate, factors that may influence measurements should be carefully considered. Such factors include: background radiation due to photon scattering by, or excitation of, surrounding material, counting dead-time effects (see section 4.5), and radiation-attenuation within a sample. Trace analysis. Detecting a small amount of an element requires particular attention, since the indication signal produced by such analysis can be so weak that it becomes indistinguishable from the background signal. It is, therefore, essential to obtain the maximum possible signalto-background ratio by judicious choice of the excitation energy, detector type, and when possible the inspected object itself. Trace analysis works best with small samples, where the effect of radiation scattering and attenuation is small. It may also be advisable to focus on detecting only one element, rather than measuring simultaneously multiple elements, so that the detection system can be optimized towards the characteristic energy of that element. Reference [696] provided the following recommendations for performing trace elements by fluoroscopic emission:

Monoenergetic sources are preferred over conventional x-ray tubes or bremsstrahlung sources, since the latter produces a continuum of scattering radiation that can interfere with the characteristic fluoroscopic x-rays. Therefore, characteristic x-ray tubes (x-ray tubes with a suitable primary target, or a supplementary secondary target, see section 8.7.2) or isotopic sources (e.g. or should be used.

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While the excitation energy needs to be slightly greater than the K or L absorption-edge energies of the elements to be analyzed, see section 8.7, it should not be too high to avoid introducing significant overlapping background by Compton scattering. The emitted radiation should be detected at angle near 90°, with respect to the incident radiation, since at this angle the probability of Compton scattering is minimal; in accordance to the Klein Nishina relationship of Eq. (3.41). To minimize absorption loses within an inspected specimen, its thickness should not exceed the thickness beyond which an increase in thickness does not appreciably increase the intensity of the emitted fluoroscopic radiation; hence the highest sensitivity is obtained with relatively thin specimens. The detection system should be designed to provide maximum detection efficiency and minimum dead-time loses (see section 4.5). Classification by Atomic Number. The classification of x-ray fluoroscopic emission according to the above mentioned categories depends to a great extent on the intent of the user. What matters is that there is a radiation source available to cause excitation and that a suitable detector is used to measure the emitted x-rays. In this regard, reference [24] classified elemental detection with fluoroscopic emission according to the atomic-number, Z, as follows: Z

(up to K): excitation energy is low, < 4 keV, requiring the use of proportional-counter (gas) detectors to provide the needed energy resolution for low-energy peaks.

21

(Sc – Zn): excitation energy is from 4 to 9 keV, making it possible to employ proportional, scintillation or semiconductor detectors. Excitation is usually achieved with radioisotopic sources.

31

(Ga – Ba): with the excitation energy between 9 and 33 keV, a number of radioisotopic sources can be used in this regard (see Table 2.7), along with mainly scintillation detectors; although proportional counters and semiconductor detectors are also applicable.

58

(Lanthanides): the excitation energy for these rare-earth elements varies from 33 to 55 keV, but their characteristic energies, from the and levels, interfere with each other, which makes it difficult to resolve their fluorescence spectrum without the use of a


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detector with a high-energy resolution such as the high purity germanium detector, see section 4.3. Photon excitation of these elements can be caused by a number of radioisotopes: while electron excitation can be introduced by

(a beta source with a maximum energy of 224 keV) [697].

(Hf and beyond): with a relatively high excitation energy (55 are to 99 keV), isotopic sources such as and needed. Only scintillation and semiconductor detectors are suitable for this relatively high photon-energy. Since it is vital in fluoroscopic emission to have the right source energy to excite the element(s) of interest, the radiation source used is identified in brackets when discussing the applications below. Note that stating a kV value indicates the use of an x-ray machine as a primary source, while the presence of a slash (/) after a source signifies that the primary source is accompanied by a target that emits the excitation radiation when the target is excited. Since there is an enormous number of applications, only some representative examples of x-ray fluoroscopic emission (XRF) are given below. Food and Agriculture Industry. Photon excitation was used for the analysis of orchard leaves (40 kV W/Mo) for Cr, Mn, Fe, Ni, Cu, Zn, As, Br, Pb, Sr and Pb [696, 269], dried vegetables (60 kV Ag/Nd), [269]. The method was also utilized for and freeze-dried fish the analysis of Mn, Fe, Co, Cu, Zn, As, Br, Rb, Sr and Zr in tobacco, using and sources [689]. Process Industries. XRF is used in the inspection of paint for toxic components (60 kV Ag/Nd). The method was also employed to determine the concentration of bromine in a liquid catalyst used in a petrochemical plant, by exciting the bromine’s 11.9 keV x-rays with an a 59.6 keV photons bombarding a silver target, producing 22.1 keV x-rays. Chlorine in rubber rhenium (a catalyst for hydrogenating of fine chemicals in oil, and arsenic in aqueous solutions were also analyzed [269] Other solutions analyzed by XRF include copper in electrolytic solutions and uranium in aqueous solutions [24]. Coatings were also analyzed for the determination of lead, titanium, mercury, copper and arsenic in paintings, such as those applied to stove finishing, latex paints and inks [24]. The concentration of uranium and plutonium in highly radioactive solutions is determined in nuclear fuel reprocessing plants The technique was also used for the determination of the presence of gaseous uranium

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inside cylinders [270]. X RF is also used for monitoring and subsequent control of gas emissions from industrial furnaces, and for detecting trace metals in process industries and in the feed water of nuclear power plants [698]. Coating and Substrate Interference. When a coating and a substrate contain a common element, the use of XRF to detect elements in the coating becomes problematic, due to interference from the substrate. This is encountered for example when Zn/Fe (galvanneal) coating is used on steel, where the Fe fluorescence emerges from both the coating and the steel substrate. Reference [699] overcame this interference by using two collimated x-ray beams as the excitation sources, one directed normal to the surface and the other at a large inclined angle. The inclined beam travels a longer distance within the substrate, so that when it reaches the substrate its intensity is reduced. Therefore, the inclined beam is used to detect the Fe fluorescence in the coating, while the normal beam is utilized for Zn fluorescence.

Metal Processing. XRF is used for analysis of lead in free-machining steel added to to improve the steel's machining properties and Mn, P, S and Si in blast furnace heats (molten liquid poured in an openhearth steel making process (Cr tube/Cl) and Cr, Mn, Ni, Nb and Mo in stainless steel (Rh tube) [269]. The method has also been utilized for the determination of the following elements in various types of steel with isotopic sources: Cr Mo and NB W and Pb [24]. The same reference also reported the use of XRF to determine Pb in leaded brass Cu in Cu/Sn Sn in Cu/Sn Ni in Ni/Cu/Zn and Al alloy Sn in bronzes and gunmetal and Sn in Sm/Pb solder Mineral Processing and Geological Samples. Chlorine and lead in mineral process materials are analyzed with XRF [269]. Glass, pottery and rock specimens were analyzed for K, Ca, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Ga, As, Se, Br, Rb, Sr and Pb (42 kV Mo secondary tube) [696]. Geological materials were investigated using the XRF technique for measuring the content of Au Ag V U etc. [24], Slurries can be analyzed on-line with XRF to determine the concentration of Pb calcium tin barium zinc copper etc. [24] In the construction industry, XRF is used


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for determining the concentration of Mg, Al, Si, Ca and Fe in (Rh tube or [269, 24]. Environmental Samples. XRF was used for the analysis of particulate filters for Ar, Ca, Ti, Cr, Zn, Fe, Ni, Cu, Zn, Pb, Br, Rb and Sr (42 kV Mo tube) [696]. Reference [643] reported the use of the method to measure the concentration of pollutant around tin mining and smelting operations: Al, Si, Ca, K, As, Ni, Fe and Ti (20 kV excitation potential) and Zn, Sn, W, Bi, Pb and Th (40 kV with a thick rhodium filter). A similar process was used for analyzing suspended dust particulates within and around cement plants [700]. Water is also analyzed for the determination of trace metals [24]. Heavy elements in plants are also detected with the XRF technique for Mn, Fe, Ni, Cu, Zn and Pb Br and Sr [24]. The concentration of chromium in air breathed by workers, during welding chromium-nickel steel, was also determined with XRF [270]. Others. Other interesting applications of XRF include the analysis of genuine and counterfeit bills by comparing their composition and for the forensic analysis of fired or of unfired pistol powder residue [24]. Modern fake reproduction of ancient porcelain, on an object tiles and clay work were also detected by analyzing their composition using XRF [270]. Reference [701] also suggested the use of 80 keV K level of lead to determine its concentration in Pb-Zn deposit ores, with the excitation caused by source photons scattered within the medium. XRF was also used in the characterization of a North Sea reservoir by analyzing stripped samples [702]. Excitation of uranium and plutonium K x-rays, by or 150 kV x-ray sources, and L x-rays by 30 or 55 kV x-ray sources were used for the analysis of both elements in samples of nuclear fuel at different cycle stages, e.g. ores, reprocessing solutions and mixed oxide fuel pellets [703]. The gold-colored layer on the scull piece of a medieval iron-based helmet as the excitation source [406]. Using an Xwere analyzed using ray tube (15 kV, Mo target and Zr filter), and and sources, the XRF technique was used to characterize archaeological ceramics, by measuring their Ca, Fe, Ti, Zr, Ni, Cu, Zn, Rb, Sr, Ba and Y content [704]. PIXE. Particle-induced x-ray emission (PIXE), discussed in section 8.7.3, plays an important role in aerosol analysis [705], particularly in the analysis of very small samples and thin targets, due to the limited range of charged-particles causing atomic excitation. Quantita-

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tive analysis with PIXE is limited to elements of a mass-number of 11 or higher (Na and beyond), due to the lower energy-loss (degradation) necessary for excitation, and the lower x-ray production cross-section of lower atomic-number elements [706]. Reference [267] reported that aerosol analysis represents about 20% of all PIXE applications, and included analysis of samples drawn from urban atmosphere, underground mines, stratospheric and air particles. In addition, PIXE is used for the analysis of water samples for trace amounts of elements [271]. PIXE is also utilized for the analysis of geological samples, such as rocks, mineral drill cores, deep-sea ferro-manganese nodules, etc. [271], and analysis of art and archaeology [707]. Stainless steel foils and iron substrates were and microbeams, as well as a 2 MeV analyzed using a 5 proton beam [708]. X-ray excitation by alpha-particles is also utilized in the alpha-proton-x-ray spectrometer (APXS) to analyze in-situ the composition the surface of Mars in the Pathfinder mission [632, 633, 634] and in the Surveyor lunar missions [635], see section 12.1.5. The ionoluminescence method, see end of section 8.7.3, has been used, in combination with PIXE, for rare-earth element analysis [709], such as in characterizing zircon mineral grains [710]. The method has been also used for the analysis of diamond and other crystals [711], and for the study of ore metal segregation between magmatic brine and vapor [712].

12.2.2.

Composition Indication

Photon interactions, as indicated in section 3.4, are mainly interactions with the individuals electrons of the atom, or with the atom as a whole. Therefore, photon interactions tend to provide atomic, or more precisely atomic-number, indications, rather than element-specific indications. For a compound, photon interactions provide indications that depend on the effective atomic-number of the compound, as defined in appendix E. Such indications can be used for distinguishing between two materials that are different in their atomic-number, but may be close in their density, or for the detection of the presence of a class of materials in a certain range of atomic-numbers. Since the most dominant photon-interaction process, Compton scattering, depends on the electron-density of the material, see section 11.1, it alone does not give composition indications; except in the case of hydrogen-rich material, as discussed in section 12.3.4. However, composition indications can be provided by using a combination of Compton scattering and some other photon interaction. At low-energy, the photoelectric effect (photoabsorption) becomes dominant, and is strongly dependent on the material’s atomic number. Using Eqs. (3.30) and (3.40), one can express the ratio between the macroscopic cross-sections for the photoelectric effect


563

and Compton scattering as:

where Z is the effective atomic-number of the material, see appendix E, N is the atomic-density, the subscripts and c refer, respectively, to the photoelectric and Compton effects, E is the energy at which the interaction takes place and the value of as indicated following Eq. (3.30), varies from 3 to 5, depending on Z and Therefore, at a given energy, the ratio between the cross-section of the photoelectric effect and that of Compton scattering becomes dependent on the atomic-number. Note that the use of the ratio of the two reactions, rather than relying only on the strong dependence on Z of the photoelectric effect, is necessary to eliminate the dependence of the latter on the material’s electron’s density. The question now is how to devise simultaneously two independent indicators that reflect the occurrence of both the photoelectric effect and Compton scattering. A number of possibilities exist, as schematically shown in Figure 12.1, and discussed in the ensuing subsections.

12.2.2.1

Critical-Edge Absorption

If the photon source energy is around the critical absorption-edge of an element, the intensity of the transmitted or scattered radiation would considerably decrease, and the element can be detected within a sample. Elemental tomography using this approach was proposed [713], employing beams from synchrotron-radiation accelerators (see section 2.1.5.1), since such beams can be tuned to the energy of the element of interest. However, the photon energy that corresponds to the absorption-edge of elements is quite low, limiting this elemental tomographic approach to small samples.

12.2.2.2

Dual-Energy Transmission

One can perform two transmission measurements, one at high energy, and the other at a lower photon energy, over the same path length. In this approach the indication obtained is an integral indication over the entire path length; Figure 12.1.a. The measurement model for this method can be formulated with the aid of Eq. (6.1) as:

564


where I refers to the intensity of the transmitted radiation through a material of thickness, is the intensity at zero thickness, is the macroscopic cross-section, and and c refer, respectively, to the photoelectric effect and Compton scattering. In the model of Eqs. (12.5a) to (12.5c), it is assumed that the Compton scattering cross-section at is negligible compared to that of the photoelectric effect, thus the total cross-section at is approximately equal to At energy, E, because of the dominance of the total cross-section is set equal to Compton scattering. Using Eq. (12.4), one can see that the logarithmic ratio of the transmission measurements (transmittance), Eq. (12.5c), provides an indication of the effective atomic-number of the material present along the traversed distance, If the transmitted radiation encounters more than one material along then the Z indication will be


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a weighted average of the atomic-number of the encountered material in accordance to the portion each element occupies across the distance This dual-energy transmission method is the basis of the dual-energy x-ray imaging method used in detecting suspect materials in passenger luggage, see section 13.5. Reference [714] suggested the use of three monochromatic, filtered xray beams for the detection of the concentration of elements (Cl, O, N and C), by monitoring the photoelectric effect (absorption) of photons at energies of 60, 65 and 70 keV, and reconstructing a tomographic image at each of those energies. In a similar fashion, two different energies, within the energy spectrum of transmitted x-rays (less than 25 keV), were employed to determine the mass-fraction of elements within materials composed only of hydrogen, carbon and oxygen, such as combustion materials [715].

12.2.2.3

Transmission and Scattering

Another approach to composition-indication is to record a transmission measurement at low-energy, for the photoelectric effect, while monitoring photon scattering from the same incident beam. Since Compton scattering is possible at all energies, according to Eq. (3.40), this approach can be used to obtain a composition (Z -number) indication of the material encountered along the path of the transmitted radiation; though the scattered photons are attenuated by the surrounding materials as shown schematically in Figure 12.1.b. Modeling the transmission measurement, T, at using Eq. (12.5a) and the scattering measurement, S, with the aid of Eq. (7.12), one obtains:

is the macroscopic cross-section of the radiation before scatwhere tering (along a distance and is that after scattering (along a is the macroscopic cross-section for Compton scattering, distance K is a system constant that incorporates the source strength, detector efficiency and system geometry. Note that because of the dominance of the photoelectric effect at energy its cross-section is used in place of the total cross-section. The composition indication provided by and is dependent to some extent on the di-

this method, via mensions of the object, unlike in the dual-energy transmission method (section 12.2.2.2) where dependence on the object thickness, is elim-

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inated, see Eq.(12.5c). On the other hand, the transmission-scattering method provides indications that cover a more diverse portion of the object, than that is covered by the scattered and transmitted radiation, unlike the dual-energy transmission method which only spans one chord of the object, as indicated in Figure 12.1. The transmission-scattering method, like the dual-energy transmission method, is also employed in the radiograhic imaging of passenger luggage, see section 13.5.

12.2.2.4

Dual Scattering

A third approach is to utilize a high-energy source, and monitor photons scattered at high energy, i.e. after a single collision, and those that scattered after many collisions, Figure 12.1.c. The latter photons would be at low-energy so that they are attenuated by photoelectric absorption as they travel towards the detector. The ratio of the two scattering measurements would then be indicative of the effective atomic-number of the material covered by the scattered photons. This can be shown by formulating the scattering measurements, similar to Eq. (12.6b), as follows:

where and are system constants at the high and low scattering energies, respectively, is the electron-density, the bar designates some “lumped” cross-section value over the many interactions that radiation goes through until it reaches the lower energy, F and G refer to some function formulations, all other parameters are as defined following Eq. (12.6c), and use is made of the expressions in Eq. (12.4) to arrive at the arguments of the functions. Note that inherent in Eq. (12.7a) is the assumption that photons scatter only once before reaching the detector. However, even with a few collisions, one would still expect to be a function of since Compton scattering will remain dominant. The lumping of the cross-sections in Eq. (12.7c) is possible, since after a few collisions photons would tend to “forget” their point of origin and behave as an independent “cloud” of photons that is not directly related to the photon source and can be “lumped” into an equivalent point. The function can be separated, by proper choice of the detection energy, into two functions, so that This function separation is justified by the fact that the scattering of


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low-energy photons is dependent on and the attenuation process is dominated by photoelectric absorption, which makes the two processes mutually exclusive (i.e. a photon is either scattered or absorbed but not both). In between the low and high energy, the two processes of photoelectric absorption and Compton scattering are competitive, with neither one dominating the other. In that region, it would not be possible to use a “lumped” parameter to arrive at a model like that of Eq. (12.7b), since the photon flux distribution would still be dependent on the source photons and their behavior during the first few collisions. The low and high energy windows need, therefore, to be carefully chosen so that is an atomic-number indicator that is independent of density. In addition, the low-energy scattering should be monitored at a distance sufficiently away from the source, to allow photons to lose enough energy so that the photoelectric effect becomes dominant. Thus, the dual-scattering method provides an indication over a wide volume of the inspected medium. However, as can be seen by comparing Eqs. (12.5a) to (12.5c) and (12.6a) to (12.6c) with Eq. (12.7a) to (12.7c), the dualscattering method is not a direct atomic-number indicator. The dual-scattering method is employed in a litho-density tool in oil exploration for examining rock and mineral formations; with providing the density signals, as discussed in section 11.1, while identifying various rock and minerals [40] and for in situ bulk density of surface formations and average atomic-number [716, 717]. The method has also been proposed for detecting explosives in luggage [718], and narcotics hidden in cargo containers [719]. The same modality was used for the determination of coal face ash content [720], employing a low-activity (1.8 MBq) source along with a small (0.35 MBq) source as a gain stabilizer, i.e. a marker with respect to which energy is calibrated. A similar approach was used for the determination of ash in coal seams intersected by boreholes [721, 722]. The application of the same approach to delineate iron deposits and determine their grade in borehole logging is reported in reference [723]. Reference [724] defined a spectral sensitivity matrix of multiscattered radiation which relates linear variations in the material properties to those of the spectra.

12.2.2.5

Dual-Energy Scattering

A fourth approach in composition indication is to monitor the Compton scattering of photons at two different source energies, one at a higher energy where the attenuation of the scattered photons is mainly via Compton scattering, while the second source energy is lower so that scattered photons are attenuated by photoelectric absorption, Figure 12.1.d. This method eliminates the needed to place two scattering detectors

568


away from each other as in the dual-scattering method, and does not require access from two opposite sides of an object as in the case with methods employing transmission measurements. The dual-energy scattering process can be modeled using Eq. (7.12) as follows:

where H refers to the high-energy source, L to the low-energy one, and the other notations are analogous to those used in Eqs. (12.7a) to (12.7c). Note that the formulation of Eq. (12.8b) assumes single-scattering, or an equivalent “lumped” scattering process. This method, as Eq. (12.8c) shows, does not provide a density-independent indicator, but its dependence on the atomic-number, Z , is stronger (to the power than the other methods, which also reduces the dependence of on density. An example application of this method is in the use of backscattering of (1.17, 1.33 MeV) photons to determine the grade of iron ore in samples (iron content), by detecting photons scattered to 46-180 keV for low-energy scattering and 200-1000 keV for high-energy scattering. The ratio of these measurements were reported to provide a densityindependent iron-content indicator [384]. However, in manganese-rich ores, such technique can give a misleading indication, due to the proximity of the atomic-numbers of Mg (25) and iron (26). Elaborate analysis of the energy spectrum of backscattered photons, see section 7.5.6.1, from (662 keV) was also shown to provide rock properties, such as heavy-element content, density and grain size, and was also used to determine the diameter of a borehole [219].

12.2.2.6

Coherent Scattering

Aside from the photoelectric effect, advantage can be taken of the coherent (Rayleigh) scattering process, which also has a cross-section that is strongly dependent on the atomic-number, see Eq. (3.63). Since Rayleigh scattering is a coherent wave interaction that causes only a small change in the direction of the incident radiation, while not changing its energy (see section 3.4), a scattering detector needs to be placed in the proximity of the path of the incident radiation beam, see Figure 12.1. As explained in section 3.4.3.1, the photon energy does not change when Rayleigh scattering occurs, but is altered by Compton scattering, Eq. (3.37). Therefore, Rayleigh scattering can be distinguished


569

from Compton scattering by the photon energy. This, however, requires the use of a monoenergetic source, for ease of discrimination between the two effects. Also, at the small scattering-angles at which Rayleigh scattering dominates (see section 3.4.3.1), the energy change associated with Compton scattering, as can be deduced from Eq. (3.37), would be also small. Therefore, a detector with good energy resolution is required to distinguish between the two modes of scattering, as they need to be measured at the same angle so that the same point of scattering (as defined by the intersection of the incident and scattered beams) is monitored. In Rayleigh scattering, the source energy has to be reasonably low, as Eq. (3.4.3.1) indicates. One of the isotopic sources listed in Table 2.7, such as can be used for this purpose. Although these sources provide monoenergetic photons, which makes it easy to identify Rayleigh scattering by its lack of energy change, the radiation intensity of such sources tends to be quite low, unless a large amount of radioactivity is employed. Therefore, effort was made to make use of monoenergetic photons from x-ray machines. In one application, a secondary tantalum target was used within a 150 keV x-ray machine to produce the Ta (57.5, 57.3 keV) and (66.9 keV) lines [725, 726], which are at about isotopic source (59.5 keV). The the same energy produced by an same workers, using a scattering angle of 12°, also applied the so-called “source/detector filter” technique to avoid the use of a high-resolution expensive photon detector to distinguish between Rayleigh and Compton scattering. An erbium filter was used, as it has an absorption K edge at 57.48 keV, which increases its photon absorption from to Therefore, with this filter placed in the path the incident beam, it attenuates the 57.5 keV peak of the source significantly, reducing both the amount of Rayleigh and Compton scattering, resulting in a total scattering count rate, that can be expressed as:

where the subscript s emphasizes the fact that the incident source beam was attenuated by the erbium filter, T(E) is the attenuation factor introduced by this filter at the source energy E ( = 57.5 keV), and R and C refer, respectively, to the amount of ‘unfiltered’ Rayleigh and Compton scattering signals. Now, by removing the filter from the path of the incident beam and placing it in the in the path of the scattered beam, i.e. detected beam, the detector will record a count rate, that can be expressed as:

570


where is the energy of the scattered photons as determined by the Compton scattering kinematics, Eq. (3.37), at the angle of scattering. Note that the energy of photons after Rayleigh scattering stays at the same energy as that of the source. Using Eqs. (12.9) and (12.10), one can show that the Rayleigh-to-Compton scatter ratio (see section 7.3.10) can be expressed as:

Note that due to the nature of the source and filter involved. The scatter ratio of Eq. (12.11) is a strong function of the atomic-number of the scattering medium, as indicated earlier, and was confirmed by measurements [725]. In principle, the effective atomicnumber of materials of atomic-number from six to 83 can be determined by the Raleigh-to-Compton ratio. Applications of the Rayleigh-Compton scatter ratio include: measuring the surface composition of heavy elements, in particular titaniumrich alloys containing aluminum and zirconium [727], and the analysis of bronze or silver-copper alloys [728]. The same method was applied to the determination of the effective atomic-number of compounds of effective atomic-numbers less than 20 [729]. This ratio technique was also utilized for measuring the concentration proportions in substances of major compounds of low atomic-number; such as fat and water content in milk or in meat, and reaction products in organic chemistry [730]. The method was also used in the investigation of carbonization (conversion to carbon) of olive stones by heating them up to high temperature [731]. The ash content in coal samples was also determined by the Compton-Rayleigh scatter ratio [732].

12.2.2.7

Pair Production

In applications where it is not possible to inject a positron emitter within the object to be interrogated, as in the case with solid objects, positron emission may be introduced via the pair-production interaction of photons, which produces a pair of electrons and positrons. At photon energy above 1.022 MeV, the pair-production interaction comes into play, as discussed in sections 3.4.4 and 8.4. Positron annihilation occurs almost immediately and within a very short distance from its point of origin, and produces two 511 keV photons that can be used in emission imaging (discussed in section 8.8.3). The unique energy of these photons makes it possible to distinguish them from scattered photons, or those produced by bremsstrahlung radiation resulting from the recoil electrons of Compton scattering. The photoneutron interaction, discussed


571

in section 8.3, may also lead to the production of positron emitters, particularly by the activation of light elements. Since the cross-section for pair production, Eq. (3.73), is proportional to where Z is the atomic number, positrons induced by this reaction will be strongly indicative of the atomic-number (hence composition) of the positron-emitting material. This ability to distinguish between elements of different atomicnumbers makes this method particularly suited for locating high atomicnumber (heavy) objects in less dense matrices [733]. Reference [734] proposed the use of this method for inspecting the position and condition of rebars inside steel reinforced concrete. Pair-production was also used to measure the ash content (high atomic-number minerals) in coal, along with Compton scattering, since the intensity of annihilation gamma-rays depends on both the atomic-number and density of the material while that of the scattered photons depends only on its density [735]. Isotopic sources that are suitable for inducing pair production are: (1.27 MeV), (1.17, 1.33 MeV), (1.76 MeV) and (69.98 y half-life, 2.615 MeV from decay of daughter Linear accelerators can also be used in this regard, offering the advantage of a high intensity source, but with continuous energy distributions. Reference [736] investigated the use of a 6 MeV accelerator, showing the change in positron emission intensity with atomic-number, Z, from Z = 14 (silicon in sand) to Z = 82 (Pb), while reference [733] studied positron emissions from Z = 4 (Be) to Z = 82 using a source. In the latter work, the 511 keV photons of positron-annihilation were segregated from the rest of the photon spectrum using a high resolution gamma detector (HPGe), while reference [736] reported the use of a difference-filter method, see section 15.2.1.2, to avoid the employment of an expensive energy resolving detector.

12.3.

Hydrogen Measurement

This entire section is devoted to hydrogen, because of its natural and industrial importance. Hydrogen is the most abundant isotope in nature. It is the “maker of water”, as its name means in Greek. Detection of hydrogen is, therefore, associated with the detection of moisture, wetness, dampness and steam. Hydrogen is also an essential component of the many hydrocarbon compounds encountered in biological structures, petroleum and its produces, polymers, etc. Moreover, hydrogen interacts with metals forming hydrides that can cause embrittlement and subsequent deterioration of metallic structures.

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Hydrogen Index. The hydrogen concentration is often indicated, for convenience, by the hydrogen index ( HI ):

The atomic-density of hydrogen in water at standard temperature and pressure (room temperature and atmospheric pressure, STP ) is hydrogen atoms per of water. For hydrocarbons, the HI value can be very small (for gases) to close to unity for some of the heavier oils, depending on composition, phase (gas or liquid) and temperature and pressure. It interesting to remark though that while the HI value for pure water at STP is unity, under the same pressure and temperature, the HI value for saline water is only 0.92 [40]. This reduction in the hydrogen content is due to the fact that the dissolved salt (NaCl) displaces hydrogen, thus reducing its atomic-density. Methods of Detection. Hydrogen has three main basic properties that makes its amenable to detection by radiation: 1 It has about the same mass as a neutron, making it the most effective neutron-slowing down nuclide (see section 3.5). 2 When it captures a thermal-neutron, it emits a characteristic highenergy (2.2232 MeV) gamma-ray (discussed in section 12.1.1). is the only isotope 3 It is the only neutron-free nuclei, therefore ratio of unity, where Z is the atomic-number and A is the with mass-number. Neutron Slowing-Down. The hydrogen nucleus is easily detectable by neutrons. Due to its superb slowing-down power, the amount of fast-neutrons slowed-down (by scattering) in a medium is a direct indication of its hydrogen content in that medium. As indicated in chapter 4.4, the detection of neutrons is most efficient at the thermal energy. Therefore, the slowing-down of neutrons is often detected at the thermal energy using one of the common thermal-neutron detectors and crystals). Note that neutrons need not reach the thermalenergy to provide indications on the presence of hydrogen. Measuring neutrons as they are slowed-down to the epithermal energy (say between 0.1 eV and 1 keV) is also indicative of the hydrogen content. This is particularly useful when measuring a small amount of hydrogen that is not sufficient to fully slow the source-neutrons down to the thermal-energy.


573

Thermal-Neutron Capture. Hydrogen has also a good neutron capture cross-section for neutrons (about 330 mb [176]). This neutron -capture process is accompanied by a characteristic gamma-emission at an energy of 2.2232 MeV (see Table 8.3), which is used to uniquely determine the hydrogen concentration. Since thermal-neutron sources are not readily available, a fast-neutron source can be used if the amount of hydrogen in the inspected medium is sufficient to slow-down the neutrons to the thermal-energy where they can be readily captured. In such arrangement, one can view the capture of slowed-down neutrons and the subsequent gamma emission as a means of indirectly detecting thermalneutrons. The advantage of detecting generated gamma-rays, instead of measuring the thermal-neutron flux, is that gamma-rays are more penetrating than photos, thus a gamma-ray detector would cover a larger volume than a thermal-neutron detector, providing a larger domain of influence. However, this is not an efficient detection process due to the usually small neutron-capture cross-section of the inspected material, in comparison to that of a neutron detector, and to the divergence of the emitted gamma-rays over a wide area away from the gamma detector. Change in Indication. The microscopic cross-section for inelastic scattering of beta-particles with the atomic electrons is a function of the atomic-number, at a given source energy, as Eq. (3.26) indicates, and the macroscopic cross-section is, in turn, a function of Also, the macroscopic cross-section for Compton-scattering is proportional to see Eq. (3.51). The value of is equal to about 0.5 for all atoms, with the exception of where it is equal to unity. Therefore, the presence of hydrogen enhances the probability of both inelastic beta-particle scattering and Compton photon scattering, for the same material density. This is useful in detecting hydrogen when it is present at a quantity that is small enough not to affect the material’s density, but is sufficiently large to show an overall enhancement of the scattering of beta-particle or photons. Hydrogen-Related Properties. The detection of hydrogen is usually used as indicator of water and other hydrogen-containing compounds, but other material properties can also be related to the hydrogen content. For example the lack of hydrogen can be used as a measure of the void (vapor) volume-fraction of boiling water, since the hydrogen concentration in the vapor phase is negligible in comparison to that in the liquid phase up to about 10 MPa in water. Similarly, since rock grains (such as quartz, calcite, etc.) contain no hydrogen, the presence of hydrogen in a ground formation is indicative of the voided

574


(pores) volume, through which water and other hydrogenous materials can exist. The fraction of that void is known as porosity. Hydrogen content can also be related to the asphalt-cement content of paved roads. Asphalt mixes consist mainly of the asphalt cement, aggregates, and air voids. While the amount of air void can be determined by an overall density measurement, see chapter 11, the asphalt content can be estimated from a hydrogen measurement. Asphalt is a bituminous derivative of petroleum containing a wide variety of hydrocarbons, while aggregates consist mainly of aluminates and silicates of calcium. Therefore, hydrogen is predominantly present in the asphalt cement, though it is also present in the water of the mix and within the minerals in the aggregate. However, it is generally assumed that the amount of asphalt is directly proportional to the hydrogen content in the mix, and a hydrogen measurement is, therefore, indicative of the asphalt cement content.

12.3.1.

Neutron Slowing-Down

Scatterometery (section 7.5), neutron transmission (section 6.1), the lifetime of a fast-neutron (section 9.4), or neutron activation (section 12.1.1) can be used as indicators of the slowing-down of neutrons by collision with the hydrogen nuclei. Neutron-slowing down is accomplished after neutrons encounter a few collisions with the hydrogen in the medium, see section 3.5. However, some extraneous factors affect this process and may give misleading indications. Although neutrons lose most energy per collision when interacting with hydrogen, they also lose energy, though to a lesser extent, by colliding with other elements present in the medium, see section 3.5. Also, slow-neutrons are absorbed by elements other than hydrogen. Lithium, boron and chlorine are some of the strong neutrons absorbers that may be present in a practical situation. These absorbers remove neutrons that would have otherwise interacted with hydrogen, and thus can influence the hydrogen measurement. Also some elements may have strong resonances in their absorption cross-section at higher energies, typically in the keV range. These resonant absorbers will reduce the number of neutrons available for slowing-down by hydrogen, and in turn lead to an underestimation of the hydrogen content. Therefore, the composition and density of a dry medium can affect the neutron flux distribution, and in turn the response of a device in the presence of hydrogen. Theses effects can be accounted for to a large extent by calibrating the device in a medium similar in its elemental content to the investigation medium.


575

Measurement Models. The measurement model for the response of a hydrogen measurement device that relies on neutrons slowing-down can in general be expressed as:

where N is the device’s response (say, count rate) measured at a hydrogen density of is the count rate at zero hydrogen content (i.e. due to the contribution of radiation background and the matrix material in which hydrogen is embedded), K is a constant that represents the total cross-section of the medium for the slowed-down neutrons and the distance they travel in the medium before reaching the detector (as this depends on the source-detector arrangement), and C is a system constant that incorporates factors such as the source strength, detection efficiency, etc. The model of Eq. (12.12) is based on the notion that the number of slowed-down neutrons increases linearly with hydrogen content, but also decreases exponentially with hydrogen content as hydrogen self-absorbs the slowed-down neutrons. As schematically shown in Figure 12.2, the hydrogen content can be measured in a small confined volume, or within an extended large medium. For these two limits, the model of Eq. (12.12) can be applied as shown below. Confined Medium. Water in a pipe and a soil sample placed in a small test tube are examples of confined media, where the neutron attenuation can be ignored, and Eq. (12.12) reduces to the linear equation:

This is the model used for two-phase flow measurements [213]. Extended Medium. Ground soil, borehole, and a large water tank are examples of extended media, where all neutrons are slowed-down regardless of the hydrogen concentration, as they can travel an unlimited distance. Then the linear dependence in Eq. (12.12) can be replaced by a constant, leading to the model:

where the constant C is replaced by another constant that also depends on the investigated medium. This is the model used in neutron well-logging tools for hydrogen-index measurement [40], where the neutron source is located within the ground with the aid of an access tube. Obviously, only neutrons reaching a detector will be measured, thus the response of a device is confined to a “domain of influence” around the

576


detector. If the source and/or the detector are placed at the surface of the ground, or the surface of some other extended medium, such as a concrete structure or an aggregate material, the response of the device will be complicated by the escape of neutrons away from the object. This skews the detector’s domain of influence, by virtue of having a large portion of the source’s field-of-view outside the inspected medium. An approximate, but more encompassing, model of the device’s response can be derived from two-group diffusion analysis, with one group for epithermal-neutrons and the second for thermal-neutrons [238, 737]. It should be kept in mind that the use of the diffusion theory, described in section 3.6.4, for this problem is an approximation. Strictly speaking the diffusion theory should not be used for determining the neutron flux near a boundary (due to the associated strong flux gradient near the surface), which is the case with a detector measuring the neutron flux on the surface of an object. Nevertheless, the diffusion analysis, with the help of some empirical measured parameters, can be used for preliminary analysis to identify the parameters that influence the response of the device. Such analysis can also be readily and more faithfully per-


577

formed with Monte Carlo simulations, see section 16.2. Regardless of the method used to analyze the performance of the device, it is customary to use calibration curves to relate the response of a detector to the hydrogen content, or some other related quantity. It is important to validate the calibration process periodically to ensure that the detector response does not drift as a result of some extraneous effects [738]. The slowing-down of neutrons was used to measure the concentration of carnallite in rock salt, making use of the high water-content of carnallite crystals [343]. The same technique was utilized for measuring the concentration of sulfuric acid in pipelines, by the hydrogen content of the acid. The technique was also applied to the measurement of hydrogen content per unit volume, hence the water content, of coal slurry [390]. Many applications has been reported for the use of neutron scattering for hydrogen as indicative of water content, moisture or wetness, see section 11.4. Backscattering of fast neutrons was proposed as a method for detecting plastic landmines, by the increase in the hydrogen content of explosive materials, and their casings, in comparison to soil [739, 740]. Similarly, a hand-held device is used for detecting hydrogenrich materials, such as narcotics, hidden behind panels made of steel, wood, fiberglass, and even lead-lined materials [741, 742, 743]. An interesting application of neutron moderation combined with a microwave moisture gauge was reported for determining the moisture and oil content in soil samples, to determine the extent of oil contamination and the effectiveness of a contamination process [744]. While the neutron-scattering measurement determines the total hydrogen content in soil (from water moisture and oil), microwaves measure only the water content; with the difference in the indication of the two gauges providing an estimate of the oil content. In order to enhance neutron moderation in a small (cylindrical) sample, an iron reflector of fast-neutrons was used to force fast-neutrons to pass the sample many times. Similarly, a microwave cavity resonator with a slit was used to cause the microwaves to pass through the sample repeatedly, enhancing the moisture measurement sensitivity. Lifetime. The lifetime, or die-away time, of pulsed fast-neutrons, discussed in section 11.3 for measuring porosity in geological formations, can also be used for measuring hydrogen content in extended media, since porosity is indicated by hydrogen which is predominately present in water and oil fluids filling pore spaces in rock. Neutrons slowed-down by hydrogen can be detected by the their late time of arrival to a detec-

578


tor. Time-tagging neutrons can, therefore, be used to distinguish neutrons slowed-down by hydrogen from those fast-neutrons scattered by heavier elements. This process was proposed for the detection of landmines, by their higher hydrogen content compared to that of many types of soil [745]. By placing a small source within a fission chamber, a time-trigger is registered when the neutrons are emitted. Neutrons scattered back to a detector after some delay-time (about 5 ms), were considered to be slow-neutrons, the intensity of which is indicative of the hydrogen concentration. Neutron Transmission. Hydrogen content can also be measured with a neutron transmission technique. If a fast-neutron source is used, hydrogen will in effect “soften” the neutron-energy spectrum, as source neutrons will lose considerable amount of energy. Measuring the fastneutron flux is not as efficient as measuring slow neutrons. A thermalneutron detector can be used, but then one would be, in effect, measuring neutrons scattered in the forward direction. On the other hand, if a thermal-neutron detector is covered with a slowing-down material (such as polyethylene) to enhance the detection efficiency by slowingdown the incident neutrons, one would be measuring the transmitted fast-neutrons. However, the detector’s response will also be affected by the hydrogen content in the detector’s moderating material, which complicates the relationship between the detector’s count rate and the hydrogen content of the examined object. If the object does not contain a strong-neutron absorbing material, a thermal-neutron beam (extracted from a nuclear reactor or a neutron-thermalization assembly) can be used as a source in a transmission-based technique. Since hydrogen is a reasonably good neutron-removing element (by scattering and absorption) , the intensity of a beam will decrease exponentially with hydrogen content. This method is the essence of neutron radiography, as discussed in section 13.2. The method has also been used for measuring the voidfraction of two-phase (boiling-water) flow [481], and for measuring the asphalt-cement content of bituminous mixes by placing a sample in a stainless steel pan [746]. Using a source and an NE-213 organic scintillator, fast-neutron transmission was used for measuring the water content distribution in a soil layer packed in a column [747]. The content and distribution of hydrogen in graphite and in zirconium was also measured by the transmission of neutron beams from an isotopic source [748]. Thermal-neutron transmission is also used for hydrogen and water content measurement, due to the higher absorption cross-section of water in comparison to that of many materials. Example applications in-


579

clude measuring the moisture content in pottery [749] and in glass [750], studying humidity transport in building materials, and measuring the porosity of crystalline rocks for assessment of contaminant transport (with water filling the pores) [751]. The transmission of slow-neutrons was also utilized for measuring the hydrogen content in zirconium metal and to study the interactions between hydrogen and uranium [752]. Neutron-transmission, as the model of Eq. (6.2) indicates, is affected by the material density (which determines the macroscopic crosssection) and the material thickness. However, an associated gammatransmission, using the Neugat method described in section 6.5.3, can be used to account for these density and thickness effects. This method has been used for measuring the water content in wool, wheat, latex rubber, acrylic paint and alcohol, and the fat content of meat, dry wool and dairy products [343, 753, 754, 755]. The same method was also used for measuring the hydrogen content in coke, taking advantage of the fact that the transmission of fast-neutrons is mainly affected by the hydrogen concentration and mass per unit area (areal density), while gamma-transmission depends only on the areal density [640]. In source was the work reported in the latter reference, a collimated used, surrounded by a polyethylene moderator to slow-down and scattered neutrons back towards a detector, hence increase their detection probability.

12.3.2.

Scattering into Resonances

A neutron technique that is quite sensitive to the presence of hydrogen in small amounts, is known as the HYSEN (HYdrogen Sensitive Epithermal Neutron) technique [756], also referred to as the Notched Spectrum Technique [757]. As the name implies, the technique relies on the use of epithermal (0.25 eV to 1 keV) neutrons. Such neutrons are usually extracted in the form of a beam from a nuclear reactor, to provide the high neutron-intensity required for good sensitivity. The spectrum is then “notched”, i.e. part of its neutrons are removed, using a thick (3 to 6 mm) “filter” made of a material with a high absorption cross-section of neutrons within this energy. Materials that exhibit high (kilobarn) resonances in their absorption cross-sections include indium, silver and rhodium, see section 15.2.2.2. However, indium is the preferred filter material, because its most abundant isotope, (95.72 %), has a very high cross-section. Indium also is widely used as an activation foil to measure the thermal-neutron flux. A beam of epithermal-neutrons passing through a thick filter of indium, as schematically shown in Figure 12.3, will be depleted of neutrons in the energy range of 1 eV to 1 keV. By supplementing this filter

580


with a thin (a mm or so) layer of cadmium, most of the sub-cadmium (< 0.5 eV) neutrons will also be eliminated. Therefore, the spectrum of the neutrons emerging after filtering would be cut–off below 0.5 eV and would be “notched” in between 1 eV and 1 keV. If these filtered neutrons are allowed to pass through a thin foil made also of indium (a 1 mm alloy of 0.05% In in then only neutrons in the energy range outside the windows of the filter (between 0.5 and 1 eV and above 1 keV) will be subjected to absorption by the foil, but at a lower rate due to the lower cross-sections outside the range of resonances. Therefore, this thin foil acts as a reference (background) indicator of the beam’s effect on the sensing foil, another thin foil placed behind the test target, as shown in Figure 12.3. Now if a hydrogen-containing target, say a metal, is placed behind the reference foil, the hydrogen in the target will slow-down some of the higher energy neutrons, thus filling in the “notch” in the spectrum. The metal, on the other hand, hardly affects the neutron energy. Therefore, the emerging beam will be richer in neutrons within the resonance range, and in the sub-cadmium (below 0.5 eV) range, where the cross-section is quite high. When this emerging beam of neutrons interacts with a second foil made also of indium, it will have then a high probability of activating the target. The neutron activation of leads to the


581

formation of which decays with a half-life of 54.29 min, releasing gamma energies that are easily detectable, say by a Na(Tl) detector. The dominant gamma-energies released and their relative yields are: 2.112 MeV (15.5%), 1.097 MeV (56.2%), 1.293 MeV (84.4%), 1.507 MeV (10.0%), 818.70 keV (11.5%), 416.86 keV (27.7%), where the percentage refers to the relative yield [12]. The amount of activation of the second (detection) foil, less that produced in the first (reference) foil, would then be proportional to the hydrogen content of the test target. The emitted photons can also be detected by a film positioned behind each detection foil to provide a radiograph. A modified arrangement of this method that enhances the signal-tobackground ratio, relies on detecting neutrons scattered off-the-beam, rather than those in the direct path of the beam. This can be achieved by using a hollow foil, with the opening diameter of the hole sightly greater than that of the beam [757]. In such arrangement, only neutrons scattered off-the-beam are detected. This arrangement reduces significantly the activation of the reference target and the detection target, by the source neutrons, since there are no longer subjected directly to the neutron beam. Moreover, since neutron scattering by hydrogen is in the forward direction (for single scattering), see section 3.5.1, scattering is favored in the direction of the detection foil. It was found that maximum activation occurs at a scattering angle of 60°. Thus by positing the annular target to detect neutrons scatters by between 45° and 80°, optimum activation of the target is obtained, while minimizing direct exposure to the source beam [757]. The metal, on the other hand, scatters neutrons isotropically but hardly affects, their energy. However, if the amount of hydrogen is sufficiently large to cause multiple scattering, some of the neutrons scattered by the hydrogen will reach the reference foil, increasing the reference signal, hence reducing the signal-to-background ratio. The method is sensitive to hydrogen levels in the range of parts per million [757] The HYSEN technique has been used for measuring hydrogen in steel, titanium aluminide intermetallic compounds (TiAl), obsidian, silicon, diamond and zirconium [758]. A variation of the HYSEN technique relies on the use of an iron filter. Unlike indium, silver and rhodium, which are strong neutrons absorbers in the keV range, iron allows neutrons of energy of about 24.5 keV to pass unaffected. This is due to the sudden decline in its scattering-cross section from an average value of about 12 b to about 0.5 mb. Therefore, subjecting a beam of neutrons to a thick iron sheet will tend to remove most of the neutrons of the beam, by scattering and absorption, except those with an energy of 24.5 keV, which will go through the shield virtu-

582


ally unaffected. If this filtered monoenergetic beam is made incident on a test object also made of iron, it will pass though it unaffected, except if the iron contains hydrogen. Hydrogen will scatter the neutrons down in energy to anywhere from the beam’s energy to the thermal-energy, as dictated by the kinematics of neutron scattering, Eq. (3.81). If the hydrogen content is not too high, and the test object is not too thick, less say than 50 mm, source neutrons will tend to suffer no more than one collision, with increasing probability at scattering angels of 40° or more [759]. At a scattering angle of 40°, the neutron energy after a single collision of 24.5 keV, according to Eq. (7.15), is about 14.4 keV. Therefore, by positioning a detector capable of measuring neutron energy in the keV range at about 40° off the beam, one can monitor the amount of scattering by hydrogen, which is in turn proportional to the hydrogen content in the sample. Reference [759] reported measuring the hydrogen content of steel in the parts per thousand range, after unfolding the pulse-height spectrum of a proton-recoil gas detector to obtain the neutron energy. This method is also applicable to measuring the hydrogen content in other metals.

12.3.3.

Beta Particles

While all other stable nuclides have a ratio of about 0.5, for hydrogen is equal to unity, where Z is the atomic-number and A is the mass-number. This unique feature of can be exploited with electron-dependent radiation interactions, such as photons and chargedparticles, to detect the presence of hydrogen. A beta-particle technique was proposed, as early as 1954, to determine the hydrogen content in liquids [760]. This device, and similar systems, depend on the fact that the microscopic cross-section for inelastic scattering with the atomic electrons, which leads to the eventual absorption of beta-particles, is a function of the atomic-number for a given source energy, as the integration of Eq. (3.26) over all scattering angles indicates. Consequently the macroscopic cross-section, becomes a function of with where is the mass-density and u is the atomic mass unit. Since the energy distribution of beta-particles permits their attenuation to be approximated by an exponential function, with an attenuation coefficient, see Eq. (3.23), like is also a function of Note that the expression for in Eq. (3.24) does not include dependence on since for most elements is equal to 0.5. However in the presence of hydrogen doubles in value to unity and accordingly significantly increases, resulting in an increase in the attenuation of beta-particles for the same material density and thickness. The same concept can be used in principle with


583

Compton scattering, since its microscopic cross-section is also a function of see section 12.3.4. However, since the microscopic cross-section for photons is much smaller in magnitude than that of beta-particles, the latter type of radiation offers more sensitivity to changes in the hydrogen content. The measurement model for this beta-particle attenuation technique can be expressed with the aid of Eqs. (3.23) and (E.14), with A = 1 for H, as:

where I refers to the intensity of the incident radiation, is the intensity in the absence of the object, is the thickness of the object, refers is its to the weight-fraction of an element, A is its mass-number, microscopic cross-section, H refers to hydrogen, refers to other elements as in the inspected material, and u is the atomic mass unit. Since where is a the indicated above, is a function of Z, say microscopic cross-section per electron, then keeping in mind that Z = 1 for H, and for all other elements, Eq. (12.15) can be rewritten as:

with the last step made possible by the fact that since the summation excludes hydrogen. Therefore, the weight fraction of H in a test object of known thickness, and a pre-determined density, can be calculated from a transmission measurement by the relationship:

The model of Eq. (12.16) contains two main approximations; namely is element-independent and that for all elements other than hydrogen. While the latter assumption is not a bad one, particularly for light elements, the former assumption is not very adequate for elements of high Z value, where scattering by the electrostatic field of the nucleus becomes important, see sections 3.3.2 and 12.4.2. The nature of the chemical bonding of the material can also affect the value of However,

584


for light elements, from Z = 1 to about Z = 10, beta-scattering by the is atomic electrons dominates, and it is reasonable to assume that independent of Z, since then according to Eq. (3.26). The model of Eq. (12.16) is also based on the exponential relationship of betaparticle attenuation, Eq. (3.23), which by is itself is an approximation. Nevertheless, the method has been used for measuring the hydrogen content in hydrocarbons, as they contain mainly elements of The hydrogen content can also be measured in the backscattering modality. Then the scattering response can be represented by the relationship [238]:

where use is made of Eq. (12.16), is the response for a sample of an is the response in the absence of the sample. infinite thickness, and is proportional to In the presence of elements of high Z values, Z, as scattering (elastic and inelastic) of beta-particles by the nucleus becomes more dominant, consequently Then the models of Eqs. (12.15) and (12.17) will have an extra Z-dependent term. While it can be accommodated this complicates the process of determined by prior calibration of the device’s response to the various expected elements in the examined material. It should be noted that due to the small depth of penetration of beta-particles, the use of the method is limited to the analysis of thin sample of liquids, about 2 mm thick. The sample needs to be housed in cells with thin windows made of a low density packing material, such as “Melinex”, to allow source particles to enter and leave the sample. The method is, therefore, most useful for analyzing hydrocarbons, which are binary mixtures of H and C for which the H/C ratio can be determined with this method.

12.3.4.

Compton Scattering

Compton scattering can also take advantage of the fact that is equal to unity for hydrogen, and is equal to 0.5 for all other elements, to determine the hydrogen content. As Eq. (3.51) indicates, the cross-section for Compton scattering is proportional to and thus for the same material density, the cross-section in the presence of hydrogen would be much higher than in its absence. This approach was used for determining the moisture content of wood chips [179], by monitoring the scattering of photons emitted from a source. This measurement is facilitated by the fact that the low moisture content of wood chips does not affect much its density, while it enhances its Compton scattering probability.


585

The same approach, also with a source, but in the transmission modality, was used for determining the hydrogen content of hydrocarbons; resulting in a linear relationship between the logarithm of the count rate and where is the material density and is the weight-fraction of hydrogen in the analyzed solution [24]. Multiple was used for measuring the density scattering of gamma-rays of and water content of soil [216], by taking advantage of the increase in the count rate caused by the doubling of the ratio in the presence of hydrogen.

12.3.5.

Cold Neutrons

Radiation responds mainly to the presence of individual atoms or nuclides, thus it provides elemental (rather than molecular) indications. Therefore, radiation techniques cannot, generally, sense the chemical bond in which a hydrogen atom exists. This should be kept in mind when detection water, which may be present as “free” or “bound” molecules. inherent in the composition of a material, while Bound water is the free-water is that due the water seeping through the material, such as moisture or in that in pores. Non-nuclear techniques such as the measurement of the dielectric constant, microwave absorption and magnetic resonance imaging can be used to discriminate between the two types of water, since their response depends on the chemical composition (molecular binding energy) of materials. However, quasi-elastic neutron scattering of cold-neutrons has been used to quantify the conversion of water from free to bound states, as in the hydration of Portland cement due to the interaction of water with tricalcium silicate [761]. Because of their low energy, the scattering of cold-neutrons is affected by the translation motion of water molecules, resulting in a difference in the scattering behavior of free and bound water molecules.

12.4.

Material Content Analysis

Content analysis aims at determining the relative content, or concentration, of known components of a material. The relative content can either be a volume fraction, or a mass fraction. For a mixture of components, the volume fraction of the the component, is where is the volume occupied by component and V is the total volume of the mixture. The mass fraction, of component is expressed as where and refer, respectively, to the density of component and to that of the mixture. From these definitions, one can show that

586


Note that the quantity for a very small or amount of component is often expressed in parts per million (ppm). In order to be able to distinguish between different materials within a mixture, these materials must affect radiation in different ways. Unlike the elemental and composition determination described in sections 12.1 and 12.2, content analysis assumes that the nature of the material present in the mixture is known in advance. However, most techniques for elemental analysis can also be applied to content analysis, as shown in the ensuing sections, which address these methods according to the nature of the radiation used.

12.4.1.

Alpha Particles

Alpha-particle transmission can be used for detecting a binary mixture made of two materials of different densities, since the range of alphaparticles is dependent on the material’s density, see Eq. (3.14). The short-range of alpha-particles limits their use to gases, and necessitates performing measurements in a gas chamber within which the source and detector are placed. With a thick source, i.e. a source that self-absorbs some of the emitted alpha-particles, particles leaving the source will have an energy that varies from zero to the a maximum source energy, Then the dense component when present at a 100% concentration will stop entirely the transmission of alpha-particles through the sample, when the source-to-detector distance is equivalent to the range of alphaparticles in the gas at On the other hand, if the sample contains only the lighter component, the number of transmitted particles will be maximum. Therefore, in a binary mixture of the denser and the lighter components, the number of transmitted particles will depend on the relative concentration of the two components. One then would expect the count rate to vary linearly with concentration, so that the weightof the lighter component can be estimated as:

fraction, where

is the count rate at and C is the count rate at A surface-barrier semiconductor can be used to count the transmitted alpha-particles. It is important to maintain a constant gas pressure and temperature, or to correct for their change, since they directly affect the gas density. This method was used for controlling the mixing of helium and oxygen gases to a specified value [238]. An ionization chamber, see section 4.2.2.1, can also be used for measuring the relative content of binary and ternary gases. The measured ionization current, as shown in section 9.1, is a function of the ionization cross-section, defined by Eq. (9.1), which is in turn, like any macroscopic cross-section, is a linear function of the rel-


587

ative content of the two components of a binary mixture (see appendix E). This method was used for measuring the concentration of small amounts of added gases, such as CO, alcohol, and vapors of fatty acids in air [24]. This application is particularly useful for monitoring hazardous gases in the atmosphere of chemical plants and mines. The method was also used for analyzing mixtures of gases (hydrogen/nitrogen, hydrogen/ethylene, hydrogen/carbon-dioxide, nitrogen/nitrogen-dioxide, nitrogen/carbondioxide, ethylene/ether and helium/xenon) [24]. Ternary mixtures were also analyzed using two independent measurements. These two measurements can be attained at two ranges of operating voltage: plateau and low voltage (see section 9.1). Alternatively, two separation distances between the electrodes can be used to change the radius of the ionization zone, in Eq. (9.2). A nitrogen-hydrogen-ethane mixture was analyzed by this method using a small (28 mm diameter) and a larger (70 mm diameter) ionization chambers [24]. Alpha sources used in these applications include and

12.4.2.

Beta Particles

The strong dependence of the scattering cross-section of betaparticles, on the atomic number, Z, see Eqs. (3.26) and (3.28), can be used to distinguish between two components of various atomic-numbers in a binary mixture. One obvious advantage of beta-particles in a backscattering arrangement is that it is relatively easy to shield the detector from direct exposure to the source particles, because of the limited penetrability of beta-particles. However, the interrogated sample, if fluid or gas, has to be enclosed within a container of a thin widow to avoid absorption of the beta-particles by the walls of the container. Backscattering of beta-particles can also be made independent of material density by ensuring that the thickness of the inspected material is larger than the range of incident particles, so that all incident particles have a chance to interact within the medium. Then the amount of backscattering will be independent of the value of the range, hence independent of the material’s density. The number of backscattered beta-particles where Z is the atomic-number is approximately proportional to of the scattering atom [762]. Therefore, the amount of backscattered beta-particles is dependent on the composition of the scattering material. However, one must keep in mind that the domain of influence of such scattering measurement is within a distance that is no large than the particle’s range, thus any nonuniformity in the distribution of the mixture outside the range would be not be detected.

