High-Energy Ball Milling

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High-energy ball milling

© Woodhead Publishing Limited, 2010

Related titles: Solid-state hydrogen storage: Materials and chemistry (ISBN 978-1-84569-270-4) The next few years will see an emergence of hydrogen fuel cells as an alternative energy option in both transportation and domestic use. A vital area of this technological breakthrough is hydrogen storage, as fuel cells will not be able to operate without a store of hydrogen. The book focuses on solid state storage of hydrogen. Part I covers storage technologies, hydrogen containment materials, hydrogen futures and storage system design. Part II analyses porous storage materials, while Part III covers metal hydrides. Complex hydrides are examined in Part IV and Part V covers chemical hydrides. Finally, Part VI is dedicated to analysing hydrogen interactions. Nanostructure control of materials (ISBN 978-1-85573-933-8) Nanotechnology is an area of science and technology where dimensions and tolerances in the range of 0.1 nm to 100 nm play a critical role. Nanotechnology encompasses precision engineering as well as electronics, electromechanical systems and mainstream biomedical applications in areas as diverse as gene therapy, drug delivery and novel drug discovery techniques. Nanostructured materials present exciting opportunities for manipulating structure and properties at the nano scale and the ability to engineer novel structures at the molecular level has led to unprecedented opportunities for materials design. This new book provides detailed insights into the synthesis/structure and property relationships of nanostructured materials. This is a valuable book for materials scientists, mechanical and electronic engineers and medical researchers. Ceramic matrix composites: Microstructure, properties and applications (ISBN 978-1-85573-942-0) Ceramic matrix composites (CMCs) combine a range of properties such as high hardness, low density and resistance to high temperature which make them valuable materials in applications as diverse as body armour, power plants, automotive and aerospace engineering. This authoritative book reviews the five main types of CMCs. Part I focuses on fibre, whisker and particulate-reinforced ceramic matrix composites. Part II explores graded and layered ceramics, while Part III covers nanostructured CMCs. Refractory and speciality ceramic composites are reviewed in Part IV. Finally, Part V is dedicated to non-oxide ceramic composites. Details of these and other Woodhead Publishing materials books can be obtained by: • •

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High-energy ball milling Mechanochemical processing of nanopowders Edited by Małgorzata Sopicka-Lizer

Oxford

Cambridge


New Delhi

Published by Woodhead Publishing Limited, Abington Hall, Granta Park, Great Abington, Cambridge CB21 6AH, UK www.woodheadpublishing.com Woodhead Publishing India Private Limited, G-2, Vardaan House, 7/28 Ansari Road, Daryaganj, New Delhi – 110002, India www.woodheadpublishingindia.com Published in North America by CRC Press LLC, 6000 Broken Sound Parkway, NW, Suite 300, Boca Raton, FL 33487, USA First published 2010, Woodhead Publishing Limited and CRC Press LLC © Woodhead Publishing Limited, 2010 The authors have asserted their moral rights. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the authors and the publishers cannot assume responsibility for the validity of all materials. Neither the authors nor the publishers, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming and recording, or by any information storage or retrieval system, without permission in writing from Woodhead Publishing Limited. The consent of Woodhead Publishing Limited does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from Woodhead Publishing Limited for such copying. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. Library of Congress Cataloging in Publication Data A catalog record for this book is available from the Library of Congress. Woodhead Publishing ISBN 978-1-84569-531-6 (book) Woodhead Publishing ISBN 978-1-84569-944-4 (e-book) CRC Press ISBN 978-1-4398-2974-5 CRC Press order number: N10169 The publishers’ policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has been manufactured from pulp which is processed using acid-free and elemental chlorine-free practices. Furthermore, the publishers ensure that the text paper and cover board used have met acceptable environmental accreditation standards. Typeset by Toppan Best-set Premedia Limited Printed by TJ International Limited, Padstow, Cornwall, UK


Contents

1

Contributor contact details

xi

Introduction to mechanochemical processing M. Sopicka-Lizer, Silesian University of Technology, Poland

