Safety of VVER-440 Reactors: Barriers Against Fission Products Release

Safety of VVER-440 Reactors

Vladimír Slugeˇn

Safety of VVER-440 Reactors Barriers Against Fission Products Release

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Vladimír Slugeˇn Slovak University of Technology Ilkoviˇcova 3 81219 Bratislava Slovak Republic [email protected]

ISBN 978-1-84996-419-7 e-ISBN 978-1-84996-420-3 DOI 10.1007/978-1-84996-420-3 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library © Springer-Verlag London Limited 2011 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher and the authors make no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: eStudioCalamar, Girona/Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

The aim of this work was to increase the nuclear safety of the VVER-440 by improving fission product limitation systems (barriers) and implementing special nondestructive spectroscopic methods for the testing of structural materials (mostly steels). All theoretical and experimental studies performed were done to improve the deterministic approach to defence in depth for the VVER-440. Defence in depth is an extremely important principle for assuring nuclear safety in nuclear power plants, and this work focused on the barrier system through which this principle is achieved: • • • •

nuclear fuel matrix; fuel cladding; integrity of the primary circuit; confinement system.

All of these barriers are described in Chapter 4 of this work, which contains the most important topics that comprised the objectives of the author’s previous (and present) investigations. The integrity of the barriers was evaluated mostly from a materials degradation perspective. The contributions of ageing, neutron irradiation and thermal treatment were also studied in view of the expected extension to the operation of VVER-440.

Bratislava, December 2010

Vladimír Slugeˇn

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Contents

Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

2

Nuclear Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

3

Defence in Depth of VVER-440 Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Accident Prevention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Accident Mitigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 General Illustration of Defence in Depth . . . . . . . . . . . . . . . . . . . . . . .

5 6 7 8

4

Barriers Preventing the Release of Fission Products . . . . . . . . . . . . . . . . 17 4.1 First Barrier: the Nuclear Fuel Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.1.1 Properties of UO2 Nuclear Fuel . . . . . . . . . . . . . . . . . . . . . . . . 17 4.1.2 Grain Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.2 Second Barrier: Fuel Cladding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.2.1 Leakage Monitoring Techniques for VVER-440 Reactors . . 26 4.2.2 Leak-testing Performance at the Bohunice NPP . . . . . . . . . . . 28 4.2.3 Occurrence of Leaking Fuel Assemblies and Probable Causes of Leaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.2.4 The Mast Sipping Method for VVER-440 . . . . . . . . . . . . . . . . 30 4.2.5 The Pool Sipping Method for VVER-440 Fuel at the Wet Interim Burned Fuel Storage at Jaslovské Bohunice . . . . . . . 30 4.2.6 Slovak Activities Focusing on a New Design for the VVER-440 Fuel Assembly . . . . . . . . . . . . . . . . . . . . . . 36 4.3 Third Barrier: Integrity of the Primary Circuit . . . . . . . . . . . . . . . . . . . 39 4.3.1 Reactor Pressure Vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.3.4 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

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Contents

4.4 Contribution to VVER-440 Steam Generator Safety . . . . . . . . . . . . . . 126 4.4.1 Corrosion of VVER-440 NPP Steam Generators . . . . . . . . . . 126 4.4.2 Advantages of Mössbauer Spectroscopy in Corrosion Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 4.4.3 Safety Analyses of Slovak Steam Generators and the Latest Upgrades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.4.4 Experimental Evaluation of Corrosion Products Using Mössbauer Spectroscopy Analyses . . . . . . . . . . . . . . . . 132 4.5 Leak Tightness Calculation for a Container for Transporting Burned-up Fuel Assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 4.5.1 Components of Container C-30 . . . . . . . . . . . . . . . . . . . . . . . . 150 4.5.2 Criteria for Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 4.5.3 Model for Calculating the Leakage . . . . . . . . . . . . . . . . . . . . . 152 4.5.4 Releasable Activity of a Radionuclide Under Normal and Accidental Conditions During Transport for the C-30 Container . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 4.5.5 Determining the Standard Leakage Rate of the C-30 Transport Container . . . . . . . . . . . . . . . . . . . . . . . . 155 4.6 Fourth Barrier: Containment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 4.6.1 Design Features of the Containment System . . . . . . . . . . . . . . 157 4.6.2 Design Basis for the Containment System . . . . . . . . . . . . . . . . 158 4.6.3 Containments for VVER-440 Reactors . . . . . . . . . . . . . . . . . . 158 5

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Abbreviations APFIM A ACAR AZ BC BCC BM c C CEMS DC DB DBTT DPA DTM e E Econd Ed EF Em ER EBO EMO FWHM HAZ HV10 NPP I IAEA ILEEMS ISFSF k kB LDA LOCA LT M MCA MELT MS MTR

Atom probe field ion microscopy Activity Angular correlation of annihilation radiation Active zone Bubbler condenser Bubbler condenser containment Base material Speed of light Concentration Conversion electron Mössbauer spectroscopy Positron diffusion constant Doppler broadening Ductile-to-brittle transition temperature Displacements per atom Diffusion trapping model Elementary charge Energy Energy of lower edge of conduction band Ionisation energy level of defect d Fermi energy Energy of monochromatic radiation Positron binding energy to Rydberg states Bohunice nuclear power plant Mochovce nuclear power plant Full width at half maximum Heat-affected zone Vickers hardness for a load of 10 kg Nuclear power plant Intensities of positron lifetime component International Atomic Energy Agency Integral low-energy electron Mössbauer spectroscopy Interim Spent Fuel Storage Facility Number of different defect types Boltzmann constant Local density approximation Loss of coolant accident Lifetime Mass Multichannel analyser Maximum entropy for lifetime Mössbauer spectroscopy Material testing reactor

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x

me m m0 n nC n N o-Ps Q p p P p-Ps PAS PIE PKA Ps PWR PC r r0 rc rd R RCS RPV S SANS SC SCA SG SKA SLD SSP STM STN t t0 T Tm TAC TEM TRIM TT USE

Abbreviations

Electron mass Effective positron mass Electron or positron rest mass Density of free electrons Positron density Total electron density Number Ortho-positronium Inelastic energy loss Free hole density Electron momentum Positron penetration depth profile Para-positronium Positron annihilation spectroscopy Postulated initiating events Primary knock-on atom Positronium Pressurised water reactor Primary circuit of the NPP Positron vector Classical electron radius Capture radius Defect radius “Relative” line shape parameter Reactor coolant system Reactor pressure vessel Annihilation line shape parameter Small-angle neutron scattering Secondary circuit of the NPP Single-channel analyser Steam generator Secondary knock-on atom Structural lattice defect Standard surveillance program Simple trapping model Slovak Technical Norms Time Time zero Temperature Melting temperature Time-to-amplitude converter Transmission electron microscopy Transport of ions in matter Transition temperature Upper shelf energy

Abbreviations

v VC W wt% WM ı VC "0 "r  ˚ ˚C     eff  0 C ˙



xi

Thermal positron velocity Positron potential Wing parameter Mass percentage Weld material Positron detrapping rate Positron potential step Dielectric constant Relative permittivity Flux Fluence (implantation dose) Positron work function Enhancement factor Annihilation fraction positrons Positron trapping rate Annihilation rate Effective annihilation rate Positron trapping coefficient Positron trapping coefficient for a neutral defect Positron trapping coefficient for a positively charged defect Microscopic cross-section Macroscopic cross-section Angular deviation of annihilation quanta Positron lifetime

Indices a b d dis i, j s st t v

Annealing Bulk Defect Dislocation Counting index Surface Shallow trap Trap Vacancy

Chapter 1

Introduction

The potential of even non-military, beneficial applications of nuclear energy to present exceptional hazards was recognised from very early on during their development. Therefore, even before action had been taken to build the first civilian nuclear energy systems, developers had already resolved to impose an exceptionally high level of safety on such systems. This objective, which was unprecedented in industrial development, has been maintained and improved upon throughout the evolutionary process that followed. The objective has not always been achieved, but the safety record has been remarkably good when compared to those of other new technologies when they were introduced. Only a few large accidents causing public anxiety have occurred, and only one of these has led to radiation-induced public health effects. An early step that contributed to this record, and that later had singular importance, was the widespread adoption of an unparallelled means of protection at watercooled and moderated reactors: strong, tight enclosing structures that were designed to prevent the release of any radioactive material from a nuclear installation. This came to be refined into a strategy for nuclear plant safety called “defence in depth”, based on the use of several successive protective barriers as several levels of defence, as well as further protective methods for ensuring the continued integrity of these barriers. Even if one level of protection were to fail if called upon, others would continue to provide protection. This structured protective process includes both safety systems and safety practices. At different stages in the historical development of nuclear energy, attention has focused upon various safety concerns that have arisen, leading to the solution of a succession of safety questions. The completeness and effectiveness of the protective practices adopted in response to these questions are now based on lessons learned (including those from severe accidents in nuclear power plants) and on the well-developed field of engineering, and cover both engineering systems and human factors. Radiation damage, and its attendant effect on a wide spectrum of properties of materials, is a central issue in many advanced technologies, ranging from ion-beam processing to the development of fusion power. The practical objective is to develop V. Slugeˇn, Safety of VVER-440 Reactors. © Springer 2011

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1 Introduction

improved materials performance and improved lifetime predictions by relating property changes to a large number of material and irradiation variables. Radiation effects involve the interaction of a multitude of physical processes. Although the range of materials, microstructures, physics, and properties that are encompassed by radiation effects is enormous, this work focuses mostly only on the embrittlement of reactor pressure vessel (RPV) steels. Embrittlement is a technologically and economically important problem that affects the operation and safe lifetimes of nuclear power plants around the world. The most important parts of the RPV impacted by radiation effects are those around the reactor core. Neutron radiation causes the brittle-to-ductile transition temperature to increase significantly, leading to an increased possibility of RPV fracture. A great deal of research effort has been directed at developing improved methods for predicting embrittlement and for resolving related problems. Much of the early work was purely empirical, but over the last few decades embrittlement has been a global focus of fundamental research, including controlled experiments to identify the underlying mechanisms. Key parts of this research have involved the application and development of sophisticated tools for characterising nanoscale embrittlement features as microstructural evaluations. The results published here are derived mostly from the author’s experiences and original measurements obtained using positron annihilation spectroscopy and Mössbauer spectroscopy obtained during the last two decades and explained in the frame of the current state of knowledge in material science. Experimental non-destructive techniques based on positron annihilation phenomena and the Mössbauer effect were used to study real reactor pressure vessel and steam generators. Positron annihilation spectroscopy and Mössbauer spectroscopy were applied to investigate chemical composition, irradiation and post-irradiation heat treatment effects on the microstructures of steels, in order to enhance our understanding of the mechanisms of anomalous structural degradation after irradiation. Mössbauer spectroscopy was used also for corrosion and ageing studies. This work strives to contribute to increasing the nuclear safety of VVER-440 reactors by: • Analysing the existing “defence in depth” system for VVER-440 reactors from a materials point of view and improving it based on national and international experience and trends; • Analysing and improving the system for limiting fission product release from nuclear fuel to the environment via different barriers; • Utilising new non-destructive spectroscopic methods such as positron annihilation spectroscopy and Mössbauer spectroscopy to test materials used in the nuclear industry; and • Proving that the selected spectroscopic methods are effective for evaluating the lifetimes of the main components of VVER-440 reactors.

Chapter 2

Nuclear Safety

Electricity production is a phenomenon that has been connected very closely to industrial development for more than a century. Each viable method of producing electricity has specific advantages and possible detrimental effects. In the statement of the general nuclear safety objective, “radiological hazard” refers to adverse health effects on both plant workers and the public and radioactive contamination of land, air, water or food products. It does not include any of the more conventional type of hazards that are associated with any other industrial endeavour. The protection system associated with a nuclear power plant is effective, as stated in the objective, if it prevents the plant from significantly increasing the risk to public health or the risk of other damage to individuals, society and the environment compared to the risk posed by industrial activities that are already accepted. In this context, risk is defined as the arithmetic product of the probability of an accident or an event and the adverse effect it would produce. These health risks are estimated without taking into account the countervailing and substantial benefits that nuclear and industrial activities bestow, in terms of better health and other aspects that are important to modern civilisation. When the objective is fulfilled, the level of risk posed by nuclear power plants does not exceed that from competing energy sources, and is generally lower. If another means of electricity generation is replaced by a nuclear plant, the total risk will generally be reduced. To compare the risk resulting from nuclear plants with other industrial risks to which people and the environment are exposed, it is necessary to use calculational models in risk analysis. In order to make full use of these techniques and to support the implementation of this general safety objective, it is important to formulate quantitative targets or “safety goals” [1]. These safety objectives and principles are indicated in Table 2.1. In the next chapter, the concept of “defence in depth” will be described in detail.

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Specific principles Siting

Proven engineering Quality assurance practices

General technical principles

Design

Accident prevention

Defence in depth

Defence in depth principles

Responsibility of operating organisation

Radiation protection objective

Safety culture

General nuclear safety objective

Objectives

Fundamental management principles

Principles

Table 2.1 Safety objectives and principles of nuclear power plants

Manufacturing and construction

Human factors

Accident mitigation

Regulatory control and verification

Technical safety objective

Commissioning

Operation

Safety assessment Radiation and verification protection

Accident management

Operating experience and safety research Emergency preparedness

4 2 Nuclear Safety

Chapter 3

Defence in Depth of VVER-440 Reactors

Defence in depth is one of the most important principles, since it underlies the safety technology employed in nuclear power plants. All safety activities, whether organisational, behavioural or equipment-related, are subject to layers of overlapping provisions which are designed to ensure that if a failure should occur it would be compensated for or corrected without causing harm to individuals or the public at large. This idea of multiple levels of protection is the central feature of defence in depth, and it is repeatedly used in the specific safety principles applied in nuclear power plants. Two (related) principles of defence in depth are defined: accident prevention and accident mitigation [1]. The defence in depth concept provides an overall strategy for safety measures and features of nuclear power plants. When properly applied, it ensures that no single human or mechanical failure leads to danger to the public, and even combinations of failures that are only remotely possible would lead to little or no injury. Defence in depth helps to establish that the three fundamental safety functions (controlling the power, cooling the fuel and confining the radioactive material) are preserved, and that radioactive materials do not reach people or the environment. The principle of defence in depth is implemented primarily by means of a series of barriers which should in principle never be jeopardised, and which must therefore be violated in turn before harm can occur to people or the environment. These barriers are physical, confining the radioactive material at successive locations. The barriers may serve operational and safety purposes, or may serve safety purposes only. Power generation is only allowed if this multibarrier system is not jeopardised and is capable of functioning as designed. The reliability of the physical barrier is enhanced by applying the concept of defence in depth to each barrier in turn, protecting each with a series of measures. Each physical barrier is designed conservatively, its status is monitored, and all plant processes capable of affecting it are controlled and monitored during operation. Human aspects of defence in depth are brought into play to protect the integrity of the barriers, such as quality assurance, administrative controls, safety reviews, independent regulation, operating limits, personnel qualification and training, and safety culture. Design provisions – including those for normal plant systems as well as those for V. Slugeˇn, Safety of VVER-440 Reactors. © Springer 2011

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3 Defence in Depth of VVER-440 Reactors

engineered safety systems – help to prevent undue challenges to the integrity of the physical barriers, the failure of a barrier if it is jeopardised, and damage to multiple barriers in series. Safety system designers ensure that the different safety systems protecting the physical barriers are as functionally independent as is practicable under accident conditions. All of the levels of defence are available at all times when a plant is operating at normal power. The existence of several levels of defence in depth is never a justification for continued operation in the absence of any other level(s). Severe accidents in the past have been the result of multiple failures, both human and equipment failures, due to deficiencies in several components of defence in depth that should not have been permitted. System design according to defence in depth includes process controls that use feedback to enable tolerance of any failures which might otherwise allow faults or abnormal conditions to develop into accidents. These controls protect the physical barriers by keeping the plant in a well-defined region of operating parameters where barriers will not be jeopardised. Care in system design prevents cliff edge effects which might permit small deviations to precipitate into grossly abnormal plant behaviour and cause damage. Competent engineering of the barriers and protective measures for them, coupled with feedback to maintain operation within the optimal range, lead to a record of smooth, steady performance in producing electricity on demand. Such a record indicates the proper implementation of one of the most important indicators of the success of defence in depth: operation with little or no need to call upon safety systems. The multibarrier system protects humans and the environment in a wide range of abnormal conditions. Planned countermeasures are provided, as a further component of defence in depth, against the possibility that radioactive material might still be released from the plant.

3.1 Accident Prevention The design, construction, operation and maintenance of nuclear power plants are all geared toward the generation of electricity reliably and economically as their primary objective. In accordance with the general safety management principle regarding a safety culture, the safety implications of decisions in all these areas must be borne in mind. The first method of preventing accidents is to strive for such high quality in plant design, construction and operation that deviations from normal operational states are infrequent. Safety systems are used as a backup to feedback in process control to prevent such deviations from developing into accidents. Safety systems make use of redundancy and diversity of design and the physical separation of parallel components, where appropriate, to reduce the likelihood of the loss of a vital safety function. Systems and components are inspected and tested regularly to identify

3.2 Accident Mitigation

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any degradation which might lead to abnormal operating conditions or inadequate safety system performance. Abnormal conditions that could possibly affect nuclear safety are promptly detected by monitoring systems that trigger alarms and in many cases initiate corrective actions automatically. The operators are trained to quickly recognise the onset of an accident and to respond properly and in a timely manner to such abnormal conditions. They are also well trained in and familiarised with appropriate operating procedures. Thus, the prevention of accidents depends on conservatively designed equipment and good operational practices to prevent failure, quality assurance to verify the achievement of the designed intent, surveillance to detect degradation or incipient failure during operation, and steps to ensure that a small perturbation or incipient failure does not develop into a more serious situation. A number of deterministic as well as probabilistic safety assessments have been performed for a range of nuclear power plant designs in different countries. They show that sufficiently low probabilities of severe core damage are attainable. When effective preparation is made in relation to accident management and mitigating the effects of severe accidents, the results of these probabilistic safety assessments are consistent with the general nuclear safety objective. Probabilistic safety assessment also guides design and operation by identifying potential accident sequences that could contribute excessively to risk. Measures can then be taken to reduce this contribution.

3.2 Accident Mitigation Provisions for accident mitigation extend the defence in depth concept beyond accident prevention. Accident mitigation provisions come in three kinds: accident management, engineered safety features and off-site countermeasures. Accident management includes planned and ad hoc operational practices which, under circumstances in which the design specifications of the plant are exceeded, make optimum use of existing plant equipment in normal and unusual ways in order to restore control. This phase of accident management has the objective of restoring the plant to a safe state with the reactor shut down, continued fuel cooling assured, radioactive material confined and the confinement function protected. In such circumstances, engineered safety features would act to confine any radioactive material released from the core so that discharge to the environment would be minimal. These engineered safety features include physical barriers, some of which have the single purpose of confining radioactive material. Off-site countermeasures are available, going beyond the level of protection provided in most human endeavours, to compensate for the remote possibility that safety measures at the plant might fail. In such a case, the effects on the surrounding population or the environment would be mitigated by protective actions, such as sheltering or evacuation of the population, and by preventing the transfer of radioactive material to humans via food chains and other pathways.

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3 Defence in Depth of VVER-440 Reactors

3.3 General Illustration of Defence in Depth The use of defence in depth in nuclear power plant design and operation involves three fundamental principles. Defence in depth provides the basic framework for most nuclear power plant safety. The concept has been refined and strengthened through years of application. All safety analysis for nuclear power plants, both deterministic and probabilistic, revolves around evaluating the performance of the plant subject to different modes of defence in depth, and the reliability of these modes [1]. There are many such modes that can protect people and the environment against the possibility and the effects of accidents at nuclear power plants, which vary according to the challenges to the plant generated by different abnormal events. The modes can be classified according to the severity of the challenge, measured in terms of extraordinary demands on equipment and staff performance or in terms of any resultant plant damage. This latter classification is illustrated in the second line of Table 3.1. Table 3.1 shows events (second line) in order of severity, increasing from left to right. The classes start with states of normal operation that pose no challenge to the safety of the plant. The challenges arising from anticipated abnormal occurrences would be countered in a straightforward manner by the appropriate responses of normal plant systems. More severe challenges would accompany the third category of complex operating events, bounded by design basis accidents. For these, engineered safety features would be required to supplement the protection afforded by normal plant systems. At the extreme of the scale of severity are accidents beyond the design basis, for which management measures are required to limit the consequences of damage. The lengths of the boxes on the line labelled “events” are not intended to indicate any scale of probability of the events listed in them. If a representative probability scale were shown, only normal operational events would have a probability high enough to be visible on the diagram. Nevertheless, this approach provides a simple illustration of the defence in depth required for each event. The third line of the diagram is labelled “control”. It shows the normal plant actions that satisfy requirements for events encountered in normal operation or in anticipated operational occurrences. A separate set of measures would be required for complex operating events that have much lower probabilities of occurrence. These begin to include accident management at the upper end of the range, including measures to ensure the retention of fission products and other radioactive materials in cases where some damage to fuel might have occurred. For severe accidents beyond the design basis, accident management would come into full play, with normal plant systems, engineered safety features and off-site emergency measures employed to mitigate the extent and effects of the accident. The other lines show how the strategy, systems, procedures and barrier integrity depend on the class of the event and its severity. The entire picture in each case is provided by the vertical axis through the event at its indicated severity. For instance, an accident beyond the design basis with a severity at the lower end of the range might generate damage to the reactor core that precludes reuse of the

3.3 General Illustration of Defence in Depth

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Table 3.1 Overview of defence in depth [1] Strategy

Accident prevention

Operational state of the plant

Normal operation

Anticipated operational occurrences

Accident mitigation

Level of defence in depth

Level 1

Level 2

Objective

Prevention of abnormal operation and failure

Control of abnormal operation and detection of failures

Essential features

Conservative design and quality in construction and operation

Control, limiting and protection systems and other surveillance features

Control

Design basis and complex operating states Level 3

Severe accidents beyond the design basis

Post-severe accident situation

Level 4

Level 5

Control of accidents below the severity level postulated in the design basis

Control of severe plant conditions, including prevention of accident progression, and mitigation of the consequences of severe accidents, including confinement protection

Mitigation of radiological consequences of significant releases of radioactive materials

Engineered safety features and accident procedures

Complementary measurements and accident management, including confinement protection

Off-site emergency response

Normal operating activities

Control of accidents in design basis

Accident management

Procedures

Normal operating procedures

Emergency operating procedures

Special emergency operating procedures

Response

Condition of barriers

Normal Engineered safety operating systems features Area of specified acceptable Fuel fuel design limit failure

Colour code

NORMAL

Off-site emergency preparations Severe fuel Fuel damage melt

POSTULATED ACCIDENTS

Uncontrolled fuel melt

Loss of confinement

EMERGENCY

fuel elements, perhaps with extensive distortion and failure of cladding, but with no melting of the fuel itself. Such an accident would release some radioactive materials into the primary coolant circuit, with consequences beyond those for which detailed provisions are made in emergency operational procedures. Less prescriptive and more indicative special operating procedures would then be used by the operating staff to limit the extent of the release of radioactive materials from the primary coolant circuit and to restore the plant to a controlled and cooled state. These procedures would make use of normal plant systems, engineered safety features and special design features of the plant. Mitigation at this level of severity would

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3 Defence in Depth of VVER-440 Reactors

be so successful that there would be no appreciable release of radioactive material beyond the confinement, so no off-site emergency measures would be called upon. A second, complementary view of defence in depth is given in Figure 3.1, which shows the relation between the physical barriers and the levels of protection that together constitute defence in depth. This shows the interaction among these components as a series of obstacles between the radioactive material in its normal state and any harm to the public or the environment as a result of its dispersal due to an accident. Figure 3.1 shows radioactive material in the centre. A first level of protection in defence in depth is a combination of conservative design, quality assurance, surveillance activities and the general safety culture that strengthens each of the successive obstacles to the release of radioactive materials. The first three physical barriers are the fuel matrix, the fuel cladding and the boundary of the primary coolant system. All nuclear power plants now operating or under consideration have all of these barriers; some gas-cooled reactors also have another barrier in the form of a graphite moderator into which fuel particles with a graphite or ceramic coating are embedded. The second level of defence in depth is operational control, including response to abnormal operation or to any indication of system failure. This level of protection is provided to ensure the continued integrity of the first three barriers. Together these constitute the normal operating systems and barriers. A third level of protection is afforded by the engineered safety features and protective systems which are provided to prevent the evolution of failures of equipment and personnel into design basis accidents, and design basis accidents into severe accidents, and also to retain radioactive materials within the confinement. The fourth barrier is the confinement layer, unless it has been shown that its function is provided by other means. The fourth level of protection comprises measures that include accident management, which are directed at preserving the integrity of confinement. The fifth level is that of off-site emergency response, which is aimed at mitigating the effects of the release of radioactive materials to the external environment. The possible routes for fission product transport in the NPP are shown in Figure 3.2 [1]. Although VVERs represent less than 10% of the world’s nuclear capacity, in the Central and Eastern European region they are very important, as they produce 5– 50% of the electricity of the countries that use them. This region is currently faced with a very difficult economic situation; the GDP of every country in this region decreased by 20–50% in the 1990s, so most of these countries do not have sufficient financial resources to replace their reactors in the foreseeable future. This situation has triggered the instigation of several national and international programmes to check and enhance the safety of these plants and to start a systematic life management programme in every country [1]. All of the barriers employed in the defence in depth strategy for the VVER will be discussed in the following chapter. Analysis will focus largely on the VVER-440

3.3 General Illustration of Defence in Depth

Safety and protection systems, engineered and special safety features

Normal operating system

11

Fission products

General means of protection; conservative design; quality assurance; safety culture

First barrier: fuel matrix Second barrier: fuel rod cladding Third barrier: primary coolant boundary First level: prevention of deviation from normal operation Second level: control of abnormal operation Third level: control of accidents in design basis Fourth barrier: confinement Fourth level: accident management including confinement protection Fifth level: off-site emergency response

Figure 3.1 Relation between physical barriers and levels of protection in defence in depth

type reactor, and will be complemented by some selected technical articles about special problems towards which the author has directed research activities. At the start of 2009, a total of 437 nuclear power plants in 31 countries were available worldwide to supply energy. Among these, 50 VVER units were in operation (see Table 3.2). Moreover, 13 VVER units were under construction and 15 were

12

3 Defence in Depth of VVER-440 Reactors

fission products in fuel

fission products accumulate under the fuel rod cladding

fission products

escape due to diffusion

fuel rod failure

escape due to surface contamination

fuel washing

escape due to leak failure and fuel melting deposition

corrosion products

coolant activity

activation

activation products

coolant leakage deposition

desorption

purification

desorption

showers

activity in containment accumulation at filters vent expulsion

containment leakage

activity propagation into atmosphere

deposition

total dose

Figure 3.2 Possible transport routes for fission products

being decommissioned (see Tables 3.3, 3.4 and 3.5). Three basic types of this pressurised water-cooled and moderated reactor are actually operated in Central and Eastern Europe: the VVER-440/V230, the VVER-440/V213, and the VVER-1000. Such a large number of operational units makes for a large experience and knowledge base. Since 1963 (when the first VVER-210 prototype became operational)

3.3 General Illustration of Defence in Depth

13

Table 3.2 VVERs currently in operation around the world Country (ISO code)

Station

Net electricity generating capacity (MW)

Model

AM BG BG CN CZ CZ CZ CZ CZ CZ FI FI HU HU HU HU RU RU RU RU RU RU RU RU RU RU RU RU RU RU RU SK SK SK SK UA UA UA UA UA UA UA UA UA UA UA UA UA UA UA

ARMENIA-2 KOZLODUY-5 KOZLODUY-6 TIANWAN 1 DUKOVANY-1 DUKOVANY-2 DUKOVANY-3 DUKOVANY-4 TEMELIN-1 TEMELIN-2 LOVIISA-1 LOVIISA-2 PAKS-1 PAKS-2 PAKS-3 PAKS-4 BALAKOVO-1 BALAKOVO-2 BALAKOVO-3 BALAKOVO-4 KALININ-1 KALININ-2 KALININ-3 KOLA-1 KOLA-2 KOLA-3 KOLA-4 NOVOVORONEZH-3 NOVOVORONEZH-4 NOVOVORONEZH-5 VOLGODONSK-1 BOHUNICE-3 BOHUNICE-4 MOCHOVCE-1 MOCHOVCE-2 KHMELNITSKI-1 KHMELNITSKI-2 ROVNO-1 ROVNO-2 ROVNO-3 ROVNO-4 SOUTH UKRAINE-1 SOUTH UKRAINE-2 SOUTH UKRAINE-3 ZAPOROZHE-1 ZAPOROZHE-2 ZAPOROZHE-3 ZAPOROZHE-4 ZAPOROZHE-5 ZAPOROZHE-6

376 953 953 1000 412 412 427 412 930 930 488 488 437 441 433 444 950 950 950 950 950 950 950 411 411 411 411 385 385 950 950 408 408 405 405 950 950 381 376 950 950 950 950 950 950 950 950 950 950 950 Total: 35 233

VVER V-270 VVER V-320 VVER V-320 VVER V-428 VVER V-213 VVER V-213 VVER V-213 VVER V-213 VVER V-320 VVER V-320 VVER V-213 VVER V-213 VVER V-213 VVER V-213 VVER V-213 VVER V-213 VVER V-320 VVER V-320 VVER V-320 VVER V-320 VVER V-338 VVER V-338 VVER V-338 VVER V-230 VVER V-230 VVER V-213 VVER V-213 VVER V-179 VVER V-179 VVER V-187 VVER V-320I VVER V-213 VVER V-213 VVER V-213 VVER V-213 VVER V-320 VVER V-320 VVER V-213 VVER V-213 VVER V-320 VVER V-320 VVER V-338 VVER V-338 VVER V-320 VVER V-320 VVER V-320 VVER V-320 VVER V-320 VVER V-320 VVER V-320

14

3 Defence in Depth of VVER-440 Reactors

Table 3.3 VVERs that have already been shut down Country (ISO code)

Station

AM BG BG BG BG DE DE DE DE DE DE RU RU SK SK

ARMENIA-1 KOZLODUY-1 KOZLODUY-2 KOZLODUY-3 KOZLODUY-4 GREIFSWALD-1 (KGR 1) GREIFSWALD-2 (KGR 2) GREIFSWALD-3 (KGR 3) GREIFSWALD-4 (KGR 4) GREIFSWALD-5 (KGR 5) RHEINSBERG (KKR) NOVOVORONEZH-1 NOVOVORONEZH-2 BOHUNICE-1 BOHUNICE-2

Net electricity generating capacity (MW) 376 408 408 408 408 408 408 408 408 408 62 197 336 408 408 Total: 5459

Model VVER V-270 VVER V-230 VVER V-230 VVER V-230 VVER V-230 VVER V-230 VVER V-230 VVER V-230 VVER V-230 VVER V-213 VVER-70 VVER V-120 VVER V-120 VVER V-230 VVER V-230

Table 3.4 VVERs under construction (2009) Country (ISO code)

Station

Net electricity generating capacity (MW)

Model

BG BG CN IN IN IR RU RU RU UA UA SK SK

BELENE-1 BELENE-2 TIANWAN 2 KUDANKULAM-1 KUDANKULAM-2 BUSHEHR-1 BALAKOVO-5 KALININ-4 VOLGODONSK-2 KHMELNITSKI-3 KHMELNITSKI-4 MOCHOVCE-3 MOCHOVCE-4

953 953 1000 917 917 915 950 950 950 950 950 405 405 Total: 11 315

VVER V-466 VVER V-466 VVER V-428 VVER V-412 VVER V-412 VVER V-446 VVER V-320 VVER V-320 VVER V-320I VVER V-320 VVER V-320 VVER V-213 VVER V-213

Table 3.5 Overview of VVER operational status globally (2009)

VVERs currently in operation VVERs that have already been shut down VVERs currently under construction

Number of units

Total net electricity generating capacity (MW)

50 15 13

35 233 5459 11 315

3.3 General Illustration of Defence in Depth

15

until the present (with the VVER-1000/V466 being used in many countries around the world) – equivalent to about 1000 operational reactor years – none of the VVERs have ever had a nuclear accident (as defined for INES > 3). The robust design and relative simple operation enabled by new I&C techniques result in a robust base for the safe use of these units into the future. The countries that joined the EU after 2004 (Slovakia included) have decided to close their VVER-440/V230 units, despite directing a great deal of effort and investment their way, as well as their good operational and safety features and collective history. This was done more for political reasons than because of insufficient safety standards. Instead of frustration or protests, a proactive and constructive approach is important. It is obvious that there was not enough knowledge and information about VVER design and safety in 1992 at the Munich G8 meeting, where it was decided that VVERs/V230 could not be upgraded to world safety standards at reasonable expense. In order to avoid the recurrence of such a situation and other possible misunderstandings in the future, the safety design, features and practices associated with reactors must be open, transparent and well presented to the entire nuclear community. Nuclear (VVER) safety research has changed significantly in the last 20 years. Unlike in the past, national institutions have increased their responsibilities in the nuclear area. Independent nuclear regulatory authorities were created in many countries. State or private research organisations have decreased their numbers of employees, but have also increased their quality and competence. Many of them are currently active globally, and are producing excellent results.

Chapter 4

Barriers Preventing the Release of Fission Products

4.1 First Barrier: the Nuclear Fuel Matrix The nuclear fuel most commonly used in NPPs is ceramic UO2 pellets with different levels of 235 U enrichment. In comparison with other fuel materials, this matrix releases a low rate of fission product.

4.1.1 Properties of UO2 Nuclear Fuel A deep knowledge of the properties of the nuclear fuel employed is essential for reliable behaviour during plant operation. The most important properties of UO2 that are affected by production technologies are: • enrichment of the fissionable additives (235 U, 239 Pu, 241 Pu); • chemical purity and stoichiometric coefficients (for example the purity, and the need for F < 10 ppm, H2 < 1 ppm, etc.); • density, microstructure, plasticity; • exact geometrical features (for example the pellet diameter is  0.013). These properties depend on how the fuel material is manufactured. Each technological step can influence the properties. There are many ways to obtain uranium dioxide for use as the basic material in ceramic nuclear fuel. The most common are: • • • • •

reduction of UO3 obtained from the uranylnitrate; ammonium diuranate (ADU) reduction; oxidation of uranium in a water bath or in water vapour; reduction of U3 O8 ; direct conversion of UF6 .

In the following steps, the UO2 is passed through a granulation process. There are only two technologies that can be applied here. In the wet granulation process, a soft UO2 powder is processed with binders. Then it is precompacted, dried, broken, and V. Slugeˇn, Safety of VVER-440 Reactors. © Springer 2011

17

18

4 Barriers Preventing the Release of Fission Products

pressed with lubricants. The other possibility is a dry granulation process, where UO2 is cold pressed, broken again, mixed with lubricants, and pressed. The options for pelletizing include: • • • • • • • •

cold pressing in the die and sintering; warm isostatic pressing; extrusion pressing and sintering (warm, cold); tempering, pressing and sintering; swaging; vibration compacting in the die; high-energy forming; tandem rolling.

A pressure of 1–5 t/cm2 (100–500 MPa) is used during pressing, and the content of lubrication oils cannot exceed 0.5 weight%. The sintering process is done in an H2 , H2 /N2 or H2 C CO2 atmosphere. Afterwards, the surface is ground and the cylinderlike UO2 can be used in the pile. 4.1.1.1 Sintering Technology Sintering is a process in which a compact of a crystalline or non-crystalline powder is heat-treated to form a single, coherent solid. In general, three types of sintering processes are important to the production of ceramics: • Vitrification – heat treatment which produces enough viscous liquid at the firing temperature to completely fill the porous spaces in the original powder compact. This process is relatively inexpensive and is of particular importance in the production of porcelain and clay-based ceramics. • Liquid-phase sintering – the composition is such that enough liquid forms at the firing temperature to allow easy rearrangement of the particles, but not enough to fill the initial porosity; subsequent solution and re-precipitation of the solid in the liquid phase then allows the particles to be reshaped and a dense body is formed. This method is often effective and reasonably inexpensive, but the resulting grain boundary phase may be detrimental to high-temperature mechanical properties (e.g., creep resistance). • Solid-state sintering – all constituents of the compact remain solid during the entire process; all densification is achieved by changing the grain shape. Sintering aids that will not form a liquid may be added in amounts ranging from a few hundred parts per million to over 20%. This method is preferred for the production of technical ceramics (e.g., nuclear fuel pellets) with good mechanical, electronic or optical properties, particularly when optimal high-temperature properties are required [2, 3]. The important variables in the sintering process are: • the processing temperature; • the time spent at each stage of the process;

4.1 First Barrier: the Nuclear Fuel Matrix

19

• the particle size and the size distribution of the ceramic powder; • the composition of the system, including additives and atmosphere; • the processing pressure applied when hot pressing or a controlled atmosphere is used. Obviously, this work is concerned with solid-state sintering, because it considers the nuclear field, especially the properties of fuel pellets.