588


A measurement model can be developed for beta-scattering with the premise that the amount of scattering depends on the macroscopic scattering cross-section of beta-particles in a mixture, For an object thicker than the range of incident beta-particles, the amount of absorption of beta-particles can be assumed to be constant, since the particles will be able to travel their entire range. Also since the range of betaparticles is small, the effect of divergence, Eq. (3.6.2), can be assumed to be about the same for all scattered particles. It is, therefore, reasonable to assume that the amount of scattered beta-particles is proportional to Since the microscopic cross-section of beta-particles is a function of the atomic-number, as Eqs. (3.26) and (3.28) indicate, then using for a mixture can be expressed as: Eq. (E.21),

where and refer, respectively, to the effective mass and atomic numbers of component, which can be calculated from the elemental values as shown in appendix E, and is a constant value that depends and nuclear on the relative importance of the atomic scattering effects, as determined by Eqs. (3.26) and (3.28). The approximation in Eq. (12.18) results from the fact that for most elements and materials (except pure hydrogen). Note that since for beta-scattering by atomic electrons, Eq. (3.26), the scattering crosssection, Eq. (12.18), is affected predominately by the nuclear scattering of beta-particles. As Eqs. (3.26) and (3.28) show, nuclear-scattering predominates over scattering by electrons by a factor of Z, and the two mechanisms of scattering have the same probability of occurrence only with hydrogen, Z = 1. Therefore, the presence of hydrogen can be distinguished from other elements and compounds by the virtue that its value is equal to unity, which enhances its scattering cross-section. This fact is used for the detection of hydrogen, as discussed in section 12.3. With the aid of Eq. (12.18), one can use the following model for the scattering of beta-particles in a mixture:

where is the measured detector response for component in the mixture when Obviously, one scattering measurement makes the technique only viable for measuring the content of binary liquids; with the relationship providing a second known quantity. Beta backscattering was used to measure the amount of dissolved salt in liquids, and the analysis of hydrocarbon liquids mixtures [238]. Refer-


589

ence [287] described an instrument, using a source and an ionizationchamber detector, for determining the hydrogen-to-carbon ratio in hydrocarbon liquids encountered in petrochemical processes, covering an H/C ratio from 1 (light fuel oil) to 2.5 (naphtha feedstock). The same method was used for measuring the ash content of coal, taking advantage of the fact that the effective atomic-number of ash is about 13, compared to 6 for the carbon of the coal. Finely-ground, air-dried coal samples were analyzed using the backscattering of a [323]. The method was also used for determining the tungsten content in iron [763]. Composition analysis of tin/lead plating on printed circuit boards by the beta-backscatter method, using a source, was also reported [764]. For materials with high Z, the sensitivity of the scattered radiation to changes in the atomic-number is not as pronounced as in the case of light materials where the change in the value of Z is quite high, see Eq. (12.18). However, using the energy of scattered beta-particles, one can segregate scattering by different elements. The maximum energy of the backscattered beta-particles depends on the atomic-number of the scattering element. Since the scattering cross-section of beta-particles increases with Z, see Eqs. (3.26) and (3.28), elements with higher atomicnumber scatter back beta-particles early in their passage through the material, thus scattered back higher energy beta-radiation before they travel deep into the medium. The maximum energy of backscattering was also observed to be independent of the energy of the incident betaparticles; provided that the incident beta-particles have an energy that exceeds the maximum-energy of backscattering [765], and that the material thickness is larger than the range of the particles in the material so that all beta-particles would have been subjected to scattering. The maximum energy of the scattered beta particles, is proportional where the value of varies from 3 [766] to 5 [765]. The latter to reference reported the following relationship:

Therefore, energy-discrimination can be used to determine the content of the element of the highest atomic-number in a sample, provided that its atomic-number is quite different from that of other present elements. This can be achieved by shielding the detector with a sheet of material (such as aluminum) that is sufficiently thick to absorb all beta-particles except those that are backscattered by the element of the highest atomicnumber. Then, the intensity of the detector response will be proportional to the content of the element of highest Z-value. This method is useful for the analysis of metal alloys and for the determination of the content of the additives with the highest atomic-number, such as tung-

590


sten and molybdenum in iron, niobium in chromium, and lead in lead glasses [766]. The use of this method for the determination of iodine and mercury in aqueous solutions was also reported [179]. For a ternary mixture, two independent measurements are required, in addition to the relationship: where is the weightfraction of each species in the mixture. Beta-scattering, as discussed above, can provide one measurement. Beta-transmission can be used to provide the other measurement. However, beta-transmission measurements introduce two difficulties. First, for beta-transmission to be recordable, the thickness of the sample has to be less than the range of the source particles. This conflicts with the requirement of having a material thickness larger than the range to make beta-scattering independent of material density, as discussed above. Therefore, the transmissionmeasurement needs to be performed separately on a thin sample of the mixture. Even then one would be faced with the second difficulty of beta-transmission: the dependence of the transmission coefficient on the material’s density, as evident by Eq. (3.24). However, by performing an independent density measurement, say by simply weighing a known volume of the sample, the dependence on density can be accounted for. The combination of beta-scattering and transmission was used for measuring the relative weight fraction in ternary liquids of hydrogen, carbon and oxygen [767, 768], or hydrogen, carbon and fluorine [767]. Beta-particles are also used in ionization chambers for analyzing the content of gases, using the method discussed in section 9.1. This is the method widely used in gas separation by chromatography to analyze the content of the carrier gas [24]. Beta particles are preferred for this purpose because of their large range, which permits the surveying of a larger gas volume, allowing their use in industrial environments. As explained in section 9.1, the ionization current is a function of the ionization crosssection, defined by Eq. (9.1), which in turn, like any macroscopic crosssection, depends on the relative content of the two components in a binary mixture (see appendix E). Therefore, the method is directly applicable to the content analysis of binary mixtures from a single measurement of the ionization current. For multi-component mixtures, say of N components, N – 1 measurements are required, to determine the relative concentration of each component. Such measurements can be obtained by recording the ionization current at N – 1 stations, e.g., one at the plateau region (described in section 9.1) and the rest at lower voltages. This approach was considered for the analysis of gas, up to a five-component mixture and [24]. Beta-ionization and chambers employ one of the following beta sources:


591

Beta particles, emitted from sources such as and and directed into a stream of an inert gas (such as helium or argon) would lose their energy by inelastic scattering with the gas molecules and, when collected by an anode would produce a constant electric current. However, when an electron-capture gas is introduced into the steam, the slowed-down (to the thermal-energy) electrons would be absorbed by the introduced gas, lowering immediately the electric current. Vapors emitted from volatile compounds, such as nitrogen-based explosives, fertilizer and some household cleaners, produce such electron-capturing gases. Although electron-capture detectors cannot discriminate between different types of electron-capturing gases, when combined with chromatography, or other separation means (see for instance reference [769]), it can be used to characterize certain types of vapors, as those listed above.

12.4.3.

Photons

Low-Energy Transmission. For photons to be able to distinguish between different components in a mixture, they must interact differently with each component. This occurs when the components are sufficiently different to affect the macroscopic cross-section of photons. This most readily occurs at low photon-energy. A number of applications of the transmission and scattering of low-energy photons are discussed here. Low-energy sources are used for measuring the concentration of higher atomic-number elements in hydrocarbons, such as sulfur, lead and chlorine, due to the higher cross-section of these elements at low energy, see Eq. (3.30). Sulfur (one of the elements responsible for the acidification of rain when emitted as sulfur-dioxide during fossil-fuel burning) absorbs low-energy photons more effectively than carbon and hydrogen. For example, for photons emitted from a low-energy photon source of an average energy of about 5.9 keV (see Table 2.7), the total removal (incoherent scattering + absorption) cross-section for S is 11.2 kb/atom while it is only 0.213 kb/atom for C and 0.577 b/atom for H [19]. This large difference in cross-sections makes it possible to detect the presence of S in oil and organic materials through a radiation-transmission technique. A thin sample layer need to be used for this purpose to avoid full attenuation of this low-energy radiation. The same method is also useful for the detection of chlorine in hydrocarbon materials, since Cl has a removal cross-section of 14 kb/atom at 6 keV. Other low-energy photons, such as (22 to 26 keV), see Table 2.7, can also be used for this purpose. However, the same level of photon-energy can be produced by the bremsstrahlung of on zirconium (15 – 50 keV) or from beta-particles emitted from (18.6 keV maximum energy) as they travel through a heavy metal, such as zirconium, titanium in tritiated

592


zirconium hydride or titanium hydride foils. This method was used for the measurement of sulfur content in the oil refining industry and for the determination of chlorine in liquid and epoxy plastics and chlorinated hydrocarbons [179]. With a slightly higher photon energy, the radiation transmission was same technique, with the 60 keV of used for the determination of heavy-metal salts (such as uranium) in solutions. Low-energy photon sources has been used for determining the content of a heavy element (Pb) in a light solution (gasoline and lead nitrate) [24], taking advantage of the enhanced contrast of lead absorption at low photon energy, Eq. (3.30). Both (photon energy less than 85 keV) and bremsstrahlung sources, on a uranium target (60-150 keV) and on antimony or on molybdenum (15-50 keV), were used for this purpose. Low-Energy Scattering. The scattering of low-energy photons can also be used for content analysis. The amount of scattered photons, though directly proportional to the mass-density for most materials (see section 11.1) is suppressed by photon absorption by the photoelectric effect. Since the latter effect is a strong function of the atomic-number, Eq. (3.30), materials with a high atomic-number scatter back less photons than those with high atomic-number. Therefore, the backscattering of low-energy photons can be used to distinguish between materials of different composition. This method, with a 85 keV photons from a source was used for determining the shale (ash) content of coal; taking advantage of the fact that while the atomic-number for coal is nearly equal to 6, the effective atomic-number of the mineral content (shale ash) is about 13 [762]. Low-energy sources used for this purpose (84 keV) and (60 keV) [24], (22 keV) [390] include and (13.60 keV) [323]. At these low energies, the medium can be considered to be infinite in size, allowing the use of the measurement model of Eq. (7.51). Then the scattering response of the detector, by the S, can by related to the fractional (per weight) ash content, relationship [390]:

where K is a system constant and and refer, respectively, to the scattering and total macroscopic cross-sections, per unit mass, of the designated material, estimated at some effective energy between that of the source and the detected photons (see section 7.5). The sensitivity of


S to changes in the ash content,

593

can be expressed as:

where use is made of Eq. (12.21). Reference [390] indicated that the highest sensitivity occurs at a source energy of about 15 keV, since the use of a source (13.60 keV). At lower energies, the probability of Compton scattering, see Eq. (3.51), is quite low to cause significant scattering, making it while at higher energies, Compton scattering dominates which reduces the contrast. One complicating factor almost equal to of operating at the optimum energy range is the interference of fluoroscopic emissions from iron, (see section 8.7), which has a K-absorption edge at 7.111 keV, that may overlap the energy range of the detected scattered photons. The strength of this high-intensity peak varies with the iron concentration, but it can be removed, at the detector side, by energy discriminating or by the use of an aluminum filter so that the increase in the count rate by Fe K-fluoroscopic emission is compensated for by the attenuation introduced by the filter material. The source energy determines the energy of the photons scattered within the medium, and in turn the amount of photons present at the excitation energy of the K x-ray of iron. Changing the source energy also affects the amount of fluoroscopic emission. It turned out that at 15.8 keV, the increase in detector counts due to fluoroscopic emission is offset by a decrease in the amount of backscattering, without the use of filtering or energy discrimination. According to Eq. (12.22), higher-energy sources, such as those emitted by (84 keV) and (60 keV), have a theoretical sensitivity to the ash content, but with such sources the scattering process is not fully saturated and the model of Eq. (7.45) should be used. Then the scattering response would be mainly sensitive to density changes, which can be correlated to the ash content [390]. Another factor that affects the measurement of ash content is the hydrogen (in moisture) content, which increases the value from about 0.5 for all other elements to 1 for H (where Z is the atomic number and A is the mass number). This enhances the amount of Compton scattering, by increasing The problem becomes, in effect, a three-component system of coal, ash and hydrogen. Using analysis similar to that of Eq. (12.22) for such ternary-component problem, reference [390] concluded that the optimum source-energy for maximum sensitivity to ash content would

594


be between 60 keV and 22 keV In addition to measuring ash content, backscattering of low-energy photons was used for in situ measurement for the lithology (average atomic-number) of formations [716, 717], and for the determination of ash content in coal [770], see also section 12.2.2.4. Dual-Energy Transmission. Dual-energy (high and low) photon sources can be used, in the transmission modality, to determine the elemental content of a material composed of two elements, one has a high atomic number (Z), while the other has a low atomic-number. The presence of the high atomic-element is amplified at the low-energy due to its higher photoelectric cross-section, Eq. (3.30), while at high-energy the contribution of both elements is based only on their atomic-density. This method was used for the determination of the relative content of tin and lead in solder foils [24]; using a source (1.17, 1.33 MeV) and bremsstrahlung sources. The dual-energy photon or transmission technique was also used in the measurement of ash content in coal [640, 771, 772], by viewing the oil as consisting of two materials: hydrocarbons and ash and taking advantage of the fact that ash has an effective atomic-number greater than that of the coal matter. The sources employed for this purpose were: (59.54 keV) and (356.01, 302.85 keV) or (662 keV) [323, 640], or the two-energies source (22.6 and 88 keV) [773]. of a The dual-energy transmission method was used to determine the density and ash content of coal slurry, within a flow cell of constant and known thickness, using the 60 keV and the 662 keV energies, of respectively [390]. For a solid (coal plus ash) weight fraction, and and liquid (water) s, with an ash fraction and a coal fraction weight fraction, (1 – s), the transmission density can be expressed using the measurement model of Eq. (6.1) as:

where is the transmission intensity for an empty cell, is the mixture’s density, and is the macroscopic cross-section per unit mass (mass-attenuation coefficient), and is the thickness of the measurement cell. The low-energy transmission signal is dominated by the mineral (ash) content due its high atomic-number (about 13) and the subsequent prominence of the photoelectric effect, see Eq. (3.30). On the other hand, the high-energy signal is only a function of since the value of is not a function of the atomic-number, see Eq. (3.51) keeping in mind that for all elements except H. Therefore, the ratio of the transmittance, – In at low-energy to that at high-energy is


595

indicative mainly of see discussion around Eq. (12.22), while the If the ash content, is same value at high energy is indicative of known, then the ratio of the two transmission measurements can be used to determine the solid content, Alternatively, if the water content, is measured, e.g. by neutron slowing-down, (see section 12.3), then the two transmission measurements can be used to determine the ash content. Dual and triple energy transmission of photons emitted from an source was used for the determination of the purity of gold [774]. Dual and multi-energy gamma-transmission was also employed for measuring the volume-fraction of oil, water and void in multiphase-flow systems, see section 11.5.11. Rayleigh-to-Compton Scatter Ratio. The Rayleigh-to-Compton scatter ratio method, discussed in section 7.3.10, was used for measuring fat or water content in milk products or in meat [730], using the 60 keV photons of an source. The same technique was also used in the backscattering configuration to detect the elemental content of binary alloys (Ag-Cu, Sn-Cu and Au-Ag) with a source [728], taking advantage of the larger scattering angles (47° and 90°) for Rayleigh scattering attainable with high atomic-number elements, see Eq. (3.64).

12.4.4.

Neutrons

The absorption of neutrons can be used to determine the content of neutron-absorbing elements present within a less absorbing medium. Neutron absorption is highest at low energy, thus thermal-neutrons are usually employed for this purpose. Natural elements that have high, or reasonably high, thermal-absorption cross-sections include: lithium (70.7 b), boron (759 b), chlorine (33.2 b), cobalt (37.2 b), silver (63.6 b), cadmium (2.450 kb), hafnium (102 b), iridium (426 b), gold (98.9 b) and mercury (375 b); where the values in bracket is the thermal-neutron absorption cross-section for elements at their natural abundance [28]. In addition, some rare-earth metals are good thermal-neutron absorbers: neodymium (50.5 b), samarium (5.8 kb), europium (4.6 kb), gadolinium (49 kb), terbium (25.5 b), dysprosium (930 b), holmium (66.5), erbium (162 b) thulium (103 b), ytterbium (36.6 b) and lutetium (77 b). Neutron absorption can be monitored either directly by its effect on the population of incident thermal-neutrons, or indirectly by the characteristic gamma-rays promptly emitted following neutron capture. The latter approach is discussed in section 12.1.1.1, and provides the ability for discriminating between various neutron-absorbing elements that may be present in a medium. However, when the inspected medium is

596


a mixture of a highly-neutron absorbing material and a weak-absorbing substance, it is advantageous to directly monitor the thermal-neutron flux. This is because the neutron absorption cross-section is higher cross-section, as the former incorporates all than the capture neutron-absorption reactions, such as the (n,p), (n,d) and reactions. Thermal-neutrons are also easily measurable using one of the detectors discussed in section 4.4. Since readily available neutron-sources are fast-neutron emitters, thermal-neutrons need to be generated by slowing-down fast-neutrons. However, the moderation process (see section 15.3) can be incorporated in the design of the device. Thus, three possible basic configurations for a neutron-absorption device can be configured, as schematically shown in Figure 12.4, and discussed below.


12.4.4.1

597

Transmission

The most direct way to the determination of the content of a neutron absorber in an object is to subject a thin sample of the object to a beam of thermal-neutrons, as schematically shown in Figure 12.4.a. The object has to be thin to avoid complete absorption (blackness) of the beam, since the beam is attenuated exponentially according to Eq. (6.1). Therefore, for a binary mixture of a strong neutron absorber of weight and a weak absorber of weight fraction, the measurefraction, ment model of a neutron transmission device can be expressed as:

where I is the intensity of the transmitted beam at thickness and is that for zero thickness, and A refer, respectively, to the microscopic thermal-neutron and mass-number of each component, is the mixture density, is the thickness through which the neutrons are transmitted, and u is the atomic mass unit. In arriving at the model of Eq. (12.24), use is made of Eq. (E.14) and it is assumed that absorption is the main should neutron-removal process; otherwise the total cross-section, The model of Eq. (12.24) indicates that if the be substituted for thickness of the object and the basic nuclear properties of its can be determined, two components is known, the weight-fraction, provided that the density is also known. If the latter is not known, the transmission measurement will provide an estimate of which can be expressed in terms of parts per million. For optimum statistical counting conditions, the thickness, should be such that the absolute value of the argument of the exponential function in Eq. (12.24) should not exceed the value of 2, when evaluated at maximum expected concentration of an absorber, see section 14.2. This thickness can be quite small for a strong absorber. Moreover, extracting a thermal-neutron beam requires a bulky moderating assembly or a nuclear reactor. Thermal-neutron transmission is most often used in neutron radiography, as a qualitative indicator of the presence of absorbers, see section 13.2. The technique is also used in cross-section measurements of materials, see for example references [775, 776, 777]. The system set-up for such measurements can be useful in devising neutron-transmission systems. The use of thermal-neutron transmission has also been reported, for determining the water content in materials, see section 12.2. Transmission of fast-neutrons directly emitted from isotopic sources is also used in content analysis when the cross-sections of the components

598


involved is sufficiently different. In addition to measuring hydrogen content, as indicated in section 12.2, the method was, for instance, used for the analysis of silver concentration of coins [778, 779].

12.4.4.2

Flux Depression

The transmission method discussed in section 12.4.4.1 above is useful when a beam of thermal-neutrons is available, say from a nuclear reactor, or an existing thermalization facility. However, if a new system is to be designed using an isotopic source, constructing a thermalization assembly and extracting a beam from it, is not the most effective process of utilizing a source, since only a small fraction of the source neutrons will be thermalized and extracted by a beam port. It is more efficient to insert the inspected material, or a sample of it, within a thermalization assembly containing a moderating material around a fast-neutron source, as schematically shown in the left-hand-side configuration of Figure 12.4b. Of course, if the inspected material itself is a moderating material, there is no need to use a separate moderator, as shown in the right-hand-side of Figure 12.4b. In the latter configuration, it is possible to place the source and detector in the same enclosure (providing a compact device), since thermal-neutron detectors are not very sensitive to the source’s fast-neutrons. In either case, the moderating material slows the source’s fast-neutrons, creating a “cloud” of thermal-neutrons within the assembly. The presence of material containing a strong neutron absorber will create a depression in the neutron flux, that can be measured with the aid of a thermal-neutron detector inserted either in the proximity of the inspected object, or if possible within the object itself. The amount of flux depression would then depend on the concentration of the neutron-absorbing species in the inspected object. A measurement model can be developed to estimate the amount of flux depression, using the equations presented in section 9.3. However, the modeling process is approximate. Therefore, it is more convenient to calibrate the detector using samples of various known concentrations. This flux-depression method was used for the determination of the boron content in samples of the feedstock of a plant producing a heatresistant (refractory) material [289]; since the presence of boron at high concentration lowers the strength of the material due to the migration of the small boron atoms through the material as it is heated. The method can also be used to measure the concentration of boron in metal alloys (added to improve hardness), glass, glass-reinforced plastics, mineral,


599

rock, detergents3, etc; and cadmium in metals and their alloys and in zinc solutions, etc. [24]. The method was also used for measuring indium in tin, hafnium in zirconium, gold in copper, tantalum in niobium, manganese in aluminum and cobalt in iron [24]. Flux depression can also be used to determine salt (NaCl) content in an extended water medium, with the water providing the moderating material and chlorine being the thermal-neutron absorber [238]. The same method is applicable to the measurement of aqueous salts that contain boron, cadmium, potassium, silver and iron. Note that although the latter two elements are not good absorbers of thermal-neutrons, theirs microscopic cross-section is much larger than that of water: 2.07 b and 2.62 b for potassium and iron, respectively, and 0.66 b for water [28]. The technique was also used for measuring the gadolinium content in the presence of other rare-earth elements [24].

12.4.4.3

Backscattering

If the mixture containing the neutron-absorbing material also contains a neutron-moderating material, the latter can be used for slowing-down the fast-neutrons of the sources thus eliminating the need for a separate moderating assembly or an external beam. This provides flexibility in locating the neutron detector, which can be inserted within the inspected medium itself or located outside of it. However, the latter arrangement is preferred as it enables passive and on-line inspection of an object. This arrangement, as schematically shown in Figure 12.4c, allows the use of a fast-neutron source and the measurement of backscattered slowneutrons. The source and the detector can be placed in the proximity of each other, since thermal-neutron detectors are not too sensitive to fast-neutrons. This not only provides a compact device but also enables “one-side” inspection, an added flexibly. An empirical measurement model for this backscattering method is given by [781]:

where is the detector response at concentration of the absorbing material, is the response at zero concentration, is a system constant, and and are attenuation constants, per unit concentration of absorbing material, the value of which depends on the nature of the 3

The use of borate as a builder in laundry detergents sequesters calcium ions, lowers the interfacial tension between fatty soils and water, enhances the negative surface charge characteristics of pigment soils and provides the wash liquor with alkalinity and significant pH buffering capacity; all have a beneficial effect on detergency performance [780].

600


moderating materials. The parameter in Eq. (12.25) can be viewed as the intensity of the thermal-neutron “cloud” created within the material. The number of neutrons reaching a detector is then attenuated The deviation from this simexponentially with increasing value of ple exponential behavior, the second term in Eq. (12.25), is caused by the fact that the “apparent” size of the thermal-neutron “cloud” is affected by the concentration of the absorbing material. At low values of neutrons far away from the detector can still reach it, while at very high concentrations these neutrons would be absorbed before reaching the detector. That is, at low concentrations, the “cloud” appears to the detector to be larger than it would have been at high concentration where the absorbing material in effect masks the far-way neutrons. The second exponential term in Eq. (12.25) is, therefore called the “visibility” term [781]. At high concentrations the value of the visibility term becomes negligible, and the detector response changes exponentially as Therefore, the value of can be determined by the slope of as it the line that best fits the logarithm of the detector response, In varies with at high concentrations, while the value of is determined axis. At low concentraby the intersection of this line with the tion, the intersection of the best-fit line of with the while the constant is simply the detector response is Obviously the value of has to be greater than that of for at the thermal-neutron “cloud” to become invisible at high concentration. This indicates too that the detector response at low value of is quite sensitive to small changes in that is, the device has a better contrast at low absorber concentrations, often a desirable feature.

Neutron backscattering has been used for on-line measurement of boron in boric acid in an effluent solution in a nylon processing plant [289], with the hydrogen and carbon of the nylon acting as the moderator. A device was designed for monitoring the gadolinium concentration in the shutdown system of a CANDU reactor [781, 782]. CANDU reactors inject gadolinium nitrate dissolved in heavy-water into the reactor as one of two methods for terminating the nuclear chain reaction (the other method is the injection of cadmium rods). The gadolinium solution is stored in tanks, and is injected into the reactor, when needed, via pipelines connected to the reactor. The backscattering method provides a simple method for continuously monitoring the gadolinium concentration in the tank to alert reactor operators to any changes in concentration.


12.4.4.4

601

Neutron Die-Away

The neutron decay-time technique, discussed in section 9.4, can be used to measure the macroscopic cross-section of thermal-neutrons in an extended medium, such as rocks. The neutron lifetime in rock is 900 ms for quartz, but is only 5 ms for saline formation water (due to the presence of chlorine in the latter) [40]. Thus the lifetime of thermalneutrons is used to discriminate between salt water and oil, in petroleum explorations. Typically a 14 MeV pulsed-neutron generator is used for this purpose. Such generators are compact and can be gradually inserted into a borehole to examine a formation at various depths. Fast-neutrons are eventually slowed-down, mainly by the hydrogen in the formation, to the thermal-energy, and then begin to dissipate at a rate that depends on the thermal-neutron macroscopic-absorption cross section, according to the measurement model of Eq. (9.13). The thermal-neutron population can be measured directly with a thermal-neutron detector. However, such measurements would provide only local indications from the area surrounding the detector, since thermal-neutrons from farther away would be absorbed in the formation before reaching the detector. Therefore, the thermal-neutron population is recorded directly by the gamma-radiation resulting from its capture. Such gamma-rays have a higher penetration depth than thermal neutrons, thus provide a more global indication of the thermal-neutron population, covering a range of about 0.35 m [40]. Either gamma-rays of energy above 2.223 MeV (produced by the capture of thermal-neutrons by hydrogen), or all photons of energy above 50 keV, can be recorded. The former has the advantage of avoiding counting background gamma-rays from natural radioactivity (see section 8.8.2) and scattered photons, while the latter produces a higher count rate but requires correction for the gamma-ray background [40]. By measuring the neutron population at two different time intervals, the decay time of the thermal-neutrons can be determined, which in turn enables the calculation of the macroscopic absorption cross-section, using Eq. (9.14). Alternatively, the decay time-constant may be measured by determining the relative decay rate is the change in the count-rate over a period and N is where the average count rate within this interval. This is a finite-difference approximation of Eq. (9.12), which provides an estimate of for a as determined by the temperature of given thermal-neutron velocity, the medium (see section 3.5). However, this finite-difference approach is not practical since it requires a very small value of to provide an adequate estimate of the decay rate. To overcome this difficulty, a dynamic self-adjusting approach is used, as explained below.

602


If the count rate is measured at two consecutive time intervals, one starting at time and the second interval over a period over a period starting at time then using the exponential measurement and in these two inmodel of Eq. (9.13), the resulting counts, tervals can be related to each other as:

When as Eq. (12.26) shows, Therefore, the dynamic adjustment approach uses a series of pulses, and estimates the ratio in each pulse. With an electronic circuit, the value of is adjusted so that approaches a value of 2, during the next pulse. The process is repeated until then which enables the determination of The electronic signal maintains the value of until the value of changes and the process is repeated. This is the process used in one of the thermal-neutron decay tool of Schlumberger [40], which employs a source that provides a pulse of a duration of every where the value of which determined as explained above. When a second detector is added to such instrument at a position far-away from the first one, the ratio of the counts of the two detectors (near/far ratio) is indicative of the formation’s porosity. Since porosity in rocks is related to the hydrogen content, as explained in section 12.3.1, this ratio is nearly indicative of the hydrogen content. The reason being that neutrons reaching the far-detector are faster neutrons since they would have managed to travel a longer distance without being slowed-down and captured. Therefore, the higher the count rate of the far-detector, the less slowing-down neutrons would have suffered, hence the lower is the hydrogen content. Scaling the far-detector count rate by that of the near detector compensates for the local absorption of neutrons. The inverse of this scaled quantity becomes then indicative of porosity [40]. Thus aside from measuring a thermal-neutron dieaway tool also provides a measure of porosity. Note that a low porosity indicated by such a device may also be due to the presence of a gas, because of the low hydrogen-density in gases. The lifetime, or die-away time, of neutrons slowed-down from 14 MeV to the epithermal energy range was also used to measure the hydrogen content in geological formations [783]. A detector, covered with a gadolinium foil to cut-off thermal neutrons, was used to record the slowing-down of 14 MeV neutron pulses. The advantage of measuring


603

epithermal-neutrons, rather than thermal-neutrons, is that epithermalneutrons are less sensitive to the other neutron-absorbing materials that may be present in the surroundings, such as chlorine. The method is particularly useful when examining air-filled holes and formations where strong thermal-neutron absorbers, such as boron and gadolinium, are present [784]. The neutron die-away method can also be used for detecting fissile materials in nuclear waste drums using a pulse of 14 MeV neutrons [785]. As these neutrons are slowed-down in the drum and by the surrounding material, they would induce fission. The presence of neutrons after the termination of the pulse is then indicative of the presence of fission materials (as small as 1 mg of and However, since the amount of thermal-neutrons produced is greatly affected by the presence of neutron moderating and absorbing materials, reference [785] suggested relying as well on measuring the fission induced by epithermal neutrons. The latter fission is dominant within a short time-period (about 100 following the termination of the pulse.

12.4.4.5

Neutron Activation

Although the neutron-activation techniques discussed in section 12.1.1.1 aim mainly at detecting specific elements, multi-elemental analysis can be used as an indication of the presence of a certain material. For example, contamination of food stuff with soil can be distinguished by the presence of aluminum and silicon, with the two elements detectable by the production of via the thermal-activation reaction These two and the epithermal/fast neutron reaction reactions were used for monitoring the soil content in shredded sugar cane (soil is introduced by modern cane harvesters) [384].

12.4.5.

X-ray Fluoroscopic Emission

The x-ray fluoroscopic emission (XRF) discussed in section 8.7 can also be used for content analysis, by focusing on one element, rather than on many elements as it is the case with elemental analysis, discussed in section 12.2.1. Since the x-ray emission from elements of low atomic-number is lower in energy than that of high atomic-number materials, XRF is particularly useful for measuring the content of metals in hydrocarbons, e.g. iron and cobalt in lubricant’s and silver content in photographic emulsion [179]. A compact XRF device was also used for determining the total sulfur content in coal samples, using as an excitation source and a krypton-filled proportional counter as a detector [786, 787, 788]. The same approach was also used for measuring the content in ambient air and in stacks of a tobacco curing plant [789].

604


Uranium enrichment, i.e. the concentration of in enriched uranium is determined by measuring the 186 keV peak and comparing its intensity to that of a standard sample; or by thorough analysis, using a highresolution detector, of the uranium K x-ray profile in the region 89 to 100 keV, where both and have characteristic peaks [790]. The x-ray fluorescence method (EDXRF) was also used to determine the lead concentration in aerosol samples [791]. Lead concentration on painted surfaces was measured in situ using and to excite the lead characteristic x-ray, with the emissions measured using an detector [792].

12.4.6.

Mössbauer Spectroscopy

As indicated in section 6.5.5, the Mössbauer technique is most useful for determining the iron content, since natural iron contains 2.1% and the latter isotope has a strong recoilless-absorption of gamma-rays at room temperature. However, using indirect indications, the technique can be used to determine the concentration of alloying elements in steel carbides and two-phase alloys (such as Fe-Ni-Cr, or Fe-Ni-Mn) [178]. The method is also useful for distinguish between different phases of steel, such as ferromagnetic ferrite and paramagnetic austenite phases, or different steel alloys [178]. In particular, the determination of retained austenite in steel, a quantity that directly affects the quality of steel, can be determined with Mössbauer Spectroscopy. Amorphous ferromagnetic alloys are uniquely studied by this technique, as it provides characteristic spectrum patterns that can be used for studying the crystalization process of amorphous alloys and the amount and location of hydrogen introduced into the alloy [178].

12.4.7.

Natural Radioactivity

Airborne gamma-ray is routinely used to produce maps of natural background activity from K, U and Th. A large volume (50 L) NaI(Tl) detector mounted on an airplane flying at height of about 120 m on a spaced grid lines can produce such maps, enabling the discovery of uranium deposits [348, 793, 794]. Surveys of seabed, using an HPGe detector, has been also useful in identifying areas of deposited radionuclides from the outfall of nuclear reprocessing plants [348].

12.4.8.

Combined Techniques

Content analysis sometimes requires the application of more than one ND E technique. This is illustrated here by considering the case of the bulk analysis of coal, one of the materials for which radiation techniques


605

for content analysis are well-developed [640]. The discussion here is based on references [554] and [640] Coal consists of the basic coal matter (C, H, O, N, S), ash (incombustible minerals, such Al and other silicates), inherent moisture (bound water) and free moisture (from external wetness). The main combustion parameter is the energy released per unit mass (also called caloric value or specific energy), which is directly related to the carbon content. The coal’s ash and moisture content also affect its combustion. Using elemental analysis with the fast-neutron prompt-gamma activation method (see section 12.1.1), the carbon and hydrogen content can be determined [554]. The density of a bulk amount of coal can also be measured with backscattering of gammarays, see section 11.1. The carbon content and the coal’s bulk density can be correlated to its specific energy. For a particular type of coal, the C/H ratio tends to be constant. Therefore, the presence of moisture will introduce an excess of hydrogen, and hence reduce the C/H ratio. This ratio along with the coal density can, therefore, be related to the moisture content of the coal. This correlation fails, however, if the moisture content is high, as the associated increase in the hydrogen content affects the coal’s density, and it also reduces, by slowing-down, the amount of fast-neutrons available for activating the carbon of the coal, which in turn affects the estimated H/C ratio. The slowing-down of fast-neutrons, see section 11.4, can then be used to measure the moisture content. The determination of ash content can be obtained from the prompt emission of 1.78 MeV gamma-rays by the inelastic scattering of fast-neutrons. Alternatively, an increased ash content would increase the bulk density of the coal due to the increased mineral content. This in turn tends to affect the overall carbon and hydrogen content, allowing the correlation of the three parameters (density, C and H activation yields) with the ash content [554].


Chapter 13 IMAGING

13.1. 13.1.1.

Photon Radiography Film Radiography

Film photon (x-ray or gamma-ray) radiography is used in numerous industrial applications: for inspecting welds in fabricated structures and in pressure vessels, establishing the soundness of cast products, and for the detection of flaws, void spaces and inclusions. In welds, radiography can detect hot tears, shrinkage cracks, trapped gas (blowholes), slag inclusions, lack of fusion, and lack of penetration. In castings, pipe (round cavities at center of an end surface), shrinkage, hot tears, blowholes and sand or slag inclusions may be detected [795]. Although radiography is conventionally used for flaw detection, it is also useful for inspecting process equipment for trouble shooting, such as for detecting flow blockage [286], determining the position of a frozen valve and measuring the extent of corrosion or scale buildup inside pipes and containers, etc. [238]. Radiography is particularly useful for detecting corrosion in irregular regions, such as areas of pipe around welds [286]; the higher penetrability of gamma-radiography is advantageous in this regard. In light materials, such as graphite and beryllium, it may be difficult to detect small cracks and voids, because of the small difference in radiation attenuation between the material and void. However, the contrast of a radiograph can be enhanced by soaking the object in a liquid containing heavy elements, such as carbon tetrachloride [179], that penetrates into the defects and enhances radiation attenuation within the void space. Radiography is also used in quality assurance and product assessment, as for example in the pre-deployment 607

608


assessment of conductive tether of the Tethered Satellite System Reflight (TSS-1R) [796]. X-ray radiography of composites has been used to examine glass and boron-fiber reinforced materials for volume-fraction and fiber alignment [797, 798]. However, radiography of carbon-fiber reinforced composites is more difficult, because of the small variation in density of the material in the composite, and their low-density which does not make them amenable to photon absorption. Nevertheless, some attempts have been made to overcome this hindrance, by for example incorporating lead-glass tracers in the fiber material to increase photon absorption [799]. Detection of delamination by transmission-radiography is almost futile, due to the integrated (along the radiation path) nature of radiographic indications. Also debonding of adhesive joints when made with metal adherends is quite difficult to detect. While the presence of metal masks the low-density adhesive material, the void space created by debonding does not affect the intensity of transmitted radiation. The latter problem can be overcome with a scattering technique (see section 10.2), while neutron radiography (section 13.2) provides sensitivity to hydrogen-rich adhesives. Gamma-ray sources, mainly and are widely used in industrial radiography. However, unlike x-ray machines which tend to emit photons in a confined direction, isotopic sources emit radiation in all directions. Therefore, while performing radiography with these sources, access to the radial area around the source must be restricted for safety reasons. However, using a source collimator, the incident radiation can be confined to only the part for which it is necessary to produce a radiograph. This results in an intrinsically safe system with significantly reduced radiation controlled-access area (during exposure), see for example the radiography system reported in reference [800].

13.1.2.

Radioscopy

The term radioscopy is used to refer to real-time, and near real-time, non-film detection, display, and recording of x-ray and gamma-ray images. Standards and guides for radioscopy are available [801, 802, 803]. Real-time radiography is the term more often used to refer to radioscopic systems, but the method is also known as fluoroscopy [7, 134]. Real-time radiography provides an immediate visible image of the inspected object. This is accomplished by projecting the transmitted radiation on a fluorescent (zinc-sulfide or cesium-iodide, sodium dopped) screen, which illuminates visible light with an intensity proportional to the intensity of the incident radiation. The viewer is protected from direct exposure to radiation by covering the back of the screen with a thick sheet of spe-

Imaging

609

cial lead glass. The use of fluorescent screens though convenient comes at the expense of reduced image quality (spatial resolution and material contrast), in comparison to film radiography, due to the coarser grained structure of the screen and its low contrast gradient and the lower optical contrast [7]. But the main limitation of fluorescent screens is the low brightness of the image, which makes it difficult for the eye to observe fine image details. However, images can be enhanced with the aid of an intensifier tube. The light from the fluorescent screen bombards a photocathode to generate electrons that are accelerated by an applied high-voltage to produce a small but very intense visible image on a fluorescent screen inside the image intensifier. The image can then be viewed through a television monitor or recorded by a camera. An image on a fluorescent screen can be photographed with a camera to produce a permanent record. The process is then called photofluorography [134]. However, the image details and resolution can be severely curtailed in this process. Video camera can also be used to capture the radioscopic image to produce a motion picture, in a process known as cinefluorography [134]. Perhaps the most widely encountered application of real-time radiography is screening carry-on passenger baggage at airports. In order to reduce the exposure to photographic films that may be present in the baggage, a short-duration pulse of x-rays is used. Such systems typically employ a fixed vertical linear array of photodiodes to detect the transmitted x-rays when the baggage traverses the radiation source as it travels on the conveyor belt [7]. The recorded measurements are electronically amplified, stored and enhanced, then displayed on a television monitor. This method of image recording does not, however, produce the fine details required in industrial applications for flaw detection in welds and castings. A number of industrial applications have made use of real-time radiography. Reference [7] cites the following examples: high-speed inspection of welds: submerged-arc welds in shipyards, pipe-welds on lay barges and in construction yards; sorting of casting such as automobile wheels; inspection of rubber tires for correctness of metal insertions; observing the flow of molten liquid during castings; inspection of rocket motors and radioactive waste drums using a large gamma-ray sources; and even the radiographing of a full-sized aero-engine running on a test-bed using a 8 MeV accelerator. Some recent applications in this and other areas are discussed below. On-line inspection of arc welding with real-time radiography makes it possible to study and control the welding pool and the heat-affected zone during the welding process. It becomes then possible to detect, and

610


monitor on-line, defect formation in the weld and to study metal fusion and filler-metal/base-metal interaction and metal transfer in the welding pool. Radioscopy may also be used for post-service real-time remote testing of weld quality, using information on weld quality received from automatic recognition of real-time radiographic images. For example, an arc welding process control was developed using radiography as a feedback [804, 805, 806, 807]. Real-time radiography was also considered for offshore use to inspect under-water pipelines and assess the quality of circumferential welds [808]. Radioscopy was also used for inspecting manufactured casts, to detect defective castings and to obtain information, on the type and position of defects, that can be relayed back to operators for correction [809]. Monitoring the evolution of molten-liquids is another attractive application of radioscopy. A number of applications have been recently reported in this regard. Molten liquid visualization applications include: monitoring bismuth flow through filters placed in the mold, used in the casting industry to physically remove inclusions in the material and improve the fluid flow within the mold assembly [810]; observing natural convection flow during melting and solidification of a gallium-indium alloy [811, 812, 813]; viewing crystal/melt to study interface dynamics during indium antimonide crystal growth [814, 815, 816, 817]; following the density-field of a layer of liquid gallium, laterally confined in a small cavity, heated from below and cooled from above [818]; examining the flow of a polymer-resin-fluid through a volume of a reinforcement material (fiber glass mats or fabrics) in manufacturing matrix composite materials [819]; and studying liquid-metal behavior in molds of stainless steel and gold [820]. Radioscopy has also proven to be useful for in situ monitoring the progression of wear and damage; as it was used for example to study the effect of laser surface alloying of Ni, Cr on the fretting wear behavior of 6061 aluminum alloys [821]. The terminal damage state of notched composites over a wide range of cross-ply graphite reinforced epoxy specimens was also monitored with real-time radiography [822], which enables the studying of damage initiation and evolution processes in highly filled polymeric material under various loading conditions [823]. Highresolution real-time digital radiography makes it also possible to detect corrosion and cracking in hidden structures of aircraft [824], as well as in turbine-engine components, and composite materials [825]. With realtime radioscopy, it is also possible to examine economically long sections of insulated piping [826], rather than relying on the tedious process of film-based radiography. A real-time digital radiographic examination system, that utilizes a linear array of solid-state detectors instead of a

Imaging

611

film, was developed to aid in the detection of flow-accelerated corrosion and other wall thickness degradation in insulated or uninsulated piping systems [827]. Other example applications of real-time radiography include: investigating the macrostructure of high-temperature superconductors [828]; determining the slag accumulation (slag pool depth as a function of time) in the aft end of the Titan solid rocket motor upgrade [829]; and examining solid rocket motors to obtain information about propellant burning and cracking [830].

13.1.3.

Flash Radiography

Flash radiography is used to record images in a very short duration (a few microseconds). The technique is also known as high-seeped radiography [134]. This is achieved by the use of a pulsed source of radiation. In order to obtain a good quality image within such a duration, the radiation beam has to be very intense. Such a high intensity x-ray source requires a very intense electron beam (as high as 2000 amp), which is in turn produced by the application of a very high-voltage pulse and the use of pointed (needle shaped) cathodes (to increase the current density at the surface of the cathode) [4, 7, 135]. A high-power laser pulse can also be focused onto a solid or gaseous target at very high intensities to produce relativistic and MeV electrons and ions that, in turn, produce x-rays. High-intensity, high-energy photons can also be produced in a linear accelerators, as in the case of the Flash X Ray, or FXR, system of the Lawrence Livermore National Laboratory [831]. Flash radiography enables the imaging of items in motion, by recording rapid sequential images. Therefore, most applications of flash radiography are in imaging events in motion. Some recent examples of these applications are given here. In impact studies, flash radiography was used to image debris resulting from the impact of solid spheres into thin plates to study the impact failure and fragmentation properties of the material from which the spheres were made (tungsten carbide, steel, copper, aluminum, tantalum or titanium) [832, 833, 834, 835]. The technique was also used to study the state and velocity of thin titanium plates accelerated to high velocities (10.3 - 10.9 km/s) with an explosive three-stage launcher to examine their integrity during the acceleration process [836]. The motion of long tungsten projectiles fired against unconfined alumina targets with steel backing was photographed with flash radiography to study the influence of scaling the dimensions of the projectiles [837]. Also, the movement of a 0.5-1.0 g aluminum fragment launched at a speed of 11.2±0.2 km/s was observed in-flight with flash radiography, to study the effectiveness of its launcher [838]. Flash ra-

612


diography was also used to observe, and determine the volume-fraction (void fraction), of steam, produced when water interacts with melt or high temperature solid clouds [839]. Flash radiography is useful for imaging jet formation and propagation. Example applications include: studying the penetration of a copper jet in Plexiglas [840]; characterization of jets produced by explosive charges [841, 842]; and for investigating jet-driven circulating flow in closed liquid-metal combustion [843]. Flash radiography was also used to study the internal processes of closed liquid metal combustion systems [844]. The radiographs obtained from flash radiography can be used to interpret dynamic events, by simple visual observations, or extracting density information from the digitization of the radiographs. Examples of quantitative analysis of flash radiographs for shock-wave hydrodynamics analysis are given in reference [845]. With soft (low energy) flash x-rays, lower density materials can be imaged. For example, with soft x-rays it was possible to image the flow of argon streams in ambient air [846], and to visualize flow phenomena (entrainment and streamlines) in coating flows [847]. Images of air bubbles in an old newspaper fiber suspension [848] and in bleached softwood kraft pulp suspensions were also obtained with flash radiography [849].

13.1.4.

Microfocus Radiography

As discussed in section 6.3.1.2, penumbra is one of the factors that affect the quality of an image, and is a problem caused by the finite size of the source. Therefore, with a very small size source, the penumbra effect can be reduced or even eliminated. By electrostatically focusing the electrons bombarding the target on an x-ray tube of a focal spot size of a few micrometers, it is possible to produce a very small (mircofocal) source. However, because of the cooling limitations of such a small target, the intensity of microfocus x-ray tubes is quite low [7, 135]. With such a source, it is possible to detect small flaws by placing the examined object close to the source and positioning the recording device (film or fluorescent screen) at some distance from the object. This is because as Eq. (6.11) shows, for a very small focal spot size, one can afford to increase the film-to-object distance, L, and decrease the source-to-object without significantly increasing the geometric unsharpness distance, of the image. A decreased value of reduces the amount of divergence of the source photons, making the source appear to the image as a more confined beam, so that the source covers an area on the surface of the object that is not different in size from the size of the source itself. The detectability of small flaws is further enhanced by increasing the

Imaging

613

value of L, allowing in effect a geometric magnification of the object as it is projected on the receiving film, or screen, over a wider area. This magnification process, known as projective or shadow radiography, virtually eliminates any image blurring that may be caused by radiation, as the scattering photons are unlikely to reach the recording medium, at least in an area surrounding the projected image, due to the large distance between the object and the recoding medium. These factors combined, enables microfocus radiography to detect flaws of a size about equal to that of the source [4], which makes it possible to examine flaws in the range, found in brittle materials, such as ceramics. In addition to the use of microfocal radiography in detecting flaws in ceramics [850, 851], the method has been used to analyze the failure of heat-coupled thermionic (rhenium and a molybdenum-rhenium) energy converters [852]. The technique was also utilized in the characterization of silicon-carbide specimens, and proved useful in detecting high-density inclusions and isolated voids [853]. Welded repairs on turbine blade tips were also monitored with microfocus x-rays [7]. The welding parameters of small tube-to-tubesheet welds of a steam generator were also evaluated and optimized using microfocal radiography [854]. Microradiography was also used for detection corrosion, such as for the characterization of corrosion pitting in 2024-T3 aluminum alloy [855]. The technique was applied as well to image the thickness variation of electrically deposited Cu-composite coatings placed on a rotating desk electrode [856]. The same reference reported the use of this technique to image archeological pieces found in a Roman villa. Real-time microfocus radiography was used, with the help of a digital image processing system, to determine how discontinuities are created during light-metal casting, following the entire casting process from the filling of the mould until the completion of solidification [857]. The produced images were used for determining changes in metal density, to identify the solidification phase, and to observe the creation and propagation of discontinuities in the sequence of stored images. Microfocus radioscopy was also employed to detect very small defects in ceramic products with high speed and reliability [858]; and for the internal inspection of critical electronic assemblies such as potted modules, populated printed wire boards and ‘black boxes’ with an ultra small focal spot size [859].

13.1.5.

Megavoltage Radiography

For imaging objects of large areal densities (mass density × thickness), it may be necessary to employ high-energy x-rays produced by linear accelerators, typically in the energy range of 4 to 8 MeV [7, 135],

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but higher-energy sources have been used. Most reported applications of megavoltage radiography is in medical imaging during radiotherapy (portal imaging), to take advantage of the high photon-energy used in cancer treatment, see for example reference [860]. However, 1 to 3 MV x-rays are useful for imaging steel thickness from 50 to 200 mm, while 3 to 8 MeV x-rays can be used for radiographing up to 0.3 m of steel [7]. Radiography of cargo containers and vehicles was also performed with the aid of a high-energy linear accelerator similar to that used in radiotherapy [861, 862, 863]. This system is a direct descendant of a rocket container x-ray inspection system, developed to support on-site verification measures included in the arms control agreement with the former system was also developed for Soviet Union. An isotope-based radiography of vehicle and cargo [864]. The 6.13 and 7.12 MeV gammarays emitted from the decay of were also proposed for use in radiography [865]. Such a source can be transported in a small pipe (after irradiating the parent material of or see section 2.2.4) and used to image objects that are difficult to access using other sources [665].

13.1.6.

Low-Energy Radiography

While the radiography of large and dense objects requires the use of megavolt photons, as discussed in section 13.1.5, imaging of thin and lowdensity materials requires photons of low-energy. With x-ray tubes, the maximum energy of emission is controlled, as discussed in section 2.2.1 by the applied voltage, which can be readily reduced to as low as needed. However, to enable low-energy photons, below about 40 keV, to leave the tube housing, the tube must be equipped with a thin widow of a light material. Typically beryllium windows less than a mm thick or a polyester film are used for this purpose [7, 135]. An interesting way to producing the intense low-energy x-rays that can be used in flash radiography (see section 13.1.3) is by the use a high-power laser pulse focused on the surface of a solid. This results in the creation of high-temperature plasma that emits an intense pulse of photons in the extreme ultra-violet (EUV) and the soft x-ray (XUV) regions of the electromagnetic spectrum. The technique employing such a laser source is called laser radiography. These intense sources are useful for flash radiography [866], to resolve small structures such as an imprint on a thin foil [867, 868]. Low-energy x-rays are also useful in performing microradiography. Notice that microradiography differs from microfocus radiography, discussed in section 13.1.4, in the fact that the former does not need a microfocused beam as it employs a regular x-ray beam. However, microscopic details (void, discontinuities, and material constituents) can

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be observed in microradiography as it images thin sections using very slow (fine grains) films placed closely below imaged sections (preferably enclosed in a vacuum cassette) [134]. The developed film is then viewed via optical magnification by a factor of 50 or more. The use of low-energy photons facilities the imaging of such thin sections. Low-energy photons have a high photoelectric cross-section, which enables good absorption within a thin object, and a high material-contrast due to the strong dependence of the cross-section on the atomic-number, see section 3.4. Microradiography is used to inspect metallurgical sections for corrosion, pitting and damage [869, 870, 871]. Example applications of microradiography to polymers include: examining the dispersion of pigment in polyethylene [872], and of magnetic-oxide in polymer matrix, and for imaging the fiber orientation distributions of resin samples filled with short glass fibers at various strains [873]. The technique has been also used to study cemented joints in corrugated cardboard, to distinguish between natural and cultured pearls, and to image the distribution of inorganic spray materials on foils [134].

13.1.7.

Bremsstrahlung Radiography

An interesting emission method of imaging was proposed in reference [874, 875], where the bremsstrahlung (x-ray) radiation associated with the transport of beta-particles within matter is used to reconstruct an image of the beta-source. For a beta-source such as the maximum range in water is about 7 mm, but most of the particles are stopped in the fist few millimeters (see section 3.3.2). Consequently most of the bremsstrahlung radiation is produced in the proximity of the source where the intensity and energy of beta-particles are still high. Therefore, the intensity of the emitted bremsstrahlung radiation is indicative of the position of the beta-source. An image of the distribution of the beta-source within the object can be obtained. However, the energy of the emitted x-rays peaks at an energy of about 30 keV, limiting penetrability of the emitted radiation. This method, theretofore, can be used to image low-density materials, such as plastics and organic materials.

13.1.8.

Laminography

Laminography, as the name indicates, is the process of imaging thin layers within a object. However, unlike computed tomography, discussed in section 6.4, the image is not reconstructed to obtain pixel-by-pixel information. The radiographed layer is virtually defined by moving the source and the film synchronously in opposite directions, as schematically shown in Figure 13.1. The intersections of the radiation projections

616


will have in common one plane, called the focal plane. Points on the focal plane will always be projected at the same locations on the film, and hence will be imaged sharply. All other points of the plane will be projected at varying locations on the film, providing a superimposed background image, around the image of the focal plane. The location of the focal plane is determined by the relative positioning of the source, object and film. By moving one of them, a new focal plane can be imaged. The laminographs of many adjacent slices provides a three-dimensional image [876]. Along with a microfocused x-ray source, laminography can provide layer-by-layer radiographs in “slices” a few micrometers in thickness. Therefore, laminography is useful for imaging thin multilayered struc-

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tures, such as ball grid arrays [877, 878] and printed circuit boards. In fact, most of the reported applications of laminography are in the manufacturing of microelectronic circuit boards. The technique is used for the detection of soldering anomalies (such as voids, disbonds and insufficient solder) that are difficult to find or are hidden on the newer packaging interconnect technologies, see for example references [879], [880] and [881]. X-ray laminography inspection is, therefore, an effective tool for screening defects in complex printed circuit boards before their functional testing [882].

13.1.9.

Scatterography

Although scatter imaging is not as widely used as the conventional transmission-based imaging techniques, scatter imaging, or scatterography, offers some advantages, as discussed in section 7.6. Unlike transmission imaging, which requires the source and the detector (or image receptor) to be placed at two opposite sides of the object aligned with respect to each other,scatterography allows placing the source and the detector on the same side. This permits same-side imaging, a useful feature when imaging extended or thick structures. While transmission provides an integrated indication along the path of the incident radiation, see for example Eq. (6.1), scattering can provide point-wise indications, i.e. an indication at the point of scattering. The scattering process is, however, a complex one, since scattering events can overlap each other making it difficult to extract a meaningful image without mathematical unfolding of the measurements, as discussed in section 7.7. However, superficial and near-surface images, and images of light materials can be obtained with direct recording of scattered radiation, as exemplified by the applications presented below. An x-ray backscattering device, called the Comscan [883, 884], is employed in a number of applications. This system uses an array of detectors, with each detector’s field-of-view defining a small voxel on the surface of the object upon intersection with an incident x-ray beam. The intensity of the scattered radiation forms the image, with higher intensity indicating higher material-density and vice versa. This imaging approach was also applied to the imaging of: plastics [885]; castings; aircraft- and automobile structures [886]; an aluminum cast car wheel and an aluminum weld [887]; a glass-reinforced plastic/foam sandwich material [888, 889]; carbon-fiber-reinforced plastics [884]; a plaster painting (fresco); a mummified body, and a medieval bronze clasp [890]. Comscan was also used for the detection of second-layer and metal loss in aircraft structures [891, 884], and for the under-water inspection of sonar domes [892, 893, 894, 895].

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Another Compton-scatter imaging system, called AIDES (Automated Inspection Device for Explosive Charges in Shells) was used as the name applies for imaging shells to detect porosity [896, 897]. The system employed a collimated bremsstrahlung beam (using a 5.6 MeV linear electron accelerator), and six collimated detectors for point-by-point imaging of the shell. Scatter imaging can also be used in real time-imaging. For this purpose, a system was designed employing a 100 to 200 kV x-ray tube and scintillation plates and two image intensifies, along with a charge-coupled device ( CCD ) camera as the readout device [898]. A low-energy/low-dose x-ray backscatter system is available for personnel imaging for detecting materials concealed under clothing [899]. The use of scattering necessitates the scanning of one side at a time (front and back). Isotope-based systems are also used in scatterography. A was designed for void detection in light alloys and plastics [308]. The same reference also mentioned the use of the technique to produce images of aluminum castings, used in the automobile industry, to detect voids of about 2 mm in diameter. Another radioisotope-based Compton scatter system, using a weak source, was also proposed, for detecting voids in sections of steel, polyethylene and an inorganic ceramic cement [900, 901]. The combination of scattering and transmission imaging was considered for imaging vehicles and large cargo containers, with a pair of 450 kV x-ray sources and their corresponding detectors to give two transmission images and two scatter images of the inspected vehicle during a single scan by sweeping (fly-spot) the x-ray beams along the object [902, 903, 904, 905]. The above scatter radiographic methods rely on imaging voxels defined by the intersection of the confined fields-of-view of the source and the detector. Thus, image information is derived directly from the incident radiation beam, after the photons scatter, within the voxel, towards the detector. This imaging approach is in essence based on single scattering. Proper confinement (collimation) of the source and the detector fields-of-view is, therefore, essential in these systems. The two fields-ofview must also intersect to form the imaging voxel. This intersection requires proper alignment of the source, object and detector. Although this alignment process can be cumbersome, it enables three-dimensional imaging, since the voxel(s) can be located anywhere in the space, by proper positioning of the source and the detector. There is, however, a class of imaging systems that are less vulnerable to these alignment process, as they rely on imaging photons that migrated away from the

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source. These migrated photons form a “cloud” of radiation from which photons scatter to detectors. If the distribution of this cloud is disrupted by the presence of abnormalities, the response of the detectors monitoring this cloud will be altered accordingly. One version of this imaging process is the lateral migration radiography system designed for landmine detection [906, 907, 908, 909]. In this system, a collimated beam of x-rays is directed towards the ground and a set of collimated and uncollimated detectors are used to monitor photons that are laterally migrated away from the source beam. The wide field-of-view of the uncollimated detectors makes their response dominated by the flux of highest strength, which is that of photons near the surface. On the other hand, with the collimated detectors, the effect of photons scattered from the ground surface is less dominant, thus they are sensitive to photons emerging from both the surface and depth of the ground. The images produced by these detectors are in effect contours of the detector counts, from which the presence of an anomaly can be identified. Another approach of scatter imaging that relies on mapping photons scattered over a wide volume, with the aid of open (unconfined) detectors, was proposed for imaging pipe walls for the detection of wall thinning (due to corrosion) [910, 911, 912]. The system uses a collimated source with two detectors placed at equal distance but at opposite sides of the source, with the source-detector assembly mounted on the pipe walls and rotated around the surface of the pipe with a stepping motor to map the entire circumference of the pipe. To eliminate detectordependence on the distance from the pipe surface to the detector, the use of a dual-energy source was suggested. The scattering of low-energy photons results mainly from near the surface of the pipe walls, while the more penetrating higher-energy photons scatter from everywhere. The ratio between the counts produced by higher-energy photons to that of the lower-energy ones tended to remain constant as the distance from the detector to the pipe changed. The magnitude of the ratio was shown to be indicative of the pipe wall thickness. Therefore, the contours of this ratio, obtained as the device scans the pipe, provides indications of changes in pipe thickness.

13.1.10.