1

Part I Basic science of mechanochemistry 2

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3

3.1 3.2 3.3 3.4 3.5

Mechanism and kinetics of mechanochemical processes F. Kh. Urakaev, Institute of Geology and Mineralogy SB RAS, Russia Introduction General issues Calculation of t–P–T conditions at point of contact of milling tools and treated particles Mechanism of mechanochemical processes Kinetics of mechanochemical processes Use of kinetic equations Conclusions References Kinetic behaviour of mechanically induced structural and chemical transformations G. Mulas, Università degli Studi di Sassari, Italy; and F. Delogu, Università degli Studi di Cagliari, Italy Introduction Mechanochemistry Outline of experimental methods Degradation of chlorinated aromatics Hydrogen absorption on Mg2Ni/Ni composite

7

9

9 15 16 22 27 32 40 40

45

45 46 48 50 53 v


vi

Contents

3.6 3.7 3.8

Catalytic hydrogenation of carbon monoxide Future trends References

4

Materials design through mechanochemical processing M. Senna, Keio University, Japan Introduction Benefits of a mechanochemical route for materials design Theoretical aspects of modern mechanochemistry Composite oxides in electromagnetic applications Organic synthesis and utilization of spontaneous chemical reactions Conclusions and future trends References

4.1 4.2 4.3 4.4 4.5 4.6 4.7 5

5.1 5.2 5.3 5.4 5.5 5.6 5.7

Kinetic processes and mechanisms of mechanical alloying F. Delogu, Università degli Studi di Cagliari, Italy; and G. Mulas, Università degli Studi di Sassari, Italy Introduction Fundamentals of mechanical alloying processes in ball mills A phenomenological model of mechanical alloying kinetics Collecting and analysing experimental data on the kinetics of mechanical alloying reactions Mechanisms of chemical mixing on the atomic scale Future trends References

Part II Mechanochemical treatment of different materials 6

6.1 6.2 6.3

Mechanochemical synthesis of complex ceramic oxides T. Rojac and M. Kosec, Jozˇef Stefan Institute, Slovenia Introduction Mechanisms and kinetics of mechanochemical reactions in complex oxide systems Mechanochemical synthesis of complex oxides with various properties


57 59 60

63 63 64 67 68 80 84 85

92

92 93 95 98 103 106 108

111

113 113 114 126

Contents 6.4 6.5

Future trends References

7

Production of intermetallic compound powders by a mechanochemical approach: solid–liquid reaction ball milling D. Chen, Y. Jiang, J. Cai and Z. Chen, Hunan University, People’s Republic of China; and P. Huang, Central South University, People’s Republic of China Introduction Experimental equipment and methods As-milled products obtained from solid–liquid reaction ball milling Reaction mechanism of solid–liquid reaction ball milling Conclusions Acknowledgement References

7.1 7.2 7.3 7.4 7.5 7.6 7.7 8

8.1 8.2 8.3 8.4 8.5 9

9.1 9.2 9.3 9.4 9.5 9.6

Mechanochemical processing of non-oxide systems with highly covalent bonds M. Sopicka-Lizer, Silesian University of Technology, Poland Introduction Manufacturing non-oxide powders by mechanochemical processing Mechanochemical processing of reactive systems Conclusion References Mechanochemical synthesis of metallic–ceramic composite powders K. Wieczorek-Ciurowa, Cracow University of Technology, Poland Introduction Composite powder formation: bottom-up and top-down techniques Monitoring mechanochemical processes Examples of applied high-energy milling in the synthesis of selected metallic–ceramic composite powders Copper-based composite powders with Al2O3 Nickel-based composite powders with Al2O3


vii 139 141

149

149 151 152 158 164 164 164

167

167 169 180 188 188

193

193 194 203 205 207 214

viii

Contents

9.7

Other possible variants of the synthesis of metal matrix– ceramic composites in Cu–Al–O and Ni–Al–O elemental systems using mechanical treatment ex situ and in situ Conclusions Acknowledgements References

9.8 9.9 9.10 10

10.1 10.2 10.3 10.4 10.5 10.6

Mechanochemical synthesis of organic compounds and rapidly soluble materials A.V. Dushkin, Institute of Solid State Chemistry and Mechanochemistry SB RAS, Russia Introduction Solid state mechanochemical synthesis of low-molecularweight organic compounds Effect of solid particles aggregation on reactivity in mechanochemical reactions Synthesis of rapidly soluble materials for pharmaceutical applications Future trends References