4.1.1.2 The Driving Force for Sintering The primary driving force for sintering is a reduction in the free surface energy of the system. This is accomplished by reducing the area of the surfaces and interfaces of the compact, which can be achieved by a combination of two processes that occur simultaneously during the sintering of a ceramic powder compact: densification and coarsening (grain growth) [2, 4]. Densification is the process of replacing the free surface energy with grain boundary energy, while coarsening involves reducing the free surface or grain boundary energy. Thus, the microstructural changes that occur during sintering are brought about by the combined effects of coarsening and densification processes. The relative contributions of these two subprocesses depend on the processing variables: temperature, time, composition and particle size. The driving force for sintering (a reduction in excess surface free energy) is translated into a driving force that acts at the atomic level (thus resulting in atomic diffusion) by means of differences in curvature that inherently occur in different parts of the three-dimensional compact. These differences in curvature create chemical potential and vacancy concentration differences, and thus control the direction of matter transport. The relationship that links surface energy, curvature and concentration differences is the Gibbs–Thomson equation:   2˝ C.r/ D C1 exp ; (4.1) rkB T where: C.r/ is the vacancy concentration under a surface which has a radius of curvature r; C1 is the vacancy concentration under a plane;  is the surface energy; ˝ is the volume occupied by a vacancy; kB is the Boltzmann constant; T is the temperature. The Gibbs–Thomson equation applies to concentrations of dilute species and is therefore applied to vacancies which are in dilute solution in the solid rather than to the atoms themselves. Once the flow equations are known in terms of the vacancies, the equivalent flow in terms of atoms follows directly.

20

4 Barriers Preventing the Release of Fission Products

In the powder compact, the vacancy concentration will be different in regions with different curvatures, resulting in vacancy gradients and thus vacancy flow. The rate of mass transport is described by Fick’s first law of diffusion: J D D

dc ; dx

(4.2)

where: J is the vacancy flux; D is the vacancy diffusion coefficient; dc=dx is the concentration gradient. During the initial stages of sintering, there will be a net flow of vacancies from the neck that forms between particles. This flow of vacancies is exactly equivalent to a flow of atoms in the opposite direction, thus resulting in neck formation. It is often helpful in the case of ceramics to consider an alternative representation of the driving force for atom movement. In this representation, a flow of atoms stems from the normal pressure differences which occur in regions of the solid close to surfaces with different curvatures. This representation leads to a diffusion flux which can be written as: D dP J D ; (4.3) kB T dx where: J is the vacancy flux; D is the vacancy diffusion coefficient; kB is the Boltzmann constant; T is the temperature; dP =dx is the pressure gradient. Surface energy forces create regions with different pressures under different curvatures. Atoms will tend to flow from regions of high pressure to regions of low pressure. This concept avoids the need to rely on atom movements due to vacancies; it therefore also applies to systems in which atoms move by other defect mechanisms. This approach that links atom movement to pressure differences has the benefit of directly describing the diffusive deformation of dense polycrystalline materials caused by an applied stress (creep). Sintering rate equations for ceramics have been developed according to the assumption that behaviour caused by pressure differences during sintering is similar to diffusion creep behaviour. The rate of deformation caused by an applied stress is given by the general equation:     AD b m  n "D ; (4.4) kB T G g where: " is the rate of deformation; A is the dimensionless constant;

4.1 First Barrier: the Nuclear Fuel Matrix

21

D is the appropriate diffusion coefficient; kB is the Boltzmann constant; T is the temperature; g is the shear modulus; b is the magnitude of the Burgers vector; G is the grain size;  is the applied stress; m; n are constants that depend upon the transport mechanism. Low temperature (in relation to the melting point of the material) creep of metals is usually controlled by dislocation movements, because their structures contain sufficient active slip systems and have small Peierls stresses (the force needed to bring about dislocation movement) [4–8]. Deformation can also be controlled by dislocation climb, a process requiring vacancy diffusion. At high temperatures, deformation in metals is usually controlled by diffusion creep mechanisms that do not involve dislocation movement. In ceramics, however, diffusion creep may be the dominant mechanism under most processing conditions due to the small number of slip planes, the high Peierls stresses, and to the need to move stoichiometric amounts of the different atomic species present in the material (both anions and cations for an ionic compound).

4.1.1.3 Stages of Sintering Investigations of sintering behaviour have commonly been simplified by assuming that the densification takes place in stages. The sintering process is usually modelled with three stages: • initial – the individual particles of the green compact, which remain readily identifiable, are bonded together by neck growth between the particles, and grain boundaries form at the junctions between particles; • intermediate – characterised by interconnected networks of particles and pores; • final – the structure is composed of space-filling polyhedral and isolated pores. There are no clear-cut divisions between the three stages. During the initial stage, the individual particles of the green compact, which remain readily identifiable, are bonded together by the growth of necks between the particles, and a grain boundary forms at each junction between two particles. The initial stage ends when the growing necks begin to impinge on each other, or at  5% shrinkage.

4.1.2 Grain Growth The reduction in the free surface energy of the system is achieved by reducing the surface area by one or a combination of the following three processes:

22

4 Barriers Preventing the Release of Fission Products

• replacing the gas/solid interfaces with lower energy solid/solid interfaces (densification); • converting many small particles into fewer large ones (coarsening); and/or • reducing the grain boundary area through grain growth (coarsening). Grain growth means increasing the grain size in a single-phase material or the matrix grain size in a material with second-phase particles. The sum of the individual grain sizes is constant, and the increase in average grain size is thus due to the disappearance of some of the grains, usually the smaller ones. In practice, one distinguishes between normal or continuous grain growth and abnormal or discontinuous grain growth [6]. During normal grain growth, the individual grains are relatively uniform in size. However, during abnormal grain growth, some of the grains grow more rapidly than the others. When they have consumed all of the other grains, the remaining grains may again be relatively uniform in size. Large grains are desirable because less fission gas is released from a nuclear fuel with large grains during irradiation, they permit higher discharge burnup, and using large grains reduce the amount of irradiated fuel that needs to be stored and reprocessed [5].

4.1.2.1 Methods of Producing a Large Grain Structure in UO2 Methods that can be used to produce a large grain structure in UO2 can be divided into the following categories [5]: • purely thermal treatment of the UO2 ; • modifying diffusion coefficients by changing the stoichiometry; • chemical methods, which generally involve the use of additives. UO2 pellets are commonly sintered in hydrogen at 1770 °C for periods of about 4 h. At the end of this period, the grain size is typically about 10 µm. If the sintering is prolonged, the grain size will increase but at a diminishing rate, since the rate of grain growth is related to the grain size by k dD D n dt D and



E k D k0 exp  RT

(4.5)  ;

where: dD=dt is the grain growth rate; D is the grain size; E is the activation energy; R is the gas constant; T is the temperature; k0 is a constant; n is another constant; it usually has a value somewhere between 1 and 2.

(4.6)

4.1 First Barrier: the Nuclear Fuel Matrix

23

Grain growth occurs at all stages of the sintering process. Most theories and models of grain growth consider coarsening only during the final stage of sintering, as the primary goal of the sintering of ceramics is to achieve high density while maintaining a fine, uniform grain size, and most ceramics that sinter well do not undergo excessive grain growth until nearly full density is reached. The simplest model of grain growth considers the movement of a single grain boundary in a pure, dense material. There is a free energy difference G across a curved grain boundary:   1 1 G D Vm C ; (4.7) r1 r2 where: G is the difference in free energy; r1 ; r2 are the principal radii of curvature;  is the surface energy; Vm is the molar volume of atoms moving across the boundary. This free energy difference provides the driving force for the boundary to move towards its centre of curvature. The rate of boundary movement is proportional to the curvature, and thus inversely proportional to the average grain size and proportional to the ability of the atoms to cross the grain boundary. The rate of grain growth is then:  Dgb dG  ; dt G

(4.8)

where: dG=dt is the rate of grain growth;  Dgb is the grain boundary; G is the average grain size. Soluble impurities can segregate towards or away from a grain boundary, provided the resulting effect is to reduce the free energy of the system. There is a complex relationship between the velocity of a grain boundary, the diffusivity of the impurity, and the interaction of the impurity with the grain boundary. Qualitatively, at high boundary velocities, faster-diffusing impurities will exert the greatest drag. At low velocities, slower-diffusing impurities will cause the greatest drag. In the highvelocity case, only the fast-diffusing atoms can remain at the boundary and affect its mobility. In the low-velocity case, the fast-diffusing atoms will be able to redistribute themselves quickly enough to maintain the lowest energy distribution, while the slower diffusing atoms will obstruct boundary movement. Increasing the impurity concentration or decreasing the temperature will change the diffusive behaviour and thus increase the drag effect of the impurity [9–12, 16]. The low-velocity case, which is thought to be applicable to normal grain growth in single-phase ceramics, has been examined. In this case, the boundary velocity can

24

4 Barriers Preventing the Release of Fission Products

be written as:

 vb D Fb

Mb 1 C Mb ˛Co

 ;

(4.9)

where: Fb is the driving force; Mb is the boundary mobility; Co is the bulk impurity concentration; ˛ is the drag force on the grain boundary for unit volume and unit concentration when the boundary velocity or solute diffusion time is small. Second-phase particles or other inclusions in the microstructure will also inhibit grain growth. As a grain boundary moves past a particle, the area of the boundary is reduced by an amount equal to the cross-sectional area of the particle. The surface area, and the surface energy, must increase if the boundary is to pull away from the particle. The particle thus exerts a restraining force on the grain boundary of Fmax D  rgb :

(4.10)

 Dgb dG D Fb  Fp   G ; dt G

(4.11)

The grain growth is then:

where: Fb is the force on a curved boundary; Fp is the maximum drag force of a particle;  is the surface energy of the grain boundary. If there are a number of inclusions at the boundary, the boundary driving force may be insufficient to move it past the inclusions. The grain size limit in this case is: Glim Š

3a ; 4Vv

(4.12)

where: Glim is the grain size limit; a is the radius of each randomly dispersed spherical particle; Vv is the volume fraction. Pores can behave much like inclusions in retarding grain boundary movement. However, the situation is more complex since – unlike most inclusions – pores can move by diffusion. Pores move by transferring atoms from the front of the pore to the back. This transfer can take place by any of the diffusion mechanisms with a surface source. The effect of a pore on boundary movement will depend upon its mobility relative to that of the boundary and the geometry of the system [13, 15].

4.1 First Barrier: the Nuclear Fuel Matrix

25

For simplicity, pores are often modelled as being spherical; however, the pore cannot actually be spherical if there is a driving force for diffusion. The pores can remain attached to the moving boundary if the velocities of the pore and the boundary are equal: vp D vb

(4.13)

and vb D NFp C

Mp Fp ; Mb

(4.14)

where: vp is the velocity of the pore; vb is the velocity of the boundary; N is the pore density at the boundary; Mp is the mobility of the pore; Mb is the mobility of a pore-free boundary; Fp is the maximum force exerted on the boundary by the pore. The boundary and pore separate if:   vp D Fp Mp < vb D Fb  NFp Mb

(4.15)

or Fb > NFp C

Mp Fp : Mb

(4.16)

Small pores can move faster than large pores [14]. Many large pores will exert a large restraining force on a boundary. During the early portion of the final stage of sintering, both the grains and the pores are small. These small pores will not exert much drag on the boundary unless there are many of them. Whether the pores remain attached or not will depend on the relative velocities of the pores and boundary [15, 17]. During the later stages of sintering some grains may grow to be much larger than the average grain size if conditions are favourable, often trapping pores within the grain, resulting in a reduced final density. These large grains may also reduce the strength of the material by acting as stress concentrators. A large grain surrounded by small grains will have many grain boundaries, each with a small, convex (from the perspective of the large grain) radius of curvature. Each of these boundaries will have a high driving force, causing it to move away from the large grain, thus further increasing the size of the grain and promoting further growth. Milled powders often have a few very large grains that may grow abnormally. Such growth can also occur in regions with fewer than average second-phase particles or low solute concentrations, and is very likely to occur when pores become so small that they no longer restrain boundary movement. Density variations in a sample may lead to a wide grain size distribution, allowing abnormal grain growth [5, 6, 18–21].

26

4 Barriers Preventing the Release of Fission Products

4.2 Second Barrier: Fuel Cladding The fuel cladding is the second barrier, and (from the viewpoint of normal operation) the most significant barrier preventing the release of fission products into the reactor coolant. Regular and proper leak testing of fuel assemblies is an inevitable requirement that is closely related to not only operational regulations but also attempts to assure optimal operation from a radiation protection point of view.

4.2.1 Leakage Monitoring Techniques for VVER-440 Reactors In the core of a nuclear reactor, a wide variety of radionuclides are produced as a result of fission and activation processes. The fuel cladding is the most important protective barrier that prevents the release of most of the fission products from the fuel matrix into the coolant. The walls of the primary circuit serve as the next protective barrier that prevents the movement of radionuclides from the primary to the secondary circuit. When the cladding fails the coolant interacts with the fuel; fission products migrate – depending on their volatilities – into the coolant through “tight” defects, while fuel fragments may also get into the primary coolant if there are “open” defects in the cladding. Because of their multiple protection systems, nuclear reactors can be and often are operated in the presence of a certain number of defective fuel elements, but safety aspects and the long-term effects of contamination must be taken into account. There is also an economic limit on operating with failed fuels, bearing in mind the safety limit set by the nuclear regulatory authority. Monitoring fuel performance is an especially important task when the fuel policy of the reactor permits operation in the presence of defective fuels [22–24]. By monitoring the activity concentrations of several short-lived radionuclides (e.g., iodine and noble gases) in the primary coolant, fuel defects can be identified, and the defect type (tight or open) and number of leaking elements can be assessed. Major nuclear characteristics of the defective element, such as burn-up and the original 235 U enrichment, can be determined by measuring the activity ratios of certain long-lived nuclides (e.g., cesium, transuranium), so failed elements can be localised. The concentrations of the radionuclides originating from both the uranium concentration of the core and defective fuels are measured regularly. Iodine and cesium nuclides are measured by gamma spectroscopy. Occasionally, alpha and beta spectrometric analyses are performed to determine transuranium and strontium isotopes, respectively. Fuel leakages are qualitatively indicated by a sudden increase in the concentrations (spiking) of fission products, especially noble gases and iodine nuclides. The appearance of less volatile nuclides in the coolant (e.g., transuranium nuclides) suggests the occurrence of open defects. The following mathematical approaches can be used for quantitative fuel characterisation.

4.2 Second Barrier: Fuel Cladding

27

4.2.1.1 Surface Contamination It is assumed that the shortest-lived iodine isotope, 134 I, originates only from surface contamination of the reactor core. Thus, the amount of transuranium is calculated from the 134 I concentration.

4.2.1.2 Defect Type Two major types of defect can be distinguished without the need to define their sizes exactly: tight and open. Tight defects allow mostly volatile fission products to migrate into the coolant after some retention, while open defects also permit the release of fuel fragments into the water. Two release mechanisms can be distinguished: • Releases from tight defects are characterised by a high 131 I to 133 I concentration ratio, assuming the preferential accumulation of the longer-lived nuclide in the fuel element; • Releases from open defects are characterised by a low concentration ratio of 131 I to 133 I, assuming the relatively free leakage of all iodine nuclides. The leak model can be determined by applying a criterion, the ratio of the corrected activity concentrations (Acorr / of 131 I and 133 I, where the actual concentrations of the longer-lived iodine nuclides (131 I and 133 I) are corrected for surface contamination according to the following equations: I-131 I-131 AI-131 corr D Ameas  Abg

(4.17)

AI-131 bg

(4.18)

DK

K I-131 D

I-131

:AI-134 meas

I-131 :Y I-131 I-131 Cˇ I-134 :Y I-134 I-134 Cˇ

;

(4.19)

where:  is the decay constant (s1 /; ˇ is the cleanup rate of the water cleanup system (s1 /; Y is the fission yield (no units). The following criteria are applied. There are fuel elements with tight defects in the core if AI-131 corr  0:7 : AI-133 corr

(4.20)

There are fuel elements with open defects in the core if 0:2
0:5 MeV) Base metal Weld E > 1:0 MeV Base metal Weld

V230(440)

V213(440)

V320(1000)

215 11.8 3.840 3.980

215 11.8 3.840 3.980

320 10.9 4.535 4.660

0.140 0.210 12.26 17.1 325 30 268 0.240 268 296 6

0.140 0.210 12.26 19.2 325 40 268 0.228 268 296 6

0.193 0.286 17.65 24.6 350 40 289 0.317 289 322 4

2:3  1024 1:6  1024

2:6  1024 1:8  1024

6:3  1023 5:7  1023

1:4  1024 1:0  1024

1:6  1024 1:1  1024

3:7  1023 3:4  1023

4.3 Third Barrier: Integrity of the Primary Circuit

41

antiseismic features. This type has been described as having the first generation of RPVs, and was designed in the late 1960s. The PVs were welded by an automatic submerged arc using Sv-1OKhMFT welding wire and AN-42 flux. Of the 16 pressure vessels, produced nine are not clad with stainless steel: Kola 1 and 2, Armenia 1, Novovoronezh 3 and 4, Kozloduy 1 and 2 and Greifswald 1 and 2. Only limited evaluation of their initial properties was carried out, so there is only a limited amount of data on them and no archive material that is available for current assessment – no surveillance specimens were included in these reactors.

VVER-440-213 The VVER-440-213 was introduced in the 1970s. There are variants of it (like those that house the nuclear steam supply system in a containment structure, as in the two units at Loviisa in Finland). The main difference between the V213 and the V230 is in the provision of mitigation systems for the effects of severe accidents. Generally, the interiors of the pressure vessels of the V213 and VVER-1000 are clad with stainless steel, while many of the Russian V230 vessels (Kozloduy included) are not. These reactors contain surveillance specimens to provide detailed information about the state of the RPV, and when specimens in the first “chains” were tested, a significant difference between the actual and the assumed mechanical properties was observed – the change in properties was greater than had previously been assumed. Because of this, a large and comprehensive analytical programme was carried out on the VVER-440-230 materials to evaluate the current state of the plants and to develop mitigation methods for the effects of irradiation.

VVER-1000 There are two types of VVER-1000: V-302 and V-320. The first of these 1000 MWe units became operational in 1980 at Novovoronezh (unit 5). They are usually built in modules with twin units, all of which have four loops, horizontal steam generators, and all of them use 1000 MW steam turbines. It is worth noting that the welds of some VVER-1000 units have nickel contents of up to 1.9 wt%, and thus can exhibit a marked sensitivity to irradiation. A diagram showing a comparison of the two main types of VVER pressure vessel, the 440 and the 1000, is shown in Figure 4.8, while Figure 4.9 shows the position of weld 4 – the weld exposed to the highest neutron flux. The rationale for the small diameter of the VVER-440 was that it had to be possible to ship the forged and welded ferritic RPV over land by road or rail, which placed a major constraint on its dimensions – particularly its maximum diameter. This, in turn, led to a thinner PV (which also made it lighter) because the diameter was reduced. This design feature had further repercussions on the end-of-life fluence experienced by the RPV because it was subjected to a higher neutron flux due to the smaller water gap between the active core and the PV. However, these particular

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4 Barriers Preventing the Release of Fission Products

Figure 4.8 Comparison of the VVER-440 V-213 (left half ) and 1000 (right half ) pressure vessels

pressure vessels were made at a time when the effect of high neutron fluence on mechanical properties was not well understood. An important early influence on pressure vessel size may have been the ability of steel plants to produce ingots for forging that were large enough to eliminate the need for welds in the beltline regions of the VVERs. In addition, the VVERs have certain notable characteristics: • The vessel is welded to the circuit pipe work on site. • The decreased vessel diameter compared with a PWR results in a smaller water reflector gap and a higher neutron flux at the vessel, which in turn leads to greater potential for changes in mechanical properties due to irradiation. • The decreased mass of the vessel necessitated higher strength properties and a decreased wall thickness. • Two types of nozzle ring are used, upper ones for coolant outlet nozzles and lower for the inlet nozzles. This approach requires a weld between the upper and lower nozzle rings and leads to a temperature partition in the vessel. There is no temperature gradient in the circumferential direction in any nozzle ring. Because there are two nozzle rings and a special control rod design, the pressure vessel is longer. • Pressure vessels are only made from forgings (i.e., from cylindrical rings and plates forged into domes). The spherical parts of the vessel bottom and cover are

4.3 Third Barrier: Integrity of the Primary Circuit

43

Figure 4.9 The main, lower, part of the VVER-440 (V-230) RPV showing the locations of the girth welds and the weld subjected to the highest fluence (weld 4)

stamped from forged plates. In Russia, the forged domes were made from two smaller plates and welded with electro slag techniques (which must be followed by quenching and tempering). In the former Czechoslovakia, the forging was a large plate made from a single ingot because no axial welds are allowed in the vessel. Inlet and outlet nozzles are not welded into the nozzle ring but machined from a thicker forged ring for the 440 vessels and forged from a thick forged ring for the VVER 1000 vessel. • The compositions of the steels and welds are different from those used in Western pressure vessels. • Not all of the pressure vessels were clad with stainless steel. The earlier VVER440/230 PVs were unclad.

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4 Barriers Preventing the Release of Fission Products

• All of the austenitic steels used for cladding, internals and primary piping that are in contact with the water coolant are stabilised. High-strength, resistant Cr-Mo-V steel was developed for the VVER-440 RPVs from the very start of the VVER programme. This ferritic steel containing 0.13– 0.18 wt% C (for thicknesses of up to 400 mm) was designated 15Kh2MF (in the nomenclature converted from the Cyrillic script), and its composition is shown in Table 4.5. The “A” or “AA” at the end of the alloy type in Table 4.6 means “high purity clean steel” that is normally used in the beltline region. The steel was teemed in vacuum into 100–200 tonne ingots and forged. The chemical composition and

Table 4.5 List of chemical elements used in Russian designations of VVER PV materials [35] Russian

English transcription

Symbol

Element name

A Al M P V Bj B Dm Le L C Z D E M H B Q C E T U Q X X

[A] [Yu] [L] [R] [F] [Vi] [V] [Gl] [Kd] [K] [S] [Sh] [G] [D] [M] [N] [B] [P] [S] [E] [T] [U] [P] [Kh] [C]

N Al Be B V Bi W Ga Cd Co Si Mg Mn Cu Mo Ni Nb Pr Sm Se Ti C P Cr Zr

Nitrogen Aluminium Beryllium Boron Vanadium Bismuth Tungsten Gallium Cadmium Cobalt Silicon Magnesium Manganese Copper Molybdenum Nickel Niobium Praseodymium Samarium Selenium Titanium Carbon Phosphorus Chromium Zirconium

Table 4.6 Base materials for VVERs

Cylindrical rings for PV Other parts of the vessel Cover Free flange Stud bolts and nuts

V-230

V-213

V-320

15Kh2MFA 15Kh2MFA 25Kh2MFA 25Kh3MFA 25Kh1MF

15KhMFAA 15Kh2MFA 18Kh2MFA 25Kh2MFA 38KhN3MFA

15Kh2NMFAA 15Kh2NMFA 15Kh2NMFA – 38KhN3MFA

4.3 Third Barrier: Integrity of the Primary Circuit

45

the heat treatment of the steel were chosen to ensure that it had the required values for mechanical strength, ductility and toughness, as well as satisfactory weldability. The composition of this steel also ensured increased resistance to temper embrittlement during vessel fabrication, thermal ageing and irradiation embrittlement. The requirements for high strength and high toughness in vessels of these thicknesses were achieved by oil quenching from about 980 to 1000 °C and then tempering at about 680–700 °C (for VVER-1000, Q D 910–930 °C and T D 640–660 °C). The compositions of VVER steels together with their guaranteed mechanical properties are taken from [36]. The base materials used in VVERs are listed in Table 4.6, while welding materials are given in Table 4.7. The compositions of the various steels are given in Table 4.8, and additional compositional requirements for the steels used in core shells are given at the end of this table. The guaranteed mechanical properties for the VVER steels are given in Table 4.9, and the Russian code values for the irradiation embrittlement coefficient AF are given in Table 4.10. In order to ensure that the properties of heat-affected zones are maintained during welding, and resistance to hot and cold cracks (as well as under-clad cracks), it became necessary to provide a high preheat temperature of 350–400 °C for welding. The development of the VVER-1000, the 1000 MW version of the VVER, led to a change in the requirements for the pressure vessel materials. For example, the required strength was increased and Tk (the equivalent of RTNDT ) decreased from 0 to 25 °C. However, the irradiation conditions for the RPV became less severe – the irradiation temperature increased to 290 °C and the fluence decreased to 6  1023 nm2 (E > 1 MeV). As a result of the increased strength and ductility requirements and a wide ranging evaluation programme, 15Kh2MFA was replaced with a high nickel alloy steel, 15Kh2NMFA (Cr-Ni-Mo-V type). The increased nickel content increases the strength of the ferrite without decreasing its toughness, but it does increase the susceptibility of the ferrite to temper, thermal and irradiation embrittlement with an accompanying weld that reflects the altered base metal composition. Vanadium, which was added to the earlier steels to increase resistance to thermal ageing, produces a fine-grained tempered bainite, which imparts strength but is more difficult to weld than higher-nickel steels, which require high preheat temperatures. Consequently, higher-nickel, lower-vanadium steels were chosen for the VVER-1000s. As will be seen later, the technology associated with these new

Table 4.7 Welding materials for VVERs V-230 Automatic submerged arc wire Automatic submerged arc flux Electroslag wire Electroslag flux Manual arc (repair) electrode

V-213

V-320

Sv-10KhMFT(U) Sv-15KhMFT(U) Sv-12Kh2N2MFA(A) + AN-42(N) + AN-42(N) +FC-16(A)Sv09Kh6NMTASv-13Kh2MFT Sv-13Kh2MFT V1+KF-30 + OF-6 + OF-6 Sv-16Kh2NMFTA N-3, N-6 N-3, N-6 + OF6 RT-45A, RT45AA, RT-45B

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4 Barriers Preventing the Release of Fission Products

Table 4.8 Composition of materials (wt%) for VVER pressure vessels Materials

C

Mn

Si

P

S

Cr

Ni

Mo

V

15Kh2MFA

0.13 0.18

0.30 0.60

0.17 0.37

Max. 0.025

Max. 0.025

2.50 3.00

Max. 0.40

0.60 0.80

0.25 0.35

18Kh2MFA

0.15 0.21

0.30 0.60

0.17 0.37

Max. 0.025

Max. 0.025

2.50 3.00

Max. 0.40

0.60 0.80

0.25 0.35

25Kh3MFA

0.22 0.25

0.30 0.60

0.17 0.37

Max. 0.025

Max. 0.025

2.80 3.30

Max. 0.40

0.60 0.80

0.25 0.35

15Kh2NMFA Sv-10KhMFT + AN-42

0.13 0.18 0.04 0.12

0.30 0.60 0.60 1.30

0.17 0.37 0.20 0.60

Max. 0.020 Max. 0.042

Max. 0.020 Max. 0.035

1.80 2.30 1.20 1.80

1.00 1.50 Max. 0.30

0.50 0.70 0.35 0.70

Max. 0.10 0.10 0.35

Sv-10KhMFT + AN-42M Sv-12Kh2N2MA0.05

0.04 0.12 0.50

0.60 1.30 0.15

0.20 0.60 Max.

Max. 0.012 Max.

Max. 0.015

1.20 1.80 1.40

Max. 0.30 1.20

0.35 0.70 0.45

0.10 0.35 –

+ FC-16 Sv-12Kh2N2MA0.05

0.12 0.50

1.00 0.15

0.45 Max.

0.025 Max.

0.020

2.10 1.40

1.90 1.20

0.75 0.45

– –

+ FC-16A Sv-13Kh2MFT

0.12 0.11

1.00 0.40

0.45 0.17

0.012 Max.

0.015 Max.

2.10 1.40

1.90 0.40

0.75 0.17

–

+ OF-6

0.16

0.70

0.35

0.030

0.030

2.50

0.80

0.35

Sv-09KhGNMTAA

0.04

0.45

0.15

1.20

1.0

0.40

+ KF30 or (NF-18M)

0.10

1.10

0.45

2.00

1.5

0.70

SA533B,Cl1

Max. 0.25

1.15 1.15

0.15 0.15

Max. Max.

Max. Max.

– –

0.40 0.70

0.45 0.60

– –

SA508,Cl3

0.15 0.25

1.20 1.50

0.15 0.35

Max. 0.025

Max. 0.025

– –

0.40 0.80

0.45 0.60

–

Allowable impurity levels. Additional requirements for materials in core shells subjected to neutron irradiation: P

S

Cu

As

Sb

Sn

P + Sb Co + Sn Co

15Kh2MFAA

0.012

0.015

0.08

0.010

0.005

0.005

0.015

0.02

15Kh2NMFAA

0.010

0.015

0.08

0.010

0.005

0.005

0.015

0.02

specification steels progressed and vessels were built, but in practice the nickel content reached 1.5–2.0 wt%. Unfortunately, the surveillance samples that were placed in the actual RPVs to give detailed information on irradiation effects were located in a steep neutron flux gradient region of the reactor, and the temperature in that surveillance region was also higher than the appropriate region of the RPV itself, sothe data gained are difficult to interpret and will require further investigation. The existing database of actual materials used in practice is limited. Many (approximately half) of the earlier VVER 440-230 pressure vessels were unclad. For the others, the vessels were clad by automatic strip welding under a flux, using two layers. The first layer was an austenitic material (Sv07Kh25N13), and the second was a layer at least three beads thick of stabilised (with niobium) austenitic

4.3 Third Barrier: Integrity of the Primary Circuit

47

Table 4.9 Guaranteed mechanical properties (Rp0:2 , 0.2% offset yield strength; Rm , ultimate tensile strength; A5 , % elongation; Z, % reduction in area on failure; Tk0 , initial ductile-to-brittle transition temperature) Rp0:2 (MPa) 15Kh2MFA SA weld metal 25Kh3MFA 15Kh2NMFA 15Kh2NMFA SA weld metal A533B,Cl1 A508,Cl3

431 392 628 490 490 422 345 345

Room temperature Rm A5 (MPa) (%) 539 539 736 608 608 539 551 551

14 14 12 15 15 15 18 18

Z (%) 50 50 50 55 55 55 – 38

350 °C Rp0:2 Rm (MPa) (MPa) 392 373 590 441 441 392 285 285

A5 (%)

Z (%)

Tk0 (°C)

14 12 12 14 14 14 – –

50 45 45 50 50 50 – –

0 20 – –10 –25 0 –12 –12

490 490 638 539 539 510 – –

Table 4.10 Russian code values for the irradiation embrittlement coefficient AF Irradiation temperature (°C)

Irradiation embrittlement coefficient AF

15Kh2MFA

Base metal Weld

250, 270, 290 250, 270

22, 18, 14 800 (P + 0.07Cu) + 8 800(P + 0.07Cu)

15Kh2MFA-A

Base metal Weld

270, 290 270

12, 9 15

15Kh2NMFA-A

Base metal Weld

290 290

23 20

stainless steel (Sv08Kh18N10G2B) which, in total, gave a cladding thickness of about 8 mm.

RPV Steel Microstructure An excellent overview of the area of structural damage to RPV steels was published in [37]. The microstructures of RPV steels are typical of those of annealed bainite and martensite and low-alloying carbon steels [38]. In the structure of the base material, traces of native acicular composition (termed “sorbite”) are evident (Figure 4.10a). Ferrite can occur locally at grain boundaries (Figure 4.10b) at levels of 1% (at the surface on the side of the RPV) to 7% (in the middle of the wall of the RPV). The austenite grain diameter ds is distinctly average at 76 µm [39]. The carbidic phases can be divided into the following categories, depending on their size (Figure 4.11): • Thick carbides – M3 C and M7 C3 (Figure 4.11a); • Fine carbides – MC (Figure 4.11b).

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4 Barriers Preventing the Release of Fission Products

Figure 4.10 Sorbidic microstructure of the base material with a traces of native acicular composition and b local ferrite isles

Figure 4.11 Precipitation of a the carbides M3 C and M7 C3 into the grain boundaries, and b fine carbides of MC in RPV base materials [40]

Some metastable carbides such as M6 C were identified, but their occurrence was only confirmed for materials annealed for very long periods ( 60 h). The identification of hyperfine molybdenum carbide-nitrite precipitation (< 0.5 nm) was performed using the APFIM technique. The precipitation occurs at grain boundaries and subgrains, and the typical grain size is 0.2 µm [39]. MC carbides precipitate inside the microstructure and spherical particles form. Baker–Nutting orientations define the relations between vanadium carbides (VCs) and the ferritic matrix [40] f100gVC kf100g˛ ; h100iVCk h100i˛ :

(4.24)

As well as these carbidic phases, globular inclusions (sulfides: MnS) are also detected that are  1 µm in size. The dislocation structure of the RPV changes (Figure 4.12) with the number of anneals. In the final state, the average dislocation concentration is  2  1014 m2 for the BM (15Kh2MFA steel) [41]. The microstructure of the welding metal is based on acicular and eutectoid ferrite. The acicular ferrite has blunter rods due to the annealing of the welding splice.

4.3 Third Barrier: Integrity of the Primary Circuit

49

Figure 4.12 The dislocation structure of RPV steel [40]

Figure 4.13 a Precipitation of M3 C and M7 C3 carbides in grain boundaries of the welding heatimpacted zone, and b uneven distribution of fine MC carbides in grains boundaries of the welding heat impacted zone [42]

700

800

T [°C]

600

AUSTENITE

FERRITE

BAINITE + MARTENSITE

500

400

HV10 [a.u.]

600

HARDNESS

400

200

10

20

30

40

t8/5 [s] Figure 4.14 ARA diagram for the weld cycle conditions used with 15Kh2MFA steel [42]

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4 Barriers Preventing the Release of Fission Products

As the grains grow under maximum temperature gradients, their microstructural character is heterogeneous and non-isotropic. Two types of carbidic phase were observed in the volume: M3 C and M7 C3 . The dislocation concentration is 1.2– 2:0  1014 m2 . The welding heat impacted zone consists of an acicular mixture of martensite and banite. The average grain size is double that of the base material (ds D 120 µm) [41] and contains an average dislocation concentration of  2:5  1014 m2 . The segregation of carbides into M3 C and M7 C3 was identified in grain boundaries and the matrix (Figure 4.13). The microstructure of the welding impacted zone is shown in Figure 4.14.

4.3.1.2 Radiation Damage Characteristics of Primary Damage Processes When metallic materials are irradiated with particles such as neutrons, protons and electrons with sufficiently high energies, interactions of the incident particles with the atoms of the irradiated material lead to dynamic disturbances and changes in the regular atomic ordering of the crystal lattice. These processes are accompanied by the formation of characteristic lattice defects which affect both the microstructure and the structurally sensitive macroscopic properties of the irradiated material. As they travel through the crystal lattice, the bombarding species interact with the lattice atoms and transfer energy to them. This process can cause damage to the crystal lattice, which can be classified into three types: • The production of lattice atoms that have been shifted from their regular lattice positions – also known as displacement damage; • Changes in chemical composition that occur when the bombarding particles are stopped completely before exiting the lattice (called ion implantation) or when the particles are captured by atomic nuclei, resulting in transmutation; • The excitation of electrons and the ionisation of atoms (which does not produce permanent damage in metals). The elementary interaction that occurs between an incident particle and a lattice atom is a collision. This binary process occurs in a time of < 1017 s, and the surrounding lattice can be considered to be at rest during this time period (the frequency of the thermal oscillations of the atoms is  1013 s1 ). The collisions with the lattice atoms lead to changes in the directions of motion of the incident particles, known as scattering. These collisions can be either elastic or inelastic. A collision is considered elastic when the internal states of all particles involved are not changed by the collision, or when the total kinetic energy of both species remains constant. In inelastic collisions, some of the original energy is lost, so E1 D T1 C T2 C Q ;

(4.25)

4.3 Third Barrier: Integrity of the Primary Circuit

51

where: E1 is the initial kinetic energy of a particle prior to the collision; T1 and T2 are the kinetic energies of the two particles; Q is the inelastic loss. The kinetic energy T transferred to the lattice atom during an elastic collision can be expressed by the following equation in the classical hard sphere approximation, which can be applied to metals in the centre-of-mass coordinate system [43]: T D

4M1 M2 .M1 C M2 /

2

E sin2

 ; 2

(4.26)

where: M1 and M2 are the masses of the incident particle and the lattice atom at rest; E is the energy of the incident particle;  is the scattering angle. The maximum value of Tm in a head-on collision ( D 180 °C) is expressed by Tm D

4M1 M2 .M1 C M2 /2

E:

(4.27)

The atoms knocked out of the lattice positions by impinging particles – which are called primary knock-on atoms (PKAs) – can have various energies from zero to Tm , even for monochromatic incident radiation. In addition, the PKA energy spectrum depends on the incident particle type (mass, charge) and energy. Differences in the PKA energy spectrum lead to differences in the damage caused. The formation of a PKA is equivalent to the formation of a vacancy–interstitial defect pair (or Frenkel pair). The minimum energy required for displacement is called the displacement threshold energy, Td , and its mean value (independent of the crystallographic direction) ranges between 20 and 50 eV for all metals. In contrast to the displacement of atoms due to elastic collisions, transmutation processes (also termed chemical processes) occur continuously throughout the whole irradiation period. Their frequency depends on the energy spectrum of the particles and on the composition of the irradiated material, but only slightly on the irradiation temperature. Transmutation processes result in the creation of new isotopes (via (n,  ) reactions) or other chemical elements (via (n, ˛), (n, p) or (n, ˇ) reactions). In practice, the most important consideration in this context is the formation of atoms of inert gases, especially He (and H), which has been observed in a number of materials. The presence of these gases strongly affects defect interactions during irradiation at elevated temperatures as they readily diffuse at elevated temperatures, are barely soluble in the lattice, and are chemically inert, thus greatly affecting the development of microstructure within the material during irradiation.