Emission Imaging

Emissions can arise from a radiotracer injected into the medium, radioactive materials that is already present, or from reactions induced by an external source. Emissions in the form of photons can be readily imaged with a gamma-camera, see sections 4.3.2 and 8.8.4. Flow visualization with radiotracers often employs a gamma camera. For example, a scintillation gamma-camera was used for imaging the movement of

620


radiotracers for velocity, trajectory and particle density measurements, in fluidized beds [913, 914] and chemical reactors [915]. Gas-flow inside a fluidization test bed was visualized with the aid of a gamma-camera (190 keV energy, 13 s half-life) observing the emissions from a source [916]. Also, fluid displacement in thin slabs of porous media were source as a tracer observed with a gamma-camera with the help of a in the water phase [917]. Using the same method, the flow of an oxygen and oil (labeled with 140 keV, 6 hour) gas (labeled with was imaged to study the degasification process of a gas merged with a feed stream of heavy oil, by spiking each phase separately with the gamma emitter [916]. Images of the flow of bulk solids (silica spheres) (392 keV, in a storage bunker were obtained by immobilizing 1.658 hour half-life) on some spheres [916]. The location, distribution, and intensity of gamma-ray emitting sources in nuclear sites can also be surveyed with the aid of a gammacamera, see for example references [918], [919], [920], and [921]. The Compton-scatter camera, as discussed in section 8.8.4, offers the ability to provide images at arbitrary image planes. By reconstructing images with such camera at different planes, the location of high intensity ‘hot spots’ can be determined. Therefore, the Compton-scatter camera has found applications in nuclear waste to identify hot spots in mixed waste, image large objects or contaminated areas, and for monitoring production, deployment, shipping and storage of nuclear warheads and components [922, 923]; as well as for imaging radioactive areas in a nuclear fuel reprocessing plant [923, 924]. The indirect imaging technique of coded-aperture, commonly used in astrophysics imaging, is employed to image weak sources of radiation, by blocking the emitted radiation with a mask containing holes of a certain pattern. Radiation emitted from various points in the object that passes the coded-aperture mask, and detected on a scintillation screen, produce a pattern that can be deconvoluted to produce an image of the source intensity and location. Positron emission induced by the pair-production reaction of highenergy photons is also proposed for elemental imaging, see section 12.2.2.7. Reference [925] reported the use of positron emission for imaging oil flow on surfaces. The flow of oil down two planes of different inclinations in a simple aluminum and Perspex tower, in a static journal bearing and on lubricating-oil bearing race, was imaged by labeling the oil with a positron emitter (1.13 hour, half-life) produced from the decay of (270.8 days, half-life).

Imaging

13.1.11.

621

Diffraction Imaging

Patterns produced by x-ray diffraction, discussed in section 7.8.1, can also be recorded on a film. A number of arrangements can be used [134]. The basic Bragg arrangement involves the use of a monoenergetic narrow beam of x-rays and rotating the material specimen until a distinct refraction pattern is recorded. The lattice spacing can then be calculated from this pattern using Bragg’s law, Eq. (3.66). When a multienergetic beam is used (Laue’s method), the examined object stays stationary and dense spots appear corresponding to the planes in the crystal where Bragg’s law is satisfied at the various source energies. Both above arrangements are suited for examining single crystals. The Debye-Scherrer-Hull method overcomes this problem by using a powdered form of a polycrystalline material; hence the name powder method. The powder sample is enclosed in a fine glass capillary or suspended on a fiber or a flat ribbon of a low-density material [134]. The powdered sample offers many random lattice planes that can diffract an incident monoenergetic x-ray beam, producing many pattern fringes from which lattice information can be deduced. In the forward-scattering arrangement, typically used to examine thin samples, a small lead block is placed on the film to prevent the incident beam from fogging the film [134]. To examine the surface of a material, a backscattering modality is utilized. An alternative to film radiography is the use of a microchannel to measure radiation diffracted towards a particular direction. The parallel channel of the plate acts as collimator tubes that limits the detected radiation to that diffracted from a particular region in the medium. A wide x-ray beam can then be used to provide wide-area imaging [926, 927]. The applications of x-ray diffraction are too enormous to individually list here, but the reader can consult references such as [65] and [235].

13.2.

Neutron Radiography

Neutron radiographs are recorded using converter screens, see section 4.4.3.2, which generate beta or gamma radiation that can be recorded on a film. For thermal neutrons, foils of gadolinrhodium ium indium cadmium and silver have been used as converter screens, using the reactions given in the square brackets. These reactions enable direct recording of neutron exposure into a conventional radiographic film [134, 928]. Scintillation screens (zinc sulfide) containing boron are also used, with the alphaand lithium particles of the reaction producing light in the scintillator that can be

622


registered on a photographic film, or used to provide a real-time image with the aid of an image intensifier [928]. Light-emitting screens, combined with a large-aperture lens such as those based on system and accompanied with charge-coupled devices (CCD’s), are capable of detecting single neutron events, and thus are employable with low-intensity sources [929, 930]. The use of large amorphous-silicon sensors, instead of the CCD’s, can also provide a high light-coupling between the scintillation screen and the sensor, and eliminate the need for a lens system. For indirect exposure, using the so-called “transfer” method, converter screens made of gold 2.695 days], indium 54.2 minutes] or dysprosium 2.33 hours] are exposed to neutrons, and after the exposure is terminated the screens are removed and brought into contact with a radiographic film [134, 928]. The relatively long half-life of the reaction products, given in the square brackets, makes these isotopes particularly useful for the indirect neutron-radiography methods. Neutron radiography is advantages in two types of applications. First in imaging light materials, where the electron-density is too low to affect photons, particularly when the light material is masked by a more dense material. Secondly, in imaging materials emitting gamma-rays, such as irradiated nuclear fuel elements [931, 932], that produces interference with the photons of x- or gamma-ray radiography. The fissile material remaining in spent nuclear fuel, as well as the fission products, are also good absorbers of neutrons, while the conversion plates, see section 4.4.3.2, used to record the neutron image, are not sensitive to photons. Neutron radiography requires, however, access to a nuclear reactor or large neutron sources; although efforts are made to produce low-flux and mobile systems [933, 934, 935, 936, 937, 938, 939, 940, 941]. Isotope-based real-time neutron-radiography systems are also available, see for example reference [942] which a system. Neutron radiography is a well-established method to the extent that standards of applications are available [943, 944, 945]. Some representative applications are given here. Hydrogen. A unique ability of neutron radiography, and thus one of its main applications, is the detection of hydrogen. For example, neutron radiography was used to visualize small amounts of hydrogen in hydrogen storage alloys, such as [946]. The detection of hydrogen in metal is of particular relevance because of the brittle effect it introduces. Corrosion products are usually hydroxides, thus neutron radiography is more suited for detecting corrosion than other NDE methods that typically detect corrosion by metal loss [928], which occurs only when a

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623

significant amount of corrosion has taken place. Radiography is helpful in this regard, and was used to detect hydrogen in zirconium alloys utilized in nuclear reactors [947], and hydrogen diffusion in a palladium metal [948] and in a titanium aluminide alloy [949]. Neutron radiography is also more suited for composite materials than photon radiography, due to the low density of the composites. Therefore, neutron radiography can be used to detect voids inclusions and transverse cracks [950] and to determine the resin content of a composite [951]. It is also suited for imaging composite joints with metals, since the adhesive material tends to be more neutron absorbing than the metal [952, 953]. Neutron radiography is also used in imaging honeycomb structures, composites and adhesive layers in aircraft structures [954, 955, 956, 957]. Rubber, plastic seals and other neutron-absorber gasket material can also be examined with neutron radiography, even in metallic assemblies [928]. Epoxy-potted small electronic devices can also be imaged with neutron radiography, since the potting material is usually rich in hydrogen [928]. Neutron radiography is also used to image electrical relays employed in satellites and spacecraft [958], to disclose the presence on any undesirable hydrogenous materials such as a loose insulation [928]. Water. Hydrogen in water, as steam, moisture or two-phase flow, was also observed by neutron radiography. For example, steam generation due to direct contact of hot metal with water was visualized by neutron radiography [959, 960]. The transport processes of moisture and hydrogenous liquids in porous building materials [961, 962, 751], and other porous media [963, 964] was also studied with neutron radiography. The introduction of hydrogen-containing fluids (water or oil) into the pores of a media enables the imaging of the flow distribution in such media [965]. Scanning neutron radiography, where a single narrow beam scans across an object elevated in front of the beam, was utilized in measuring moisture concentration profiles during drying of brick and kaolin clay [966]. In situ measurement of water transport within Nafion in polymer electrolyte fuel cells was also visualized with neutrons [967]. Neutron radiography has also found use in imaging historical artifacts [928] to reveal hydrogen or moisture related details which are not observable by other means.

Flows. Another interesting application is the use of real-time radiography in the design of nozzles for subcooled hot water by imaging the water flow through the nozzle [968]. Many workers also applied neutron radiography to image the two-phase flow in metallic pipe, ducts and channels [969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980, 981]. The

624


flow of water in heat exchangers was also studied with neutron radiography [982, 983]. Visualization and measurement of nitrogen gas-molten lead/bismuth two-phase flow in a rectangular pool made of titanium 5 mm in thickness) were performed [984, 985], since neutrons more easily penetrate such metallic thickness than photons. Neutron radiography proved also useful in the visualization of internal flow in refrigerator components [986, 987, 988, 989, 990, 991]. The water uptake in plant roots was also studied with neutron radiography [992]. The method was also used to study fluid-rock interaction, water infiltration into a porous rock and the displacement of heavy-water by oil and water flooding of a clay-rich rock [993]. Dynamic neutron radiography was used to image the micro architecture and oil infiltration in Visingso sandstone reservoir [994]. Reference [928] reported the use of neutron radiography to study the movement of water/moisture in concrete samples with time and temperature. By observing, with dynamic neutron imaging, the falling of a spheres in a silicate melt, the viscosity and density of the melt was measured at high temperatures and moderate pressures [995]. Backscatter imaging of neutron is also employed for the detection of hydrogenous materials. Reference [996] reported the use of a neutron-sensitive imaging-plate placed close to the object to detect the neutrons scattered from quartz cells containing water; with a neutron beam extracted from a reactor. Neutron Absorbers. Materials containing highly neutron-absorbing elements are obviously natural candidates for neutron radiography. Such elements can be introduced as contrast enhancers into less neutronabsorbing materials to enable imaging of such material, as indicated by some of the examples discussed here. One of those highly neutron absorbers is which can be produced by beta-decay of and the latter can be present in the metal as result of exposure to tritium in fusion and bubbles enable the heavy-water fission reactors. The formation of investigation of tritiated metal samples with neutron radiography [997]. Lithium, another good neutron absorber, was also useful in a number of applications of neutron radiography, such as: imaging of lithium-bearing ceramics and glasses [949]; evaluating the reversibility of rechargeable commercial lithium batteries [998]; and the study of lithium-ion transfer in solid ionic conductors [999, 1000, 1001, 1002, 1003, 1004]. The high neutron absorption cross-section of gadolinium makes it an attractive image enhancer, and was used in the neutron radiography of aircraft aluminum alloys (by the application of an aqueous solution of gadolinium nitrate for the detection of corrosion [957, 1005]; the detection of residual core in the casting of air-cooled turbine blades by the addition

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of gadolinium compounds to the core material [1006, 1007]; and for the study of cracking in concrete [1008]. Gadolinium in the form of gadolinium chloride aerosol was used in real-time neutron radiography to observe the deposition of a neutron absorbing aerosol in a standard cellulose acetate cigarette filters [1009, 1010]. Cadmium was also used in the visualization of liquid-metal flow, by using particles made from a gold-cadmium intermetallic compound as a tracer for visualization of molten liquids [1011, 960, 1012]. Sand coated with was also used for imaging particles in a fluidized bed [1013]. Needles to say, materials containing boron are also good candidates for neutron radiography [1005]. Tracer particles made by bonded to vinyl resin were used to observe material flow in a fluidized bed [1013]. Reference [24] reported the use of neutron-radiography for the determination of rareearth elements (lanthanides) in minerals (monazite and bastnaesite) by placing thin section of the minerals in between thin plates soaked with boron and shielded from gamma-rays with lead sheets. The assembly was then exposed to thermal-neutrons and the ratio of the tracks produced in the developed film with and without the thin mineral sheets, were taken as indicative of the concentration of the neutron-absorbing lanthanides. The neutron absorption of rare-earth elements was also used to examine the ceramic in investment-cast turbine blades, made by molding metal around a ceramic core in which open cooling passages are created by leaching [928]. The injection of gadolinia into the ceramic core further enhances the image. Ceramic capacitors can also be inspected with neutron radiography [928]. The difference in the neutron absorption cross-sections of indium and gallium (with the former more than an order of magnitude larger than the latter) enables the neutron radiography of a gallium-indium alloy to measure any macro-segregation in its solidified ingots [1014]. The neutron absorption ability of uranium was also exploited in determining its concentration in Black Sea sediment samples [1015]. Neutron-absorbing materials (such as sodium-borate or gadolinium nitrate) dissolved in neutron-transparent fluids (such as heavy water and halocarbon oils) were also used to study fluid flow in porous media [965]. The same workers used a metal alloy containing cadmium to measure, with digitized neutron radiography, the porosity patterns etched during the reactive (acidation) dissolution of pores. Neutron radiography was also used to detect explosive materials, even when encased in metal. Explosives (HMX, RDX, PETN) have a total crosssection for thermal-neutrons of about 1.28 to compared to for lead. Therefore, the for stainless steel and presence of these explosives with metallic shells and casing can be easily detected. Neutron radiography was, therefore, used to inspect ammu-

626


nition cartridges for the detection of ammunition filling [2, 1005, 1007], and to image explosive lines (used to separate components and eject military pilots), and explosive bolts and detonators [928]. A system was considered for imaging small quantities of metal-encased explosives [1016]. The detection of paper separation-washers and plasticcomponents of fuses was also accomplished by neutron radiography [7]. Nuclear Materials. Neutron-radiography is useful in a number of applications in the nuclear-power industry. It can be used to image fresh fuel to determine its enrichment level since is a much stronger thermal-neutrons absorber that [928], due to the fission of the former by thermal-neutrons. Irradiated fuel, in spite of its high gamma-radiation emission can be imaged with neutron radiography using the transfer method discussed at the beginning of this section. The used converter screen are only sensitive to the neutrons, attenuated by the fuel, but not to the gamma-radiation of the fission products, due to the absence of the film. The image is then transferred from the converter screen to a film, away from the fuel. The imaging of irradiated fuel enables the determination of fuel burnup, i.e. the reduction in the concentration of using the same concept discussed above for fresh

fuel. [928]. Reactor control rods, typically made of cadmium, are also imaged by neutron radiography [928].

Neutron Transparent Materials. Neutron radiography is also useful for imaging low-absorbing materials, such as aluminum, within a more neutron-absorbing medium. For example, neutron radiography was used for inspecting the space shuttle’s solid rocket booster which include aluminum components that may corrode or entrap moisture [1017]. Fast Neutrons. Most of the applications discussed above rely on the use of slow-neutrons (thermal) due to their ease of detection. However, epithermal and fast neutrons are also used in radiography. The so-called transfer technique is often employed, where activation foils are used as the recording medium and the intensity of the gamma-ray produced from the activation process is later recorded on a photosensitive film or a gamma-sensitive scintillation screen [1018]. However, directimaging methods are emerging. For example, the tracks produced on plastic sheets (CR39) were used to image neutrons of energy between 0.1 and 10 MeV [1019]. References [1019] and [1020] reported the use of a converter screen made of polypropylene and ZnS(Ag), in which fastneutrons collide with the hydrogen of the material producing recoiled protons that in turn give rise to luminescence in ZnS(Ag), and the emit-

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ted light can either be recorded on a film or displayed on a television screen. Radiographic images of fast-neutrons can be obtained by measuring the energy of neutrons emitted from a pulsed-source using the time-of-flight method (see section 4.26). The radiograph is then reconstructed from the detected neutron intensity at the source energy. The advantage of this method of measurement is that it eliminates the effect of scattered radiation, and the interference of gamma-rays, by utilizing only uncollided neutrons (i.e. those with the same energy as the source) in formulating the image [1021]. The penetrability of fast-neutrons makes it possible to image light objects enclosed in dense material, such as void in uranium and air-oil two-phase flow in a thick iron block [1019] and in air-water two-phase flow in a 4 × 4 rod-bundle near a spacer [1022]. Reference [1023] also presented a method for imaging neutron sources within a nuclear missile that relies on the use of a neutron camera (similar to that of the Compton camera described in section 8.8.4). The neutron camera monitors the double-scattering of a neutron with the elements of two consecutive arrays of organic-scintillator, and the direction of the incident neutron direction vector is reconstructed from the provided information. Fastneutrons were also used for radiographing thick laminated composite materials [1024]. Very high-energy neutrons (from spallation sources) were also studied for future use in radiography, due to their high penetrability and the direct proportionality of their cross-section to where A is the mass-number [1025]. The latter feature makes it possible to better distinguish light and heavy elements with neutron radiography, in comparison to photon radiography where the contribution of light elements is much weaker than that of heavy elements. To detect fast-neutrons, reference [1025] suggested the use of a converter screen (tungsten or copper plates) that produce protons when bombarded by neutrons. The position of the proton, hence the neutron on the screen, can be determined by a two adjacent multiwire detectors, or by the localized measurement of the electron avalanche produced by the protons on the converter plate [1026]. Alternatively, a matrix of scintillating optical fibers can be employed. Fast-neutron radiography was also used for testing components of space launch vehicles, using a small proton cyclotron and a beryllium target [1027]. Inclusions in Iron. Imaging non-ferrous material present in iron can be performed by iron-filtered neutrons [1028]. Iron has several minima in its total cross-section, at energies in the keV range, specifically, 24, 78 and 134 keV, allowing neutrons at this energy range to pass through reasonably large thickness (up to 200 mm) of iron. Other inclusions in iron,

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such as a Al, Cu, or Pb, will tend to attenuate the neutrons more within these energies, and will accordingly leave a noticeable change in the recorded signal. However, to detect neutrons at these specific energies, neutron spectrometry must be performed. Reference [1028] reported the use of a pulsed photoneutron source (accelerator) that employed 30 MeV electrons on a water-cooled tantalum target. The neutrons were moderated with polyethylene, filtered with two Fe layers (140 mm and 100 mm in thickness) and collimated with borated paraffin and lead collimator. Time-of-flight measurements, see section 4.25, were then used to detect scintillating detector. From the recorded the neutron energy with a neutron intensity at the iron filter energies, at different locations across the objet, radiographs or even tomographs of the object can be constructed. Neutron Diffraction. Recorded neutron-diffraction patterns, see section 3.5.5.1, are a from of radiography. For example, neutron imaging was employed to examine bulk polycrystalline materials, such as the Alnico iron alloys used industrial permanent magnets [1029]. The diffracted cold neutrons were recorded on a scintillator equipped with a lead-glass microchannel plate, placed between the sample and the detector. The microchannel acted as a tube-like collimator to prevent crossover of neutrons diffracted from various locations.

13.3.

Charged-Particle Radiography

Beta Radiography. Beta-particles, though not very penetrating, are useful for imaging thin layers, such as paper sheets [1030, 1031] or oil and were utilized paintings [238]. Low-energy beta-sources, for radiography of forensic documents [1032]. The surface of thicker objects can also be photographed by capturing backscattered beta-particles foil), this method was on a film. With an extended beta-source used to radiograph the surface of a sandstone rock sample containing uraninite, to identify uranium bearing phases [1033].

Electron Radiography. Electrons can be used for imaging in two modalities: transmission (see section 6.6.3) and emission (discussed in section 8.5.1). In the transmission modality, the electrons are generated in a foil of a high atomic-number material (typically lead) by bombardment with x-rays. The generated electrons are transmitted through a thin sheet of material and recorded on a film underneath the sheet to obtain an image of the distribution of its material. This process is, therefore, analogous to that of beta-radiography discussed above, except that

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the use of x-rays allows the generation of a high intensity electron field. To avoid the simultaneous generation of an x-ray image, high-energy photons are employed; a 300 to 400 kV machine with a heavy filter (typically copper) to remove lower energy photons. This methods was used to image papers for watermarks, fiber distribution and ink overprint, and to authenticate rare postage stamps [7]. The technique is also applied to the imaging of wood shavings, leaves, and thin sheets of rubber and plastic [134]. The other modality of electron emission is used to image the surfaces of thick metallic objects. As discussed in section 8.5.1, electrons on the surface of the inspected object are generated with x-rays and the emitted electrons are recorded on a film placed on top of the surface. The source x-rays are filtered to eliminate the low-energy photons that can produce an x-ray image on the film. Electron emission imaging was performed, under low vacuum conditions, on polished sections of a steel-concrete interface to examine whether the formation of any of the hydration products of cement is favored at this location [1034]. The technique was also used to study the dissolution of dental enamel [1035]. Metallic pigment in printed paper (a stamp) was also detected using this method [134]. Proton Radiography. Protons offer the ability to measure small thickness changes, since unlike photons and neutrons, they are easily attenuated by matter. Proton radiography was used to study of the temporal and spatial behavior of shock propagation in a high explosive sample using 800 MeV protons [1036]. Radiography with protons was also considered as a means for examining the safety and reliability of nuclear weapons stockpiles [1037, 1038]. A 800-MeV proton radiography facility has been developed for imaging dynamic objects, such as the evolution of a high explosive burn [1039]. The scattering of 500-1000 MeV protons was also considered for three-dimensional reconstruction of an object with only one exposure, by tracking the passage of the incident scattered beams [1040]. Protons in the GeV energy range can interact with the nucleons (protons and neutrons) of the nucleus in a “quasielastic” fashion that has the characteristic of collision between two particles of identical mass. These collisions result in angular-deviation of the protons. The trajectory of the incident beam and protons scattered in the forward direction can be recorded on a scintillation screen, and used to compute the three-dimensional coordinates of the interaction vertices. The intensity of the interaction vertices reflect the density of the material scattering the protons. This method was used to radiograph

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an electric motor [1041], and to detect defects in 50-mm thick copper and uranium pieces and a liquid hydrogen target [1042]. Ionoluminescence Imaging. The visible light emitted from a material subjected to MeV ions, called ionoluminescence, can produce information on the chemical bonds, energy band structure in semiconductors and impurities and defect distributions in crystals. Proton-beam (2.5 MeV) luminescence was used to image the grains of a zircon mineral and a thin membrane of organic material (Kimfol) [1043].

13.3.1.

Autoradiography

The term “autoradiography” indicates to a “self-induced” image, in the same way “autography” refers to a person’s own handwriting. Autoradiography is, therefore, the imaging of a material emitting radiation. It is thus a from of emission imaging (see section 8.8.3). The radioactive material producing the radiation emission can be introduced in a number of ways as the applications discussed in this section demonstrate. The technique is usually applied to charged-particle emission to provide superficial (surface) images, due to the short range of charged-particles; although imaging of gamma-ray emission is also possible as discussed in section 8.8.4. Natural Radioactivity. Autoradiography lends itself to the imaging of materials containing natural radioactivity. Therefore, the method is (a beta useful for determining the U and Th (alpha emitters) and emitter) content in rocks [1044]. Nuclear emulsions, see section 4.2.1, are typically used for detecting these particles, as they contain a higher concentration of finely grained silver halide than photographic emulsions. The number of tracks left on an emulsion plate is directly proportional to the concentration of the emitting material in the monitored medium (mainly the surface of the medium due to the short range of alpha and beta particles). Since both U and Th are alpha emitters, the recorded images reflect their total concentration, but empirical relationships can be used to determine their relative concentration [1044]. Nuclear Fuel. Nuclear fuel elements can be autoradiographed to determine the fuel distribution and cladding (metal sheath) uniformity in fresh and the fission-product in spent (irradiated) fuel [134]. Fresh fuel emits radiation by the decay and spontaneous fission of its fuel, while spent fuel emits radiation by the decay of its fission products. The radiation emitted is recorded on a film to assess various properties of the fuel elements. When the fuel is uncladed (no metal sheath), or when

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the cladding is uniform, the distribution the film density can be related to the fuel content in the element, see for example reference [1045]. On the other hand, for a uniformly loaded fuel, the film density becomes an indicator of the cladding thickness, and fuel-pellet welds and end plugs [1046]. For spent fuel, a slow (large grain) film is used because of the high intensity of the emitted radiation. The image obtained on the film will then reflect the concentration of the radioactive fission products. Selective autoradiography is also used to distinguish between mixed nuclear fuel uranium and thorium in uraniathoria pellets, by taking advantage of the difference in alpha-particle energy of the daughters of uranium and thorium [1047]. A special film with annealing and pre-etching treatment was used to obtain sufficient track density from the very low specific activity of natural uranium and thorium, and to enable distinguishing between their tracks. The distribution of plutonium on the surface of a pellet, after diffusion annealing, was also obtained by alpha-autoradiography [1048]. Alpha-autoradiography was also utilized to determine the concentration of transuranium nuclides in the primary coolant of a nuclear power plant deposited on filters [1049]. Void that may be present in containers used to store spent fuel can also be detected with autoradiography [1050]. Tritium. In studying metal hydride formation, caused by migration of hydrogen into metal grain boundaries or other discontinues, (a beta emitter) can be used as a substitute for hydrogen, and the autoradiographs of the hydrogen distribution can be monitored by placing a radiographic film next to the specimen [238]. This process was used recently to study the distribution of hydrogen in Ni-based super alloys [1051]. The autoradiography of was also used for studying the effectiveness of a detritiation (tritium removal) process of steel activated in a nuclear fusion facility before disposal as a nuclear waste [1052]. Similarily, the distribution of hydrogen in intermetallic compounds [1053] and in a (Zr, Ti, Ni) alloy [1054], was investigated by means of tritium autoradiography.

Sulfur. Another useful isotope for autographic imaging is (a beta emitter, 87.32 day half-life) which when introduced in welding as a base material, or into the electrode of the welding torch, can be used to visualize how sulphur is distributed into a weld, and from where the sulphur content originates [179]. The same isotope can be introduced into molten steel for later study of the material homogenization by autographing slices of the solidified ingot [7]. The isotope (a beta emitter, 14.262 day half-life) was also used in the autoradiography of

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the leaching of phosphate in structured clay soil [1055]. The positrons emitted from (a positron emitter, 2.6019 y half-life) was used in the study of the diffusion behavior of sodium in poly (ethylene oxide)-poly (vinyl acetate) films [1056]. Activation. The examined object may also be activated in a reactor or by an accelerator. For instance, to study the material transfer from a projectile to the barrel of a rifle, the plating of bullets were irradiated in a reactor to produce (a positron and a beta emitter, 12.700 h half-life) and after shooting the rifle, the distribution of the active material in the inside of the pipe was autoradiographed (after cutting the pipe along its axis) [179]. More recently, the distribution images of C and O in steels and B and O in Al alloys was studied by charged-particle activation-autoradiography, after irradiating the samples with ions (a positron emitter with generated in a cyclotron [1057]; producing a 20.39 min half-life) from B, or C and (a positron emitter with a 109.77 minute half-life) from O. Neutron-induced autoradiography was also applied for measurement of Li-concentration profile in Al-3.5Li and Fe-4.34Ni alloys during solidification [1058]. The distribution of boron implanted into silicon [1059] and in boronized specimens of steel [1060] was also studied with neutron autoradiography. Another application of autoradiography is in determining the efficiency of a polymer chipblender by labeling the chips with a chemical tracer (indium) and irradiating the samples in a nuclear reactor to produce a beta emitter (1.0 MeV maximum energy, 54 min half-life) [1]. The irradiated samples were then autoradiographed on a film and the results analyzed to determine the blending efficiency. Neutron-induced autoradiography also enabled the measurement of the concentration of uranium and boron in some minerals (lorandite, realgar, stibnite, orpiment and dolomite), making use of the tracks produced by the (n,fission) reaction products and the reaction [1061]. Mineral samples were placed in contact with an etched-track detector foils (for uranium detection) and a phosphate-glass etched-track detector (for boron detection) and irradiated in a reactor. Neutron-activation autoradiography was also used for the imaging of paintings [1062, 1063].

Iron. Labeled isotopes, such as (a beta emitter, 44.472 day halflife), can be used to study the distribution of iron in a medium, e.g. iron in magnetic recording tapes or iron ions in the residue of an etching solution [179]. The transport of oxygen in scales growing on nickel atmosphere, was studied by labeling the material and cobalt, in a

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with and subsequently autoradiographing it using the nuclear reaction [1064]. Environmental. Autoradiography has also been useful in environmental studies. For example, the accumulation of waterborne mercury in fish and snow crab brain was studied by injecting the fish with (a beta emitter, 46.612 d half-life) and performing a whole-body autoradiography [1065, 1066]. Autoradiography was also helpful in the identification and analysis of a radioactive particle in a marine sediment sample [1067]. The penetration depth of radiological contamination through the thickness of transite (an asbestos-cement building material) was also investigated by progressively removing layers of material and subsequent autoradiography of the exposed surfaces [1068]. Real Time. One recent attempt to produce real-time digital autoradiographs includes the use of a field-effect transistor integrated on highresistivity silicon (depfet), in the form of a panel of many depfet pixel detectors, as an image receiptor, called a bioscope [1069]. This transistor is attractive for use in real-time autoradiography because of its very low noise at room temperature, its information storage capability and its thin and homogeneous entrance window. This device was used for imaging beta-emissions from a source [1070].

13.4. Tomography 13.4.1. Photon Tomography Although x-ray computed tomography (CT), described in section 6.4, is widely used in medical imaging of the human body, the demands of CT in industrial applications are quite different. In industrial imaging, a wide range of shapes, sizes and densities are encountered and the required spatial-resolution can vary from a few micrometers to centimeters. On the other hand, unlike medical imaging, in industrial radiography the radiation dose delivered to the object is usually of no concern, and object-movement (by patient breathing and nervousness in medical imaging) does not present a problem. Hence, a longer time can be used to acquire the image in industrial radiography. There is also priori information on the nature of the object that can be taken into consideration in reconstructing the image. Therefore, effort has been devoted to developing CT systems especially suited for industrial applications [1071, 1072]. For example, a system was developed specifically for improved tomography of a rocket motor by concentrating the measurements, computations, and radial-resolution at the periphery of the

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test specimen [1073]. Effort was also made to construct tomographic images from the digitization of radiographic images, particularly those obtained with fine resolution using microfocused x-rays [1074, 1075, 1076]. Gamma-ray tomography, which is not used in medical applications due to radiation dose constraints, is employed in industrial radiography, as it provides higher penetrability, see for example reference [1077]. For example, a fourth-generation (see section 6.7), gamma-ray system was used by the steel industry for process control of product (I-beam) manufacturing [1078]. CT can be viewed as a sophisticated nondestructive method for examining the internal details of industrial objects. Tomography is a NDE method with its own standards and guides [1079, 1080, 1081, 1082, 1083, 1084]. Tomography can be used to measure the dimensions of industrial parts, determine their density distribution and detect flaws, find their location and characterize their shape, size and composition [1085]. The collection of many adjacent tomographs (image slices), enables the formation of three-dimensional images. Some of the applications of photon (x- and gamma-rays) computed tomography are given here.

Flaws. A typical NDE application of CT would be in determining the internal location of flaws and discontinuity that are difficult to discern with other methods. Therefore, CT was used for detecting and quantifying the presence and extent of intergranular stress corrosion cracking (IGSCC) in pipe specimens [1086]. Tomography with or sources was also applied to the detection of small cracks caused by hydrogen ingress into carbon steel samples [1087]. CT was also applied to the inspection of bridge weldments [1088]. X-ray tomography was also employed to locate voids inside of injection molded parts [1089]. Ceramics. X-ray-computed tomography is useful in examining ceramic materials. It was used for the localization and the quantitative determination of density differences in dry-pressed alumina compacts [1090]. The determination of the density gradients in slip cast ceramics with CT was correlated with stress distribution in slip casting1 [1091]. CT was also used to quantify internal flaws in a ceramic body [1092]. With microfocused x-rays, x-ray microtomography were performed to detect small flaws on ceramic and metal matrix composites [1093].

1 A slip cast is a porous mold shaped in the negative image of the desired component and filled with a slip consisting of a suspension of fine ceramic particles, which after drying forms the solid component

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Composites. Computed tomography is quite useful in inspecting composite materials, since conventional radiography does not enable separation of indications from overlaying layers. For example, x-ray CT was used in the study of moisture transfer in composite materials [1094]. Xray computed tomography was also used to examine inshore mine-hunter hull composite material [1095], and to inspect other high-performance polymer composites [1096]. Microfocus tomography is useful in damage detection of various continuous-fiber metal matrix composites [1097]. A real-time CT system was also employed to characterize and monitor the growth of defects in composite materials as they undergo destructive testing [1098], High-resolution x-ray tomography also enabled the measurement of the growth of silicon carbide in a woven Nicalon-fiber composite during chemical vapor infiltration, to measure the densification within individual fiber tows and to follow the closure of macroscopic pores in situ [1099]. The microstructure of a chemical vapor infiltrated SiC/SiC ceramic matrix composite was also quantitatively characterized using three-dimensional maps obtained from CT [1100].

Rubber. Computed tomography was utilized to assess the aging of carbon-black-filled materials, and to study the thermo-oxidative degradation and stabilization of rubber materials [1101, 1102, 1103, 1104, 1105]. Microtomography was employed to image the internal structure of carbon-black-filled isobutylene-p-methylstyrene-pbromomethylstyrene (PIB-PMS/BrPMS) curing bladders before and after use-to-failure in the manufacturing of automobile tires [1106].

Manufacturing. CT is a useful tool in manufacturing, particularly in rapid prototyping, reverse engineering and meteorology [1107]. Rapid prototyping refers to processes used to manufacture prototype models of physical objects from CAD (computer-aided-design) data sources by constructing parts gradually, layer-by-layer. CT can be useful in this regard by generating the layer-by-layer information needed to produce three-dimensional numerical representation of scanned components for which parts are to be produced [1107]. In this regard, CT is also useful in generating the CAD data for older designs for which no CAD data are available; such data are needed in many modern numerically controlled machining tools. CT data can also be used in meteorology, to check the dimensionality of a manufactured component, by comparing threedimensional rendered data obtained from CT to those of the design data to ensure consistency.

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Multiphase Flow. X-ray tomography is also useful in multiphase flow studies. For example, it was used to investigate multiphase flow in packed beds [1108, 1109, 1110] and to measure the void-fraction distribution in vertical annulus gas-liquid two-phase flow [978] and in testsections representing pressurized water reactor rod bundles [1111, 1112]. Gamma-ray tomography, applied mainly to image dense objects, was used to measure the void-fraction spatial variations in an air-water bubble column [1113]. Solidification. A CT system was developed for monitoring the progression of solidification in metal (pure aluminum and its alloys) casting melted in a resistance heater furnace, using a 6 MeV linear accelerator to produce a series of time-lapse images showing the movement of the liquid/solid interface during solidification [1114, 1115, 1116, 1117]. The solid fraction of a growing mush generated by directional solidification of aqueous ammonium chloride solutions was also determined by x-ray tomography [1118].

Concrete and Asphalt. A mobile CT unit (employing a source) was designed for inspecting reinforced concrete columns [1119], while pieces of structural concrete were imaged with CT [1120]. Microtomography was applied to the detection of internal damage and measuring crack growth in small mortar cylinders of Portland cement loaded in uniaxial compression, to resolve internal features that are only a few microns in size [1121], and to study the aggregate structure of asphalt concrete [1122]. CT was also used to compare quality and physical conditions of asphaltic mixtures of field specimens [1123, 1124, 1125, 1126]. Exploration. In petroleum exploration, x-ray CT was used to study the swelling and swelling-induced fracturing of cylindrical samples of drained shale in contact with water-based mud placed in a central cylindrical borehole [1127]. Frequent CT images were taken over a 24-hour period (allowing detection of subtle features during swelling), and used to generate quantitative maps of density, subtracted time lapse images, and three-dimensional reconstructions to map failure and fracture patterns. Mud/shale interactions were also studied with x-ray CT in well-bores modeled using steel vessels [1128].

Nuclear Materials. High energy, 2 MeV x-rays were used in the characterization of nuclear waste drum, along with the energy spectrum of the gamma-rays emitted by nuclear materials, to inspect and categorize radioactive waste as low level, transuranic, or mixed waste [1129]. To-

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mography of radioactive reactor fuel samples, pellets and bundles, was performed with radioisotopic source and after subtracting the background radiation (with proper shielding of the object) [1130]. Aerospace. In the aerospace industry, high-energy (megavolt) x-rays were introduced for CT imaging of large and dense objects, such aircraft structures [1131]. Reference [1132] reported the use of CT, with x-ray sources varying from 150 kV to 9 MV, for various aerospace structures and ancillary equipment, such as castings, organic composites and electronics. Three-dimensional CT was also used for rocket motor inspection [1073].

Others. Computed tomography is currently used for inspecting passenger luggage at airports [1133, 1134]. It was also used in the inspection of electrical components and printed wiring assemblies [1135]. A field-transportable CT system (using 160 kV x-rays) was devised for inspecting wooden power poles [1136]. In studying geological structures, x-ray tomography was applied to sandbox experiments to analyze the kinematics of evolution, as well as the three-dimensional geometry of faults in basement-controlled wrench faulting [1137]. A dosimeter consisting of an ion chamber and a housing containing electronics [1120] was also imaged with CT. X-ray tomography was also utilized to image a fibrous polypropylene cartridge filter, and in the investigation of Egyptian mummies [142] Utlrafast. Ultrafast CT scanning systems are emerging, where the scanning process is sped-up by the sequential emission of x-rays from many small individual x-ray sources (targets) surrounding the object. These source are triggered by sequential and rapid electrical switching of an electron beam, see for example reference [1138]. Ultra-fast x-ray tomographic scanners enable the studying of fast-transient multiphase flow phase-distributions [1139, 1140]. 13.4.1.1

Region-of-Interest Imaging

Region-of-interest imaging with computed tomography (see section 6.5.2) was used in a number of applications. As summarized in reference [1141], these applications include: detection and geometrydetermination of shrink cavities in valve castings; imaging the geometry of localized defects in electrical insulators due to electric discharge and of extended defects in thin-walled tubes; and the determination of pore size in ceramics. A real-time region-of-interest-imaging system, with gamma-ray transmission tomography, was also developed to determine

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and control the shape and position of solid-liquid transition in semiconductor manufacturing [1142]. 13.4.1.2

Computed Laminography

This is an approach for imaging flat extended components that are difficult to image with conventional tomography, where the extended size of the plane prevents the accumulation of transmission projection in directions tangential to the plane. The laminography method, discussed in section 13.1.8, provides a limited number of projections that can be utilized in the numerical reconstruction of the images of the plane [1143]. The limited number of projections provided by laminography is compensated for by introducing some a priori information. Numerical reconstruction also removes the background component caused by points outside the focal plane, thus producing sharper images. Reference [1144] presents the results of using this method for imaging circuit boards and weld seams.

13.4.2.

Neutron Tomography

As with neutron radiography, neutron-transmission tomography is particularly useful for imaging hydrogen within other matrix materials. Reference [1145] calculated the minimum detectable mass-fraction of hydrogen in various elements, for different neutron tomography sources: cold (1 meV), thermal (0.025 eV) and fast (14 MeV). The results are shown in Table 13.1. Examples of reported tomography for hydrogen content include the imaging of: cylindrical iron and polyethylene samples (48 mm in diameter) [1019]; compacted soil to detect the different water content levels and to identify the soil composition [1146]; inspection of aircraft fan blades to detect very low levels of hydrogen in a titanium jet engine blades of fully assembled and partially disassembled aircraft [1147, 1148, 1149, 1150, 930]; evaluation of hydrogen content in metallic samples (nickel samples containing a solution) [1151]; detection of corrosion of aluminum, due to build of [1152]; imaging of aircraft honeycomb structures glued between aluminum plates [1152]; and imaging of water in a carnation flower [1153]. Neutron tomography was also used to examine damaged reactor fuel assemblies [928]. Computer tomography was also applied to the analysis and restoration of archaeological samples, for the investigation of small bronze objects [1154]. Reference [1155] suggested the use of digital read-out of charge-coupled devices (CCD’s), along with a scintillating screen and a lens system, in neutron tomography, for fast data acquisition and enhanced spatial resolution.

Imaging

13.4.3.

639

Scatter Imaging

Radiation scatter imaging has also been used in some applications. The main advantage of scatter-imaging systems is that they do not require, like transmission, access to two opposite sides of the object, thus enabling, if necessary backscatter imaging. In addition, images obtained with Compton scattering provide a direct indication of the electrondensity of the material, since the Compton scatter cross-section is directly proportional to density, (see section 3.4). However, as discussed in section 7.2.1, the attenuation of photons before and after scattering weakens the scattering signal, thus this technique is best suited for imaging low electron-density (low atomic-number materials). However, a linear accelerator (6 MeV) as the photon source allowed imaging through a thick and dense wall (8 mm) of steel [1156]. A standard guide for x-ray Compton-scatter tomography is available [1157]. The backscatter imaging of gamma rays (88 keV from was used to detect a corrosion flaw in an aluminum block [1158, 1159], while x-ray backscatter tomography was used to measure the thickness of multilayered walls of light composite materials or denser components provided by powder metallurgy [1156]. Ninety-degree scattering of (662 keV) collimated photons was also used for imaging dense inclusions (lead or copper) in a lighter matrix (aluminum) [181]. Reference [1160] lists the following industrial applications of Compton backscatter tomography: detection of cracks, voids, and inclusions in composite materials, inspection of offshore structures, and inspection of concrete for steel rebar and void enclosures, inspection of aircraft, automobile, and nuclear power industry components. The scattering of fast (14 MeV) neutrons was also used to image the flow of boiling water in a pipe [228]. A combination of gamma/neutron transmission and scatter imaging was proposed for inspection of cargo containers [1161]. While neutrons

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are more effectively slowed-down by interactions with the hydrogen nuclei, gamma-rays are (Compton) scattered by the atomic electrons, hence are more affected by heavy elements. Therefore, the scattering of neutrons and photons provide different but complementary indications. The transmission of neutrons and photons also further confirm the scattering indications, since the intensity of transmitted neutrons tends to be inversely proportional to the hydrogen content while that of photons decreases with increasing content of heavy elements. The combination of these four indicators was proposed for the detection of contraband materials, such as explosives, agriculture products and large sums of money.

13.4.4.

Emission Tomography

Positron emission tomography had found use in some industrial applications. Using water labeled with a compound containing a positron emitter the flooding of water through a porous sandstone saturated with brine/oil was imaged with positron-emission tomography (see section 8.8.3) [1162]. The same reference reported the use of the technique to image the dehydration of water-in-oil emulsions. Photoninduced positron-annihilation radiation-emission was also considered for imaging dense materials, due to the high probability of pair-production in such materials [736, 733]. The tracking of a single small labeled glass bead was used to image the motion of particulate solids, by monitoring the two 511 keV photons associated with the annihilation of the emitted positrons [1163]. The mapping of neutrons emitted from a nuclear weapon was also considered for distinguishing between different types of warheads and missiles, for treaty verification purposes, using neutrons produced by the spontaneous fission of the plutonium in nuclear weapons [1164]. Emission tomography with sources placed within the fluid container was also considered for industrial flow visualization [1165].

13.4.5.

Proton Tomography

Proton beams are also used in computed tomography, with energies up were to 230 MeV [1166]. Proton beams (5 to 7 MeV) focused to 5 used to perform microtornography on capillary tubes and low-density foams, by measuring the residual energy transmitted through the sample. This technique was also used to image direct drive inertial fusion confinement target [1167], and the density of a scorpion stinger [1168].

Imaging

13.5.

641

Imaging for Material Content

Relying on the principles of composition analysis discussed in chapter 12, a number of imaging techniques have emerged to provide material-distribution images. Example applications of these methods are discussed here.

13.5.1.

Dual-Energy Imaging

The ability of dual-energy radiography, discussed in section 6.5.3, to distinguish between organic and non-organic materials, by their density and atomic-number, had made it possible to use this method to image airport passenger luggage for the detection of contraband materials, particularly explosives [1169, 1170, 1171, 1172]. A tomographic system for the same purpose was also developed [1173]. An isotope-based system for for imaging cargo containers has been also considered, using for low-energy photons [1174]. A syshigh-energy photons and tem that uses two energy-groups of an (1.11 TBq) source was also investigated; with a 310.4 keV group containing the 296.0, 308.5 and 316.5 keV energy lines, and a 469.1 keV energy representing the 468.1, 484.6 and 489.1 keV lines [1175]. Dual-energy neutron tomography was employed to image the distribution of water through porous rock [1176]. The use of dual-energy enhances the imaging of small amounts of hydrogen by selecting the second neutron energy so that the other neutron absorbing materials have about the same cross-section in both energies, with the first energy being in the subthermal range where the hydrogen cross-section is highest. Time-of-flight energy discrimination, along with a moderated pulsed-neutron source, was used in this application. The ability of dual-energy (high and low) x-ray imaging to distinguish materials, see section 12.2.2, was used to determine the distribution of water, air, and solids in soil, as well as the soil’s dry bulk density (with 80 kV and 120 kV x-rays) [1177]. Multiple energy x-ray tomography was also suggested for use in imaging mineral samples to determine their principal components [1178, 1179].

13.5.2.

Critical-Edge Tomography

The critical-edge method of elemental identification, discussed in section 12.2.2.1, which uses a tunable photon source that matches the Kabsorption edge of the element of interest was used to image, using transmission tomography, the concentration of uranium in a sample of pitchblende (an ore composed mainly of [1180, 1181, 1182]. The method was also applied for the identification of elements such as Zr,

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Nd, Ba and Sm, using Mo, Sb, Cs, Ce and Gd filters in a boric acid matrix [1183].

13.5.3.

Transmission / Scatter Imaging

As discussed in section 6.5.1, by combining transmission tomography (section 6.4) and scatter tomography (section 7.7), density and composition (atomic-number) information can be obtained. Reference [1184] achieved that by performing these measurements separately using monoenergetic photons: the 60 keV of for transmission, and the for scattering. On the other hand, references [163, 164] 662 keV of presented an x-ray (102 kV) algorithm that relies on recording simultaneously the transmission and scattering measurements. While scatter imaging with photons provides electron-density maps, transmissiontomography reconstructs the total cross-section images that contains both electron density, via Compton scattering, Eq. (3.51), and strong dependence on the atomic number, through the photoelectric effect, Eq. (3.30). While reference [163] used the total cross-section obtained from transmission tomography to approximately correct for the attenuation factors associated with the scattering process, Eq. (7.12), reference [1184] applied a constrained least-squares process to deal with the nonlinearity of the problem (see section 7.7.3). X-ray scattering can also be used, along with transmission-radiography, for detecting explosive materials in passenger luggage [1185], where a rotating chopper-wheel and a stationary slit are used to form a thin beam that raster scans a bag. Either backscattered or forward scattered photons are detected, and used in combination with transmission to provide a density and atomicnumber indications. Within the x-ray energy used, 100 to 140 keV, the photoelectric-effect will still be dominant for metals, suppressing both the transmission and scattering signals. On the other hand, for common organics, Compton-scattering dominates in both measurements, without affecting much either indication due to their low density. Explosive materials, and some narcotics, on the other hand, influence both indications more strongly that most organics but less effectively than metal, thus enabling their detection. 13.5.3.1 Resonance Imaging Radiographic elemental images can also be obtained by fast-neutron transmissions for elements that exhibit resonances in their cross-sections, such as C, N and O, as explained in section 12.1.3. With a pulsed source, and time-of-flight energy measurements, elemental tomographic images were obtained [173, 661, 1186]. Resonance absorption of photons was also considered for imaging of cargo containers to detect contra-

Imaging

643

band materials such as explosives and narcotics [1187, 1188]. Explosives are detected by their high nitrogen concentration via the resonance absorption of 9.17 MeV photons, produced by the reaction, while narcotics are detected by their high chlorine via the resonanceabsorption of 8.21 MeV photons produced via the reaction. These gamma producing reactions require, respectively, the use of protons (produced in an accelerator) of energies of 1.75 or 1.89 MeV and targets employing or Tomographic images are produced from the preferential absorption of these gamma-rays by recording the intensity of the transmitted radiation at different orientations, by rotation and vertical translation of a baggage carousel, or a cargo container. The dip in the neutron cross-section of iron at 24.3 keV (an antiresonance) makes it easier to detect inclusions in iron using iron-filtered neutrons. A time-of-flight neutron radiography/tomography was used in [1189] to detect the presence of 1 mm thick copper within an iron block of 0.20 m thick, and to image the internal structure of cylinders made of Cu-Fe-Pb and Cu-Fe-Al. The time-of-flight technique, see section 4.5.5, facilitates the acquisition of neutron-transmission measurements at the anti-resonance energy 13.5.3.2

Bragg Cutoff Imaging

Below the Bragg cutoff, see section 3.5.5.1, the neutron cross-section drops significantly. This phenomenon can be used to detect the presence of a material by radiographing with cold neutrons at energies just above and below its Bragg cutoff energy. The presence of such material would be indicated by an abrupt enhancement in the amount of transmitted neutrons at energies below the cutoff energy. Time-of-flight measurement with a pulse neutron source facilitates the performance of such elemental imaging. This technique is called time-gated energy-selected (TGES) neutron radiography, and has been applied for the detection of beryllium (5.2 meV) and carbon (2 meV) [1190].

13.5.4.

Photon Coherent-Scatter Imaging

This method of imaging, discussed in section 7.7.4, was applied to the detection of explosives in luggage, taking advantage of the unique diffraction patterns of the investigated material [1191, 1192, 1193, 1194, 1195, 1196, 1197]. The technique was applied to food materials for detecting foreign bodies (such as soft plastics in meat and confectionery products), natural contaminants (such as fruit stones in processed food), and distinguishing between fat and bone tissue in meat processing applications [312]. Reference [1198] reported the detection of macrolon in choco-

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late, blue foil in bacon, cherry stones in cherry jam and wood and bone in chicken breasts, while reference [1199] showed images demonstrating the detection of plastic and glass fragments contaminants in a chocolate phantom. Small-angle scattering complements conventional transmission tomography by providing composition indications [1200, 232], and enables the characteristics of some light materials, such as plastics, that cannot be resolved by transmission tomography alone [1201]. Reference [1202] discussed a number of potential industrial applications of coherent x-ray scatter including: mixing or ice formations during the freezing of food products; discrimination between oil and water; precipitation of colloids in chemical processes, sorting of plastics in recycling facilities; and detection of gem stones in minerals..

13.5.5.

Emission Imaging

Emissions produced by the reactions discussed in chapter 8 can be used to produce tomographic images. For instance, the characteristic gamma emission from thermal or neutron activation of certain elements can be utilized to image objects for their elemental content. This approach was employed in imaging small and large objects, from airline passenger luggage to shipping containers, for the purpose of detecting contraband materials [1203]. The 511 keV photons emitted by the annihilation of positrons, produced following the reaction were also considered for imaging nitrogen in containers for the purpose of detecting nitrogen-rich explosives [627]. References [1204, 1205] presented a nitrogen-camera system for imaging the nitrogen content of concealed explosives by monitoring the gamma-rays detected after irradiating the object, pixel-by-pixel (20 x pixel area), with a pulsed beam of 50 MeV electrons. The camera itself is made a set of scintillator detectors. These electrons produce photons that in turn activate a variety of elements in the volume around the irradiated surface, but (a positron emitter, 11 ms halflife) and (a beta emitter, 20.2 ms half-life) are produced with high yield via the reactions and and In addition, neutrons are also produced by the induced photons interacting within the accelerator and surrounding materials. As these neutrons are slowed-down and captured they will also produce activation gammarays within a short period (about 10 ms following the incident pulse). Gamma emission will continue for another 30 ms or so, as a result of the bremsstrahlung of the decay beta-radiation, the de-excitation of (produced by the beta decay of and the annihilation of the positrons emitted by These gamma emissions, in total, constitute the nitrogen camera signal, although not all these emissions are attributable to

Imaging

645

the presence of nitrogen. However, the main gamma-emitter that competes with nitrogen is the gamma emitted by the photoactivation of which although present at low abundance (1.1%) has a high photoactivation cross-section (with a threshold energy of 25.1 MeV). However, emissions from the photoactivation of can be discriminated against, in principle at least, by the energy of the emitted radiation, since only produced by nitrogen activation generates 511 keV positron annihilation radiation. Also, the maximum energy of the positrons emitted by the decay of is about 16.3 MeV, which is higher than the 13.37 MeV maximum energy of the beta of with the result that the bremsstrahlung photons produced by are higher in energy than those produced by This feature can be used to further discriminate between the two isotopes, hence the elements they are produced from. Another way of discriminating against produced by activation is to employ a beam of energy below the 25.1 MeV threshold-energy of the reaction, which is also below the 30.6 MeV thresholdenergy of the reaction but is above the 17.5 MeV threshold energy of A combination of emission and transmission imaging was proposed for evaluating the radionucluide content of drums containing low-level waste [1206]. Using an external source, transmission tomography is performed to obtain an attenuation-coefficient image of a section. The obtained attenuation-coefficient, adjusted for energy dependence, is then used in emission imaging to correct for the attenuation of the emitted radiation from its point of origin to the detector location. In this technique the energy spectrum of the emitted radiation is used to identify the radioactive nuclide in the drum. Particle-induced x-ray emission (PIXE), discussed in section 8.7.3, can also be used in imaging small samples (less than a few mm), by monitoring the emitted x-rays and relating their energy to the characteristic energy of the originating element. References [1168, 1167] introduced such a tomographic systems, using microprobe ion beams, to image the distribution of Zn and Mn in the sting of a scorpion [1168], Br and I in a direct drive inertial confinement fusion target [1167], and Ni or Cu in metal wires [1167].


PART IV: DESIGN


Design

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The most challenging task for a designer of a radiation-based device is perhaps to justify its use in industrial settings that are adverse to the use of ionizing radiation. In Chapter 1, some justifications for the use of such devices, v.s. the use of other non-radiation techniques, are presented. However, reference [1207] provided an excellent summary of the features that one can use for promoting the application of radiation instruments in measurement and control. These are: Non-Contact: no direct contact with the inspected medium is required, thus measurements with high temperature, high pressure, toxic, acidic, viscous or otherwise “difficult” process materials are made easier.

External: equipment used, sources and detectors, are placed outside the interrogated system so that the devices can be fitted while the plant is on-line. They are also readily accessible for checking and maintenance.

The exception is when a radioactive material needs to be introduced within the interrogated object, such as when radiotracers are employed. But even then, the measuring equipment (detectors) are usually external to the material. Reliable: the failure rate of radiation devices that use radioisotopes is quite low, since such sources are self-powered and require no maintenance (except for leak checks every few months, see chapter 5). The technology of nuclear electronics is also well proven. Therefore, the mean time between failures is low.

System breakdowns are often caused by mechanical components. The designer should keep in mind that the mean-time between failures is determined by that of the weakest component of the system. However, radiation imaging systems with moving parts (such as scanning mechanisms) are routinely used in airport luggage-inspection and in medical diagnosis. Energy Efficient: the power requirements of radiation detection equipment is generally quite low, and no power is needed to generate radiation when radioisotopes are used. Therefore, such devices can be made “intrinsically safe” from an electrical point of view.

However, the use of accelerator-based radiation generators entails the utilization of high-voltage power supplies.


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Uniqueness: in many cases conventional techniques cannot meet all measurement needs, and radiation devices can provide information that is not simply attainable by any other means. There are, however, many situations in which a nucleonic gauge provides the only sensible answer to a measurement and control problem.

Regulatory Burden: the effort associated with the licensing and operation of radiation devices is perceived by some as being taxing. However, such effort ensures a safe and secure operation and use. Regulations are usually introduced for a reason: to ensure safety of workers and the public. Moreover, there is no reason why the routine regulatory checks need be any more time-consuming than those associated with any other plant-installed instrument.

Cost: radiation devices tend to be more costly than other conventional devices. However, taking into account their non-intrusive nature, the saving offered by radiation devices can offset their cost; by eliminating the need to alter or modify an existing plant system to accommodate an instrument, and by avoiding the shutdown of plant to install, repair and maintain instrumentation devices. The savings from this source [installation and commissioning] alone will, in the majority of cases, exceed the cost of the instrument.

As reference [1207] states: Nucleonic gauges can, therefore, compete on an equal footing with conventional gauges and should certainly be among the instrument options considered for any plant or process.

The same reference [1207] concludes by stating: Instrument engineers are finding that for difficult measurement problems, nucleonic instruments possess advantages offered by no other type of instrumentation. There is also an increasing awareness that properly installed, they present no hazard to the work-force. On the contrary, by providing what is in many cases superior control of potentially hazardous process materials, they are a positive enhancement to the safety of operating plant.

Reference [1207] supports the above quoted statements with two case histories: density/level gauges to control foam/liquid in oil gas separators, and control of boric acid flows. One can make similar arguments for most of the applications reported in Part III of this book. Marketing. Successful implementation of radiation-based technologies requires good marketing. Strategies for good marketing of radiation devices include [1208]:

Identifying the needs of a potential user.

Design

651

Demonstrating how a device, whether conceived, developed or available, meets the user’s requirements. Showing the economic and operational benefits of the device. Identifying, if necessary, any adjustments or improvement that may be needed for a device to better meet the user’s requirements. Overcoming the apprehension of potential users and their resistance to accepting radiation technology by an honest approach to the matter, referring to similar systems already in place in other sites, and comparing the risk to other competitive methods that may require contact, intrusions or are simply incapable of meeting the user’s needs. Convincing a potential user of a device is only the first step in the design process. Many technical design aspects and considerations must be dealt with, to provide an accurate, fast, safe and a minimum-cost device. This Part of the book discusses these design issues, which are defined in more detail in chapter 14.


Chapter 14 PERFORMANCE PARAMETERS AND DESIGN ASPECTS

14.1.