Part III Mechanochemical processes in metal powder systems and other applications 11

11.1 11.2 11.3 11.4 11.5 11.6 11.7 12

12.1

Mechanochemical plating and surface modification using ultrasonic vibration S.V. Komarov, Nippon Light Metal Co. Ltd, Japan; S.E. Romankov, N. Hayashi and E. Kasai, Tohoku University, Japan Introduction Key concepts Surface modification and coating treatment of as-obtained substrates Surface treatment of precoated substrates Production of nanostructured coatings Conclusions and future trends References Mechanochemically activated powders as precursors for spark plasma sintering (SPS) processes R. Orrù, R. Licheri, A.M. Locci and G. Cao, Università degli Studi di Cagliari, Italy Introduction


217 219 220 220 224

224 225 229 235 244 245

249

251

251 253 255 260 267 272 273 275

275

Contents 12.2 12.3 12.4 12.5 12.6

Experimental materials and methods Results and discussion Conclusions and future trends Acknowledgements References

13

Synthesis of titanium dioxide-based, visible-light induced photocatalysts by mechanochemical doping S. Yin, Q. Zhang, F. Saito and T. Sato, Tohoku University, Japan Introduction Titanium dioxide and its photocatalytic applications Synthesis of anion-doped, titanium-dioxide, visiblelight induced photocatalysts by mechanochemical doping Future trends Acknowledgement References

13.1 13.2 13.3 13.4 13.5 13.6 14

14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 15

15.1 15.2 15.3 15.4 15.5 15.6

Soft mechanochemical synthesis of materials for lithium-ion batteries: principles and applications N.V. Kosova, Institute of Solid State Chemistry and Mechanochemistry SB RAS, Russia Introduction: principles of soft mechanochemical synthesis of solid inorganic compounds Reactions of LiOH with anhydrous oxides Reactions of LiOH with solid hydroxides Reactions of LiOH and Li2CO3 with crystal hydrates and acidic salts Conclusions Future trends Acknowledgements References Materials for lithium-ion batteries by mechanochemical methods L.C. Yang, Q.T. Qu, Y. Shi and Y.P. Wu, Fudan University, China; T. van Ree, University of Venda, South Africa Introduction Lithium-ion batteries Mechanochemical preparation of cathode materials Mechanochemical preparation of anode materials Solid electrolytes from mechanochemical methods Conclusions


ix 277 282 296 297 297

304

304 305 310 325 326 326

331

331 333 344 348 354 357 357 357

361

361 362 365 374 397 400

x

Contents

15.7 15.8

Acknowledgement References

401 402

Index

409



(* = main contact)

Chapter 3

Editor and Chapter 1

G. Mulas* Dipartimento di Chimica Università degli Studi di Sassari via Vienna 2 07100 Sassari Italy E-mail: [email protected]

M. Sopicka-Lizer Faculty of Materials Engineering and Metallurgy Akademicka 2A Silesian University of Technology 44-100 Gliwice Poland E-mail: malgorzata.sopicka-lizer@ polsl.pl

Chapter 2 F. Kh. Urakaev Institute of Geology and Mineralogy SB RAS Acad. Koptyug Av., 3 Novosibirsk, 630090 Russia E-mail: [email protected]; [email protected]

F. Delogu Dipartimento di Ingegneria Chimica e Materiali Università degli Studi di Cagliari piazza d’Armi 09123 Cagliari Italy E-mail: [email protected]

Chapter 4 M. Senna Faculty of Science and Technology Keio University 3-14-1, Hiyoshi Yokohama 223-8522 Japan E-mail: [email protected]

xi © Woodhead Publishing Limited, 2010

xii


Chapter 5 F. Delogu* Dipartimento di Ingegneria Chimica e Materiali Università degli Studi di Cagliari piazza d’Armi 09123 Cagliari Italy E-mail: [email protected]

P. Huang School of Material Science and Engineering Central South University Changsha 410082 People’s Republic of China

Chapter 8

G. Mulas Dipartimento di Chimica Università degli Studi di Sassari via Vienna 2 07100 Sassari Italy E-mail: [email protected]