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4 Barriers Preventing the Release of Fission Products

Binary elastic collisions between the moving particle/atom and the stationary lattice atom represent the dominant mechanism for the formation of primary defects in metal crystals, and are natural elementary steps in all models and computer simulations of damage processes. Some of the characteristic parameters of any type of radiation are described below. • The flux of particles (e.g., neutrons, protons, electrons) incident on the material is given by the number of the particles with energy E that pass per second through an area of 1 cm2 perpendicular to the direction of incidence of the radiation. It holds that Z1 D

'.E/dE ;

(4.28)

0

where: is the integral particle flux (m2 s1 /; '.E/ is the differential flux of particles with energy E (flux density, m2 s1 MeV1 ). Assuming that the neutron energy spectrum is constant, the overall effect of radiation on the material over the irradiation period tr is given by its fluence ˚ (m2 /: Ztr ˚D

Ztr Z1 .t/dt D

0

'.E; t/dEdt : 0

(4.29)

0

• Cross-sections are parameters that characterise the interaction between the incident particles and the material. They depend on the type of atoms being irradiated atoms and the type of radiation. Geometrically, the microscopic cross-section can be considered to correspond to the area occupied by the target particles perpendicular to the path of the impinging particles. • The corresponding macroscopic cross-section ˙ is related to a given group of atoms, usually to the number of atoms per volume unit, and is given by the relationship ˙ D N ;

(4.30)

where N is the number of target atoms per unit volume. Its dimensions are m1 , and it is inversely proportional to the mean free path of the particle in the material. In a multi-component material, the macroscopic cross-section is given by the sum of the contributions of the individual components.

4.3 Third Barrier: Integrity of the Primary Circuit

53

Interactions of Neutrons with Materials Because the neutron has no electrical charge, it does not need to overcome repulsive coulomb forces to interact directly with the nucleus. This interaction depends on the energy of the impinging neutrons. The atoms are shifted from their normal lattice positions due to interactions with neutrons through two fundamentally different mechanisms: • A neutron collides with an atomic nucleus, resulting in an energy transfer of greater than Td to the nucleus, which is not, however, changed by this process. Such collisions can be either elastic or inelastic. The incident neutron must possess an energy of  102 eV for such a collision to occur. • A neutron is captured by a nucleus, producing an excited compound nucleus with a mass of (M2 C 1) which is unstable and decays over a very short time period ( 1016 s), resulting in the emission of neutrons, protons and  photons or fission products. The nuclear recoil caused by the emission of the decay products can lead to atom displacement, just as in the previous case. In contrast to PKAs, these atoms are termed recoil atoms [44]. It is important to emphasise that (i) the contribution of the recoil atoms to the radiation damage increases with increasing incident neutron energy, and that (ii) PKAs and recoil atoms behave identically along their paths through the crystal lattice: they continue to generate displaced atoms until their kinetic energies are exhausted. Note that the neutron capture can occur with both thermal neutrons and fast neutrons with energies above 2 MeV. A considerable proportion of the interactions of thermal neutrons with crystal atoms are inelastic. In such cases, nuclear decay is accompanied by the emission of one or more  quanta, and the reaction is denoted (n,  ). The energy T transferred to the recoil atom is then given by the equation E2 ; (4.31) 2M2 c 2 where E is the energy of the emitted photon. The total energy of the photons produced during each event corresponds to the bonding energy of a neutron with a nucleus. Mean T values are on the order of 102 eV – sufficient to produce displacement. The time and the angular correlation between the individual photons determine whether atomic displacement occurs. It has been found that (n,  ) reactions are the only type of reaction that can be neglected, as their contribution to atomic displacement is small compared to those of other reactions. On the other hand, the contribution of inelastic interactions to radiation damage increases with increasing energy of the incident neutrons. T D

Collision Cascades The formation of a PKA as a result of particle impingement is equivalent to the formation of a vacancy–interstitial pair lattice defect, and is a basic structural defect

54

4 Barriers Preventing the Release of Fission Products

produced by radiation. If the kinetic energy of the PKA is on the order of tens or more of eV, the PKA continues to move through the crystal lattice and to collide with further atoms, generating secondary, tertiary, etc., displaced atoms. The collision cascades are thus formed in a similar manner to the formation of Frenkel pairs, and the whole collision cascade takes a very short time (> 1013 s); see Figure 4.15. In the first branching stage of the collision cascade chain, where the PKA energy is still relatively high, the individual collisions occur relatively far from each other, and the motion of each atom in each collision is determined by the individual binary collision. Isolated interstitial atoms and vacancies are formed along the trajectory of the PKA. As the kinetic energies of the individual atoms decrease along the path of the PKA, the distances between the collisions also decrease, until they become comparable to the interatomic distance. A considerable amount of energy (eV/atom) is concentrated in the final part of the PKA pathway over a very short time ( 1013 to 1012 s) and within a very small volume ( 104 atoms). This leads to a collective atomic rearrangement in this region, and to the formation of random and irregular clusters of vacancies surrounded by an envelope of interstitial atoms escaping from the centre of the disturbed region (called the depleted zone); see Figure 4.15b. At incident particle energies, the cascades exhibit a tendency to separate into subcascades; see Figure 4.15a [46–48]. Two approaches to modelling the final stage of the path of the PKA – where the collisions occur at very short intervals and the collision cascade is thus very dense – have been described. Both of these approaches are intimately connected. In the first phase, collective dynamic atomic motion occurs over several tens of picoseconds, and atomic relocation occurs at random. This transitional phase in the development of the cascade is named the displacement spike [49]. The energy distribution among the atoms during collisions is affected in two ways by the regularity of the crystal lattice. In focusing replacement collisions, the energy or mass (atom) is transferred over relatively large distances ( 102 atomic distances) with very small losses. Focusing occurs at low energies (100 eV) and greatly affects the PKA distribution. The second process is channelling, during which the atom is transported through tunnels in the crystal lattice bordered by densely occupied crystal planes. The atomic path length in the channel is relatively long ( 20 nm).

Figure 4.15 Schematic representation of a a displacement cascade, and b a depleted zone (open circles are vacancies; filled circles are interstitial atoms) [40]

4.3 Third Barrier: Integrity of the Primary Circuit

55

Figure 4.16 Model of a damage zone

Both of these processes can give rise to the displacement of atoms from the centre of the damage zone by up to 20 nm, which limits spontaneous recombination. Figure 4.16 depicts a model of a damage zone that includes these processes [49]. The atomic configuration during the displacement spike phase is apparently unstable and heads back to equilibrium after this phase. The first stage involves the instantaneous recombination (collapse) of closed Frenkel pairs. As soon as the energy transferred between atoms during collisions drops below Td , it is dissipated in the form of increased thermal vibrations. The corresponding heat pulse is named the thermal spike [45]. The temperature corresponding to the local change in intensity of the vibrations of the lattice atoms can reach melting point after a certain amount of time. A number of mechanisms can contribute to collapse, especially: • Thermal transport (the motions of vacancies against the thermal gradient from the periphery to the cascade centre); • Nucleation and growth (in the central region with a high vacancy concentration); and • The motions of interstitial atoms (along the concentration and temperature gradients). The development of an energetic collision cascade can be split schematically into several phases. The thermally activated motions of elementary point defects result in changes in the microstructural state of the irradiated material. Number of Atomic Displacements The number of atoms displaced or the number of Frenkel pairs formed by the gradual dissipation of the energies of the impinging particles in the crystal lattice is one

56

4 Barriers Preventing the Release of Fission Products

of the basic parameters that characterise the collision cascade. Damage formation can be considered a two-step process: • the formation of PKAs as a result of elastic collisions between bombarding particles of kinetic energy E and the lattice atoms; each PKA receives a amount of kinetic energy T within the interval hTd ; Tmax i; • the formation of multiple displacement atoms as a result of elastic collisions of the PKAs (each with a kinetic energy T ) and the lattice atoms. The simplest quantity to describe the collision cascade is the number of displacements (or Frenkel pairs) formed during the development of the cascade. The number of point defects formed is proportional to the damage energy. The kinetic energy of the moving and stationary particles is always divided up in the same way in subsequent collisions. If the PKA has kinetic energy T , then, after n collisions, each of the 2n species formed has energy T =2n . The collision cascade ends when the magnitude of this energy decreases below the threshold displacement energy Td (or 2Td ). The number of displacements v.T / is then given by Table 4.11. Table 4.11 Number of displacements Kinetic energy T of PKA

v.T /

T < Td Td < T < 2Td T D 2Td

0 1 T =2Td

These relationships lead to the Kinchin and Pease model [50]. They are valid for a number of simplifying assumptions. This model forms the basis for a number of further refinements, primarily calculating the damage energy and estimating the displacement limit Td more realistically. The number of Frenkel pairs v.T / formed by PKAs with energy T is given in the Torrens–Robinson–Norgett model [51] by the relationship: v.T / D k

Tdam ; 2hTd i

(4.32)

where: Tdam D T  Q is the portion of the PKA energy that corresponds to elastic collisions and leads to permanent radiation damage; Q is the total energy lost during inelastic collisions in the collision cascade; k is the displacement efficiency, which depends on T ; hTd i is the mean displacement threshold energy in various crystallographic directions.

4.3 Third Barrier: Integrity of the Primary Circuit

57

Average Number of Displaced Atoms per Lattice Atom dpa The parameter dpa gives the average number of displaced atoms per lattice atom. The calculation of dpa for reactor radiation requires a knowledge of (i) the neutron spectrum, (ii) the neutron flux or fluence, and (iii) the effective displacement crosssection d .E/, which gives the probability an atom of the target substance being displaced as a result of a collision with an impinging neutron. The number of displacements (dpa) caused by a single neutron d .E/ is obtained via the relationship Z1 d .E/ D

s .E/.E; T /vd .T /dT ;

(4.33)

0

where: s .E/ is the probability that the impinging neutron will collide with an atom of the substance; .E; T / is the probability that the displaced atom will receive energy T in the collision; vd .T / is the number of secondarily displaced atoms. The value of dpa is then given by the expression dpa D  d ˚ ; where  d is the spectrally averaged displacement cross-section: R1 d .E/'.E/dE d D 0 R 1 ; 0 '.E/de

(4.34)

(4.35)

and '.E/dE is the neutron flux in the energy interval from E to .E C dE/. Ztr Z1 ˚D

'.E; t/dEdt 0

(4.36)

0

is the neutron fluence. Multiplying the dpa value by the number of atoms per unit volume yields the theoretical number of interstitial atoms formed by the radiation per unit volume of the irradiated substance. The displacement rate K (dpa s1 ), corresponding to the rate of formation of interstitials or vacancies during the irradiation, is given by the relationship Z1 K D d

'.E/dE : 0

(4.37)

58

4 Barriers Preventing the Release of Fission Products

The quantity K 1 therefore corresponds to the time required to attain one displacement per atom. Other parameters employed in analyses of radiation damage include the PKA energy spectrum, the mean number of displacements per PKA, the mean PKA energy, etc.

Effects of Radiation Damage on RPV Steel Neutron irradiation of steels used in the construction of nuclear reactor pressure vessels can lead to the embrittlement of these materials – an increase in the ductileto-brittle transmission temperature and a decrease in the fracture energy – which can limit the NPP. Embrittlement is manifested as a reduction in the fracture toughness and a shift in the ductile-to-brittle transition temperature (DBTT) to higher values, as shown schematically in Figure 4.17. The upper limits on neutron fluence for RPV materials are listed in Table 4.12 [52].

UNIRRADIATED

IRRADIATED

USE (J)

reduction in upper shelf energy

increase in transition temperature

TT (°C)

Figure 4.17 Schematic showing the effect of neutron irradiation on the impact properties of RPV steels (USE, upper shelf energy; TT, transition temperature) [53] Table 4.12 Maximum neutron fluences for various RPVs (VVERs) during their operational lifetimes Part of RPV

VVER 440 (230)

VVER 440 (213)

VVER 1000 (320)

.En > 0:5 MeV/ Base material Weld material

2:3  1024 1:6  1024

2:6  1024 1:8  1024

6:3  1023 5:7  1023

.En > 1 MeV/ Base material Weld material

1:4  1024 1:0  1024

1:6  1024 1:1  1024

3:7  1023 3:4  1023

4.3 Third Barrier: Integrity of the Primary Circuit

59

Low-temperature Brittleness The irradiation embrittlement of ferritic steel is a special manifestation of lowtemperature brittleness. A transition from ductility to brittle failure with decreasing temperature is observed for many metals and alloys, but primarily for those with the body-centred cubic (bcc) crystal structure. This phenomenon was first explained via Ioffe’s well-known scheme (Figure 4.18). In this scheme, the nature of brittle failure is determined by the ratio between the temperature-dependent flow stress (yield stress y ) and the temperature-independent brittle fracture stress (bf ), which characterise the material’s resistance to the cleavage. The temperature corresponding to y D bf is referred to as the transition temperature. Ioffe’s explanation of cold embrittlement can be characterised in a number of ways. It is well known that absolute brittle failure of metals is not encountered in practice. As a rule, traces of slip deformation are seen on the surface of a material that has undergone brittle failure. However, signs of plastic deformation on the fracture surfaces of macroscopically brittle specimens do not by themselves constitute incontestable proof that deformation precedes fracturing, as opposed to both mechanisms occurring simultaneously. The most vulnerable point in the classical theory for this phenomenon is the quantitative discrepancy between actual values of brittle fracture stress (500– 2000 MPa for steel) and the theoretical cleavage stresses of crystals. This contradiction can only be resolved by assuming that the metal always contains stress concentrators, which is not usually borne out in reality. Hence, at present, the prevailing opinion is that brittle crack initiation is induced by plastic deformation. Current theories of brittle failure are based on dislocation models in which crack initiation occurs due to slip dislocation coalescence. The failure process consists of three stages:

σinY σirrY σ (MPa)

σinbf

Δσγ

σirr Tin

Tirr

Tirr

TT (°C) Figure 4.18 Scheme for the transition from elasticity to brittle failure during tensile tests of irradiated metal ( , yield stress; TT, transition temperature) [54]

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4 Barriers Preventing the Release of Fission Products

1. Generation of free dislocations; 2. Coalescence of slip dislocations into cavity dislocations; 3. Growth of the crack formed by cavity dislocations. Stages 1 and 2 are governed by the tangential stress, while stage 3 is determined by normal stress. Ductile-to-brittle failure transition criteria are based on our knowledge about dislocations. They reveal the most important features and parameters that govern material susceptibility to brittleness. Using these criteria, a quantitative analysis of the main factors that affect radiation embrittlement of steel can be attempted. One of the first attempts was to obtain an expression for the ductile-to-brittle transition temperature [54] using certain simplifying assumptions with respect to the temperature dependence of yield stress and effective surface energy. The derived expression has the following form:  2 Tt D  C C 

4qG0 K  Kl

 12

;

(4.38)

where: Tt is the transition temperature;  is the thermal component of yield stress; q is a coefficient that characterises the stress–strain state; G is the shear modulus;  is the effective surface energy, which is the sum of the free surface energy 0 and the work involved in plastic deformation; l is the grain size; 2, C and K are constants. Hardening is therefore of paramount importance in the radiation embrittlement of a metal. It exhibits plastic relaxation at the stage of crack initiation and prevents the crack from blunting during the growth process. The shift in Tt upon increasing the yield stress is also implied by the Ioffe scheme. Structural changes in materials induced by radiation damage may give rise to other effects which, along with hardening, can affect embrittlement quite appreciably under certain conditions. Irradiation Embrittlement Irradiation embrittlement involves many variables (for illustration see Table 4.13). The most important of these are the irradiation temperature, the neutron fluence (the neutron dose), the neutron flux (the neutron dose rate) and the chemical composition of the irradiated material. Irradiation embrittlement of pressure vessel steels irradiated at 290 °C is now believed to be the result of irradiation-induced fine-scale microstructural features of defects. These act as obstacles to the free movement of dislocations, thereby producing an increase in the yield strength (hardening) and in the ductile-to-brittle

4.3 Third Barrier: Integrity of the Primary Circuit

61

Table 4.13 Changes in the mechanical properties of 15Kh2MFA steel due to scalable neutron irradiation [54] ˚ (m2 ); En > 0:5 MeV

Tir (°C)

Rp0;2 (MPa)

Rm (MPa)

A (%)

TT50 (TT38 ) (°C)

Czechoslovakianproduced BM [53]

– 7:3  1023 1:2  1024

– 288 288

515 583 600

629 684 693

22 20 21.7

70b 47b 34b

Russian-produced BM [53]

– 7:3  1023 1:2  1024

– 288 288

548 611 647

658 696 715

21.1 21 20.2

64b 26b 25b

BM [39]

– 2  1023

– 280 ˙ 5

553 713

655 811

20.7 19.5

53 11

BM [38]

–

–

431

Max. 735

14

–

Steel

a

BM [41]

– 1  1025

– 275

527 879

639 880

10 4.2a

41 141

BM [41]

– 5:2  1024

– 275

475 750

600 761

17.9a 6.4a

7 123

BM [42]

–

–

675

563

21

21

a b

A TT38 : nonirradiated samples tested at 20 °C

transition temperature (embrittlement). Theoretical and experimental observations suggest that these defects are mainly of two types [53]: • radiation damage clusters – vacancy clusters or microvoids created by neutron– lattice atomic interactions; • metallic clusters – solute clusters that form during irradiation due to the enhanced solute diffusivity resulting from the elevated point defect population. About 70–80% of the embrittlement effect is attributed to the metallic clusters or, more precisely, to the coherent Cu clusters or precipitates. The influence of the Cu clusters and P clusters is attributed to an age or precipitation hardening mechanism. The importance of Ni content in the embrittlement process has become apparent, but the physical role of Ni (dependent on or independent of Cu content) is not well understood. Current experimental results are not conclusive in attributing any influence to Mn. Moreover, it was shown that Si reduces irradiation sensitivity. In some cases Ni, Mn and Si clusters, in addition to P clusters, were at least as significant as the Cu clusters or precipitates. It is important to note that in these cases the specimens came from surveillance programmes or from RPV steels, which contain  0.1% Cu. On the other hand, most of the data, which showed prevailing Cu-rich clusters, came from MTR irradiations and were for steels and alloys with > 0.1% Cu. The irradiation conditions in surveillance programmes are more appropriate for simulating those of an actual pressure vessel wall.

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4 Barriers Preventing the Release of Fission Products

Post-irradiation annealing results [55] suggest that microvoids or vacancy clusters are responsible for about 20–30% of the embrittlement effect in commercial RPV steels. Although such defects were detected in irradiated model alloys, there is no solid evidence for their detection in commercial RPV steels. In the current models of irradiation embrittlement, no contribution is attributed to these vacancies. Most of the recovery effect is due to the growth of large irradiationinduced Cu precipitates (overaging) at the expense of smaller ones (reducing the number of dislocation pinning points). After annealing, there will be less Cu in solid solution. Therefore, one would expect that if the steel is re-irradiated, the reembrittlement rate should be less than the original embrittlement rate [53]. Radiation Creep Radiation creep (Figure 4.19) is observed in all types of reactors where the operational temperature  0:5Tm. Increasing the irradiation causes the radiation creep to accelerate, increasing the vacancy concentration and shifting the temperature at which the abovementioned effects occur. At low values of mechanical strain, there is a directly proportional relationship between radiation creep speed and neutron flux [56]. t (°C) 600

500

400

1E-03

-1

Creep speed (h )

σ = 100 MPa 1E-04

Radiation creep

1E-05

Temperature creep 1E-06

1/T (K -1.10 4 ) Figure 4.19 Radiation and temperature creep in the austenitic steel 08Cr18Ni9Ti for a dose of 1:1  106 dpa s1 [57]

Residual and Alloying Elements From the perspective of materials research, the aim is to identify the role of residual and alloying elements in the irradiation hardening and embrittlement of nuclear pressure vessel steels. The residual elements, especially copper, phosphorus, and

4.3 Third Barrier: Integrity of the Primary Circuit

63

nickel as an alloying element, play an important role in irradiation hardening and embrittlement. However, until very recently it was not possible to define the microstructural changes produced by irradiation. The progress made in examining the microstructure using new techniques such as positron annihilation spectroscopy (PAS), transmission electron microscopy (TEM) and Mössbauer spectroscopy (MS) made it possible to identify the irradiation-induced defects described in the following subsections. Effect of Copper. Residual elements, Cu especially, seriously affect the sensitivity of steel to irradiation. Experiments on iron, simple and complex iron alloys, and pressure vessel steels have shown that irradiation embrittlement is markedly increased in the presence of Cu [58, 59]. It was concluded that a Cu content of more than about 0.1 wt% has a determinable effect, although there are some indications that such an effect may be found with Cu contents as low as 0.03 wt% [60]. Increasing the Cu content of irradiated RPV steel can cause an irradiation-induced shift in the ductile–brittle transition temperature TT (see Figure 4.20). Extensive research experiments were carried out to define the effects of Cu (and other residual elements) more accurately and quantitatively, and to examine the mechanisms by which Cu participates in the embrittlement process. TEM was used to examine the defects and changes in microstructure produced by irradiation. It became evident that the defects in RPV steels caused by neutron irradiation were too small to be detected by TEM. These investigations, coupled with the observed recovery in the mechanical property changes (obtained through annealing treatments), suggested a model in which vacancies interact with small Cu clusters to form defect aggregates that are more stable and more numerous than those ordinarily formed in the absence of Cu. The clusters of Cu atoms serve as nucleation sites for defect aggregates [58, 59].

UPPER

ΔTT [°C]

200

LIMIT

150

100

50

1e+17

5 0.3

%

% 0% 0.25% 0.20 0. 3

0.1

1e+18

5%

0.1

0%

8 0.0

1e+19

%

L

M LI E R .0 8 0 08 W O =

IT

.0 Cu 0 % P= %

1e+20

FLUENCE [n/cm2], En > 1 MeV

Figure 4.20 Predicted shift in transition temperature (TT as a function of fluence and Cu content) [53]

64

4 Barriers Preventing the Release of Fission Products

Studies of Cu-bearing alloys have shown a high density of scattering centres that were absent in the Cu-free control alloy irradiated under identical conditions. These centres were identified as three-dimensional aggregates, < 1.5 nm in diameter, which could comprise either Cu atoms alone or in combination with vacancy point defects produced during irradiation. These clusters were believed to be the obstacles to glide dislocation that are responsible for irradiation hardening [61]. Wood et al. [62] used atom probe field ion microscopy (APFIM) to study pressure vessel steel (A 302B) irradiated at 290 °C to about 2  1019 n/cm2 . Both Cu and P-rich regions (clusters) were detected in the steel. Their combined number density was  1015 cm3 . The segregated Cu was often associated with P and Al in diskshape regions < 10 nm in diameter. Additional P clustering occurred in rod-shaped regions, the largest of which was < 1 nm in diameter and at least 8 nm long. Both types of solute clusters were believed to have vacancies associated with them. The formation of solute clusters during irradiation resulted in the depletion of Cu and P in the matrix. Cu-rich particles (or clusters) were also detected in RPV steel weldment after irradiation [62]. The presence of irradiation-induced copper precipitates of clusters in the irradiated RPV steel (A 302B) was confirmed in more detail by Solt et al. [63], and Curich defect clusters were detected. The mean particle radius was  5 Å (0.43– 5:1  1019 n/cm2 ), and increased to 7–9 Å as the neutron fluence was raised. The clusters were considered to be composed of two components, Cu and vacancies or Cu and Mn atoms. The Cu content in the particles was determined from their magnetic vs. nuclear contrasts. The investigation of irradiated RPV steels [64] by APFIM revealed that their microstructures were complex, involving a variety of ultrafine Cu-enriched atmospheres, clusters and precipitates, P clusters, and Mo carbides and nitrides. The Curich atmospheres and clusters were significantly enriched in Mn and Ni (and Si in the case of welds). Phosphorus was frequently observed in the vicinity of these atmospheres, clusters or precipitates. The investigations showed that the matrix was depleted in Cu and P as a result of irradiation. Figure 4.21 shows a character plot obtained using APFIM of a Cu atmosphere in irradiated steel, while Figure 4.22 illustrates the classification of the Cu atmospheres and clusters into precipitates. However, there are some cases in which the main metallic clusters formed in the irradiated RPV steel were not Cu clusters. Auger et al. [65] used TEM, SANS and APFIM to study the microstructural features that evolved in two RPV steels (16MND5) irradiated in NPP surveillance programmes. The study revealed that solute atoms such as Ni, Mn and Si segregated into clusters. Sometimes Cu atoms were associated with these clusters. In addition to its effect of increasing the irradiation sensitivity of steel, there are indications that the high Cu content in RPV steel retards the recovery of its mechanical properties during the post-irradiation annealing process. Effect of Phosphorus. The effect of P content is mainly to increase the irradiation sensitivity of RPV steels. However, it has less of an effect than Cu, and this effect

4.3 Third Barrier: Integrity of the Primary Circuit

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F

M

F

F

F

F

F

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M

F

M

F

S

F

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F

M

F

M

F

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F

F

F

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S

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S

M M

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C

M

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M S

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S

F

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F F F M F

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N

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N

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F

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N

F

F

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F

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F

F

F

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F

F

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F

F

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F

O

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M

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N

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M

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F

Key: C - Cu

F

F

F

M

F

M

F - Fe

M F

C

F

N

C

M

M - Mn

F

F

F

F

F

F

F

F

N - Ni

F

C

F

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O

M C

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M F

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S - Si O - Mo

Figure 4.21 Character plot of a Cu atmosphere in irradiated steel (the atmosphere is defined by the localised increases in Cu, Ni and Mn) [64]

was attributed to a mechanism similar to that of temper embrittlement, related to irradiation-enhanced diffusion to and weakening of ferrite–carbide interfaces. To determine the effect of P, the US NRC Regulatory Guide Rev. 1 included a “P term” in the formula (Equation 4.38) used to determine the embrittlement caused by irradiation: r 5 fluence : (4.39) TT D Œ40 C 1000.%Cu  0:008/ C 5000.%P  0:008/

9 1019 The effect of P was greatest when the Cu content was low (< 0.1%). Increasing the P content from 0.003 to 0.025 caused TT to increase by 75 °C when the Cu content was 0.015. When the Cu content was raised to 0.035, the corresponding increase was 16 °C [53]. This explains why an analysis of databanks (predominantly containing data on low P–low Cu and high P–high Cu steels) failed to show the effect of P. Jones and Buswell [66] found that the irradiation embrittlement of RPV steels increased most rapidly with the phosphorus content when the copper content was < 0.03 wt%. The sensitivity of changes in the mechanical properties of the steel to

66

4 Barriers Preventing the Release of Fission Products

a)

b)

c)

d)

Figure 4.22 Diagrams of the classification of Cu atmospheres and clusters into precipitates: a atmosphere, b cluster, c precipitate, and d coarsening [65]

the P content reduced as the Cu content was raised. At Cu levels typical of modern PWR RPV steels (Cu < 0:1 wt%), MTR (material testing reactor) and surveillance data confirmed a significant effect over the range 0.002–0.03 wt% P. The average increase in transition temperature was 20–30 °C for each extra 0.01 wt% P at a Cu content of about 0.05 wt% and a neutron fluence of 0.5–7  1019 n/cm2 . The lower value was for the lower fluence, and vice versa. SANS and APFIM examinations [62,67] showed that phosphorus formed several types of clusters depending on the chemical composition of the steel. This result was found in pressure vessel steels and model alloys, as mentioned above. Phosphorus clusters were often enriched in Ni and occasionally in C. In general commercial RPV steels, these features were present at a much lower number density than the Cu clusters. In cases where the Cu level was very low, or if the P content was increased, the number density of these P clusters became significant. Beaven et al. [67] detected P clusters in irradiated A533B steel, which has 0.002 wt% Cu. The number density of these clusters increased with increasing P content, while its average radius remained nearly constant at 0.5–1 nm. In contrast, when the Cu content was

4.3 Third Barrier: Integrity of the Primary Circuit

67

raised to 0.3 wt%, they found that the clusters were Cu-rich clusters, and that P addition led to a refinement of the defect microstructure, possibly by influencing the kinetics of microstructural development via interactions with vacancies. The observation of P clusters in irradiated steels led to the conclusion that the deleterious effect of P was caused by precipitation hardening and the depletion of P in the solid solution. The effect of P on irradiation embrittlement was also attributed to segregation leading to temper embrittlement. However, there is direct physical evidence of radiation-induced P segregation at grain boundaries. Effect of Nickel. The contribution of Ni content to irradiation hardening and embrittlement was not realised until recently. The Ni effect was noticed in the case of RPV steel plates, forging, as well as weldments. It was shown that this effect is important for steels with Ni contents of > 0.4 wt% [59]. Materials with high Cu and Ni contents will have high irradiation sensitivities, while those with low Cu and Ni contents will be practically insensitive to irradiation [53]. Most of the published data show that the Ni effect is very dependent on the Cu content, and the Ni content does not appear to have any influence when the Cu content is low (< 0.1 wt%). This suggested the existence of a synergistic mechanism resulting from interactions between Cu and Ni. Odette and Lucas [68] investigated the effect of Ni content on the irradiation hardening responses of five sets of steels (30 alloys) with Ni contents of 0–1.7% and with various Cu (0.01–0.4 wt%) and Mn (0.01–1.7 wt%) contents, heat treatments and microstructures. The results showed that the Cu-bearing commercial steels (0.2–0.4 wt% Cu) exhibited increased hardening with increased Ni content and neutron fluence. For Cu contents of less than

140 120

ΔTT (°C)

100 80 60 40 En > 0.5 MeV Tirr= 270 °C

20

Φ=1x10

0.0

0.4

0.8

1.2

1.6

20

2

n.cm

2.0

Ni (wt%) Figure 4.23 Transition temperature shifts for RPV steels with various Ni contents (and 0.05 wt% Cu and 0.01 wt% P) due to irradiation (˚  1  1020 n cm2 )

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4 Barriers Preventing the Release of Fission Products

0.1 wt%, the Ni effect was somewhat lower than it was for higher Cu contents, and was manifested only at high fluences. The Ni effect may occur through the effect of Ni on the irradiation-induced microvoids. Ni may segregate to these microvoids and stabilise them, and/or it may control their formation through its influence on the microstructure. On the other hand, the synergistic effect was assumed to be a result of the participation of Ni in Cu-rich clusters formed during irradiation (Figure 4.23). Microstructure examinations [61] showed that the enhanced hardening observed with increasing Ni content in RPV steel was accompanied by a reduction in the mean size of Cu-rich clusters and an increase in cluster density. Cu-rich atmospheres and clusters induced by irradiation exhibit significant Ni enrichment. The results [69] of calculations of the Ni and Mn concentrations in the Cu-rich phases suggested that the combined concentration of Mn and Ni in the Cu-rich phases in irradiated RPV steels was 30% or more. A study [69] of FeCuNi alloys showed that an irradiated ternary alloy contained Cu,Ni-rich clusters. The Ni/Cu ratio was 1:3, as compared to 1:50 for the particles found before irradiation. Nickel was also found to be associated with P-rich clusters. Nickel affects both the size (decreasing it) and the distribution (makes it more homogeneous) of the Cu-rich clusters (or precipitates). It is also seen in the com-

Figure 4.24 Distribution of radiation defects in clusters (a, c) and energy transfer to the lattice in an idealised metallic alloy (b, d) for (a, b) 15 keV and (c, d) 150 keV primary knock-on atoms

4.3 Third Barrier: Integrity of the Primary Circuit

69

positions of these clusters as well as those of the P-rich ones. Because these clusters are assumed to act as obstacles to dislocation motion, resulting in hardening and embrittlement, Ni can contribute to irradiation hardening and embrittlement by influencing and participating in these clusters. Studies [61–64] of RPV steels in surveillance programmes have confirmed that the metallic clusters of Ni with Mn and Si form due to irradiation. The formation of solute clusters during the irradiation of RPV steels resulted in the depletion of Cu and P in the matrix, but an investigation showed that Ni retards this depletion. 4.3.1.3 Computer Simulations In order to simulate ion stopping and ion ranges in RPV steels it is possible use the TRIM (Transport of Ions in Matter) software. A collision model is considered linear if, after an ion has collided with an atom, the atom only goes on to collide with stationary atoms in the target, and never with atoms that have already been set in motion by a previous event (Figure 4.24). The simulation results for an idealised steel alloy (with a composition of 94% iron, 4% chrome and 2% nickel) have been published [70].

4.3.2 Methods One of the main tasks of nuclear-reactor safety research is assessing the integrity of the reactor pressure vessel (RPV). The properties of RPV steels and the influences of thermal and neutron treatments on them are routinely investigated by macroscopic methods such as Charpy V-notch and tensile tests. It turns out that the embrittlement of steel is a very complex process that depends on many factors (thermal and radiation treatment, chemical compositions, conditions during preparation, ageing, etc.). A number of semi-empirical laws based on macroscopic data have been established, but unfortunately these laws are never completely consistent with all data and do not yield the required accuracy. Therefore, many additional test methods are needed to unravel the complex microscopic mechanisms responsible for RPV steel embrittlement. Our study is based on experimental data obtained when positron annihilation spectroscopy (PAS) and Mössbauer spectroscopy (MS) were applied to different RPV steel specimens, which are supported by results from transmission electron microscopy (TEM) and appropriate computer simulations. 4.3.2.1 Generalities A few experimental techniques are capable of visualising microstructure, such as transmission electron microscopy (TEM), high-resolution TEM, field-ion microscopy (FIM) and atom probe FIM, which give information about the local arrangement at a particular point in the specimen. However, there is no method that

70

4 Barriers Preventing the Release of Fission Products 2

10

101

Defect size (mm)

Defect concentration (%)

STM/AFM

0

10

-1

10

OM

-2

10

-3

10

X-ray nS TEM scattering

-4

10

-5

10

10-6

PAS

-7

10

-7

-6

-5

-4

-3

-2

-1

0

1

10 10 10 10 10 10 10 10 10

Depth (mm)

STM/AFM

1

10

OM

0

TEM

10

X-ray scattering

10-1

nS

-2

10

-3

10

PAS

-4

10

-7

-6

-5

-4

-3

-2

-1

0

1

10 10 10 10 10 10 10 10 10

Depth (mm)

Figure 4.25 General overview of the applicability ranges of some spectroscopic techniques [71]. OM, optical microscopy; nS, neutron scattering; STM/AFM, scanning tunnelling microscopy/atom probe ion microscopy

can be used to fully characterise the structure of the material, which is why it is necessary to combine several techniques in materials science [71]. In particular, the most powerful method for studing lattice defects, due to the high sensitivity of positrons to open volume defects such as vacancies, vacancy clusters, voids, dislocations, grain boundaries, etc., is positron annihilation spectroscopy (PAS). A diagram illustrating the applicability of PAS and other techniques as a function of defect size and density versus depth in material is shown in Figure 4.25. Thus, PAS represents a non-local experimental technique that is sensitive to microstructural defects at the atomic scale. A well-established theory of positron annihilation phenomena is currently available. Especially for metallic materials, it is possible to perform ab initio calculations of positron parameters for various defects and atomic arrangements [72, 73].

4.3.2.2 Positron Annihilation The positron – the antiparticle of the electron – was first predicted by Dirac [74]. Initial experimental indications of an unknown particle were found in cloud-chamber photographs of cosmic rays [75]. This particle was identified later as the positron, which was thus the first antiparticle to be discovered. The annihilation of positrons with electrons in matter was first studied in the 1940s. It was discovered early on that the conversation of energy and momentum that occurred during the annihilation process could be utilised to study the properties of solids. A positron bound to an electron – which is the lightest known atom – is analogous to a hydrogen atom, except that the proton is replaced by a positron. This e C  e  state is called positronium (Ps). It was predicted by Mohorovicic [76] and discovered by Deutsch [77].