Performance Parameters

A measuring device provides an indication of a physical parameter. The design of a measurement system must, therefore, deal with both the nature of the measured value and the corresponding physical parameter. In radiation devices, the measured value can be a count (pulse) rate or a current or a voltage corresponding to the measured pulses. A pulse-height distribution can also be measured, from which the energyspectrum can be derived. In any case, one needs to find a relationship via a between the physical parameter, P, and the measured quality, measurement model, M, as discussed in Part II of this book. That is:

where M(P) designates that fact that is a function of P, with the function determined by the model M, and K is a system-constant that incorporates system parameters that are not included in the measurement model, such as the source strength, detector efficiency, etc. The constant K can be obtained by calibration. Alternatively, calibration and P. can provide a graph, or an empirical relationship, between The measured parameters, and the corresponding physical parameters, can themselves be functions of the following independent variables:

with being a vector in space defining the spatial dependence of P or refers to the time dependence, and designates the concentration of a species (atom or nucleus) of type i that influences P and and N is the total number of species considered. In global gauging 653

654


(chapter 11), where an indication representative of the entire volume is and P are only functions of and the At steady-state, obtained, becomes dependent only on the composition of the examined material. For a fixed composition, becomes a direct indication of P, with the latter being for example, thickness, density, etc. Probing (chapter 10) in space, or at a aims at obtaining an indication at a fixed position, number of such positions, one at a time. In imaging (chapter 13), and but for tomography, where an image is obtained P are functions of are obtained at given values and become only at a section, P and function of and In elemental mapping, one aims at obtaining an but can also be at a certain point indication that is a function of for probing, over the entire volume (independent of for bulk (at indication, or a function of for imaging. All the above mentioned indications can be time-varying, which requires one to pay attention to the dynamic behavior of the measured signal; see section 17.4. Radiation measurements are also subject to statistical fluctuations, and the data acquisition process should be such that a certain level of statistical confidence in the results is attained. The design of a system should also be statistically optimized, as discussed in section 14.2. In general, designers aim at determining and optimizing the following parameters: Accuracy. This is the difference between an “indicated” value and a “true” value. Designers should aim at minimizing this difference to attain high accuracy. Verification against independent measurements or calibration can be used to measure or assure the accuracy of obtained measurements. Calibration of a device during operation, or every time the device is restarted, is needed to guarantee the accuracy of the device under different operating conditions.

Precession. One of the main design goals is to achieve a high degree of repeatability and reproducibility of a measurement, obtained for the same value of P under the same setup conditions. A low degree of statistical spread in the measured indication is required for high precession. Designers need also to specify the smallest and highest obtainable indication value, i.e. the range of the device. Tolerance is the term used to describe variation about the mean output of a device for a given exact condition. The tolerance of a device may vary with the range of

Performance Parameters and Design Aspects

655

measurements. In such a case, the designer must report the tolerance of the device at different ranges of operation. The obvious approach to obtaining good precision is to increase either the counting time or the source intensity. Statistical consideration, see section 14.2, can be used to determine the counting period for a given count rate provided by a certain source strength. While in some applications a long counting time may be acceptable, it is often desirable to obtain precise measurements at high sampling rate, i.e. within a short counting period. Radiation safety considerations may also constrain the intensity of the source that can be utilized to avoid a bulky, heavy or cumbersome shielding. Even if a large source can be used, dead-time and pile-up loses (see section 4.5) may impose a limit on the source intensity that can be used while being able to electronically process the detected signals. Resolving Power. This is the smallest change in P that can be detected with a certain confidence level [1209]. The resolving power, is a measure of the precision in determining a physical parameter P. Two parameters, and that are close to each other can be distinguished from one another if the difference in their value is greater than the statistical uncertainty associated with their value. At a 68% confidence level, see appendix G, the statistical error associated with the difference in value between and is equal to where refers to the statistical variance which is assumed to be equal to the measurement in accordance with Poisson statistics (see appendix G). A device measures instead of P, but is related to using relationship (14.1), by:

where the measurement model of Eq. (14.1) is assumed to be a continuous function, enabling the last step in Eq. (14.2). When and are where and are the close in value, and measurements corresponding to respectively. Then, one can also assume that Therefore, the smallest measurable actual change in P, or the resolving power, is given by:

Note that, when the measurement ceases to change with P, i.e. when would approach infinity, providing no resolution power, as one would expect.

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Signal-to-Noise ratio. Generally refereed to as S/N, the signal-tonoise ratio is defined as:

where is the fluctuation of the signal around which can be caused by statistical variation or electronic noise. Obviously, the value of S/N should be as high as possible. The effect of statistical fluctuations is addressed in appendix G. Other sources of noise may be viewed as those introducing a constant relative-error (electronic noise) or a constantabsolute error (systematic instrument or indication error). When these sources of error are statistically independent from each other their variability can be added for a measured signal as follows [1210]:

where refers to the variance due to statistical fluctuations, is the relative error due to electronic noise and is the absolute systematic error. Electronic noise is generated by detectors and associated electronics. Such noise can be due to changes in temperature (semiconductor detectors and photomultipliers), magnetic (photomultipliers and signalprocessing electronics), and power supply/ high-voltage instability (proportional counters and electronics). While minimizing the source of noise is certainly desirable, strengthening the detected signal is also a sure way to enhance the S/N ratio. The signal can be intensified by using an efficient detector for the radiation type and energy at hand, matching the output of the detector with the proper amplifying electronics, (e.g. matching the frequency of the light emitted by a scintillator to the type of cathode used in a photomultiplier), and using the proper preamplifier type and setting (see section 4.5). Signal-to-Background ratio. Referred to here as S/B, the signalto-background ratio is expressed as:

where is the background measurement, due to radiation scattering, source leakage, natural radioactivity, etc. However, sometimes, system noise is also viewed as part of the background signal, particularly to account for the statistical fluctuations of the background signal as discussed in appendix G. A signal that is very close in magnitude to the background signal is vulnerable to signal noise, as


657

the noise may make the signal closer in value to the background signal. The value of imposes a limitation on the resolving power, i.e. the detection limit, as can be deduced from Eq. (14.3) by setting where is the recorded gross-measurement. Then, (assuming that is independent of P). Using Eq. (14.3), with this leads to the following “lower limit of detection ” [1209]:

Eq. (14.7) provides a quantitative estimate of the effect of the background measurement on the detection limit which can be useful in determining whether effort in lowering the background signal is worthwhile. Contrast/Sensitivity. Designated here by C, the contrast is the relative change in due to a change in P, or:

A good contrast, i.e. a high value of C, assures that a small change in the physical parameter, P, produces a large change in the measured paramObviously the contrast affects the resolving power, Eq. (14.3), eter, and the lower limit of detection, Eq. (14.7). Resolution/Precision. Resolution is the detectable change of any of the independent parameters listed in relationship (14.1) that correspond to the smallest measurable change in say That is,

where

is the concentration of element

Stability. Allowance should be made to ensure stability against shortand long-term variations [410]. Short-term and long-term variations in system and environmental conditions should be taken into account. Short-term variations may include temperature, pressure, high-voltage

658


supply, magnetic noise, etc. Long-term effects may include decay of a radioactive source or deterioration of the target in an accelerator-based source, changes in detector characteristics, etc. Periodic verification and calibration of the system is an obvious necessity when dealing with longterm effects. On the other hand, short-term effects may be handled with compensating electronics, comparative measurements with a standard well-controlled object, or by post-processing compensation for ambient effects. Artifacts. In an imaging system, a number of image artifacts can be produced, and effort should be made to eliminate or minimize such artifacts. An artifact is any image feature that does not exist in the imaged object. Since the actual details of an imaged objet may not be known, artifacts can make it difficult to interpret a recorded image. However, understanding the nature and sources of artifacts that may be introduced by a certain imaging system can be helpful in interpreting images produced by that system. The following types of artifacts may exist [160]: Physical Artifacts. These are produced by idealization inherent in the interpretation process. For example, in a transmission-based system, scattering can produce artifacts in the image indicating less attenuation than actually is the case. With a multienergetic source, beam hardening produced by the absorption of lower-energy radiation early in the beam path, will also produce an apparent decrease in the attenuation capacity of the object. Similarly, in a scatter-imaging system based on singlescatter events, multiple scattering can result in an artifact indicating an apparent increase in the amount of scattering. In emission-imaging, artifacts are produced by radiation attenuation which reduces the amount of radiation detected, and by scattering that can increases its strength . Geometric Artifacts. Object geometry (curved or irregular), source geometry (size, uniformity and divergence) and detector geometry (size and collimation) can also produce artifacts by creating irregular image voxels. Misalignment of the source-object-detector geometry also produces geometric artifacts, called parallax artifacts. Systemic Artifacts. These are caused by effects other than those introduced by physical or geometric reasons. Such factors include, source irregularities, detector drift and afterglow (i.e. delayed response), electronic noise, etc.


659

Reconstruction Artifacts. In computer-reconstructed imaging, the image reconstruction algorithm can introduce its own artifacts, due to error propagation, round-off error, etc. Figure-of-Merit This is a design parameter that combines

more than one feature, and is used when improvement in one parameter

comes at the expense of other parameters. For example,

provides the best possible combination of a strong signal, and a high contrast. A figure-of-merit can also incorporate parameters such as cost, radiation exposure, size or weight of shielding, etc.

14.2.

Statistical Optimization

The measurement model of a particular technique or a system can be used along with the provisions of statistical counting discussed in appendix G, to design for optimal statistical conditions. Let us reconsider the generalized measurement model of Eq. (14.1):

. Assuming that the function M is a continuous function, so that it can be

so that: inverted to determine the value of P, from

where is a function that relates to P, and is in effect the inverse of the function M(P). In order to determine the value of P with highest accuracy, its error should be minimized. The statistical variance in P, Var(P), is related to the statistical variance, in the measurement by the rule of combining errors, Eq.(G.4), as follows:

where refers to the error in P, which is equal to as discussed in appendix G. The nature of the function, M, and its inverse, G, in a radiation-based application depends on the type of radiation and its energy, which in turn determines the value of the macroscopic crosssection, of the inspected material. For minimum error in P, one must choose so that:

Using Eq. (14.13), this leads to:

for optimum counting statistics, i.e. minimum error in statistical counting for a given source strength.

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Transmission. To demonstrate the above optimization process, let us

consider the use of a transmission technique, modeled by Eq. (6.1) as:

where I is the measured intensity for a material of thickness, is and is the cross-section the measurement in air (i.e. when of some type of radiation at some energy that needs to be optimized. and Comparing Eqs. (14.16) and (14.1), one can see that The inverse of Eq. (14.16) is given by

which upon comparison with Eq. (14.12) shows that

With I being the measured radiation count rate, according to Eq. (G.3)

the statistical variance in a count is equal to the count itself, that is,

Using relationship (14.15), one can show that:

This is the well-known condition for optimizing transmission-based systems, see for example reference [238]. The reader can verify that the second derivative of the error in P, hence the error in i.e. is positive at which confirms that the error in is minimum at Note that the same condition arises when optimizing a transmission system for best resolution, see Eq. (14.26), since in essence good counting statistics leads to a better ability to resolve changes in system parameters, i.e. better precession. The condition of Eq. (14.18) suggests that the radiation type and energy should be chosen such that it provides a total cross-section, Eq. (14.18) is equivalent to stating that that is the thickness of the material should not exceed the equivalent of two mean-free-paths of the radiation used. Under this condition, the average number of collisions the radiation encounters in a material would be equal to 2. Since not all collisions will lead to scattering towards the transmission detector, the buildup effect, see section 6.1, would not be too severe under these optimized conditions to violate the inherent assumptions behind the measurement model of Eq. (6.1), refer to section 6.1. The above process is equally applicable if one is to measure the value or any other quantity linearly related to it (such as the electronof density in the case of Compton scattering.) The reader can prove this and optimizing for Therefore, for a given value of by setting material type, density and thickness, one can select the source type and


661

energy that satisfies the condition of Eq. (14.18) for optimum counting statistics. Instrument Error. A very high count will also reduce the statistical variability in the detected measurement, and subsequently in the evaluated physical parameter, as one can deduce from Eq. (14.13). A very intense radiation source, or counting for a very long period, will achieve this objective. Both such conditions are used in practice to reduce the statistical uncertainty. Even under such conditions of low counting statistical uncertainty, some other instrument error may arise from effects external to counting; e.g. variability in film quality in radiography or instability in the high-voltage applied to a detector. Then, it is reasonable to assume that the variance of the measurement, is indepen-

dent of the optimization parameter, Eq. (14.15), leading to:

and one can set

in

for optimum conditions for instrument error (not related to counting variability). Applying the above condition to transmission leads to the requirement that Off-Optimum Conditions. For transmission measurements, between the conditions of Eqs. (14.18) and (14.19), one can state that the optimum range for operating a transmission-based device is when for best counting and instrument variability conditions. Note that total variance in the estimated parameter is given by:

where the subscript and refer, respectively, to counting and instrument effects. Operating at would ensure minimum error due to instrument variabilities, while operating with would minimize the statistical counting error. At the device would be very sensitive to variabilities in the measurements, that is, a small error in the measured value would lead to a large error in the estimated parameter, since the response curve given by Eq. (14.16) would be quite steep in the sensitivity of to changes in slope. On the other hand, at P would be quite poor, as the response curve would tend to saturate. In or so, it becomes quite difficult to obtain statistically practice, if acceptable measurements with a source of a reasonable strength, due to the severe attenuation of the source. Therefore, a thickness equal to

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is called the “blackness” thickness or “saturation” thickness, beyond which an instrument becomes insensitive to small changes in the system parameters. Complex Problems. The above analysis was performed for a simple case of transmission with a source of a fixed energy, hence a fixed value of and in a uniform medium, i.e. was not a function of distance. The analysis becomes more complicated when dealing with changes in radiation energy and material uniformity, as the measurement model becomes more complex to be amenable to a simple differential analysis such as that presented above. The same situation may rise when dealing with other techniques, where the measurement model is either too complex or may not exist at all. Then, sensitivity analysis using numerical simulations and laboratory experiments will need to be employed. However, when possible measurement models should be simplified, such as by using the concept of equivalent energy discussed in appendix 6.4, to facilitate the performance of the above optimization analysis. The results of such analysis can then be used as an approximate indication of the optimum measurement conditions around which calculations and experiments may be attempted.

14.3.

Design Objectives

The designer of a device should aim at optimizing performance parameters that are relevant to the problem at hand. Such optimization can be achieved by: Selecting the most suitable radiation source. Section 14.4 examines the factors that should be considered when choosing a source. However, such sources can be modulated in direction or energy, or even in some cases intensity, to better suit the designer needs. Section 15.1 discusses the design of source collimators to confine the incident radiation to a particular direction. Methods to alter the energy of radiation emitted by a source, or to confine it with a certain energy range, are addressed in chapter 15. Choosing the most appropriate indication method: transmission, scattering, activation, etc., and the associated physical modification process (section 14.5). Finding the detector that most effectively and efficiently measure the desired parameter (section 14.6). Studying various effect parameters, using calculations and/or experiments (chapters 16 and 17).


663

Reducing the radiation background (section 17.3). In addition, a proper radiological shielding must be provided (section 16.3). Devices employing radioisotopes or particle accelerators must be also licensed with the appropriate regulating authority. Section 17.2 discusses some of the regulatory issues. Many of the design calculations required in the design process can be performed using the powerful Monte Carlo method of radiation interaction and transport simulation (chapter 16). However, such calculations do not usually incorporate all measurement aspects encountered in the laboratory. Thus experimental verification of the design is essential (chapter 17). Experiments are also used to calibrate a device. Lessons learned from the experimental testing process can then be incorporated in the design and construction of a prototype device suitable for field testing (chapter 18). Field testing for performance evaluation can then be followed, lessons from which can be incorporated in the design of the device (section 18.1). The protection of intellectual property associated with a novel device should also be of concern to the designer (section 18.2).

14.4.

Source Selection

Chapter 2 described various types of available radiation sources. If a designer is to rely on a source that readily exists within the inspected material, such as when the material contains natural radioactivity or is radioactive, then the main design effort will in the modifying physics and the detection system. However, when an external source is to be selected, or an internal source is to be introduced, the choice of the source is crucial to the design. The choice of a source relies on the type of modifying physics employed for the detected indication. However, there are some basic source parameters that a designer must be concerned with. These can be summarized as follows: 1 Nature of emitted radiation: photons, neutrons or charged-particles. 2 Method of radiation generation: by machines or isotopic sources. 3 Energy of emitted radiation. 4 Intensity of emitted radiation (number of radiation entities per second).

Note that the source-energy refers to the energy of a single particle, or a photon, while the source intensity is the number of particles emitted per unit time. The above parameters not only affect the selected modification modality and detection system, but also the portability of a device, which

664


depends mainly on the size of the source and the associated shielding. More often than not, a source needs to be altered in energy or direction to better suit the designed device, as discussed in chapters 15. This section focuses on the above basic parameters.

14.4.0.1

Source Nature

One can use the following basic facts to choose a radiation source for a given application: Charged-particles: are affected by the electrostatic (coulomb) field of the atom, thus have a limited penetration range, and interact only with the nucleus when they have a high energy. Photons: interact mainly with the atomic electrons, and result in nuclear interactions only at high photon-energy. Neutrons: interact always with the nucleus.

Charged-particles, whether employed as sources, or detected as scattered or emitted radiation, are limited to use in small samples or gases, due to their poor penetrability. The same conclusion applies to techniques employing low-energy photons, as incident or emerging radiation. With such not-too-penetrating radiation, effort must be made to remove any obstacles in the path of radiation, by for instance performing measurements in a vacuumed cell and the use of thin-window detectors. When dealing with light (low atomic-number) materials, neutrons are generally preferred, since such materials are not too rich in electrons to significantly affect photons. On the other hand, charged-particles can penetrate larger sections of such materials, making it possible to exploit the use of charged-particles. Heavy (high atomic-number) materials are electron-rich, thus strongly affect incident photons. However, if a heavymaterial is too thick, photons may not be able to penetrate deep inside the object, but neutrons may. If the source is to be an internal source, such as in radiotracers, charged-particles are usually excluded because of their limited penetrability, which makes it difficult to detect the emitted signal outside the object. The activity released by these particles may be detected by sampling or an intrusive measurements [276]. However, such charge-particles, in the form of open (unsealed) internal sources present a biological hazard, if inhaled, ingested, or absorbed by the skin. Unless charged-particles and photons are energetic enough to produce nuclear interactions, or are sufficiently low in energy to induce atomic excitation, the indications they provide are electron-density dependent, due to the electron-dependent nature of their reactions. On the other


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hand, neutrons more easily penetrate the nucleus, because they are neutral, and can produce nucleus (hence element) related indications. The selection of the type of radiation can be viewed as an optimization of the cross-section of the material, to provide optimum performance in contrast and/or resolution. This is in essence a source energy optimization problem, see section 14.4.3, applied to various radiation types. For example, in transmission radiography, the optimum spatial resolution is attained when where is the total cross-section of the inspected material and is its thickness, see section 14.2. Therefore, for a given material and a given thickness, one should choose the radiation source type and energy that result in a value of as close as possible to It is the thicker the object that can clear also that the lower the value of be inspected with optimal spatial resolution. On the other hand, if one needs to distinguish between two materials, the contrast provided by one material should be different from that of the other. Since the contrast for radiography, as Eq. (14.22) indicates, is proportional to the larger the difference in the value of for the two materials, the better the ability of a radiographic system to distinguish between the two materials. For this reason, fast-neutrons were preferred, than photons, for radiographing a light material, such as lithium, surrounded by a dense material, such as uranium, due to the larger difference in the neutron cross-sections of the two materials [1026]. The cross-sections in Table 14.1 illustrate this point. The Table shows that, per unit mass, the maximum photon cross-section for Li and U are about equal, while those for neutrons are quite different. The lower fast-neutron cross-sections for these two elements, than those of photons or thermal-neutrons, make fast-neutrons more penetrating of the material.

14.4.1.

Radiotracers

In choosing a radiotracer, the half-life of its radioactive element should be considerably longer than the counting period, otherwise decay corrections have to be introduced. Obviously, the chemistry of a radiotracer material has to be such that it remains suspended or dissolved in the

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material into which it is embedded. The emitted radiation has also to be sufficiently penetrating of the inspected medium and its container so that it can reach a detector located outside the medium. For liquids, the following radiotracers are available in different chemical forms suitable for use in aqueous or organic liquids [445]: (14.959 h, 1.369 and (35.30 h, 0.554.348 and 776.517 MeV), where the 2.754 MeV) and values in brackets indicate, respectively, the half-life and the energy of the principal photons emitted [12]. For gas radiotracers, the following radioisotopes may be used [445]: (12.32 y, beta: 18.587 keV), (109.34 min, gamma: 1.294 MeV), (4.480 h, beta: 0.841 MeV, (5.243 d; gamma: 0.151 keV; 3934.4 d, beta: 0.687 MeV) and beta: 0.346 MeV), where the values in brackets are the half-life, type of radiation emitted and the maximum energy of emitted beta-particles, or the most intense gamma energy for photons [12]. Note that is also suitable for water and steam, as it can be included in the form of (tritiated water). For beta-emitters, the walls of a container need to be equipped with a thin window in front of the detector to allow radiation to exit the system for detection. Other open sources that can be used as radiotracers include [2]: and

14.4.2.

Source Generation

Radiation can be generated either by the decay of a radioactive material (an isotope) or by a nuclear interaction. The latter typically involves the acceleration of charged-particles to an energy that is sufficiently high for the particles to penetrate the field of the nucleus. However, some isotopic sources are based on nuclear interactions without accelerating the incident charged-particles, as in the case of alpha-reaction neutron sources (see section 2.3.1.1) and photoneutron sources (see section 2.3.2). The choice of the type of source production depends on many factors. To assist the designer, advantages and disadvantages of each type of source generation are discussed below. Radioisotopes are generally small in size, but are of limited emission intensity and are subject to reduction in intensity by radioactive decay. Therefore, internal sources are mainly radioisotopes, due to the obvious difficulty of introducing bulky accelerators into an inspected medium. Portable devices also benefit from the small size of isotopic sources. Although radioisotopic sources have the advantage of being self-powered, i.e. do not require external power supplies, they emit radiation continuously thus cannot be turned-off. The latter makes it necessary to equip them with biological shielding at all times. They are also classified as nuclear materials that require special licenses to acquire, transport, use and


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dispose of. Isotopic gamma sources have also the advantage of emitting discrete and often monoenergetic photons, since the emitted photons originate from the decay of the nucleus. On the other hand, neutrons produced from isotopic sources possess a wide energy distribution, as indicated in section 2.3. Accelerator-based radiation sources have in general features that are contrary to those of radioisotopes. Accelerator-based photon sources, such as x-ray machines (which are based on electron acceleration) have a wide energy distribution, see section 2.2.1. On the other hand, monoenergetic neutrons can be generated via accelerator-based devices, see section 2.3.1. They tend to be bulky and require a power source, but neutron generators also provide highly intense radiation and can be turned off. Therefore, accelerator-based sources can be stored, when not in use, in a non-shielded area. The intensity of emitted radiation can also be controlled by the current of the accelerated incident chargedparticles, while the energy of generated radiation may be adjusted by varying the acceleration potential. However, such radiation generators require special care in operation and maintenance, and in some cases need highly trained and specialized personnel to operate them. Although accelerator-based sources are not subject to radioactive decay, the target upon which the charged-particle impinge may be depleted or damaged. Cooling of such targets may also be necessary at high radiation emission rate. The cost of an accelerator-based source tends to be higher than that of a radioisotope; although for very high intensity sources, radioisotopes may prove to be comparable in cost or even more expensive, if one includes the cost of disposal. The licensing requirements of such devices tend, therefore, to be more lenient than that of radioisotopes.

14.4.3.

Source Energy

The source energy not only determines the penetration depth of the radiation, but also governs the way radiation will interact with the material of the interrogated medium, as discussed in chapter 3. For chargedparticles, the value of the range determines the maximum depth of penetration of the particles, a quantity that is typically small in value. The range of a given charged-particle at a certain energy in a given material can be evaluated using a library such as SRIM-2000 [47], or using the approximations given in section 3.3. Unlike charged-particles which are continuously affected by the electrostatic field of the atom, neutrons and photons can travel some distance without suffering any interactions at all until they encounter an atom to interact with. However, the penetration depth of photons and neutrons can be roughly taken to be equal to about five mean-free-paths,

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since after such distance most of the original beam of radiation would have interacted with the material; only 0.67% of the incident beam survives. This value is arrived at using the transmission model of Eq. (6.1), with the total macroscopic cross-section being equal to the reciprocal of the mean-free-path. The value of the cross-sections for different elements and at different radiation energies can be found in one of the many available libraries such as ENDF [78] for neutrons and XCOM [19] for photons. These libraries also provide the interaction cross-sections for various modes of interactions, thus can be used to determine the suitability of a proposed type of reaction and the possible interferences from other reactions. For an example of source optimization for an x-ray transmission tomography system see reference [1211]. When dealing with multienergetic sources, determining the depth of penetration and the interaction probability is a challenging task, since each value of the source energy will provide a different value for the penetration depth. One can either use a bounding approach that involves employing the maximum and minimum source energies to provide limits for the penetration depth and the interaction probabilities, or use an equivalent single energy (see appendix F) to determine an effective value for these parameters. A more rigorous approach is to employ Monte Carlo simulations to determine these parameters, see section 16.2. If the optimal energy cannot be found in one of the commonly available sources, one of these sources may be modified in energy using moderators in the case of neutrons (see section 15.3), or filters in the case of photons and neutrons (as section 15.2 shows). If the device to be designed involves the use of multiples sources of different energy or radiation type, the designer must ensure that each source provides a significantly different type of indication, otherwise the use of multiple sources would be redundant. For example, reference [1212] studied the criteria for the selection of photon energy in a dual-energy system for oil-water-gas mixture composition measurement. In addition to penetrability, one also should chose the source energy that assures best contrast. Let us consider the case of a radiationtransmission technique, such as radiography, which can be depicted by the exponential attenuation measurement model of Eq. (6.1):

where I is the intensity of transmission at thickness of a material of and is the intensity in the absence of the a total cross-section material. The contrast, C, of such device to a change in due to say the presence of a void flaw, can be expressed using relationship (14.8)


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as:

High penetrability is manifested by a high value of I, which can be attained, in accordance to Eq. (14.21), by choosing a source that provides normally the highest energy possible. However, the smallest value of reduces the contrast, as dictated by Eq. (14.22). A a low value of figure-of-merit can be defined as:

Then, a source energy that produces a value of that maximizes the value of in Eq. (14.23) will produce the most optimum system in penetrability and contrast. Note that is maximum when i.e. when the mean-free-path is equal to the thickness of the material. to the above problem, by Reference [1025] proposed alternative defining as the time it takes the signal corresponding to a flaw to reach an intensity level five standard-deviations away from the flaw-free signal; with the best being the lowest time. That is, for a flaw that results in a change in I, becomes equal to the time it takes to reach a value of where is the standard deviation in I. Since, as shown in appendix G, for radiation counting, then is the time for to reach a value of This provides a tradeoff between the decrease in contrast, lower value of with the increase in penetrability, higher value of I. The value of also ensures that the indication due to a flaw is well beyond the statistical fluctuations in the value of I. The value of this figure-of-merit is experimentally measurable. This definition of is particularly useful when the source energy can be varied experimentally; as was the case described in reference [1025], where a tunable high-energy source utilizing a high-energy proton beam on a tungsten target (producing neutrons of energy from 0.1 MeV to 1 GeV) was used. The same concept is also applicable to x-ray machines, where the value of the applied voltage can change, to alter the maximum photon energy. The source energy can also be selected to optimize the resolution or precision of a device. Again in the transmission-based radiographic system discussed above, one can optimize the source energy for the spatial For such a system, using Eqs. (14.21) and (14.9), the resolution, spatial resolution can be expressed as:

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One can take equal to one standard deviation of I, since below this error level, the statistical confidence in the value of I would be quite poor. Using the Poisson statistics of counting, appendix G, along with Eq. (14.21), Eq. (14.24) becomes:

An optimum value for is then obtained when the derivative of with respect to is equal to zero, that is when:

Then the optimum source energy is the energy that results in a value of that is equal to Another way of looking at this conclusion is that the best spatial resolution is obtained when the mean-free-path is equal to half the thickness of the inspected specimen. Interchanging with in the above analysis would have led to the same conclusion, that is the optimum conditions for observing changes in for a fixed thickness, is also when providing then optimum material contrast. Note that the same conclusion is reached from a statistical point view, see section 14.2.

14.4.4.

Interfering Radiation

Radiation sources almost always emit more than one type of radiation. Neutron-emission is usually accompanied by gamma-emission; a gamma-source may also emit beta-particles, while beta-sources may emit photons. Such secondary emissions can interfere with measurements. Therefore, attention must be made to the choice of radiation source and accompanied detectors, in order to ensure that the obtained indications are not greatly influenced by secondary radiation. For this reason, a neutron source may be preferable than an Am/Be source, due to With neutron the lower gamma-field per neutron associated with generators, the detector may be equipped with gamma discrimination electronics (see section 4.5). While gamma-sources can be easily shielded against beta-emission, simply by the material of the source container, it is more difficult to remove gamma-emission from beta-sources since the use of any shielding material will eliminate beta-emissions. Therefore, it is important to choose beta sources with a low gamma yield. In this and are pure (or practically pure, in the case regard, of beta-emitters, while is a beta-source with low gamma emission (0.7%). Although is also a pure beta emitter, its low energy (maximum 18.6 keV) limits its use.


14.5.

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Selection of Technique

A measurement technique, as explained in Part II, is defined by the nature of its indication, i.e. absorption, transmission, scattering, secondary emission, or a combination of thereof. The modifying physical process, see chapter 3, enables the development of a measurement model that relates the measured indication to the quantity of interest. The availability of a measurement model, not only facilitates interpretation of measurements when a device is operating, but it can also aid the designer in assessing the performance of a device before constructing it. If a measuring device is too complex to enable the development of a measurement model, the designer must rely on detailed simulations or experiments. Some general guidelines for the choice of an indication technique are given here.

Transmission. Transmission is perhaps the most straightforward indication technique, as it has a well-defined path line from the source to the detector, which makes it easy to define the inspected portion of the object. Since transmission relies on measuring uncollided radiation, its indication carries radiation that has the same energy as that of the source; a feature that can be used with monoenergetic sources to eliminate the effect of scattered radiation reaching the detector from the object or surroundings. Also, such energy information in a source of wide spectrum may be used to obtain elemental composition information. However, the information obtained is a “compressed” (integral) indication of the material present within the radiation path line, and is affected by the material thickness. While tomography can “descramble” this compressed information, it requires multiple exposures from many directions. The modifying physics associated with transmission is that of “removal” of radiation from the incident beam, by absorption and/or scattering. Therefore, if a medium is “opaque” to radiation, no useful indication would be deduced. On the other hand, if a medium is too transparent to radiation, the change in indication, caused by changes in the interrogated medium, may be too small to be measurable. Scattering also affects the indication by the “buildup” process that increases the transmission intensity, see section 6.1. The signal-to-background ratio (S/B) for transmission has an upper limit of unity, since the background signal is the transmission indication obtained in the absence of the object. On the other hand, the transmission signal can be quite strong, as it measures the uncollided radiation. Thus the signal-to-noise (S/N) ratio for transmission is quite high.

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Scattering. Perhaps, the main limitation of the transmission method is that it requires access from two opposite sides of the object, a circumstance that may not be available in some situations, as in the case of examining large structures. Backscatter indications can be useful in such applications. The scattering process is normally associated with change in radiation energy, which can be used to distinguish the scattered radiation from that of the source. The energy change in single scattering can also be associated with the scattering angle, as is the case with Compton photon-scattering (section 7.2.1) and neutron elasticscattering (section 7.2.2), providing localized “pointwise” information (section 7.3). Such localization can also be obtained by collimating both the source and the detector to define a small inspection volume, or by utilizing the unique energy-angle relationship of Compton scattering, Eq. (3.37), or that of neutron elastic-scattering, Eq. (3.80). Global inspection is also possible with scattering as it can cover a large volume (section 7.5), if no collimation of the source and detector is used. The lack of collimation enables more efficient use of a radiation source, since radiation collimation is an elimination process that reduces the amount of radiation emanating from the source or reaching the detector. Indeed, one can even argue that scattering is the “natural” way of inspection, since it is the process used by the naked eye to view objects by light reflection. However, a sophisticated interpretation process, provided by the brain in the case of the naked eye, is required to interpret scattering indications. Radiation is scattered from within the medium, unlike light which is reflected only off surfaces. This further complicates the interpretation process. The strength of the scattering signal is quite weak, resulting in a low signal-to-noise (S/N) ratio. On the other hand, the signal-to-background ratio (S/B) can be quite high. Theoretically the S/B ratio for scattering has no limit; if the background signal is brought to zero, S/B for scattering approaches infinity. This enables scattering techniques to provide better material contrast. Scattering also provides three-dimensional information, unlike the two-dimensional (geometric projection) nature of transmission. Emission. The third indication modality is that of secondary emissions, i.e., the emission of radiation which is different in type from that of the source. This is a powerful method for elemental identification, since such emission can be characteristic of the elements involved (chapter 8). However, producing such emissions usually requires an intense radiation source, or a long exposure time, to produce an acceptable signal-to-noise (S/N) ratio. The intensity of emitted radiation is also affected by the distribution of the primary radiation, which in turn is


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affected by the nature of the interrogated medium. This can make the interpretation of the emitted signal quite difficult, not only in terms of intensity due to the distribution of the primary radiation within the medium, but also by the change in energy of the emitted radiation by scattering within the medium. The signal-to-background ratio (S/B) for secondary emissions can be quite high; approaching infinity since in the absence of the element (s) giving rise to secondary radiation no emission occurs. Therefore, the selectivity, contrast to element(s) of interest, can be quite high. However, activation of elements in surroundings can add to the background signal. Also, interference between elements that give similar emissions can be a problem. In some cases, the detector used may be sensitive to both the primary and secondary radiation, which further complicates the signal analysis process. The primary radiation may also damage the detector of the secondary radiation. Natural radiation emission, or emission from radioactive materials, eliminates the need for primary radiation. However, attention should be paid to the fact that the distribution of the emitting material in a medium also affects the indication signal. Absorption. The absorption indication process, which can be monitored in a variety of ways, as discussed in chapter 9, is mainly useful when interrogating materials that have affinity to absorbing a certain type of radiation. The absorption indication is similar to that of transmission, since both rely on detecting the removal of radiation from the incident radiation. Indeed, transmission techniques are sometimes referred to as absorption techniques. The distinction made here between the two methods is that transmission monitors the signal “transmitted” from the source to detector within a well-defined path through the object. On the other hand, absorption monitors the removal of incident radiation from anywhere the radiation source reaches, including that of scattered radiation. Combined Indications. The use of one type of indication is not exclusive of others. For instance, along with transmission, one can measure the scattered radiation, or even the emitted radiation, since the detectors needed for these techniques do not have to reside at the same location as the transmission detector (s).

14.6. Detection System 14.6.1. Detector Selection As chapter 4 showed, a wide variety of detectors are available for various types of radiation. The choice of a detector for a given application is

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often dictated by the radiation type and energy, and whether a measurement requires a detector with energy-resolution capability. Obviously a high detection efficiency is desirable, but the energy resolution provided by such an efficient detector may not be sufficiently good for the application at hand. A compromise has then to be made between efficiency and resolution. It is advisable to test in the laboratory the operational properties of selected detectors, since those reported by manufacturers are often performed using certain electronic equipment and settings that may not be necessarily identical to those in a different laboratory. Detectors and associated electronics may drift in their settings, and may be affected by field conditions such as heat and moisture. Therefore, routine performance checks should also be conducted to ensure the accuracy and reliability of measurements. In addition to these basic factors, practical specifications such as size, weight, ruggedness, and whether the detector is hygroscopic, and even cost, can be as important as radiation-detection properties. The response of some detectors may also vary with temperature, while some may require special cooling arrangements. In applications where the count rate is high, or the those that require a fast response-time, the detector’s decay time is important as it determines the time beyond which the detector is ready to receive a new signal. If such time is not sufficiently large, signal pile-up will occur, leading to underestimation of the actual count rate. In scintillator detectors, the detector may continue to emit light after the termination of radiation signal, causing an “afterglow” problem that may be problematic in applications with high sampling rate.

14.6.2.

Electronics

The designer of a radiation-device has a variety of electronic systems to chose from, depending on the needs of the devised system, as discussed in section 4.5. The designer may also be involved in providing the specifications required for the miniaturization of electronics for field use. In experimental testing of a developed device, one almost always is faced with the task of selecting the proper settings for various components of the electronics system, such as the pulse shaping-time, the amplification level, the lower window for discriminating against electronic noise, etc. Problems such as pile-up of signals, dead-time losses and signal timewalk may also be encountered. Section 4.5 provides some guidance on dealing with such problems, but the user’s experience and familiarity with the system is crucial in selecting such parameters.


14.6.3.

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Detector Collimation

In some applications, detector collimation may be necessary to confine the field-of-view of a detector to a certain direction or region in the inspected object. The principles discussed in section 15.1 for source collimation are equally applicable to detector collimation, except that the detector is placed at the receiving end of the collimator, rather than at its entrance as is the case with source collimation. Therefore, a collimator converging in geometry towards the detector is preferable as it allows radiation to reach the detector without colliding with the walls of the collimator (hence losing energy). A converging collimator also confines the exposed surface of the detector to a small area, see for example references [209] and [230]. Slit and Pinhole. When it is possible to cut-off radiation with a thin material, as in the case of charged-particles and photons, slit and pinhole collimators can be used. These collimators are of a very small length, L, thus they do not provide much collimation in terms of direction, but they can control the projection of radiation on a detection (or imaging) plane, as shown in Figure 14.1. As the same Figure shows, the sides of a slit collimator are parallel, while the pinned nature of a pin-hole collimator enables it to receive and deposit radiation over a wider fieldof-view. Nevertheless, the two collimators are quite similar and their names are often used interchangeably. With low-energy radiation, a slit collimator can be also used. This is simply a narrow slit in a thin plate through which radiation can pass. Also similar to the Soller source collimator discussed in section 15.1.2, a multi-slit collimator can be used. This type of collimator is known as slat collimator [158], and allows the detection of well-collimated radiation arising from the object at adjacent locations. Such a collimator is, therefore, useful in systems requiring precise directional information, as in the case of transmission-computed tomography discussed in section 6.4. Magnifying and Minifying. To decrease the divergence of radiation, a long collimator must be used, as is the case with source collimation discussed in section 15.1. A a narrow hole drilled in to the collimator’s material will provide a pencil-beam collimator. The collimator’s length should be such that only radiation incident on the hole in a direction perpendicular to its cross-section will pass through. When the holes are all parallel to each other, the collimator is called a parallel-hole collimator. The collimator hole can be shaped as a cylindrical, or a rectangular duct to provide a pencil-beam collimator. A collimator that converges towards the source of radiation (arising from the object) can

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be also be used, to reduce the size (“minify ”) radiation projection on the recording medium. Alternatively a diverging collimator can be employed to magnify the projections [158], see Figure 14.2.


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Foucsed. A collimator with many holes is called a multibore collimator. Such a multihole collimator system can also be utilized to provide multiple individual projections. When a multibore collimator consists of holes that converge towards the detector, it is called a focused collimator [158], as it minifies the projected radiation towards a small area on the detector. On the other hand, a magnifying multihole collimator can be used to increase the size of the projection of radiation on the detection plane.

Manufacturing. The material used for constructing source collimators, see section 15.1, can also be used for manufacturing detector collimators. However, usually a single source collimator is needed, unless the source is quite wide to enable the use of multiple collimators. Multiple adjacent collimators are, however, more often used with detectors, since large-size detectors and imaging plates are readily available. The manufacturing of such collimators can be difficult, particularly when using lead, but tungsten, steel, tin, aluminum, or even graphite are used; with the lighter material more suited for lower energy photons. Photon collimators are usually made of lead, but lead is a soft material that is difficult to machine, while casting lead does not usually produce precise collimators.

Reference [1213] reported an interesting method to fabricate a highresolution collimator with a large number of rectangular slots (49) for detectors employed in Compton scatter imaging (see section 7.6). The method involves first defining the volume to be left empty in the body of the collimator, i.e. the volume that constitutes the shape of the collimated radiation, with carbon-epoxy strips, manufactured one-by-one by polymerization under press between two plane plates. The manufactured strips were then held in place by wedging them at each end into holes precisely machined (with a laser beam) into epoxy-resign plates. The two support plates and the carbon-epoxy strips formed a mould, within which tungsten powder impregnated with epoxy resign, was slowly lowered, while vibrating it to ensue high-density of powder, achieving a density close to that of lead. The strips were then removed by expanding the mold by warming it up, allowing easy removal of the strips. Another method for manufacturing precise collimators was reported in reference [1214]. The method involves the use of foam sheets, thin film adhesive, along with lead foils (with 2% antimony and 0.5% tin), stacked together to form one-dimensional parallel and converging slice collimators.

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Energy Discrimination. Detector collimation may also be provided by energy discrimination when possible. This “soft” (or electronic) collimation process is possible when monitoring monoenergetic radiation. The fact that radiation did not change energy from its point of origin to the detector is an indication that no interactions have taken place, thus this energy defines the path of radiation from its origin to the detector. This concept of collimation can also take advantage of the unique relationship between energy and angle of elastic scattering of neutrons, Eq. (3.80), or Compton scattered photons, Eq. (3.37), in single collisions of monoenergetic radiation, see for example references [228] and [230]. Attention should be paid, however, to the fact that a detector is not a point, and the energy recorded at a detector may correspond to more than one point of scattering [210]. Coincidence measurement of positron annihilation radiation is also a form of “soft” collimation, since the emitted photons have a unique (511 keV) energy that when monitored in coincidence at two opposite directions define the location of emission. This is the process used in positron emission tomography, see section 8.8.3. Crosstalk. In the simultaneous collimation of array of detectors, aligned next to each other, attention should be paid to the “crosstalk” between detectors, i.e. the effect of radiation scattered by the collimators of adjacent detectors, or by the other detectors themselves. Care should by taken in constructing such collimators so that they are aligned properly with respect to each other and to the detectors.

Although collimators are usually used to confine the field-of-view of the detector to within a particular direction, a collimator also acts as a detector shield that minimizes exposure to background radiation, or radiation from outside the area of interest. Thus detector collimation increases the signal-to-back ground (S/B) ratio. However, at the same time, the strength of the detected signal is much weaker for a collimated radiation than the case if the detector were not collimated. Therefore, detector collimation decreases the signal-to-noise (S/N) ratio, as the detected signal becomes more vulnerable to noise effects.

14.6.4.

Filtration

As in the case of sources, see section 15.2, it is often desirable to filter a certain range of energy of radiation reaching a detector. With an energysensitive detector, this can be achieved electronically by discarding the portion of the detector’s pulse-height corresponding to the unwanted range of energy. This can also be performed numerically after digitally


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collecting the pulse-height spectrum. It is sometimes, however, desirable to physically filter some of the radiation reaching the detector. Detector filtering is useful, for example, in removing an undesirable component that overwhelms the energy response of the detector. Filtering can also enable the use of detectors that do not have good energy resolution, since such detectors offer higher counting efficiency and are less expensive. All source-filtering methods discussed in section 15.2 are also suitable for filtering detectors, since radiation reaching a detector can be viewed in NDE as an “indirect source” of radiation, modified by the inspected object.


Chapter 15 SOURCE MODULATION

Commonly available sources can be modulated in direction, energy, or intensity, to better suit the designer’s needs. The reader is reminded here that energy refers to the energy of a single radiation entity (a neutron, a photon, or a charged-particle), while intensity refers to the number of entities emitted per unit time. Section 15.1 discusses the design of source collimators to confine incident radiation to a particular direction. Section 15.2 shows how filters can be used to either confine radiation energy to a certain range or cutoff unwanted portion of a source’s energy spectrum. Methods to alter the energy of neutrons by slowing them down (moderation) are discussed in section 15.3, while multiplication of neutrons to increase their intensity is discussed in section 15.4.

15.1. Source Collimation 15.1.1. Design Parameters Due to the corpuscular nature of atomic/nuclear radiation, at most of its practical energy range, radiation collimation is performed by elimination, i.e. removing radiation from a source by absorption or scattering. Thus collimation is in effect not the most effective way of utilizing a radiation source, since a significant portion of the radiation emitted from the source is lost in the collimation process. A non-collimated source also provides a wider area of exposure to radiation, but that comes at the expense of loss of localization of indication, a desirable feature in probing and imaging. The lack of collimation also results in an increased background, as the source radiation may directly reach the detector and is scattered by the surroundings. Confining a radiation source into a 681

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beam localizes object’s exposure (radiation field) and results in a significant reduction in radiation background, but that comes at the expense of reduced source utilization. Since radiation collimation is provided by elimination, a collimator is a constructed by creating a cavity within a block of material. The size of the block (shielding) material has to be such that sufficient material is provided in all directions to block the passage of unwanted radiation. Therefore, shielding principles can be used to determine the dimensions of the collimator’s body, see section 16.3. However, as shown in this section, there are many factors that affect the design of a collimator. Therefore, numerical simulations and/or experiments should be used to confirm that the design of a collimator meets expectations. Monte Carlo simulations, see section 16.2, are best suited for this purpose, as the method can easily accommodate the collimator geometry and can provide rich information, without extensive experimentation. The characteristics of an ideal collimator are: Spatial distribution: uniform profile across the field of exposure, with a sharp decrease in density at the edges of the field. Energy: the energy distribution of collimated radiation should be identical to that of the source, such that only uncollided radiation should pass through the collimator. Direction: the direction of the emitted radiation should be identical, or nearly identical, to the geometric shape of the collimator’s port (cavity).

A number of parameters needs to be taken into account when designing a collimator. These parameters are: Geometric parameters: (Figure 15.1) source size, distance between source and collimator entrance, collimator length, L, size of collimator’s aperture, D, size of the field of exposure, W and distance from collimator’s exit to the irradiated object, Collimator shape: parallel, converging, diverging, multistaged (sequential combination of shapes), see Figure 15.2. Radiation type and energy: which determines the nature of the material from which the collimator’s body is manufactured.

The above parameters are discussed in this following sections.

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15.1.2.

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Geometry

The size and shape of a collimator port depends on factors such as the source size, the desirable field size of radiation on the surface of an object, and the proximity of the source and object to the collimator’s ends. Source size is either the physical size of an isotopic source or the size of the target bombarded by accelerated charged-particles in an acceleratorbased generator or an x-ray machine. The source size introduces a penumbra effect as shown in Figure 15.1, where the width of the collimated incident beam increases from W to due to the source size, s. The penumbra effect creates an extended region at the edges of the beam and the penumprofile, as Figure 15.1 shows. As bra effect disappears. The source intensity in the penumbra’s zone, i.e. beyond W, tends to taper off gradually, while within W the source’s intensity tends to be reasonably uniform, as sketched in Figure 15.1. For this reason, it is desirable to have the smallest possible source size. From the geometry of Figure 15.1, one can show that:

and

Eq. (15.2) indicates that the penumbra effect is reduced, i.e. when the source is small in size is small). For a fixed source size, the penumbra effect can be reduced by bringing the object as close as possible to the collimator’s exit (small value of by increasing the collimator length, L, and/or by increasing the distance from the source to

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the entrance of the collimator, or a combination of the these parameters. Note, however, that increasing L and/or comes at the expense of reduced intensity on the surface, due to radiation divergence, see section (3.6.2). Eq. (15.1) indicates that the size of the radiation field at the object, W, depends directly, as expected, on the size of the collimators aperture at the exit, D, and can be increased by reducing L and/or and increasing Note that the above analysis is applied in one plane (cross-section) of the collimator, but the same principles are applicable to any cross-section of the collimator. Typically, however, the dimensions determined for one plane apply to all other planes to provide a symmetric collimator. The field size, W, is determined by the size of an object, for full exposure, or by the size of the area to be projected on the object. Therefore, according to Eq. (15.1), the designer can control the values of L, and for a given source size to achieve the desired value of D. The values of D and L are typically related to each other by the collimator lengthto-diameter ratio, as discussed below. The value of and should be as close as possible to zero to minimize the effect of radiation divergence. Practical considerations typically dictate the values of and i.e. how close the source and the object can be brought to the proximity of the collimator’s openings at both its ends. It may, however, be advantages in some cases to increase the value of to decrease the amount of radiation scattered from the detector towards the desired field of exposure. If the source size is large, the size of the radiation field reaching an object can be confined to a small area by reducing the size of the collimator aperture, D, or by increasing the collimator length, L, as Eq. (15.1) indicates. The radiation source can also be placed away from the collimator entrance, to increase the value of in Eq. (15.1), but that can result in increased radiation background due to the spread of the radiation away from the collimator. However, the decrease in D and the increase in a both result in a reduction in the fraction of source particles utilized in collimation, while the increase in L and result in decreased intensity by divergence. Alternatively, a converging collimator can be utilized, as shown in Figure 15.2, to confine the radiation field reaching the object into a small area. Such a collimator can also act as a partial shielding for the source, if the thickness of the collimator is sufficiently large. An ideally collimated beam of radiation consists of parallel rays. However, since radiation diverges with distance, a perfectly collimated beam is impossible to obtain. Collimation, therefore, results in a cone-shaped beam. However, the magnitude of divergence of that cone can be reduced to such a small value that the radiation emerging from the collimator becomes for all practical purposes a parallel beam. The degree of di-

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vergence is measured by the cone’s half-angle which, as can be concluded from Figure 15.1, is the angle of deviation from the central axis of the radiation emerging at the exit of the collimator, when and are all set to zero. The smaller this angle, the closer the emerging beam to being perfectly collimated. This is obviously archived by reducing the collimator’s diameter-to-length ratio. Since this ratio is typically quite small in value, the inverse of this ratio, is often used as a measure of the degree of collimation, with when the beam is perfectly collimated. Note that moving an object away from a collimator, i.e. increasing will lead to a smaller divergence angle. Therefore, often replaces L in the ratio calculations. In the radiography, the distance is taken as the distance from the film to the collimator’s exit [928]. For a short collimator, the angle is called the acceptance angle, since for a point source placed at the entrance at the exit of the collimator defines of the collimator the angle within which radiation is not eliminated by collimation. Shape. The parallel-collimator geometry of Figure 15.1 can be provided with a right-circular cylindrical hole, or a rectangular parallelepiped port in the collimator’s body. However, this parallel geometry can be replaced with a tapered collimator geometry to provide a coneshaped beam, or a fan-beam (a fan-shaped slit). The collimator can take the shape of a diverging (from the source) or converging (towards the object) cone, as shown schematically in Figure 15.2. The tapering geometry of the collimator usually follows the principles of geometric optics. A conical collimator diverging linearly from the source follows more naturally the path of emitted radiation, thus is generally preferred over a uniformly tapered or a converging conical beam [1215], as it produces a more uniform beam and has a reduced penumbra effect. However, a converging collimator is more suited for confining radiation emitted from a large source into a small area on the surface of the object. Radiation scattering on the interior walls of a converging collimator has also a lower chance of reaching the object than in the case of a uniformly tapered, or a diverging, collimator. When it is possible to completely eliminate incident radiation with a thin layer of material, as in the case of charged-particles, and lowenergy photons and neutrons, slit collimators can be used. A number of adjacent slits can provide a wide-beam of collimated radiation, consisting of many narrow individual beams. One common configuration is known as the Soller collimator, named after Soller who introduced this slittype collimator for use in x-ray experiments [1216]. This collimator consists of a number of thin sheets compiled together to form a set of

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long, narrow, rectangular cavities. Radiation can only pass through such slits, with each slit providing a narrow beam of radiation. This type of collimator is obviously useful when a thin sheet of material is sufficient to absorb diverging radiation and radiation scattered off the walls of the slits. Thus metal sheets are used for charged-particle and low-energy photons. For thermal and cold neutrons, metal (aluminum, steel or brass) sheets, coated with a neutron absorbing material such as cadmium, are used, but Mylar blades coated with gadolinia bearing paint are also utilized [1217].

15.1.3.

Beam Profile

The quality of collimation is affected by four factors: (1) the penumbra effect discussed above, (2) the natural diverging nature of radiation, (3) direct radiation leakage through the collimator’s material, and (4) radiation scattering off the internal walls off the collimator’s port. The intensity of radiation exiting a collimator (i.e. the beam profile) is governed by the law of divergence, discussed in section 3.6.2. If a collimator is short, the distance from a source (or its center) to an edge at the exit of the collimator can be considerably larger than that from the center of the source to the center of the collimator’s exit. This produces a significant reduction in beam intensity at the edges of the collimated beam, in comparison to its center. The result is a nonuniform beam intensity distribution. For a longer collimator, the relative change in distance, and consequently intensity, between the center and the edges of the beam is much smaller, producing a more uniform beam. Using

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a long collimator, however, reduces the beam intensity as the distance of divergence increases. If the length (and consequently the attenuating thickness of the collimator’s material) is not sufficiently large, the source radiation will penetrate the collimator’s material producing radiation at the edges of the collimated beam. This will distort the beam profile. Radiation reflected off the walls of the collimator can also add to the distortion of beam uniformity. However, the more significant effect of scattering is the lowering of the mean energy of the collimated radiation. The scattered radiation is lower in energy than the source radiation and can reach all points of the beam profile, contaminating the collimated radiation with lower-energy radiation. If for some reason a non-uniform beam profile is not needed, for example to block exposure of radiation to a particular region of the object, the shape of the beam profile can be altered by placing a suitably shaped block of a radiation-absorbing material, (also called a compensator) in the field-of-view of the beam. The purpose of a compensator is to remove some radiation from beam regions where radiation flux is unwanted. Such compensators are widely used in radiotherapy to shape beams to protect vulnerable organs and to compensate for the non-uniformity of the body. Compensators are typically made of strong radiation-absorbing materials, and for fast-neutrons (where no strong absorbers exist) aluminum can be used as it has a good fast-neutron removal cross-section [1218].

15.1.4.

Divergence and Alignment

After constructing a collimator, it is important to ensure that it is properly installed. That is, the source, object and detection system are aligned together. It is also desirable to measure the degree of convergence, i.e. the acceptance angle, to ensure that the collimator is operating as designed. Although the length-to-diameter, ratio can be directly measured, such measurement does not ensure the straightness and alignment of the collimator. A standard method is available for determining the ratio for collimators and for testing for alignment in neutron radiography [1219]. The method relies on observing and analyzing the radiographs of a test object centered at different planes perpendicular to the axis of the beam. A well-aligned beam will maintain the same object geometry at various planes. From the size of the image at different planes, the degree of beam divergence can be calculated. A misaligned beam will produce skewed object images. The approach can be used whenever it is possible to record a radiographic image of the source radiation. Reference [1220] presented an extension of this standard method that also allows the determination of the centerline of the

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beam by monitoring the position of a radiation-absorbing wire on the image.

15.1.5.

Collimation of Charged-Particles

Collimation of charged-particles is relatively easy due to their short range. Thus, a small thickness of a material can completely absorb the source radiation. Therefore, a collimator can be designed by simply containing the source in a container within which a hole in created in the shape of the desired collimator, e.g. a narrow cylinder for a pencil beam. The electric charge of the particles also enables the application of an electric field to direct the charged-particles towards a particular direction. This is the process used in particle-accelerators to drive charged-particles towards the target.

15.1.6.

Photon Collimation

Lead is usually used in fabricating photon-collimators due to its high density and high atomic-number, which gives it a large total crosssection, particularly for photon absorption, see section 3.4. Lead, however, is a soft metal that is difficult to fabricate, while castings is also difficult particularly for accurate and small-aperture collimators. Therefore, steel inserts are usually used to define the domain of a beam port. Even then, ensuring alignment and straightness of these inserts is difficult to achieve. Although tungsten is easier to fabricate, it is an expensive metal. The use of metal makes it also possible to design flexible collimators, that is collimators that provide a varying field-of-view. Although, such collimators are mainly used in radiotherapy to control a patient’s exposure to radiation, they can also be useful in industrial applications requiring a varying field size. A varying-field collimator can be made of a set of adjustable radiation-opaque interleaved vanes, and is known as a multileaf collimator. This collimator can open and close, with the aid of a motor to regulate a collimator’s aperture and its tapering angle. Design aspects of such collimator for medical applications are reported in references [1221], [1222], [1223], [1224], and [1225]. Although a photon collimator-material, such as lead or tungsten, are good attenuators of photons, they also scatter radiation. Scattered radiation can reach the field of exposure, reducing in effect its effective energy since the scattered photons have a lower energy than the source radiation. Section 15.1.7 discusses ways to reduce the effect of scattered fast-neutrons. Some of these measures are also applicable to photons.

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15.1.7.