M. Sopicka-Lizer Faculty of Materials Engineering and Metallurgy Akademicka 2A Silesian University of Technology 44-100 Gliwice Poland E-mail: malgorzata.sopicka-lizer@ polsl.pl

Chapter 6

Chapter 9

T. Rojac* and M. Kosec Electronic Ceramics Department Jozˇef Stefan Institute Jamova cesta 39 1000 Ljubljana Slovenia E-mail: [email protected]

K. Wieczorek-Ciurowa Faculty of Chemical Engineering and Technology Cracow University of Technology 24 Warszawska 31-155 Cracow Poland E-mail: [email protected]

Chapter 7 D. Chen*, Y. Jiang, J. Cai and Z. Chen School of Material Science and Engineering Hunan University Changsha 410082 People’s Republic of China E-mail: [email protected]

Chapter 10 A.V. Dushkin Institute of Solid State Chemistry and Mechanochemistry SB RAS Kutateladze 18 Novosibirsk 630128 Russia E-mail: [email protected]



xiii

Chapter 11

Chapter 13

S.V. Komarov* Nippon Light Metal Co. Ltd Nikkei Research & Development Center Kambara 161 Shimizu-ku Shizuoka-shi Japan E-mail: sergey-komarov@nikkeikin. co.jp

S. Yin*, Q. Zhang, F. Saito and T. Sato Institute of Multidisciplinary Research for Advanced Materials Tohoku University Katahira 2-1-1 Aoba-ku Sendai Japan E-mail: [email protected]

S.E. Romankov, N. Hayashi and E. Kasai Tohoku University, IMRAM Katahira 2-1-1 Aoba-ku Sendai-shi Japan

Chapter 12 R. Orrù* Dipartimento di Ingegneria Chimica e Materiali Università degli Studi di Cagliari piazza d’Armi 09123 Cagliari Italy E-mail: [email protected] R. Licheri, A.M. Locci and G. Cao* Dipartimento di Ingegneria Chimica e Materiali Università degli Studi di Cagliari piazza d’Armi 09123 Cagliari Italy E-mail: [email protected]

Chapter 14 N.V. Kosova Institute of Solid State Chemistry and Mechanochemistry SB RAS Kutateladze 18 Novosibirsk 630128 Russia E-mail: [email protected]

Chapter 15 L.C. Yang, Q.T. Qu, Y. Shi and Y.P. Wu* New Energy and Materials Laboratory (NEML) Department of Chemistry and Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials Fudan University Shanghai 200433 China E-mail: [email protected] T. van Ree Department of Chemistry University of Venda Thohoyandou 0950 South Africa


1 Introduction to mechanochemical processing M A Ł G O R Z ATA S O P I C K A - L I Z E R, Silesian University of Technology, Poland

Abstract: This chapter discusses the development of mechanochemical processing in various systems throughout its short history and shows the most impressive industrial application of the technique. A brief description of the complex action that takes place during powder mechanochemical processing is also included. Key words: crystal disordering, mechanochemical, metastable equilibrium, process feature.

Mechanochemical processing (MCP) can be defined as ‘a powder processing technique involving deformation, fracturing and cold welding of the particles during repeated collisions with a ball during high-energy milling’. Using mechanical energy to grind down various materials dates back to the beginning of human history and the application of flints to make a fire can be seen as an example of a mechanochemical treatment of materials. However, throughout the centuries, mechanical milling only involved diminution of particles without changing their structure and/or properties. The effect of chemical reactions initiated by mechanical action was found at the end of 19th century when Carey Lea first reported that the halides of gold, silver, platinum and mercury decomposed to halogen and metal during fine grinding in a mortar (Carrey Lea, 1893). His paper was published just after Ostwald introduced the term mechanochemistry in 1891. Heinicke’s much later definition (Heinicke, 1984) that ‘mechanochemistry is a branch of chemistry which is concerned with chemical and physicochemical transformation of substances in all states of aggregation produced by the effect of mechanical energy’ has been widely accepted. Since then the main applications of mechanochemical treatment of materials were found initially within the field of extractive metallurgy, where the process was used as a pretreatment step prior to leaching and extraction in order to increase the solubility of the minerals in question. The application of this rather simple technique to manufacturing advanced materials was driven by the industrial necessity to develop an alloy combining oxidedispersion strengthening (ODS) with γ′-precipitation hardening in a nickelbase superalloy intended for gas turbine applications. Benjamin’s work in the late 1960s showed that mechanochemical alloying (MA) must be used 1 © Woodhead Publishing Limited, 2010