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Early experiments with positrons were dedicated to the study of electronic structure, for example Fermi surfaces in metals and alloys [78,79]. Various experimental positron annihilation techniques based upon the equipment used for nuclear spectroscopy underwent intense development in the two decades following the end of the Second World War. In addition to angular correlation of the annihilation of  quanta, Doppler broadening of the annihilation line and positron lifetime spectroscopy were established as independent methods. By the end of the 1960s, it was realised that the annihilation parameters are sensitive to lattice imperfections. It was discovered that positrons can be trapped in crystal defects; i.e., the wavefunction of the positron is localised at the defect site until annihilation. This behaviour of positrons was clearly demonstrated by several authors (e.g., MacKenzie et al. [80] for thermal vacancies in metals, Brandt et al. [81] in ionic crystals, and Dekhtyar et al. [82] after the plastic deformation of semiconductors). The investigation of crystal defects has since become the main focus of positron annihilation studies. When a positron is emitted from a source and then penetrates into a solid, it quickly loses kinetic energy until it reaches the thermal level (Figure 4.26). This thermalised positron moves around in the solid by diffusion and finally annihilates with an electron. The trapping of positrons in defects is based on the formation of an attractive potential at open-volume defects, such as vacancies, vacancy agglomerates, and dislocations. The main reason for this potential is the lack of a repulsive positively charged nucleus in such a defect. The sensitivity range for vacancy detection in metals starts at about one vacancy per 107 atoms. This extremely high sensitivity is caused by the fact that the positron diffuses about 100 nm through the lattice and

Figure 4.26 Schematic representation of the path of a positron in a solid [83]

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4 Barriers Preventing the Release of Fission Products

probes a high number of atoms until annihilation. When the positron is trapped in an open-volume defect, the annihilation parameters are changed in a characteristic way. The positron lifetime increases in an open-volume defect due to its low electron density. Momentum conservation during 2 annihilation leads to a small angular spread in the collinear  quanta or a Doppler shift of the annihilation energy. Properties such as the density and the momentum distribution of the electrons participating in the annihilation can be determined in a positron experiment. Analysing the annihilation radiation thus gives the possibility of defect detection. The clustering of vacancies, a typical reaction to defects, may be observed as an increase in the defect-related lifetime due to the resulting decrease in the electron density. Positrons diffusing through matter can be captured in special trapping sites. As shown in early studies, these trapping centres are crystal imperfections, such as vacancies and dislocations. The wavefunction of a positron captured in such a defect is localised until it annihilates with an electron of its immediate surroundings into  -rays. Since the local electron density and the electron momentum distribution are modified with respect to the defect-free crystal, the annihilation radiation can be utilised to obtain information on the localisation site. The different positron techniques are based on analysing the annihilation radiation. The principles of the basic positron methods are illustrated in Figure 4.27 [84].

Figure 4.27 a Scheme for positron experiments, and b illustration of positron annihilation -rays from different environments [84]

Annihilation Phenomena When a positron is emitted from a source, and penetrates into a solid, it quickly loses its kinetic energy to thermal energy. The thermalised positron moves around in the solid by diffusion and finally annihilates with one of the electrons in its surroundings. All of the energy from the electron–positron annihilation is converted into two annihilation  -rays, which can be detected. The annihilation rate of a positron is determined by the local electron density in the locale of the positron. Thus, positrons

4.3 Third Barrier: Integrity of the Primary Circuit

73

can be used to probe the local electronic structure of a solid. Moreover, positrons can be trapped by defects in a solid due to the reduced repulsion between the positrons and the positive ions at these defects. Therefore, positron annihilation spectroscopy (PAS) also provides valuable information about the electronic structures of defects. In addition, it is possible to identify defects in solids as well as to determine their concentration using PAS. The interaction of a positron with metallic materials will be explained in depth in the following subsections. Positron Injection and Thermalisation The kinetic energy E of the emitted positron cannot be greater than the so-called end-point energy Emax D Q2mc 2 . The energy distribution of the emitted positrons (see Figure 4.28 for example) can be approximated by the formula [85] q    2 dN D D E E C 2mc 2 E C mc 2 Emax  E ; (4.40) dE where: m is the rest mass of the positron; D is a normalisation coefficient. The positrons emitted by radioactive nuclei typically have kinetic energies on the order of  102 keV. Energetic positrons in condensed media rapidly lose their energies. In a condensed medium, positrons slow down to thermal energies E  kB T , where kB is the Boltzmann constant. At the highest positron energies (E > 102 eV), the most important processes are elastic ion core scattering and inelastic scattering off both core and valence electrons [86,87]. In the case of metals, excitations of conduction electrons dominate at lower energies (0:1 eV < E < 102 eV) [88]. Finally, -3

4x10

-3

dE/dN

3x10

-3

2x10

-3

1x10

0

0

100

200

300

400

E [keV] Figure 4.28 Energy distribution of positrons emitted by a 22 Na source

500

600

74

4 Barriers Preventing the Release of Fission Products

when the positron energy has degraded to a fraction below  0.1 eV, scattering off phonons prevails [89]. A simple model of positron thermalisation in metals is presented in [90]. This approach is used to estimate positron thermalisation times for the metals considered in this work. Positron energy loss per unit distance in the medium may be expressed by the stopping power: dE : (4.41) dx The stopping power is usually calculated in terms of a “continuous slowing-down approximation”, according to which energy losses occurs almost continuously in small portions through collisions with electrons in the medium. Hence, this approximation ignores the link between the energy changes and momentum (directional) changes induced by collisions. The slowing-down time of a positron from an initial energy Ei to a final energy Ef is S D

r t D

m 2

ZEf Ei

dE p : ES

(4.42)

The stopping power S for positrons differs from those for heavy particles or electrons due to the fact that positrons are light but distinguishable from electrons. The stopping power for positrons reaches its maximum at the energy Em . Positron stopping times ts in the highest energy region (E > Em  102 eV) can be estimated very accurately with the formula [90] ts Œps Š

17:2 E 1:2 ŒMeV ; d Œg=cm3 i

(4.43)

where d is the density of the medium. The end-point energy of emitted positrons may be considered to be Ei in order to estimate the maximum ts . Since ˇ C sources of interest emit positrons with Ei > 0:5 MeV, it is clear that ts  1 ps in all metals. Thus, ts values are very short compared to the lifetime B of free positrons. In metals, the lifetime B lies in the interval 100 ps < B < 200 ps. The stopping times ts for the materials of interest in this work are shown in Table 4.14, where the end-point energy for 22 Na is used. Further energy losses from

Table 4.14 Positron thermalisation times [90] Metal Cu Fe Al Ni V Cr a b

d (g/cm3 /

EF (eV)

Ec (eV)

ts (ps)a

tR (ps)

tph (ps)b

tt (ps)b

8.96 7.86 2.70 8.90 6.10 7.19

14.96 11.69 11.15 15.46 17.75 20.85

0.12 0.08 0.15 0.13 0.21 0.26

0.93 1.06 3.08 0.94 1.36 1.16

2.86 5.02 1.56 2.52 1.11 0.85

8.92 9.10 5.76 8.60 6.02 5.51

12.71 15.18 10.40 12.05 8.49 7.52

The values of ts relate to a 22 Na ˇ C source; i.e., end-point energy Emax D 0:545 MeV The thermalisation times tph and tt are for room temperature T D 20 °C

4.3 Third Barrier: Integrity of the Primary Circuit

75

positrons of energy E < 102 eV are caused mainly by excitations of conduction electrons. The stopping power SR for excitations of conduction electrons was derived by Ritchie [88] for positrons in a conducting electron gas with Fermi energy EF : r 5 2 m 2 E 2 : (4.44) SR D 105 „ m EF For a positron slowing-down time of tR to an energy Ef  Em , Equation 4.44 yields tR D

105 „EF : 8 Ef2

(4.45)

Finally, when the positron energy decreases to a fraction of an eV, scattering off longitudinal acoustic phonons dominates [89,91]. The formula for the positron stopping power for phonon excitations Sph is given in [90]. The notion of Sph is based on a continuum representation of the material. The local atomic structure is ignored. The deformation potential energy W , which is related to the energy needed to deform the medium locally, is introduced. This quantity is not well defined and is model dependent. The phonon stopping power of a medium of density d Sph D

2 m3 W 2 E;  d „4

(4.46)

is proportional to W 2 , which makes Sph sensitive to the choice of W . A relation appears to exist between the deformation potential W and the Fermi energy EF : W D bEF ;

(4.47)

Depending on the model, the constant b can take values of between 2=5 and 2=3. In the following calculations, b was set to 0.575 [90]. The dependencies of SR and Sph on positron energy are shown in Figure 4.29 for Cu and Fe. There is clearly some critical energy Ec . Phonon scattering dominates for E < Ec , while the most important process for E > Ec appears to be excitations of conduction electrons. The critical energy Ec can be obtained from the equation Sph .Ec / D SR .Ec / :

(4.48)

Using Equations 4.44 and 4.46 gives 5

Ec D

105b 2 m 2 EF3 p 2 d „3

! 23 :

(4.49)

The values of Ec for some metals are shown in Table 4.14. The thermalisation time tR in the energy region Ec  E < Em where excitations of conduction electrons play a dominant role may be calculated from Equation 4.45 with the substitution Ef D Ec .

76

4 Barriers Preventing the Release of Fission Products

Figure 4.29 Dependence of stopping power on positron energy for a Fe and b Cu [90]

The integration of Equation 4.41 with Equation 4.45 over the range 32 kB T  E  Ec yields the phonon scattering thermalisation time tph : ! s Ec tph D 4tR 1 : (4.50) 3 k T 2 B Increasing the temperature results in a slow decrease in tph . The temperature dependence of tph for each of the metals considered in this work (i.e., Cu, Al, Fe, Ni and Cr) is shown in Figure 4.30.

60 Fe Cu Ni Al Cr

50

t ph (ps)

40 30 20 10 0

100

200

300

400 T (K)

500

600

700

Figure 4.30 Temperature dependence of the phonon thermalisation time tph for some metals [90]

4.3 Third Barrier: Integrity of the Primary Circuit

77

Thermalisation times tR and tph are collected in Table 4.14. Values of tph correspond to room temperature (T D 20 °C). The total thermalization time tt D ts C tR C tph ;

(4.51)

is shown in the last column of Table 4.14. Thermalisation times for the slowingdown process of positrons with E < Em were calculated in [89] by solving the Boltzmann equation for the positron momentum distribution in a homogeneous medium. Positron scattering off conduction electrons and phonons were included. It was found that, for E < 3kB T , the positron energy E closely approximates an exponential function as it approaches the thermal energy 32 kB T . In the case of Al, the times needed to reach mean energies of 1:01 23 kB T and 1:001 23 kB T are 5.65 ps and 8.38 ps, respectively, at room temperature. Note that these results are in surprisingly good agreement with the simple model used here, which for Al gives (Table 4.14) tR C tph D 7:32 ps. One can immediately conclude that thermalisation times are very short compared to positron bulk lifetimes B . The fact that positrons reach thermal energies very quickly is important for the application of the positron method. Clearly only thermalised positrons annihilate. The momentum of positrons is thus very small compared to the momentum of the electrons with which they annihilate. It is evident from Table 4.14 that positron scattering off phonons occupies more than 50% of the thermalisation time. Therefore, the positron spends most of the slowing-down process with an energy slightly above the thermal energy. This fact is important for the possible trapping of non-thermalised positrons.

Positron Diffusion The thermalised positron is further scattered by phonons and diffuses until it annihilates with an electron (or is eventually trapped). During its lifetime (  1010 s), it can diffuse over a volume of about 1000 Å [83]. The diffusion process of a positron e C can by characterised by a diffusivity D C and a mobility C , which are related by the Einstein equation D C D kB TC ;

(4.52)

where kB is the Boltzmann constant and T is the absolute temperature. The positron diffusivity is of great importance – it determines how fast the positrons reach the traps (i.e., sites where they can form bound states). The diffusion of positrons in solid is limited by the scattering of positrons by phonons [92]. Under the simplest assumptions (an isotropic phonon spectrum with a linear dispersion curve, elastic scattering), this gives the following expression for the mean free path of the positrons: lC D

„4 c12 %0 ; m2C "2d kB T

(4.53)

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4 Barriers Preventing the Release of Fission Products

where %0 and c1 are the density and the longitudinal sound velocity of the material; "d is the deformation potential constant for positrons; mC is the effective mass of a positron; „ is the Planck constant. The deformation potential constant is defined as follows. A uniform dilatation changes the energy of the free positron ground state "c by ı" D "d :

(4.54)

"d may be obtained by calculating "c as a function of the lattice parameter. From Equations 4.51 and 4.52, it follows that 3

D

C

D

1

2 2  2 %0 c12 „4 5

1

2 2 3mC "d .kB T / 2

:

(4.55)

Equations 4.52–4.54 cease to hold below a critical temperature of [92] T0 D

12mC c12 : kB

(4.56)

Below T0 , the phonon–positron scattering is no longer elastic and the effectiveness of phonons in shortening the positron mean free path is strongly reduced. In pure materials, this should lead to a rapid increase in D C with decreasing temperature (see Figure 4.31). In pure metals at low temperature, the scattering of positrons by conducting electrons can occur, which can moderate the temperature dependence of the diffusivity. This effect can be estimated from a treatment of the diffusivity of positive muons [93]. The positive particles with effective mass mC interact with the conducting electrons through a screened Coulomb potential with Thomas–Fermi scattering. The result for the diffusivity of these particles takes the form DC D h

3 2 .3/ C

2 3

i

"F h  2 kB T me



me mC

2 :

(4.57)

In Equation 4.57, me is the electron mass, "F is the Fermi energy of the conducting electrons, and .3/ D 1:20, a value of Riemann’s zeta function. The quantity h=me D 7:274  104 m2 s1 is the quantum of circulation. For the ratio mC =me D 1:5 and "F D 10 eV, we get  D C D 2T 1 K m2 s1 : (4.58) The temperature dependence of DC for Al and Mo approximately follows the T 1=2 law predicted by Equation 4.55 over a wide temperature range. The deviation in

4.3 Third Barrier: Integrity of the Primary Circuit

79

1

T

-1

10

-1 /2

T

-9

10

10

-5

10

-4

10

-3

-2

10

-1

10

(-H

e D

-7

10

ν

ph o "a sel no di f-l nab oc as at al si ic iza ste ho ti d pp on in g"

+

/k

b

-5

10

T)

el as sc tic at ph te on rin o g n

+

2

D [m /s]

in el a sc stic at p te ho rin n g on

+

e -3

10

sc at te r

in g

-1

10

0

10

10

1

T / Tm

Figure 4.31 Temperature dependence of the positron diffusivity D C in a metal, and different limiting mechanisms [94]

the direction of a slightly stronger temperature dependence for temperatures T  T0 is caused by the low effectiveness of elastic e C –phonon collision and, at high temperatures, by the curvature of the phonon dispersion curves. The last fact was not taken into account when deriving Equation 4.55. Typical room-temperature values of D C , which are in the range 1–2  104 m2 s1 , are in agreement with Equation 4.55 if we take into account measured elastic constants, the ratio mC =me ( 1.5), and the deformation-potential constant "d . From a comparison of Equations 4.55 and 4.58, it follows that the phonon scattering is higher than the electron scattering at all temperatures, with the possible exception of very low temperatures, where T =T0  1. However, at these temperatures, l C is limited by residual impurities, even in the purest metals available. If we use Equation 4.53, the value D C .293 K/ D 2  104 m2 s1 and mC D 1:5me , we obtain the room temperature value of the mean free path of positrons l C .293 K/ D 6:9 nm, and l C .30 K/ D 69 nm. These values may be compared with the mean diffusion length corresponding to the positron lifetime :  1=2 LD D 2D C  :

(4.59)

For D C D 2  104 m2 s1 and  D 2  1010 s, we obtain LD D 0:28 µm. Thus, LD l C over the range where Equations 4.53–4.56 are applicable, and we see that the picture for the motion of the positrons is appropriate [94]. A particle with effective mass m , velocity v and kinetic energy " D .m v/=2 loses energy by the emission of acoustic phonons at the rate [95] "2 m4 v 3 dE 8 c12 D d 4 D .kB T /1=2 "3=2 : dt %0 „ 3 DC

(4.60)

80

4 Barriers Preventing the Release of Fission Products

In Equation 4.60, the deformation potential constant has been eliminated using Equation 4.55. By integrating Equation 4.55 between "d D 3kB T =2 and "2  "1 , we obtain the following relation for the thermalisation time associated with the emission of thermal phonons:  1=2 C 3 D tem D : (4.61) 8 c12 Using the D C data for Al [96] gives tem .20 K/ D 37 ps and tem .500 K/ D 5 ps. This estimate disregards both the excitation of electron–hole pairs and the absorption of phonons. The latter phenomenon is stronger at higher temperatures, leads to gains in the kinetic energy and lengthens the thermalisation period. So far we have considered weak positron–phonon interactions, which can be handled by a scattering mechanism and contributions to the effective positron mass mC . Positrons in metals do not give rise to long-range electric fields because the charge on the positron is screened by conducting electrons. Hence, an optical polaron is not formed; instead, we can expect the formation of an “acoustic polaron”. The localisation of electron wavefunctions in the interstices leads to an increase in positron charge density here and repels the ion cores away from the positrons. The localisation of wavefunctions leads to an increase of the kinetic energy of the positron, and the increase in the positron–ion separation to a decrease in the potential energy of the system. In addition to this, lattice deformation also yields an increase in energy. The following situations may arise [94]: • The acoustic polarons are stable – the formation of strongly localised, positively charged particles surrounded by “deformation clouds” leads to a lowering of the total energy of the system. They can be considered quasiparticles with effective mass mC > me . So far, it is not clear whether such states can prevail in any metal, although analogous states for positive ions and muons are always stable owing to their greater masses. • The acoustic polarons are metastable or unstable. In the case of metastable polarons, the acoustic polaron states may be partially occupied at higher temperatures. Therefore, positrons spend on average a temperature-dependent fraction f of their life in the metastable state. The interesting case is when the decay rate of the metastable state is smaller than or comparable to the positron annihilation rate. In both the stable and the metastable cases, the higher-temperature diffusion of positrons proceeds by the “adiabatic mechanism”, and the following equation approximately holds for the hopping frequency:   HC v D vD exp  ; (4.62) kB T where H C is a small activation energy (H C > 0) and vD is the Debye frequency. For the positron diffusivity, the following equation will then hold:   HC C C 2 D D .1  f /D0 C f vD d exp  ; (4.63) kB T

4.3 Third Barrier: Integrity of the Primary Circuit

81

where d corresponds approximately to the distance between interstitials and D0C is the diffusivity given by Equation 4.55. The result of Equation 4.63 will be dominated by the first term in all cases when f is not very close to unity (vD d 2 is not much larger than 107 m2 s1 /. The temperature variation of the positron diffusivity according to Equation 4.55 is shown qualitatively in Figure 4.31.

Positron States in Solids Ab initio determination of positron states in solids is possible on the basis of a generalisation of the density-functional theory [97, 98]. In the two-component densityfunctional theory, the ground-state energy of a system of electrons and positrons in an external potential Vext is written as a function of the electron (n / and positron (nC ) densities: EŒn ; nC D F Œn C F ŒnC

Z C Œn .r/  nC .r/ Vext .r/dr “ n .r/nC .r 0 /  drdr 0 C Ecep Œn ; nC ; jr  r 0 j

(4.64) (4.65) (4.66)

where F Œn denotes the following one-component functional for electrons or positrons: “ 1 n.r/n.r 0 / F Œn D T Œn C drdr 0 C Ec Œn : (4.67) 2 jr  r 0 j T Œn is the kinetic energy of non-interacting electrons or positrons and Ec Œn is ep the exchange-correlation energy between indistinguishable particles. Ec Œn ; nC

in Equations 4.64–4.66 is the electron–positron correlation-energy functional. The ground-state electron and positron densities that minimise EŒn ; nC can be calculated by a generalised Kohn–Sham method [99], which requires the solution of the following set of one-particle Schrödinger equations for electrons and positrons:

 ep 1 ıEc Œn

ıEc Œn ; nC

 r 2 i .r/ C  ˚.r/ C i .r/ D "i i .r/ 2 ın .r/ ın .r/ (4.68)

 ep 1 ıEc Œn

ıEc Œn ; nC

C  r 2 iC .r/ C  ˚.r/ C iC .r/ D "C i i .r/ ; 2 ınC .r/ ınC .r/ (4.69) where Z ˚.r/ D

n .r 0 / C nC .r 0 / C n0 .r 0 / 0 dr jr  r 0 j

(4.70)

82

4 Barriers Preventing the Release of Fission Products

is the total Coulomb potential and n0 .r/ denotes the (positive) charge density for an external potential Vext . The electron and positron densities are calculated by summing over the occupied states n .r/ D

X

ji .r/j2 ;

nC .r/ D

i  EF

NC X

jiC .r/j2 ;

(4.71)

i

where EF is the Fermi energy and NC is the number of positrons. There is not usually more than one positron in the sample at a given time; i.e., the number of positrons NC D 1 and nC .r/ D j0C .r/j2 :

(4.72)

In order to solve Equations 4.68 and 4.69, it is necessary to know the exchangecorrelation energy Ec Œn and the electron–positron correlation energy functional ep Ec Œn ; nC . The local density approximation (LDA) is often used. The exchangecorrelation energy is approximated in LDA as Z Ec Œn D n.r/"c .n.r// dr ; (4.73) where "c .n/ is the exchange-correlation energy per particle in a homogeneous electron gas, and is known from Monte Carlo simulations [100]. The functional derivative of Ec Œn is called the exchange-correlation potential  @ n 2c .n/ ıEc Œn

D : (4.74) c .n/ D ın.r/ @n The interpolation formula that gives the electron–positron correlation energy functional was found by Boro´nski and Nieminen [98]. The positron annihilation rate  is proportional to the overlap between the positron and electron densities. In the LDA approximation [72], Z  D  r02 c n .r/nC .r/g.0I n ; nC /dr ; (4.75) where g.0I n ; nC / is the electron–positron pair correlation function evaluated at the positron in a homogeneous two-component plasma with positron density nC and electron density n . A practical interpolation formula for g.0I n ; nC / was presented in [98]. Furthermore, r0 is the classical electron radius and c is the speed of light. Trapping Model The potential sensed by the positron at open-volume defects (e.g., monovacancies or vacancy clusters) is lowered because the positive ion cores reduce the repulsion. The transition from the delocalised state to the localised one is called positron trapping.

4.3 Third Barrier: Integrity of the Primary Circuit

83

The energy difference between the localised and the delocalised state of the positron (the positron binding energy for the defect) is transferred to the host solid. The transport of the positron from the point of thermalisation to the vicinity of a trap and the transition from the delocalised to the trapped state is necessary for positron trapping in defects. Clearly, two limit cases can occur: • The diffusion-limited regime, where trapping is essentially controlled by transport factors. The transport factors (the diffusion of the positron to the neighbourhood of a defect) are likely to be dominant when the rate of transition from a free to a trapped state for a positron already present in the vicinity of a trap is so high that the stochastic positron density is depleted around the defect. A typical example is positron trapping at grain boundaries or in large precipitates [101]. • The transition-limited regime or the propagation regime, when positron motion can be described as Bloch wave propagation. Positron trapping in monovacancies is an example of the transition-limited regime [101]. In practical situations any intermediate case is possible. In the case of the transitionlimited regime, the link between positron states in the specimen and the experimental positron lifetime spectrum is provided by the simple trapping model (STM) [103]. Let m.t/ denote the probability that positron will be present in the specimen at time t. In the case of an ideal crystal (i.e., if no defect is present in the specimen), positrons will be delocalised in the material. The time when positron thermalisation is accomplished is chosen as t D 0, so m.t D 0/ D 1. The probability m.t/ decreases exponentially with time: m.t/ D eB t ;

(4.76)

where B is the annihilation rate of delocalised positrons. If the specimen contains N types of defects which are capable of capturing a positron, then m.t/ D

N X

mi .t/ ;

(4.77)

i D0

where m0 .t/ and mi .t/ (i  1) denote the probability that the positron is free or is trapped by the i -th kind of defect, respectively, at time t. The kinetic equations for the trapping process may be written as 0 1 N N X X dmi .t/ D  @i C Kij A mi .t/ C Kij mj .t/ : (4.78) dt j ¤i

j ¤i

Above, i (i  1) denotes the annihilation rate of a positron trapped by the i -th type of defect. The annihilation rate of a delocalised positron is B 0 :

(4.79)

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4 Barriers Preventing the Release of Fission Products

Kij is the rate of positron transition from the i -th state to the j -th state, where a delocalised positron is denoted by i D 0, and a positron trapped by the k-th defect by i D k. It should be pointed out that restricting ourselves only to the transitionlimited regime implies that the transition rates have no spatial dependence. The binding energy of a positron trapped by a defect is usually large enough (a few eV) that detrapping (i.e., escaping from the trap) is negligible. This means that Kij D 0 for all i  1, j  0. Equations 4.78 may be rewritten as 0 1 N X dm0 .t/ D  @ B C K0j A m0 .t/ (4.80) dt j ¤i

dmj .t/ D j mj .t/ C K0j m0 .t/ ; dt

j D 1; 2; : : : ; N :

(4.81)

Furthermore, we assume that there is no trapping of non-thermalised positrons; i.e., m0 .t D 0/ D 1 ;

mj .t D 0/ D 0 ;

j D 1; 2; : : : ; N :

(4.82)

The solution of Equations 4.81 with boundary conditions (4.82) gives the following for the probability m.t/: 2 3 N N X X K0j K0j 5 ef t C m.t/ D 41  ej t ; (4.83) B  i C " B  i C " j ¤0

j ¤0

P where " D N j ¤ 0 K0j and f D B C " is the effective annihilation rate of free positrons. The measured quantity in positron lifetime measurements is the time when the positron annihilates. t D 0 corresponds to positron emission. This means that the shape of the positron lifetime spectrum S is S.t/ D 

dm.t/ : dt

(4.84)

The real positron lifetime spectrum is the convolution of S with the resolution function of the spectrometer. Moreover, some background arises from random coincidences, and the contribution from positrons that annihilated in the source must also be added. From Equations 4.83 and 4.84, it is clear that the shape of the positron lifetime spectrum predicted by STM is the sum of two exponential components: S.t/ D j I0 ej t C

N X

j Ij 0 ej t ;

(4.85)

j D1

where the relative intensities of the defect components are Ij D

K0j ; B  j C "

j D 1; 2; : : : ; N :

(4.86)

4.3 Third Barrier: Integrity of the Primary Circuit

85

PN

The first component I0 D 1  j ¤ 0 Ij relates to free (delocalised) positrons. A useful test of the self-consistency of the STM is the relation N X

j Ij D B ;

(4.87)

j D1

where j Ij are measured in a material with defects, while B is determined experimentally or theoretically for a defect-free material. By self-consistency we mean that the assumptions which lead to Equations 4.80–4.82 (i.e., transition-limited regime, no pre-thermal trapping and no detrapping) are fulfilled. Inequality in the relation (4.87) may also suggest that there are more than N types of defect in the specimen. The trapping rates K0j are directly connected to the concentration cj of the j -th type of defect: K0j D j cj :

(4.88)

The quantity j is called the specific trapping rate (or trapping coefficient), and it expresses the positron trapping rate for a unit concentration of the j -th type of defect. The specific trapping rate depends on the electronic and atomic structure of the defect, so it is a characteristic quantity for a given type of defect. However, in general, the specific trapping rate may also depend on the temperature of the material, because it determines the energy distribution of the thermalised positrons. Thus, positron lifetime measurement is capable of providing information about the local electronic structure of the defects. Moreover, it is possible to identify the defects present in the specimen and to calculate the concentrations of different types of defects. Positron diffusion to the defects does not limit the trapping rate in the transitionlimited regime. Therefore, the specific positron trapping rate is simply the transition rate between the delocalised and the localised state, and it is given by Fermi’s golden rule [104]. In the case of the diffusion-limited regime, the positron diffusion equation (4.78) must be solved. However, the shape of the positron lifetime spectrum obtained is a sum of exponential components, even when a single type of defect is present in the material. It was shown by Brandt and Paulin [105] that for a material with just one kind of trap, the exact solution may be approximated formally by the same equations as the CTM ones (4.70 and 4.71). In that case, the trapping rate K does not have the form of (4.88) but instead also depends on the dimension and shape of a defect and on the positron diffusion constant DC . The trapping rates for various shapes of traps (precipitates), cylindrical pores (dislocations) and spherical voids are described in [106]. It must be pointed out that positron trapping in precipitates is possible only when the positron ground state energy in a precipitate is lower than that in matrix. Nevertheless, it was shown by Dupasquier [101] that the simple approximation used in [106] systematically underestimates the intensity of the defect component.

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4 Barriers Preventing the Release of Fission Products

Interaction of Positrons with Defects Monovacancies The experimentally and theoretically determined lifetimes of positrons trapped in monovacancies lie in the interval 150–300 ps for metals. The positron lifetimes in monovacancies calculated by LDA [72] and the experimental ones are shown in Table 4.15 for the metals relevant to the present work. The positron binding energy EB for monovacancies is typically a few eV in transition metals, and it is dissipated by electron–hole excitations [104]. Thus, detrapping from monovacancies does not occur in metals. The computed EB values for the metals of interest found in the literature are collected in Table 4.15. It was shown by Hodges [102] that positron trapping in vacancies is a transition-limited process, and the specific trapping rate 1V is independent of temperature [73, 106]. The same result was also obtained experimentally [107,108]. Calculations based on Fermi’s golden rule [102] and experiments [106, 109] have both revealed that 1V D 1014–15 s1 in metals. For the experimental determination of 1V , it is necessary to independently measure the absolute concentration of monovacancies in the specimen. Such experiments were performed at elevated temperatures, where the equilibrium concentration of monovacancies is high enough to make the contribution from trapped positrons to the PL spectrum significant [110]. Kluin et al. [107] have correlated positron lifetime, dilatometry and lattice parameter experiments. Another way is to perform electron irradiation at low temperature [109]. The irradiation-induced Frenkel pairs are frozen in the lattice, and their concentration may be obtained by measuring the residual resistivity and dividing it by the resistivity of a Frenkel pair.

Table 4.15 Properties of positrons trapped in metal vacanciesa [72] exp

Material

th 1v (LAD) (ps)

1v (ps)

EB (eV)

1V (1014 s1 at)

Cu

188 185 [112]

180 [96] 179 [114]

1.1

1:2 ˙ 0:2 (l= l  a=a) [96]

Fe

190 176 [113]

170 [106] 175 [114]

3.0

11 ˙ 2 (e  irr.) [108]

Al

253 252 [112]

245 [96] 251 [112]

2.3 1.8 3.36

2.5 (theory) [111]

Ni

184

180 [100]

2.6

V

181

191 [72]

2.0

Cr

201

180 [72]

2.6

a

th The lifetimes of positrons trapped in monovacancies 1v and the binding energies EB were calculated using the LDAapproach. Some results obtained using another approximation have been exp added for comparison. 1v denotes the experimental lifetime of positrons trapped in vacancies. The specific trapping rates 1V were calculated using Fermi’s golden rule or were determined experimentally using an electron irradiation experiment (e irr.) or dilatometry and lattice parameter measurements (l= l  a=a).

4.3 Third Barrier: Integrity of the Primary Circuit

87

Some experimental and theoretical values of 1V for the metals of interest are listed in Table 4.15. The lowest vacancy concentration detected by PL spectroscopy may be estimated using two-state STM (i.e., Equations 4.80–4.88), where N D 1. From Equation 4.87, one can write K1 K01 D

I2 .B  2 / : I1

(4.89)

If one assumes I2 D 5% as a lower limit on the relative intensity of the defect component that can be resolved in the PL spectrum, then Equation 4.89 gives min K1

 108 . Thus, using Equation 4.88, one obtains a minimum detectable vacancy min concentration c1

 107 at1 . On the other hand I1 D 5% represents the minimum relative intensity of the free positron component that can be resolved in the PL spectrum. We then find, using the same procedure as shown above, that the maximum detectable vacancy max min concentration c1

 103 at1 . This means that if c1 > c1

, almost all positrons will be trapped at monovacancies (saturated trapping) and it will be possible to determine the vacancy concentration. Vacancy Clusters The lifetimes of positrons trapped in small vacancy clusters were calculated using the LDA approach. As the lattice relaxation around the cluster has a relatively small influence on positron annihilation parameters, it was not included in the calculations. The results show that the lifetime of a positron trapped by a divacancy does not differ a lot from that trapped by a monovacancy (it increases by about 10 ps for Fe and 20 ps for Al). However, the lifetime increases rapidly when the cluster grows into a two-dimensional trivacancy and then into a three-dimensional tetravacancy [72]. For large clusters, the lifetime saturates at around 500 ps. The dependence of the positron lifetime in vacancy clusters on the free volume of the cluster expressed as the number of vacancies comprising the cluster is shown in Figure 4.32. The specific trapping rate NV for small (N < 10) spherical clusters of N vacancies may be approximated as NV  N 1V :

(4.90)

The trapping rate to larger vacancy clusters, the sizes of which are comparable to C , also becomes limited by positron transport to the vicinity of the defect. Thus, the trapping process is shifted from the transition-limited regime into the intermediate regime. For large voids, the trapping may be limited mainly by positron diffusion to the defect. As the result of this, the positron-specific trapping rate NV becomes dependent on temperature.

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4 Barriers Preventing the Release of Fission Products

450 400

τNV [ps]

350 300 250 Al Ni Fe

200 150

0

2

4

6

8

10

12

14

16

18

Vacancy (Number) Figure 4.32 Dependence of the lifetime of a positron trapped at a vacancy cluster on the number of vacancies N in the cluster. The NV values were calculated with the LDA approximation. The solid lines are only included to guide the eye. The deviations from the smooth curve reflect the discrete structures of the clusters [72]

Dislocations Theoretical calculations have revealed that the dislocation line is only a shallow trap for positrons [112, 115] (binding energy < 0.1 eV). On the other hand, the lifetimes of trapped positrons observed in plastically deformed metals [116] are only slightly lower than the lifetimes of positrons trapped in vacancies. Smedskjaer [117] suggested that the pure dislocation line is a weak positron trap, and explained the long lifetimes seen in experiments by invoking point-like defects (vacancies, jogs) associated with the dislocation. For example, a binding energy of 0.92 eV for vacancies at the edge-dislocation line was calculated in [113] for Fe. Once a positron arrives at the core of a dislocation, it diffuses very quickly (pipe diffusion) until it finds a vacancy attached to the dislocation or a jog of the dislocation; it is then trapped and annihilates there. This explanation was also supported by further calculations [112]. Calculated lifetimes of positrons trapped in dislocations and corresponding binding energies are listed in Table 4.16. The trapping rate for the final states in dislocations is limited by the number of dislocations, so it is possible to determine the dislocation density in the specimen from positron lifetime measurements. The specific trapping rates D for dislocations were obtained by correlating positron lifetime measurements and data from transmission electron microscopy (TEM) or other techniques capable of determining dislocation density (e.g., X-ray diffraction profiles) [118]. In metals, D lies in the range 105 to 104 m2 s1 . Thermally activated detrapping of positrons trapped in a dislocation core (an initial shallow trap) may occur at elevated temperatures, which makes D temperature dependent [102].

4.3 Third Barrier: Integrity of the Primary Circuit

89

Table 4.16 Calculated lifetimes and binding energies EB of positrons trapped in the core region of a dislocation line and in defects associated with dislocation [112] Annihilation site

(ps)

EB (eV) 0.06 0.8 1.2

Cu [93]

Œ11N 2 dislocation line Vacancy on the Œ11N 2 dislocation line Vacancy in the stacking-fault region

114 166 177

Fe [107]

Edge dislocation line Jog on the edge dislocation line Vacancy on the edge dislocation line Œ11N 2 dislocation line Vacancy on the Œ11N 2 dislocation line Jog on the Œ11N 2 dislocation line [111] dislocation loop

117 117 140

Al [93]

174 225 224 191

0.1 1.0 1.3 0.4

Table 4.17 Lifetimes D and specific trapping rates D for positrons trapped at dislocations Material

D (ps)

D (104 m2 s1 )

Cu

179 ˙ 2 [119] 155 [120]

0:66 ˙ 0:09 [119]

Fe – screw dislocation

142 [118]

0.51 [118]

Fe – edge dislocation

165 [118]

0.70 [118]

Fe

150 [77]

Al

235 [121] 215 [122] 220 ˙ 2 [116]

0.45 [121]

The experimental lifetimes of positrons trapped at dislocations and the specific positron trapping rates for dislocations at room temperature are collected in Table 4.17. The different lifetimes for screw and edge dislocations in single-crystal Fe were reported in [118]. According to this work, edge dislocations exhibit larger specific trapping rates D and lifetimes than screw ones. Similar to vacancies in the previous section, it can be shown that the minimum dislocation density detectable by PL spectroscopy is %D  1012 m2 . On the other hand, if %D  1016 m2 , almost all positrons are trapped at dislocations (saturated trapping), and only the contribution from the trapped positrons is resolved in the PL spectrum. Grain Boundaries Positrons may be trapped by grain boundaries (GBs) in metals. Nevertheless, trapping in GBs is likely only when the mean linear dimension of the grains does not exceed a few µm. This means that the grain size is comparable to (or smaller than) the positron diffusion length LC , and some of the positrons have a chance of reaching a GB by diffusive motion. The movement of a positron to a GB substantially limits the positron trapping rate in GBs [91].