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Fast-Neutron Collimation

Collimation of fast-neutrons is not as straightforward as photon collimation, since there are no materials that can completely absorb neutrons, to enable their confinement in a particular shape or direction. Nevertheless, some general methodologies have emerged, arising from the design of neutron radiography devices [1226, 1227] and the earlier use of 14 MeV neutrons in radiotherapy, [1215, 1228, 1229, 1230, 1231, 1232, 1233]. These aspects are summarized below. Due to the lack of a perfect material for fully absorbing fast-neutrons, many neutrons tend to re-emerge from the walls of a collimator. Some of these re-merging neutrons can scatter towards the area of exposure projected by the collimator on the object. Scattering from the collimator walls also produces slow-neutrons (due to collisions within the body of the collimator) that can alter the energy of the extracted neutron beam. This lowers the quality of the extracted beam, which should have the same energy distribution as that of the source. Therefore, the design of a fast-neutron collimator requires paying attention to the collimator as both an eliminator of neutrons and as a scatterer. The design aspects used in other types of radiation are still applicable to the design of a fastneutron collimator, but special attention have to paid to the contribution of neutron scattering by the collimator’s walls. Since there is no effective material for absorbing fast-neutrons, eliminating fast-neutrons can involve the use of neutron moderating materials (see section 15.3), which are used to slow-down neutrons to about the thermal-energy where they are readily absorbed. However, moderating materials are also good scattering materials, as they slow-down by neutron collisions. Scattering associated with these collisions can deteriorate significantly the quality of the beam profile in terms of energy. Therefore, metals are found to be more suitable as collimator material, if the energy-quality of the beam is of a prime importance. Neutrons scattered off the interior walls of a collimator tend to have encountered no more than one collision, and thus would not have lost much energy if scattered by a metal, see Eq. (3.80). It is preferable to use a dense metal to provide a large number of interactions within a small volume, to reduce the size of the collimator’s material. Thus, iron and tungsten are preferred as collimator materials. Lead, although highly dense, is not employed due to its lower neutron cross-section; but it may be used, as a liner of the walls of the collimator’s port, and at the latter stage of the collimator, to provide shielding against any gamma-rays that may have been produced within the collimator’s material by neutron activation. Even with iron and tungsten, a large thickness of metal is required to provide complete elimination of source neutrons, making the collimator length quite large

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(from 0.4 to 0.6 m for 14 MeV neutrons). This increases considerably the weight of the collimator, making it difficult to design interleaved collimators to provide continuously variable field sizes, as in the case of photons. However, reference [1233] presented a variable fast-neutron collimator system, consisting of sets of jaws mounted on non-concentric circular rails that allow movement of the jaws to control the degree of tapering of the collimator. A a computer-controlled multileaf collimator for fast-neutrons has also been recently reported [1234]. Although tungsten is more expensive than iron, it does not leave behind residual activity. The activation of iron by fast-neutrons is via The reaction product, is a gammathe reaction emitter with a half-life of 2.58 hours. This can leave residual radiation for hours following the termination of neutron production with an accelerator, causing some radiological-protection and material handling problems. On the other hand, tungsten has a low activation cross-sections for fast-neutrons. The high cost of tungsten, and the difficulties associated with its fabrication, rule it out in many cases as a suitable collimator material. With an iron collimator, lead can be used, as explained above, to attenuate the gamma-rays produced in the collimator’s material. Scattered neutrons affect the profile of the extracted beam by creating of wide tail (penumbra) at its edge. Scattering from the collimator’s walls is affected by the geometric parameters shown in Figure 15.1, as well as by collimator’s material and the source energy. As the distance, between the source and the collimator’s entrance decreases, the solidangle subtended by the walls of the collimator at the source increases. This, leads to increased neutron scattering near the inner walls of the collimator. However, practical limitations often put restrictions on the distance from the source to the target. Although it is desirable to increase this distance, to reduce scattering, a very large distance decreases also the intensity of neutrons extracted from a collimator, due to the divergence effect. Also a long distance can make it difficult to align the collimator with the source. Moreover, source neutrons that do not reach the collimator’s entrance will scatter in the surroundings, requiring additional biological shielding or radiation protection precautions. A longer collimator, larger value of L, provides more opportunity for source neutrons to scatter from the walls. While a shorter collimator length reduces scattering, it can increase neutron leakage longitudinally through the shielding material, defying the collimator’s main function as a neutron eliminator. The larger the required field-size, W, the larger will be the size of the aperture, D, at the collimator’s exit, as Eq. (15.1) indicates, and the higher the chance that scattered neutrons will reach the object. The

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field size is determined by the area of the object that needs to be exposed to neutrons. To reduce scattering, this area should to be as small as possible. The uniformity of the beam profile is easier to attain if the field size is small, since the effect of radiation divergence on the beam profile would not be very strong. However, a small-area results also in an ineffective utilization of the source neutrons, as most of the source particles would have been lost in the collimation process. A small exposure area may also necessitate multiple scans of the object to cover a wider area. As the target is moved away from the collimator’s exit, (large value of a smaller number of the scattered neutrons will be able to reach the target, since scattered neutrons emerge from the collimator at various angles and diverge away from the target. By applying the divergence law (see section 3.6.2), one can conclude that the amount of scattered neutrons in the beam at the target locations decreases as increases. However, moving the object far away from the source reduces as well the intensity of collimated (uncollided) neutrons, due to the same divergence effect. The effect of scattering can be reduced by shaping a collimator so that the amount of scattered radiation reaching the object is reduced. This can be achieved by the use of a secondary collimator placed closer to the source and tapered so that neutrons scattered by this collimator do not directly reach the walls of the second (primary) collimator, without passing through the collimator’s body. This is best achieved by the use of a combination of converging/diverging collimators [1230, 1232], as shown in see Figure 15.3. Neutrons suffering collisions in the walls of the secondary collimator will themselves be collimated to some degree. The widening of the aperture of the primary collimator enables scattered neutrons in the other collimator to leave the collimator without further collisions in the walls of the primary collimator. Even though these neutrons may reach the object, their higher energy (due to the elimination of additional collisions) and their divergence over the length of the primary collimator reduces their effect on the overall quality of the beam profile. This dual-stage collimator increases the total length of the collimator, reducing the intensity of particles at the collimator’s exit, by radiation divergence. In addition, the use of the converging collimator near the source reduces the thickness of shielding material for a certain solid angle, resulting in increased leakage. The collimator’s material and source energy also affect the scattering cross-section, and consequently determine the amount of scattering in the collimator and the energy of the scattered neutrons. Therefore, for instance, a fast-neutron collimator designed for a neutron source

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will not be suitable for use with a 14 MeV neutron generator. As mentioned earlier, both iron and tungsten are good fast-neutron attenuators. One of their advantage is that they both have an angular scattering cross-section for fast-neutrons that peaks in the forward direction. This encourages neutrons incident on the inner sides of the collimator to scatter forward towards the sides of the collimator away from its aperture, which in turn reduces the magnitude of the scattering component at the exit of the collimator. The inclusion of a second-stage collimator (following the primary collimator) made of a hydrogenous material, such as polyethylene, can further slow-down, and consequently absorb, the neutrons scattered from the metal of the collimator [1228]. A further third-stage collimator made of lead can absorb the 2.223 MeV gamma radiation produced by neutron activation of the hydrogenous material, as well as function as a beam trimmer to decrease the penumbra. However, that additional second stage will scatter low-energy neutrons towards the object, and worsen the beam’s quality be reducing its mean neutron energy.

15.1.8.

Collimation of Thermal-Neutrons

Slow-neutrons can readily be eliminated using an absorbing material, such as lithium, boron, cadmium or gadolinium. Cadmium is often used as it is readily available in malleable metallic sheets and it has a well-defined cut-off energy of 0.5 eV. The absorption cross-section of

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cadmium increases from a few barns at above 0.5 eV to 7500 b at 0.5 eV, and remain high throughout the thermal-energy range, see Figure 3.6. Therefore, layers of cadmium as thin as 0.5 mm are very effective in removing neutrons below 0.5 eV. Since, there are no readily available sources for thermal-neutrons, these neutrons are produced by the moderation of fast-neutrons, as discussed in section 15.3. Containment moderation, discussed in section 15.3.2, lends itself to neutron collimation, as a large thermalneutron population is generated within the container and can be extracted through a beam port. Therefore, the discussion on thermalneutron collimation focuses here on collimating containment-moderated thermal-neutrons, although collimators can also be used to confine the field-of-view of neutrons slowed-slown by the other two methods of moderation (blockage and reflection) discussed in section 15.3. Beam extraction from a moderating assembly is achieved by creating a beam hole within the assembly to allow neutrons to escape, as schematically shown in Figure 15.4. If the moderating material is made of a liquid (light or heavy water), or a soft hydrocarbon material (paraffin or polyethylene), steel or aluminum can be used to shape the beam port and maintain its integrity. As for other types of collimators, using optical principles in shaping the collimator also helps its uniformity. That is, a diverging conical collimator tends to provide a more uniform beam profile than a converging one or a parallel beam. The aperture of the beam is usually defined by the desired size of the field. The length of the collimator can be extended all the way inside the assembly to where the source is positioned, but this can come at the expense of a high fast-neutron component within the beam. Since there is a number of good absorbing materials for thermalneutrons, such as cadmium, it is possible to reduce the beam’s penumbra by placing extended cadmium sheets at the collimator’s exit to eliminate neutrons directed towards the edges of the beam. The uniformity of the beam can also be improved by lining the inner walls of the collimator’s port with cadmium, or making the collimator walls using a hydrogenous material (such as polyethylene) loaded with a neutron absorbing material, such as boron or lithium. Thermal-neutron absorbing materials on one side of the collimator’s walls will absorb neutrons scattering towards it from the other side of the collimator. This reduces neutron scattering and the penumbra associated with it. In a large-size field, these neutron-absorbing materials can be used as beam compensators to shape the beam profile into any desired configuration. For good beam quality, the presence of both fast-neutrons and gammaradiation in the extracted beam should be minimized. Fast-neutrons

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may be present due to incomplete thermalization of the source’s neutrons, while gamma-radiation may be emitted directly from the source or may arise from the capture of thermal-neutrons in the moderator and/or collimator material. While fast-neutrons cannot be entirely eliminated, since no material can fully absorb them, the presence of fast-neutrons can be reduced by ensuring that some hydrogenous material is present in front of the source before the inlet of the collimator. This can be done by not extending, within the moderating assembly, the beam port all the way to the source location. This material between the source and the collimator’s entrance will provide a cushioning effect by slowing-down source neutrons and scattering them off in all directions before they enter the collimator. Since some neutron detectors are also sensitive to gamma radiation, it may also be desirable to reduce the gamma-ray content in the thermalneutron field. In this regard, the use of lithium on the collimator walls, to improved the uniformity of the thermal-neutron profile, is more preferable than boron. This is because neutron-absorption in boron results in the production of 0.48 MeV gamma-ray from the excited state of and cadmium neutron-capture arising from the reaction also has many lines of high-energy photons, while neutron capture by produces which is not a gamma-emitter. The gamma-field can also be reduced by placing a high-density metal with a low thermal-neutron absorption cross-section around the collimator and in the path of the neutron beam to remove the gamma-radiation while allowing neutrons to path through. Both lead and bismuth are preferred in this regard than

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aluminum and steel. Although aluminum is less absorbing of thermalneutrons than iron, it is still 15 times more absorbing than bismuth, and 2.5 times more absorbing than lead [28].

15.2. 15.2.1.

Filtering X-Rays

X-ray filtering aims at either producing monoenergetic photons from an x-ray source, or eliminating the low-energy tail of the x-ray spectrum to increase the effective energy of emitted photons. One way to produce a monoenergetic beam of photons is to use an x-ray machine equipped with a secondary target that emits characteristic fluorescence x-rays, see section 2.2.2.2. However, filtering can also be used for this purpose. Different methods of filtering are discussed below.

15.2.1.1

Balanced Filters Balanced filters aim at isolating characteristic radiation from the rest of the continuous spectrum of an x-ray machine, see section 2.2.1. Such a peak can be isolated by applying two materials with absorption (K) edges in their photoabsorption-cross section just below and just above the energy range of of the x-ray target, where the photon flux peaks. The photoabsorption cross-section decreases with energy, in accordance to Eq. (3.30), until it reaches the K-edge (i.e. the energy equivalent to the K-shell of the electron in the atom), where it increases sharply, then drops again according to relationship (3.30) following the absorption edge, see Figure 8.2. Consequently, the amount of radiation transmitted through a filter will increase continuously with energy until it reaches an energy equal to the K-edge of the filter, where it abruptly drops to a very low value, after which it increases again with energy. Therefore, if two filters are chosen so that the difference in their transmission is maximized at their K-edge energies, and minimized everywhere else, maximum transmission will occur at the energy range around the characteristic K edge of the target of the x-ray machine. This condition of maximizing the difference is mathematically expressed with the aid of Eq. (6.1) as, For

which requires that

maximize:

and leads to:


696

where the subscripts 1 and 2 refer to the two filters, is the source is the intensity of radiation transintensity at the K-edge energy, mitted through the filters, is the value of the total cross-section at is the thickness values the K-edge energy, is the filter thickness and at maximum difference of transmission between the two filters. The other desirable feature of no-photon transmission outside the energy band defined by the K-edges can be expressed mathematically as: For

which leads to, where is the source intensity at energy indicates that the integral is performed outside the energy range defined by is some effective-energy, the K-edge cross-sections of the filters, and see appendix F, that reduces the integrals in Eq. (15.5) into equivalent simple exponential terms. Obviously, the optimum conditions of relationships (15.3) and (15.5) cannot be attained simultaneously, since the first condition requires that both filters have the same thickness, while the latter condition requires different values. Nevertheless, near-optimum conditions can be obtained by selecting near-optimum thickness values. Then if an energy spectrum, is collected with the first filter, and a spectrum is measured in the presence of second filter (in place of the first filter), the difference should be maximum at photon energy between and minimum everywhere else. Therefore, this filter requires and balancing the source at all energies expect within the desired energy band, hence the name “balanced filter”. For commonly used x-ray machines employing tungsten, the energies lie in the range from 59.31 to 57.97 keV, providing in effect a peak at about 59.5 MeV. Then yttrium, with a K-absorption edge at 61.30 eV, or thulium with a K-edge at 59.33 keV, can be used for one filter to define an upper energy-bound of the filter window, while erbium, K-edge at 57.48 keV, can define the lower energy window [1235].

15.2.1.2

Difference Filters

The balanced filter discussed in section 15.2.1.1 relies on the abrupt change in the attenuation-coefficient which occurs around an energy corresponding to the K edge of the filter material, thus it cannot be used at

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energies higher than about The difference filter overcomes this hurdle by using two filter materials that are equally absorbing of photons up to some cutoff energy but one is more absorbing than the other at where E is the photon energy. This is achieved by choosing filter materials that differ considerably in their photon-absorption cross-section at the energy that needs to be filtered out, and using the difference in the count rate recorded in the presence of each filter alone in front of the source of radiation. The fact that the photoelectric effect for uranium dominates over other reactions, even at 500 keV, makes it a suitable filter for isolating the 511 keV photon energy associated with positron annihilation [736]. The other filter needs to be made of material dense enough to remove photons below typically a metal. If the two filters are designed so that they equally transmit photons at then the following condition must be satisfied:

where the exponential factors quantify the amount of attenuation provided by each filter, neglecting scattering, the number refers to the two is the total cross-section at and is the filter thickfilters and ness. The relative difference between counts of the two filters at 511 keV, can be expressed as:

where S(511) is the unfiltered count at 511 keV, and is the total cross-section at that energy. The left-hand-side of Eq. (15.8) represents the filter’s efficiency, i.e. the number of counts recorded by the difference filter versus the count obtained with an equally efficient energy resolving detector. Therefore,

Using Eqs. (15.7), (15.8) and (15.9), one can show that the optimum

conditions for maximum difference between the two filters occur when:

1

The largest K edge of all naturally occurring elements is that of uranium and is equal to 116 keV.

698


Reference [736] reported, for optimum foils thickness of 2 mm (uranium) for the first filter and 3.8 mm (tantalum) or 13 mm (silver) for the second filter, for maximum difference in counts at 511 keV. A difference filter can also be designed using foils made of the same material by reducing the counting time associated with the less absorbing detector. In this “same-material difference filter”, the counting periods of the two filters, and are chosen such that their integrated counts at are equal, that is:

where is the unfiltered count rate at and is the total crosssection of the filter material. Then, the relative difference in counts at can be expressed as:

Eq. (15.12) clearly shows that the larger the value of the greater the difference, Note that for optimum conditions, i.e. zero difference at the thickness of the second filter for a given value of must be determined using Eq. (15.11). With a uranium filter of thickness and a relative counting period of with in for a uranium metal 18.900 density, Eq. (15.11) gives a value of for the second uranium filter. Reference [736] numerically demonstrated that this unbalanced difference filter substantially increases the filter’s efficiency, i.e.

15.2.1.3

Cutoff Filters

It is often desirable to cut-off the low-energy tail of x-ray photons, to ‘harden’ the spectrum, i.e. increase its effective energy. The common way of achieving this is to place a thin layer of filter material in front of the source, or in some cases in front or the detector, or film in the case of radiography. Lead is used for this purpose. The thickness of the lead filter is in order of a mm, 0.25 mm for 150 kV x-rays, up to 1.5 mm for 1 MV x-rays [7]. These low-thickness values allow absorption of the lowenergy photons without much energy reduction, by Compton scattering in the filter, of higher-energy photons. Combinations of lead and tin, as well as of tungsten, holmium and neodymium, have been used.

Source Modulation

15.2.2.

699

Neutrons

Neutron filtering aims at either removing neutrons of a particular energy-range (absorption filter), or allowing neutrons of a certain energy range to pass through while damping the rest of the energy spectrum (a pass-through filter). Some of these filters are discussed below, based on their acting energy range.

15.2.2.1

Fast Neutrons

Fast neutrons are quite difficult to filter out since there is no material that can fully absorb high-energy neutrons. Nevertheless, there are some elements that have a strong influence on fast-neutrons. For instance, iron has the ability to reduce neutron energy by inelastic scattering down to about 0.845 MeV [176], at which inelastic scattering ceases to occur (cutoff energy of inelastic scattering). Therefore, iron can be used to shift the neutron energy of a fast-neutron source towards lower energies. An iron layer of about 100 to 120 mm in thickness is required for this purpose [24]. Bismuth is also used as a pass-through filter for neutrons while reducing the gamma radiation associated with neutron production. Bismuth is preferred over lead for removing the gamma radiation, associated with neutron production, because of its smaller neutron crosssection. Reference [1236] proposed the use of 100 mm of bismuth for neutrons extracted from a reactor. Silicon is particularly useful for filtering out fast-neutrons while allowing thermal-neutrons to pass through, as it has a low cross-section for slow neutrons but a reasonably high cross-section for fast-neutrons via the reaction [1237]. The strong dip in the neutron cross-section of oxygen at 2.37 MeV [176] can be used as a pass-through filter to produce neutrons at this energy [29, 1238]. However, because of the low density of oxygen, a large thickness is required, even when liquid oxygen is used. Moreover, is transformed to upon irradiation, presenting an explosive hazard [29].

15.2.2.2

Epithermal Neutrons

Absorbing. Epithermal neutrons are easier to filter out because of the resonances in the cross-section encountered in many elements in this neutron-energy range. Materials that exhibit high (kilobarn) resonances in their absorption cross-sections include indium, silver and rhodium; with filter energy ranges as listed in Table 15.1. In addition to the elements listed in Table 15.1, the following can be (125 eV), used as absorption filters: natural CsI (5.6 eV), (2.850 Kev) (335 eV, 1.098 keV, 2.335 keV), Cu (578 eV) and

700


where the energy in brackets is the dominant resonance energy [1239]. Reference [37] also listed Hf (1.10 eV), (1.06 eV), Ir (0.66 eV), Er (0.58 and 0.46 eV), Eu (0.39 eV) and as absorption filters. Many other elements with resonant absorption cross-sections can be utilized for filtering, as usually done in activation analysis, see section 8.1.3. Uranium has also four, strong and well defined, resonances, at 6.671, 20.872, 36.680 and 66.020 eV that can be used for filtering [72]. For example, reference [1240] reported the use of tungsten and sodium as filters to reduce the interference of these two elements in the activation analysis of geological samples. Absorbing filters can be used in inverse-filtering to obtain monoenergetic neutrons from a source of a wide energy spectrum. This is achieved by a filter-difference technique, where measurements are taken in the presence and in the absence of a filter, with the difference providing a net indication of the neutrons at the absorbing filter energy, or energies. Reflecting. In some applications, it is desirable to reflect back neutrons towards the inspected object. Nickel has a large (resonance) elastic scattering cross-section in the range of 3 to 30 keV, while titanium has these resonances in the range 10 to 30 keV. Thus, either element can be used as a filter that scatters back neutrons, while allowing higher energy neutrons to pass through [1241]. These same filters tend also to absorb low-energy neutrons. In effect, they act a filters that enhance the back reflection of neutrons in the 5 to 24 keV range. Moderating. Producing neutrons in the epithermal range (1 eV to 10 keV) necessitates the elimination of fast and thermal neutrons, and often as well the reduction of the gamma field. This requires the use of a moderating material with a slowing-down power that is not too high to fully thermalize neutrons emerging from a fast-neutron source, but

Source Modulation

701

with sufficient ability to moderate the neutrons to the epithermal range. (sapphire) is used as an enhancer of epithermalIn this regard, neutrons. Reference [1236] reported the use of 400 mm of this material to slow-down fast-neutrons from a reactor to the epithermal-energy, without increasing the intensity of thermal-neutrons. Fluorine is another attractive mild moderator. Fluorine has a relatively low thresholdenergy (116 keV) [27] for inelastic scattering, compared to other elements (typically about 1 MeV). Its inelastic scattering cross-section is also quite high, peaking to about 3 b at 2.7 MeV. This high inelastic cross-section, combined with the relatively high mass-number (10) makes a mild moderator that “softens” higher energy neutrons without slowing them down to the thermal energy. Reference [1242] suggested the use of fluorine in a compound or along with an iron pass-through filter, to enhance the production of neutrons in the epithermal-energy range. A combination of Al and F, in the form can also be used for this purpose [1243]. A composite material commercially known as FLUENTAL 2 combines the characteristics of the above materials. This is a mixture of (69%), Al (30%) and LiF (1%), and has a density of [1244]. The absence of hydrogen in this material reduces its moderating ability, while the presence of lithium facilitates the removal of any thermalneutrons without subsequent emission of gamma-rays. Lithium fluoride also lowers the porosity of the material, to achieve a higher density. The relatively high density of the material gives it also some gamma removal absorbs some of the epithermal-neutrons, due capacity. Note that nature of neutron absorption, where E is the neutron energy, to the see section 3.5.6.2. However, the amount of neutron absorption can be controlled by depleting the content of lithium. Resonance Pass-Through. Some nuclides exhibit localized minima in their elastic scattering cross-sections, called anti-resonances. These minima result from the interference of the s-waves of potential scattering, see section 3.5.6.2, and typically occur at energies below several hundred keV [29]. The minima allow selective transmission of neutrons at energies corresponding to these anti-resonances. The strong resonances that immediately follow these anti-resonance result in the removal of higherenergy neutrons. Iron is one of those elements, as it has a low scattering cross-section window at 24.3 keV, which makes it a suitable filter for producing a beam rich with neutrons at that energy [29, 1245, 1189]. 2

FLUENTAL is produced by VTT – Chemical Technology: (http://www.vtt.fi/ket /ket1 /bnct/fluental.htm, accessed Nov 2002).

702


Supplementing an iron filter with Al and S help reduce the content of higher energy neutrons without degrading the quality of the 24.3 keV neutrons [1245]. Scandium provides a similar effect at 2 keV and was used to produce 2 keV neutrons, from nuclear reactors [29, 1245, 1246]. However, windows at higher energies allow faster neutron to pass through the filter, but these higher-energy neutrons can be suppressed using a secondary filter. Reference [1246] pointed out that a joint filter consisting of Sc, of of and of Co is an effective filter for producing 2 keV neutrons with low high-energy content. Also, reference [1245] reported that adding Mg, Al, S, To, V, Cr, Fe and Co to a Sc primary filter improve the quality of 2 keV neutrons extracted from a reactor beam, Other pass-through filters include: (0.060 keV), (0.160 keV), (0.186 keV), (0.400 keV), (0.500 eV), (2.2 keV), (4.0 keV), (4.5 keV), (14 keV), (47 keV), (48 keV) and Si (55 keV and 144 keV ), where the energy in brackets is the resonance-energy at which filtered neutrons are obtained [29].

15.2.2.3

Thermal Neutrons

Absorbing. Thermal-neutrons can be easily removed using one of the many neutron absorbing elements, such as cadmium, boron, lithium, and dysprosium gadolinium, samarium, europium Neutron absorption by most of these filters results in the production of gamma rays, the intensity of which can be reduced using a bismuth filter [1247]. However, lithium does not produce such capture-gamma radiation, as it relies on the reaction with the reaction product being a beta (not a gamma) emitter. Cadmium offers a severe cutoff of neutrons below about 0.5 eV, unlike the other absorbers for which the neutrons absorption-cross section tends to decrease with energy in accordance to the relationship of section 3.5.6.2, where E is the neutron energy. This so-called cross-section, where is the neutron speed, reduces as well the intensity of epithermal-neutrons. An interesting flexible filtering unit for use in neutron radiography is presented in reference [1248]. It consisted of two symmetrically placed cylindrical lead diaphragms plated with cadmium. Half-cones were made inside these diaphragms, and by rotating them the beam diameter can be varied continuously. The unit was also equipped with Cd and In (see Table 15.1) filters that can be moved into the neutron beam to cut-off low-energy neutrons, when needed.

Source Modulation

703

Pass-Through. Silicon has a low cross-section of about 2.3 b up to the resonance range in the keV range [27] where it significantly increases. Bi and Pb exhibit a similar behavior. Therefore, these elements can be used as pass-through filters for thermal-neutrons. A single-crystal silicon is preferred in this regard than polycrystalline silicon, due to the lower cross-section of single-crystal compared to that of polycrystalline silicon (0.3 b versus 2.3 b) [1236],

Softening. The effective energy of thermal-neutrons can also be reduced beyond their corresponding ambient temperature value of dictated by the Maxwell-Boltzmann distribution, Eq. (3.89), where is the Boltzmann constant and T is the medium’s temperature. This reduction (softening) in energy is used in some applications, such as neutron radiography, to increase the neutron absorption of materials where the cross-section is high at lower energies. Also if this softening effect is significant, it can result in the production of cold-neutrons, as discussed below, section 15.2.2.4. Reference [1249] compared the performance of three filter materials for use in neutron radiography. It concluded that a 30 mm thick Be filter has a modest effect on reducing the effective energy from 25 meV to about 21 meV, while 150 mm thick Bi and 150 mm of Pb can reduce that to about 11 meV and 7.3 meV, respectively. However, all these filters, at the stated thickness, reduced the beam intensity by about a factor of ten. These filters also help remove gamma-rays from neutron beams, due to their high atomic-number. A quasi-single crystal sapphire quartz quasi-single crystal bismuth, and single crystal lead fluoride can also be used to soften the thermal-neutrons. However, measurements showed that the quasi-single crystal sapphire at ambient temperature is a better filter than liquid nitrogen cooled silicon (Si), quartz (SiO2) and bismuth (Bi), for discrimination between thermal and fast-neutrons, or for softening the Maxwellian spectrum [1250]. The Bragg cutoff phenomenon discussed in section 3.5.5.1, can used to remove higher energy neutrons from the thermal-neutron spectrum, as it favors the transmission of neutrons below the Bragg cutoff energy. Beryllium has a Bragg cutoff energy at 5.2 meV, and is commonly used to “soften” the spectrum of thermal-neutrons. This comes, however, at a considerable reduction in the overall intensity of transmitted neutrons due to the relatively high cross-section of Be at the thermal-energy. Other materials that exhibit a similar behavior include: C (2 meV), Al (4 meV), Si (5 meV), Mg (2.6 – 2.9 meV), Bi (2 eV), Fe (5 eV), Zr (2.5 – 3 eV) and Pb (2 eV) or their compounds or crystals, where the values in brackets is the Bragg cutoff energy [1190].

704

15.2.2.4


Cold Neutrons

Filtering cold neutrons aims at producing neutrons within a certain wavelength range, or removing the effect of higher energy neutrons. Using a single crystal, Bragg diffraction, Eq. (3.66), can be used to produce neutrons of a certain wavelength, hence energy, at a particular direction. This requires, however, judicious orientation of the incident beam and the diffracting crystal, and of course a high quality crystal. The appearance of a single crystal can also be imitated using multilayers of thin films of different scattering cross-sections, acting like a two-dimensional crystal [37]. The Bragg cutoff method of filtering neutrons, discussed above in section 15.2.2.3, can be utilized to reduce the content of neutrons of energy above the Bragg cutoff-energy of the filter material. Polycrystalline materials can be used for this purpose. Cooling such filters assures also a large increase in the neutron population at higher energies [37], hence providing more effective filtering. Commonly used filter materials include beryllium, silicon, sapphire or pyrolytic graphite. For low-cost filters suitable for use in cold neutron radiography, reference [1251] suggested the use of a polycrystalline beryllium filter cooled by liquid nitrogen, long enough (1 m) to discriminate against gamrna-rays. Curved wave-guides can act as filters [37]. Cold neutrons are reflected from smooth surfaces, because the neutron refractive index is slightly less than one, see section 3.5.5.2. Therefore, neutron wave-guides can be constructed from smooth surfaces, typically boron glass plates coated with as it has a large scattering cross-section. However, the critical angle3 below which total reflection occurs is very small, hence the necessity for long guides. Nevertheless, if the wave guide is curved, neutrons of short wavelengths tend to travel along the concave walls of the curved guide, and the guide acts as a filter that passes low-energy (high wavelength) neutrons. In order to suppress fast-neutrons and gammarays, references [1253] and [1252] suggested the use of a 3 m long filter consisting of parallel stacking of curved glass plates covered with The combination of the Bragg reflection of a single crystal single and bending was studied in reference [1254] as a possible means of filtering.

3 The critical angle, is given by where is the wavelength, N is the atomicdensity of the reflecting material, is its coherent-scattering length, rad for and only rad for natural Ni, with in nm [1252].

Source Modulation

15.3.

705

Neutron Moderation

Source energy is determined by the nuclear decay, or nuclear interaction mechanism, that generates radiation. While the source energy cannot be elevated, it can be moderated to a lower energy. For chargedparticles and photons, there is no need to moderate the source energy, since as shown in chapter 2, there is a variety of sources with various energies to choose from. The situation is different for neutrons, where there are no sources that directly produce thermal-neutrons, as indicated in section 2.3.3. Therefore, the discussion on source moderation is limited here to the moderation of neutrons. Also, it may be desirable to soften (i.e. reduce the energy of neutrons) emitted from a particular neutron source. However, it should be kept in mind that moderation is in effect a removal process, in which not only neutron absorption occurs, but also radiation divergence and escape, from surfaces not directly facing the desired field of exposure, take place. Therefore, moderation comes at the expense of reduced utilization of the full strength of a source. The processes of source thermalization and softening is accomplished by the slowing-down or moderation of neutrons emitted from fastneutron sources. Either isotopic sources, or neutron generators, can be used for this purpose. Since in this moderation process, a good number of neutrons are lost, by absorption, divergence and leakage, it is important to choose both a source and a moderating material that provide the highest thermal-neutron flux per unit source. Obviously, a source with lower energy is easier to thermalize, and hence will provide the highest utilization factor (thermal-neutron flux per unit source, for a given moderator). Accordingly, among the common neutron sources, listed in Table 2.14, is the most attractive source for thermalization, as it provides neutrons with low energy. However, the short half-life of this photoneutron-source and the associated high gamma-ray background (see section 2.3.2) are disadvantages that limit its use. The next most suitable source for thermalization is then as it has the second lowest energy among the other common sources listed Table 2.14.

15.3.1.

Moderating Materials

A wide variety of neutron-moderating materials are available. However, the most common materials are light water heavy water carbon hydrides such as polyethylene, paraffin, etc.), graphite (carbon), and beryllium. The moderating ability of such materials is measured by two parameters. The first is called the slowing-down power, defined as:

706


where is the macroscopic scattering cross-section of the material, evaluated at the energy at which the neutrons scatter, and is the average logarithmic energy decrement per neutron collision and is given by [28]:

where A is the mass-number of the scattering element. For a compound, is evaluated by weighting the elemental values by the weight fraction and the scattering cross-section. The second parameter is called the moderating ratio, and is defined as:

where is the absorption cross-section of the material at the thermal energy. The slowing-down power measures how well a moderator slows-down neutrons, while the moderating ratio represents the ability of a moderator to slow-down neutrons without absorbing them. Carbon hydrides and water have a large slowing-down power, while beryllium, carbon and heavy water have large moderating ratios. Table 15.2 provides a summary of the above moderating materials, as well as other materials that have special characteristics that make them suitable for use in some applications. For example, provides also shielding for the gamma-radiation emitted along with neutrons. Beryllium, a light metal, is expensive and brittle, but has the lowest absorption cross-section among metals. Water-extended polyester (WEP) is fire resistant, unlike paraffin and polyethylene which have low flashing and melting points. However, one disadvantage of hydrogen-containing moderators is that when hydrogen absorbs thermal-neutrons it produces 2.223 MeV gamma-rays, which require biological shielding and may interfere with neutron counting if the detector used is sensitive to gammarays. Liquid moderators, such as light water and heavy water is quite expensive. It should be noted can leak and evaporate, while that helium would have been a good moderating material, but it is only available as gas and even at high pressure its slowing-down power is too low. Some metals are also attractive as moderators. Although a neutron does not lose much energy per collision upon scattering with a metal (due to the high mass-number of metals), it can encounter many collisions if the microscopic scattering cross-section is high. The high density of metals further enhances the scattering probability, by increasing the macroscopic scattering cross-section. Titanium, nickel and molybdenum are metals that are attractive as moderators, as they have a large (reso-

Source Modulation

707

nance) elastic scattering cross-section [27]. Reference [593] reported the use of a combination of nickel (enclosing the source) and polyethylene to moderate the neutrons of a source. Lead, tungsten and iron, which are used for gamma shielding, have also large inelastic scattering cross-sections, and thus alter the neutron energy. However, tungsten, because it has many possible excitation levels (hence many possible outgoing energy levels), tends to be a more effective moderator of neutrons by inelastic scattering [594]. Uranium and thorium also have high inelastic cross-sections, but at above about 1 MeV produce fission neutrons, which can interfere with their moderating effect. Neutron moderation can be achieved in a number of ways, as schematically shown in Figure 15.5. In the first arrangement, the slowed-down neutrons are produced within the moderating material itself. This is

708


called here moderation by containment and requires either a beam extractor to deliver the neutrons to the outside of the moderator, or the introduction of the interrogated object inside the container. Such arrangement is best suited for isotopic sources, which are sufficiently small to be placed in a pool or within a canister containing the moderating material. The second arrangement is simpler and requires only the placement of a slab of a moderating material in front of the source to slow-down neutrons before they emerge from the other side of the slab. This process is called here block-moderation, since the emitted neutrons are slowed-down before emerging from the slab. This arrangement is suited for neutron generators, which are large in size to be placed inside a container. In the third arrangement, the moderating material is used as backing material which reflects, and slows-down, the source neutrons. This arrangement is suited when mild moderation of the source energy is required. The thickness of material through which neutrons have to path until they are slowed-down, depends on neutron-energy, the type of moderating material, and the energy to which the neutrons needs to be moderated. A simple approach is given here to determine an approximate value of the radius of a spherical canister. However, Monte Carlo simulations, see section 16.2, should be used to refine this estimate, assess the use of more than one moderating material, or the employment of other moderation geometries and arrangements. The simple approach is as follows: Determine the average source energy,

say 2 MeV for a

source.

Source Modulation

709

Choose the desired average energy to which the source neutrons are to be moderated, say the thermal-neutron energy, 0.025 eV. Choose a moderating material, say light water, and find the value of its average logarithmic energy decrement per collision, see Table 15.2. For Calculate the average number of collisions to moderate the source using the relationship [28]: neutrons to the desired energy,

For the example values given above, Find the macroscopic scattering cross-section of the moderating material, Since the cross section varies with neutron energy, which changes with collisions, an accurate value is not obtainable using a simple calculation. However, the values tabulated in Table 15.2, which are evaluated at some epithermal energy, can be used as a first approximation, regardless of the source and moderating energies. For Since the mean-free-path of a neutron, i.e. the average distance between collisions, is equal to and collisions are required, the radius of a spherical canister should then be equal to For the above example values, the required radius would be cm, i.e. 134 mm. It should be kept in mind that the above method provides very crude estimates, as it uses average values and in effect assumes that the slowedneutrons are moving in a straight line with same energy, which is of course completely unrealistic. Nevertheless, the obtained values can be used as a first guess in a subsequent numerical simulation study to optimize the design. It should be kept in mind that moderating materials also function as shielding materials, see section 16.3. Reference [1241] investigated the use of a number of moderating materials in a spherical canister arrangement to optimize the design of source. The main conclusion of this study thermal-neutrons from a is that none of the moderators, by themselves, provide optimum thermalization. Moderators with high slowing-down power soften the neutron spectrum more than the same volume of high moderating-ratio material; however, they capture part of the thermalized neutrons. A combination of a high slowing-down moderating material and material with a high

710


moderating-ratio is, therefore, desirable. For example, surrounding the source with a small core of material with a high slowing-down power, followed by a high moderating-ratio, such as prosuchas vides an optimum combination. While would soften the neutron spectrum of the source, it would not absorb many neutrons because of its small volume. The softened neutron spectrum is then easier to moderate with the less slowing-down material, without losing neutrons to absorption. Surrounding the assembly with another layer of increases the thermal flux throughout the moderating assembly, by acting as a neutron reflector. The moderating assembly of reference [1241] for the inner layer, 150 mm of for the secutilized 50 mm of ond layer and 100 mm of for the reflector. Using the macroscopic scattering cross-section data of Table 15.2, the first layer will cause on average 6.8 collisions, while the second layer gives 5.25 and the third layer 13.6 collisions, for a total of average number of collisions of 25.65. This number is greater than the 19.6 collisions estimated in the example given earlier for slowing-down neutron from 2 MeV to 0.025 eV using water alone. The additional 6.05 collisions compensate for the lowerwhich is used to reduce neutron absorption. slowing down power of

15.3.2.

Moderating by Containment

Placing a source in the middle of a moderating material is a very effective way for slowing-down source neutrons, as it entraps neutrons within material and increases their chance of colliding with the nuclei of the material. Collided neutrons are also likely to be subjected to more scattering by the surrounding material, which further enhances the slowing-down process. Since the objective of the process of moderation by containment is to keep most of the neutrons within the container to increase their chance of slowing-down, it is important to decrease neutron leakage. This in turn will reduce the amount of material required and decrease the size of the assembly. For a minimum amount of moderating material, a spherical canister should be used, with the source placed at its center. A sphere offers the smallest surface-to-volume ratio, hence a minimum amount of neutron leakage and maximum retention of neutrons within the system for further moderation. However, it is often more practical to fabricate and handle a cylindrical container. If this is the case, the thickness of the moderating material should remain equal in all directions to the radius of an equivalent moderating sphere placed around the source. This can be done by using a cylindrical canister of a diameter equal to its height, with both being equal to the diameter of the equivalent moderating sphere. Then, the volume of the cylinder, as well its radius,

Source Modulation

711

becomes 1.5 times larger than that of the equivalent sphere that can be inscribed within the cylinder. The increased volume will scatter back some neutron towards the moderating medium, causing more scattering and a slightly increased thermal-neutron flux. Although, the increased volume will also cause more neutron absorption, such absorption would be primarily of neutrons that would have escaped the system if a spherical container were used. Similarly, the increase in the surface area of the cylindrical canister would not increase neutron leakage, in comparison to that of the sphere, since neutrons reaching the surface would have been scattered, or absorbed by the added material in the cylinder before reaching its surface. In summary, the cost of using additional material in a cylindrical canister is somewhat compensated for by the increase in thermal-neutron flux within the assembly. An alternative containment geometry is to place the source in a pool of a moderating material, preferably at the middle of the pool, to increase the effectiveness of the moderation process. This geometry is particularly suited for liquid moderators. Moderating by containment is more practical for use with isotopic sources, due to their small size, but provisions can be made to leave a vacant space within the container to insert the head of a neutron generator. In moderation by containment, the highest thermal-neutron flux is near the center of the assembly, where the source strength is maximum, leakage is minimum and neutron reflection is at its peak. Therefore, to be able to utilize these neutrons, a neutron-beam needs to be extracted out of the moderator, or alternatively the object exposed to the thermalized neutrons can be placed within the container. The latter alternative, though preferable as it enables better use of the thermalized neutrons, is not always practically possible, while beam extraction requires special consideration, as discussed in section 15.1.8. In a moderating assembly, or for that matter a nuclear reactor, a fast and epithermal-neutron beams can also be extracted with the aid of a collimator, see section 15.1.8. The collimator of such an assembly can be equipped with a filter that favors the passage of fast and or epithermalneutrons. A thick (0.4 m) single-crystal silicon was reported to be a good band-path filter for producing thermal-neutrons, as it has a low (0.3 b) cross-section for thermal-neutrons [1236, 1257]. An equal thickness of alumina was also shown to be capable of slowing fast-neutrons to the epithermal energy range, while also reducing the gamma-ray content of the beam [1236, 1257]. A 100 mm layer of bismuth was also found preferable than lead in reducing the gamma-content of the extracted beam, due to the lower cross-section of Bi, compared to Pb.

712

15.3.3.


Block Moderation

In this moderation process the passage of source neutrons is blocked by a slab of a moderating material placed in front of the source. This will cause the source neutrons to collide within the slab and lose some of their energy. The neutrons that emerge from the other side of the slab will have an energy distribution that is “softer” (lower in energy) than that of the source. This approach is more suited for neutron generators than for isotopic sources, since the larger size of the generator makes it cumbersome to insert the head of a neutron generator within a container full of moderating material. Moreover, unlike radioisotopes where neutron emission is isotropic, neutrons emitted from neutron generators tend to peak in the forward direction, making them more amenable to block moderation. However, even in reactor beams, block moderation is employed in the form of filtering to favor the generation of epithermalneutrons over thermal ones, or to “soften” the thermal-neutron flux, as explained in sections 15.2.2.2 and 15.2.2.3, respectively. In order to allow a maximum number of neutrons to escape from the block’s moderating material, the area of the surface from which the moderated neutrons emerge has to be as large as possible. This is why a slab geometry is preferred, as opposed to curved geometries. Although, the field of neutrons emerging from the slab will cover a wide area, most of the neutrons will arise from the area closest to the source location, where the neutron intensity is highest. It is also possible to place a beam extractor (collimator), see section 15.1.8, in front of the slab to confine the neutrons. The increase in the surface area of the moderating material comes at the expense of a reduction in the effectiveness of the moderating material, in comparison to moderation by containment, since a larger portion of the neutrons will escape before being subjected to slowingdown. In addition, for isotropic sources, where only neutrons directed towards the slab are slowed-down, the rest of the neutrons, emitted away from the slab, are not utilized. However, the source can be blocked at more than one side, allowing each side to function as a source of sloweddown neutrons. Of course, if the source is blocked in all sides, the blockage becomes in effect equivalent to moderation by containment , as neutrons will be internally reflected from one block to another. In spite of its above mentioned limitations, this moderation arrangement has a number of advantages. It allows easy access to the source, so that the source can be easily retrieved and perhaps used in another application. The method also accommodates the physical size of neutron generators, and allows easy access to them for adjustment or maintenance. In addition, unlike in moderation by containment, there is no

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need for the interrogated object to intrude within the moderating material. Although block-moderation is geometrically simple, as it requires only the placement of a slab in front of the source, the determination of the thickness of the slab is not a straightforward task. The thickness of the slab has to be chosen so that it is sufficiently thick to moderate the neutrons, but not too thick to entrap them or absorb them within the block. A too-thin slab will allow most of the source neutrons to pass unaffected by the moderating material, with a few neutrons being moderating, resulting is a slightly softened neutron spectrum. Therefore, a thick slab will absorb most of the slowed-down neutrons within the moderating material. A thick slab may also absorb low-energy neutrons emerging directly from the source, and in effect harden the source spectrum of the neutrons emerging from the other side of the source. This will occur only if high-energy source neutrons can succeed in escaping from the slab, while lower-energy neutrons (from the source or as a result of slowing-down) are absorbed within the slab. Of course, the slab, if thick enough, can become a neutron shield, allowing only a very small fraction of the source neutrons to escape. Due to the competing effects described above, Monte Carlo calculation, see section 16.2, should be used to determine the optimum slab thickness for a given application. Since the scattering cross-section varies from one moderating material to another, as shown in Table 15.2, and it also depends on the neutron energy, the thickness of the slab should be designed for a given moderating material, or combination of materials, for a specific source-energy spectrum. The flux of neutrons emerging from the moderating slab can be seen to consist of two components: (i) those source neutrons that succeed in escaping the slab without colliding with the moderating materials (uncollided component), and (ii) those that are slowed-down by neutron collisions (collided component). The design of a moderating slab should aim at balancing the two components, to achieve the desired level of moderation while maintaining a high neutron output. While minimizing the uncollided neutrons maximizes the removal of high-energy (unmoderated) neutrons, its complete elimination may lead also to a severe reduction in the collided component; an indication that the slab is acting more like a shielding rather than as a moderator. On the other hand, there is a limit to how much one can increase the collided component by increasing the thickness of the slab, before neutron-absorption within the slab starts to remove most of the moderated neutrons. Nevertheless, this maximum collided component is what the designer should aim at, if a well-moderated source is desired.

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A rough guide to determining the thickness of the moderating slab is to use from one third to one half of the required radius of a sphere for moderation by containment, see section 15.3.2. The logic behind this estimate is that, while in moderation by containment a large thickness is needed to moderate and retain the neutrons, block-moderation requires neutrons to leave the system. Therefore, a smaller amount of moderating material has to be used in block moderation. At about one third to one half the radius of a moderating sphere, a sufficient moderation would have been occurred, without a considerable amount of absorption. This rough estimate should be used as an initial guess in a design process, and should be refined according to the specific requirements. One last note on neutron block-moderation, it is a process in which neutrons are delayed. That is, the slowing-down process takes time. Therefore, if a pulsed source is moderated, the duration within which the moderated neutrons are emitted will inevitably be longer than the duration of the pulse generated by the source. This should be taken into account if a moderated pulsed source is to be employed.

15.3.4.

Moderation by Reflection

Neutrons reflected off a moderating material would have encountered a few collisions, and thus moderated in energy. If the source is an isotropic source, the field of reflected neutrons will be blended with unmoderated neutrons emanating from the source away from the reflector. For neutron generators, where the source is biased in the forward direction, the moderating material can be placed in front of the source to reflect back slowed-down neutrons. Neutrons can be reflected back as a result of one collision or multiple collisions. Both will result in a significant loss of neutron energy, since as Eq. (3.80) shows, a large angle of reflection results in a large loss of energy. Multiple scattering compounds the loss of energy, from one interaction to the other. Most of the reflected neutrons are likely to emerge from near the surface of the reflector, since their chance of escaping the moderating material is higher. Theretofore, it is not necessary to use a thick moderating material to achieve good reflection. However, the reflector may be also employed as neutron shield, stopping neutrons from re-emerging from its other surface away from the source. Then the reflector’s thickness should be determined by shielding considerations, see section 16.3. The thickness of the reflector depends on the type of moderating material. A thickness equivalent to, or less than, one mean-free-path of the source neutrons in the moderating material will allow only one collision, thus providing a minimal amount of moderation. On the other hand, a

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thick reflector will permit multiple neutron collisions, resulting in more slowing-down, but the collided neutrons may not be able to scatter back towards the source. In determining the thickness of the reflector, it is advisable to start with a moderating material equivalent to one meanfree-path of neutrons at the average source energy, then examine the effect of increasing this thickness. Note also that a metallic reflector may be useful for scattering back neutrons toward the source without affecting much their neutron energy. This allows the reflector to act as a source intensifier, if the source is isotropic, by reflecting neutrons (that would have been otherwise wasted) back towards the object. Note that albedo, a term borrowed from optics, is used by some workers to quantify the reflection process. Albedo is the ratio between the radiation current reflected from a surface to the incident flux density [70]; see section 3.6 for the difference between flux and current. The albedo coefficients reported in the literature are usually obtained by performing Monte Carlo calculations. Since these coefficients were intended for use in shielding calculations, they were reported in units of radiation dose [70]. The albedo values were useful in the past when access to high-speed computers, to perform the calculations, was limited. With the advent of computers and Monte Carlo codes, it is advisable to perform radiation reflection calculations for the particular problem at hand, rather than utilize values reported by others, so that the problems’s special geometry and material can be properly taken into account. Section 16.2 provides some basic information on the Monte Carlo method. Moderation by reflection occurs involuntary in the shielding process, as neutron shielding materials are at the same time moderating materials, see section 16.3. The shielding material around a source reflects back moderated neutrons, which interfere with the neutron field of the source neutrons, if the source is isotropic. This effect can be minimized, if this is undesired, by using a neutron-absorbing element, such as boron or lithium4, within the shielding material, or wrapping its surface with cadmium, to prevent thermal-neutrons from emerging from the shielding. Eliminating reflected neutrons with higher energy is difficult to attain, as they cannot be easily absorbed. However, keeping the shielding at some distance away from the source will tend to reduce their blending with the source neutrons, as the reflected neutrons will diverge over a wide angle.

4

Hydrogenous containing boron or lithium are commercially available, see for example “www.reax.com”.

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15.4.


Neutron Multiplication

The intensity of a neutron source can be enhanced by inducing fission in a target made of a fissile material. Since readily available neutron sources emit fast, or intermediate energy, neutrons, see section 2.3, a material in which fission can be caused by such neutrons is required. The energy spectrum of the resulting neutrons will have a fission spectrum, similar to that of the spontaneous fission source of neutrons, see section 2.3.1.2. Therefore, conversion of a source spectrum to a fission spectrum can be achieved in this process. For example, neutrons emitted from a 14 MeV neuron generator can converted to fission neutrons, which are easier to moderate than the original neutrons, by directing the generator’s neutrons toward a fission target and utilizing the emerging neutrons as a converted source. As Table 15.3 shows, fast fission (at some representative energy range) can occur in both isotopes present in natural uranium, and as although thermal-neutron fission is much more probable well as in and The fission cross-section of and at the for thermal-energy is zero, or is essentially zero, since the fission of these nuclides require an energy of at least 1 MeV [28]. Therefore, the presence of a moderating material in front of the source, to slow-down the neutrons, will enhance considerably the fission process. This is the essence of operation of nuclear reactors, which unfortunately are not portable sources suited for in situ applications. However, the positioning of a target of a fissile material in front of an isotopic source or a neutron generator can boost the neutron flux considerably, thus these targets are often called neutron “boosters”. Because of the relative unavailability and restricted use of and its special handling precautions, its not favored for use as a booster target, in spite of its higher fission yield. Natural uranium, which contains, by weight, and 99.28 % concentration) can as well as enriched uranium (with higher be used as boosters. The higher the degree of enrichment, the lower would be the thickness required for the booster to achieve the same level of multiplication. However, even depleted uranium will provide some boosting of the source strength. The wide energy spectrum of the fission neutrons distorts the energy spectrum of the original source neutrons, unless that source was a fission source such as The field of the multiplied neutrons is also wider than the field of the source, as the fission reaction can take place over a volume larger than that of the source itself. Moreover, the decay of the fission products within the booster results in the production of an additional radiation field that may require biological shielding. For a pulsed source, the multiplication process also prolongs the duration of the pulse.

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Delayed-neutron emission from the target, following the termination of a pulse, adds also a neutron background component. Nevertheless, neutron multiplication can increase the source strength by about 15 times with a target, up to 50 times with a target. The target sizes mentioned in reference [1258] were a few tens of mm in thickness, with a small target being 20 × 20 × 20 and an infinite target is assumed to have a thickness of 50 mm. These dimensions provide an indication of the range of target sizes that can be employed. In designing a multiplication assembly, care should be taken to ensure that the assembly is subcritical, with where is the multiplication factor. The multiplication factor is the relative increase in the number of neutrons in one cycle of multiplication, i.e. from the time one neutron induces fission in the multiplying medium to the time the generated neutrons are reabsorbed again to cause further fission. The lifetime of a cycle is in the order of a millisecond. A critical assembly 1) can go supercritical if it is not well controlled, while a supercritical assembly is simply out of control and becomes an explosive hazard. For the first cycle of multiplication will boost an original source strength, the number of neutrons to the second cycle to and so on. Therefore, after an infinite number of cycles, the source strength becomes equal to where (with

is the source intensification factor. Eq. (15.17) demonTherefore, strates how a subcritical assembly, intensities the source strength.

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Since the lifetime of a multiplication cycle is in the order of a millisecond, the series of Eq. (15.17) converges rapidly to in a very short time. The value of the multiplication factor depends on the nature of the multiplying medium (the probability of fission and the number of neutrons produced per fission) and on the geometry of the assembly (which determines the escape probability of neutrons from the medium). The model of Eq. (15.17) is a simple model that does not take into account the details of neutron transport within the assembly; it is in essence a point kinetics model. As the detailed Monte Carol study of reference [1244] demonstrates, the intensity of a neutron beam extracted from a multiplying assembly is considerably lower than that predicted by the model of Eq. (15.17). This is because, the model of Eq. (15.17) provides an overall intensifying factor, over the entire volume of the assembly, while neutrons extracted via a beam port within the assembly is mainly affected by neutron multiplication near the port’s boundary. This is because neutrons produced away from the port are screened from the beam port by self-absorption within the multiplication assembly. Therefore, the model of Eq. (15.17) is a first approximation that should be followed by more detailed analysis and/or experimental measurements. Aside from fission, the intensity of fast-neutrons can also be increased by reflecting neutrons towards the object, by surrounding the object with a material that is a good fast-neutron scatterer. Such a scatterer should not alter the energy of the neutrons, nor absorb a considerable amount of neutrons, otherwise it defies the purpose of enhancing the fastneutron field reaching the object without changing the source energy. The following elements are good fast-neutron reflectors: nickel, iron, molybdenum, lead, tungsten, and [594]. Fission multipliers can also be useful in applications where a high epithermal-neutron flux component is required. By placing a fission plate converter in front of an object exposed to neutrons, fission will take place immediately in front of the object, exposing it to neutrons richer in epithermal-neutrons, as the calculations of references [1259] and [1260] indicate.

Chapter 16 DESIGN CALCULATIONS

16.1.

Design Parameters

Before performing design calculations, it is advisable to segregate the design parameters in to the following categories: Device: parameters related to source, detector, and geometric arrangement. Object: parameters denning object size, shape, density, composition, homogeneity, etc. Performance: parameters that quantify the accuracy, precision, contrast, sensitivity, resolution, etc. Distortion: parameters that inadvertently affect the performance of the device, such as shielding, surrounding walls and objects, natural or spurious object heterogeneity, etc. The performance parameters are dependent parameters, since their values are determined by other parameters. Some of these parameters are controllable by design or setup, and others are beyond the designer’s or the operator’s influence. Usually a designer is faced with many parameters to deal with. It is advisable to vary one parameter at a time, and study its effect on the performance parameters. One should start with the most important (primary) parameters first, then examine the other less important (secondary) parameters. Design calculations are performed for a number of reasons: Proof-of-Concept: to demonstrate the viability of a new concept or idea. 719

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Optimization: to find the design arrangement that optimizes the performance of a device, in terms of contrast, resolution, or some figureof-merit. Parametric Study: to study the effect of various effect parameters that influence the performance of the device. Measurement Modeling: to establish and verify a measurement model for a particular device. Shielding: to design a suitable radiological shielding. Although the design tasks listed above can be performed experimentally in the laboratory, it is useful to perform such studies numerically to avoid unnecessary exposure to radiation, by performing trial-and-error experiments. Calculations also make it possible for the designer to determine the consequences of a design change in an existing device before implementing such a change, thus reducing the cost and risk of design alterations. There are, however, parameters that can only be studied experimentally, such as determining the reproducibility of results (precision), the effect of the surroundings, signal-processing electronics, and detector performance and drift effects that are difficult to numerically simulate. The most effective methods of performing design calculations is the Monte Carlo method; although analytical programs, such as those of references [213] and [1261], can be used in parametric studies. A brief introduction to this method is given in the ensuing section.

16.2.

Monte Carlo Simulation

The Monte Carlo method approximately solves a problem by the simulation of random quantities. The terminology “Monte Carlo” comes from the city of Monte Carlo in the principality of Monaco, famous for its gambling casinos. The computational algorithm is relatively simple. It consists, in general, of a process for producing a random event. The process is repeated N times, each trial is called a “random walk”, or a history. Being independent of each other, the results of all random walks are averaged together to provide an “estimate” of the quantity of interest. Unlike deterministic methods, the Monte Carlo method provides an answer with an error associated with it, so that a confidence level in the obtained results can be established. The process is similar to performing a scientific experiment and is sometimes called the method of stochastic, or statistical experiments or trials. The designer should, therefore, view the use of the method as “computer experimentation”.

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Central Limit Theorem. The essence of the Monte Carlo method is the Central Limit Theorem, also known as the law of large numbers. It states that any sequence of length N of independent and identically distributed random variables, with common mean m and variance will produce a random variable:

that is asymptotically normal i.e. reaches a normal distribution of a mean and a standard-deviation when N approaches infinity. In other words, when N is sufficiently large, the average of will approach a normal distribution. Then, the average value, can be used as an estimate of the random variable, and the statistics of this estimate is governed by those of a normal distribution. The central-limit theorem is, therefore, the backbone of the Monte Carlo method. The value of approaches the true expected value, as the number of trials approaches infinity. The variability of is estimated as:

and is called the sample variance. It is not directly an estimate of the distribution variance, but it can be stated that:

where is the estimated value of

say using Eq. (16.2). The 1 confidence interval in the estimated is defined by the interval where

Since

is not known, the following estimate is used

A useful quantity is the “relative error”, also called the “fraction standard deviation” (f.s.d.), defined as:

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An f.s.d. of less than 0.05 (5%) is usually required in Monte Carlo calculations. As Eq. (16.4) indicates, the value of hence that of the f.s.d., That is, to reduce the value of the f.s.d. by half, is proportional to the number of samples, N, must be quadrupled. Random Walks. Radiation transport is simulated in the Monte Carlo methods by tracking the history of source particles1 as they travel through a medium, encountering various types of interactions. The events experienced by the simulated particles are sampled from probability distributions in space, direction and energy (and time in timedependent calculations) that govern radiation interactions as determined by the cross-sections of the nuclei of the material in the encountered media. For more detail, refer to one of the number of the books that deal with the use of this method in solving radiation transport problems, such as references [1262] [1263] and [1264], Advantage and Limitations. The main advantage of the Monte Carlo method is its ability to handle complex geometries. Its main limitation is that it only provides solutions at specified locations, unlike deterministic methods which give solutions at all points in the space considered. This limitation is not, however, important in designing radiation devices, since in such devices one is interested also in measuring the radiation intensity at specific detector locations. However, in Monte Carlo simulations, unlike in experiments, one can position a “detector” within a medium, without disturbing it. This can enable the designer to gain insight into the radiation transport process, and get better understanding of the underlying physical processes. Codes. The most widely used code for particle transport analysis is perhaps the MCNP code [1265]. The COG code [1266] has also powerful feature that makes it attractive for use in designing radiation devices, as it can “simulate complex radiation sources, model 3D system geometries with ‘real world‘ complexity, specify detailed elemental distributions, and predict the response of almost any type of detector” [1267]. Specialpurpose Monte Carlo codes, as those described in references [1268] and [1269] have also been used. Analytical expressions for the cross-sections suitable for use in Monte Carlo simulations are give in reference [1270].

1A particle here also refers to a photon, which is simulated as an entity analogous to a particle.