2


when ordinary dispersion of oxide particles in liquid metal is not possible (Benjamin, 1970). The majority of the further work on development and production of ODS superalloys for application in the aerospace industry was done in the INCO laboratories in the USA (Ivanov and Suryanarayana, 2000). This is presently the major user of the MA process in the commercial production of nickel or iron-based high-temperature alloys which can be used at operating temperatures higher than 1300°C in carburizing or sulphidizing environments (Benjamin, 1970). Another spectacular example of commercial application where mechanochemically alloyed powders of Mg and Fe were used as heaters of MRE (meal, ready-to-eat), comes from their intensive use during the Desert Storm Operation by the USA in 1996 (Ivanov and Suryanarayana, 2000). On the other side of the world, in the former USSR, intensive studies on the application of mechanochemical processes in mineral and waste largescale processing resulted in several practical applications including treatment of tungsten-containing ore which was introduced at the Chirchik Plant or production of amalgam for children’s dentistry which was introduced at the Nikolsky Plant (Boldyrev, 2002). Development of unique grinding equipment in a variety of scales broadened the range of practical applications and new types of materials are being researched all over the world. Since 2000, more than 1500 scientific papers in the field of mechanochemistry have been published every year (Ivanov and Suryanarayana, 2000) and excellent reviews and monographs are available (Suryanarayana, 1999, 2004, 2008; Tkacova, 1989; Gutman, 1998; Arzt and Schultz, 1989; Barbadillo, 1993; Lai and Lu, 1998; Avvakumov, 1986). However, great developments in the technique itself and the accompanying milling devices have brought about new applications of MCP, broadening the range of the new materials and opening up new perspectives. There has been considerable interest in updating and summarizing existing knowledge of MCP. Mechanochemical processes use mechanical energy to activate chemical reactions and structural changes as well as particle size reduction. Under the action of cyclic loading, after breaking crystal bonds, MCP engages powder particles into a non-equilibrium state with a relaxation time of 10−7–10−3 s (Meyer and Meier, 1968). Comparison with other far from equilibrium processes (Table 1; Froes et al., 1995) shows that departure from equilibrium in MCP is faster than in rapid solidification. In addition, some long-lived defects with a lifetime of 10−3–106 s can be generated because of the solid imperfections and even if relaxed, the residual disorder remains in the activated material (Meyer and Meier, 1968). The mechanism of particle failure changes with the particle size and the structure of the particles undergoing grinding. A change in the accumulated energy relaxation from fracture to plastic deformation results in a dramatic


Introduction to mechanochemical processing

3

Table 1.1 Departure from equilibrium achieved in various processes (Froes et al., 1995)

Process

Maximum departure from equilibrium (kJ/Na)*

Solid-state quench Quench from liquid (rapid solidification) Condensation from vapour Irradiation/ion implantation Mechanical cold work Mechanical alloying

16 24 160 30 11 30

Na, Avogadro's number. * Assuming relaxation owing to kinetic effects.

increase in the strain followed by an extreme dislocation flow. Accordingly, the elastic strain energy transforms into elastic energy in the lattice defects and into structural disordering or it can be relaxed by the fracture of brittle material or crystallographic lattice rearrangement in polymorphic transformation. If more than one component is under the action of ball/powder particles collisions, then relaxation occurs by mechanical alloying, decomposition or synthesis of a new chemical compound. Thus stress, deformation and fracture initiate changes in the solids while the type and capacity of the changes involved remain a function of material’s properties (lattice bonds and crystal structure, elastic modulus, particle surface properties) and stress conditions in a milling device (the magnitude and direction of acting forces, stress rate and frequency of loading). It appears that the increase in energy of the milled powder caused by the increased volume fraction of grain boundaries and lattice disordering raises the free energy above the level of the amorphous state. A unique feature of a mechanochemically activated mixture of powders is formation of numerous reaction couples which increase with decreasing particle size and regenerate through repeated particle fracture and welding events. What is even more important, the reaction product phase does not separate the reactants as happens in ordinary chemical reactors since continuous product phase removal takes place during ball/powder particles collisions. Lack of a diffusion barrier in the reacting couples as well as formation of various defects acting as the fast diffusion paths overcomes the problem of the diffusion as the rate-controlling process. Consequently, the reaction can proceed with acceptable kinetics without the necessity of raising the reaction temperature. Therefore, several solid phase chemical reactions or alloying reactions occur at ambient temperature during MCP or they could easily proceed for the duration of the subsequent thermal treatment if necessary.