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4 Barriers Preventing the Release of Fission Products

Precipitates The relative values of the energy of the ground state of a delocalised positron differ in different materials. This makes it possible to trap a positron in a precipitate with low positron ground-state energy. A common reference energy level, the so-called crystal zero, can be uniquely defined for both electrons and positrons in perfect solids. Therefore, the energy levels in the calculations are measured relative to this internal quantity. The electron chemical potential  is defined as the distance of the Fermi levels from the crystal zero (see Figure 4.33). Similarly, the distance of the lowest positron energy level from the crystal zero defines the positron chemical potential C (Figure 4.32). The crystal zero is related to the Coulomb potential, and it can be defined for example as the average electrostatic potential in the infinite lattice, or the average value of the electrostatic potential on the surface of the Wigner–Seitz cell. When the solid is considered to have a surface facing the vacuum, the distance from the electrostatic potential level, which a test charge feels in the vacuum (the vacuum level) to the crystal zero, is the surface dipole potential  (Figure 4.32). An electron and a positron have the same absolute value but different signs of  due to the opposite electron and positron charges. The distance between the absolute Fermi energy level and the vacuum level defines the electron work function ˚ [72]: ˚ D    :

(4.91)

The positron work function ˚C is the difference between the lowest energy state level and the vacuum level [72] ˚C D   C :

(4.92)

Both ˚ and ˚C are measurable quantities and they do not depend on the position of the crystal zero. In the case of two metals A and B that are in contact, the Fermi levels equalize themselves across the interface. As a result, an interface dipole with

positrons

electrons vacuum

Φ–

Δ crystal zero

0

µ–

Fermi level

µ+

–Δ bottom of

valence band

Φ+ lowest band vacuum

energy

Figure 4.33 Electron and positron potentials and energy levels near a metal surface. is the dipole potential at the surface, ˚ , ˚C denote the electron and positron work functions , and  and C are the electron and positron chemical potentials, respectively. Arrows pointing upwards and downwards denote positive and negative quantities, respectively

4.3 Third Barrier: Integrity of the Primary Circuit

91

B a potential difference of A   C is formed (Figure 4.34). The difference between the lowest positron energies on the different sides of the interface is [72] A;B A B B A B EC D EC  EC D A    C C  C :

(4.93)

It is useful to define the following quantity, which is called the positron affinity: AC D  C C :

(4.94)

The positron affinity is a bulk property of a given homogeneous material and is not related to the interface between two materials. The more negative the positron affinity, the deeper the positron energy level in the solid. The difference between the lowest positron energies of two materials in contact can now be written as A;B B EC D AA C  AC :

(4.95)

The positron affinities for some metals calculated in [72] are shown in Table 4.18. It is also possible to obtain the positron affinity experimentally from the positron and electron work functions: AC D  C C D ˚  ˚C :

(4.96)

If and only if the difference between the positron’s affinity for the host matrix and for the precipitate is positive will the precipitate attract the positron, making localisation or trapping in the precipitate possible. Despite this, the size of the precipitate must be large enough for the positron to be trapped. In the case of a spherical potential, the minimum radius for a bound state is [106] 0:31 rc Œnm D p ; A ŒeV

(4.97)

where A is the difference in the positron’s affinity for the matrix and for the precipitate.

positrons

electrons

A

µ–B

0

µ–A

valence band energy

A

B

B

crystal zero

µ+A µ+B bottom of lowest band

Figure 4.34 Electron and positron potentials and energy levels near a junction between two metA B B als A and B. A  , C ,  , C denote the electron and positron chemical potentials for metals A and B, respectively

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4 Barriers Preventing the Release of Fission Products

Table 4.18 Calculated [72] and experimentally deduced [123]a positron affinities AC

a

exp

Material

Ath C (eV)

AC (eV)

Cu Fe Al Ni Cr V

4:81 3:84 4:41 4:46 2:62 3:44

4:4, 4:4a 4:3a 3:8, 4:0a 2:6a

The experimental values were deduced in [80] from the measured positronium formation potentials

It should be pointed out that positrons can also be trapped by misfit defects at the matrix–precipitate interface or by defects inside a precipitate, despite the positron’s affinity for the precipitate.

Thermal Equilibrium When a positron has reached thermal equilibrium with the medium, its scattering is overwhelmingly dominated by phonons. This scattering is usually quasi-elastic and does not affect the average positron momentum distribution. Thus, the momentum distribution of a thermalised positron has a time-independent form which is close to the Maxwell–Boltzmann distribution [72]. The average value of the square of the positron’s thermal velocity is ˝ 2˛ 3kB T v D ; m

(4.98)

where T is the temperature of the medium. The effective positron mass m consists of the contribution from the positron band structure and the positron–electron correlation [124]. Typically, in condensed matter, m Š 1:5 m [106]. Furthermore, the root of the mean squared positron velocity vC is introduced as p vC hv 2 i : (4.99) Using Equation 4.99 and estimating the effective positron mass shown above yields p vC Œnm=ps Š 5:5 T : (4.100) In the classical picture, the movement of the thermalised positron is a near-isotropic random walk [91]. The mean free path of thermalised positrons (i.e., the mean distance between two scattering events) is lC D vC Ph ;

(4.101)

4.3 Third Barrier: Integrity of the Primary Circuit

93

where Ph denotes the relaxation time for positron scattering off phonons. In metals, Ph is on the order of  10 fs. Thus, the positron mean free path in metals appears to be a few nm. Mean free paths calculated using Equation 4.100 for the metals related to this work are shown in Table 4.19. The evolution of the positron spatial distribution f .r; t/ is conventionally described by the diffusion–annihilation equation [72] @f .r; t/ D DC r 2 f .r; t/  ŒB C K.r/ f .r; t/  r Œvd .r/f .r; t/ C fi .r; t/ ; @t (4.102) where DC is the positron diffusion coefficient and vd is the positron drift velocity due to external fields. The annihilation rate of free (delocalised) positrons is denoted by B . The trapping rate at defects K.r/ is generally spatially dependent. The source term is denoted by fi .rI t/. The diffusion equation is often solved at the time-independent steady-state limit, which is DC r 2 f .r/  ŒB C K.r/ f .r/  r Œvd .r/f .r/ C fi .r/ D 0 :

(4.103)

The semi-classical random walk theory gives the following expression for the positron diffusion coefficient: 1 1 2 DC vC lC D vC Ph : 3 3

(4.104)

Table 4.19 Important quantities connected with positron movement in metals [96, 125] Material

˛ 1 (µm)a

lC (nm)b

DC (cm2 s1 )c

LC (nm)d

Cu

29.8

4.9

1.6 1:7 ˙ 0:5 (DB + Ps) 1:1 ˙ 0:2 (Ps)

133–139 140 ˙ 20 110–114

Fe

34.0

11.9

3.8 > 1 (PD)

200–206 > 100

Al

99.0

4.4

1.4 1:7 ˙ 0:2 (DB + Ps)

146–154 170 ˙ 10

Ni

30.0

6.9

2.2

145–153

V

43.8

6.4

1.4

127–133

Cr

37.2

5.5

1.8

135–147

a b c

d

A 22 Na ˇ C source is assumed; i.e., the end-point energy Emax D 0:545 MeV. Mean free path at room temperature (T D 300 K). Positron diffusion coefficient at room temperature. For experimental values: PD, positron depolarization experiment; DB, Doppler broadening measurement of the annihilation line-shape parameter S ; Ps, positronium fraction measurement. Mean diffusion length at room temperature for the defect-free material. For the free positron lifetimes, we used the bulk lifetimes calculated by GGA and the experimental ones shown in Table 4.17. If the non-negligible defect concentration is included, the parameter L+ will be smaller.

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4 Barriers Preventing the Release of Fission Products

In solids, DC reaches values of 0.1–3 cm2 s1 s at room temperature. The diffusion constant may be equivalently expressed by the Einstein relation DC D

kB T Ph : m

(4.105)

The relaxation time Ph for positron scattering off phonons can be calculated using the deformation potential approximation [126] r 8 „s Ph D ; (4.106)  9 .m kB T /3=2  2 where s is the sound velocity in the medium and  is the positron–phonon coupling constant. In the standard deformation potential approximation 2 D

Ed2 „s ; 2ds

(4.107)

where d is the density of the material and Ed is the deformation potential constant, which is defined as Ed D V

@EC : @V

(4.108)

The symbol EC denotes the total energy of the crystal with the positron in its lowest state (Bloch state at k D 0), and v is the crystal volume. In metals, Ed is typically on the order of  23 EF (EF is the Fermi energy) [73]. Positron diffusion constants calculated using Equation 4.105 are listed in Table 4.19. Some experimental values of DC that can be found in the literature are also included for comparison. We can see that there is relatively good agreement with the experimental values. Positron scattering off phonons leads to the following temperature dependence of the diffusion coefficient: 1 DC  p : T

(4.109)

The mean diffusion length LC of the positron is defined as the mean distance from the point of thermalisation that the positron reaches by diffusion movement. This quantity is related to the diffusion coefficient by the relation [72] p LC D DC f ; (4.110) where f is the effective lifetime of a free (delocalised) positron: f D B C K.r/ :

(4.111)

The values of the diffusion length for some metals are listed in Table 4.19. Clearly, LC determines the region in the medium that is probed by a single positron during

4.3 Third Barrier: Integrity of the Primary Circuit

95

its lifetime. The wavelength of a thermalised positron s 2„ 293 ŒK

C Œnm D  Š 5:2 m vC T ŒK

(4.112)

is significantly greater than the lattice constant (˛  0:1–0.5 nm) in solids. Thermalised positrons in condensed matter therefore behave as waves, and we speak of “free” or “delocalised” positrons. Note that the wavelength of a proton is more than three orders of magnitude shorter. This means that the behaviour of thermalised hydrogen atoms and all other atoms is close to that of heavy classical particles. Hence, a positron travels through a material volume of approximately 2C LC , i.e., a region containing about 107 atoms. From Table 4.19, it is clear that in metals 1 LC > lC > C : ˛

(4.113)

This means that a positron travels the furthest (on average hundreds of µm) in a metal during its thermalisation, which in turn ensures that PAS provides non-local information on the microstructure of the studied material. A thermalised positron in a defect-free material travels a distance of hundreds of nm, its mean free path is a few nm, and its wavelength is a few tenths of a nm. Application of PAS to Investigations of RPV Steel Positron annihilation spectroscopy can provide essential information about the deterioration in the mechanical properties of RPV steels (microstructural defects and precipitates) during their irradiation, which is known as neutron embrittlement. Currently, there are three main techniques based on annihilation phenomena: positron lifetime spectroscopy, Doppler-broadening spectroscopy and angular correlation measurements. Positron Lifetime Spectroscopy Positrons can assume several states, each of which gives a characteristic lifetime i D 1=i . The positron lifetime spectrum (i.e., the probability of annihilation at time t/ is thus the sum of the associated exponential decay components: X dn.t/ D Ii i exp Œi t ; dt i X av D Ii C i ; 

X

Ii D 1 ;

(4.114)

i

(4.115)

i

with relative intensities Ii . Here, n.t/ is the probability that a positron is still in existence at time t after its emission. Experimentally, the lifetime of a positron is the time delay between its emission and its annihilation.

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4 Barriers Preventing the Release of Fission Products 5

a) 10

b)

Counts

1.27 MeV

+e

γ

102

+

_e

511 keV

PM

Start

Sample

3

10

γ Start

SCA 1.27 MeV

–

γ

Stop 511 keV

MCA TAC

PM

Scintillator

Stop

log N

22 Na Source

104

Delay

l SCA 511 keV

101 0

100

200

300

400

500

Channel

Figure 4.35 a Lifetime spectrum, and b scheme of a lifetime measurement system [84]

To facilitate  – coincidence measurements, positron emission should be accompanied by a suitable start signal from a nuclear de-excitation, like the 1.28 MeV photon in the case of the 22 Na isotope. The 511 keV annihilation photon serves as the stop signal. The positron source is then sandwiched between two identical pieces of the sample material. The lifetime spectrometer consists of a start and stop detector (see Figure 4.35), each constructed by coupling a fast scintillator to a photomultiplier. The timing pulses are obtained by differential constant-fraction discrimination. The time delays between the start and stop signals are converted into amplitude pulses, the heights of which are stored in a multichannel analyser. Good time resolution is typically 200–250 ps (FWHM). Doppler-broadening Spectroscopy The motion of the annihilating pair causes a Doppler shift E D

1 cpL ; 2

(4.116)

where pL is the longitudinal momentum component of the pair in the direction of the annihilation gamma emission. This causes the broadening of the 511 keV annihilation line (see Figure 4.36). The shape of the 511 keV peak is in fact the onedimensional momentum distribution of the annihilation radiation: Z1 Z1 L.E /˛

dpx dpy %.px ; py ; pz / ;

(4.117)

1 1

2 pz D .E  m0 c 2 / : c

(4.118)

A Doppler shift of 1 keV corresponds to an angle deviation of 3.91 mrad. The Doppler broadening is experimentally measured using a Ge gamma detector. For measurements of bulk specimens, the same source–sample sandwich is used as in the lifetime experiments. The typical resolution of a detector is around 1 keV at

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a)

97

b)

Si

22 Na Source

S parameter

Intensity

(511keV ± 0.75keV)

Sample

+ +e

γ

W parameter (511keV ± 3.0keV) (511keV ± 6.1keV)

_e

511 keV

MCA

Stabilizer

Ge Detector

γ

–

ADC

Memory

511 keV LN2

504

506

508

510

512

514

516

518

γ−ray energy [keV]

Figure 4.36 a Typical Doppler-broadening spectrum, and b scheme of a Doppler-broadening measurement system

500 keV. This is considerable compared to the total width (2–3 keV) of the annihilation peak, meaning that the experimental lineshape is strongly influenced by the detector resolution. There have been attempts to deconvolute the peak, but the most practical scheme is still to use various shape parameters to characterise the 511 keV line. Angular Correlation The angular correlation of the 2 -annihilation photons is measured with the system described in Figure 4.37. The annihilation photons are detected in coincidence by NaI scintillation counters, which are shielded from direct view of the source. The lead collimators in front of the detectors define the instrumental angular resolution (1 mrad). To archive counting rates, the detectors and slits are made as long as possible in the x-direction. The single-channel analyser (SCA) is tuned for 511 keV photons, and the device simply counts the coincidence pulses as a function of the angle z . a) 3.5

b) 4

2

2.0 0 1.5 –2

1.0

px

Differentiate (x102)

Counts (x103)

3.0 2.5

py pz

γ

Magnet

γ

Sample

Θy

e+ Magnet Slit

0.5 0.0 –30

–4

Slit Θx

S1

S2

Coincidence

–20

–10

0 Θ (m rad)

10

20

30

Memory

Figure 4.37 a Typical 1D ACAR spectrum, and b scheme of an angular correlation measurement system

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PAS Data Treatment. The lifetime spectra are resolved into two components, a long lifetime due to positrons trapped at defects (d / and a short lifetime that mainly comes from free positrons in the matrix. For general interpretation, it can be considered that the positron lifetime (PL) technique is a well-established method for studying open-volume-type atomic defects and defect impurity interactions in metals and alloys. The lifetime of positrons trapped at vacancies, vacancy–impurity pairs, dislocations, microvoids, etc., is longer than that of free positrons in the perfect region of the same material. As a result of the presence of open-volume defects, the average positron lifetime observed in structural materials is found to increase with damage [127, 128]. The simple trapping model (STM) can be used to interpret the results from PL measurements [129]. According to this model, for positrons implanted into a homogeneous solid with a bulk lifetime b D 1=b and with N different kinds of homogeneously distributed microscopic defects with lifetimes i D 1=i and trapping rates i , the annihilation spectrum will consist of N C 1 exponentials. Through defect trapping, the bulk lifetime will be reduced to 0 D 1=.b C /, where D

N X

i

(4.119)

i D1

denotes the total trapping rate, whereas the characteristic lifetimes i associated with defects remain unaltered, and the corresponding intensities are Ii D i =.b C   i / ;

i D 1; : : : ; N :

(4.120)

Finally, for the average lifetime av , which can be measured with accuracy, one obtains !, N X .i C / : av D 1 C i =i (4.121) 1

Using the previous equations we can derive the microscopic structure (i.e., the kinds of defects and their concentrations) from the experimentally determined lifetimes and intensities if the problem is homogeneous. This premise, however, does not hold for RPV steels completely. In inhomogeneous problems, the diffusion of positrons from the various implantation sites to the trapping centres must also be considered [125, 130]. However, the mathematical difficulties associated with the corresponding diffusion-trapping model (DTM) [73] have so far prevented exact solutions from being obtained for all but the simplest problems [116, 117]. Thus, it is impossible to qualitatively analyse the very detailed experimental results obtained with a pulsed positron beam. Hence, while the lifetime method yields information regarding the electron density in the region of electron–positron overlap through the determination of positron decay rates from various states in the metal, the method of angular correlation and Doppler broadening (the momentum technique) gives information regarding the

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electron moment in this overlap region through the shape of the angular ( ) and energy (E) distributions of the annihilating  -rays. These shapes are usually characterised by one or more “lineshape parameters”. The most commonly used ones are the normalised peak counts determined in an interval around D 0 (in angular correlation) or E D 0 (in Doppler broadening). These measure in various – but qualitatively equal – ways the differences between annihilations with electrons of low momentum and annihilations with electrons with high momentum. These changes in the annihilation characteristics yield information on whether the positron annihilates in a defect-free region of the crystal or from a defect site. The angular correlation PAS measurement is based on the evaluation of the 511 keV  -photon distribution. The total momentum of both  photons arising during the moment of annihilation is equal to the momentum of the annihilated .e C ; e  / pair. Because the e C is thermalised before the annihilation in the material, its momentum can be neglected. Therefore, the angular distribution of the  -photon pairs depends on the local electron momentum distribution in the observed material. This fact is frequently used in the study of mechanical, thermal or radiation-induced defects in materials [131]. The central parameter S is defined as the ratio of the counts in the central region of the annihilation line to the total number of the counts in the line (Figure 4.36). In the same way, the wing parameter W is the relative fraction of the counts in the wing regions of the line. Due to their low momentum, annihilations with valence electrons fall predominantly in the region of the S parameter. Mainly core electrons have momentum values high enough to contribute to the W parameter, respectively. In order to get maximum information out of the parameters, proper selection of the energy windows is important. The central window for S is chosen so that it covers about 50% of the total peak (S  0:5). The W window should be far enough from the peak to ensure that mainly core annihilations are accepted. 5 P

Spar D

i D 5 30 P

Ni ;

i D 30 6 P

Wpar D

(4.122)

Ni

i D 13

Ni C 30 P

i D 30

13 P i D6

Ni :

(4.123)

Ni

The usefulness of positron annihilation studies of metallic substances relies on the fact that the characteristics of the annihilation process depend almost entirely on the initial state of the positron–many-electron system. Since energetic positrons are rapidly thermalized after entering condensed matter, if they are not bound to electrons, the characteristics of the annihilation process in most cases depend on the initial state of the many-electron system where positrons annihilate. The energies,

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momenta, and times of the gamma rays emitted during the annihilation can be measured with high precision using modern detector systems. Therefore, the state of electrons in metallic substances can be identified by studying the positron annihilation process characteristics. The annihilation lifetime can be determined by lifetime measurement. The momentum distribution of the annihilation gamma rays can be measured using the method of the angular correlation of the two collinear annihilation gamma rays, and the energy distribution using the method of Doppler broadening. Using these measurements, the characteristics of the state of electrons in metallic substances, such as the momentum and density distributions of electrons, the structure of a Fermi surface, and the properties of defects and voids can be studied. The shape of the angular correlation distribution profile is a superposition of two contributions. Annihilation of the positron with the conduction electrons results in a contribution that has the approximate shape of an inverted parabola, while the contribution of the high-momentum core electrons is reflected in a broad, Gaussian-like distribution. When the core electron density is reduced, as is the case for a positron trapped in a vacancy, the contribution of the conduction electrons is enhanced and a narrower distribution is measured. Therefore, changes in the shape of the angular correlation distribution profile reflect a reduction in annihilation with core electrons [127]. Munich Pulsed Low-energy Positron System (PLEPS) For almost 15 years, a low-energy pulsed positron system has been in operation at the Institut für Nukleare Festkörperphysik, Universität der Bundeswehr Münich [132]. It is well established that low-energy pulsed positron beams [133, 134] have demonstrated their usefulness in the study of properties at surface or nearsurface regions. Building on the experience gained from the first design [135], this system was upgraded in various stages [136] over the following years. The set-up of the latest version of the beam system is shown in Figure 4.38. The source and prebuncher configuration is basically the same as in the previous version [136]. A wellannealed tungsten transmission moderator (single-crystalline foil, h100i, thickness of 1 µm) is used to generate the low-energy positrons. The moderator can be annealed in situ with an electron gun. The dc beam after the moderator is prebunched with a sawtooth buncher device, which is explained in detail in [133]. The measured time distribution of the prebunched positrons at the entrance slit of the chopper is about 2 ns (FWHM). This width is mainly caused by the energy spread (E  0:4 eV FWHM) of the moderated positrons [133,136]. The positrons, which travel in a longitudinal magnetic guiding field of about 7 mT, are deflected by 90ı and enter the new chopper device with an energy of 200 eV (see Figure 4.39). This chopper is a double-plate system with an external resonator, positioned outside the vacuum system. The deflection plate D1 is coupled to a 50 MHz sine wave of amplitude Uo superimposed on a dc voltage of about Uo . At the minimum (0 V), no transverse field is acting on the positrons. However, due to the magnetic guiding field, the positrons

4.3 Third Barrier: Integrity of the Primary Circuit

Figure 4.38 Schematic view of the latest version of the low-energy pulsed positron system

Figure 4.39 Schematic view of the chopper

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4 Barriers Preventing the Release of Fission Products

that then begin to sense the transverse field start to gyrate. An adjustable aperture is positioned at a distance corresponding to a flight time of 2.5 ns from the centre of D1 , where the elongation is largest. Positrons which pass through the aperture arrive at the deflection plate D2 after 10 ns. The rf voltage is in phase with D1 but is shifted by a dc voltage of Uo . Therefore, these positrons see no deflection field at all. Only positrons within the prebunched pulse of about 2 ns (FWHM) can pass through the chopper. This chopper is located far upstream of the sample/detector position in order to minimise the background caused by annihilating positrons at the chopper plates. After a second 90 bend, the pulsed positrons enter the new 50 MHz buncher, as shown in Figure 4.40. This device is in principle a classical double-gap buncher with a travel time of 10 ns for the positrons through the drift tube. When compared to a =4 coaxial resonator, the double-gap resonator is preferable because of the shorter length and the lower rf power consumption resulting from two bunching gaps. The rf power is fed in by a coupling loop and a pick-up loop is used for control and regulation pur-

Figure 4.40 Schematic view of the double-gap buncher

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103

Figure 4.41 Schematic view of the optical column

poses. Fine tuning can be performed via an adjustable plunger. This type of buncher has been found to be very stable; no readjustments or permanent fine tuning is necessary. High-frequency amplitudes of some 100 V are needed. The overall master frequency for all bunching and chopping components is 50 MHz. The master oscillator and the rf power amplifiers for the chopper and the buncher are newly designed

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and incorporate modern electronic components. The new optical column is shown in more detail in Figure 4.41. After the buncher, the positrons enter a drift tube. This drift tube is necessary in order to adjust the travel time of the positrons independent of their final energy. The subsequent accelerator is configured as a simple voltage divider. The large overlapping accelerator rings are specially shaped to obtain the optimum beam optic. After the accelerator, the positrons pass through a Wien filter, which allows the suppression of back-reflected positrons from the sample in order to minimise disturbances from side peaks in the lifetime spectra. The following Faraday cage, which is larger than the previous version, is separated from the vacuum system above by a differential pumping stage. With a vacuum of the order of 107 mbar in the region of the high-frequency components, it is possible to achieve a vacuum of about 109 mbar in the sample region. The sample station is also newly designed and rebuilt. The distance between the sample and the detector has been reduced further. Specimens which are at high voltage can now be investigated in the temperature range 30–600 K. Starting with a primary source of 30 mCi (1.1 GBq), a count rate of up to 4 kHz can be obtained with the BaF2 scintillation detector. The scintillator crystal itself is a truncated pyramid with a base of 40 mm  40 mm and a height of 35 mm that is coupled to a Philips XP2020Q. The overall time resolution (pulsing plus detector system) of 250 ps (FWHM) is stable over the beam energy range of 3–20 keV employed. The experimentally determined beam diameter is about 2 mm. Up to ten samples can be stored in a magazine and transferred under vacuum conditions to the measuring position. The upgraded system has been operating successfully for about a year. It has been found to be very stable and easy to operate. As an example of results from a recent investigation, a lifetime spectrum of hydrogen-implanted silicon is shown

Figure 4.42 Example of a positron lifetime spectrum

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105

in Figure 4.42. The background shows almost no structure. The count rate (with a reduced energy window) was 1600 c/s and the peak-to-background ratio is 3000:1.

4.3.2.3 The Mössbauer Effect The phenomenon where  -ray photons are emitted and absorbed by nuclei in a crystalline lattice without any energy being lost due to nuclear recoils and without incurring any thermal broadening is known as the Mössbauer effect. It was discovered by Rudolph Mössbauer in 1957 [137], and its influence has grown in many branches of physics and chemistry, particularly during the last thirty years. Its unique feature is in the production of monochromatic electromagnetic radiation with a very narrowly defined energy spectrum that allows the resolution of minute energy differences. The Mössbauer effect is of fundamental importance because it allows us to estimate the hyperfine interactions between the nucleus and the surrounding electrons, but the effect is only observed in the solid state. Thus, the Mössbauer effect can be summarised as the resonant emission or absorption of a  -ray in a solid matrix without degradation due to nuclear recoil or thermal broadening that gives an energy

Figure 4.43 a Emission and b absorption lines are Doppler broadened, resulting in c a small overlap between them. Adapted from [104]

4 Barriers Preventing the Release of Fission Products N(v)

106

A

γ S

> 2Γ

γ D

v 0

v

Figure 4.44 Arrangement used to observe the Mössbauer effect. S is the source, A is the absorber and D is the counter. Adapted from [138]

distribution that is dictated by the Heisenberg uncertainty principle (see Figures 4.43 and 4.44). Because the hyperfine interactions are frequently temperature dependent, and because of the complexity of the hyperfine structure, low- and high-temperature measurements are usually needed to improve the results of the fitting procedure, to refine the temperature dependence of some relevant hyperfine parameters, and finally to better characterise the samples.

Hyperfine Interactions The energies of nuclear states are weakly influenced by their chemical environment. It is possible to detect these extremely small effects because of the high definition of the  -ray energy in the Mössbauer effect. There are three main interactions to consider: • A change in the electric monopolar or Coulombic interaction between the electronic and nuclear charges, which is caused by a change in the size of the nucleus when it moves between ground and excited states. This is observed as a shift of the absorption line away from zero velocity. This shift is known as the chemical isomer shift, designated by the symbol ı (in mm/s); see Figure 4.45a. • A magnetic dipole interaction between the magnetic moment of the nucleus and the internal field (intrinsic or extrinsic to the atom in origin). The result is a multiple line structure in the spectrum known as magnetic hyperfine splitting, and labelled Bhf ; see Figure 4.45b. • An electric quadrupole interaction (denoted  or QS) between the nuclear quadrupole moment and the local electric field gradient tensor at the nucleus. This also results in a single- or double-line spectrum (i.e., a doublet); see Figure 4.45c. It is important to note that these three effects can occur simultaneously.

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107

Figure 4.45 Three main types of hyperfine interactions: a monopolar interaction, b electric quadrupolar interaction and c magnetic dipolar interaction. Adapted from [138]

Chemical Isomer Shift The Mössbauer experiment compares the source and absorber, so that the chemical isomer shift is given by

1 ıR ıD Ze2 R2 (4.124) jS .0/absorber j2  js .0/source j2 ; 5"0 R where: "0 is the permittivity of the vacuum; Ze is the charge on the nucleus; R is the radius of the spherical nucleus; jS .0/j2 is the non-relativistic Schrödinger wavefunction at r D 0. This can then be related quite simply to the measured shift in Doppler velocity units, v, by   c vD ı; (4.125) E where c is the velocity of light and E is the energy of each  photon. For chemical applications, it is often sufficient to compare chemical shift values using the simplified expression

ı D constant  js .0/A j2  js .0/B j2 ; (4.126)

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4 Barriers Preventing the Release of Fission Products

where A and B are two different chemical environments (B is either the source matrix or a reference absorber). It is important to realise that jS .0/j2 is the s-electron density at the nucleus, and not the s-electron in the formal chemical sense. If ıR=R is positive, a positive value of the chemical isomer shift, d , implies that the s-electron density at the nucleus in A is greater than that in B. The chemical isomer shifts of two different resonances for the same series of compounds should be related purely by the difference in ıR=R. Accurately calibrating the chemical isomer shift scale for a particular isotope is not without its difficulties. The change in nuclear radius, ıR=R, cannot be determined independently of the chemical environment, which means that the electron density jS .0/j2 must be estimated by molecular orbital methods in at least two compounds before a value of ıR=R can be obtained. The observed lineshift is not entirely caused by the chemical isomer shift. There is another generally smaller contribution termed the second-order Doppler shift. The emitting or absorbing nucleus is not stationary – it is vibrating at its position in the lattice. The period of its vibration is much shorter than the Mössbauer lifetime, so the average displacement and velocity are effectively zero, but the mean-squared values of the velocity, hv 2 i, are finite. hvi is zero, so only the second-order term in hv 2 i can influence the Mössbauer resonance. This gives rise to a shift in the Mössbauer line of ıE hv 2 i D 2 : E 2c

(4.127)

It is obvious that hv 2 i increases with temperature. The contribution of the second-order Doppler shift to the observed chemical shift is smallest at absolute zero, but it is still finite because of the zero-point motion of the nucleus. In the case of 57 Fe Mössbauer spectroscopy, the isomer shift values are quoted relative to the spectrum for ˛-Fe taken at room temperature. Magnetic Hyperfine Interactions The nucleus possesses a magnetic moment m when the spin quantum number I is greater than zero. Its energy is then affected by the presence of a magnetic field, and the interaction of m with a magnetic flux density of B is formally expressed by the Hamiltonian H D   B D gN I  B ;

(4.128)

where N is the nuclear magneton (eh=4 mp D 5:04929  1027 A m2 or J T1 ) and g is the nuclear g-factor (g D =.IN /). Solving the Hamiltonian gives the energy levels of the nucleus in the field as Em D 

B mZ D gN BmZ ; I

(4.129)

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109

where mZ is the magnetic quantum number, which can take the values I; .I  1/; : : : ; I . In fact, the magnetic field splits the energy level into (2I C 1) non-degenerate equispaced sublevels separated by B=I . In a Mössbauer experiment, there may be a transition from a ground state with a spin quantum number Ig and a magnetic moment g to an excited state with a spin quantum number Ie and a magnetic moment e . In a magnetic field, both states will be split. Transitions can take place between sublevels provided that the selection rule mZ D 0; ˙1 is obeyed. In the case of iron, the resulting Mössbauer spectrum contains six resonance lines, but is nevertheless symmetrical about the centroid. The relative intensities of these six transitions are given by 3:x:1:1:x:3, where x is zero if the  -ray direction is parallel to the direction of magnetisation (the magnetisation is either parallel or antiparallel to the hyperfine field, according to the Fermi content term), 4 if the  -ray direction is normal to the direction of magnetisation, and 2 if the sample is randomly oriented (e.g., in a powder). Electric Quadrupole Interactions An electric quadrupole transition is a  -ray transition between the hyperfine multiplets of the nucleus in its ground and excited states. Only those nuclear states with I > 1=2 have a nuclear quadrupole moment and hence show quadrupole hyperfine splitting. Thus, it is often possible to observe a quadrupole interaction in the Mössbauer spectrum that derives from the excited nuclear state. The nuclear quadrupole moment Q is a measure of the deviation from spherical symmetry of the nuclear charge. It is expressed by Z   eQ D %r 2 3 cos2   1 d ; (4.130) where Ce is the charge of the proton and % is the charge density in the volume element dt at a distance r from the centre of the nucleus and at an angle  to the axis of the nuclear spin. Q is often quoted in units of barns. The electrostatic potential at the nucleus due to a point charge q at a distance r is given by V D q=.4"o r/, where "o is the permittivity of the vacuum. The interaction of the nuclear quadrupole moment with the electronic environment is expressed by the Hamiltonian 1 H D  eQrE ; 6

(4.131)

where rE represents the electric field gradient at the nucleus, and is a tensor quantity. If the electric field gradient tensor has axial symmetry ( D 0), the energy levels are given by EQ D

e2 qQ  2 3Iz  I.I C 1/ ; 4I.2I  1/

(4.132)

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4 Barriers Preventing the Release of Fission Products

where the quantum number Iz can take the (2I C1) values of I; .I 1/; : : : ; I . The resulting Mössbauer spectrum is a doublet with a separation called the quadrupole splitting. The 1=2 ! 3=2 transition thus produces a well-resolved doublet of Mössbauer lines. In the case of cubic symmetry, the resulting spectrum shows a single unresolved line [138, 139]. In practice, both electric and magnetic interactions contribute simultaneously to the hyperfine structure. Application of Mössbauer Spectroscopy A Mössbauer spectrum exhibits different components relating to different Mössbauer atoms at different sites in different neighbourhoods. The parameters of the components in the Mössbauer spectrum can show which component relates to Mössbauer atoms located at sites that are undisturbed by structural lattice defects, and which relates to atoms located at defect-correlated sites [140]. Therefore, the author applied MS to the investigation of RPV steel microstructure. To the best of the author’s knowledge, MS has only rarely been used to investigate nuclear power plant (NPP) materials so far. The most significant advantage of this method when investigating steels is its high sensitivity to changes in the atomic configurations of resonant atoms (57 Fe) in the immediate neighbourhood of an interstitial atom. By probing hyperfine interactions, Mössbauer spectroscopy provides information on magnetic state, electrical interactions, electric field gradients, chemical bonding, local crystal symmetry, lattice defects, dynamic parameters, elastic stress, etc. [140]. Structural lattice defects (SLDs) are defects in the regular construction of a crystal or crystalline grain. They may be point defects, such as vacancies and interstitial atoms. Here, we will mainly consider the production of SLDs by irradiation (radiation damage), since radiation defects are by far the most common SLDs probed in Mössbauer spectroscopy (MS) investigations. MS is highly suited to investigating microscopic defect properties. By “microscopic” we mean that the hyperfine parameters determined from a Mössbauer spectrum are particularly sensitive to local conditions at the site of the Mössbauer atom and its immediate environment. The Mössbauer effect (ME) is therefore also capable of providing microscopic information about defects in this region. In metals where other microscopic methods are not sufficiently powerful, a method like MS has a wide range of applications in relation to SLDs. There are other microscopic methods that can be used to investigate SLDs that originate in the same way, such as microscopic studies, scattering measurements, stored energy, strength or fracture investigations, etc. It is very important to combine Mössbauer measurements with other methods, preferably methods that are sensitive to totally different defect properties. Promising work has been done by combining MS and PAS. Simultaneous measurements with various methods on the same samples is the optimal approach. Such work (experimental and theoretical) is rewarding: while improving the microscopy of lattice defects is itself an interesting area of research, it is also of great technological importance for future nuclear reactor development in relation to the problem of severe radiation damage.

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MS Data Treatment The Mössbauer spectrum is a record of the transmission of resonant  rays through an absorber as a function of the Doppler velocity with respect to the source. It is therefore quite simply a record of transmission as a function of the energy of the incident radiation (Figure 4.45). The isomer shift (IS), quadrupole splitting (), quadrupole shift (2"), line width ( ), hyperfine field (B), asymmetry parameter ( ), and polar angles defined by the directions of the  beam and the hyperfine field with respect to the principal axes of the electric field are the hyperfine parameters that are characteristic of nuclei in a particular chemical environment. In most cases, these different kinds of interactions are present simultaneously. Each different nucleus will contribute to a doublet or a sextet to the Mössbauer spectrum. Since each component (i.e., subspectrum) in the spectrum relates to a particular nuclear environment, the area of the component provides information about the proportion of nuclei in that chemical environment. When a nucleus absorbs a  -ray photon, hyperfine interactions slightly change the energy of the photon upon its re-emission. The recoil-free energy of a typical transition is so precisely defined that its line width corresponds to the energy change produced by applying a Doppler velocity of 1–10 mm/s. Therefore, at a particular relative velocity between source and absorber, the source energy will precisely match the nuclear energy level gap and resonant absorption will be maximised. The Doppler velocity will be zero if the source and absorber are structurally and chemically identical [139, 140]. It is necessary to emphasise that the proportions of the crystalline, amorphous and interfacial phases are taken to be proportional to their absorption areas, provided that the recoilless fractions are identical for all three kinds of iron sites.