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Setup. The process of setting up a device design-problem in such a Monte Carlo code is analogous to an experimental setup. One needs a source, detectors, and an object with a certain geometry, size and material. One must be aware, however, of any simplifications made in setting up the Monte Carlo problem and their effect on the results. Unlike in the laboratory, one can eliminate the surrounding shielding, since there is no risk of radiation exposure. The shielding can be added at a later stage to examine its effect on the performance of a device, as part of a parametric study. Monte Carlo simulations also require the user to identify the modifying physical processes to be studied. For instance, in a neutron-transport problem, once can choose to simulate also the gamma-rays emitted following neutron capture or inelastic scattering, or can focus only on the neutron-transport problem. Similarly, electrons generated from photon interactions, and the subsequent secondary reaction they induce, can be examined or ignored. Such flexibility enables the designer to perform separate interaction-effect studies, if so desired. Estimators. Detection in Monte Carlo simulations is achieved by a tallying or scoring processes that estimate the particle fluence, and fluence-like quantities (such as energy deposition). In any of the fluenceestimators, the response function of an actual detector can be used as a multiplier of the particle fluence. Tallies estimate the particle fluence based on: the number of particles crossing a surface, number of collisions within a volume, or the number of track-lengths of particles within a volume, or the probability of particles reaching a point (or a ring) in space. The latter is know as the “expected-value” estimator, since it does not require the simulated particle to reach the detector site, but rather it determines at every scattering event the probability of the scattered particle reaching a detector site. This “point detector” estimator is also known as the “next event estimator”, as it estimates the probability of the next scattering “event” being at the detector site, without actually transporting the particle to the detector’s site. The point-detector estimator is a popular one, as is easy to set-up and enables one to designate many detection locations without having to simulate the detector geometry in details. However, a point detector should not be located within positions where scattering events are expected, since the nextevent probability includes the effect, where R is the distance from the collision point to the detector site, in accordance of the law of divergence (see section 3.6.2). When R is close or equal to zero, the estimated particle-fluence approaches infinity and the point-detector estimator becomes unbounded. One can, however, include an exclusion zone (sphere) around the detector to prevent such singularity-causing scores.

724


Random-Walk Termination. Monte Carlo codes also require the designation of some means to terminate a random walk. A random-walk is automatically stopped when a particle escapes the system’s geometry or when it is absorbed. However, the latter option is not usually available, since allowing absorption of particles makes it difficult to track radiation in highly absorbing media. Therefore, a weight of unity is typically assigned to the source particle. The weight is reduced by the non-absorption probability each time a particle encounters a collision. The particle is then allowed to survive and the random walk continues in this so-called “non-analog” process. However, the random walk may be terminated when a particle has low weight, below a pre-assigned cutoff value. Similarly, a random walk may be terminated when a particle’s energy reaches a value below a certain cutoff energy. Time-cutoff can also terminate a random walk that may have exceeded a pre-determined maximum age, with the age being the time since the particle’s generation as determined by its speed and distance of travel. The user has, however, to be careful not to prematurely terminate random walks, to avoid loss of valuable information. When possible, it is preferable to let random walks be terminated naturally as the particle escapes into a “universe” outside the domain of study. The domain of study includes the source, object, detectors and shielding, if present, and some surrounding air space. Often, the designer may want to replace air by “void” when radiation interactions in air can be ignored. This speeds up the computations by avoiding the tracking of particles in air. This also eliminates scatters that may occur in air near the site of a point detector, adversely affecting its response. Number of Random Walks. The total number of random walks must be also specified, or one can equivalently specify the execution time in terms of computer processing units (cpu’s). The required number of random walks (or particles) is determined by the level of acceptable uncertainly, keeping in mind the provisions of Eq. (16.4) that relative where N is the number of samples (random error is proportional to walks). The results of Monte Carlo simulations must also satisfy the requirements of the central-limit-theorem discussed above, that is a sufficient number of histories, N, must be followed to allow the estimated value to be approximately normally distributed. The evidence that a solution has reached a value that satisfies that theorem is that the value of estimated quantity does not change much by increasing the number of histories, i.e. the solution converges, and that the estimate error decreases as N increases. It is also important to ensure that the estimated values are obtained from distributions without “holes”, i.e. sampling is

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performed over the entire range of a distribution. The MCNP code [1265] performs a number of statistical checks to ensue that the above conditions are satisfied. When reporting Monte Carlo results, one must state both the estimated quantity and the error associated with it, as done when reporting experimental results.

Importance Sampling. If the required level of accuracy cannot be attained by increasing the number of random walks, one may resort to “importance sampling” or “biasing”. Such biasing techniques are designed to encourage particles to travel towards favored areas, directions, energy, or time intervals, while compensating for this biasing process by adjusting the weight designated to the biased particles. Biasing methods should be applied only by experienced users and after trying a few biasing schemes. Importance sampling is based on the concepts of splitting/ Russian roulette or path-length stretching. In splitting, more particles are created in regions, directions, or energies of importance but with reduced weight, such that the total weight of the created particles is equivalent to that of the split particle. Russian roulette is applied to kill unimportant particles, while allowing the occasional particle to survive with an enhanced weight to make up for the lost particles. Path-length stretching artificially reduces the macroscopic cross-section to allow the particle to penetrate deeper into the material, but with a weight accordingly adjusted to compensate for the lower probability of penetration. The process is also called exponential transformation, since it affects the exponential nature of radiation transport, see section 3.6.3.

Comparison to Experimental Results. Relating the results obtained from Monte Carlo simulations to those provided experimentally is a non-trivial task. The Monte Carlo results are all normalized to one source particle. Therefore, one must know the source strength used in the experiments, which is not usually possible. Experimental effects such as detector efficiency and resolution, surroundings, electronic drift or signal pile-up, can produce results that differ from those predicted by simulations. However, the general trend of the results obtained from Monte Carlo simulations should be similar to those of experiment. If not, one must investigate the cause for the difference. This by itself can point to important factors that influence the performance of a device, to which the designer may not have paid enough attention. Once the same trend is obtained in experiments and simulations, a calibration process can be established to relate the results of the two methods to each other.

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Uses. Many examples for the use of the Monte Carlo method in device design are available in the literature, some of which are summarized below. System Design and Modeling. The Monte Carlo method has been widely used to model and design various system components, such as:

Moderator and collimator design for neutron radiography [1236, 1256, 1271, 1272]. Characterization of photon collimators [1273]. Modeling of source, collimator and tomographic data acquisition in single-photon emission computed tomography [1274, 1275]. Modeling of a linear accelerator x-ray beam [1276]. Testing of radiography designs and objects without experimentation [1277, 1278]. Design of an active (fission-induced) neutron fuel rod scanner [1279]. Development of Compton scattering systems [163, 211, 229, 319, 910, 1280, 1281, 1282, 1283]. Design and development of fast-neutron scattering devices [213, 226, 228, 489, 505, 782, 1284, 1285]. Investigating fast-neutron transmission spectroscopy systems [1286, 1287, 1288]. Studying pulsed fast-neutron analysis for detection of explosives and narcotics [1287, 1288]. Modeling of a neutron dispersion tool for porosity measurement in oil well-logging [1289], and verification against measurements so that the simulations can be used to assess the suitability of a device for use in difficult simulations [783]. Calculating the intensifying factor of a neutron multiplication assembly [1244].

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Parametric and Effect Studies. The Monte Carlo method is wellsuited for parametric studies since most of the parameters can be readily changed. Example studies include:

Examining effect of geometry, structural materials and bulk density [1290, 1291, 1292, 1293, 1294, 1295, 1296], and selection of detector [1297], in neutron-activation. Studying the effect of scattering on transmission radiography [1298, 1299] and tomography [1300]. Assessing mudcake and other environmental effects in borehole logging density [1301, 1302] and porosity measurements [1303, 1289, 1304]. Determining influence of source-detector geometry, shielding arrangement and chemical composition of medium of a neutron/gamma moisture/density surface gauge [1305]. Device Response. The Monte Carlo method is also useful in establishing the response/calibration curve of a system. This process is utilized in:

Prompt gamma activation analysis [1306, 1307]. Porosity measurement with fast neutrons [1308, 1309, 1310, 1311]. Surface soil moisture and density measurement with neutrons and gamma rays [1305]. Monte Carlo simulations can also determine the domain of influence of a device, or the response of a detector. The method was used, for example, to: Calculate the size of the sphere of influence (depth of investigation) of density measurement devices [1312]. Compute the response function of a detector [1313, 1314, 1315, 1316, 1317, 1318]. Examine the effect of detecting unintended particles, e.g. neutrons on a gamma detector [1319]. Simulate detector coincidence counting [1320, 1321, 1322]. Determine the best design for a neutron detector that records only thermalized neutrons emerging from a specific direction [1323].

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Measurement Modeling. The Monte Carlo method is quite useful in verifying analytical measurement models and in determining the domain of their validity. Many of the assumptions incorporated in a measurement model can be introduced in the simulations, then gradually removed to examine their effect on the results. For example, one can verify a model based on single scattering against Monte Carlo simulations based on single scattering, then introduce double scatters, triple scatters, and so on, to determine the number of the scatters beyond which measurement model becomes inadequate. Adjoint Calculations. The adjoint particle flux is the flux obtained when the source and the detector are interchanged, i.e. the detected particles are tracked back to their source of origin. This requires transposing the cross-sections so that particles are transported from lower energy to the higher source energy. Unlike the normal transport process where particles lose energy to up to a minimum value (a zero or the thermal-energy), adjoint transport of particles upwards in energy is unbounded. Therefore, the adjoint scattering cross-section are formulated in a discrete fashion, i.e. from a mutigroup cross-section set, so that the particles can be transported to well-defined energies. The discretization of particle-energy provides obviously an approximate solution that depends on the width of the employed energy groups. Nevertheless, the value of the adjoint flux is indicative of the particle’s importance, that is, regions of high adjoint-flux are the ones in which particles have most influence on the solution of the problem. Therefore, the adjoint flux can be used for “biasing” a forward flux problem, using the adjoint flux from a reference problem, see for example reference [1324]; or from a simplified solution as done in reference [1325] using a diffusion solution. There are other useful applications of adjoint calculation [1263]. When the same reaction rate (say activation rate of neutrons) is to be calculated for various sources (e.g. thermal, epithermal and fast neutrons), adjoint calculations can be used to determine the most suitable energy. The adjoint method is also useful when the phase-volume of detector is too small (in time, energy, angle or space) to provide good statistical estimate in forward Monte Carlo simulations.

16.3. 16.3.1.

Shielding General

Radiation shielding is an integral part of any radiation-based device for obvious safety reasons. Although the main objective of shielding design is to reduce radiation exposure to personnel to as low as reasonably

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achievable, see chapter 5, the shielding designer should also pay attention to the effect of shielding on radiation background, see section 17.3. Radiation shielding is addressed in a number of textbooks [1326, 1327, 1328], including those that deal with reactor shielding [1329, 1330]. However, a short summary of the shielding design process is given here. Allowed Dose. The first step in radiation shielding is to determine the maximum permissible dose to personnel, in accordance to regulations and to the ALARA principle discussed in chapter 5. Ensuring that personnel do not exceed this maximum can be achieved by reducing the time of exposure, and staying as far away as possible from the source of radiation to take advantage of radiation divergence with distance, see section 3.6.2. Once the time of exposure and the distance from the source are determined, shielding is the only remaining option for radiation dose reduction. Before proceeding with shielding design and calculations, it is important to estimate the dose for an unshielded source. The ratio between the dose for an unshielded source and the maximum allowable dose defines the factor by which the dose is to be reduced. The source specifications provided by the manufacturer provide an estimate of the dose for an unshielded source, typically at 1 m from the source. This dose may need to be adjusted for distance (if different form 1 m), and source decay. Simple shielding calculations can be based on the so-called half-value layer, which is the thickness of a certain material that reduces the intensity of a given type of radiation of a certain energy to half its value. Therefore, if it is required to reduce the unshielded source dose the number, of required half-value layers is such that by a ratio Note that the half-value layer is equal to where is = the total cross-section of the shielding material at the source energy, using the maximum energy to be on the conservative side. In addition to accounting for the attenuating effect of the shielding material, advantage should also be taken of the reduction in radiation exposure with distance, in accordance to the law of divergence, section 3.6.2. Charged Particles. It is relatively easy to shield against chargedparticles as they continuously lose energy when interacting with matter. The value of the range, Eqs. (3.14) and (3.21), can be used to determine the thickness needed to shield completely against charged-particles. For alpha-particles, shielding is not necessary, as the dead layer of the human skin stops alpha-particles. Beta-particles are slightly more penetrating, but can be shielded against using plastic or aluminum foils. It is not desirable to use dense metals such as steel or lead for shielding against beta-particles, since they produce secondary x-rays by the

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bremsstrahlung effect. Safety glasses should also be worn to protect the eyes against beta-particles. More energetic accelerator-produced particles can also be shielded against in the same way. However, due to the intensity of radiation produced, secondary emissions by photons produced by the bremsstrahlung effect, and in some cases by the subsequent emission of neutrons (photoneutron interactions), become the dominant radiation against which shielding needs to be provided. Photons. Gamma and x-rays are shielded against by electron-rich materials such as lead, steel and concrete, since photons interact mainly with the electrons of the atom. Tungsten and depleted uranium may also be used for photon shielding, in spite of their higher cost. Because of their higher density, depleted uranium and tungsten make it possible to design more compact photon shielding. Neutrons. Being neutral in charge, neutrons interact with the nucleus. The most effective way of shielding against them is to slow them down to the thermal energy, using a hydrogen-rich material, then absorb them, with a proper neutron absorber. Water, paraffin wax, polyethylene, etc. are good materials for neutron shielding. When using water, loss of liquid by leakage should be guarded against, while paraffin wax and polyethylene can be a fire hazard. However, water-extended polyester (WEP) is fire resistant. Thermal-neutron absorbing materials boron suitable for shielding are those containing lithium and the rare earth elements samarium and cadmium europium gadolinium dysprosium where the isotopes in brackets are the most effective neutron-absorbing natural isotopes of the element. Neutron absorption is usually accompanied with gamma absorption, except in the case of Also, neutron sources emit gamma-rays. Therefore, some gamma shielding is usually required along with neutron shielding. Gamma-rays that accompany neutron emission should be shielded against by placing a gamma-shield around the neutron source, to directly reduce the gamma field. The outside of the neutron shield should also be enclosed in a metal shield to cutoff secondary gamma emissions. A number of advantage are offered by concrete as an outside shielding, as it contains both light elements for neutron shielding and heavy elements for gamma shielding. Concrete is also economical, reliable, structurally useful and versatile, but is not mobile if it is not in a brick form. Soil is also a useful shield for neutron and gamma-rays, but its use may not be always practical. Tungsten is also a more effective neutron shield than lead, due to its many inelastic nuclear levels [594].

Design Calculations

731

Intense Sources. In shielding intense sources or accelerators in a special room, a number of geometries can be quite effective [1331]. The most effective shielding method, in terms of amount of materials, is that in the form of a cavity around the source. This geometry is obviously useful when the inspected object and the device’s detectors can be placed within the cavity, or when a transfer system is available to position the object in front of the source. A labyrinth geometry designed to block direct streaming of the source radiation to the outside of the room provides a convenient design and lends itself to poured or solid-block concrete construction. Pit- and well-type shielding is another effective geometry, since earth can provide shielding in all but the vertical direction. Such shielding arrangement is useful in a basement-floor area. A roll-away door can be installed over the pit to prevent radiation leakage above the source. This type of shielding requires obviously a transfer mechanism to move the inspected object to and from the cavity. Basements, corners, and similar locations provide natural shielding, and should be used when possible. It should be kept in mind that if no top shielding is provided, backscattering of radiation by atmospheric air can result in an increase of a few percent in the radiation dose. This, so called “skyshine” effect, should be taken into account when performing shielding calculations. After constructing the designed shielding, a radiation survey should be conducted under operating conditions, to ensure the adequacy of the shielding and to assess whether there is no radiation “streaming” through air gaps or cracks that may be present in the shielding. Attention should also be paid to stray radiation arising from leakage (transmission) through the source housing and/or collimator, and from scattering or emission by the interrogated object. Open (Unsealed) Sources. When dealing with open (unsealed) sources, such as in radiotracer applications, attention should be paid to the internal hazard of radiation. A distance should be kept from the source. Handling a source with long tongs, will significantly reduce exposure to its radiation. When handling beta sources, the eyes must be protected, by wearing safety glasses or Plexiglass helmets. The risk of dust must be considered in dry processing of radioactive materials, and it may necessary to wear breathing filters to protect against radioactive dust. The workplace should be well marked and guarded. Precautions must be taken so that radioactivity will not inadvertently be ingested. Bioassays need to be performed at regular intervals for users handling and typically at levels greater than 5 MBq. More frequent bioassaying is required for pregnant women. Contamination monitoring must take place regularly. Emergency plans for dealing with minor and

732


major contamination should be well-defined and practiced in advance, on non-radioactive materials. Additional precautions are needed when dealing with and The nucleus of is mall in size, being a hydrogen isotope, it can enter the body via inhalation and skin absorption. It decays by beta-emission (6 keV, mean energy). If exposed to tritium, one can reduce the committed dose by increasing fluid intake, and bioassaying should be performed as a follow-up. Phosphorus-32 emits highly energetic beta-particles (1.71 MeV) that penetrate 8 mm in the body, resulting in a high radiation-dose, particularly to the hands and the face. Therefore, one should not handle uncovered and inadequately shielded vessels containing

16.3.2.

X-Ray Machines

A number of reports provide information on methods, materials, and data for shielding against x-rays due to their wide use in medical applications, see for example references [1332] and [1333]. Photons produced by an x-ray machine are emitted within a specific orientation determined by the focal-spot-size of the beam and the angle of inclination the target makes with the incident electrons. The emitted beam may be further confined to a specific direction, shape and size by means of a slit or a cone collimator, see section 15.1. A “beam catcher” (a shielded hole) can be used to capture an incident beam after it traverses an inspected target. A beam may also be directed to an enclosed and shielded box in which the object to be examined is inserted. If it is not possible to confine a beam to within the domain of a beam catcher or to enclose an object and associated detectors within a shielded box, a separate shielded room should be used to contain a device and the associated x-ray machine. In any of the above mentioned configurations, shielding of x-rays focuses on placing a primary shielding downstream of the emitted radiation. Advantage can be also taken of the reduction of radiation intensity with distance (divergence) by defining a no-access (cordoned) area around the machine. Since x-ray machines can be turned off and the intensity of the emitted radiation can be varied (by changing the current), the radiation dose resulting from exposure to x-rays should be based on their total time of use and the current employed. The exposure per unit workload is the parameter typically used to quantify x-ray exposure. The exposure per unit workload at one meter from a source, K, can be expressed as [1333]:

Design Calculations

733

where P is the maximum permissible exposure (Gy/week), (m) is the radius of the area around the x-ray machine that need to be cordoned, W (mA min/week) is the work load, T is the occupancy factor (degree of occupancy of the area behind the cordoned zone), and U is the utilization factor (fraction of T during which the x-ray beam is directed towards the area of interest). The work load, W, is the product of the total time of use in a week and the operating current (mA) at the which the machine operates, a value that should be determined using the maximum planned operating time and current. The occupancy factor, U is the fraction of time within the week during which the area behind the cordon is occupied by personnel. Obviously, if an x-ray machine is used in a open or if no one occupies the area behind a barrier around area, and no shielding is required. Thus, the machine, U = 0, then the smaller the value of K, the more shielding is required. Calculation curves are available relating the value of K to the minimum required thickness of certain shielding materials (lead and concrete) at various xray operating voltage, see reference [1333]. The concept of the half-value layer, i.e. the thickness required to reduce the radiation dose by 50%, can also be applied to determine the thickness required for shielding against x-rays, see reference [1328]. The primary shielding itself, as well the floor and surrounding walls, will scatter radiation backwards and side-ways. Such scattered radiation may reach personnel working behind, or in, the neighboring areas. A secondary barrier must be provided to protect against the scattered radiation, by blocking it with a secondary shielding. The thickness of such a shielding can be obtained from the same graphs of K versus thickness of the shield, but with the following value, of exposure per unit workload at one meter from the source:

where P and W are as defined in Eq. (16.7), d (m) is the distance from the source to the scatterer, D (m) is the distance from the scatterer to the secondary shielding, a is ratio of the scattered-to-incident exposure, and F is the field area i.e. area projected on the scatter by the primary beam as it diverges with distance. The value of a depends on the incident radiation energy and the angle of scattering with respect to the central axis of the incident beam. Values for a are given in reference [1333]. The factor 4 in Eq. (16.8) empirically increases the value of K to take into account that fact that the scattered radiation has a lower energy than the incident radiation, but the same graphs for K versus the minimum shielding thickness are evaluated at the incident energy.

734

16.3.3.


Isotopic Gamma Sources

The dose rate, (to an accuracy of about 20 percent) from an unshielded gamma source of energy from 70 keV to 4 MeV, can be approximated as [1328]:

where is the source activity, E, is the photon energy, is the number of photons of energy E per source disintegration, R is the distance from the source to the point at which the dose is received, and the constant values in Eq. (16.9) are necessary for matching the units expressed after each parameter. For example, to estimate the dose rate for an unshielded source, 370 Bq in activity, at 0.1 m from the source, one must first From Table 2.10, one can see that estimate the values of E and one at energy of 1.173 MeV and the emits two photons (thus, other at 1.333 MeV. Therefore, . With Bq, R = 0.1 m, using Eq. (16.9), one obtains:

Note that at a distance of 0.2 m, the dose rate will drop to 3.1 mSv/h, that is doubling the distance reduces the dose by a factor of 4, while reducing the source activity to half its value, would reduce the dose rate only by a factor of 2. To illustrate the effectiveness of shielding, let us calculate the exposure rate for the same source considered above, at the same distance of 0.10 m from the source, if it is 370 MBq housed in a lead container which is 25 mm thick. At the photon energy of this source, 11 mm of lead will reduce the absorbed dose by a factor of half (the half-value layer) [1328]. Therefore, 11 mm is equivalent to = 2.27 half-value layers. Accordingly, 25 mm will reduce the dose by a factor of The dose at 0.1 m for unshielded source, calculated above to be 12.5 mSv/h, is now reduced to 12.5 × 0.207 = 2.6 mSv/h. That is a 25 mm of lead is more effective in reducing the dose than the doubling of the distance from the source to the receiving point, and is equivalent to reducing the source activity by a factor of about five (5). Note also that in the above calculations, the absorbed dose in mSv/h and the exposure in mGy/h are identical in value, since the factor in Eq. (5.2) is equal to unity for photons. Reference [1328] provides graphs for determining the half-value layer at different photon energies for water, concrete iron and lead.

Design Calculations

16.3.4.

735

Neutrons

Neutron shielding calculations are not as straightforward as those of photons. Considerations have to be given to the neutron energy, as fast neutrons have a higher radiation weight (quality) factor than thermal neutrons, as discussed in chapter 5. In addition, one must take into account both the primary gamma-radiation that almost always accompanies neutron emission and the secondary gamma-radiation arising from neutron activation of the surroundings. Neutron shielding calculations are, therefore, usually performed with the aid of computer codes. However, reference [1334] provides useful data that enables quick shielding calculations for a source. As a guide, shielding should reduce the flux to below the values given in Table 16.1. The neutron flux, at a point can be estimated assuming a point source by the relationship:

where S is the source intensity (neutrons/s), R is the distance from the source to the point of interest, is the removal (for dose-equivalent reduction) macroscopic cross-section. Table 16.2 lists the removal crosssection of some useful materials for fission and 14 MeV neutrons. For a given maximum allowed dose rate, Table 16.1 can be used to give an estimate of the maximum flux allowed, at the source energy. Eq. (16.10) can then be used with the aid of the information in Table 16.2 to provide an estimate of the thickness, t, of a particular shielding material at some distance, R, from the source, for a given source strength. Note, however, that the thickness obtained from this procedure is a crude approximation and should be validated against more sophisticated calculations using the codes discussed below. Such a rough estimate is, however, useful as a staring point (first estimate) for the calculations.

16.3.5.

Computer Codes

A number of radiation transport codes can be employed for more detailed radiation calculations. The simplest approach is to use the point-kernel method, in which volumetric radiation sources are approx-

736


imated by a distribution of point sources, each of which contribute to the total dose rate or flux at any given detection point. A point-kernel code, such as QAD [1337], calculates the mean-free-path and the corresponding buildup factor between each source point and the detector point by means of ray tracing. The buildup factor takes into account the scattering component of the dose rate. For full solution of the radiation transport problem within a shielding material, discrete-ordinates codes can be used. These codes approximate the gradient term in the transport equation, Eq. (3.116), by a finite difference technique known method. The scattering integral in as discrete ordinates or Carlson’s the equation is approximated by expanding the differential cross-section by a Legendre series which allows the integral to be computed by quadratures. The problem can be solved in one-dimension (ANISN code), two dimensions (DORT code) or in three dimensions (TORT code), all three codes are available in one package called DOORS [1338]. However, the method is not well-suited for use in air due to the low density, hence low macroscopic cross-section, of air. Typically, therefore, the discrete transport method is used to determine the flux distribution at the surface of the shielding, then a point-kernel code is utilized to calculate the transport of radiation in air. For complex geometries, a Monte Carlo code, such as MCNP [1265], can be used. However, since shielding problems tend to be deep-penetration problems, in which radiation is significantly attenuated, the Monte Carlo solution of the radiation transport problem can produce results with a high level of uncertainty, unless some form of “biasing” (importance sampling) techniques are applied, see chapter 16. Nevertheless, the COG Monte Carlo code [1266] was designed to solve deep-penetration radiation-shielding problems in arbitrarily complex three-dimensional geometries, involving coupled transport of photons, neutrons, and electrons. The coupling process in this and other codes enables the calculations of secondary emissions, e.g. neutrons giv-

Design Calculations

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ing rise to gamma-rays by activation, photons producing electrons, and the latter generating x-rays by the bremsstrahlung effect, etc. It should be noted that radiation transport codes calculate the radiation fluence, while shielding calculations require an estimate of the radiation dose; which is the energy absorbed in tissue multiplied by the radiation dose quality factor or radiation weight factor (see chapter 5). Conversion factors between flux and dose are available and could be used, see for example reference [1339].


Chapter 17 EXPERIMENTS

17.1.

Experimental Aspects

Laboratory experiments should be performed following design calculations to validate the design, and demonstrate that idealizations and simplifications introduced in the calculations do not undermine the viability of the concept upon which the design is based. Experiments are also used to validate a developed measurement model, and to obtain calibration data necessary to determine the system constants needed to relate the model results to the experimental ones. Experiments can also be performed to refine a model so that it takes into account practical considerations, or to establish an empirical model when an analytical model cannot be established. Exploratory experiments may precede design calculations, to establish that a conceived system is practical, when the design calculations are too complex to perform, or when the properties of the inspected object cannot be well characterized. Before performing experiments, a clear experimental plan should be formulated. The following planning steps are recommended: Setup. The layout of an experiment should be well-defined in advance, including radiation shielding (see section 16.3). Necessary approvals and licensing to perform experiments must be obtained in advance, see section 17.2. Equipment and Supplies. Obviously there is no point in starting an experiment without the availability of all the needed equipment of sources, detectors, test objects, electronics, data acquisition system, shielding material, etc. If substitutes are made, a justification should be noted, along with the anticipated effect on the experimental results, 739

740


if any. Detectors and associated electronics should be tested individually before starting an experiment. Parameters. All system parameters that need to be experimentally investigated should be identified in advance. As a rule, one should vary one parameter at a time, while keeping all other parameters fixed; otherwise it becomes difficult to assess the effect of one parameter over that of others. It is advisable to categorize the parameters as primary parameters, those anticipated to have a major impact on the performance of the device; and as secondary parameters, those of less importance. The effect of the primary parameters should be assessed first. Attention should also be paid to the time-varying nature of parameters, if any, as discussed in section 17.4. Range of Parameters. The maximum and minimum values of each parameter to be investigated, and the steps of changing a parameter should be determined in advance. One should also ensure that the desired range is experimentally sustainable within the planned setup of an experiment. Statistical Considerations. To ensure that the desired precession level is attained, the provisions of counting statistics described in appendix G should be followed. Test Plan. A well-devised test plan should include a list of the experiments to be carried out, the sequence of their execution, and the goal and procedures needed to conduct each step. Crucial experiments that need to be satisfied first should be clearly identified, since there is no point in proceeding any further if the major objectives are not met. It is also advisable to conduct some familiarization experiments before accumulating the required data. Such preliminary experiments can also be used to determine any shortcomings that may exist in the experimental setup or the test plan. Documentation. A log book, or a computer file, should be kept describing experiments and their objectives. All setup parameters should be recorded, along with any relevant notes that may be useful in future data analysis and documentation. Troubleshooting. Experimental frustration arises when inconsistent results, or results contradicting the expected trend, are obtained. Troubleshooting usually starts by focusing on the electronics and the detec-

Experiments

741

tors, to ensure their stability and reliability. In a mixed field of radiation, e.g. neutrons and photons, one type of radiation may be influencing the other radiation type in an undesirable way. Some detectors electronically drift when operated for a long time, or when subjected to a high temperature. When numerical simulations were performed in advance confirming the theoretical viability of a concept, the experimentalist should focus on the difference between the experimental and simulation setups. Radiation shielding and surrounding walls may produce scatter or activation radiation that introduces a large background component. Methods to reduce radiation background are discussed in section 17.3. Source-object-detector alignment may be crucial for the performance of a technique, but may not have been well implemented experimentally. A collimator of a source or a detector may not be as levelled as one would have anticipated. Sometimes, the designer may need to perform further numerical simulations to better understand or diagnose a problem encountered in the laboratory but was not considered important in the initial stages of simulation. For example, the size and the response function of a detector may have not been initially fully simulated, but may prove to be experimentally vital. Evaluation. Preliminary evaluation of experimental data should be conducted in conjunction with experiments to ensure that the experimental program is proceeding in the right direction. Full evaluation should be conducted after finishing an experimental program. In reporting experimental data, one should keep in mind that an experimental result is not worth reporting unless an estimate of its uncertainty (error) is also given with it. The reported uncertainty should include that associated with the statistical fluctuations, see appendix G, and other sources of error. The results of an experiment can be used to determine the accuracy, contrast, resolution, and any other desired performance parameters. Lessons Learned. The first proof-of-concept experiments, when successful, constitute the demonstration phase of a developed device. This phase is often followed by the development phase, see section 18.1. Lessons learned from the demonstration phase are vital to ensuring the development of a successful prototype device. Experience gained in the demonstration phase should be reported, and recommendations for design changes, procedure improvement, safety and operational precautions, etc., should be documented.

742


The following sections address the basic aspects of licensing, background reduction and dynamic analysis of experimental data. Statistical analysis of data is discussed in section G.

17.2. Licensing 17.2.1. General The use of radiation sources and devices are regulated by national authorities. The holders and users of such sources and devices must abide by these regulations, by obtaining proper licenses and adhering to their conditions. Although regulations vary from one jurisdiction to another, there are some common themes that are discussed here. Readers are advised to consult their local regulations before possessing and using radiation sources and devices. For accelerators and large facilities a regulating agency may require an application to acquire a radiation source before purchasing. A license to operate needs, in many cases, to be obtained before using a source or a device. In addition, a final license for routine operation, or for use under field conditions, may be required. In general, applications are made in the from of a safety report that may include information on: Purpose and activities of the radiation device or facility. Organization operating the device, its safety administrative procedures and policies, personnel in charge of device, and any other third parties involved in operating the device. Detailed description of device, including radiation source, control system and handling mechanism, supported with drawings and diagrams. Location of facility and a description of rooms in its vicinity. Assessment of hazards and precautions of radiation, radiation dose and shielding, any sources of secondary radiation, contamination, or internal hazards e.g. by inhalation. Precaution against radiation hazards, including personnel and area monitoring, access control, alarms, and handling of radioactive materials. Procedures and methods used to calibrate personal dosimeters and radiation survey meters. Assessment and precautions against non-radiating hazards, such as toxic and flammable materials, high voltage, high pressure, high or low temperature, etc.

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Environmental impact on ground water and the atmosphere. Operating procedures. Interlock, security and safeguard procedures, when required. Restrictions, if any, on neighboring sites. Radioactive waste identification and handling. Emergency procedures. Training procedures. Plans for eventual decommissioning of device and disposal of source and contaminated material. The ultimate goal of the licensing process is to convince regulating authorities that protection is provided to both the general public and the workers at all time. Regulators tend to distinguish between three different types of radiation sources: x-ray machines, particle accelerators and radioisotopes. This distinguishing is based on the fact that the first two sources of radiation can be turned off when the source is not in use, thus requiring no major safety precautions while in storage or transportation. Radioisotopes, on the other hand, continuously emit radiation, necessitating protection and shielding at all times. While x-rays are produced via atomic interactions, see section 2.2.1, they do not usually cause nuclear transmutation, unlike the case with particle accelerators where nuclear transmutation within the machine and the surrounding structures can result in radionuclides that have to be taken into account in radiation safety analysis. General licensing and safety issues that are required for all types of radiation sources and devices are first discussed, followed by aspects specifically related to the three types of radiation sources. Licensing authorities require evidence of: shielding, monitoring, warning, training, disposal of waste and emergency planning. A brief discussion on each of these aspects is given below. Radiological Shielding. Radiation shielding must be provided for most forms of radiation sources, as discussed in section 16.3.

Personnel Monitoring. Personnel working with radiation devices and sources are required to wear radiation dosimeters (badges) to record their personal radiation exposure, see section 5.4. These are personal monitors and must not be exchanged with others. When not in use, dosimeters should be stored in a secure and properly shielded location.

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Periodically, typically monthly, the dosimeters are to be read, and their results in the form of radiation exposure reports, should be kept as a permanent record that can be made available for examination by authorities. Radiation workers should be informed periodically of the results. If reported dose to a worker exceeds the maximum limit for the monitored period, the worker should be notified immediately. Such worker should not be allowed further exposure to radiation for an amount of time equivalent to the monitored period. An individual accidentally exposed to a high dose should undergo medical examination. Pregnant women are subject to special dose limits and monitoring procedures. Bioassaying is required for persons that may be exposed to volatile (which are absorbed in the thyroid gland), or and Area Surveying. In addition to radiation dosimeters, each radiation laboratory should be equipped with survey meters to measure radiation level in the working area. These survey meters should be calibrated periodically to ensure that they are providing correct readings. The meters should also be used to monitor radiation level in neighboring areas (around, above and below the laboratory) to assure non-radiation workers that the radiation level in their area of work does not exceed the public-allowed dose rate. Areas where unsealed (open) sources are used must be monitored for possible contamination. Warning and Precautions. Precautions and procedures must be established to ensure radiation source and generators are never utilized outside their shielding, and that no personnel can be present within the confined shielding of the source or an operating machine. Radiation warning signs must be placed in a proper location alerting personnel to the presence of a radiation-emitting device. The names and phone numbers of personnel that can be contacted in case of emergency should also be posted. Training. Training of personnel is a must. No one should be allowed to handle a radiation source or operate a radiation emitting device without prior training, and without being fully aware of the responsibilities and the risk associated with exposure to ionizing radiation. Operators must fully understand and appreciate the nature of the radiation sources and devices under their control. Emergency Planning. Emergencies are excursions from normal operation conditions that may lead to exposure to a high dose of radiation, contamination of clothing, intake of radioactive material by ingestion,

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inhalation or through a cut or a wound, or the release of radioactive materials to the environment, beyond allowed limits. It must be demonstrated to regulating authorities that reasonable precautions are taken to prevent the occurrence of such accidents. An emergency plan should be prepared in advance to deal with accidents that may arise from the installation, testing, repair, or modification of a radiation source or associated equipment. Personnel must report an accident immediately, and not hide any adverse situations. An accident report should be written, indicating the time, date and location of the event, the names of involved persons, the concerned equipment, the circumstance surrounding the occurrence of an accident, and the actions, if any, that were, or will be, taken to control, correct or eliminate the cause of an accident. Future training programs should be revised after the accident to ensure a similar event is not likely to occur. Waste Disposal. Radioactive waste includes residual amounts of radioactivity, disposable containers, partially decayed or surplus radioactive sources, expended accelerator targets, contaminated material, etc. Such materials have to disposed of in an authorized and safe manner. Provisions and procedures for waste disposal must be in place. Small amounts of radioactivity may be disposed of locally; gases to the atmosphere, liquids to sewers, and solid to garbage. If allowed, such disposal should be done safely and within legal limits specified by regulators. Accumulation of large amounts of waste should be avoided. Transportation of waste to an external waste disposal facility should be done in accordance with regulatory procedures, to safeguard the environment, and in accordance with the ALARA principle (see chapter 5). Shipped waste should be transported in containers that are shielded to lower radiation exposure to values below the allowed limits dictated by the regulations of the jurisdiction within which the waste is to be transported. A waste container should also be labeled with a proper radioactive sign, indicating the radiation dose at the surface of the container.

Exemption Quantity. Small quantities of radiation, also called below scheduled quantities, are usually exempt from regulations. A scheduled quantity is the minimum amount of activity of a particular radionuclide that is subject to regulation. That quantity depends on the radiotoxicity of the nuclide, which in turn depends on the nature and energy of the radiation emitted, its half-life, its time-of-residence within the body (biological half-life) if internally absorbed, the nature of critical organs that absorb the nuclide if ingested, and the chemical toxicity of the nuclide. Therefore, the scheduled quantity varies considerably from one

746


nuclide to another. Typically, however, the scheduled quantity for most is about 40 GBq and for radionuclides is about 0.4 MBq, but that for is only 40 kBq. However, the reader should consult local authorities for their adopted values of scheduled quantities. The scheduled quantity defines the maximum activity of a certain type of nuclide that can be purchased and used without a license. The scheduled quantity (SQ) is also used to determine whether direct disposal of a radionuclide to the environment is permitted. Typically, 0.01 SQ per liter of water of a diluted nuclide can be discharged to the sewer, 0.001 SQ per cubic meter of air can be released to the atmosphere, while 1 SQ per kg of solid waste material, but a maximum of 0.3 SQ may be disposed of in a single waste container or a bag. The dilution factors apply before the radioactive material is released to the environment. The stated values may vary from one jurisdiction to another, and may be updated by the authorities from time to time. Any radioactive labels and warnings should be destroyed before placing permitted-to-dispose waste in common garbage, to avoid unnecessary panic to the public.

17.2.2.

X-Ray Machines

X-ray generators, and devices employing them, are typically covered under industrial safety codes for x-ray equipment, see for example reference [1333]. Some guidance on issues that may arise in licensing devices employing x-rays are given here. Shielding. Shielding of x-ray machines is required during operation to ensure that limits of personnel radiation exposure are not exceeded. In performing shielding calculations, radiation scattered off shielding, and surrounding walls and floors, must be taken into account; see section 16.3. If a machine is used within an open area, a restricted-access zone should be clearly marked, and radiation warning signs be posted. Stray radiation, arising from leakage through the housing of an x-ray machine, or scattering by the surroundings, should be monitored and recorded periodically. In industrial applications of x-rays, there is no reason for an x-ray machine operator to stand near an unshielded beam during exposure. However, if such circumstances arise, for whatever reason, the operator must wear appropriate protective clothing (leadrubber aprons and gloves), or stand behind a protective screen. Under no circumstances should an operator stand directly in front of an x-ray beam.

Equipment Safety. X-ray machines are usually equipped with safety features that prevent inadvertent emission of x-rays. It is, however the

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responsibility of the user to ensure that such features are present and functional. For example, an x-ray machine should be equipped with a secured off-switch, a timer that controls the duration of exposure, or an ON/OFF switch that requires continuous pressure by the operator to maintain x-ray production. The control panel should also be equipped with meters (voltage and current), lights, etc. that are discernible, clearly labeled, and a locking device that requires insertion of a key before the production of x-rays. An x-ray tube should also be housed in a tube-support that maintains the tube’s position without tipping, excessive drift, or vibration. Separate warning lights or indicators should be available to indicate when the machine is energized. The control panel should contain a mechanism to trigger audible and visible signals when the x-rays are produced. The name of the manufacturer and the model designation of the machine should be labeled, on both the control panel and the x-ray machine itself. The manual of the x-ray machine should be available to the operator at all times; no operator should be allowed to operate a machine without being familiar with the contents of its manual. A warning signs should be clearly affixed on the control panel, so that it is visible and identifiable from at least a distance of one meter. Safety Precautions. Safety precautions and procedures should be in place to ensure that an x-ray machine is not inadvertently operated. If the x-ray machine is enclosed in a shielded chamber with an access door, an interlock should be connected to the control panel to prevent radiation emission when the door is open, and to shutdown the machine if the door is opened. Visible warning lights should also be installed to indicate when the machine is in operation. A pre-warning audible signal should also be used to alert personnel that x-ray are about to be generated. All these warning device should be tested routinely to ensure their functionality. When not in operation, the x-ray machine should be secured by removing its operating key from the control panel. The license will also likely require that safety instructions and laboratory procedures be well laid-out, and posted near the control panel of the machine. Training. Training of personnel should not only deal with operating the x-ray machine, but also should focus on understanding the content and intent of radiation and equipment safety codes. In addition to basic radiation safety training, operators and users should understand the particular characteristics of their machine. Operating procedures described in the operating manual of the machine must be strictly followed and

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incorporated into the training program. A log-sheet should also be used to prompt users to abide by safety precautions. Such a log sheet should include the name of the operator, the time and purpose of use, whether operating and safety manuals are readily available, and the operating parameters used. The operator should be made aware that failure to follow designated safety and operating procedures can lead to a disciplinary action.

17.2.3.

Radioisotopes

Regulating agencies issue guidelines and procedure for acquiring, handling and disposing of radioisotopes, see for example reference [1340]. The main aspects of such guidelines are presented here. Unsealed Sources. Licensing of open (unsealed) sources requires that a user demonstrates a great deal of care and attention in handling the radioisotopes. An up-to-date inventory of radionuclides should be maintained, listing activity, physical and chemical form, location of use and disposal of waste, if any. All unsealed sources must be stored in a shielded container marked with a radiation warning sign, with labels indicating type of nuclide, activity on stated date, and its physical and chemical form. All sources should be stored in a fireproof safe area, with sufficient shielding to reduce the radiation dose to permissible levels. Gaseous and volatile radioisotopes must be kept in a ventilated fume hood. Rooms containing the storage area should display a warning sign, and a list of the stored isotopes. Security personnel and fire marshals should be made aware of the presence and content of the storage area. Food or beverage of any kind must not be stored or consumed in areas where radioactive sources are used or stored. Open sources should be handled on trays or benches, covered with disposal absorbent sheets, separately from non-radioactive areas to avoid contaminating the latter. Procedures that may result in airborne radioactivity must be handled in a fume hood, while those involving powdered material must be handled in a glove box. Sealed Sources. Sealed sources can be either free-standing, i.e. not permanently installed in a device, or are a part of a device. In either case, the licensing process will require users to keep a record of the source type, chemical and physical form, its a activity on a specific date, and the name of manufacturer and type and number of device (if applicable). Locations where the source is used and stored must also be identified and clearly labeled with proper warning signs. Provisions must be made to ensure that sealed sources are protected and shielded at all times;

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suitable locking mechanisms may be used for this purpose. Leak tests must be performed, and documented, on regular basis, to ensure the integrity of the sealing metal or container. Sources should be handled with care, using forceps and with proper protection when warranted. When appropriate, a source should be equipped with a shutter to shield the source when it is not in use. When in use, a proper shielding must be provided to reduce radiation exposure to permissible levels. All mechanisms, if any, associated with the use of a source must be checked and maintained on regular basis.

17.2.4.

Particle Accelerators

Particle accelerators are given special attention in licensing as they give rise to high-energy charged-particles (electrons, protons or ions). In addition to shielding against the primary particle produced in an accelerator-based facility, attention should be paid to secondary radiation. Radiation is produced in such facilities via a nuclear reaction, that almost always results in the emission of gamma-rays. Moreover, the slowing-down (bremsstrahlung) of charged-particles resulting from such interactions is accompanied by the emission of x-rays. Neutrons can be also produced by direct interaction of the accelerated particles, or as a result of photoneutron interactions. The emitted neutrons can activate elements in the surrounding materials, producing activation gamma-rays that need to be shielded against. Therefore, the shielding design should aim at providing protection against both the primary and the secondary radiation. Moreover, neutron activation of the structure material of the accelerator can be a source of contamination, if breakage of the structure occurs or when performing maintenance on the accelerator. Therefore, special handling equipment should be used when dealing with accelerator components. For neutron generators, reference [1335] provides an excellent source for information on safety, as well as operation and troubleshooting of various types of systems. In the generation of neutrons via the reaction, some of the is displaced from the accelerator’s target. The displaced tritritium tium is usually kept within a vacuum chamber around the target and deposited on its walls. However, if the pressure in the chamber is accidentally raised to atmospheric pressure, the tritium will be dislodged from the chamber walls and could be released to the environment. Therefore, licensing such systems requires provisions to monitor the tritium level in the surrounding environment, as well as monitoring tritium contamination on adjacent surfaces. Tritium and activation products can also present a hazard, even when the accelerator is shutdown. An emergency evacuation plan should also be in place, if the source is used in a closed

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space. In addition, bioassaying (urine analysis) of personnel working in such accelerators is required to detect any body intake of tritium. Note that acquisition of a tritium target will require a radioisotope license, since tritium itself is a radioactive substance. Accelerators are normally enclosed in shielded rooms, or vaults, equipped with door and interlock systems, so that the power to the accelerator is cut-off when the door is opened. Accelerators should also be equipped with interlock systems to prevent damage to the accelerator and over-exposure of personnel, when one of its main systems (power supply, cooling, vacuum, etc.) are not properly functioning. Danger of implosion of an accelerator’s vacuum chamber, and subsequent release of radioactivity should also be considered in the safety analysis of the accelerator. Deuterium, being an isotope of hydrogen, presents an explosion hazard, if leaked. Electric-transformer oil, in the high-voltage system, as well as some of the organic solvent used to clean the generator, are flammable. A procedure should, therefore, be in place to deal with accidental fire, assuring the use of carbon-dioxide fire extinguishers, while avoiding water, foam or powder extinguishers, as they can cause severe damage to the equipment and instrumentation. Pressurized gas, that may be used for high voltage isolation, and fluid in pneumatic systems, present a pressure hazard that can cause a serious accident. Therefore, maintenance procedures should include depressurizing such systems to atmospheric pressure before working with them. Area alarms consisting of warning lights and appropriate warning signs should also be in place. Since such accelerators employ high-voltage systems, high-voltage safety precautions should be taken into account. The power-supply housing should be grounded by connecting it to a water pipe. All capacitors should be discharged before performing maintenance on the power supply, extreme caution should be taken when working in a vicinity of the accelerator or on its control panel, and the accelerator must be equipped with warning lights and signs. Regulators can also require that certain safeguards be established to ensure that accelerator and associated equipment are secured from sabotage. Sealed Tubes. Neutron generators with sealed tubes are less burdensome in licensing than conventional particle-accelerators, since the sealed vacuum tube maintains the tritium reactivity within the tube. The gas-pressure inside the tube is maintained by a passive hydrogen absorption material, such as titanium that absorbs hydrogen at high temperature and drives it out at low temperature, with the temperature controlled with the aid of a filament inside the pressure regulator. The target can be replaced, and disposed of, when the tritium level in

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the target is depleted. The sealed target must be treated with a great deal of care during operation and replacement to avoid releasing tritium as a result of tube rupture. All other safety precautions against emitted radiation, high voltage, etc. also apply.

17.3. Background Reduction 17.3.1. Definition and Origin of Background Background reduction is an important aspect of any measurement technique, since the measurement signal is contrasted against background measurement. A background signal can be defined as any component that interferes with the desired signal. Therefore the definition of background depends on the NDE technique used. General background problems associated with radiation counting are addressed in section 4.5.7.2. For each of the methods discussed in Part 5.4, the background can be defined as follows: Transmission: radiation scattered by the object or the surroundings to the detector, as well as any secondary emission that may be introduced by the source and is measurable by the detector. Scattering: radiation reaching the detector directly from the source, and any secondary emissions recorded by the detector. Emission: transmitted or scattered radiation to which the detector is sensitive. In any of the above methods, background can arise from: Radiation Type: detecting an unintended radiation, e.g. gamma radiation in a neutron measuring system. Radiation Energy: interferences with the energy range of interest, e.g. by emissions from an undesirable material, or broadening of the detector response due to its intrinsic characteristics. Detector Field-of-View: radiation reaching the detector from outside its intended field-of-view, e.g. due to scattering on the inside wall of a detector’s collimator, or leakage through the collimator’s walls. Background radiation can be caused by secondary radiation, either produced by the source itself or a result of radiation interactions within the object. For example, neutron sources almost always produce gamma radiation, to which the detector may be sensitive. Also neutrons may activate some elements within the object, producing secondary gamma emissions. Some beta-sources also emit gamma radiation, while fast electrons

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(or beta particles) can produce gamma emission by the bremsstrahlung process. Pulse-shape discrimination, see section 4.5.5.4, is helpful in this regard, since the pulse-height produced by one radiation type tends to have a rise-time different from that of the other radiation types. Impurities in the detector material can contribute to radiation background, if they are themselves radioactive. Reference [1341] studied the radioactivity in material used in fabrication of radiation detector systems in particular, NaI(Tl) and germanium detectors. Observed naturally occurring radioactive materials include: daughters of and daughters of and and The radionuclides: and were also observed. The same reference reported that aluminum is the major source of natural radioactivity, with electronic components and sealing rings contributing while a smaller amount. Stainless steel may also contain produced by cosmic neutrons interacting with was found in steel stored above ground. Cosmic rays also produce and in copper. Lead contains that can introduce a significant background component. Solder materials contain and its daughters: and [107]. Statistical fluctuations can also cause the background signal to interfere with the recorded signal, when the signal-to-background ratio is low. Section 14.2 discusses the statistical considerations that should be taken into account to reduce the statistical effect of the background signal. Some methods for reducing the background signal in the indication modalities listed above are given in the sections below.

17.3.2.

In Transmission

By Design. Scattering to the detector in a transmission-based device can be reduced in a number of ways. In the design stage, the designer should choose the source energy that, for the size and material of object to be examined, minimizes radiation scattering. Monte Carlo calculations, discussed in section 16.2, can be quite helpful in this regard. By Collimation. Also, a narrow source beam, provided by a long collimator, limits the exposure area of the object and hence reduce the amount of scattered radiation. For example, reference [1342] reported the use of a honeycomb collimator to reduce scattering in neutron radiography. This, however, reduces the effectiveness of utilizing a radiation source, since most of the emitted radiation is eliminated in the collimation process. The source collimator itself may introduce its own scattered radiation. However, collimating the detector can reduce the amount of scattering by limiting its field-of-view to that corresponding

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to transmission radiation. Detector collimation can also allow the use of a wide, or fan-shaped beam, with the detector field-of-view defining the path of the detected transmitted radiation. However, the detector collimator can also introduce its own scattering background. By Energy. If the source is monoenergetic, and a detector with some energy resolution is used, energy discrimination can be utilized to electronically discard the counting of the scattered (lower energy) radiation. Lower-energy radiation tends to suffer more scattering than higher energy radiation. In addition, scattered radiation reaching a transmission detector has a lower energy than that of source radiation, due to the energy reduction introduced by the scattering process. Therefore, discrimination against low-energy radiation can help greatly in reducing the effect of scattering. Such discrimination can be performed electronically if the detector has some energy resolution. Alternatively, discrimination can be accomplished physically using a proper filter material, as explained in section 14.6.4. If the source has a wide energy spectrum, electronic energy discrimination becomes difficult, as the scattered radiation from higher energy can overlap with the source radiation emitted at a lower energy. Note also that coherent (Rayleigh) scattering of photons does not result in any energy change, and is produced at small scattering angles, as discussed in section 3.4.3.1. Thus, it is difficult to eliminate Rayleigh scattering by collimation or energy discrimination.

By Time-Gating. Scattered radiating has a longer travel path and a lower energy. Thus, scattered radiation takes a relatively longer time to reach a detector than uncollided radiation transmitted to a detector. This allows the use of time discrimination, or time gating, to eliminate background radiation due to scattering. By Distance. Distance can also be used to reduce the effect of scattering; the farther away the detector from the object the lower the amount of scattering. This is because the scattered radiation tends to diverge over a wide angle, and its intensity is reduced with the inverse square of distance; see section 3.6.2. However, incident source radiation, even if collimated, also follows the same law of divergence, but the transmissionto-scattering ratio will tend to decrease with distance. With a Beam-Catcher. Scattering to a detector may also arise from the surrounding shielding, floors, walls, etc. It is desirable, therefore, to measure transmission at locations away from such enclosures. For a fixed-beam system, a beam catcher, also called a beam dump, in the form

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of a deep hole with a wall downstream of the object and the detection system can decrease the scattering competent tremendously, by trapping the scattered radiation within the beam catcher.

17.3.3.

In Scattering

Methods based on measuring scattered radiation faces two major background components. The first is from direct exposure of detectors to source radiation and the second component is due to scattering from surrounding walls, floors and shielding materials. Radiation emitted from an object as a result of excitation or activation of material in the inspected object can also add to the background component in scattering measurements. However, the latter component is usually not as prevalent as the other two components, since the probability of radiation emission by excitation or activation is generally much lower than that of scattering or absorption. By Energy. Energy discrimination can eliminate the uncollided radiation arising from a source and reaching a detector, if the source is monoenergetic. Secondary radiation, tends also to have characteristic energies that can be discriminated against. When an inspection technique relies on measuring the single scattering of neutrons or photons, the unique energy-angle relationship of neutron scattering, Eq. (3.80), or Compton scattering, Eq. (3.37), can be employed to monitor the scattering associated with a particular angle (direction) of scattering, if the incident radiation is well-collimated and is monoenergetic. The effect of multiple scattering in a system based on single-scattering can also be reduced by energy discrimination to cut-off the low-energy multi-scattered radiation. Energy discrimination can also be used to distinguish between Rayleigh scattered photons, which produce no energy change, and Compton scattering in which photons lose energy. By Shielding. Shielding a detector from direct exposure to a source is the obvious approach to block source radiation from reaching directly the scattering detector. However, shielding also scatters radiation, contributing to the background radiation. Radiation scattered by the shielding has an energy lower than that of the source, and thus can be removed by energy discrimination or by placing a radiation absorbing material (a filter) in front of a source or a detector. By Collimation. Collimating the source and the detector can also help reduce the scattering background component, by eliminating undesirable radiation that would otherwise reach the detector. However, like

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shielding, a collimator’s material can increase the amount of scattering. Lining inside walls of a collimator with a radiation absorbing material, or incorporating such material within its structure, can reduce the effect of collimator scattering. By Distance and Location. Distance can also be helpful in reducing the scattering background component. Scattered radiation diverges with distance over a wide angle, in accordance with the divergence law, section 3.6.2. Therefore, placing a detector as far away as possible from scattering walls, or placing these walls as far as possible from the detector, help reduce the background component of wall scattering. Since radiation scattered within walls tends to be absorbed inside the walls themselves, these walls can be shaped or oriented to enhance their selfabsorption effect. One should also position, and align with respect to the source, the scattering detector to obtain a high signal-to-background ratio, see references [319, 1343, 1344]. Obviously, one should place the scattering detector off the direct path of the incident radiation, and at locations where the streaming of source radiation through the source shielding is minimal. High-Energy Background. Although most scattered radiation from these walls tends to have a low energy, due to the many collisions encountered within the walls, radiation scattered from near the surface of walls tend to be high in energy. Source radiation leaking through the source shielding also contributes to this high-energy background. The lower efficiency of most detectors to higher energy radiation reduces to a great extent the contribution of this radiation to the background component. However, if the amount of high-energy background radiation is significant, it should be reduced. Keeping the detector away as much as possible from the source reduces this high-energy component, since high-energy (uncollided) radiation emerges from the source, while that scattered within the object tends to be clustered into the region closest to the source’s location. High-energy discrimination can be useful in this regard, particularly when the signal of interest is that of lowenergy radiation. Detector orientation can also help reduce the effect of high-energy background radiation. Orienting the detector, so that the path-length of radiation passing through it is minimal, will reduce the effect of higher-energy background radiation by lowering their detection efficiency. The same effect can also be reduced by choosing a smaller detector. In general, when detecting low-energy radiation, the detector active length should not exceed the “blackness” length for that radiation, i.e. the length beyond which all incident low-energy radiation is

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absorbed. Exceeding that blackness length will make the detector more sensitive to the higher-energy background radiation, while not enhancing the efficiency for the desirable low-energy radiation.

17.3.4.

In Emission

The background radiation encountered with radiation emission is in many ways similar to that of scattering. As in scattering methods, background radiation can emerge from the surroundings and the collimators. Therefore, many of the measures discussed in section 17.3.3 above for dealing with scattering background, can be applied to reduce the emission background. However, in emission-based methods, the scattered radiation itself constitutes a background component, as the emitted radiation is scattered within the inspected object and by the surroundings. By Energy. The characteristic energy of the emitted radiation can be used to discriminate against undesirable emissions. Interference between emissions from two entities with close energy of emissions can also be viewed as a background signal, particularly when one of those entities is present in the surrounding structure. Therefore, attention should be paid to selecting the activation or excitation source energy and choosing the materials used in constructing the surrounding shielding and collimators, so that the background component is minimized or the emission signal is sufficiently higher than that of the background radiation. Source Radiation. The source inducing emission can itself contribute to the background signal, when the detector is sensitive to the source radiation. When possible, filtering the source (see section 15.2) to remove unnecessary radiation can reduce the background signal. It should be also kept in mind that accelerator-based radiation sources result in lower background than isotopic sources, since the latter sources generate radiation continuously and can produce emissions in the surroundings even when the inspected object is absent. It is desirable, therefore, when using isotopic sources, to physically separate the source and the inspected object, even when the measured radiation has a low life-time since longer-lived activation may also be produced. Activation or excitation of detector material may also add to the background radiation and must be considered when low-level counting is to be performed. By Geometry. Making use of distance and geometry, as discussed in section 17.3.3, can also help reduce the background component. Therefore, attention should be paid to placing the detectors away from the

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surrounding walls, and positioning them at locations that provide a high signal-to-background ratio. By Delayed Detection. Monitoring delayed emission after removing the interrogated object from the irradiation field is an obvious way for reducing the effect of background radiation. When this is not possible, measuring radiation emissions after turning off the source, or using a pulsed source and measuring emissions between pulses, can also be helpful in this regard. Time gating is also effective in reducing the scattering background signal when a pulsed source is used, since the scattered radiation tends to take a longer time (has a larger path length) before reaching a detector. By Coincidence. Coincidence measurements, see section 4.5, are particularly useful in reducing the radiation background component in methods that rely on positron annihilation. The emitted pair of 511 keV photons reaches two detectors located at opposite directions almost simultaneously, since photons travel at the speed of light. Radiation emission by beta-decay usually produces a nucleus in an excited state that promptly decays by gamma emission. When possible, coincidence detection of the beta and gamma emission can be very effective in isolating the radiation emitting nuclide, and suppressing radiation emission from other nuclides and that resulting from scattering [15]. Anticoincidence measurements are also useful for discriminating against high energy radiation, particularly cosmic-rays. Here the primary detector is surrounded by a secondary detector, and the pulse in the primary detector is only accepted if no coincident pulse is detected in the secondary detector [15]. High-energy radiation succeeds in passing through both detectors, depositing energy and producing a pulse in both detectors, and thus can be eliminated by coincidence indications. The same process of anticoincidence is also useful in removing radiation that does not deposit its full energy within the primary detector. As this radiation escapes the primary detector, it will also deposit energy in the secondary detector, resulting in a signal in that detector that is almost in coincidence with the first one. In photon detection, this incomplete energy deposition produces Compton continuum in the detector, see section 4.3.2. Then the anticoincidence method is known as the Compton suppression technique.