4


In a summary of MCP’s features, the application of this technique to the manufacture of advanced materials provides an opportunity to make products with unique characteristics, which may be difficult to produce in any other way. These products have the following benefits: •

•

•

•

•

•

exceptionally high reactivity of the resultant crystalline powder particles, besides substantial size reduction, because of their higher free energy accumulated in the defective crystal lattice and increased grain boundary volume; significant decrease in crystalline grains at the nanometer level or transformation to an amorphous structure as a result of growing crystal cell disordering when the mechanochemical treatment is lengthened; extension of solid solubility over the range of the equilibrium owing to the formation of a metastable equilibrium between the terminal solid solution and an amorphous phase; formation of micro(nano)-structured dense composite particles with a homogeneous distribution of (nano)dispresoids if the various elastic properties of the mechanically activated particles are employed; nucleation of various composites and complex oxides at ambient temperature by formation of hetero-bridging bonds as a result of intimate mixing under controlled shear stressing in the dry solid process and short range atomic transfer across the boundaries of solids, which no other method, like photo-, magneto- or plasma chemical processes, could achieve; synthesis at room temperature of a variety of equilibrium solid compounds without transition phases and/or without the need to use solvents because numerous reaction couples are formed and there is continuous removal of diffusion barriers.

This book presents the application of MCP to a variety of systems and the latest advances, challenges and future trends are described. Each chapter has been written by an internationally well-established and experienced researcher. The book starts by dealing with kinetics problems that arise during the action of MCP; generalized equations are constructed followed by the presentation of experimental research on kinetics in the chosen systems. Then the effects of mechanochemical treatment in a variety of systems and special application of the activated novel materials are covered. Finally, the drawbacks of the method (contamination, production cost) are discussed.

References arzt e. and schultz l. (eds) (1989). New Materials by Mechanical Alloying Techniques, DGM Informationgesellschaft, Oberursel, Germany.


Introduction to mechanochemical processing

5

avvakumov e.g. (1986). Mechanical Methods of Activation of Chemical Processes, Nauka, Novosibirsk. de barbadillo j.j., froes f.h. and schwarz r. (eds) (1993). Mechanical Alloying for Structural Applications, ASM International, Materials Park, OH. benjamin j.s. (1970). ‘Dispersion strengthened super alloys by mechanical alloying’, Metall Trans V, 1(10), 2943–51. boldyrev v.v. (2002). ‘A historic view on the development of mechanochemistry in Siberia’, Chem Sust Develop, 10, 3–10. carrey lea m. (1893). ‘On endothermic reactions effected by mechanical force: Part I’, Am J Sci III, xlvi, 241. froes f.h., suryanarayana c., russel k.c. and ward-close c.m. (1995). Proceedings of the International Conference on Novel Techniques in Synthetics and Processing of Advanced Materials, Singh J. and Copley S.M. (eds), TMS, Warrendale PA, 1. gutman e. (1998). Mechanochemistry of Materials, Cambridge International Science Publishers, Cambridge, UK. heinicke g. (1984). Tribochemistry, Academy Verlag, Berlin. ivanov e. and suryanarayana c. (2000). ‘Materials and process design through mechanochemical routes’, J Mater Synth Process, 8(3–4), 235–44. lai m.o. and lu l. (1998). Mechanical Alloying, Kluwer Academic, Boston, Massachusetts. meyer k. and meier w. (1968). Kristal Technik, 3, 399. suryanarayana c. (1999). Non-equilibrium Processing of Materials, volume 2, Pergamon Materials Series, Oxford. suryanarayana c. (ed) (2004). Mechanical Alloying and Milling, Marcel Dekker, New York. suryanarayana c. (2008). ‘Recent developments in mechanical alloying’, Rev Adv Mater Sci, 18, 203–11. tkacova k. (1989). Mechanical Activation of Minerals, Elsevier, Amsterdam.