4.3.3 Results 4.3.3.1 New Three-detector Set-up for the One-dimensional Angular Correlation of Positron Annihilation (1D-ACAR) Technique Angular correlation PAS involves evaluating the 511 keV  -photon distribution. The total momentum of both  photons that are generated at the moment of annihilation is equal to the momentum of the annihilated (e C , e  ) pair. Because the e C is thermalised before its annihilation in material, its momentum can be neglected. Therefore, the angular distribution of the  -photon pairs depends on the local electron momentum distribution in the observed material. This fact is frequently used in the study of mechanical, thermal or radiation-induced defects in materials [84, 141]. A new three-detector set-up was developed to measure irradiated RPV-steel specimens. It was necessary to minimise the unwanted 60 Co  -ray contribution to achieve precise measurements. This set-up is described in detail in [179].

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4.3.3.2 Comparison of Western and Russian RPV Steels by PAS and MS Techniques In total, eight unirradiated specimens from different commonly used RPV steels have been studied using PAS lifetime techniques since 1996 (mainly using PAS equipment from Rijksuniversity Gent). JRQ and EGF are Japanese and German ferritic steels that are often used as reference base metals in the construction of Western nuclear reactors. The sample 73W is an American Linde0124 weld metal. Aside from these, two surveillance specimens of base materials from Belgian nuclear power plants (NPP) at Doel (D4) and Chooz (CH) were studied. In order to compare Western types of RPV steels to Eastern types, 15Kh2MFA (specimens YA and YTA) and 15Kh2NMFA (XTA) RPV steels were measured too. This Russian second-generation Cr-Mo-V type of RPV steel has been used commercially in VVER-440 and VVER-1000 nuclear reactors built in the Central and Eastern European countries since the 1970s. Detailed results on this were published in [193].

4.3.3.3 MS-based Comparison of Original Irradiated and Unirradiated Surveillance Specimens Used for One, Two and Three Years in an Operating VVER-440 Reactor Only a few studies which suggest that MS is a potentially interesting tool for investigating the microstructural aspects of irradiation embrittlement of RPV steels have been performed so far [141–143]. In the framework of the Extended Surveillance Specimen Program 24, specimens designed especially for MS measurement were selected and measured in the as-received state before being placed into the core of the operational nuclear reactor [144]. The specimens (absorbers) consisted of 25–40 µm thick foils. Due to the higher neutron embrittlement and ageing sensitivity of VVER 440 (V-230) nuclear reactors, our study focused on the Russian 15Kh2MFA steel used in this older VVER440 reactor type. The samples were subjected for one, two and three years to a neutron fluence ranging from 7:8  1023 m2 to 2:5  1024 m2 . Taking into account the fact that the irradiation of the specimens was enhanced by their close proximity to the reactor core (leading to an “accelerating” factor of about 10), radiation treatment of the specimens after three years was equivalent to about 30 years in the real pressure vessel (the projected lifetime of VVER-440 V-230 reactors). More about this study can be found in [194].

4.3.3.4 PAS-based Comparison of Original Irradiated and Non-irradiated Surveillance Specimens Used for One, Two and Three Years in an Operating VVER-440 Reactor In the framework of the Extended Surveillance Specimen Program [144], several specimens that were originally prepared for Mössbauer spectroscopy measurements,

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but which were also suitable for PLEPS measurement because of their individual size (10  10  0:05 mm) and their polished surfaces, were selected and measured before and after their irradiation near the core of the nuclear reactor. For the first time, the pulsed low-energy positron system (PLEPS) [132] was used to investigate neutron-irradiated RPV steels. This system enables the study of microstructural changes in the region from 20 to 550 nm (depth profiling) within small and very thin (< 50 µm) specimens, therefore reducing the unwanted contribution from 60 Co radiation to the lifetime spectra to a minimum. This contribution is the limiting factor on the investigation of highly irradiated RPV specimens with conventional positron lifetime systems. Several approaches have been considered so far in order to tackle this problem where the 60 Co prompt-peak interferes with the physical part of the positron lifetime spectrum [145–147]. Aside from the PLEPS technique, one acceptable solution seems to be a triple-coincidence method using a 22 Na source [145, 147]. In this case, three  rays – one with an energy of 1274 keV and two with energies of 511 keV – accompany each event of positron annihilation, while only two  -rays result from the 60 Co decay. However, compared to conventional two-detector systems, the requirement for triple coincidence drastically reduces the rate of accumulation of positron lifetime spectra [145, 148]. In comparison, PLEPS reduces the measuring time by a factor of 500 and also enables the estimation of the defect concentration.

4.3.4 Discussion and Conclusions One of the most important tasks of nuclear-reactor safety research is to check the integrity of the reactor pressure vessel. Based on the results obtained, it is possible to conclude that the test methods used here could permit substantial progress to be made in the microstructural study of RPV steels and in the optimisation of the temperaturetime regime for the regenerative post-irradiation thermal treatment of RPVs. Steel embrittlement is a complex process that depends on various factors (thermal and radiation treatment, chemical compositions, conditions during preparation, ageing, etc.). The properties of reactor pressure vessel (RPV) steels and the influences of thermal and neutron treatments on these properties are routinely investigated by macroscopic methods such as Charpy V-notch and tensile tests. A number of semiempirical laws based on macroscopic data have been established, but these laws are unfortunately not completely consistent with all data and do not provide the desired accuracy [172–178]. Therefore, many additional test methods have been developed to unravel the complex microscopic mechanisms responsible for RPV steel embrittlement. RPV embrittlement poses one of limiting factors on the lifetimes of the vessels used in current nuclear power plants (NPPs). This problem is very serious in Eastern (Russian) nuclear reactors (VVERs). This is because VVERs employ a narrower gap between the outside surface of the core barrel and the inside surface of the RPV than is used in Western RPVs. The neutron flux and consequently the neutron

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fluence at the RPV wall is generally much higher for VVER-440 type reactors than for other equivalent types. This influence of neutron flux (even for neutrons with energies of > 0.1 MeV) on RPV embrittlement is much more pronounced than other contributions, such as those from the coolant temperature or the operational pressure in the primary circuit. Clear differences between Western and Eastern types of commercial RPV steel were observed using PAS LT and MS. According to the results from the PAS mean lifetime analyses, the observed differences in the values and behaviours of successive annealing curves are caused by different chemical compositions and different steel preparation technologies. This fact is particularly notable for 15Kh2MFA steel, for which the base material and a simulated heat-affected zone were studied simultaneously. Changes in steel microstructure due to a starting phase transition from bcc to fcc were observed in all Western types of RPV steels using PAS at  725–750 °C. For Russian RPV steels, this phase transition was not observed up to 800 °C. The same phenomenon also appeared with MS, where the presence of paramagnetic austenite was clearly detected at 750 °C in Western batches of steels and at 800–850 °C in Russians steels. The MS results show that MS distribution analysis can be used to distinguish between different steel types. Small differences in carbon concentration between Western base (JRQ) and weld (73W) metal is reflected in the small area fraction of the cementite doublet for the weld metal. Differences between Eastern- and Westerntype RPV steels are reflected in the overall shape of the derived Hhf . The larger fraction of “perturbed” area for the Eastern steel, the differences in Hhf and ı .Fe/ values, and the absence of a carbide doublet subspectrum are all due to the fact that the overall alloy-element concentration (especially Cr and V) for Eastern steels is larger than for Western-type steels. From MS measurements performed on the Western RPV steels A533B Cl.1 (JRQ, HSST03) and Linde 0124 weld (73W), we can conclude that the thermal treatment (up to 700 °C), irradiation (up to D 5  1019 n/cm2 ; En > 1 MeV) and post-irradiation heat treatment did not affect the MS parameters substantially. On the other hand, the first MS measurements performed on the Russian RPV steel 15Kh2MFA, irradiated with comparable neutron fluence ( D 6:71019 n/cm2 ; En > 0:5 MeV) in the framework of the Surveillance Specimen Program, confirmed observable changes in the MS parameters. By comparing the hardness course of the simulated heat-affected zones (HAZs) of the steels 15Kh2MFA and 15Kh2NMFA, it was found that the precipitation hardening of 15Kh2NMFA steel takes place faster than that of 15Kh2MFA steel. This means that shorter dwell times are sufficient to complete the precipitation re-ageing, so acceptable strength and plastic properties can be attained. The curves for the hardening kinetics at different temperatures were calculated using a temperature-time parameter called the Hollomon–Jaffe parameter: Hp D .20 C log t/T  103 ; where T is the annealing temperature in K and t is the duration of heating.

(4.133)

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Results are shown in Figures 4.45 and 4.46. During the heat treatment, a different level of structural tempering from that associated with the initial conditions takes place, depending on the temperature and duration of tempering. In principle, a varying degree of bainitic-martensitic mixture decomposition is involved. Moreover, secondary hardening by carbide-forming alloying elements also occurs. The structures from the initial conditions up to a significant hardness drop at 650 °C after 20 h of dwell time were analysed in steps, and are described in [79] in detail.

a) 0.160

Sample YT33 successively annealed in vacuum

Lifetime (ns)

0.150 0.140 0.130 0.120 0.110 13

14

15

16

17

18

19

20

21

22

H.-J. parameter

b) 60

Area under first sextet in ILEEMS spectrum

Area (%)

55 50 45 40 13

14

15

16

17

18

19

20

21

22

19

20

21

22

H.-J. parameter

c) Hardness HV10

500

Samples YT33 - YT64

450 400 350 300 250 200 150 13

14

15

16

17

18

H.-J. parameter Figure 4.46 Comparison of a PAS lifetime, b ILLEMS and c HV-10 results as a function of the Hollomon–Jaffe parameter for 15Kh2MFA RPV steel (identical specimens of the simulated heataffected zone, reactor VVER-440)

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The time dependencies for the hardening of the simulated HAZs of the steels 15Kh2MFA and 15Kh2NMFA were studied and compared with PAS lifetime and ILEEMS parameters (see Figures 4.46 and 4.47). There was a significant correlation between the hardness maxima on the one hand and the minima of the positron mean lifetimes and the Fe contents on the other. There is also an observable shift a) 0.160

Sample XT1 successively annealed in vacuum

Lifetime (ns)

0.150 0.140 0.130 0.120 0.110 13

14

15

16

17

18

19

20

21

22

21

22

21

22

H.-J. parameter

b) 0.160

Sample XT1 successively annealed in vacuum

Lifetime (ns)

0.150 0.140 0.130 0.120 0.110 13

14

15

16

17

18

19

20

H.-J. parameter

c) 500

Samples XT1 - XT32

Hardness HV10

450 400 350 300 250 200 150 13

14

15

16

17

18

19

20

H.-J. parameter Figure 4.47 Comparison of a PAS lifetime, b ILLEMS and c HV-10 results as a function of the Hollomon–Jaffe parameter for 15Kh2NMFA RPV steel (identical specimens of the simulated heataffected zone, reactor VVER-1000)

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in extreme values to the level of the Hollomon–Jaffe (H-J) parameter in the case of 15Kh2NMFA steel containing more nickel (extreme values at H-J  16) with respect to 15Kh2MFA steel (extreme values at H-J  17) that contains more chromium. This finding implies that: • At temperatures of about 500 °C, carbides (M3 C, MC) precipitate at grain boundaries and their presence causes maximum hardness; • The positron mean lifetimes reach their minimal values because defects such as vacancies, Frenkel pairs and clusters have vanished by the annealing stage; • The area of the first sextet in the ILLEMS spectrum is minimised through the annealing process because the maximum concentration of alloying atoms (in the close neighbourhood of Fe atoms) is on the surfaces of steel specimens. Specimens from the Slovak Extended Surveillance Specimen Program studied using the pulsed low-energy positron system (PLEPS) were measured in the as-received state and after being located in the operating nuclear reactor for one, two and three years using Mössbauer spectroscopy (MS). The deterioration of RPV steel specimens resulting from fast neutron bombardment is observable through the decrease in the pure ˛-iron component (fixed in all analyses at Hhf;2 D 33:0 T). This decrease was balanced by increased Hhf1 values of the first component, which can be attributed to the contributions of various atoms (Cr, Ni, V, Cu, Mn, etc.) at firstneighbour positions to the Fe atoms. Significant differences between the base and weld metals were observed, but the behaviour of the MS parameters following irradiation was similar in both cases (see Figure 4.48). While the values decreased during the first year of irradiation, they remained almost stable (base metals) or increased slightly (welds) upon increased irradiation treatment. It appears that the expected changes in material microstructure (the precipitation of elements like Cu or Cr, mainly in carbides) occurred mainly during the first period (1–2 years).

pure-Fe (%)

Area under Hf line of

40 30 20

S2 BM (3.unit) S2 BM (4.unit) S2 W (3.unit) S2 W (4.unit)

10 0 0

1E+24 2E+24 3E+24 Neutron fluence [m-2]

Figure 4.48 Changes in the area S2 under hyperfine field line of the component assigned to pure ˛-iron atoms that do not have any other elements in the first- or second-neighbour positions. The RPV specimens were irradiated for one, two and three years in the operational third and fourth units at Bohunice NPP (Slovakia). BM, base metal; W , weld

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These results confirm that the local environment of the Fe atoms in the bcc lattice of RPV steels as well as the creation of new defects that are observable by PAS techniques almost stabilises after some initial changes. On the other hand, longterm thermal treatment (at about 290 °C) can cause some defect re-annealing, and acts in the opposite manner to radiation-induced defects. Interactions between fast neutrons and lattice atoms can transfer energies ranging from a few eV to tens of keV. The primary knock-on atoms (PKAs) lose energy though interactions with both the bound electrons and the atoms of the solid. If the energy transferred to a lattice atom is greater that some threshold value Ed (typically > 40 eV), then the atom will be displaced from its lattice site, creating a Frenkel defect (i.e., a vacancy and an interstitial). If the PKA energy is much greater than a few keV, the PKA is able to displace many atoms, rapidly entering a regime where collisions occur at each lattice spacing (a displacement cascade). It is important to understand that during the evolution of a cascade, not only is a heavily damaged region containing a large number of displacement atoms produced, but that considerable point defect motion, recombination and clustering can also subsequently occur. Both vacancy and interstitial point defects are expected to be mobile in the temperature ranges of most operating pressure vessels. However, they are also expected to interact with solute atoms. Based on extensive positron studies performed on 15Kh2MFA steel [37,149,150] and metallurgical and TEM studies [40, 151], as well as MS results [152], it is clear that irradiation-induced carbides play an important role in strengthening and radiation embrittlement. TEM results for irradiated 15Kh2MFA steels show that the radiation damage has a heterogeneous structure, and contains dislocation loops and very fine VC or V4 C3 precipitates. Dislocation loops predominate in bainite structures, while VC is present mostly in the ferritic grains of the weld metal. According to several small-angle neutron-scattering (SANS) measurements performed on 15Kh2MFA steels [153], the reason for the irradiation hardening seems to be finely dispersed defects within the range 1–4 nm. Further, in steels containing residual levels of elements such as copper that are in supersaturated solution, radiationenhanced diffusion will occur at these temperatures, which leads to the formation of small clusters which can again harden the matrix [40]. Generally, thermal treatment together with neutron irradiation lead to a microstructure consisting of small clusters (< 5 nm in diameter) which hinder the free movement of dislocations, thereby producing an increase in the yield stress, the hardness and the ductile-to-brittle transition temperature of the material. In order to elucidate whether such a precipitate can trap positrons, the positron affinities AC for the host material and the precipitate were calculated [154]. The AC values were found to be relatively high and the positron lifetimes very short for perfect MC carbides. This fact confirms that perfect MC (M Cr, V, Ti, Mn, Fe, Zr, Nb) carbides are very dense materials that cannot trap positrons when embedded in the Fe matrix. In general, from a PAS point of view, radiation damage can be interpreted as a combination of radiation-induced point defects, dislocations and small vacancy clusters [129, 130] that occur mainly in the region of the precipitate– matrix interface.

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According to our measurements obtained using different lifetime techniques (at Gent, Bratislava and Munich) and our many attempts to fit the spectra with several components, the structures of RPV steels are so complex that only one or two steel components can be practically considered for PAS analysis. It is important to be very precise during sample preparation in order to exclude potential contributions from oxides, the source, back-diffusion, etc. A long positron lifetime component 2 D 260 ps, as reported in [155] from an extensive study of an Fe-1.25% C alloy, and attributed to positron trapping in cementite (Fe3 C) and at the cementite-ferrite interface, was not observed in our spectra (probably due to the tenfold lower concentration of C in the RPV steels we studied). PAS can identify not only differences between Western and Russian types of steel but also differences in the technologies used to prepare the same type of steel. It was confirmed that Russian steels are more sensitive to elevated temperatures (annealing) and their heat-affected zones were the most sensitive regions to thermal and neutron embrittlement in the reactor. The minimal values of mean lifetime (at about 500 °C) in the case of Russian steels confirm that the temperature used to anneal the first and second units of Bohunice NPP (Slovakia) and Loviisa NPP (Finland), 475 °C for 144 h, was chosen correctly. A rapid increase in vacancy-type defect formation in the temperature region 525–600 °C was observed in the Russian steels. The positron lifetime in Western steels decreases slowly up to about 750 °C, where a phase transition from a bcc to an fcc structure occurs. Many PAS works have focused on identifying optimal annealing procedures. One of the most appreciated of the author’s contributions to the “positron community” from an industrial point of view was the PAS-based confirmation of the optimal annealing temperature of 15Kh2MFA RPV steel (as shown in Figure 4.49). The figure shows the temperature region for annealing and shows that annealing at 500 °C causes the creation of a large number of small defects that are very probably connected to carbide precipitation. Positron annihilation can cause an increase in vacancy type defects due to irradiation [149, 157–168, 180], but the loads used during the RPV’s operational lifetime (1020 n/m2 ) are too small to produce large changes in positron annihilation parameters. Irradiation temperatures of around 300 °C cause the partial annealing of small (vacancy) defects, so that the positron lifetime remains practically unchanged or decreases after the initial period (this probably occurs after Cu, P and/or carbide precipitation, and is connected to restructuring). For more information, see [181] and Figure 4.50. An interesting depth profile was observed in the near-surface region in base as well as weld metals for Russian VVER-440 RPV steels (Figure 4.51). The increased defect concentration after the initial period of irradiation is much easier to see in the near-surface region. It decreases with depth into the bulk. A plausible explanation is linked to Cu precipitation and segregation at grain boundaries. Positron annihilation can also recognize nanosized defects. In Figure 4.52, the positron lifetime is affected by not only the number of vacancies in the defect but also its diameter. The graph shows two curves obtained using two different enhancement factors: one from Boronski and Nieminen [98] and the other from Stachowiak

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500

156.0 159.0 162.0 165.0

180

168.0 171.0

300

174.0

175

177.0 180.0

170

100

100 200

165

400

425

450

475

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t (°C)

300 400

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158.2 168.1 178.1 188.0 197.9 207.8 217.8 227.7 237.6

Depth (nm)

200

τ1(ps)

Depth (nm)

400

500 400

Figure 4.49 3D presentation of positron lifetime results for irradiated (neutron fluence: 1:25  1024 m2 ) and annealed Sv-10KhMFT steel (VVER-440 weld metal)

2.5x1024 151.0 169.6 188.3 206.9 225.5 244.1 262.8 281.4 300.0

2.0x10

300

1.5x1024

275 250

24

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MLT (ps)

225

0.0 100

200 300 400 Depth (nm)

500

176.0 204.4 232.8 261.1 289.5 317.9 346.3 374.6 403.0

200 175 100

2.5x1024 2.0x1024 1.5x1024 1.0x1024 5.0x1023 0.0

ce (m -2 )

5.0x1023

200

300

Depth

400

(nm)

Fluen

Fluence (m-2)

24

500

Figure 4.50 3D presentation of PLEPS results (MLT) for irradiated Sv-10KhMFT steel (weld metal). The first  140 nm were neglected due to possible surface defects

and Lach [182]. For the curve obtained using the factor from [98], we can see that the saturation of the lifetime with increasing cluster size is too slow. The reason for this is the incorrect behaviour of the corresponding enhancement factor at low electron densities (although the limit for zero electron density is correct). This is avoided in the approach used in [182], but in this case the resulting lifetimes are a bit too short for small vacancy clusters. Note that the positron surface state was not considered in these calculations [72]. These calculations were used also for positron studies of ITER first-wall materials [183]. It is not easy to assign the positron lifetime to just one type of defect. Calculated positron lifetimes for different types of defects in pure iron and different carbides in low-alloy Cr-Mo-V steel are shown in Table 4.20.

4.3 Third Barrier: Integrity of the Primary Circuit

a)

121

ZM - irradiated 270-290 250-270 230-250 290

210-230

270

190-210 170-190

250 MLT [ps]

150-170

230 168 210 266 190 170

Neutronfluenc

b)

510 2.5424

1.6424

7.81

0

23

150

Distance to the surface [nm]

381

e [m -2]

ZK-irradiated 260-270 250-260 240-250

270 260 250 240 230 220 MLT [ps] 210 200 190 180 170 160

230-240 220-230 210-220 200-210

Distance to the surface [nm]

7.8123 0

160-170

1.6424

170-180

2.5424

180-190

510 465 422 381 314 302 266 232 199 168 139

190-200

ce fluen tron Neu

-2 [m ]

Figure 4.51 3D presentation of PLEPS results in the form of the dependence of MLT on the neutron fluence in VVER-440 a base (ZM) and b weld (ZK) metals. The first  140 nm were neglected due to possible surface defects

However, due to a FWHM of around 200 ps, it is difficult to distinguish between all types of defects. Thus, the most common approach adopted is to group defects together (usually into two groups). One group comprises small defects like dislocations and mono- and divacancies together with the bulk value, while the second lifetime is mostly assigned to vacancy clusters. There have been several attempts to distinguish between edge and screw dislocations, which are characterised by life-

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Figure 4.52 The calculated dependence of the positron lifetime on vacancy cluster size in Cu. The full line was calculated according to Stachowiak–Lach approach. The dashed line was calculated according to the Boronski–Nieminen approach

Table 4.20 Calculated or measured positron lifetimes in Fe or in carbides Material Fe (bulk) Fe (dislocations) Fe (monovacancy) Fe (divacancy) Fe-3 vacancy cluster Fe-4 vacancy cluster Fe-6 vacancy cluster VC V0:86 Cr0:09 Mo0:04 Fe0:01 C Mo2 C Mo1:4 Cr0:6 C Cr7 C3 Cr23 C6 Mn26 C6 Fe3 C

Positron lifetime (ps)

Reference

110 165 175 197 232 262 304 99 105 112 116 107 112 99 101

[184] [185] [184] [185] [185] [185] [185] [186] [186] [186] [186] [186] [186] [186] [186]

times of 145 ps (screw) and 165 ps (edge) [187]. According to that work, positrons are mostly trapped at dislocation lines (65–85% of the positrons in the Russian RPV steel 15Kh2MFA had lifetimes of  150 ps).

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Of particular interest is the concentration of defects as a function of the irradiation dose and the thermal treatment used. Generally, these effects can be explored in positron studies only if the bulk lifetime can be resolved from the shortest lifetime, which is attributed to annihilation from defects. In the present case of saturation trapping, this proved impossible. Therefore, based on the individual lifetime spectra, we can only conclude that the total trapping rate  is larger than about 1010 s1 . However, using the variation of the mean lifetime av as a function of positron implantation energy, we can even estimate  in the case of saturation trapping. The problem was fully analysed in [188, 189]. Based on this theory, the total defect concentration can be estimated as:  Cd D (4.134) spec   I2 1 1  D Cd D  ; (4.135) I1 b d where: I1 ; I2 are the intensities of the positron lifetimes; b is the positron lifetime in the bulk; d is the positron lifetime in the defect. Figures 4.53 and 4.54 present results for  (the trapping rate) obtained using the procedure described above. The plausible value of 1015 s1 [129] was assumed for the specific trapping rate spec . Because of slight surface oxidation, this evaluation of  results in a systematic underestimate. A lower limit of 10 ns1 for  may be derived within the framework of the STM, since we have observed saturation trapping at defects. According to the results from our measurements performed on different irradiated RPV steels, the total trapping rate  in ns1 as well as the total defect concentration cd (the same values, but in ppm) increase slightly for both base and weld materials as a function of the irradiation dose (see Figure 4.52). The weld material (Sv10KhMFT) seems to be less sensitive to the changes caused by neutron irradiation or by post-irradiation heat treatment than the base material (15Kh2MFA) (see Figure 4.53). Nevertheless, the differences in the positron trapping rate  were not too large. It seems reasonable to relate the observed trapping rates with those derived for trapping in precipitated carbides from electron microscopic images [72]. Accordingly, in 15Kh2MFA, the trapping rate in chromium carbides (Cr7 C3 , Cr23 C6 ) is predicted to be Cr D 1:8  108 s1 , and that in vanadium carbides as VC D 2:2  1010 s1 [72]. Thus, precipitated vanadium carbide could indeed account for the observed trapping rates. On the other hand, as shown by calculations [163], positrons experience a repulsive potential from carbides embedded in an iron matrix. Therefore, only the defects at the iron–carbide interface could provide acceptable trapping sites for positrons. The total trapping rate  and the defect concentration cd are stable or increase slightly for 15Kh2MFA steel as a function of the Hollomon–Jaffe parameter, which

124

4 Barriers Preventing the Release of Fission Products Annealing experiment in region of (400–550°C/0.5h) ZM1Y – base metal irradiated for 1 year ZK1Y – weld metal irradiated for 1 year 40

κ [ns-1] = cd [ppm]

30

20

10 ZM1Y ZK1Y 0 15

16

17

18

Hp = T.(20+logt)10-3

Figure 4.53 The total trapping rate versus the Hollomon–Jaffe parameter in isochronally annealed (step 25 °C) specimens of base (ZM) and weld (ZK) alloys after one year of irradiation in the reactor (neutron fluence:  7:8  1023 m2 ). The lower limit for , as derived from saturation trapping according to the STM, is 10 ns1

Irradiated RPV–steels after 1, 2 and 3 years in reactor 20 18 16

ZM3Y

κ [ns-1] = Cd [ppm]

14 ZM2Y

12 10 8

ZM1Y

6

ZK3Y

4

ZK2Y Zk1Y

2 0 15

15,2

15,4

15,6

15,8

16

Hp=T.(20+logt)10-3

Figure 4.54 The total trapping rate versus the Hollomon–Jaffe parameter in RPV specimens from base (ZM) and weld (ZK) alloys after one, two and three years residence in reactor irradiation chambers (neutron fluence: 7:8  1023 m2 to 2:5  1024 m2 ). The lower limit for , as derived from saturation trapping according to the STM, is 10 ns1

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calculates the combined influence of the annealing temperature T (K) and the time t (s) [78,190]. In the range 15.5–16.5 (corresponding to the temperature region 400– 450 °C), the defect concentration increases. On the other hand (Figure 4.53), there is a marked decrease in defect lifetime in the same range. A simple explanation for this could be the dissolution of precipitates and defect clusters, which would reduce the average size of the defects and – by the same process – increase the concentration of the defects. Some new PAS lifetime techniques such as positron microscopy [191] appear to be very promising for studying defects. Figure 4.55 shows a comparison of the defect imaging achieved using cathodoluminiscence (CL) and SEM with pictures obtained using positron microscopy in Munich (University of Bundeswehr). The most important problem is actually the relative low positron beam intensity. It will be significantly improved after moving this unique microscope to the FRM II reactor in Garching. A very effective materials study in the near-surface region can be performed using a positron microscope. To improve this technique, a special approach was developed in the PAS group in Munich that was based on cutting specimens at a very acute angle; see Figure 4.56 or [191, 192]. In the past few years, several original irradiated RPV steel samples have been investigated by PAS in order to elucidate microstructural changes due to the thermal and neutron treatments resulting from the operating conditions in NPPs. The main aim of such investigations has been to increase the safety margin before RPV brittle fracture. The only way to reduce this irradiation embrittlement is thermal annealing. Non-destructive test methods like PAS in combination with proven destructive test methods can aid progress in optimising the temperature–time regime for post-irradiation thermal treatment. This approach is especially useful in the case of highly radioactive materials, and also in those cases where only small amounts of irradiated materials are available.

Figure 4.55 Comparison of defect imaging by a cathodoluminiscence and b SEM versus pictures obtained using positron microscopy in Munich

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Figure 4.56 Explanation of a positron annihilation lifetime technique based on positron microscopy for studying vacancy-type defects as a function of material depth [192]

In the future, the application of PAS techniques to the development of new types of steels with well-defined parameters (materials for fusion reactors, etc.) or to evaluations of the effectiveness of post-radiation heat treatments can be foreseen. The utilisation of a high-precision positron microscope in RPV steel investigations would surely be a good example [156].

4.4 Contribution to VVER-440 Steam Generator Safety 4.4.1 Corrosion of VVER-440 NPP Steam Generators The steam generator is the most corrosion-sensitive component of a nuclear power plant (NPP). Corrosion and metallurgical defects – when exposed to thermal and pressure treatment involving the bombardment of the base material with chlorine ions – can cause various kinds of damage to metals, including corrosion cracking. Different types of corrosion attack are presented in Figure 4.57. The structure of the corrosion layer and examples of corrosion cracks in CrMoV steels are presented in Figures 4.58 and 4.59, respectively. Steam generators (SGs) are generally one of the most important components in any nuclear power plant (NPP), and they are an important influence on safe long-

4.4 Contribution to VVER-440 Steam Generator Safety A

B

127 D

G4

Figure 4.57 Types of corrosion attack: A, steady attack; B, non-steady attack; C, spotted attack; D, hole attack; E, point attack; F, subliminal attack; G, selective attack; I, intercrystalline attack; J, transcrystalline attack; K, extraction attack; L, corrosion cracks

α-Fe2O3 γ-Fe2O3

Fe3O4 Steel

Figure 4.58 Typical corrosion layer in a construction material (carbon steel) and types of oxides that arise in a water-steam environment

term operation. Russian water-cooled and water-moderated reactors (VVER) are unique because of the horizontal disposition of the SGs. This configuration has several advantages (large inventory of cooling water in a loss of coolant accident, good accessibility, large heat exchange surface, etc.) but also some disadvantages, which must be taken into account during NPP operation and maintenance. Material degradation and corrosion/erosion processes are serious risks to reliable long-term operation. About 10–15 years ago, the feed water pipes were changed in all of the SGs in all four units at Bohunice (V-1 and V-2: in total 24 SGs). A new pipe system design was also introduced.

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Figure 4.59 Examples of a corrosion cracks and b the growth of corrosion fatigue (CrNiMoV steel)

The variability of the properties and the compositions of the corrosion products of stainless Cr-Ni and mild steels as a function of the operating conditions (temperature, acidity, etc.) of the NPP is so large that, in practice, it is impossible to determine the properties of the corrosion products from the theoretical data only in a real case. Since decontamination processes for the materials of VVER-440 secondary circuits are under development, it is necessary to obtain the information required by measuring and analysing real specimens [140].

4.4.2 Advantages of Mössbauer Spectroscopy in Corrosion Studies As mentioned earlier, the phenomenon where a  -ray photon is emitted and absorbed by nuclei without any energy loss from nuclear recoil and without thermal broadening is known as the Mössbauer effect. Its unique feature is the production of monochromatic electromagnetic radiation with a very narrowly defined energy spectrum that allows minute energy differences to be resolved [138, 139]. Mössbauer spectroscopy (MS) is a powerful analytical technique because of its specificity for one single element and because of its extremely high sensitivity to changes in the atomic configuration in the near vicinity of the probe isotopes (in this case 57 Fe). MS measures hyperfine interactions, and these provide valuable and often unique information about the magnetic and electronic states of the iron samples, their chemical bonding to coordinating ligands, the local crystal symmetry at the iron sites, structural defects, lattice-dynamical properties, elastic stresses, etc. [140,195]. Hyperfine interactions include the electric monopole interaction (i.e., isomer shift), the electric quadrupole interaction, (i.e., quadrupole splitting), and the magnetic dipole (or nuclear Zeeman) interaction (i.e., hyperfine magnetic splitting).

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These interactions often give us a detailed insight into the structural and magnetic environment of the Mössbauer isotope. Indeed, more than four decades after its discovery (1958), Mössbauer spectroscopy continues to develop as a sophisticated scientific technique, and it is often the most effective way of characterizing a range of structures, phases, and metastable states. In general, a Mössbauer spectrum shows different components if the probe atoms are located at lattice positions that are chemically or crystallographically nonequivalent. For instance, from the parameters that characterise a particular Mössbauer subspectrum, it is possible to establish whether the corresponding probe atoms reside in sites that are not affected by structural lattice defects, or whether they are located at defect-correlated positions. Each compound or phase that contains iron has characteristic parameters in its Mössabauer spectrum. This means that the method is suitable for quantitative as well as qualitative analysis. Mössbauer spectroscopy is also non-destructive and requires only relatively small quantities of samples ( 100 mg) [169–171, 196–198]. In the work described here, Mössbauer spectroscopy was used to perform a precise analysis of the phase compositions of corrosion products in selected areas of primary and secondary circuits and SGs. Interpreting the results obtained with respect to the safety and long-term operation of the NPP is not an easy or straightforward task. However, we can draw upon over 25 years of experience in this field, so there is already a good foundation for evaluating the results. Optimising the chemical regimes used during reactor operation as well as the decontamination and passivation regimes would appear to be an excellent way to apply this experience.

4.4.3 Safety Analyses of Slovak Steam Generators and the Latest Upgrades The safe and reliable operation of steam generators is essential to the safe operation of the whole NPP, but it is also crucial to the economic parameters for the unit. The steam generator must be able to transfer the heat from the reactor in all regimes: during normal operation or when an accident has occurred. It is well known that VVER-440 units have horizontal steam generators with much larger amounts of cooling water in the SG tank than the vertical steam generators normally used in western NPPs. These horizontal steam generators undoubtedly provide larger margins in cases where primary coolant is lost through incident or accident. On the other hand, due to their horizontal design as well as their six loops with additional welds and pumps, they occupy a huge area, which is a limiting factor in the containment construction of the units. Exchanging steam generators is an extremely difficult task (and, in some reactor types, an almost impossible one), so the optimal operation and clever maintenance (upgrades) of SGs is one of the essential duties of NPP staff. Based on operational experience, mitigating damage and leak tightness defects in pipelines or collectors takes up much more time and money than prevention mea-

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sures. Bear in mind that there is currently a drive in the nuclear industry towards prolonging the lifetimes and increasing the power of NPPs (one of the essential goals of European Commission 7FP-NULIFE). Fortunately, VVER-440 steam generators were designed with a huge power reserve (it is possible to overload them by 20%). Aside from several leakages in the primary pipes ( D 16 mm), which in the case of VVER-440 SGs are relatively easily solved (blended), corrosion deposits in the feed water piping system have been found in many VVER-440 units [199]. Damage to this system has mostly been caused by corrosion/erosion attacks on materials known as “black steels,” which are insufficiently resistant to corrosion. Based on experiences from Finland, other countries (including Slovakia) have changed the old feed water piping systems of the SGs in their NPPs. At this point, it is worth noting that the incident at unit 2 of the Paks NPP (Hungary, 2003) related to the cleaning of fuel assemblies in a special tank, which was necessary due to insufficient passivation of the pipelines in the SG after steam water pipe system exchange in 1997. All of the steam generators at the four VVER-440 units in Bohunice were gradually modified. At that time, there were two options for the new feed water pipeline system, namely the Vítkovice a.s. design and the OKB Gidropress design. The former solution was selected and later implemented as the so-called Bohunice solution. Ten years of experience with the upgraded steam generators have since been gained. A detailed description of the VVER-440 steam generators delivered to Bohunice NPP is provided in [200–202]. The safety analyses were performed in 1977 by OKB

Figure 4.60 VVER-440 (Bohunice) steam generator: cross-section (Bohunice renovation)

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131

Gidropress according to the Russian norms. The Russian designer and manufacturer made the feed water pipelines (secondary side) from carbon steel (GOST norms 20K and 22K). The water inlet pipe was connected to the T-junction. From this point, two pipelines with nozzles distributed the cooling secondary water within the space between the primary pipes. Several problems that had occurred in other NPPs were published in [195, 197, 198, 203]. One disadvantage of such steam generators is the poor accessibility to the T-junction and the pipes in the bundle. The steam generator denoted RGV-4E is a one-body SG [200–202]. The heatexchange area is incorporated inside as the surface of the bundle of primary pipes, and has a U-shape. The ends of these pipes are fixed to the walls of the primary collector. Inside the SG body are several separators and a system for steam water distribution. The PGV-4E steam generator permits dry steam production with a pressure of about 4.61 MPa at a temperature of about 258 °C. The basic 1977 design was improved after 1994 by installing a new feed water pipeline system. There was also a change in the type of steel used in these pipes. Instead of conventional carbon steel, austenite steel was used in the distribution boxes as well as the feed water pipes.