17.4.

Dynamic Analysis

Aside from the statistical fluctuations of radiation counting, addressed in appendix G, time-dependent parameters can affect the obtained in-

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dications. Obviously, one must correct for the decay of a radioisotope source and fluctuations in the intensity of radiation generated by machines and nuclear reactors. In addition, when the interrogated object is in motion, or is undergoing temporal changes, it will affect the nature of the obtained indication. Some of the methods that can be used to deal with these time-dependent effects are discussed here. Changes in radiation source intensity can be dealt with, when possible, using a reference signal obtained with a detector that either monitors the source directly, or indirectly via interactions with a stable object. For instance, radiation leakage through the shielding of the source can be used as a reference signal, with respect to which time-varying measurements can be adjusted. Alternatively, the intensity distribution of the source can be measured in advance and used to account for the source fluctuations.

17.4.1.

Expected-Value Analysis

Let us assume that the source intensity distribution with time is known and is defined by the probability density function where is the probability of the source having intensity between I and be related to I at any moment in time. Let the measurement by: where is some known function. Since I changes with time, one will expect also to be time-varying. Two estimates of the measured value of can be evaluated: (1) by taking the value of corresponding where the symbol < . > refers to the expected value, to or (2) by estimating directly. The first estimate is associated with the expected value of the source distribution, and not the expected does not incorporate value of the parameter of interest. Thus fluctuation in the properties of the inspected medium. The first estimate is analytically expressed as:

This estimate is the correct (“actual estimate”) of as it corresponds to the value that would have been obtained if the source had a constant, non-fluctuating, intensity equal to < I >. The second estimate is given by:

where between

is the probability of the measurement Q having a value and at any moment in time, note that

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The estimate of given by Eq. (17.3) incorporates all possible fluctuations in introduced by the source, the medium, etc. Therefore, corresponds to the experimentally measured value. Time Bias. Obviously if is linearly related to I, the two estimates of obtained by Eqs. (17.2) and (17.3) would produce the same result. However, if is a non-linear function, the two approaches of Eq. (17.2) and (17.3) will produce two different estimates of the value of keeping Moreover, if the value of is affected in mind that by fluctuation associated with changes with time in the properties of the inspected medium, then the two estimates of will not be equal in value. Therefore, the difference between the two estimates, and introduced by defines the measurement bias in the value of fluctuations in the inspected medium. This bias can be defined by the relative “error”

where use is made of the fact that This bias parameter quantifies the difference between the measured value and the actual value. It can be zero in a linear system, but can be positive (indicating an overestimation) or negative (for underestimation). The evaluation of the bias defined by Eq. (17.4) requires a priori knowledge of the distribution of the source and the inspected medium with time. Note that using the distribution Eq. (17.3) can be expressed in terms of making use of the fact that thus eliminating the need to determine in advance. Reference [1345] presented this approach and applied it to study the source distribution effects in a measurement system that utilizes a nuclear reactor for measuring a fluctuating medium (boiling water).

17.4.2.

Frequency Analysis

If it is not possible to determine in advance the time-distribution of a source or a medium, frequency analysis should be performed in order to determine the dominant frequencies that affect the time variability of the measuring system. A number of excellent textbooks are available on this method of analysis, such as reference [1346]. A brief summary is given here, guided by reference [1347]. A time-varying signal can be viewed as being composed of a set of individual signals of varying frequencies and amplitudes. Fourier analysis allows the determination of the amplitudes of these signal components

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and the definition of phase relationship among various frequencies. For a measured time-dependent signal, the corresponding Fourier transform is given by:

where

refers to frequency and to time. The transform describes in terms of amplitude and frequency content. The integration required by Eq. (17.5) can be performed numerically, using with the aid of readily available fast Fourier discrete digital values of transform (FFT) computer software packages. An approximation of is given by:

where the values of provide discrete power values at frequency intervals apart, where is the time sampling interval (assumed constant), i.e. and N is the number of recorded measurements. The Fourier transform is a complex function, with real and imaginary terms. The square of its magnitude, is a measure of the The amplitude of is “power” contained within of the ratio of the while the phase-shift is the inverse tangent The amplitude frequency imaginary and real components of versus describes how the signal amplitude varies spectrum, with frequency. However, the power frequency spectrum, versus is more often used for analyzing the signal content. The area under the power spectrum plot is a measure of the power of while the area under the curve between and is the power contained in the signal within that frequency interval. Since in practice measurements are performed over a finite time periods, say rather than an infinite time period as required by the integral has to be such that it is sufficiently long in Eq. (17.5), the value of so that it statistically reflects, with reasonable accuracy, the behavior of the system. In other words, an observation period greater than should not change the Fourier Transform and the associated amplitude is determined in turn by the and power spectral density. The time number of samples, N, with where is equal to the inverse of the sampling frequency, The sampling theorem requires that the sampling rate must be more than twice the highest frequency, contained in the measured signal, that is or equivalently

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If the sampling frequency is less that

all actual fre-

quency content in the original signal above will appear as alias frequencies of less than In other words, all actual frequencies above will be folded back and received as lower frequencies in the Fourier is called the Nyquist frequency. To transformation. The frequency avoid this alias phenomenon, the sampling rate should be chosen to correspond to the maximum expected frequency. In addition, the signal must be filtered to remove any frequencies above The resolution of a discrete Fourier transformation, Eq. (17.6), is given The accuracy of the spectral amplitude representation by depends on the value of Different values of should be varied and the resulting amplitude distribution be compared to determine the value of that provides an acceptable level of precision.

17.4.3.

Movement

Another dynamic situation is encountered when the object is moving as in the case of a fluid flow, a flying object, or material on a conveyor belt. The same dynamic situation arises when the device is moving, while the object is stationary. The number of counts emitted from monitoring such time-varying inspection volume must be corrected for by a factor that depends on the speed of motion, and the width of the inspected volume along the direction of movement, The correction factor, P, is equal to unity, if where is the counting period, and is equal to if This factor P represents the probability that the radiation emanating from the object will be registered by the detector. An example application is discussed in section 11.5.4. If the motion is more complicated, the correction factor P will take a more complex form that may need to be determined experimentally by varying the velocity of motion and relating it to the recorded count rate.


Chapter 18 FINALIZATION

18.1.

Prototyping

The ultimate goal of a design process is to produce a device suitable for field use. The design process starts with a concept, followed by a laboratory demonstration, the development of a prototype suitable for field testing, and finally the full production of a working model. These stages of development are discussed below, guided by reference [1348]. Need and Concept Phase. The design process should be initiated by a mission need statement that outlines clearly why the device is needed, what are its desirable characteristics, where it is to be used, and when it is needed. The development of a new device usually starts with the concept phase, where an idea is conceived and its physical basis is established, preferably supported with calculations using Monte Carlo simulations. At the concept phase, the designer is also required to examine existing and alternative concepts and establish the likelihood of success, by performing a technical risk assessment that identifies potential hurdles and obstacles. It is also important at this stage, as well as in all other design stages, to involve potential users in order to ensure that the development process will lead to a practicable system. Demonstration Phase. The concept phase is followed by a demonstration phase that aims at establishing the feasibility of the proposed concept. This proof-of-concept stage is attained by accumulating experimental data that determines the functional baseline of the device, i.e. its capabilities and limitations. Before starting experiments, a test plan should be devised, identifying the parameters to be investigated, the type of experiments required and the order of carrying out these 763

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experiments, as discussed in section 17.1. Based on experience gained in this demonstration phase, the design of the system should be improved, if possible. The test plan should also be revised, so that tests in the development phase are conducted in a more orderly fashion. Unnecessary tests should be removed and new tests that may have not be initially envisioned should be added. Development Phase. The next step in the design process is the development phase that aims not only at demonstrating that the designed system meets the technical specifications, but also that it also satisfies all other needs in the day-to-day operation under various anticipated field conditions. This is done by constructing a prototype device. In the demonstration phase, a working laboratory model is usually used with little or no attention paid to environment conditions, such as heat, dust, moisture, surrounding high voltage equipment, etc., since this phase focuses more on the functionality of equipment. Problems such as detector drift, high-voltage instability, temperature variations, etc. may have been accommodated for in the demonstration phase by performing experiments within a narrow range, or for a short period of time, so that such variations do not exceed limits. However, the development prototype should accommodate such environmental and field conditions. Reliability, durability and robustness of equipment must also be considered. While in earlier phases, the experimentalist may not be have been concerned with tidiness, weight, size, or the aesthetics of the device, in the development phase all these factors should be taken into consideration. A prototype should also be tested in a double-blind fashion; that is the device should be operated by someone other than the designer, preferably the eventual user, and be tested with objects the nature of which are not disclosed in advance to the designer or the operator. At the end of this testing process, the design of the device may be adjusted and improved to better meet field conditions. The test plan should then be revised accordingly. Production Phase. The finalization of the design is achieved in the full production phase, where a production model is constructed. A rule for the production of a production model of a device states that [1348]: [T]he model must be well defined as to what it will do and how reliably will it do it, what range or ranges it will operate in, what its size and weight limits will be, what power input limits it must have, how easy it will be to maintain and support, how simple its operation will be, how safe it will be to operate, what speed of action it will have and what expendable supplies it will need during a unit time of operation.

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A production item planning program should be prepared and should include a clear statement of what the equipment will do and the conditions under which it must act. The plan should also consider the time and cost needed to make the device useful and practicable. Prior to the construction of the development/production prototype, the designer and the potential user must carefully establish together the design specifications, since subsequent changes in the specifications can be costly and time consuming. The designer should keep in mind that many units of the device may be produced. Therefore, fabricated parts should be designed so that they are as simple as possible, and off-the-shelf components and those supplied by more than one manufacture should be used as much as possible. The device should be fabricated in modules to facilitate easy maintenance and troubleshooting. Control and data collection should be computer based, with software that uses simple and clear logic that is easy to debug. Design planning must also pay attention to cost issues, and the time line for executing different tasks. Human factors and ergonomics engineering should also be considered in the early stages of the design. Provisions must also be made to accommodate alterations recommended by users of the device after working with the system for some time. The method of packing and shipping a device should be incorporated early in the design planning process, along with the process of unpacking and assembling the device and associated systems upon arrival to the user’s site. Documentation must also be prepared describing the device, its specifications components, associated computer software, operating procedure, maintenance, troubleshooting, safety precautions, etc. Testing and Evaluation. A production model should be subjected to independent testing and evaluation before field deployment, during both the development and production phases. Such testes may require the design and construction of a special testbed and test objects. Acceptance testing is then performed on site. Potential users of the device may have their own testing guidelines and criteria. Reference [1349] is an example of well-developed test and evaluation guidelines. This reference identifies the purpose of test and evaluation programs as to provide information to: verify technical performance specifications and objectives, verify operational effectiveness and suitability, provide information for assessing technical performance and risk, and provide information to support decision making. Useful information obtained during testing include: the device’s reliability, maintainability and frequency of availability, system interference and comparability with existing systems, component quality, site adaptability, etc.

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During the development phase, the primary objective of testing is to demonstrate that all specified technical and performance requirements are satisfactorily met. Operational testing focuses on the operational effectiveness and suitability of the device, as well as on the readiness of the infrastructure to accept the system. Operational suitability testing evaluates parameters such as device’s frequency of availability, compatibility, transportability, reliability, safety, etc. [1349]. After the success and acceptability of the first unit of the device, subsequent production units are subjects to testing by the manufacturer (or vendor) to ensure that the new units have the same quality and performance as the first unit. Field Familiarization. In order to verify that a site is ready to accommodate the new system, field familiarization should be conducted. This process aims at ensuring that the new device is properly and safely installed and is harmonized with existing systems and devices, and that operational procedures, system documentation and logistic support are in place [1349]. After familiarization, the device should be operated in a demonstration phase under intense scrutiny, until personnel become fully familiar with the system and a sufficient number of personnel are trained to operate it. Design refinement or adjustment of operational settings may be necessary after a period of field testing. The designer should therefore continue to monitor the performance of the device until it becomes fully accepted and understood by the user. A generic version of the modified device should be tested to verify requirement compliance and operational readiness, and to validate new functionality and to measure system performance [1349]. The responsibility of the designer does not end with the completion of the design process and the subsequent construction of the device. The designer is likely to be involved in preparing training material, or even in training operators. Experience from training, operation and maintenance of the device can also be helpful in improving the design of future generations. The designer’s input to the marketing process is also important, as indicated in the introduction to Part IV of this book.

18.2.

Intellectual Property Protection

Intellectual Property (IP) is the kind of property that results from the fruits of mental labor [1350]. Most jurisdictions provide certain legal protections for owners of such property. Issues related to protecting intellectual properties arising from engineering ideas and inventions are discussed in a number of books, among which are those of refer-

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ences [1351], [1352], [1353], [1354], [1355], and [1356]. However, the discussion given in this chapter is an overview of the issues, based mainly on references [1357] and [1350] and on the authors own experience. Laws in most jurisdictions protect intellectual property in one of four forms: Trade Secrets: protect any formula, pattern, device or compilation of information that is not a common knowledge and gives the user an opportunity to obtain an advantage over competitors who do not know, or do not use it. For example, a formula for preparing a radiotracer in a unique radiological or chemical form can be qualified as a trade secret. Copyright: protects forms of written or recorded work, that needs not to be novel or unique, but owes its origin to the author. Software for data acquisition or analysis fall under this category. Trademarks: protects any words or symbols used by a manufacture or a merchant to identify and distinguish goods or services from those produced by others. The manufacturer of a particular radiation device may assign such a trademark to the device. Patents: excludes others from making, using or selling an invention for a period of years, typically 15 to 20 years. Patents protect inventions of tangible things. Patents can be obtained for new and original designs, or for a utility (a function). Design patents protect the appearance of a product, not how it works. On the other hand, utility patents protect the functional aspects of an invention.

The designer of a novel radiation device is likely to be concerned with utility patents. Therefore, most of the discussion here is focused on such patents. It is worth, however referring to design patents as they provide an effective and inexpensive complement to the other methods of protecting intellectual property. The appearance of a device, in its compactness, flexible or aesthetic appearance, can be worth protecting. Design patents need not cover the entire device, but may be limited to a portion of the product. However, design patents cover only the ornamental features of a product not its functionality, though they are much less expensive to obtain than the more common utility patents. Utility patents can be any product, process, apparatus or composition. However, newly discovered physical laws or phenomena cannot be patented. Patents are issued by governments to encourage public disclosure of technical advances and as an incentive for investing in their commercialization [1350]. The common practices of property inheritance, selling,

768


renting and mortgage apply also to patents. They may even be taxed like any other property. To obtain a patent, the applicant must file a (1) timely application that describes a (2) new, (3) useful and (4) unobvious invention. A timely application requires the filing of an application typically within a year of disclosing the invention, say by publication, sale or public use; though some jurisdictions do not allow such grace period. A new invention by definition is that not contrived first, used or identically known by others, before the date of invention. An invention must also have a known useful purpose. An unobviousness on an invention means that “the differences between the invention and the prior public knowledge in its technical field must be such that a person having ordinary skill in this field would not have found the invention obvious at the time it was made” [1350]. The invention must be explained in the application in such a complete form that others can practice the invention, along with description, to the best of the inventor’s knowledge, of the best manner of carrying out the invention. The question that often faces an instrument developer is whether to apply for a patent or simply publish the work and be satisfied with the associated scientific credit. Given the cost of patenting, a patent should be obtained if there is a potential for commercial exploitation. Patents also give developers a right to exclude others, which further enhances the potential for commercialization. Moreover, a patent is a powerful tool for attracting investors. It should be kept in mind that the practicing of patent must not infringe on the patent rights of others, e.g. by incorporating others patent invention as a component of the commercialized product. Patent rights can be directly exploited by the inventor by commercializing the subject of the patent. Alternatively, the patent rights may be sold, licensed exclusively to others, or licensed non-exclusively to allow many parties to share the patent rights simultaneously; see reference [1358]. Patenting is a complex administrative and legal process that should be performed by a qualified patent agent. However, if an instrument developer intends to apply for a patent, records must be kept of receipts for parts and services used, if necessary, to establish when the patent was made, since patents are granted to the first inventor of the subject matter. It is also necessary to document the concept, testing results etc. When discussing intellectual properly with others, e.g. potential investors, confidentiality disclosure agreements (see reference [1359]) should be signed. Before applying for a patent, a decision has to be made on whether the invention is likely to be considered patentable, given the

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four criteria discussed above. However, a provisional patent application, allowed in some jurisdictions, may be considered. This a low-cost application that is followed by a full application, typically within a year, but it establishes the timing of the invention, and allows the inventor to assess the commercial viability of the invention. In order to prepare a valid patent application, the developer should disclose to the patent agent all necessary information, including the problems it solves, the difficulties that were overcome, any prior related inventions or published work, drawings, descriptions, etc. A patent agent will conduct a patent search to ensure that the invention has not been previously patented, and does not infringe on other patents. Following the filing of the patent application, the application is examined by the patent office, a process that can take many months. If a refusal to grant a patent is issued, the examiner’s objections will be given, but the applicant may modify the submission to deal with the examiner’s objections. That process may be repeated more than once until the examiner is satisfied, or the application is deemed unsuccessful.


Appendix A Basic Units and Constants

Units The Systéme International (SI)1 units are widely used, legislated by most jurisdictions, and required by almost all scientific journals. In radiation units, the use of “Curie” for measuring activity is replaced with the SI unit, “Bq”. The “rem” and “rad” units for absorbed radiation dose and dose equivalent, respectively, are also replaced by “Sv” and “Gy”, respectively; some workers use centi-gray (cGy) and centi-sievert (cSv) in place of the Gy and Sv, respectively. Although, the units of “eV” for radiation energy and “barn” for the microscopic cross-section are not strictly SI units, their use is permitted [1361]. Commonly used radiation units are defined below2:

1

The SI system is based on the units of meter (m) for distance, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, Kelvin (K) for temperature and mole (mol) for amount of substance; with radian (rad) for plane angle and steradian (sr) for solid angle. Derived units include: newton for force, joule (J = N m) for energy, watt (W = J/s) for power, pascal for pressure, volt (V = W/A) for electric potential, coulomb (C = A s) for electrical charge, weber (Wb = V s) for magnetic flux and tesla for magnetic flux density. The SI allowed prefixes are yotta zetta exa peta terra giga mega kilo hecto deka (da = 10), deci centi mili micro nano pico femto atto zepto and yocto see references [1360] and [1361] for more details. 2 The on-line reference [1362] (http://physics.nist.gov/cuu/Reference/unitconversions.html) provides access to a number of on-line links for conversion between units.

xxvii


xxviii

Microscopic cross-section:

Energy:

Activity:

(roentgen).

Exposure:

Absorbed dose: = 100 rad. Dose equivalent: 1 Sv (sievert) = absorbed dose in Gy × radiation weighing factors = 100 rem; see chapter 5 for weighting factor.

Constants The following are useful constants in radiation physics [13]3: Symbol

Name

Value

Avogadro’s number speed of light Planck’s constant Boltzmann’s constant elementary charge electron rest-mass proton rest-mass neutron rest-mass alpha particle rest-mass one year

3

1.007 u 1.0087 u 4.001 u

See reference [1363] (http://physics.nist.gov/cuu/Constants/index.html) for up-to-date, online, exact values.

Appendix B List of Elements and Natural Isotopes

For information on nuclear and atomic properties, visit the web site of the National Nuclear Data Center of the Brookhaven National Laboratory: “http://www.nndc.bnl.gov/”. Element

Symbol

Actinium Aluminum Americium Antimony Argon Arsenic Astatine Barium

Ac Al

Berkelium Beryllium Bismuth Boron Bohrium Bromine Cadmium

a

Am Sb Ar As At Ba

Bk Be Bi B Bh Br Cd

Atomic Number (Z) 89 13 95 51 18 33 85 56

97 4 83 5 107 35 48

Natural Isotopes A (%)a 27 (100)

121 (57.21), 123 (42.79) 36 (0.3365), 38 (0.0632), 40 (99.6003) 75 (100) 130 (0.106), 132 (0.101), 134 (2.417) 135 (6.592), 136 (7.854), 137 (11.232), 138 (71.698) 9 (100) 209 (100) 10 (19.8), 11 (80.2)

79 (50.69), 81 (49.31) 106 (1.25), 108 (0.89), 110 (12.49) 111 (12.80), 112 (24.13) 113 (12.22), 114 (28.73), 116 (7.49)

A: mass number, % natural abundance, atom percent, compiled from reference [1364].

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xxx

Atomic Number (Z ) 20

Element

Symbol

Calcium

Ca

Californium Carbon Cerium

Cf C Ce

98 6 58

Cesium Chlorine Chromium

Cs Cl Cr

55 17 24

Cobalt Copper Curium Dubnium Dysporsium

Co Cu Cm Db

27 29 96 105 66

Einsteinium Erbium

Es Er

99 68

Europium Fermium Flouroine Francium Gadolinium

Eu Fm F Fr Gd

63 100 9 87 64

Gallium Germanium

Ga Ge

31 32

Gold

Au

79

Dy

Natural Isotopes A(%) 40 (96.94), 42 (0.647), 43 (0.135), 44 (2.09), 46 (0.004), 48 (0.187)

…

12 (98.89), 13 (1.11) 136 (0.185), 138 (0.251), 140 (88.450), 142 (11.114) 133 (100) 35 (75.77), 37 (24.23) 50 (4.345), 52 (83.789), 53 (9.501), 54 (2.365) 59 (100) 63 (69.17), 65 (30.83)

… …

156 (0.06), 158 (0.10), 160 (2.34), 161 (18.91), 162 (25.51), 163 (24.90), 164 (28.18)

…

162 167 170 151

…

(0.139), 164 (1.601), 166 (33.503), (22.869), 168 (26.978), (14.910) (47.81), 153 (52.19)

19 (100)

…

152 (0.20), 154 (2.18), 155 (14.80), 156 (20.47), 157 (15.65), 158 (24.84), 160 (21.86) 69 (60.108), 71 (39.892) 70 (20.37), 72 (27.31), 73 (7.76), 74 (36.73) 197 (100)

Appendix B: List of Elements and Natural Isotopes

Element

Symbol

Hafnium

Hf

Hassium Helium Holmium Hydrogen Indium Iodine Iridium Iron

Hs He Ho H In I Ir Fe

108 2 67 1 49 53 77 26

Krypton

Kr

36

Lanthanum Lawrencium Lead

La Lr Pb

57 103 82

Lithium Lutetium Magnesium Manganese Meithnerium Mendelevium Mercury

Li Lu Mg Mn Mt Md Hg

3 71 12 25 109 101 80

Molybdenum

Mo

42

Neodymium

Nd

60

Neon Neptunium Nickel

Ne Np Ni

10 93 28

Niobium Nitrogen Nobelium Osmium

Nb N No Os

41 7 102 76

Atomic Number (Z) 72

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Natural Isotopes A(%) 174 (0.16), 176 (5.26), 177 (18.60), 178 (27.28), 179 (13.62), 180 (35.08)

…

3 (0.000137), 4 (99.999863)

165 (100)

1 (99.985%), 2 (0.015)

113 (4.29), 115 (95.71)

127 (100)

191 (37.3), 193 (62.7)

54 (5.845), 56 (91.754), 57 (2.119),

58 (0.282)

78 (0.35), 80 (2.28), 82 (11.58),

83 (11.49), 84 (57.00), 86 (17.30)

138 (0.090), 139 (99.910)

…

204 (1.4), 206 (24.1), 207 (22.1)

208 (52.4)

6 (7.59), 7 (92.41)

175 (97.41), 176 (2.59)

24 (78.99), 25 (10.00), 26 (11.01)

55 (100)

… …

196 (0.15), 198 (9.97), 199 (16.87),

200 (23.10), 201 (13.18),

202 (29.86), 204 (6.87)

92 (14.84), 94 (9.25), 95 (15.92),

96 (16.68), 97 (9.55), 98 (24.13)

100 (9.63)

142 (27.2), 143 (12.2), 144 (23.8),

145 (8.3), 146 (17.2), 148 (5.7),

150 (5.6)

20 (90.48), 21 (0.27), 22 (9.25)

58 (68.077), 60 (26.223), 61 (1.140),

62 (3.634), 64 (0.926)

93 (100)

14 (99.634), 15 (0.366)

184 (0.02), 186 (1.59), 187 (1.6), 188 (13.29), 189 (16.21), 190 (26.36) 192 (40.93)


xxxii

Atomic Number (Z) 8 46

Element

Symbol

Oxygen Palladium

O Pd

Phosphorus Platinum

P Pt

15 78

Plutonium Polonium Potassium Praseodymium Promenthium Protactinium Radium Radon Rhenium Rhodium Rubidium Ruthenium

Pu Po K Pr Pm Pa Ra Rn Re Rh Rb Ru

94 84 19 59 61 91 88 86 75 45 37 44

Rutherfordium Smarium

Rf Sm

104 62

Scandium Seaborgium Selenium

Sc Sg Se

21 106 34

Silicon Silver Sodium Strontium

Si Ag Na Sr

14 47 11 38

Sulfur

S

16

Tantalum Technetium Tellurium

Ta Tc Te

73 43 52

Terbium Thallium Thorium Thulium

Tb Tl Th Tm

65 81 90 69

Natural Isotopes A(%) 16 (99.762), 17 (0.038), 18 (0.200) 102 (1.02), 104 (11.14), 105 (22.33), 106 (27.33), 108 (26.46), 110 (11.72) 31 (100) 190 (0.014), 192 (0.782), 194 (32.967), 195 (33.832), 196 (25.242), 198 (7.163)

39 (93.2581), 40 (0.0117), 41 (6.7302) 141 (100)

185 (37.40), 187 (62.60) 103 (100) 85 (72.17), 87 (27.83) 96 (5.54), 98 (1.87), 99 (12.76), 100 (12.60), 101 (17.06), 102 (31.55) 104 (18.62) 144 (3.07), 147 (14.99), 148 (11.24), 149 (13.82), 150 (7.38), 152 (26.75), 154 (22.75) 45 (100) 74 (0.89), 76 (9.37), 77 (7.63), 78 (23.77), 80 (49.61), 82 (8.73) 28 (92.230), 29 (4.683), 30 (3.087) 107 (51.839), 109 (48.161) 23 (100) 84 (0.56), 86 (9.86), 87 (7.00), 88 (82.58) 32 (95.02), 33 (0.75), 34 (4.21), 36 (0.02) 180 m (0.012), 181 (99.988) … 120 (0.09), 122 (2.55), 123 (0.89), 124 (4.74), 125 (7.07), 126 (18.84), 128 (31.74), 130 (34.08) 159 (100) 203 (29.524), 205 (70.476) 232 (100) 169 (100)

Appendix B: List of Elements and Natural Isotopes Element

Symbol

Atomic Number (Z) 50

Tin

Sn

Titanium

Ti

22

Tungsten

W

74

Uranium Vanadium Xenon

U V Xe

92 23 54

Ytterbium

Yb

70

Yttrium Zinc

Y Zn

39 30

Zirconium

Zr

40

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Natural Isotopes A(%) 112 (0.97), 114 (0.66), 115 (0.34), 116 (14.54), 117 (7.68), 118 (24.22), 119 (8.59), 120 (32.58), 122 (4.63) 124 (5.79) 46 (8.25), 47 (7.44), 48 (73.72), 49 (5.41), 50 (5.18) 180 (0.12), 182 (26.50), 183 (14.31), 184 (30.64), 186 (28.43) 234 (0.0054), 235 (0.7204), 238 (99.2742) 50 (0.250), 51 (99.750) 124 (0.095), 126 (0.089), 128 (1.910), 129 (26.40), 130 (4.071), 131 (21.232), 132 (26.909), 134 (10.436), 136 (8.857) 168 (0.13), 170 (3.04), 171 (14.28), 172 (21.83), 173 (16.13), 174 (31.83), 176 (12.76) 89 (100) 64 (48.63), 66 (27.90), 67 (4.10), 68 (18.75), 70 (0.62) 90 (51.45), 91 (11.22), 92 (17.15), 94 (17.38), 96 (2.80)


Appendix C Relativistic Mechanics

Small nuclear and atomic particles can reach a speed close to the speed of light. At such high-speed their corpuscular behavior begins to blur with that of wave properties. This in turn affects particle kinematics (mass, momentum and energy). Relativistic mechanics is applied to describe a particle’s behavior when its speed approaches the speed of light. Since radiation particles usually move in a straight line, until they encounter an interaction, the special theory of relativity is applied. This appendix provides a short summary of the basics of relativistic analysis; for more details consult a basic physics textbook, such as references [48] and [1365]. The special theory of relativity is based on the premises that: 1 A physical law maintains the same mathematical form in coordinate systems that are in uniform relative translational motion. 2 The speed of light, c, is the same for any two observers who are in a uniform rectilinear relative motion, and is independent of the motion of the source.

In order to accommodate these two postulates, space and time are viewed together as forming a four-dimensional Euclidean space whose basic axes are, for any given observer, orthogonal and independent. In this four-dimensional space, the time is an independent variable, much like the position variables and This necessitates the introduction of a fourth component of force and momentum, and some other The proper-time interval time-like variable called the “proper time”, apart between two events whose space coordinates are a distance xxxv

xxxvi


from each other is defined by [1365]:

The time interval, can be either positive, negative or zero, so that can be real, imaginary, or singular. When is real, it resembles a “time-like” interval, while when it is imaginary it is a “space-like” interval. In the four-dimensional space, a four-vector velocity, and a corresponding four-momentum components, can be defined as:

where is the square of the ordinary 3-vector velocity, and is the “rest” (at zero speed) mass of the object.

and becomes apparent if one considers the The physical meaning of

where relativistic effects are not important. low-speed case, Then the last equation of (C.5) can be expanded1 as:

The dominant term in this expression is precisely times the wellknown non-relativistic kinetic energy, Analogously, is an energy term, which is called the total energy of the particle. This term defines the “total” energy, E:

1

Taylor series expansion:

Appendix C: Relativistic Mechanics

xxxvii

This total-energy consists of an intrinsic constant component, called “self-energy” or “rest-energy”, and a variable component acquired by motion, the kinetic energy, T. That is, The kinetic energy is equal to only for speeds that are small compared to c. can be approximated using Eqs. (C.7) The kinetic energy, and (C.6) as:

The total energy, E, is also expressed in terms of a “relativistic mass”,

so that Then from Eq. (C.7), one obtains:

The introduction of the relativistic mass simplifies the expressions for the four-vector momentum of Eqs. (C.5) to The ordinary momentum of a particle along its direction of motion is then by squaring Eq. (C.9) and multiplying it by equal to one obtains: Therefore, in a potential-free medium, the difference between the totalenergy of a particle, and its rest-mass energy, must be equal to its kinetic energy, T. That is, Then one can obtain the relationship: Therefore, for a “particle” that has a zero rest-mass (e.g. a photon or a neutrino), the momentum is simply The “equivalent” mass2, is then equal to and the velocity must be equal to c. Note that solving Eq. (C.11) for T produces two states:

The concept of negative energy is utilized to explain some physical phenomena, see section D.4. Using Eq. (C.11) can be rewritten as:

2

Recall that mass is resistance to motion.

xxxviii


The rest-mass of the electron is so small that the relativistic increase in the mass of an electron is 1% of the rest-mass for each 5 keV of kinetic energy [48]. It is a must, therefore, to treat the kinematics of electron motion in a medium relativistically [48].

Appendix D Quantum Mechanics

D.1.

Preliminaries

Conventional mechanics is concerned with the conservation of mass, energy and momentum. In radiation physics, these conservation laws, along with relativistic mechanics (appendix C), are used to describe the kinematics of an interaction, i.e. the change in energy and direction. The probability of occurrence of a particular interaction is not addressed by conservation principles. Quantum mechanics deals with this problem by providing a framework for determining the cross-section of a particular reaction. This is done by examining the effect of the potential of a target nucleus on incoming radiation, with the latter viewed as an incoming wave even for radiation with corpuscular nature. Atomic and nuclear systems can exist only in discrete quantized states of internal motion. The uniqueness of these states is what makes such systems inherently stable and reproducible. This quantum (discrete) nature becomes apparent once the wave mechanics of the interaction process are formulated. Although exact calculations with wave mechanics are not possible, they provide some insight into the nature of the cross-section and their behavior with energy. This appendix provides a short introduction to the concepts of wave mechanics. For more details, the reader should consult one of the many available textbooks on quantum mechanics. Duality of Particle and Wave. A particle moving with a momentum can be assigned an equivalent wavelength called the de Broglie wavelength, determined by the relationship:

xxxix

xl


where is Planck’s constant. For elementary particles (electrons, protons, neutrons, etc.), the wavelength is usually of the order of nuclear Therefore, dimensions, due to the small value of this duality principle is applicable only to interactions between particles with dimensions comparable to the de Broglie wavelength. Duality also means that waves can assume corpuscular properties. can be given a momentum Thus, a photon of energy and a relativistic mass where is the wave frequency, is the wavelength and is the speed of electromagnetic waves (speed of light). Classical Wave Equation. The one-dimensional form of the wave is given by: equation, in the

where is the amplitude of the wave motion, and refers to time. A general solution of Eq. (D.2) can be obtained by assuming that the spatial behavior of is completely independent of its temporal behavior, so that can be expressed as:

This enables the separation of Eq. (D.2) into to two equations, one in and the other in :

where is a constant, since each function is dependent on a separate variable. The function has one of the following solutions:

This is the solution for a simple harmonic motion. The function has the solutions:

All the these solutions have a periodical behavior as their arguments Therefore, from Eqs. (D.5) and (D.6), one can conclude change by that is the wave-number of a wave of wavelength One can choose a particular solution of the wave equation, Eq. (D.2), as:

Appendix D: Quantum Mechanics

xli

where use is made of the fact that with being the wave frequency. Substituting the above solution into the general wave equation (D.2) leads t:

This is the classical wave equation when expressed in space only, assuming periodic behavior in time.

D.2.

Schrödinger Equation

Consider a free particle, with a kinetic energy entering a system of a potential energy U. The free particles are elementary particles, such as electrons, neutron, protons, while the potential is that of an atom or a nucleus. Conservation of energy requires that total energy, remains constant. Therefore, the momentum of the particle at any state must be equal to: The wave associated with this particle according to the duality principle,

Eq. (D.1), results in a wave number, , such that:

where

Eq. (D.8) can now be expressed as:

This is the Schrödinger’s equation. When two particles, say a neutron and a nucleus, approach each other, a wave equation can be written taking into account their relative motion and center-of-mass. The three-dimensional wave equation for two particles of mass, and M, is given by [48]:

where is the relative separation distance between the two particles. The value is known as the reduced mass, and is equal to if In the case of a neutron and a heavy nucleus, the reduced mass would be equal to the mass of the neutron indicating that the center-of-mass of the two particles almost coincides with that of the heavy nucleus. The wavelength of relative motion is then given by:

xlii


The solution of Eq. (D.12) determines the states this two-particle system can presume. The simplest form of a potential field is that of a square-well model, where the potential energy of the nucleus is constant, over a distance extending from the center of the nucleus to its radius. Outside the nucleus, the potential energy follows the coulomb value where is the charge of the nucleus, is the charge of the incoming particle and is the distance to the center of the nucleus. Solution. Assuming that the solutions of the wave in the radial, polar and azimuthal directions, see Figure 3.1, are not interdependent, then a solution for Eq. (D.12) can be found using the separation of variables1:

Analogous to Eq. (D.4), one can find separation constants for the differential equations for the functions R and Y, and for the differential equations for the functions and The separation constant for R and Y is designated as for reasons that will become apparent shortly, while is used as the separation constant for the functions and for the solution of Y at a given value of Then, applying Eq. (D.14) to Schrödinger’s equation, Eq. (D.12), leads to: Radial:

Polar:

Azimuthal:

Magnetic Quantum Number. The differential equation for Eq. (D.17), is the well-known equation for simple harmonics motion, and has possible solutions analogous to those of Eq. (D.5), as 1

The process of separation of variables, is only valid if the potential, symmetric and if the separation constants are suitably chosen.

is spherically


xliii

or or a combination of. However, only integer values of (positive or negative) are acceptable solutions, since the wave function and consequently can assume only single-values for each value The integer is known as the magnetic quantum number. The of value of defines the angular momentum of a particle along an external (uniaxial) magnetic field. When applied to an atom under the effect of an external field, the energy levels of the atom split into new levels, each with a different value of although the original energy of the electron’s orbit does not depend on the value of This effect is known as the Zeeman effect. Angular-Momentum Quantum Number. Eq. (D.16) is also a mathematically familiar second-order differential equation, known as Legendre’s equation. It has two general independent solutions, each of However, when which can be written as power series in i.e. along the polar axis, both of these solutions for become infinite, When is a positive integer or zero, except for particular values of and when the resulting solutions are finite, single-valued, and continuous for all values of making them physically acceptable solutions for In the special case of becomes constant, and the solutions of Legendre’s equations are called the Legendre Polynomials The Legendre Polynomials of degree where is an integer, are defined such that:

The values of the first few Legendre polynomials are: When and the solutions of Legendre’s equation are called the associated Legendre functions, These can be expressed in terms of Legendre polynomials as:

The radial part of the solution of the wave equation, Eq. (D.15), can at its be best examined by considering an incident particle, of mass closest distance of approach, measured from the center-of-mass of the potential field of a target nucleus of mass M. Then, non-relativistic conservation of energy leads to:

xliv


where is the particle’s speed at and the total energy, W , is the initial kinetic energy of the particle (when the rest-mass energy is not included), at some distance far way from the field. At the particle is expected to be moving normal to i.e. tangential to the radius of the sphere around the potential field. The angular momentum, J, of the particle, around the center-of-mass is then:

The combination of Eqs. (D.20) and (D.21), leads to:

Therefore, at the distance of closest approach, the total energy is the sum of the potential energy and the rotational kinetic energy. Note that is equal to the moment of inertia of the system at The angular momentum, J, is a constant of motion, and thus must have the same value away from the potential field and when it approaches it. Therefore, from Eqs. (D.22), and by comparison with the last term in Eq. (D.15), one can conclude that:

which is the angular momentum of the system about an axis through its center-of-mass and normal to the polar axis. The integer is called the angular-momentum quantum number; or more accurately the orbitalangular-momentum quantum number, to accommodate bound states, such as those of the atomic electrons around a nucleus or the nucleons within a nucleus. Nuclear collisions are classified using the values, with a terminology borrowed from Rydberg’s notation in atomic spectroscopy [48], see Table D.1. The magnetic quantum number can be viewed as corresponding to the numerical value of the projection of the angular momentum, associated with on an external magnetic field. Hence according to Eq. (D.23), is an integer, and may have only any of the values from to including zero, as shown in Table D.1. Therefore, at the collisions between a free particle and a potential field of a target are called the s-wave collisions. The wave represented by any value of is called a partial wave. The summation of all these partial wave represents the wave “packet” associated with the particle. The microscopic cross-section is proportional to the intensity of waves, i.e. to the square of the amplitude of the wave obtained by the solution


xlv

of Eq. (D.12), using the particular potential of the nucleus. Note that in coherent scattering, amplitudes from different partial waves are added while preserving their relative phases, then squared to obtain the scattering cross-section. On the other hand, in incoherent scattering, partial waves are first squared, then combined to define the cross-section. With neutral particles, such as neutrons, the potential of the nucleus is the only potential that needs to be considered. With charged particles, the coulomb electrostatic field, must also be considered. Note that away from a potential field, the wave packet becomes a plane wave. S-wave collisions tend to dominate, in most collisions. Spin. Free particles and nuclei have also a spin angular momentum. That is, a particle spins around an axis passing through itself. This spin accounts in part for the splitting up of the angular momentum of a particle along an external axis. The spin states are assigned a quantum number, The spin of a free particle can be in one of two opposite directions (spin-up or spin-down), and hence assumes the values of The angular momentum corresponding to in analogy to Eq. (D.23), is equal to The nucleons of a nucleus tend to form pairs so that their individual spins and magnetic moments cancel out. Thus the spin of a nucleus with even-even nucleons (even number of protons and neutrons) is always zero, while the spin of a nucleus with an odd mass-number is in many cases entirely due to the motion and spin of the single unpaired nucleon. The spin of individual electrons forming an atom combine to produce an overall angular momentum vector, with a corresponding spin quantum number where is the spin of the electron. The number of permitted orientations of S with respect to an external in Table D.1, is (2S + 1). field direction, in analogy to The nucleons of a nucleus also combine to form an overall spin I, which is similar in nature to that of the atomic electrons. When atoms combine to from a molecule their angular moments also combine. For

xlvi


example, in the case of a hydrogen gas,

the spin of each of the

hydrogen nuclei (protons) is It is then possible that some molecules may have two protons spinning in the same direction, giving a total spin S = 1, while others spinning against each other, resulting in a total spin of zero. Since there are (2S + 1) orientations with respect to an external field direction, S = 1 can have three different orientations (states), +1,0, –1, while S = 0, has only one state. Therefore, the proton combination of S = 1 is three times more probable than that of S= 0. Molecules in the state of S = 0 are known as the otrho-hydrogen molecules, while molecules with S = 0 are known as the para-hydrogen molecules. A similar situation arises when a neutron interacts with a proton, where either triplet, S = 1, or singlet, S = 0, spin states can exist for the combined neutron-proton system, with a 3:1 probability of the former to the latter. In general for a nucleus of a spin I interacting with a neutron, two spins states can exists: and with a probability respectively. and

D.3.

Concept of Cross-Section

Free Particles. A beam of free particles of wavelength can be visualized as a set of co-cylinders whose radii are where is the wavenumber, Particles in the beam with an angular-momentum quantum number can be found somewhere in the annulus with an inner radius of and an outer radius of The area of this annulus is:

A free beam can be occupied by particles of continuous (not discrete) values of angular moment. The number of free particles that can be found between angular moments represented by is given by equation (D.24). When the beam is subjected to the field of a nucleus, these particles will occupy orbits defined by etc. An upper limit of the absorption cross-section can be represented by the area of the zones, i.e. by the maximum number of particles that can be absorbed by the potential field. For the partial wave, this upper limit is:

However, as shown later, Eq. (D.40), the maximum cross-section for the potential scattering cross section is The incident wave satisfies the wave equation, Eq. (D.12), when i.e. when the incident particles are far away from the target nucleus,


xlvii

so that the potential of the nucleus has no effect on the wave and can be set to zero, leading to:

with where E is the kinetic energy of an incident particle, which is then equal to its total energy, W, since the particle is away from the potential field. One solution for Eq. (D.26) is . Another solution can be obtained in terms of the partial waves, by the separation of variables, analogous to Eqs. (D.15) to (D.17). The radial part of the solution, similar to that of Eqs. (D.15), is the spherical Bessel function:

The plane wave for free particles has a zero magnetic quantum number since it is not subjected to the potential field of the nucleus. For the Legendre equation, Eq. (D.16), gives the Legendre polynomials The wave equation (D.26) has, therefore, the solution

where

are constants and can be shown to be given by [48]:

in order to satisfy the fact that the probability of finding a particle everywhere in the spatial space is equal to unity. Given the fact that is also a solution of the wave equation (D.26), then

which shows how the plane wave can be expressed in terms of elementary spherical partial waves. Potential Scattering. A beam of free particles can also be represented by a plane wave , where with being the velocity of the particles, and is their direction of propagation. When

this beam approaches a nucleus, it can be scattered by its potential well,

This form of scattering is, therefore, called potential scattering.

Note that is the relative velocity of approach of the incident particles

xlviii


in the center-of-mass system and its value is not altered by collision, see chapter 3. The probability of scattering by an angle can be represented in terms of the square of the amplitude of the scattered spherical wave emanating from the center of the nucleus. The scattered wave can be given the form where is a function of the wave number of the incoming wave, and the potential of the target nucleus, is used, instead of since the incoming wave The term is moving in a direction opposite to which originates from the center of the nucleus. The scattering wave is a function of not since by squaring the magnitude wave one obtains the intensity of the scattered particles, which then follows the law of divergence, section 3.6.2. The scattered wave combined with the incoming wave at a large distance, from the target nucleus, i.e. for can be expressed as: Subtracting the incident wave, scattered wave at

from the total wave gives the

Total Disturbance Wave. A solution for the total wave function, must include the effect of By analogy with Eq. (D.28), for can be expressed as: a solution for

where are constants that satisfy Eq. (D.31) and radial wave equation, Eq. (D.15), with a potential are found to have the values [48]:

is a solution of the The constants

where is phase shift of the partial wave caused by the scattering This phase shift is due to the presence of the potential potential and therefore is independent of the angle Scattered Wave. Now, subtracting Eq. (D.28) from equation (D.32), a solution for the scattered wave, can be expressed as:


xlix

which is a valid solution when decreases faster than for large [48]. Note that is a complex function, with real and imaginary components. Differential scattering cross-section. Normalizing the intensity of incident particles per unit volume to unity, that is the corresponding fluence becomes equal to particles per unit area. The number of scattered particles crossing an element of per unit time, at a location designated by the spherical coorarea dinate is the product of the probability of scattering, the area and the velocity of the elastically scattered particles, and thus is equal to Dividing this number by the incident flux, one obtains the differential cross-section for elastic scattering (into the solid angle That is:

The involves only the square of the absolute value, which can be written

as where

and

The cross-section for elastic scattering is the integral of the differential cross-section at all possible angles:

which gives:

must where the phase-shift is a functions of and and decrease faster than for very large The actual value of the phaseshifts can be obtained, at a given incident particle energy, only if the

potential of the target nucleus is known and is well-defined. This is

l


where experiment and theory meet in the process of determining the cross-sections. Using Eq. (D.34), one can show that the differential cross-section for elastic s-wave scattering is given by:

Since this differential cross-section is not dependent on the angle of scattering, the scattering of the s-wave is isotropic in the center-of-mass system (at which the above analysis is performed). The integral of Eq. (D.41) can also be shown to be in agreement with Eq. (D.40).

D.4.

Quantum Electrodynamics

The probability of interaction of charged-particles with electromagnetic fields, including that of photons, can be evaluated by representing the electromagnetic forces by “virtual” photons that are emitted and absorbed [48]. In other words, the energy of an electromagnetic field can be translated into a number of “equivalent” photons, or quanta, the number of which is small, a few times where:

The constant, is known as the fine-structure constant. The strength of coupling between a charged-particle and an electromagnetic field is, Virtual photons can be seen as representing therefore, represented by transitions between negative (Dirac holes) and positive energy states; see Eq. (C.12). The negative states are considered to be normally filled and are only observed when a vacancy is created in them. In bremsstrahlung, a charged-particle loses energy by undergoing transitions between two positive states, emitting real photons (photons in a free state). This process is accomplished by the scattering of a charged-particle first by a virtual photon from the electromagnetic field of the nucleus, then by the free photon created in the process. In pairproduction, the energy of a photon is used to lift an electron from a hole to a positive energy, by crossing an energy barrier equal to is the electron’s rest-mass [48]. The “hole” becomes then an where observable positron. Pair-production can also be seen as the result of a positron scattered by the virtual photon, then by the real photon creating an electron. Therefore, both the bremsstrahlung of electrons and the pair-production process of photons have the same nuclear cross-section, both of the order of where is a constant known Exchange of more as the classical electron radius


li

than one virtual photon introduces another a term in the cross-section, requiring the so-called radiative corrections to the cross-section. This correction is associated with the emission and reabsorption of virtual photons, and with the emission of low and high energy real photons [68]. Compton scattering can also be described by quantum electrodynamics as a combination of two processes [48]: 1 The incident photon of energy is absorbed virtually by the electron, then a real photon of energy is emitted to ensure energy and momentum conservation. 2 The electron virtually emits a photon of energy then a real photon is absorbed to conserve energy and momentum. of energy

This representation is the essence of the Klein-Nishina differential crosssection of Eq.(3.42) [48]. The involvement of more than one virtual photons introduces radiative and double Compton corrections, in the to the cross-section [51]. The emission and reabsorption order of of virtual photons leads to the radiative correction, while the double Compton effect is associated with the emission of a real photon, usually very low in energy.


Appendix E Nuclear/Atomic Parameters for Compounds and Mixtures

This appendix presents a number of approaches for calculating the atomic and nuclear parameters of a chemical compound or a mixture of elements. The application of these methods is demonstrated for water as an example of chemical compound, which can also be viewed as a mixture of hydrogen and oxygen atoms.

E.1.

Atomic Density

Consider a molecule of a molecular weight M consisting of various species (types) of atoms, each has mass-number of The number of molecules per unit mass, is:

where u is the atomic mass unit molecules per unit volume, N, is

The number of

where is the mass-density of the material. For a single element, M in Eqs. (E.1) and (E.2) is replaced by the mass number, A. For a mixture of known density, and weight fractions, of components, the atomic-density of component can be expressed as:

liii

liv


Note that density of the mixture can be calculated from the density of individual components, as:

When atomic fractions, are given, as often the case in chemistry handbooks, the atomic density of the mixture can be expressed as:

where as:

defines an effective mass-number based on the weight fractions

The atomic density, of component, is calculated as

Note that, the atomic fraction, is related to the weight fraction,

by:

where

is an effective mass-number defined as:

The effective mass-number defined by Eq. (E.8) is different from that of Eq. (E.6), yet different from that defined later by Eq. (E.18), since the definition of the effective value depends on its use.

E.2.

Electron Density

For a compound, the number of electrons per unit volume, or electron density, making use of Eq. (E.2), is equal to:

where M is the molecular-number of the compound (number of electrons per molecule), and Z is the number of electron per molecule. The electron-density for a mixture is defined as:

where species

and are, respectively, the weight (or mass) fraction of its atomic-number and its mass-number. The electron-density

Appendix E: Nuclear/Atomic Parameters for Compounds and Mixtures

lv

in Eq. (E.10) is derived by summing the number of electrons per unit volume for each species. For example, has two species (H and O), with 1, (for hydrogen), (for oxygen), M = 2 × 1 + 16 = 18, Z = 2 × 1 + 8 = 10, for the molecule. It is straightforward to show that for from Eq. (E.9) and equal to from Eq. (E.10), that is, as one would expect, Eqs. (E.9) and (E.10) are identical.

E.3.

Macroscopic Cross-Section

The macroscopic cross-section of a compound, can be calculated from the microscopic cross-sections, of its constituents as:

where is the atomic-density of atoms of type lated as:

which can be calcu-

here is the number of atoms of type in the molecule; for instance for and The expression of Eq. (E.12) can be manipulated as follows:

where is the mass-number of species hence the weight-fraction of that species is equal to Therefore, the macroscopic crosssection of the compound can also be calculated, using Eqs. (E.11) and (E.13), as:

is the macroscopic cross-section of atomic species if it had where the density of the compound. If one forms a mixture of materials each has its own density, and then the where is the after mixing had a weight fraction, volume occupied by species in the mixture and V is the total volume of where is the volume-fraction the mixture. Therefore, occupied by species Then, by substituting this expression of in the middle side of Eq. (E.14), the macroscopic cross-section of the mixture becomes equal to:

lvi


For

expressions (E.11) and (E.12) give:

Using Eq. (E.14), one gets:

which shows that relationships (E.ll) and (E.14) are equivalent, though the latter is directly applicable to mixtures. Note, however, that these two expressions are not useful when molecular vibration can affect the radiation interaction, as in the case of thermal-neutron interactions, where measured values for the molecule of interest should be used (see section 3.5). If one considers boiling water, say under saturation conditions, with a vapor phase occupying a volume-fraction, then the liquid phase will The specific volume (inverse density) have a volume fraction of can be obtained for each phase from steam tables, under a given pressure or temperature, as for the vapor phase and for the liquid phase. For this two-phase flow mixture, one can use Eq. (E.15) to calculate its macroscopic cross-section, as:

Note that since both phases are made of the same material, they both have the same microscopic cross-section and molecular weight M = 18. Therefore, in the above expression is equal to where is as calculated in the above paragraph and N is the atomic-density of . Note also that the approximation in the above in most cases (for expression is due to the fact that usually pressures less than about 10 MPa). The same expression of Eq. (E.16) could have been arrived at by viewing the macroscopic cross-sections as


lvii

the number of barns per unit volume, and weighting its value for each phase by its volume fraction.

E.4.

Effective Mass and Atomic Numbers

Since photons mainly interact with the atomic electrons, see section 3.4, it is possible to conceptualize a chemical compound as consisting of an equivalent monatomic substance of an effective atomic number and an effective mass number, With the equivalent single atom/nucleus entity, modeling of radiation interactions can be simplified (though approximately). A number of approaches for calculating theses effective values are described below.

E.4.1.

Electron-Density Based

One can define a fictitious “effective-atom” of mass-number and atomic-number while maintaining the same electron density, so that, using Eqs. (E.9) and (E.10), one obtains:

Based on Eq.(E.17), one can define the following effective mass-number:

and effective atomic-number:

For

Eqs. (E.18) and (E.19) give, respectively,

Then While for most stable and

elements is approximately equal to 0.5, but for hydrogen is equal to 1.

E.4.2.

Reaction Cross-Section Based

Since the interaction probability (cross-section) of photons is linearly proportional to density only in the case of Compton scattering (see section 3.4), then the approach discussed in section E.4.1 is valid when Compton scattering is the dominant mode of interaction. In general, one should modify the expression of Eq. (E.19) to account for the nonlinear dependence of the photon cross-section with atomic number. As

lviii


shown in section 3.4, the atomic macroscopic cross-section for photons can be expressed as: where is a function that depends on the type of interaction and the photon energy, E, and is interaction-dependent index to 5 for the photoelectric effect, for Compton scattering, 1 to 2 for pair-production and for Rayleigh scattering). For a mixture, or a compound, using expression (E.14) and substituting Eq. (E.20) for the macroscopic cross-section, one obtains:

An equivalent macroscopic cross-section can be written, assuming an effective mass and atomic numbers, and as:

Equating, the right-hand-sides of Eqs. (E.21) and (E.22), one can define

as:

where can be defined using Eq. (E.18). Obviously, for Compton scattering, Eqs. (E.23) and (E.19) become identical. However, for other types of photon interactions, one will obtain different values. For Eq. (E.23) gives the following values for for the photoelectric effect 7.96 for Compton scattering 7.25 for pair production and 7.42 for Rayleigh scattering (for Other methods for calculating the effective atomic-number rely on matching the value of (i.e. the cross-section per electron for the compound or the nucleus) with the microscopic cross-section per electron for an individual element [1366]. For example, reference [1367] measured the effective atomic-number of an W/Cu alloy by looking for the value of Z that matches the total photon cross-section of the alloy measured by narrow-beam gamma transmission.

E.4.3.

Reaction-Ratio Based

The effective atomic-number may also be deduced from the ratio of two photon cross-sections, e.g. the photoelectric-to-Compton ratio or the Rayleigh-to-Compton ratio, using the definition of those cross-sections for a compound. Using Eqs. (E.2), (3.30), (3.51) and (3.49) and (3.63),


lix

the cross-sections for the photoelectric effect, Compton scattering, and Rayleigh scattering, can be expressed as functions of the atomic-number of individual atoms in the mixture as follows:

where designates proportionality factors that are not explicitly ex-

pressed in the above relationships and takes a value form 3 to 5, as

indicated following Eq. (3.30). Then one can define the followings ratios:

The same ratios for a single element are expressed as follows:

Therefore, by comparing Eq. (E.27) with Eq. (E.29) and Eq. (E.28) with Eq. (E.30), the effective atomic-number of a compound can be expressed as [203]:

where and refer to the two reaction cross-sections that are used in determining the value of the effective atomic-number. The ratio was measured experimentally and the results obtained compared favorably with those calculated using Eq. (E.31) [203]. Note that these ratios can be used for elemental identification, see section 7.3.10.


Appendix F Effective Energy

When analyzing indications obtained from a system that employs a multienergetic radiation source, such as an x-ray source, or an isotopic neutron source, it is often convenient to consider an equivalent monoenergetic source that gives the same indication. This concept is also useful in describing the overall distribution of radiation after interacting with matter. This appendix presents some of the methods that can be used to obtain this equivalent energy. In the analysis below the source energy distribution is designated by the function, where E is the radiation energy, so that:

where is the minimum energy of the radiation emitted from the source, and is the maximum radiation energy.

F.1.

Mean Energy

The most straightforward approach is to use the average (or mean) energy of the source, as the equivalent source energy, so that:

The obvious disadvantage of this approach is that if the source energy

range spans a few decades of magnitude, the mean value will be strongly

biased toward the higher-energy radiation. For example, for radiation emissions at two energies, and with equal probability of emissions, i.e. then lxi


lxii

That is, the energy will dominate the value of have the same emission probability. Therefore, although both and the mean-energy approach to the effective-energy is only useful when the source emits energies that are not too different in magnitude from each other.