Figure 4.61 VVER-440 (Bohunice) steam generator: A–A cross-section (Bohunice renovation)

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4 Barriers Preventing the Release of Fission Products

All of the components in the renovated Bohunice feed water pipeline system were ˇ made of austenitic steel, according to the Czechoslovakian norm CSN, class 17. The advantages of this new construction include not only higher resistance against corrosion but also much more comfortable visual inspection. The renovations are illustrated in Figures 4.60 and 4.61. The feed water enters the pipeline distribution system via a nozzle and passes into the left and right inlet lines. From there, the water flows into chambers via pipes ( D 44:5  4 mm) and exits via ejectors. This flow is mixed with boiler water, so the final flow in the small primary pipes is not extremely hot and does not cause a very high thermal load. The circulation in the SG tank was also improved in the renovations, and locations with increased salt concentration were reduced. The main advantage of this approach is that a visual inspection of the feed water pipe can be performed directly due to the placement of the whole water distribution system over the primary pipe bundle. Using this system, any potential defects are easier to observe. Another advantage arises from the seven boxes with ejectors that mix the feed water with boiler water, thus decreasing the thermal load. An additional advantage is that it is possible to check and exchange of the distribution boxes if they get damaged.

4.4.4 Experimental Evaluation of Corrosion Products Using Mössbauer Spectroscopy Analyses To perform the experimental measurements, several specimens containing corrosion products were taken from different parts of all of four units at Bohunice NPP. In the first step, the corrosion process in the steam generators was studied. The corrosion layers were separated by scraping the rust off the surface, and the powder samples were studied by transmission Mössbauer spectroscopy. It should be noted that the gamma spectroscopic measurements showed no evidence of the presence of lowenergy  -radiation emission from the samples. Later, corrosion products were also collected from different parts of the secondary circuit components, and several filter deposits were analysed too. A room-temperature Mössbauer study was performed for two different steam generator materials using a conventional transmission Mössbauer spectrometer with the source 57 Co in a Rh matrix. The spectra were fitted using the NORMOS program. The original STN 12022 material used in unit 4 (SG46) for 13 years was compared to the STN 17247 steel used in unit 3 (SG35) for about five years (1994–1998). The chemical compositions of both materials are shown in Table 4.21. Samples of corrosion products scraped from different parts of the steam generators SG35 and SG46 were analysed. The corrosion particles were homogenised by granulation and sieved through a 50-µm wire sieve. The advanced evaluation of phase analyses of corrosion products from different parts of VVER-440 steam generators via Mössbauer spectroscopy is our ongoing

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Table 4.21 Chemical compositions of the investigated base materials Steam Type generator of steel

Chemical composition (weight %) C

Mn

Si

Cr

Ni

Ti

P

Cu

SG35

STN 17247

Max. 0.08

Max. 0.08

Max. 1.0

17.0– 19.0

9.5– 12.0

Min. 5  %C

Max. 0.045

–

SG46

STN 12022 (GOST 20K)

0.16– 0.24

0.35– 0.65

0.15– 0.30

Max. 0.25

Max. 0.25

–

0.04

Max. 0.3

and unique contribution to this area, and comprises over 25 years of scientific work. The early years (mostly the 1980s) were important since improvements to the Mössbauer technique were made during that period. The benefits derived from that period mostly encompass building up experience, optimising measurement conditions, and improving evaluation programs [171]. Unfortunately, not all of the specimens were well defined. Considering the different levels of technique and evaluation procedures employed, it would not be appropriate to compare results from that period with the results obtained from measurements performed after 1998.

4.4.4.1 Comparing the Corrosion Products Before and After the Changes to the SGs During the period 1994–1999, we focused our study on a comparison of the phase compositions of corrosion products taken from Bohunice NPP before and after the changes were made to the feed water pipeline system. A schematic of VVER steam generators is presented in Figure 4.62. The locations at which the corrosion specimens were scraped from the surface are also indicated. Serious damage was observed in the region of the T-junction (Figure 4.64) as well as the pipe collector and outlet nozzles on many VVER440 SGs after approximately ten years of operation [199, 204]. Therefore, the original feed water distribution system used in the SGs of Jaslovské Bohunice NPP was replaced by an advanced feed water distribution system of novel design [205, 206]. This advanced system consists of a V-shaped junction connected to the left and right water distribution chambers, both of which are located above the tube bundle, as well as a few feed water boxes with water ejectors that are inserted into the tube bundle and connected to the distributing chamber by distribution pipelines. After five years of operation in SG35, one feed water box and the corresponding distributing pipes were replaced with new ones during an NPP outage in order to allow an analysis of their overall condition and the corrosion products on their walls. For comparison, some parts of the original feed water distribution system from SG46 were cut out and analysed.

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Figure 4.62 Cross-section of SG46 (numbers indicate the positions at which the specimens were scraped off the surface)

More than 50 specimens were collected from the Bohunice NPP secondary circuit in 1998–2000. The investigation focused mainly on the corrosion processes that had occurred in SG35 (new design) and SG46 (old design). Nevertheless, additional measurements performed on the corrosion products from SG31 and SG32 confirmed that the same corrosion process had occurred in all six steam generators of one reactor unit, and that the corrosion layers are altogether identical in some places. All of the measured specimens contained iron in magnetic and also often in paramagnetic phases. The magnetic phases corresponded to near-stoichiometric magnetite ( -Fe3 O4 ), hematite (˛-Fe2 O3 ), and in some cases iron carbides. Such paramagnetic fractions produce a doublet and a singlet in Mössbauer spectra. The MS parameters are close to those of hydroxide (FeOOH) or those of small, so-called superparamagnetic particles of iron oxides (hydroxides) with a mean diameter of about 10 nm (see Tables 4.22 and 4.23). MS confirmed its excellent capacity to identify the phase compositions of steel samples despite their form (sawdust) and the relative small amounts available ( 100 mg). Our experiences in performing such measurements on different VVER440 construction materials were published in [198, 207, 208]. Among other works, [209] should also be mentioned. MS confirmed that STN 17247 steel had an austenitic structure and STN 12022 steel a ferrite structure. The differences between these two materials are quite apparent (see Table 4.22 and Figures 4.63 and 4.64). Significant differences in corrosion layers and material quality were observed during in situ visual inspections performed at SG35 (1998) and SG46 (1999), as well

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135

Table 4.22 MS parameters of the base materials used in steam generators SG35 and SG46 Sextets

Singlet

Sample (sawdust)

H1 (T)

Arel (%)

H2 (T)

Arel (%)

H3 (T)

Arel (%)

IS (mm/s)

Arel (%)

SG35 SG46

29.3 33.3

18.7 80.5

26.3 31.2

18.5 19.5

22.8 –

27.4 –

0:12 –

35.4 –

Accuracy

˙0:1

˙0:5

˙0:1

˙0:5

˙0:1

˙0:5

˙0:04

˙0:04

Table 4.23 MS parameters of corrosion products taken from the steam generator SG35a Magnetite HB Arel (T) (%)

Sample

HA (T)

Arel (%)

L754 L755 L757 L758 L789 L790 L759 L777 L786 L787 L760 L761 L762 L779

49.0 49.0 49.0 49.0 49.0 49.0 49.0 49.0 49.0 49.1 49.0 49.0 49.1 49.0

35.0 35.3 34.8 34.1 34.4 34.9 35.4 35.0 35.2 36.5 34.1 35.0 34.8 33.4

Accuracy

˙0:1 ˙0:5 ˙0:1 ˙0:5

a

45.9 45.9 45.9 45.9 46.0 46.0 45.9 45.9 46.0 46.0 45.9 45.9 46.0 45.9

65.0 64.7 65.2 62.3 65.6 64.3 63.9 65.0 64.8 56.1 64.3 63.9 56.4 62.9

rAB (a.u.) 0.538 0.546 0.534 0.547 0.535 0.543 0.534 0.538 0.545 0.651 0.530 0.547 0.617 0.531

Doublet IS QS (mm/s) (mm/s)

0.22

0.67

Arel (%)

2.0

˙0:04 ˙0:04 ˙0:5

Singlet IS Arel (mm/s) (%)

0:20

3.6

0:18 0:20

0.8 0.7

0:20 0:17 0:23 0:20 0:10

5.4 1.6 1.1 8.8 3.7

˙0:04 ˙0:5

Samples L754–L757 were taken from the feed water pipes in situ during reactor shutdown. Samples L758–L790 were taken from the same steam generator at selected parts of a feed water dispersion box (see Figure 4.65, positions 1–13)

in the MS results. The feed water tubes in SG46 were significantly corroded after 13 years of operation. Our results confirmed that a thin oxidation surface was present in the observed steam generator SG35 after five years of operational time, and the corrosion samples completely lacked base material particles. Magnetite was identified as the dominant component in all of the studied samples (see Table 4.23). The Mössbauer spectrum of surface layer in both steam generators (SG35 and SG46) is the superposition of two sextets with hyperfine magnetic fields HefA D 49:4 T and HefB D 45:8 T. Sextet HefA corresponds to the Fe3C ions at tetrahedral (“A”) sites and sextet HefB corresponds to Fe2C and Fe3C ions at octahedral (“B”) sites in magnetite’s spinel-type structure (Fe3 O4 ).

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relative transmission

1.00

0.98

0.96

0.94

-10

-5

0

5

10

5

10

velocity (mm/s)

Figure 4.63 MS spectrum of the base material of SG35

relative transmission

1.00

0.98

0.96

0.94 -10

-5

0

velocity (mm/s)

Figure 4.64 MS spectrum of the base material of SG46

In contrast to magnetite, whose spectrum is characterised by two sextets, the hematite phase present in the powders gives a single sextet. The relatively narrow line width ( ) of the ˛-Fe2 O3 (mainly 0.24–0.26 mm/s) indicates the presence of a well-crystallised phase with few, if any, substitutions of other elements for Fe. However, some spectra (mainly from filter deposits studied later) exhibited both a smaller hyperfine field and a larger width (about 0.33–0.34 mm/s), which could indicate poorer crystallinity and/or a higher degree of substitution. These findings are in good agreement with those obtained by E. De Grave [210]. Similar results (which also focus on corrosion products from VVER-440 construction materials) were published in [211–213]. For ideal stoichiometric Fe3 O4 , the quantity rAB (the ratio between the A and B subcomponent areas) is equal to 0.535. In the case where magnetite is the dominant (sole) phase in the sample, the deviation from the ideal value of rAB is minimal

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137

Figure 4.65 Positions of the corrosion product specimens taken from the feed water dispersion box (SG35)

(see Table 4.23). Significant deviations could be explained by a small degree of oxidation of magnetite, resulting in the presence of vacancies or substitution by non/magnetic irons in the octahedral sublattice. Slight levels of Fe substitution by other elements (Mg, Ni, Cu, . . . ) in the magnetite lattice is not unlikely, and this has a similar effect on the A-to-B site area ratio. Therefore, it is not possible to draw any strong, quantitative conclusions about the degree of oxidation. Qualitatively, it can be inferred that the degree must be very low. During visual inspection of a removed feed water dispersion box (1998), two undefined loose metallic particles were found lodged in one of the outlet nozzles. Both were homogenised and analysed by MS. These highly corroded parts were found to originate not from the 17247 steel but highly probably from GOST 20K steel (they were probably some particles from the corrosion deposit at the bottom of the steam generator that had been moved by flow and ejection effects into the nozzle). Mössbauer measurements on the corrosion specimens scraped from different positions on the feed water distribution system show that the outside layer consists exclusively of magnetite while the inside layer also contains hematite (Table 4.24). The amount of hematite decreases in successive steps towards the steam generator. The probable reason for this is that there is boiling water outside the system at a temperature of approximately 260 °C with high salt concentrations, while there is feed water at temperatures up to 225 °C inside. Changes can occur to the inside temperature in the region (158–225 °C) depending on the operating regime of the high-pressure pumps in the NPP secondary circuit. The most corroded areas of the original feed water distributing system are the welds in the T-junction (see Figure 4.66). Due to dynamic effects of the feed water flow, with local dynamic overpressures of 20–30 kPa or local dynamic forces of up

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Table 4.24 MS parameters of corrosion products taken from the steam generator SG46a CODE

M005 M006 M007 M008 M009 M010 M012 M013 M014 M015

Hematite H1 Arel (T) %

50.0 16.9 51.5 13.4 51.5 12.5

Accuracy ˙0:1 ˙0:5 a

Magnetite HA Arel HB Arel (T) % (T) % 49.0 49.1 49.2 49.0 49.1 49.1 49.2 48.8 49.0 48.5

35.4 36.5 25.6 35.6 32.1 36.5 31.9 25.3 9.9 6.0

45.8 45.9 45.8 45.9 45.9 45.8 46.0 45.7 45.8 45.6

H4 (T)

Base material Arel H5 Arel % (T) %

64.6 63.5 38.2 64.1 54.5 63.5 55.6 40.5 13.6 8.6

33.0 30.2 30.8 4.0 33.0 66.6 30.7 9.9 33.0 73.1 30.6 12.3

˙0:1 ˙0:5 ˙0:1 ˙0:5

˙0:1 ˙0:5 ˙0:1 ˙0:5

33.0

Doublet 1 IS1 Arel (mm/s) %

1.6

Doublet 2 IS2 Arel (mm/s) %

0.84 17.7

˙0:1 ˙0:5

˙0:1 ˙0:5

Samples M006, M008, M010 were taken from the outside surface (Figure 4.62, positions 1, 2, 3), and samples M007, M009, M012 from the inside surface of the feed water pipe (at to the same positions 1, 2 and 3, respectively). Sample M015: see Figure 4.66, position 7.

Figure 4.66 Positions of corrosion product specimens taken from the feed water dispersion tube (SG46)

to 1000 N (in the water at a pressure of about 4.4 MPa) on the inner pipe wall in the region of the T-junction, the content of corrosion products was reduced and shifted to the whole secondary circuit. Particles of SG46 base material from the feed water tube were also identified in sediments.

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139

4.4.4.2 Results from Visual Inspection of the Heterogeneous Weld on SG16 in April 2002 In the period 2002–2003 we focused on performing phase analyses of corrosioninduced damage to feed water pipelines in SG16 near the heterogeneous weld. Visual inspections were done, and original in situ specimens were scraped off. The conclusions from the visual inspections (performed on 19 and 29 April 2002 at SG16) were as follows. SG16 was dried below the level of the primary pipeline bundle and decontaminated. No defects or cracks were identified during the visual inspection of the internal surface of SG16 as well as the hot and cold collectors (after 23 years of operation). The SG16 was in excellent health, with minimal corrosion layer thickness or other deposits. Comparing with the results of the visual inspections we performed in 1998, SG16 was in better condition than SG35 or SG46 (14 and 13 years in operation, respectively). Moreover, the radiation situation after the decommissioning was twofold better. Visual inspection on 29 April 2002 focused on the heterogeneous weld, which connects a feed water pipe made of carbon steel (GOST 20K) to a new feed water pipeline system made from austenitic steel (CSN17248). Several samples were taken for MS analysis from the weld as well as the surrounding area in the form of powders or small particles (descriptions of the samples are given in Table 4.25 and Figures 4.67 and 4.68). The heterogeneous weld was well polished.

Table 4.25 Descriptions of specimens taken from the region of the heterogeneous weld Sample no.

Description

2.11 2.12 2.13

Heterogeneous weld Feed water pipeline (GOST 20), 10 cm from the heterogeneous weld Feed water pipeline (GOST 20), about 40 cm from the heterogeneous weld, close to the internal body surface of SG16 Internal body surface, about 1 m below the feed water pipe inlet Internal body surface, about 50 cm above the feed water pipe inlet

2.14 2.15

Figure 4.67 Design of SG16, viewing from the top

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Figure 4.68 Cross-section of SG16; the locations at which the specimens were taken are indicated

After visual inspection, the corrosion phase compositions of the samples taken from close to the heterogeneous weld were evaluated. The MS results are summarized in Table 4.26.

4.4.4.3 Results from SG11 (2004) Four powder specimens were taken from SG11 for MS analysis. These specimens are described in Table 4.27, and the results of the MS analyses are shown in Table 4.28. The dominant phase composition of the corrosion products taken from SG11 was hematite Fe2 O3 (66.4% at the hot collector, 80.8% at the cold collector). The rest is from magnetite Fe3 O4 , which gives two sextets H2 and H3 with contributions of 31.7% and 18.1%, respectively. The last component is a paramagnetic doublet D1 , which is assumed to be from iron hydroxides – very probably lepidocrocite ( -FeOOH). This doublet contributes 1.9% and 1.1%. The magnetite present in all samples is almost stoichiometric (the ratio Fe3C /Fe2C tends to 2.0). The significantly lower fraction of magnetite in the specimen from the hot collector can be ascribed to two parallel factors:

˙0:1 ˙0:04 ˙0:04 ˙2

8.0 75.9 77.2 41.1 51.7

Accuracy

0.25 0.26 0.26 0.26 0.26

51.9 51.6 51.6 51.6 51.8

0:18 0:21 0:21 0:21 0:21

Hematite H1 QS1 IS1 Arel1 (T) (mm/s) (mm/s) (%)

2.11 2.12 2.13 2.14 2.15

Sample

Table 4.26 Mössbauer spectral parameters

0.17 0.16 0.17 0.16 0.17

3.8 9.1 9.2 22.0 18.3

45.9 45.8 45.9 45.8 45.9

0.57 0.56 0.57 0.55 0.54

8.0 14.1 12.9 36.9 29.2

Magnetite IS2 Arel2 H3 IS3 Arel3 (mm/s) (%) (T) (mm/s) (%)

˙0:1 ˙0:04 ˙0:1 ˙0:1 ˙0:04 ˙2

49.0 49.0 49.0 49.0 49.1

H2 (T)

˙2

11.8 23.2 22.1 58.9 47.5

Mag. total (%)

Metallic iron IS4 Arel4 (mm/s) (%)

˙0:1 ˙0:04 ˙2

33.0 0:11 12.8 – – – – – – – – – – – –

H4 (T)

0:19 67.4 0:21 0.9 0:21 0.7 – – 0:21 0.8 ˙0:04 ˙0:04 ˙2

– 0.40 0.40 – 0.40

Doublet/singlet QS4 IS4 Arel4 (mm/s) (mm/s) (%)

4.4 Contribution to VVER-440 Steam Generator Safety 141

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Table 4.27 Specimens from SG11 analysed in 2004 Sample

Origin

Date of extraction

2.16 2.17 2.18 2.19

Hot collector, HC-SG-11 Cold collector, SC-SG-11 SG11 sediments SG11 cooler sediments (surface of pipelines)

9:00 h on 15/03/04 9:00 h on 15/03/04 10:00 h on 16/03/04 10:00 h on 16/03/04

Table 4.28 MS results for specimens taken in 2004 from SG11 in Bohunice V1 Hematite Sample H1 QS1 IS1 Arel1 (T) (mm/s) (mm/s) (%) 2.16 2.17 2.18 2.19

51.6 51.6 51.6 51.6

0:21 0:21 0:21 0:21

0.26 0.26 0.26 0.26

66.4 80.8 33.4 40.3

Magnetite H2 IS2 Arel2 H3 IS3 Arel3 (T) (mm/s) (%) (T) (mm/s) (%) 49.1 49.1 49.0 49.0

0.17 0.16 0.16 0.16

12.1 6.6 22.6 20.5

45.9 46.0 45.9 45.9

0.56 0.55 0.55 0.56

Doublet QS1 IS1 Arel1 (mm/s) (mm/s) (%)

19.6 11.5 42.9 38.0

0.53 0.47 0.52 0.52

0.23 0.21 0.09 0.13

1.9 1.1 1.1 1.2

• a difference in temperature ( 298 °C at the HC and  223 °C at the CC); but mostly; • The secondary water flowing in the vicinity of the hot collector is very dynamic, so it very probably removed the corrosion layer from the surface of the collector.

4.4.4.4 The Most Recent Measurements of Corrosion Products at Jaslovské Bohunice NPP (2006–2008) Six samples were collected for Mössbauer effect experiments from different parts of Bohunice NPP units 3 and 4 and prepared by crushing them to powder (Table 4.29). These samples consisted of corrosion products taken from a small coolant loop associated with the pumps (sample 3.1), deposits scraped from filters that filter SG feed water during operation (sample 3.2), corrosion products taken from SG42 pipes at a low level (sample 3.3), a mixture of corrosion products, ionex and sand taken from the filter of the condenser for TG42 (sample 3.4), a deposit from the filters after refiltering 340 l of feed water from SG S3-09 during passivation on 27/28 May 2008 (sample 3.5), and finally a deposit from the filters after refiltering 367 l of feed water from SG S4-09 during passivation on 27/28 May 2008 (sample 3.6). All of the samples were measured at room temperature in transmission geometry using a 57 Co(Rh) source. Calibration was performed with ˛-Fe. Hyperfine parameters of the spectra including the spectral area (Arel ), isomer shift (IS), quadrupole splitting (QS) and the hyperfine magnetic field (Bhf ) were refined using the CONFIT fitting software [214]. They were determined with accuracies of ˙0:5% for the relative area Arel , ˙0:04 mm/s for the isomer shift and the quadrupole splitting, and ˙0:5 T for the hyperfine field. Hyperfine parameters for the identified components (hematite, magnetite, goethite, lepidocrocite, feroxyhyte) were taken from [215].

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143

Table 4.29 Spectral parameters of the individual components in each sample analysed in the MS experiments, including the spectral area (Arel ), isomer shift (IS), quadrupole splitting (QS) as well as the hyperfine magnetic field (Bhf ) Sample

Component Component

Area (%)

Isomershift (mm/s)

Quadrupole shift/splitting (mm/s)

Hyperfine field (T)

Sample 3.1: Magnetite (A site) small coolant circuit of Magnetite (B site) pumps (17 October 2007) Goethite Hydroxide

36.3 37.2 14.4 12.1

0.28 0.64 0.36 0.36

0:00 0:00 0:25 0:70

48.90 45.60 35.80 –

Sample 3.2: deposits scraped from filters after filtration of SG feed water during operation

Hematite Magnetite (A site) Magnetite (B site) Hydroxide

15.8 32.6 41.8 9.7

0.38 0.28 0.65 0.38

0:23 0:00 0:00 0:56

51.56 49.14 45.91 –

Sample 3.3: SG42 pipelines – low level

Magnetite (A site) Magnetite (B site)

34.6 65.4

0.28 0.65

0:00 0:00

49.14 45.83

Sample 3.4: mixture of corrosion products, ionex and sand taken from filter of condenser to TG42

Hematite Magnetite (A site) Magnetite (B site) Hydroxide

9.2 45.4 40.7 4.7

0.38 0.28 0.66 0.37

0:22 0:00 0:00 0:56

51.29 49.20 45.87 –

Sample 3.5: deposit from filters after filtration of 340 l of feed water from SG S3-09 during passivation (27/28 May 2008)

Hematite Magnetite (A site) Magnetite (B site) Hydroxide

8.3 49.3 38.5 3.9

0.36 0.30 0.61 0.37

0:22 0:00 0:00 0:55

51.33 49.11 45.51 –

Sample 3.6: deposit from filters after filtration of 367 l of feed water from SG S4-09 during passivation (27/28 May 2008)

Hematite Magnetite (A site) Magnetite (B site) Hydroxide

6.4 50.3 40.7 2.6

0.38 0.29 0.66 0.37

0:25 0:00 0:00 0:54

51.26 49.14 45.61 –

All of the measured spectra contained iron in magnetic and also often in paramagnetic phases. The magnetic phases contained iron in non-stoichiometric magnetite Fe3x Mx O4 , where Mx are impurities and vacancies that substitute for iron at octahedral (B) sites. Another magnetic fraction is hematite, ˛-Fe2 O3 . Magnetic hydroxide (goethite ˛-FeOOH) was also identified in one sample. Paramagnetic fractions produce quadrupole doublets (QS) in the spectrum. Their parameters are close to those of hydroxides (e.g., lepidocrocite,  -FeOOH) or to small superparamagnetic particles of iron oxides or hydroxides with a mean diameter of about 10 nm. It should be noted that it is not difficult to distinguish among different magnetically ordered phases when they are present in a well-ordered crys-

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4 Barriers Preventing the Release of Fission Products

talline form with a low degree (or an absence) of substitution. Both the substitutions and the presence of the small superparamagnetic particles make the situation more complicated [216]. In such cases, it is necessary to perform other supplementary measurements at different temperatures down to those of liquid nitrogen or liquid helium with and without an external magnetic field [217]. The Mössbauer spectrum (Figure 4.69) of sample 3.1 (corrosion products taken from a small coolant circuit for the pumps) consists of three magnetically split components, where the component with a hyperfine field Bhf D 35:8 T was identified as goethite (˛-FeOOH). Hyperfine parameters of the remaining two magnetically split components were assigned to the A and B sites of magnetite (Fe3 O4 ). One paramagnetic spectral component appeared. Considering the aqueous environment and the pH [218], this component was assigned to hydroxide (feroxyhyte, ı-FeOOH). Sample 3.2 (deposits scraped from filters after the filtration of SG feed water during operation) also consists of three magnetically split components; two of them were assigned to magnetite (Fe3 O4 ) as in the previous spectrum, and the remaining magnetically split component was identified as hematite (˛-Fe2 O3 ). The paramagnetic part of the spectrum consisted of one doublet, whose hyperfine parameters were assigned to hydroxide (lepidocrocite,  -FeOOH). The spectrum is shown in Figure 4.70. The spectrum (Figure 4.71) of sample 3.3 (corrosion products taken from SG42 pipelines at a low level) consists of just two magnetically split components, with the hyperfine parameters assigned to the A and B sites of near-stoichiometric magnetite (Fe3 O4 ) and a relative area ratio ˇ D 1:85. Sample 3.4 (a mixture of corrosion products, ionex and sand taken from the filter of the condenser for TG42) also yielded a magnetically split component in its spectrum that corresponded to hematite (˛-Fe2 O3 ), while two magnetically split components were assigned to magnetite (Fe3 O4 ) as in the previous spectra, and the remaining paramagnetic component was identified as hydroxide. The spectrum of sample 3.4 is shown in Figure 4.72.

1.00

Figure 4.69 Mössbauer spectrum of sample 3.1: A (red) and B (dark red) sites in magnetite, as well as goethite (pink) and hydroxide (green) were identified

relative transmission

0.99 0.98 0.97 0.96 0.95 0.94 0.93 -10

-5

0

velocity (mm/s)

5

10

4.4 Contribution to VVER-440 Steam Generator Safety 1.00 0.99

relative transmission

Figure 4.70 Mössbauer spectrum of sample 3.2: A (red) and B (dark red) sites in magnetite, as well as hematite (blue) and hydroxide (green) were identified

145

0.98 0.97 0.96 0.95 0.94 0.93 0.92 -10

-5

0

5

10

5

10

5

10

velocity (mm/s) 1.00 0.98

relative transmission

Figure 4.71 Mössbauer spectrum of sample 3.3: A (red) and B (dark red) sites in magnetite were identified

0.96 0.94 0.92 0.90 0.88 0.86 0.84 -10

-5

0

velocity (mm/s) 1.00 0.99

relative transmission

Figure 4.72 Mössbauer spectrum of sample 3.4: hematite (blue), A (red) and B (dark red) sites of magnetite, as well as hydroxide (green) were identified

0.98 0.97 0.96 0.95 0.94 0.93 -10

-5

0

velocity (mm/s)

Both sample 3.5 (deposit from filters after filtering 340 l of feed water from SG S3-09 during passivation on 27/28 May 2008) and sample 3.6 (deposit from filters after filtering 367 l of feed water from SG S4-09 during passivation on 27/28

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4 Barriers Preventing the Release of Fission Products

May 2008) consisted of three magnetically split components, identified as hematite (˛-Fe2 O3 /, magnetite (Fe3 O4 ) and a paramagnetic component that was assigned to hydroxide (lepidocrocite  -FeOOH). The spectra for samples 3.5 and 3.6 are shown in Figures 4.73 and 4.74. Based on a comparison of the results from samples 3.5 and 3.6, it can be concluded that extending the passivation period causes the fraction of magnetite to rise (from 88% to 91%) in the compositions of the corrosion products. As mentioned earlier, aside from all of the hydroxides, some small superparamagnetic particles were also found. The refined spectral parameters for the individual components observed in the room-temperature (300 K) Mössbauer effect experiments, including the spectral area (Arel /, isomer shift (IS), quadrupole splitting (QS) as well as the hyperfine magnetic field (Bhf /, are listed in Table 4.29. The hyperfine parameters for the identified components (hematite, magnetite, goethite, lepidocrocite and feroxyhyte) are listed in [215]. The major fraction in all samples consists of magnetically ordered iron oxides, mainly magnetite (apart from samples 3.1 and 3.2, where goethite and hematite also

Figure 4.73 Mössbauer spectrum of sample 3.5: hematite (blue), A (red) and B (dark red) sites of magnetite, as well as hydroxide (green) were identified

relative transmission

1.00

0.99

-10

-5

0

5

10

5

10

velocity (mm/s)

Figure 4.74 Mössbauer spectrum of sample 3.6: hematite (blue), A (red) and B (dark red) sites of magnetite, as well as hydroxide (green) were identified

relative transmission

1.00

0.99

0.98 -10

-5

0

velocity (mm/s)

4.4 Contribution to VVER-440 Steam Generator Safety

147

appeared, respectively). Magnetite crystallizes in the cubic inverse spinel structure. The oxygen ions form a close-packed cubic structure with Fe ions localised at two different sites, octahedral and tetrahedral. The tetrahedral sites (A) are occupied by trivalent Fe ions. Tri- and divalent Fe ions occupying the octahedral sites (B) are randomly arranged at room temperature because of electron hopping. At room temperature, when the electron hopping process is fast, the Mössbauer spectrum is characterized by two sextets. The sextet with a hyperfine magnetic field Bhf D 48:8 T and the isomer shift IS D 0:27 mm/s relative to ˛-Fe corresponds to the Fe3C ions at the tetrahedral A sites. The sextet with Bhf D 45:7 T and IS D 0:65 mm/s is the Fe2:5C -like average signal from the cations at octahedral B sites. Fe2C and Fe3C are indistinguishable due to fast electron transfer (electron hopping), which is faster ( 1 ns) than the 57 Fe excited-state lifetime (98 ns). The magnetite unit cell contains eight Fe3C ions and eight Fe2C and Fe3C ions – 16 in total at the B sites – so the intensity ratio ˇ D I.B/=I.A/ of the two spectral components is a sensitive measure of the stoichiometry. Assuming that the room temperature ratio of the recoil-free fractions fB =fA for the B and A sites is 0.97 [219], the intensity ratio ˇ for perfect stoichiometry should be 1.94. In nonstoichiometric magnetite, under an excess of oxygen, cation vacancies and substitutions at the B sites are created. The vacancies screen the charge transfer and isolate the hopping process. For each vacancy, five Fe3C ions become trapped at octahedral sites. In the Mössbauer spectrum, these trapped Fe3C ions at the octahedral sites and the Fe3C ions at tetrahedral sites are indistinguishable in the absence of the application of an external magnetic field. Therefore, in the spectrum of non-stoichiometric magnetite, intensity transfer from the Fe2:5C to the Fe3C -like components is observed. Thus, the intensity ratio ˇ decreases markedly with the oxidation process until the stoichiometry reaches the  -Fe2 O3 phase. It should be noted that in our samples the intensity ratio ˇ is far from 1.94 (perfect stoichiometry), and varies from 0.97 up to 1.85.

4.4.4.5 Conclusions Material degradation and corrosion are serious risks to the reliable long-term operation of NPPs. The previous discussion summarises the results of measurements of the phase compositions of corrosion products obtained using Mössbauer spectroscopy; these measurements were carried out over a long period (1984–2008). The early years of this period (mostly the 1980s) were important as the work done in those years led to improvements in the Mössbauer technique [171]. The benefits of this early period were the experience gained, the optimisation of measurement conditions, and the improvement of evaluation programs. Unfortunately, the samples were not well defined during this early period, and bearing in mind the different levels of technique and evaluation procedures involved, it would not be appropriate to compare results from this period to those obtained from measurements performed after 1998.

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4 Barriers Preventing the Release of Fission Products

Replacing the STN 12022 steel (denoted GOST 20K in Russian NPPs) used in the steam-generator feed water systems is necessary and very important from an operational as well as a nuclear safety point of view. After five years of operation in SG35, the steel STN 17247 was shown to be a good solution to this problem. Nevertheless, periodical inspection of feed water tube corrosion (after 10, 15 and 20 years) was recommended. Based on the results of a visual inspection performed on 19 April 2002 at SG16 (NPP V1), the steam generator was found to be in good condition after 23 years of operation. Samples taken from the internal body surface of PG16 showed that the hematite concentration increases in the vertical direction (from the bottom to the top). The more recent results from 2008 indicate good operational characteristics and suitable chemical regimes (reducing environment) that result mostly in the formation of magnetite (at levels of 70% or higher) and small portions of hematite, goethite or hydroxides. Regular observation of corrosion/erosion processes is essential in order to keep NPPs operating at a high level of safety. The results from material analyses influence the optimisation of chemical regimes during operation, and can be used to optimise regimes during the decontamination and passivation of pipelines or secondary circuit components. It can be concluded that extending the passivation time leads to higher magnetite fractions in the corrosion products. Differences between the hematite and magnetite contents of corrosion layers taken from hot and cold collectors in SG11 in 2004 show that there is significantly less magnetite in the hot collector. This fact can be derived from two parallel factors: the difference in temperature (HC  298 °C) and (CC  223 °C), but mostly the highly dynamic secondary water flowing in the vicinity of the hot collector, which very probably removes the corrosion layer from the surface of the collector. In order to summarize our results in a form suitable for daily use under operational conditions, a “corrosion map” was created (see Figure 4.75). In this map, corrosion product phase compositions (limited to magnetite and hematite) are presented in the form of circular diagrams. Basically, when the new feed water pipeline system (made from austenitic steel) corrodes under the operational regime adopted in SG35 since 1998, magnetite is produced. In samples taken from positions 5 to 14 (see Figure 4.75 – right-hand corner), the hematite is present mostly on the internal surface of the body of the SG (constructed from carbon steel according to GOST 20K). Its concentration increases towards the top of the body and is very significant in the steam part of the SG, where flowing water removes the layer of corrosion through erosion better than it does from the dry part of the internal surface or the upper part of the pipe. The long-term study of the phase compositions of corrosion products in VVER reactors is a prerequisite for safe NPP operation over its projected lifetime. Longterm observations of corrosion status via Mössbauer spectroscopy are very useful and relatively inexpensive. Based on the results obtained, the following lines of inquiry were established for the next period:

4.4 Contribution to VVER-440 Steam Generator Safety

149

Figure 4.75 Corrosion map of Bohunice NPP V-2 (Slovakia) based on results obtained during the period 1998–2008

• bearing in mind the measured phase compositions of previous corrosion specimens, the chemical regimes used could be discussed and perhaps improved; • the chemical solutions used in cleaning and/or decommissioning processes during NPP operation could be considered, re-evaluated and optimised. In connection to the planned commissioning of Mochovce NPP 3 and 4 (announced officially on 3 October 2008), it is recommended that all feed water pipes and water distribution systems in the steam generators should be replaced immediately before starting operation with new ones constructed from austenitic steels. The Bohunice design with feed water distribution boxes is highly recommended, and seems to be acceptable from a practical point of view.

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4 Barriers Preventing the Release of Fission Products

4.5 Leak Tightness Calculation for a Container for Transporting Burned-up Fuel Assemblies The transport container C-30 for VVER-440 fuel assemblies has been used in Bohunice NPP since 1986. Therefore, they have over 13 years of experience with the safe transport of burn-up fuel. Nevertheless, new calculations have been performed in the last year in order to check the leak tightness of this container for loading with 30 or 48 fuel assemblies that have higher levels of enrichment and burn-up than those transported before. The approach used in this calculation is based on the IAEA Safety Standard Regulations for the Safe Transport of Radioactive Material – Requirements [220].

4.5.1 Components of Container C-30 The C-30 transport container is shown in Figure 4.76. The components that influence the leak tightness of the C-30 are: • the body of the container; • the lid of the container, along with nuts and an inner Viton (initially elastomer) O-ring; • ducts 1–6, each of them consisting of a case with an inner and outer weld;

Figure 4.76 The C-30 transport container

4.5 Leak Tightness Calculation for a Container for Transporting Burned-up Fuel Assemblies 151

• sleeve with a cylindrical nut opening with an ItSH (asbestos) seal, and a cover with an elastomer O-ring and a flat Cu seal. It is possible to change the covers to connect to the medium inside or to a measuring instrument, depending on the technical requirements.

Elastomer O-rings All of the O-rings were of WS1.957 type according to TGL 106-70101. They were initially manufactured from nitrile butadiene caoutchouc (rubber). Although results are given in [221] which provide evidence that this material can be used in the required range of temperatures and pressures, these elastomer O-rings have been replaced with Viton MK 634 seals (from Merkel/GNB) based on experience with transporting CASTOR containers.

Elastic Skeleton Rings An elastic skeleton ring has the shape of a hollow cylinder and consists of a spiral roll of tape made from asbestos (ItSH), with several layers glued together.

PE1000 Seals The ItSH seals have been replaced with PE1000 seals according to DIN EN 102042.1.

Cu Seals Cu seals are produced according to TGL 0-7603.

4.5.2 Criteria for Transport According to IAEA Safety Standards [220], a safe container for the transport of nuclear fuel is defined in the following way. Paragraph 656 [220] states that a delivery must be constructed according to the following rules: • When it is subjected to certain tests (defined in paragraphs 619–624), the container must be constructed such that the loss of the radioactive content is limited to a value A2  106 /h; and • After performing the exams introduced in the paragraphs 626, 627(b), 628, 629 and exams:

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4 Barriers Preventing the Release of Fission Products

Table 4.30 Releasable activities from the fuel in the C30 container Calculated activity values after 2.5 years. 30 fuel assemblies with 4.4% enrichment and a burn-up of 50 MWd/kg U Ai (Bq/container)

A2i according to [220] (Bq)

Rate Ai /A2i

H Kr 129 I 134 Cs 137 Cs

8:07  1013 1:39  1015 6:41  109 1:54  1016 2:00  1016

4  1013 10a  1  1013 Unlimited 7  1011 6  1011

2.0175 13.9 Unlimited 2:2  104 3:33  104

Total

1:88  1017

Nuclide

3

85

a

A value of 10A2 is permitted during the first week for 85 Kr.

– 627(c), if the delivery has a maximum weight of 500 kg, a total density is determined on the base of outward sizes at the maximum of 1000 kg m3 and the radioactive content is more than 1000A2 , but it is not radioactive material of special type, or; – 627(a) an accumulated loss of the radioactive content is limited during one week to a maximum of 10A2 in the case of 85 Kr and a maximum A2 for the rest of the nuclides. In the case of a mixture of radionuclides we have to apply paragraphs 304–306 except for 85 Kr, where it is possible to use the effective value A2 D 100 TBq (2000 Ci). A suitable equation for a mixture of radionuclides is: Xm D P

1

f .i / i X.i /

;

(4.136)

where f .i / is the fraction of the activity or the concentration of radionuclide i in the mixture, and X.i / is the activity in TBq. Releasable activities from the C-30 loaded with fuel were calculated at the NPP Research Institute at Trnava, and they are listed for 30 fuel assemblies in Table 4.30. Next we must take into account that an isotope like Cs is able to react with materials inside the container (water), and that the value of A2 for 129 I is unlimited in [220]. Therefore, it is possible to focus only on leaks from 3 H and 85 Kr [222, 223]; we can ignore the other isotopes.

4.5.3 Model for Calculating the Leakage The model used to calculate the leakage from the transport container C-30 complies with the ISO 12807 International Standard Safe Transport of Radioactive Materials – Leakage Testing Packages [224].

4.5 Leak Tightness Calculation for a Container for Transporting Burned-up Fuel Assemblies 153

We determine the leakage of the gases 3 H and 85 Kr via the Knudsen equation, which is the recommended approach [224]. The penetration of the gas through small cavities depends on the thermodynamic properties of the gas, flow regimes and routes. The calculation of the ideal capillary diameter is used. It is possible to use the following modified Knudsen equation for the applicable leakage range (108 to 101 Pa m3 s1 ): r  D4  2 D3 T 2 Q D 0:0123 p  pd C 1:204 .pu  pd / ; (4.137) :a u a M where: Q is the leakage rate (Pa m3 s1 ); D is the capillary diameter (the leakage hole diameter in m); pu is the upper pressure (Pa); pd is the lower pressure (Pa); T is the absolute temperature of the fluid (K); M is the relative molecular mass (kg mol1 ). The Knudsen equation can only be applied to the viscous laminar flow regime, the molecular flow regime or the transition flow regime. For predominantly laminar flow, the calculated contribution for molecular flow becomes negligible, and similarly for predominantly molecular flow, the calculated contribution for laminar flow becomes negligible. The first part of this equation represents the viscous laminar flow component, QV , which is derived from Poiseuille’s law for laminar flow, and the second part represents the molecular flow component, Qm , which is derived from Knudsen’s law for free molecular flow.

4.5.4 Releasable Activity of a Radionuclide Under Normal and Accidental Conditions During Transport for the C-30 Container The largest fraction of each radioactive isotope remains in the fuel. If the fuel assembly cladding is leak-tight according to the results of fuel leak testing, then the leakage of isotopes is very small. Using conservative assumptions, 10% is a permissible leak of activity from the fuel in the case of gaseous fission products [222, 224]. The recommended release rates for determining the activities of gaseous fission products inside the transport container but outside of the fuel rods are: • 1% during transport; • 100% during a Type B examination.

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4 Barriers Preventing the Release of Fission Products

The total releasable activity for all radionuclides under normal conditions during transport RITN is: X RITN D FCi N  FEi N  Ii ; (4.138) i

where: FCi N is the fraction of radionuclide i from the radioactive contents released into the containment system under normal conditions during transport (conservatively 10%); FEi N is the fraction of radionuclide i which is available for release from the containment system into the environment under normal conditions during transport (conservatively 1%); Ii is the activity of radionuclide i. The total releasable activity for all radionuclides under accidental conditions during transport RITA is: X RITA D FCi A  FEi A  Ii ; (4.139) i

where: FCi A is the fraction of radionuclide i from the radioactive contents released into the containment system under accidental conditions during transport (conservatively 10%); FEi A is the fraction of radionuclide i which is available for release from the containment system into the environment under accidental conditions during transport; Ii is the activity of radionuclide i. Based on this, it is possible to establish the releasable activities of gaseous fission products from the 30 or 48 fuel assemblies. Calculations were performed according to the method introduced in ISO 12807 [224] and the procedures given in [222] and [223]. The calculations are valid for the T-12 containing 30 fuel assemblies. It is necessary to determine the equivalent value A2eq to calculate the gaseous leakage from the storage container for the two most important gas products 85 Kr and 3 H. The maximum permissible activity release rates for the contents under normal and accidental conditions during transport (RN and RA , respectively) are: A2eq D

1 ˙

FCi A A2i

D

1 1014

1 D 2:857  1013 Bq 1 C 410 13

A2eq  106 D 7:936  103 Bq s1 3600 A2eq RA D D 4:724  107 Bq s1 : 7  24  3600 RN D

(4.140) (4.141) (4.142)

4.5 Leak Tightness Calculation for a Container for Transporting Burned-up Fuel Assemblies 155

The following step is to calculate the average activity per unit volume of the medium that could escape from the containment system under accidental conditions during transport (for the C-30 container this is 400 l of nitrogen; note that this will not change after loading 48 fuel assemblies because this space is also determined for the nitrogen pillow):  RTIN 0:01  0:1  D 1:39  1014 C 8:07  1012 D 3:677  1011 Bq m3 VN 0:4 (4.143)  RTIA 1  0:1  CA D D 1:39  1014 C 8:07  1012 D 3:677  1013 Bq m3 : VN 0:4 (4.144) CN D

The maximum permissible volumetric leakage rates of the medium under normal and accidental conditions during transport are: LN D

RN D 2:159  108 m3 s1 CN

(4.145)

LA D

RA D 1:285  106 m3 s1 : CA

(4.146)

It is apparent that the permissible leakage rate during normal conditions of transport is about two orders of magnitude smaller than that allowed during accidental conditions of transport, so there are stricter leakage requirements during normal transport conditions. We will therefore only consider normal conditions of transport from now on, because the container must comply with the strictest leakage conditions. QN D LN  pN D 1:194  103 Pa m3 s1 :

(4.147)

It is permissible to release half of all of the radioactive products from the C-30 container containing 30 fuel assemblies for a week following an accident according to the requirements for the transport of containers. However, this cannot be verified experimentally (so it is important to determine the standard leakage rate under normal conditions of transport).

4.5.5 Determining the Standard Leakage Rate of the C-30 Transport Container The standard leakage rate is obtained by calculating the leakage rate according to Equation 4.137 with respect to pressure conditions, flow regime type and size of capillary. According to [222] and [223], it is also possible to use an equation in which there is a conservative assumption of laminar viscous flow only, which means that there are leakages that can be detected by special tests based on a soap solution.

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4 Barriers Preventing the Release of Fission Products

For 30 fuel assemblies, QSLR;30

 2  p  0 1:012  0  D 2:194  103 D QN;30  02 3:9862  1:012 p  p2 D 1:50  104 Pa m3 s1 ;

(4.148)

where: p is the pressure of the surrounding medium (air); p0 is the maximum transport pressure of the gas inside the container. The manufacturer of the C-30 transport container is the firm GNS (Gesellschaft für Nuklear Service) in Essen, which determined that the leakage from the C-30 with a standard load of 30 fuel assemblies is QSLR D 1:9  104 Pa m3 s1 (1:9  103 mbar l s1 ). The source of activity in the container was computed for the fuel three years after reactor shutdown with a burn-up of 33 MWd/kg U (and an initial fuel enrichment of 3.6% 235 U). The C-30 transport container loaded with 30 or 48 fuel assemblies complies with the requirements for type B(U) transport if the results from leakage tests are lower than the values QSLR;30 D 1:50  104 Pa m3 s1 (for 30 fuel assemblies) or QSLR;48 D 9:42  105 Pa m3 s1 (for 48 fuel assemblies), respectively [225].

4.6 Fourth Barrier: Containment The main objective of a containment building is to keep the release of radioactive substances to the environment within acceptable limits under accidental conditions [226, 227]. The containment structure should also be designed to protect the public and plant personnel from undue exposure to direct radiation arising from the radioactivity present in the containment or in the systems within it. If this consideration is included in the design basis for the containment system, it may determine the thickness of the concrete of the containment envelope. The functional requirement for the overall containment system derives from its major objective, which is, in conjunction with other safety systems, to restrict the release of radionuclides resulting from accidental conditions to acceptable limits. The basic functional requirement that stems directly from this objective is to envelop (and thus isolate from the environment) certain systems, as the failure of these particular systems could cause an unacceptable release of radionuclides. This applies to all components of the reactor pressure boundary that cannot be safely isolated from the reactor core. The degree of containment tightness is usually defined in terms of the leak rate of the containment envelope. The leak rate is affected by factors such as: • the leak tightness of the containment envelope and isolation devices; • an elevation in internal pressure resulting from postulated initiating events (PIE); or • a reduction in pressure resulting from the effects of energy management features.

4.6 Fourth Barrier: Containment

157

The release of radionuclides from the containment envelope is determined by the following factors: • the quantity of radionuclides released inside the containment envelope; • a reduction in radionuclide concentrations in the containment as a result of radioactive decay and the effects of radioactive substance management; • the release of radionuclides from the containment before isolation; • the leak rate of the containment envelope after isolation.

4.6.1 Design Features of the Containment System The containment envelope is usually a steel or concrete building that is designed to withstand the pressure and the thermally and mechanically induced loads resulting from PIEs involving a loss of primary or secondary coolant. The containment may also consist of a number of interconnected leak-tight rooms. The isolation features of the containment envelope include the materials, valves and other devices that must seal off the system and stop penetration through the containment envelope, as well as the electrical, mechanical, instrumentation and control systems which ensure that these valves and other devices can be closed when it is necessary to isolate the containment. Energy management features are incorporated that limit the internal pressures and temperatures within the containment envelope to values that are below the design limits for the containment system and the equipment that is needed inside the containment when a design basis accident occurs. Examples of energy management features include pressure suppression pools, ice condensers, pressure-relief vacuumchamber systems, structural heat sinks, the free volume of the containment envelope, spray systems, air coolers, a sump or a suppression pool recirculation water-cooling system, and the air extraction system for the annulus in double-containment systems. Radionuclide management features work in concert with energy management features and the containment isolation system to limit the radiological consequences of accidental conditions. Examples of radionuclide management features include double-containment systems which trap any radioactive leakage between the two envelopes, containment structures upon which radionuclides plate out (i.e., are deposited), suppression pools that dissolve or entrain airborne molecular or particulate radioactive materials as the atmosphere is forced through the pool, spray systems, and particulate filter systems. Combustible gas control features are designed to deal with any hydrogen generated by metal–water reactions in the core, water radiolysis, or metal corrosion during accident conditions. Control features utilised in various designs include recombines, atmosphere mixing devices, inerting features, or devices to ensure that any burning of hydrogen occurs in a controlled fashion (such as igniters).

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4 Barriers Preventing the Release of Fission Products

4.6.2 Design Basis for the Containment System The design basis for the containment system is derived primarily from the results of the analysis of relevant PIEs. In order to determine the response of the containment system to PIEs, appropriate analyses of the thermohydraulics, structural response, radiochemistry and physical transport of radionuclides is performed. The results of these analyses are used to establish the design parameters for the containment system, including: 1. the pressure transients with respect to the containment structural envelope, and the required safety system equipment therein; 2. the temperature transients in the containment atmosphere, the containment structural envelope and the required safety system equipment within the containment envelope; 3. the differential pressure loadings imparted to structures and equipment within the containment envelope; 4. the loadings imparted to equipment and structures within the containment envelope as a result of fluid jet impingement, pipe reaction loads, pipe impact loads and internally generated missiles; 5. the structural loading resulting from external PIEs; 6. radionuclide releases into the containment atmosphere and hydrogen concentrations resulting from the PIEs; 7. other environmental conditions which are needed to specify equipment and structures, such as the radiation levels, humidity and exposure to water (including its chemical activities) caused by the PIEs. For each relevant PIE, an appropriate combination of the design parameters in items 1–7 above is analysed to determine the most severe demands on the containment system and to define the design basis, including the leak rate. The results of these analyses are used to demonstrate that: • The radionuclide releases resulting from the PIEs and other environmental consequences are below acceptable limits. • The containment system will maintain its ability to perform its safety function during and after the PIEs without impairing the operation of the safety systems that are required following the PIEs.

4.6.3 Containments for VVER-440 Reactors 4.6.3.1 Considerations for the VVER-440/V-230 The VVER-440 model V-230, units of which were operated by several countries in Central and Eastern Europe, was designed in the 1960s on the assumption that the design basis accident can be limited to a break in a 100 mm diameter pipe fitted with

4.6 Fourth Barrier: Containment

159

an orifice 32 mm in diameter. This assumption is currently judged to be inadequate according to international safety requirements, but was used to determine the capacity of the emergency core cooling system. For such a break, the spray system of the reactor building was designed to prevent uncontrolled release into the environment. For larger breaks, ranging up to the full rupture of one of two pressuriser surge lines 200 mm in diameter, large flaps were designed to open during the initial pressure peak after the accident and to release large amounts of steam escaping from the broken reactor coolant system (RCS) into the environment. In view of this initial release of a radioactive medium, and due to its other unsatisfactory features, the building surrounding the VVER-440/230 reactor is not considered a containment. Since it fulfils a confining function, it is termed a confinement. The shortcomings of VVER-440/230 confinements have long been recognised, and the newer VVER-440 model, called the V-213, is provided with an improved building that has greater leak tightness and strength, and contains a complicated system of water trays and air traps that are designed to condense steam and remove some of the air from the reactor compartments after a large break loss-of-coolant accident (LB LOCA). In such cases, the system rapidly reduces the pressure in the containment to subatmospheric values and thus prevents any significant release of radioactivity into the environment. As the main process used is steam bubble condensation in water, the system is called a bubbler condenser containment (BCC). The BCC was the answer to the problem of providing the old VVER-440 model V-230 units with a reliable containment without radically changing the design of the original hermetic compartments and without significantly increasing the maximum pressures and temperatures allowable inside the containment, which could result in the need to replace good fraction of the reactor equipment (since it is unable to withstand the high environmental demands typical of the large, dry containments used in other designs for example). However, although the BCC could have been a good solution for newly built units, it proved rather difficult to adapt it to the old VVER440/230 reactors already in operation. Therefore, these operational VVER-440/230 units continued with their original confinements, even though contemporary safety rules clearly indicated the inadequacy of such designs. However, there are several proposals for upgrading the confinements of VVER440/230 reactors. In filtered venting systems, it is possible to use mechanical filters or water filters of various designs developed by Western companies, or jet condensers developed and tested in Russia. The conceptual designs presented offer the possibility of filtering released gases of almost all their aerosol contents throughout the accident without losing the integrity of the confinement. It is also possible to provide a forced ventilation system with a filtered discharge. This would provide long-term assurance of the presence of an underpressure within the confinement in spite of high leakage rates. However, it appears that none of the VVER-440/230 units in Europe will be restarted, and all improvement activities are currently focused on the V-213 model, which will be described in detail in the next chapter.

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4.6.3.2 Considerations for the VVER-440/V-213 The VVER 440/213 has many of the enhanced reactor safety features of the new generation of VVER-440 reactors, in particular a large reserve of water for effective long-term core cooling. This is accomplished by using six horizontal steam generators that are connected by six isolatable loops to the reactor. In particular, the following basic functions must be met by the containment for the V-213: • prevention of the release (beyond a preset level) of radioactive substances outside the hermetic area (i.e., the required level of biological protection under normal operation must be assured); • management of the impact of increased pressures and temperatures, as caused by the failure of the reactor cooling system, inside hermetically sealed areas; • protection of the reactor cooling system and plant equipment from external effects inside as well as outside the containment. The containment should withstand the effects of natural forces (e.g., earthquakes, winds, frost, etc.) and human-induced activities (air transport, road transport, fires, etc.). The BCC system for mitigating the consequence of a maximum design basis accident was developed in the late 1970s. This system is used in Russia (Kola NPP), the Ukraine (Rovno NPP), the Czech Republic (Dukovany NPP), the Slovak Republic (Bohunice, Mochovce NPPs) and in Hungary (Paks NPP). The maximum accident considered in the design of the containment is a guillotine break of a reactor coolant pipeline (ND 500). The probability of this occurring is very low. Although its occurrence is hypothetical, the preset dose value must not be exceeded for the most endangered people in the surroundings of the NPP. The LOCA that is considered belongs to the most dangerous accidents that could occur. The failure of the first two barriers – the fuel cladding and the primary circuit integrity – as a consequence of the accident is postulated during the LOCA. The total free volume of the containment is approximately 52.500 m3 (for additional data, see Table 4.31). Reinforced concrete walls with steel lining form the

Table 4.31 Characteristics of different VVER-440/V213 containments Type of containment NPP Overpressure Thermal power Free containment volume Free volume/ thermal power Water volume Water volume/ thermal power Number of pipes

Units

VVER-440/V213

kPa MW m3 m3 /MW

Bohunice 150 1375 52 400 38.11

Dukovany 150 1375 52 500 38.18

Mochovce 150 1375 52 000 37.82

Paks 150 1375 51 400 37.4

m3 m3 /MW

1345 0.978

1345 0.978

1360 0.99

1354 0.985

1800 (siphon)

1800 (siphon)

1800 (siphon)

1800 (siphon)

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161

boundary of the containment; these separate all hermetically sealed areas from their surroundings. Other construction, technological and electrical items are also important for containment tightness, in particular: hermetically sealed doors, hatches, tube and cable penetrations, and protective covers for the reactor shaft and airconditioning items. A steel liner with a thickness of 6 mm is used to ensure the tightness of the reinforced concrete walls. Fast-acting isolating valves on the containment boundary are provided for the rapid isolation of systems inside the containment in the case of an accident. These fast-acting isolating valves are fitted in pairs and located on both sides of the containment in close proximity to it. Thus, during any accident inside the containment, at least one barrier has a high probability of being retained, which will stop the spread of radioactive substances into the environment of the NPP. When the unit is in operation, a minimum underpressure of 50 Pa is maintained inside the containment. Operating the containment under permanent underpressure enables the continued monitoring of its tightness, which is a significant safety aspect of this type of containment. The tightness of the containment is verified by periodical tests using an internal overpressure. The scheme of the containment is shown in Figure 4.77. The VVER 440/213 containment presents the last barrier to the release of radioactive fission products into the environment. It consists of the following main parts: • • • •

steam generator compartment; corridor; BC building with accident confinement shaft; BC system with air traps;

Figure 4.77 VVER 440/213 containment building with the bubble condenser

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• ventilation systems; • spray system. The containment consists of hermetically sealed compartments housing the reactor equipment, air-conditioning systems, the spray system and a BC building, which is connected to the hermetically sealed compartments by a corridor. The BC building contains 12 staggered floors of passive condenser and air traps equipped with check valves. The gas volumes above the water level (beyond the water seal) are connected to the air traps through double-check valves. There are four air traps into which uncondensed gases from the containment are forced to flow, and each of them is connected to three floors of BC trays. Between the volume above the water and the shaft of the bubble condenser there are two self-closing check valves on each floor whose function is to prevent the reverse flow of water from trays during a small LOCA accident. The BC system only operates under accidental conditions in conjunction with the loss of coolant of either primary or secondary circuit, resulting in pressure and temperature increases in the containment. It is started automatically by the pressure difference that arises under such conditions between the hermetically sealed and retaining areas. Operation of the BC is clearly passive. An illustration of the BC building with several floors of trays is shown in Figure 4.78. Passive reduction of the rapid increase in pressure in hermetically sealed areas during a maximum design basis accident is enabled by two basic functions of the BC: • steam condensation, achieved through the bubbling of steam on 12 floors of trays filled with water (marked as (7) in Figure 4.78); • the capture and retention of air and uncondensed gases in four air traps (13). The BC is arranged in such a way that the air–steam mixture is passed through the corridor to the BC, where the flow is distributed via the BC shaft (2) to individual floors. The mixture passes through 1806 gap-cap water seals between the ceilings and the bottoms of the floors (8, 9). After the expulsion of the water column in the inlet cap of each seal (9), the mixture bubbles through the water layer, where the steam condenses. Air and uncondensed gases are then accumulated above water level, and due to rising overpressure this mixture flows through the DN 500 double-check valve (11) to the air traps (13). The speed of this process is governed by the pressure difference between the BC shaft (2) and the air traps (13). In the case of large break LOCA, it is a very quick process (see the graph in Figure 4.79), and the dynamics of the jet flows have a significant impact on technological devices, as well as on the structures of the BC and the hermetically sealed area. Dynamic effects of the steam–air mixture flow are buffered at the inlet to the BC by a special protecting wall anchored to the structure bearing the BC trays, and in this way to the reinforced concrete building. As the accident progresses further, the pressures above the water level and in the air traps (13) equalise, while the DN 500 double-check valves (11) automatically

4.6 Fourth Barrier: Containment

1 3 5 7 9 11 13

Corridor Perforated protecting wall Perforated collectors Tray with water solution (H3 BO3 ) Cap forming water seal DN 500 double-check valve Air trap

163

2 Bubble condenser shaft 4 Gasroom 6 Lockable check valve DN 250 8 Gap for inlet of steam/air mixture 10 Check valve inlet protection duct 12 Damper device

Figure 4.78 Diagram of the bubble condenser system used in the containment

close, retaining compressed air in the trap chambers. The flow of hot water and steam from the primary circuit decreases and the pressure in the hermetically sealed area begins to fall due to steam condensation and heat transfer to the walls, and also due to the operation of an active spray system. A reverse pressure difference, when the pressure above the water seal (9) is greater than the pressure in the BC shaft (2), causes a reverse water flow from the trays to the BC shaft. Water flows along the same path through which the steam–air mixture flowed, along the ceiling of the lower floor to the perforated collectors on the front wall of the BC, and then sprays into the volume of the shaft. This passive spraying causes a further reduction of pressure in the hermetically sealed volumes. Spilled water from the trays is

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4 Barriers Preventing the Release of Fission Products

P [kPa]

MCP break

250

Safety margin in the containment pressure

218 Spray system in operation and water flowback from the trays Spray stops Spray starts

P atm [100 kPa]

100 99.8 80 0s

10 s

200s

15 min

Figure 4.79 Pressure history in the VVER 440/213 containment during a maximum design basis accident

collected at the bottom of the BC shaft and flows through the corridor to the SG compartments. From this room, the water is transferred together with the spray and primary (secondary) leak water to be sucked out with emergency system pumps. Accidents that involve the release of a small amount of coolant take a similar but slower course, with a lower expected pressure. In order to prevent the undesirable refluxing of water in a small accident, there are two special DN 250 check valves on each floor (6) that allow for pressure equalisation in front of and behind the water seal. These check valves are fitted with a special blocking system which, depending on the pressure in the volume before the hydraulic seal, automatically locks or unlocks the valve. The blocking system is set to a value of 165 ˙ 5 kPa of absolute pressure. Above this value the valve is automatically locked and does not allow the pressures to equalise. If the pressure in the shaft during accident localisation does not exceed the limit value of 165 kPa, the valves remain unlocked and, in the case of a drop in pressure before the water seal, the pressures in front of and behind the seal equalise, ensuring that the water remains in the trays. The passive function of the BC system causes a spontaneous decrease in pressure in the hermetically sealed areas with the continuous accumulation of a significant amount of released thermal energy. Full localisation of the accident is accomplished by active spraying of the SG compartments, which gradually reduces the pressure in the containment to a value of 80 kPa (absolute), when the spray system is automatically switched off. A moderate vacuum in the sealed area prevents the release of radioactive substances; this vacuum is maintained by the controlled actuation of active spray systems [228].

Chapter 5

Conclusion

The high reliability of the barrier system of a VVER is ensured by applying the concept of defence in depth. Adequate engineering of the barriers and the measures used to protect them, coupled with feedback to maintain operation within the optimal range, lead to long-term smooth and stable NPP performance in producing electricity on demand. Indeed, the most important indicator of a successful defence in depth strategy is continuous operation with little or no need to call on built-in safety systems. The present work deals with several issues connected to the system of barriers to the release of radioactive substances from VVER-440s. In Sections 4.1–4.5, the works and contributions of the author were described in detail. Results were summarised in the conclusions to each section (or in scientific articles published in relevant journals). Of course, there are many other topics that were not mentioned in this work but are still important or interesting from a nuclear safety point of view, and are thus open to investigation in the future. Due to the increasing demands on energy supplies worldwide, activities aimed at reactor lifetime extension and the construction of new nuclear power facilities (advanced GenIII, GenIV, ITER, DEMO, . . . ) continue to increase. New structural materials will also need to withstand relatively high levels of stress during operation. It is therefore crucial to develop materials that can withstand these harsh operating conditions. Candidate materials will need to fulfil challenging performance criteria, such as high thermal conductivity and/or heat resistance, low thermal expansion, a low ductile-to-brittle transition temperature shift, sufficient strength with limited loss of ductility and toughness, a low swelling rate, high creep resistance, and good corrosion resistance. These features are monitored and evaluated in operating reactors with the aim of ensuring the safety margin for long-term, safe plant operation. Macroscopic methods cannot reveal all of the processes and microstructural changes that occur during the thermal and radiation treatment of RPV steels. Therefore, the use of computer simulations of radiation-induced defect creation has become increasing popular, together with computer hardware and computational codes, in recent years. It is clear that the microscopic atomic (or electronic) structure plays an important role in the macroscopic properties of a material. Despite V. Slugeˇn, Safety of VVER-440 Reactors. © Springer 2011

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the recognized influence of a metal’s microscopic structure on its properties, our knowledge at the microscopic level is still limited. Direct observations of microscopic defects are limited by the lack of resolution of experimental techniques such as high-resolution transmission electron microscopy, and by the fact that only fully relaxed structures can be observed. With the advent of highly powerful computers, simulation at the atomic level can play an increasingly prominent role as an effective alternative to experimental observations. Computer simulations offer the ability to examine details at the microscopic scale that cannot be obtained from experiments. Nevertheless, the validity of any computational model must always be checked experimentally. In order to gain a better understanding of the microscopic mechanisms involved in irradiation embrittlement, many spectroscopic methods have been applied to many RPV steel samples. As-received, thermally treated and irradiated conditions have been considered. However, despite more than 30 years of research effort in this field, there are several key questions that are still not completely solved. The most relevant are: • What roles do alloying elements play in the microstructure of an RPV steel? • How can the analytical methods focused on steel microstructure be effectively applied? • How do we observe the effects of radiation or thermal treatment on microstructural parameters? • How do these parameters depend on the level of irradiation or thermal treatment? • Are the microstructural parameters obtained from different spectroscopic techniques or laboratories relevant and easily comparable? • How are the microstructural parameters correlated with the macrostructural ones? • How can we use our knowledge of the long-term management of the microstructure of RPV steels effectively? Nuclear safety is a fundamental condition for energy production in any nuclear facility. Its importance has increased dramatically during the last 20 years. The Chernobyl accident changed the approach and attitude to nuclear safety globally. It is evident that a culture of safety based on deep technical knowledge at all levels of the power plant will substantially influence operational and safety parameters. I hope that the work presented here on barriers that protect against the release of fission products or other radioactive substances from a VVER-400 reactor into the environment contributes to the pool of technical knowledge and the development of documents focusing on these selected areas. Nuclear safety awareness and understanding is a long-term process. Appropriate knowledge, an open mind and a careful “questioning attitude” are and will continue to be crucial to the proper application of nuclear safety. My work is continuing, with the aim being to study and solve problems connected to the nuclear safety of nuclear facilities. The results and knowledge gained can be used both directly (to help the nuclear industry) as well as for educational purposes, to adequately prepare graduate and postgraduate students or NPP staff.

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Index

A

brittle failure 59 bulk lifetime 98 Burgers vector 21 burn-up 26

ab initio calculations 70 abnormal conditions 6 accident mitigation 5 accident prevention 5 accidents 7, 8 accidents beyond the design basis 8 design basis accidents 8 management 8 mitigation 7, 10 off-site emergency measures 8 prevention 7 activation energy 22 activity concentration 28 angular correlation 95 annealing temperature 119 annihilation energy 72 annihilation parameters 72 annihilation photons 97 annihilation radiation 72 annihilation rate 72 atom probe field ion microscopy (APFIM) 64 austenitic steel 132 average lifetime av 98

C canister pool system 28 carbon steel 131 cavity dislocations 60 central parameter S 99 centring pins 39 chemical isomer shift 107 chromium carbides 123 cladding 9 coarsening 23 collision cascades 53, 56 computer simulations 36 constant-fraction discrimination 96 coolant 9 core electron density 100 corrosion 126 cracking 126 corrosion layer 142 corrosion products 128, 132 corrosion/erosion processes 127 coulomb forces 53 Coulomb potential 78, 82, 90 cross-section 52 macroscopic 52 microscopic 52 crystal lattice 53 Cu-rich clusters 68

B bainitic-martensitic mixture 115 Baker–Nutting orientations 48 banite 50 binding energies EB 86 body-centred cubic (bcc) crystal structure Boltzmann constant 20 Boltzmann equation 77 brittle crack 59

59 D Debye frequency

80

175

176 defect concentration 113 defence in depth v, 5 densification 19 density 25 density-functional theory 81 detrapping 84 diffusion flux 20 diffusion length 94 diffusion–annihilation equation 93 diffusion-limited regime 83 diminishing rate 22 dislocation concentration 50 dislocations 88, 118 edge-dislocation 88 displacement cascade 118 displacement damage 50 displacement energy 56 displacement spike 54 dissolution of precipitates 125 Doppler broadening 93, 98 Doppler broadening spectroscopy 95 Doppler shift 72, 96 Doppler velocity 111 ductile-to-brittle transition temperature (DBTT) 58 E effect of Ni 67 effective lifetime 94 effective surface energy 60 Einstein equation 77 elastic collisions 52, 56 electric quadrupole interactions 109 electron density 72 electron momentum distribution 99 embrittlement 2 enrichment 17 excitation of electrons 50 F Faraday cage 104 feed water dispersion box 137 feed water distribution system 133 feed water pipes 131 Fermi energy 82 Fermi energy EF 75 Fermi surfaces 71 Fermi’s golden rule 86 ferritic matrix 48 fission gas 29 fission product 2, 8 fission products 26

Index free dislocations 60 free positrons 74 Frenkel pair 51, 117 fuel assemblies 26 fuel cladding 26 fuel cladding leak tightness coefficient fuel element 27 fuel matrix 26 fuel rod bundle 39

32

G gamma spectroscopy 26 -photon distribution 111 Gibbs–Thomson equation 19 grain boundary 23, 89 grain growth 22 abnormal 22 discontinuous 22 grain size 22 grain size limit 24 grid entity 39 H hardening 60 health risks 3 heat impacted zone 49 heat treatment 45 hematite (˛-Fe2 O3 ) 134 heterogeneous weld 139 hexagonal fuel assemblies 36 higher-temperature diffusion 80 Hollomon–Jaffe parameter 114 horizontal disposition 127 hydroxide 134 hyperfine interactions 106, 128 I impurity concentration 23 in situ specimens 139 in-core sipping equipment 28 in-service inspection 38 industrial risks 3 INES 15 integrity of the reactor pressure vessel 113 interim spent fuel storage facility 30 intermediate absorber 38 interstitial atoms 55 iodine spike 28 ion implantation 50 ion stopping 69 ionisation of atoms 50

Index

177

iron carbides 134 irradiation irradiation conditions 45 irradiation embrittlement 60 irradiation sensitivity 64 irradiation-induced defects 63

N

K Kinchin and Pease model 56 Kohn–Sham method 81 L lattice constant 95 lattice defects 50 leak testing management 30 lepidocrocite (-FeOOH) 140 local density approximation (LDA) long-term operation 127, 129 low-alloy Cr-Mo-V steel 120

82

M Mössbauer effect 105, 128 Mössbauer experiment 109 Mössbauer isotope 129 Mössbauer line 108 Mössbauer measurements 110 Mössbauer resonance 108 Mössbauer spectroscopy 108, 128 Mössbauer spectroscopy (MS) 63 Mössbauer spectrum 109, 129 Mössbauer technique 133 magnetite (-Fe3 O4 ) 134 magnetite’s spinel-type structure 135 martensite 50 mast sipping technique 30 material degradation 127 Maxwell–Boltzmann distribution 92 Mean diffusion length 93 mechanical strength 45 melting 9 melting point 55 metallic clusters 61, 69 metastable carbides 48 microstructure examinations 68 microvoids 68 moderator/fuel ratio 38 momentum of positrons 77 monitoring systems 7 monovacancies 86 Monte Carlo simulations 82

near-surface region 125 neutron capture 53 neutron energy 52 neutron fluence 42, 112 neutron flux 46 neutron scattering 70 non-destructive test methods 125 nozzle ring 42 NPP outage 133 nuclear energy 1 first civilian nuclear energy systems nuclear fuel 17 UO2 17 nuclear installation 1 nuclear power plant 126 nuclear regulatory authorities 15 nuclear safety v

1

O octahedral sublattice 137 one-dimensional momentum distribution open defects 27 open-volume defects 71 operating regime 137 optical microscopy 70 outlet nozzles 137

96

P paramagnetic fractions 134 paramagnetic phases 134 parasitic absorption 39 parasitic neutron absorption 37 passivation 143 PCI mechanism 30 Peierls stresses 21 periodical monitoring 34 physical barrier 5, 10 Planck constant 78 positron annihilation spectroscopy (PAS) positron annihilation techniques 71 positron diffusion 77 positron diffusion coefficient 93 positron injection 73 positron lifetime 83, 98 positron lifetime spectrum 84 positron microscope 125 positron scattering 77 positron spatial distribution 93 positron stopping times ts 74 positron trapping 82

63

178

Index

post-irradiation heat treatment 39 post-radiation heat treatments 126 precipitate–matrix interface 118 precipitation 48 pressure vessel 39, 69 primary circuit 26 primary knock-on atoms 51 propagation regime 83 pulsed low-energy positron system (PLEPS) 100 pulsed positron beam 98

stainless steel 47 steam generator 126 stoichiometry 22 stopping power 75 strontium 26 structural lattice defects 110 surface contamination 27 surveillance programmes 64 Surveillance Specimen Program

R

thermal annealing 125 thermal equilibrium 92 thermal neutrons 53 thermal spike 55 thermalisation time tR 75 Thomas–Fermi scattering 78 Torrens–Robinson–Norgett model 56 toughness 45 transition temperature 60 transition-limited regime 83 transmission electron microscopy (TEM) transmutation 51 transuranium 26 trapping coefficient 85 trapping model 82 trapping of positrons 71 trapping rate 98, 123

radiation creep 62 radiation damage 1, 53 radiation damage clusters 61 radiation effects 2 radiation-induced defects 99 radiation-induced point defects radioactive material 1 radionuclides 26 random walk theory 93 recoil atoms 53 refuelling outages 28 reliability 8 reprocessing plant 31 residual elements 62

118

S safety assessments 7 deterministic 7 probabilistic 7 safety culture 5 safety objectives 3 safety systems 1 saturated trapping 89 saturation trapping 123 Schrödinger equations 81 Schrödinger wavefunction 107 scintillator crystal 104 screw dislocations 122 sediments 138 segregation 50 simple trapping model (STM) 83 single-channel analyser (SCA) 97 sintering sintering rate 20 sintering process 18 liquid-phase sintering 18 solid-state sintering 18 sipping in pool 31 small vacancy clusters 118 specific trapping rate 85

112

T

V vacancy clusters 87 vacancy diffusion coefficient vacancy flux 20 vacancy-type defect 119 visual inspection 137 vitrification 18 VVER-1000 41 VVER-440 v, 11 VVER-440/V213 12 VVER-440/V230 12 W wavefunction 72 wavelength 95 weldability 45 Wigner–Seitz cell 90 wing parameter W 99 Y yield stress

60

20

63