F.2.

Most Probable Energy

The most-probable energy is the energy corresponding to the maximum value of If used as the equivalent source energy, gives a natural bias to the radiation that has the highest probability of emission. For neutrons, the kinetic energy corresponding to the most probable velocity interval based on the Maxwell-Boltzmann distribution of thermal neutrons is used to describe the overall behavior of thermal neutrons at the thermal-energy (see section 3.5). This energy is equal to where is the Boltzmann constant and T is the absolute medium temperature. This most-probable energy approach is obviously not very adequate, if the radiation distribution does not have a prominent peak.

F.3.

Cross-Section Dependent

The overall effect of radiation depends not only on the distribution of the source radiation but also on the manner it interacts with matter. It is, therefore, appropriate to define an equivalent energy, or an effectiveas the energy corresponding to the average cross-section energy, of the medium, so that:

Since material density does not change with energy, either macroscopic or microscopic cross-sections can be used in Eq. (F.3). The material for Therefore, the which is chosen obviously affects the value of obtained value of should be used with materials that do not differ significantly in their radiation cross-section from that of the reference This approach can be further exmaterial used for calculating panded by multiplying by the modifying model of the considered phenomenon, e.g. the exponential attenuation factor in transmission, see section 6.1, or the scattering probability in scattering techniques, etc.

F.4.

Best Match

The measurement model of a particular NDE device can be used to define an effective-energy, by minimizing the difference between the response of the device produced by the model and that resulting from

Appendix F: Effective Energy

lxiii

a reference evaluated experimentally or by using detailed simulations. That is,

This requires one to find the energy that produces model results (obtained assuming a monoenergetic source) which are closest in value to the reference results (which incorporates all source energy and interactions). Though this is perhaps the most accurate approach, it works best when the problem configuration for which the reference results are obtained is closest to the situation in which the value of is to be applied.


Appendix G Radiation Counting Statistics

The statistics of radiation counting is addressed in a number of references [15, 92, 1368, 1369, 1370, 1371]. This appendix provides a summary of methods used to deal with the statistical variability associated with radiation-counting measurements. Question addressed here include: 1 How to evaluate statistical error? 2 How good are the data? 3 How to reduce the error associated with measurements?. 4 How many times should a measurements be repeated?, 5 What is the optimum counting period?

To answer these question, it is necessary to understand the nature of the Poisson statistics of radiation counting, see section 4.5.6.1.

G.1.

Poisson Statistics

In radiation counting, one is usually interested in obtaining an estimate of a count rate, (the number of radiating counts per unit time). This is obtained by recording a number of counts, C, within a finite time interval, with the count rate, being equal to If the time interval,

is measured electronically, one can assume that the time interval is

accurate and precise1. Is is required, however, to determine the level of

1

An accurate measurement is one with low bias or small systematic error, while a precise measurement has a low variance, i.e. small random variation; see section 14.2.

lxv

lxvi


confidence2 one has in the recorded counts, C, i.e. the number of photons, neutrons, etc. registered by a detector. If these measurements are not corrupted by spurious signals, some sources of which are discussed in section G.3, one can expect the measured count to follow a Poisson distribution, as discussed in section 4.5.6.1. If the mean number of counts is then according to the Poisson distribution, the probability that a measurement will give C counts is:

The variance of this distribution is equal to its mean, i.e. where is the distribution variance. The Poisson distribution approaches a normal (Gaussian) distribution, with variance equal to only when is large. The statistical problem of radiation counting can be stated as follows: Obtain an estimate of the distribution mean of the measurement and define a confidence interval around this estimated value. It is necessary to determine the confidence interval in order to determine the precision of a measurement, that is to say its variability (which arises from the random nature of the problem).

G.1.1.

Mean and Variance

Let us consider measurements, can be estimated as:

The distribution mean

The distribution variance is subsequently estimated as:

where refers to the variance of any measurement sampled from a Poisson distribution. The variance of the estimated mean, is subsequently obtained by combining all variances involved in evaluat2

The value of a measurement, should be reported along with its associated uncertainty, and confidence level; e.g. with a 68% confidence. Stating the value of a measurement without indicating the degree of its uncertainty is not worth reporting at all. The ANSI/ASME Measurement Uncertainty, Part I, ANSI/ASME PTC 19.1-1985, recommended using a confidence level of 95% in uncertainty analysis.

Appendix G: Radiation Counting Statistics

ing

lxvii

according to the rules of combining errors, as follows:

The confidence interval associated with the estimated mean is defined by where can be taken to be equal to for a 68% confidence level, see section G.1.2. That is,

The estimated mean can, therefore, be expressed as: The precision of a measurement is usually defined using the percentage error3:

This relationship confirms what one would intuitively expect: increasing or the number of registered counts, C, the number of measurements, diminishes uncertainty, i.e. decreases statistical error.

G.1.2.

Population Statistics

One can also evaluate the variance using conventional statistics, from a population of counts, or observation. For observations,

an estimate of the distribution variance can be calculated using the well-

known relationship:

The value obtained using Poisson statistics, Eq. (G.3), leads however to a better, more precise, estimate of the distribution variance, than that evaluated using Eq. (G.7). As the number of measurements, increases, both estimates will approach each other. Typically for 20 measurements or more, the two estimates of the variance are equally good. For a small number of measurements, however, it is advisable to use the variance estimates provided by the Poisson statistics. According to the Central Limit Theorem, see chapter 16, any set of independent measurements will tend to resemble a normal (Gaussian) 3

By error, it is not meant that the measurement is in error. The statistical error is a measure of the variability of the distribution from which measurements are sampled.

lxviii


distribution, as the number of observations increases. For twenty observations or more, one can claim that the statistics of the normal distribution is applicable. The standard error or the variance of the mean, can then be used to define a confidence level. One can then define the following confidence intervals: 68% of the measurements lie within 95% of the measurements fall within 99.7% is within For a small number of measurements, one cannot apply the same confidence levels to the corresponding confidence intervals. Due to the lack of a simple process for determining the confidence levels in Poisson statistics, the normal distribution confidence levels are usually adopted. One should, however, be aware that the resulting confidence levels are approximate.

G.2. Gross/Background Count Rates G.2.1. Net Count Rate In radiation counting, one is usually interested in the count rate, i.e. the number of counts per unit time. The background count rate is also recorded, and the net count rate is obtained as the difference between the gross (foreground) and background count rates. The background is usually taken as the reference level, usually recorded in NDE in the absence of the inspected object. This section deals with error calculations for the net count rate estimates. Since digital clocks are usually used for measuring the time interval with a great degree of precision, no error is assumed to be associated with measuring the counting period. Let us assume that a total of measurements, are recorded for the background, each within a counting period of The count rate would then be equal to Let the gross count with a rate be measured times; resulting in the counts for each count. The count rate, is, therefore, counting period One can then calculate the average background and gross equal to count rates, and respectively, and the associated errors and respectively, as shown below.

For the background count rate:


lxix

Similarly, for the gross count rate:

In order to evaluate the net count rate, apply:

the following relationships

One should avoid subtracting the background from individual gross measurements. This may lead to a distorted distribution of the net count rate, particularly if an individual gross count rate happens to be smaller than the background, while most of the others are larger than the background (or vice versa). It is also advisable to have two estimates of the background, one at the beginning and the other at the end of an experiment, in order to ensure stability of the system. If the average of the two sets of background measurements differ significantly, this may be an indication of electronic instability. If the system is reasonably stable, one should use the average of the two sets of backgrounds and the associated combined error in the calculation of the net count rate.

G.2.2.

Number of Measurements and Counting Period

The number of measurements and the counting period depend on the magnitude of error one is willing to accept, as well as the time


lxx

available. It is recommended that, if possible, an error of no more than 2% be obtained. The counting period should be chosen such that at least 1000 counts are observed. This leads to about 3% error in each measurement. If then three measurements are taken, the combined error would be less than 2%. A question which often arises is, if one has a fixed amount of time, available for performing measurements: should one take one single measurement over the period or record measurements each over a counting period of If the data truly follow a Poisson distribution, both approaches should lead to the same mean and variance; provided of course that the measurements are recorded sequentially with no gap in between. It is a good practice, however, to record at least three measurements for each data point, to ensure the goodness of data. Unusually large variance can provide an indication of some drifting in the electronics or some interference from undesirable effects, see section G.3. In order for the background to not significantly affect the net count rate, according to equation (G.16), must be much greater than One should have equal at least 10 times the value of If, for example, is twice as large as b, then must be at least 5 times larger than Since the background measurement is in essence a reference point, it should be recorded at least twice as many times as that for foreground (gross) measurements. That is, should be equal at In this case, should be at least 2.5 times longer than least to

G.3.

Goodness of Data

Are all the obtained data points representative of the expected physical situation? This question can be answered by performing one of the following tests: Reproducibility. Repeating an experiment as many times as possible, and observing whether the results are reproducible or not. Deviation from Mean. Examining how the results deviate from their average value; too large or too small deviations, say outside are suspicious and may unduly influence the results. Test. Goodness of data can be checked using the

criterion:


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This test is actually applicable only to normal distributions. For a sufficiently large number of measurements, 20 or more, one can apply this test. To perform this test, find from the table4, the value of the probability, corresponding to the number of degrees of freedom, and the value of It is desirable to have close to 0.5, or equivalently otherwise the test is considered to have been failed. If the data fail the test, one or two of the outliers should be discarded, using the procedure described below, and the test should be repeated. If the data still fail the test, then the collected data may be “bad”. Some possible reasons are given below. Outliers. Data points that are much smaller or larger than the mean value are called outliers. To determine whether an outlier should be rejected, use should be made of the Chauvenet’s criterion, which states that a reading may be rejected if its deviation from the mean is greater than a specific number of standard deviations given in Table G.1. For example, in a series of 10 measurements, the Table shows that the number of standard deviation away from the average, beyond which a measurement may be rejected, is Therefore, if exceed for 10 measurements, then the reading should be rejected. Note that can be estimated by the value of calculated using Eq. (G.7). A new mean, and standard deviation, should be then be calculated without this measurement, since the original values were unduly influenced by the extreme observation. A similar test for rejecting data is proposed in the document: Measurement Uncertainty, Part I, ANSI/ASME PTC 19.1-1985, using a technique called the modified Thompson technique, see for example reference [1372]. This technique is slightly more liberal in rejecting data than the Chauvenet’s criterion. Inconsistent Data. Possible reasons for statistically inconsistent “bad” include: Unstable equipment, e.g. spurious counts generated by a faulty component or an instrument. External signals that may be picked up by the apparatus and be recorded. Sparks, radio signals, welding machines, etc. produce signals that may be measurable by a pulse-type counting system. 4 The table is available on the web, see for example:

“http://fonsg3.let.uva.nl/Service/Statistics/ChiSquare_distribution.html”.

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Sufficient time for equipment warm-up may have not been allowed, or equipment overheating may have occurred.

G.4.

Current-Mode Statistics

Current-mode counting, see section 4.5, provides a time-integrated indication. The integration process is accomplished electrically with the aid of an RC circuit, which provides an indication of the count rate, In order that a true response be obtained, the time-constant, of a rate meter should be shorter than the observation time of the actual change in measured parameters. If pulses are incoming at a rate, the number of pulses, counted within a time interval would be randomly distributed around the true mean value. According to Poisson statistics, Eq. (G.3), the variance in this recorded count is However, within pulses from earlier times are also recorded and will affect the statistical variance of the recorded counts. Therefore, the variance of a must be integrated over signal recorded over some observation time the variance of the collected charge up to The charge rate collection in an RC integrating circuit of a timeconstant is given by:

where is the charge in the capacitor, q is the charge per pulse received by the circuit, is the incoming pulsing rate, and refers to time. With a initial zero charge and a constant value of the solution of Eq. (G.18) is:


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The change in the collected charge, after some time, introduction of counts, can be expressed as:

due to the

where use is made of Eqs. (G.18) and (G.19). Consequently, the variance

in is given by:

According to Poisson’s counting statistics,

Therefore,

For a measurement at time, all pulses collected from time contribute to the variance, so that

to

with the approximation obtained after performing the integration and assuming that With the same assumption, Eq. (G.19) gives Therefore, the variance in the reading of the rate-meter, observed at is given by:

Therefore, the relative error in

is given by:

An actual change in the count rate from to is fully detectable when the signal reaches a value of see Figure G.1. Below this value, the signal would still be evolving with a time-constant, say Therefore, to detect the correct value of with the range of its statistical variability, a time must or elapse so that:

lxxiv


or equivalently,

As Eq. (G.24) indicates, the variability in changes with a time-constant equal to Therefore, by squaring Eq. (G.27) to obtain the variance, one can also use the time constant for the variance, leading to:

Making use of Eq. (G.24) and assuming

then:

As Eq. (G.29) indicates, the time required to observe a change depends on the magnitude of the expected change. Shortening the value of will However, with a too small time-constant, also reduce the value of there is little smoothing of the statistical fluctuations, so that assessment of the meter’s response with time becomes highly subjective [410]. By optimizing the time-constant of the meter, genuine changes in the measurements can be captured, while smoothing out statistical fluctuations. In general, however, as relationships (G.25) to (G.29) indicate, a rapid response (small value of requires a high count rate, for changes to be observable with a small uncertainty.


G.5.

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Elemental Error

Aside from the statistical variability, other sources of error, can occur. These are called elemental errors, and their source are identified according to the ANSI/ASME Measurement Uncertainty, Part I, ANSI/ASME PTC 19.1-1985, as: Calibration Errors: these are errors associated with system calibration. Although the purpose of calibration is to minimize systematic (bias) error, some uncertainties may still exist. For example, uncertainty in knowing source strength, nature of calibration object, randomness in source emission and detector response, can introduce some variability. Data Acquisition Errors: such errors can be introduced by the electronic processing units, e.g. a multichannel analyzer, a scalar, timer, etc. Data Reduction Errors: interpolation, differentiation of data curves, peak-locating and peak-width determination schemes, etc., can introduce their own errors. Regardless of the source of errors, their contribution should be assessed and included in the uncertainty analysis. These errors can be combined using the process of Eq. (G.4).


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About the Author

Esam M. A. Hussein, Ph.D., P.Eng. is presently Professor and Chair of the Department of Mechanical Engineering at the University of New Brunswick, Fredericton, Canada. After completing his undergraduate studies and a master’s degree in nuclear engineering at Alexandria University, Egypt, he earned a PhD in nuclear engineering from McMaster University, Canada. Prior to joining the University of New Brunswick in November 1984, he was employed for four years as a Nuclear Design Engineer at Ontario Hydro (now Ontario Power Generation). Currently, he is leading a research program that focuses on the industrial and medical uses of nuclear and atomic radiation, and the detection of threat-materials. His research work has been funded by a number of government agencies, national laboratories, and industrial firms in Canada and abroad. He has published numerous scientific papers and industrial reports, and has two patents. Dr. Hussein is a registered professional engineer in the provinces of New Brunswick and Ontario, and a member of ANS, ASME, ASNT, CNS and IEEE-NPSS. He can be reached by e-mail at [email protected].

clxxxvii


Application Index

Adsorption, 458

Aerosol, 468, 561–562

Air, 468, 543, 562

chromium, 561

Aircraft, 610, 617, 624

hydraulic system, 533

structure, 455, 637

Alcohol, 579

Alloys, 598

amorphous ferromagnetic, 604

binary, 595

corrosion, 107

gallium-indium, 625

light elements, 632

precipitate, 107

precipitati on, 453

Alumina, 525

compacts, 634

Aluminum, 525, 533, 560

alloys, 624

container, 476, 479

green liquor, 527

in silicon, 553

strips, 483

Ammonium perchlorate, 533

Ammunition

cartridges, 626

Animal feed, 538

Aqueous

solution, 491, 599

Archeology, 519, 524

art, 562

artifacts, 478, 538, 543, 557, 561, 617

ceramics, 561

mummies, 637

pieces, 613

samples, 638

Argon

in air, 612

Arsenic, 559

Art work, 280

Artifacts, 280

Ash, 547

coal, 594

content, 472

Asphalt, 472, 574, 636

cement, 578

Atmospheric

air, 509

particulate, 538

Automobile, 617

wheels, 609

Backing

metal, 554

Batteries

discharge, 459

lithium, 533

Bauxite, 525, 528, 533

Beryllium, 400, 538–539, 541, 543, 643

in alloys, 542

Binary mixtures, 305

Blast furnace

heats, 560

lining wear, 450

Boiler, 492, 511

steam dry protection, 463

Borehole

diameter, 568

formation, 473

Boric acid, 642

Boron, 524, 534, 542, 554, 598

in borophosphislicate, 401

carbide, 543

enriched, 543

in effluent, 600

in minerals, 632

in semiconductors, 401

in silicon, 553

clxxxix

cxc


Borophosphislicate, 401 Brass, 533 leaded, 560 Brine magmatic, 562 Bromine, 559 Bronze, 556, 560, 570 Building material, 469, 487, 623 humidity, 579

Bullets, 632

Cadmium, 523, 599

in oil, 559

Cans

liquid, 463 Carbon fiber-reinforced plastic (CFPR), 453 Carbon, 542, 565, 643 black fills, 635

blocks, 479

in heavy metal, 553

Carbonization, 570

Cardboard

corrugated, 615

Cargo, 530, 641, 644

containers, 614, 567, 639

Carnallite, 577

Cast iron

graphitization, 472

Cast products, 607

Casting, 610, 617

light metal, 613

slip, 634

Catalyst bed

packing density, 469

Cavity, 484

462

CdTe, 554

Cells

chlorine-producing, 506 Cement, 456, 459, 469, 529, 531, 543, 561, 636

dust, 561

hydration, 585

Ceramics, 520, 542, 613, 624, 634, 637 surface, 453

Cereals, 538

Channel

open, 493 Chemical

column holdup, 459

column packing density, 469

plant, 492–493, 498, 503, 511, 515

reactors, 620

Chlorine, 524, 565

in hydrocarbons, 591

in plastics, 592

Chromium, 538

in metal, 542

Cigarettes filters, 625 Circuit boards, 589, 617, 638 Coal, 486, 526–529, 531, 533, 538, 543, 547, 567

ash, 524, 528, 567, 570–571, 589, 592

slurry, 595

bituminous, 533

bulk analysis, 605

caloric value, 532, 605

coke, 579

deformation temperature, 524

effluent, 529

rock strata interface, 472

seam density, 472

slagging index, 524

slurry, 577

specific energy, 605

strata, 479

sulphur, 532

Coating, 475–476, 481, 555 chromium, 481 Cu-composites, 613 neutron absorbing, 482 organic, 476 substrate, 560 thickness, 367 Cobalt, 538, 599, 603 on silicon, 555 Coins silver, 598 Coke, 486–487 Colloids, 644 Columns bubble, 636

catalyst, 463, 498

distillation, 490, 500

packed, 636

Combustion, 612 materials, 565 Composites, 608, 627, 635, 639 damage, 610 debonding, 455 hydrogen, 623 impact damage, 455 moisture, 635 structure, 453 Composition indication, 562 pair production, 570 Compounds atomic structure, 91 Compressor oil film, 476 Concentration, 490 Concrete, 472, 484, 487, 636, 639 boron, 554

cracking, 625

rare earth elements, 554

Application Index rebars, 455, 571

steel interface, 629

void, 455

water, 486, 624

Condensed matter

atomic momentum and energy, 103

Containers

aluminum, 476, 479

glass, 476, 479

water deposition, 458

Contamination

radioactive

in building material, 633

river, 493

Contraband, 530–531, 640, 643–644

Conveyor belt, 761

cement, 529

coke, 487

iron ore, 469, 525

luggage, 609

organic material, 472

sinter mix, 487

weight scale, 469

Copper, 533, 552, 559–560, 630

in iron, 643

pyrochemical production, 458

Corrosion, 447, 607, 610, 615, 623, 634, 639

hidden, 455

pitting, 613

underwater, 455

Counterfeit bills, 561

Cracking, 634

Creep

damage, 615

Criticality, 537

Crystalline rock, 579

Crystals, 630

dating, 520

defects, 363

Currency, 557

Dampness, 571

Dates, 520

Degasification, 620

Degasser, 515

Dehydration, 640

Dendrochronology, 518

Density, 466

local, 325

Dental enamel, 629

Deposition

organic, 457

scale, 482

Deposits, 447

hideout, 449

Detergents, 599

surfactant, 459

Deuterium, 538–539

cxci in metal, 542

Dew point, 510

Diabase

rock, 525

Diamond, 542, 562

Diffusion

coefficient, 511

Dust, 543, 561

Earth’s crust

subsurface analysis, 435

Effluent, 459

Eggshell, 476

Electrical

components, 637

insulators, 637

Electronics

assemblies, 613

epoxy potted, 623

Enclosed material, 474

Engine

aero, 609

Erosion, 447

costal, 459

Evaporator

caustic soda, 490

Evolution

kinematics, 637

Explosives, 530–533, 540–541, 550, 552, 554,

567, 591, 637, 642–644

bolts, 626

fuse, 454

lines, 626

shells, 618, 626

shock, 629

Extraterrestrial bodies, 554

Fat

bone, 643

Faulting

wrench, 637

Ferro-manganese

deep sea, 562

Fertilizer, 533, 591

Fibers, 555

densification, 635

Fill gauge, 463

Films, 365

amorphous, 453

dielectric, 553

Langmuir-Blodgett, 453

light material, 475

metal, 475, 481

on substrate, 554

organic, 476

oxide, 553

tantalum carbide, 542

Filters

moisture, 458

cxcii particulate, 561

polypropylene cartridge, 637

Fireclay, 487

Fissile material, 464, 535, 539

assay, 537, 552

Fission products, 538

Fissionable material, 539

Flame, 467, 508–509

Flarestack

fouling, 448

ice blockage, 458

Flaws, 607

Flooding, 485

Flow rate

method

constant-rate injection, 493

dilution, 493

gas ionization, 494

peak-to-peak, 492

pulse-timing, 492

pulse-velocity, 492

pulsed activation, 495

total-count rate, 492

volumetric, 491

Flow

blockage, 457, 607

dead volume, 511

distribution, 510

regime, 513–514

visualization, 612, 640

Flower, 638

Fluidized bed, 490, 620, 625

Fluids, 489

Fluorine, 543, 553

Foam, 474

Foaming, 490

Foil, 475

imprint, 614

metal, 553

plastic, 475

Foils

solder, 594

Food

contamination, 643

freezing, 644

products, 455, 643

Forensic

documents, 628

sample, 557

Foundries, 486

Frost, 468, 485

point, 510

Frothing, 490

Fuel

heavy distillate, 526

nuclear, 637

Fume, 462

Radiation Probing, Gauging, Imaging and Analysis Furnace

aluminum, 459, 493

blast, 459, 499

metallurgical, 504

steel, 509

Fusion

target, 640, 645

Gadolinium, 599

in CANDU reactors, 600

Galvanneal, 560

Gases, 467

dissolved, 490

distribution, 492, 511

emissions, 560

hazardous, 587

in air, 587

mixtures, 586

ternary, 587

multicomponent, 590

properties, 507

ternary, 587

Gem stones, 644

Geological formations, 602

Geological samples, 543

Glass, 486, 524, 528, 534, 542–543, 553, 556,

560, 598, 624

boron in, 105

chalcogenide, 543

container, 476, 479

smart, 553

soda-lime, 553

Gold, 599

foil, 542

Grain products, 533

Graphite

purity, 537

Grinding, 458

Grout, 459

Hafnium, 599

Heat exchangers, 500, 504, 624

tubes, 477

Heavy water, 514, 538

Helium

in metal, 542

in Nb and Mo, 534

Helium-oxygen mixture, 509

Household cleaners, 591

Humidity, 510

Hydraulic fluid, 533

Hydrocarbons

heavy deposits, 448

liquids, 588

Hydrogen

content, 571, 588

in air, 462

in graphite, 578

in hydrocarbons, 584–585

Application Index in iron, 582 in metal, 542, 581, 623, 638 in migration metal, 631 in obsidian, 581 in rocks, 602 in silicon, 581 in soil, 578 in steel, 581 in TiAl, 581 in wood, 584 liquid, 630 storage alloys, 622 Hydrogen-carbon ratio, 589 Hydrogen-uranium interaction, 579 Hydrology, 517 Hydrosphere, 517 Ice deposits, 448 detector probe, 463 Impact studies, 611 Impurity, 456 In situ water in polymer, 623 activation, 528 carbon in soil, 529 extraterrestrial bodies, 554 fiber densification, 635 lead in paint, 604 Mars surface, 543, 556 surface formation, 567 vessel lining, 455 water pollution, 525 wear, 610 In-flight blade inspection system IBIS, 463 Inclusions, 456, 607, 639 Indium, 599 Injection molding, 634 Ink, 559 Insulator electric, 534 Interface, 502 liquid-liquid, 490, 502–503 Iodine, 538 in aqueous solution, 590 Ion chamber, 637 Ionic conductors, 624 Iron, 533, 538, 599, 603, 643 Alnico alloys, 628 deposits, 567 in etching solution, 632 in magnetic tapes, 632 inclusions, 628 ore density, 469 ore, 486–487, 526–527, 568 shale, 548 ores, 525 processing, 487

cxciii

substrate, 562 Irrigation, 485 Jet engine blades, 638 Jets, 612 Lactose, 487 Landmines, 550, 577–578, 619 Latent heat, 508 Lattice damage, 454 dislocation, 456 Lead, 528 in gasoline, 592 in glass, 556 in lead glasses, 590 in paint, 604 ore, 561 Leak detection, 504 Leaves, 485 fabrics, 629 Level, 501 Light elements in metal, 553 Limestone, 524 Liquids, 468 non-hydrogenous, 499 ternary, 590 Lithium, 400, 535, 541 batteries, 624 in ceramics, 624 in glass, 553, 624 in ion conductors, 624 in Nb, 534 Litho-density, 567 Lithology, 547 Lubricants, 459, 532–533, 603 additives, 555 Luggage passenger, 644, 609, 637, 641–643 Lunar surface, 543, 556, 562 water, 549 Magnesium, 543 Magnetic multilayers, 453 Manganese, 525, 527, 599 Markers nighttime, 463 Mars surface, 543, 556, 562 water, 549 Masonry, 529 Materials thermal-activation, 526 Meat, 551, 570 fat, 579, 595 Membranes, 630 Mercury, 506, 523, 528

cxciv


in aqueous solution, 590

in fish and crab, 633

Metallurgical sections, 615

Metals

alloys, 532

film, 475

high purity, 538

homogenization, 631

hydride, 571

in non-metals, 401

sheet, 475

Meteorology, 519, 635

Microelectronic

circuit boards, 617

material, 534, 555

Microstructure

imaging, 364

Milk, 570, 595

fat, 579

Mine borehole

assay, 552

Mineral exploration, 548

Minerals, 524, 529, 567, 641

drill core, 562

Mixing, 420

Moisture, 484, 571

Molten liquids, 609–610, 624–625 Molybdenum in iron, 590

Motors, 630

Moulding sand, 486

Mud, 469, 636

Multiphase flow, 515, 636–637

Munition, 532

Narcotics, 530–532, 550, 552, 567, 577, 643

Natural gas, 544

Natural radioactivity, 630

Nickel, 538, 552

in metal, 542

Niobium, 543

Nitride

on silicon, 555

Nitrogen, 533, 542

in aluminum, 553

in diamond, 542

Nozzles, 512, 623

Nuclear

contamination, 620

fuel, 550–551, 561, 638

assay, 106

burnup, 626

cladding, 555

enrichment, 626

pellets, 463

reprocessing, 559, 620

rods, 536

irradiated fuel, 534, 555

material, 530, 532

missiles, 627

plant, 544

power plant, 560

spent fuel, 539, 622

warheads, 620

waste drums, 603

waste, 486, 620, 636, 645

weapons, 629, 640

Nuts, 520

Ocean, 458

Oceanography, 519

Offshore

oil riser, 455

platform, 485

structures, 639

Oil, 532, 544

crude, 526

engine, 533

flow on surfaces, 620

gas mixture, 514

in soil, 577

refinery, 494

reservoir, 529

shale, 532

water, 644

void, 595

Olive stone, 570

On-line

cement, 531

blast furnace feed, 499

boron, 540

cement, 529

coal, 524, 531

corrosion/erosion, 451

crude oil, 526

fluorine, 540

gadolinium solution monitoring, 600

iron hot ore, 530

metal films, 476

minerals, 524

neutron activation, 528

oxygen, 540

paper, 475

radioscopy, 609

slurry, 560

vanadium, 526

welds, 609

Optical diaphragm, 475

Orchard, 559

Ore

iron, 528

refining, 507

Organic

chemistry, 570

material, 472, 532, 542

Oxides

Application Index film, 553

flake, 553

on silicon, 555

Oxygen, 532, 535, 540, 565

in heavy metal, 553

in metal scales, 633

in metal, 542, 553

in silicon, 553

Packages filling, 463

Packed column, 578

Paint, 559, 579

toxics, 559

Paintings, 632

oil, 628

plaster, 617

Palaeoclimatology, 518

Palaeoenvironmental, 519

Paper, 485

air bubbles in fiber, 612

coating, 475

metallic pigment, 629

printed, 629

sheets, 628

Particulate

flow, 640

Passenger

imaging, 618

Pavement, 472

Pearls, 615

Permeability, 483, 516

Pesticide, 462

Petroleum

products, 490

Pharmaceutical

heavy elements, 556

Phase distribution, 513, 515

Phosphate, 527

leaching, 632

ore, 525

Photographic emulsion, 603

Pipelines, 577

corrosion, 448

deposit, 455

dry, 505

gas/liquid, 502

graphitization, 448, 472

heavy depositions, 448

natural gas, 492

pigs, 458

underground, 505

water deposition in gas pipelines, 457

Pipes, 610

corrosion, 607

downhole, 455

frost, 485

insulated, 610

cxcv insulation, 484

lining, 484

thermal insulation, 455

thinning, 619

wall, 477

water deposition, 458

Pitting, 615

Planetary elements, 549

Plants, 528

heavy elements, 561

roots, 624

Plaster, 487

Plastics, 617, 644

decomposition density, 469

sheets, 542, 629

sorting, 644

Plating

tin/lead, 589

Plutonium, 534, 549, 555

in containers, 537

Poles

wooden, 637

Pollutants, 532, 561

Pollution, 458

ground water, 517

Polyethylene

pigment, 615

Polymers, 453, 474, 484, 555, 615, 623

chip blender, 632

Porcelain, 556

Pores

dissolution, 625

Porosity, 483, 574, 579, 602

Porous media, 516, 623, 625

flow in, 620

Potassium, 599, 630

Pottery, 528, 560

moisture, 579

Powder

coalescence, 457

metallurgy, 639

packing density, 469

pistol, 561

Precipitate, 456

Printed

circuits, 637

Process columns

damage, 454

foaming, 454

liquid carry-over, 454

loss of pads, 454

tray fouling, 454

Process industries, 560

Product assessment, 607

Propellants, 533

Protein, 538, 551

Pulp and paper, 492

cxcvi


Pulpwood slurry, 487

Pump, 493

Quality assurance, 607

Quartz

water, 624

Radioactive

contamination, 548

waste drums, 609

waste, 501

Radon

monitoring, 461

Railway

tanker, 463, 500

track, 455

Rainfall, 488, 517

Rapid prototyping, 635

Rare earth elements, 554

Reactivity, 537

Reactor

chemical, 507

nuclear, 501

packed-bed, 502

Refractory

lining, 484

material, 598

Refrigerant, 459

Refrigerators, 624

Reservoir, 561

Reverse engineering, 635

Rhenium, 559

Rifle

barrel, 632

Rings

cogs, 455

River, 458, 493, 502

contamination, 510

Rock, 483, 528, 533, 538, 560, 562, 567–568,

630, 641

fracture, 455

properties, 350

Rocket

motor, 611, 633, 637

motors, 609

Rocks, 624

Rod bundles, 512, 636

Rotor

blade pressure, 463

Rubber, 475, 533, 559, 579, 635

sheets, 629

strips, 477

tires, 609

Rust under insulation, 448

Rutile, 542

Salt

in liquids, 588

NaCl, 599

Sandstone, 624

Sapphire, 542

Satellites, 608

Scorpion stinger, 640

Scorpion

sting, 645

Seabed

radionuclides, 604

Sealing, 504

Seals, 623

Sedimentology, 547

Sediments, 519, 533, 538

marine, 633

Seepage, 458

Seismic, 473

Selenium, 538

Semiconductors, 453, 524, 534, 538, 542,

553, 556, 630

boron, 401

manufacturing, 638

Sensitivity, 657

Separator

oil-water, 503

Sewage, 458, 510

462

Shales, 547, 636

Shaliness, 546

Sheet, 475

polymer, 476

Shock waves, 612

Silica, 456

Silicon, 553

in metal, 542

substrate contamination, 553

Silicon-carbide, 613

Silver, 599

Silver-copper alloys, 570

Sinter mix, 487

Sludge

deposits, 449

in crude oil, 507

Smoke, 467

detectors, 460

Snow, 472, 487, 498

in air, 603

in exhaust fumes, 603

Sodium

in films, 632

molten, 495

Soil, 472, 485, 487–488, 517, 529, 538, 548,

638, 641

columns, 488

in sugar cane, 603

moisture, 488

non-uniformity, 350

Application Index oil contamination, 577

Solar cells, 542, 553

Solidification

metal, 636

Solution

extraction, 459

precipitation, 459

Sonar domes, 617

Space

material, 531

Spray

inorganic, 615

Stamps, 629

Steam generator

tubes, 613

Steam, 492, 512, 571, 612, 623

Steel, 542–543, 560

aging, 456

alloying, 604

alloys, 533

austenite, 604

bearing, 555

carbon, 634

corrosion/erosion, 450–452

dephosphorization, 459

detritiation, 631

erosion, 451

free-machining, 560

manufacturing, 634

phases, 604

products, 477

shape, 477

weight, 477

radiation damage, 456

rolled, 484

scrap radioactivity, 464

sintering, 472

sorting, 557

stainless, 560

foil, 562

strip, 477

vessel, 479

Stirring, 420

Stone, 520

Storage

bunker for bulk solids, 620

underground, 502

vessel deposits, 448

Stress

residual, 456

Sugar, 554

cane, 603

Sulfur, 400, 541, 543

in coal, 603

in hydrocarbons, 591

in oil, 592

in weld, 631

cxcvii Sulfuric acid, 577

Superconductors, 611

Surface

adhesion, 448

area, 452

characterization, 453

composition, 449

condition, 447

flatness, 476

imaging, 401

impurities, 449

insulation, 448

layers, 365

porous, 452

roughness, 449

smoothness, 449

Surfactant, 454

Tank, 493, 503

chemical waste storage, 507

deposits, 449

storage, 498

Tantalum, 599

Tar sand, 527

Temperature, 501

flame, 509

Termite colonies, 510

Thermal insulation, 487

foamed, 484

Thermal-expansion coefficient, 491

Thermionic

converter, 613

Thickness, 457, 475

coating, 367

Thinning, 447

Thorium, 534, 539, 630

in soil, 548

on lunar surface, 548

Tin, 560

in lead, 594

mining, 561

on steel, 481

smelting, 561

Tires, 635

Titanium

alloys, 570

Titration, 459

Tobacco, 468, 554, 559

Tooth

human, 542

Toxics

paint, 559

Trace

analysis, 557

elements, 543

Trees, 487

Tritium

in metal, 624

cxcviii


Trucks, 530 Tubes, 512 capillary, 640 deposition on walls, 448 thinning, 477 wall thickness, 479 wall thinning, 448 Tungsten in iron, 589–590 Turbine, 493 blades, 455, 613, 624–625 engine, 610 water, 493 Two-phase flow, 495, 623, 627, 636, 639 interfacial area, 515 Underground storage cavity, 503 Underground water, 517 age, 517 Uranium, 534, 536, 559, 628, 630 depleted, 534 deposits, 604 dioxide, 542 enriched, 534 enrichment, 604 in minerals, 632 in pitchblende, 641 in sediments, 625 in soil, 548 natural, 536 particulate, 461

Uranyl fluoride, 537 Valves, 637 frozen, 607 Vanadium, 526 Varnish on tubes, 482 Vegetables, 538 dried, 559 Vehicle, 614 Ventilation, 504 Vessel, 479, 498, 500 Viscosity, 624 Void fraction, 511, 573, 578 local, 336 small tube, 513 Void in aluminum castings, 618

in ceramics, 618

in polymers, 618

in steel, 618 in uranium, 627 local, 456 size, 456 subsea grouting, 456

Voidage, 484 Volume measurement, 506 Warheads nuclear, 464 Waste nuclear, 548 radioactive, 489 water, 511 Water, 484, 579 boiling, 491 flooding, 640 free/bound, 585 ground, 519, 542 in soil, 578, 585 oil contamination, 533 pollution, 525 radioactivity, 548 trace elements, 561–562 tritiated, 539 well, 554 Weapons chemical, 530, 532 nuclear, 537, 544 Wear, 452, 610 cutting tool, 451 refractory lining, 449 Weight, 469 Welds, 607, 609, 634

seams, 638 Well logging, 502, 526, 544–545 calcium, 524 chlorine, 524 hydrogen, 524 natural emission, 545 permeability, 483 porosity, 524 shale, 524 silicon, 524 strata, 473 Wellbore casing, 495 Wetness, 484 Wheat, 487, 554, 579 Wireline logging, 473 Wires, 645 precise location, 454 Wood, 479, 487 chips, 486, 584 decomposition density, 469 shavings, 629

Wool, 579

Zeolites, 484, 555

Zircon, 562

mineral, 630 Zirconia, 553

Index

Absorption, 673

Accuracy, 654

Actinium series, 60

Activation foil, 218

Adjoint calculations, 728

AIDES, 618

Albedo, 336

Alpha particles

range, 71

sources, 22

thick source, 509

Amplifier, 221

fast, 224

wide-band, 224

Applications (see Application Index), 445

APXS, 543, 556, 562

Artifacts

image, 658

Assay

fissile material, 535

nuclear fuel, 423

Associated-particle

neutron/alpha, 531

Atomic density compound, liii mixture, liii Atomic number effective, lvii

Attenuation coefficient, 69

Attenuation law, 130, 260

Auger

effect, 81

electrons, 26, 37, 81

yield, 26

Autoradiography, 630

real time, 633

Avalanche diode, 164

Background radiation, 751

by surroundings, 237

from source, 237

natural, 238

reduction, 540

anticoincidence, 757

by coincidence, 757

in emission, 756

in scattering, 754

in transmission, 752

Background reduction, 530–531 Beam

catcher, 754

hardening, 262

Beta particles

range, 75

sources, 25

detector, 190

Binding energy, 66, 381

Bioscope, 633

Blackness thickness, 662

Bragg cutoff, 108

energy, 703

Bremsstrahlung, 37, 41, 1

beta particles, 77

beta sources, 24, 513

neutrons, 532

photon sources, 42

radiation, 32, 70, 96

Buildup effect, 263

correction, 478

Californium-252

time tagging, 537

Camera

neutron, 627

nitrogen, 644

pinhole, 350

Carbon-14

dating, 518

Charged-particles

activation, 394, 402, 541

cxcix

cc


neutron emission, 406

photon emission, 394, 543

resonance, 395, 404, 553

thin-layer, 452

coulomb force, 70

detection, 142

flash chamber, 158

GM tube, 146, 157

inorganic scintillators, 160

ionization chamber, 145, 147

multiwire, 157

nuclear emulsion, 143

organic scintillator, 161

photographic emulsion, 143

position sensitive, 157

proportional counter, 145, 152

scintillation detector, 160

semiconductors, 167

spark chamber, 158

track etching, 144

energy measurement, 147

excitation, 70

ionization, 70, 434


range, 71

scattering, 449

stopping power, 71

thin layer activation, 451

transport, 133

Chauvenet’s criterion, lxxi

Cherenkov effect, 164

Cinefluorography, 609

Cineradiography, 464

Cloud chamber, 158

Coded aperture, 620

Coincidence measurements, 231

Coincidence unit, 231

Collimation

beam profile, 686

by energy, 339

electronic, 678

energy discrimination, 678

soft, 429, 678

soft/virtual, 339

Collimator

acceptance angle, 685

alignment, 687

compensators, 693

divergence measurement, 687

focused, 677

length-to-diameter ratio, 685

magnifying, 676

minifying, 676

multibore, 677

multihole, 677

multileaf, 688

parallel hole, 675

pencil beam, 675

penumbra, 683, 690

pinhole, 675

shapes, 685

slat, 675

slit, 350, 675, 685

Soller, 685

thermal neutrons, 693

wide-beam, 685

Combined techniques, 673

Compensators, 278

Composition indication

coherent scattering, 568

critical-edge absorption, 563

dual scattering, 566

dual-energy scattering, 567

dual-energy transmission, 563

transmission and scattering, 565

Compton scattering, li, 79, 82

Compton suppression, 757

Compton-scatter camera, 431

Comscan, 617

Constant fraction discriminator, 229

Content analysis, 586

with alpha-particles, 586

with beta-particles, 587

with combined methods, 605

with Mössbauer spectroscopy, 604

with natural radiation, 604

with neutron activation, 603

with neutrons, 595

with photons, 591

with XRF, 603

Contrast, 657

Cosmogenic nuclides, 62, 459, 517, 519

Counting statistics, lxvi, 232

Cps/nv

see thermal-neutron sensitivity, 192

Cross section, 66

angular, 67

barn, 66

differential, xlix, 67

macroscopic, lv

compound, Iv mixture, lv

maximum absorption, xlvi

mean-free-path, 69

microscopic, 66–67

potential scattering, xlix

thermal neutrons, 111

bound atoms, 111

CT

see Tomography, 283

Current mode, 226

ionization chambers, 149

statistics, lxxii

Cyclotron, 29

Index Dating, 518

Delta rays, 70, 133

Densitometer

gamma, 490

multibeam, 512

Densitometry, 512

DEPFET, 633

Depth profiling, 395, 400, 402, 406, 533, 541

Design parameters, 719

Detection limit, 657

Detector

blackness, 756

collimation, 675

efficiency, 140

absolute, 140

full-energy peak, 142

intrinsic, 140

relative, 140

filtration, 679

selection, 674

Diffraction, 107

Debye-Scherrer-Hull, 621

imaging, 621

Laue, 621

neutron, 108

small angle, 108

neutrons, 107

powdered, 621

Diffusion

equation, 131

Fick’s Law, 131

theory, 131

Divergence law, 129

Doppler broadening

photons, 89

Duality principle, xl

Effective energy, lxi, 262

Electron capture, 36

Electron density, liv

compound, liv mixture, liv

Electron-capture detector, 591

Electrons, 133

cascade, 133

shower, 70, 133

sources, 27

Emergency planning, 745

Emission, 672

bulk gauging, 428

imaging, 425

line probing, 428

Emulsions nuclear, 630

Energy absorption coefficient, 246

Energy resolution

Fano factor, 234

FWHM, 234

cci Energy spectrum, 139

Error

analysis, lxv

instrument, 661

Exemption quantity, 746

Experimental aspects, 739

Figure-of-merit, 659

Filters

balanced, 696

difference method, 571

difference, 697, 700

inverse, 700

neutron, 579, 699, 711

iron, 628

neutrons, 55, 204, 536

radiation badges, 249

source/detector method, 569

x-rays, 39, 309, 593, 695

Fission chamber, 198

Fission plate converter, 718

Flash chamber, 158

Fluence, 125

Fluorescent, 81

Fluoroscopic

emission, 36

excitation, 556

yield, 26, 37

Flux density, 124

Fourier Analysis, 760

Frequency Analysis, 760

Gain stabilizer, 567

Gamma calorimeter, 501

Gamma camera, 176, 431

Gamma rays

reference sources, 47

sources, 45

low energy, 38

Gaussian distribution, lxviii

Geiger-Müller (GM) counter, 146, 157

GM tube, see Geiger-Müller counter, 146

Helium-3 detector, 194

High-voltage power supply, 220

Hodoscope, 464

Hydrogen radiator, 217

Hydrogen

index, 572

neutron slowing-down, 575

HYSEN, 579

Imaging

dual-energy, 641

emission, 425

multiple energy, 641

photon coherent scattering, 362

single scatter, 618

transmission/scattering, 642

Intellectual property, 766

Internal conversion, 26, 37

ccii


Ionization chamber, 145, 147

current mode, 149

Frisch grid, 151

gas-microstrip, 151

gridded, 151

Mircomegas, 151

Ionoluminescence,417, 562, 630

Legendre polynomials, xliii

Licensing, 742

accelerators, 749

neutron generators, 750

radioisotopes, 748

x-ray machines, 746

Linac, 29

Lithium-6 sandwiched semiconductor, 217

Lithium-6 scintillator, 205

Lithology, 524

LSDTS, 552

Marketing, 650

Mass attenuation coefficient, 69

Mass defect, 381

Mass excess, 66

Mass number

effective, lvii

MCA, 227

Measurement model, lxii, 257, 301, 653, 659,

671, 720, 728, 739

beta-particle attenuation, 583

beta-particle scattering, 368, 588

Compton scattering, 317

density scatterometers, 470

dual-energy scattering, 331

dual-energy transmission, 563, 594

emission imaging, 425

flux depression, 438, 598

ionization current, 434

natural emission, 545

neutron activation, 376, 381, 384

neutron backscattering, 599

neutron die-away, 440, 602

neutron elastic scattering, 318

neutron transmission, 597

neutron-slowing down, 575

PIXE, 415

positron annihilation, 474

positronium decay, 399

pulsed neutrons in a flow, 495

radioactivity, 422

radiotracers, 418

scattering, 312

scatterometry, 344

system constant measurement, 739

transmission optimization, 668

transmission with buildup, 478

transmission, 259

XRF, 410, 480

Measurements

dynamics, 758

time bias, 759

while drilling, 545

Monitoring, 744

Monte Carlo method, 720

Mossbauer

effect, 42

sources, 43

spectrometry, 306

spectroscopy, 452

Moving object, 761

Multichannel analyzer (MCA), 227

Multichannel sealer (MCS), 230

Natural radioactivity

sources, 61

Neugat, 487, 579

Neutron activation, 372

charged-particle emission, 373, 401, 533

cold, 523

comparator method, 377, 383

cyclic, 379, 532

double irradiation, 534

epithermal, 384

erosion/corrosion detection, 450

fast, 386

delayed activation, 532

delayed, 387

prompt, 391, 528

inelastic scattering, 373


radiative-capture, 373

thermal, 377

delayed, 379, 525, 527

prompt, 381, 523

Neutron detectors

194

activation foil, 218

190

Cadmium-based, 200

fission chamber, 198

Lithium-6 sandwiched semiconductor, 217

Lithium-6 scintillator, 205

plate and screen, 217

proton-recoil scintillator, 207

proton-recoil, 200

Neutron diffraction, 107

crystallographic texture, 364

strain/stress measurement, 364

Neutron filters, 699

absorption, 700, 702

cold neutrons, 704

epithermal, 700

fast, 699

mild moderation, 701

pass-through, 701

reflection, 700

thermal, 702

Index Neutron scattering, 100

Compton, 103

deep inelastic, 103

elastic, 100

inelastic, 100, 104

nonelastic, 105

potential, 115

probing, 448

Neutron

absorption, 436

flux depression, 436

boosters, 716

converter screens, 217

die-away time, 536

die-away, 439

fission, 106, 535

infiltration, 486

manganese bath, 540

moderating materials, 705

moderation, 705

albedo, 715

block, 712

by containment, 710

by reflection, 714

by shielding, 715

multiplication, 716

multiplicity reactions, 106

noise, 537

notched spectrum, 579

radiative capture, 105

shuffler, 537

Neutrons

cross-section, 117

anti-resonance, 643, 701 Breit-Wigner formula, 117

cold, 48

die-away time, 601

differential cross-sections, 118

Doppler broadening, 118

epicadmium, 48

epithermal, 48, 718

fast, 48

reflectors, 718

filters, 55

fission, 100

generation, 58

generators, 55

multiplicity reactions, 100

resonance integral, 118

resonances, 113, 117

sources, 50, 52, 57

51

51

14 MeV d-T generators, 54

photoneutrons, 56

thermal, 56

sub-cadmium, 48

cciii thermal, 48

treatment, 111

absorbers, 595

fission, 534

Maxwell-Boltzmann, 109

time-tagging, 53

NIM bin, 220

Normal distribution, lxviii

Nuclear emulsion, 143

Nuclear Instrument Module, 220

Otrho-hydrogen molecules, xlvi

Pair production, 1, 80, 96

incoherent/coherent, 98

Para-hydrogen molecule, xlvi

Parallax principle, 281

Particle-induced x-ray emission (PIXE), 415

Patents

design, 767

utility, 767

PELAN, 531

Performance parameters, 653

PET, 429

PFNA, 530

Photodiode, 164

Photoelectric effect, 79, 81

Photoelectric

absorption index, 435

factor, 435

Photofission, 405

Photofluorography, 609

Photographic emulsion, 143

Photomultiplier (PM) tube, 163

Photon activation, 396, 537–538

charged-particle emission, 400, 540

internal standard method, 398


Photon detection

double-escape peak, 172

electrostatic plate, 188

peak-to-Compton ratio, 173

radiographic films, 188

scintillators, 177

semiconductors, 182

single-escape peak, 172

Photoneutrons, 538

Photons

absorption edge, 82, 411, 697

absorption, 81

anti-Compton effect, 92

atomic form factor, 92

Bragg diffraction, 80, 93

Compton broadening, 89

Compton profile, 89

Compton scattering, 79, 82

attenuation coefficient, 87

cross section, 85, 87

cross-section per electron, 85

cciv


kinematics, 83

Klein-Nishina relationship, 85

defection, 80

elastic scattering, 80

fluorescence, 81

incoherent scattering function, 88

incoherent scattering, 79

inelastic scattering, 79

pair production, 80, 96

photoelectric absorption, 79

photoelectric effect, 79, 81

probing with scattering, 448

Rayleigh scattering, 80, 92

refraction, 80

relativistic Compton scattering, 89

scattering with bound electrons, 88

Thomson cross-section, 85, 87, 91

triplet production, 80

virtual, 1

PIGME, 543

PINS, 532

PIPPS, 543

PIXE, 561

ionoluminescence, 417

Poisson statistics, lxvi

Positron emission tomography (PET), 429

Positroniums, 398, 484

decay, 398

orthopositroniurn, 398

parapositronium, 398

probing, 452

Positrons, 26

sources, 28

Preamplifier, 219, 239

Precession, 655, 657

Probing

scattering, 320

at high energy, 321

at low energy, 327

attenuation averaging, 323

collinear, 338, 340–341

constant transmission, 325

dual energy, 329, 331

local density, 336

Rayleigh-to-transmission ratio, 334

signal modulation, 322

two-source & transmission, 328

with neutrons, 335

Promotion of technology, 649

Proportional counter, 145, 152

counting plateau, 156

multiwire, 157

position-sensitive, 157

quench gas, 155

Proton-recoil

detector, 200

scintillator, 207

Protons, 29

Prototyping, 763

Pulse

ballistic deficit, 222

baseline shifting, 222

dead-time losses, 240

counting, 241

detector, 241

multichannel analyzer, 242

pulsed source, 242

delay line, 222

gain stabilization, 236

gating, 239

peak pile-up, 223, 239

pile-up, 222, 238

pole-zero cancellation, 222

shape discrimination, 230

shaping, 221

single-channel analyzer, 225

Pulser, 220, 236

random, 239

Quantum numbers

angular momentum

xliv xliii

magnetic spin

xlv

Radiation dose

gray, 246

Radiation dose-equivalent, 246

quality factor, 246

rem, 246

sievert, 246

weighting factor, 246

Radiation exposure, 245–246

roentgen, 246

Radiation protection, 247

ALARA principle, 245

BSS principles, 244

distance, 248

dosimetry, 248

film badges, 249

shielding, 248

survey meters, 250

time, 247

TLD’s, 250

Radiation

kerma, 246

Radioactive decay, 133

activity, 133

decay constant, 133–134

exponential decay, 134

half-life, 134

secular equilibrium, 135

specific activity, 134

transient equilibrium, 135

Radioactivity

gamma emission, 421

natural, 60

Index Radiography, 143, 270

beta particles, 628

bremsstrahlung, 615

buildup, 272

digital, 281

dual energy, 304

electron emission, 401, 629

electron, 309, 628

emission, 630

enhancers, 607

fast neutrons, 626

film, 270–271

flash, 611, 614

high speed, 611

instant films, 280

intensifying screens, 280

laser, 614

material contrast, 275

microfocus, 612

microradiography, 614

neutron, 622

Bragg cutoff, 643

contrast enhancers, 624

converter screen, 627

real time, 622

time-gated energy-selected, 643

transfer technique, 626

pentrameter, 35, 277

printed image, 280

projective shadow, 613

proton, 629

quantification, 278

real time (Radioscopy), 608

sensitivity, 276

spatial resolution, 275

transmission versus scattering, 352

unsharpness, 271

Radioscopy, 608

Radiotracers, 417–418, 666

corrosion/erosion detection, 450

deposition indication, 420

flow velocity measurement, 420

flow-obstruction detection, 420

flow-rate measurement, 419

leakage detection, 419

location detection, 420

mixing indication, 420

probing, 449

residence time, 420

volume measurement, 419

Rayleigh scattering, 79, 92

Rayleigh-to-Compton

ratio, 363

scatter ratio, 570

Reduced mass, xli Reflection neutron

ccv specular, 108

Reflectometry

neutron, 365

Refraction, 95

Refractive index

neutrons, 108

x-rays, 95

Regulations, 742

Relativistic mechanics, xxxv

Resolution, 657

Resolving power, 655

Resonance

activation

charged-particle, 395

Rutherford scattering

alpha particles, 72

SANS, 365

SCA, 225

Scanning, 761

Scatter imaging

nonlinear, 359

point-by-point, 357

reconstructed, 356

Scattering length, 107–108

neutron, 115

Scattering, 672

alpha-particles, 366

beta-particles, 367

coherent, xlv

incoherent, xlv

ions, 369

length, 453

potential, xlvii

probing, 320

attenuation, 321

inspection volume, 320

s-wave, xliv

Scatterography, 351, 617

lateral migration, 619

real time, 618

Scatterometry, 342

dispersive technique, 347

gamma, 470

neutron, 515

ratio methods, 346

saturated scattering, 347

variable source-to-detector method, 345

Scatteroscopy, 553

Scheduled quantity, 746

Schrödinger’s equation, xli

Scintillation detectors, 159

afterglow, 162

177

BGO, 179

179

179

Cherenkov, 164

ccvi


CsF, 180

CsI, 180

efficiency, 160

gas proportional, 165

GSO:Ce, 181

inorganic, 160

NaI(Tl), 181

optical fibers, 164

organic, 161

phosphorescence, 162

Phoswich detectors, 182

photomultiplier (PM) tube, 163

position sensitive, 176

pulse shape, 161

YAP:CE, 181

Secular equilibrium, 546

Semiconductor detectors, 165

charged-particle, 167

diffused junction, 170

fully depleted, 170

Ge (HPGe), 182

photon, 184

energy resolution, 185

PIPS, 170

surface barrier, 170

Shielding, 729

charged particles, 730

computer codes, 736

gamma sources, 734

intense sources, 731

neutrons, 730, 735

photons, 730

stray radiation, 731

x-rays, 732

Shuffler

neutron, 537

Signal

filtering, 235

noise, 235

Signal-to-background ratio, 656

collimation, 678

emission, 673

scattering, 672

transmission, 671

Signal-to-noise ratio, 656

collimation, 678

emission, 672

scattering, 672

transmission, 671

Single-channel analyze (SCA), 225

Single-photon emission computed

tomography (SPECT), 429

Small-angle neutron scattering (SANS), 365

Snell’s law, 95

Source

time distribution, 758

Sources, 19, 664

energy, 667

interfering radiation, 670

radioisotopes vs. generators, 666

Spark chamber, 158

SPECT, 429

Spectrometry

slowing-down time, 551

Spectroscopy, 223

amplifier, 223

Spectrum analysis, 347

Stability, 657

Statistics

optimization, 659

Stereoradiography, 281

Straggling

beta-particles, 76

charged-particles, 71

Surveying, 744

Synchrotron, 29

TGES, 643

Thermal-neutron sensitivity, 192

Thermoluminescence

dating, 520

Thorium series, 60

Time gating, 753, 757

Time pick-off

constant-fraction discriminator, 229

leading edge, 229

time jitter, 229

time walk, 229

zero-crossover, 229

Time-Amplitude Converter, 230

Time-of-flight measurement, 231

Time-tagging

Californium-252, 578

TLA, 451

TNA, 377, 523

Tolerance, 655

Tomography, 283

aliasing, 298

back-projection, 286

central-slice theorem, 297

composition, 563

cupping effect, 302

dual energy, 641

fan beam, 285

filtered back-projection, 298

Fourier transformation, 296

gamma, 634

Gibbs phenomenon, 298

image quality, 299

least-squares solution, 285

limited projection, 478

micro, 634, 636

partial-volume effect, 301

problem formulation, 284

proton, 640

Index region-of-interest, 303 successive approximation, 288 transmission and scattering, 303 ultrafast, 637 underdetermined problem, 300 x-rays, 633 Track etching, 144 Training, 744 Transmission, 671, 673 alpha particles, 308 beta particles, 309 buildup correction, 478 divergence correction, 478 double, 475, 481 dual energy, 304 dual radiation-type, 305 electrons, 309 Mossbauer effect, 306 nuclear resonance, 306 optimization, 670 pencil beam, 268 probing, 448 radiography, 270 statistical optimization, 660 Transmittance, 260 Triplet production, 98 Uranium series, 60

ccvii Warning, 744 Waste disposal, 745 Well logging, 473 Wilson chamber, 158 Wireline logging, 473, 545 X-ray diffraction, 94 Laue pattern, 94 X-ray fluorescence (see XRF), 408 X-ray tubes characteristic, 414 filtered, 414 for XRF, 414 secondary target, 414 X-rays beam hardening, 78 diffraction, 363 filters, 695 balanced, 696 cutoff, 698 difference, 697 refraction, 95, 364 topographic imaging, 363 Xeroradiography, 280 XRF, 559 bremsstrahlung, 415 critical thickness, 412 internal source, 415 isotopic sources, 408 matrix effect, 413

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