2 Mechanism and kinetics of mechanochemical processes F. K h. U R A K A E V, Institute of Geology and Mineralogy SB RAS, Russia

Abstract: Parameters of the impact interaction between the milling tools and the material to be treated have been calculated for a series of mechanochemical reactors (comminuting devices, ball mills) using models based on non-linear elastoplastic theory for collision of solids. Possible mechanisms in the formation of nanocrystal particles and of chemical reactions taking place during crystallization have been studied. Generalized equations have been deduced for the kinetics rate constants of mechanochemical reactions and for the mechanical activation of substances in ball mills. Various examples of the application of the generalized kinetic equation to the calculations of ab initio rate constants of specific mechanochemical processes in ball mills are presented. The obtained theoretical values have been compared with experimental results. Key words: mechanochemistry, ball mills, mechanical activation, mechanochemical reactions, kinetics, theory, numerical modelling.

2.1

Introduction

The popularity and rapid development of investigations into mechanochemistry and mechanical activation (MA) (Urakaev and Boldyrev, 1999a,b,c, 2000a,b; Suryanarayana, 2001; Takacs, 2002; Koch, 2003; Miani and Maurigh, 2004; Butyagin and Streletskii, 2005; Kajdas, 2005; Butyagin, 2006; Urakaev and Shevchenko, 2007; Korchagin and Lyakhov, 2008; Urakaev, 2007, 2008, 2009) render actual character to the problem of the creation of models to describe the performance of devices used as mechanochemical reactors to predict the results of mechanical treatment of solids and to evaluate numerically the kinetics of mechanochemical processes (MP). In this context it is helpful to discuss the approaches to this problem recently proposed by Vasil’ev and Lomaeva (2003) and Butyagin (2003). In these works, the authors considered the athermic diffusion and deformation mechanisms of formation of cementite (Fe3C) upon the MA of an iron and carbon powder mixture. Note that the role of local heating caused by the impact–friction interactions of milling tools with particles of a treated 9 © Woodhead Publishing Limited, 2010

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material in the course of MA was completely ignored. This contradicts not only classical works, for example, by the Bowden-Tabor school (Bowden and Persson, 1961; Bowden and Tabor, 1974, 1986; Vick et al., 2000; Vick and Furey, 2001, 2003), but also all the practice of human history, which has aimed either to decrease heating of materials when they are treated mechanically or to use released heat, including primitive ways of making fire. The modelling of MP associated with arising short pressure or temperature pulses or the so-called t–P–T conditions (Urakaev and Boldyrev, 2000a) is built upon a rigorous thermodynamic basis. In my opinion, this basis can be complemented by invoking diffusion and deformation processes, but under no circumstances can be replaced by them. In the present work, on the basis of the models constructed for the interaction of milling tools with the substance under treatment, t–P–T conditions for different MP in ball mills are calculated. Urakaev and Boldyrev (2000b) show that the time factor (t) of the momentum of mechanical action upon the substance, along with traditional pressure and temperature characteristics, is especially important and the determining factor in the specific character of MP providing their difference from thermochemical and other methods used to perform solid state reactions. Known t–P–T conditions at the impact–friction point of contact of the particles to be treated allow traditional thermodynamic and physicochemical approaches to be used to consider the mechanism and to calculate the kinetics of MP in ball mills. Ball milling is characterized by a relative velocity W of the action of milling tools at the conjunction of particles under treatment (Fig. 2.1). For example, this case is realized in ball planetary mills (Fig. 2.2) characterized by the kinematic coefficient κ = ω/ω1 which is the ratio of the angular velocity of mill vial rotation ω1 to the angular velocity of the carrier rotation ω (scalar |ω| = 2πω, where ω is the frequency of the mill rotation); another characteristic of these mills is geometric, Γ = D/D1 which is the ratio of the distance D between the rotation axes to the radius D1 of the mill vial; Equation [2.1] follows (Urakaev, 2004, 2009): |W| = 2πωl1 [(κ + 1)2 + Γ2 − 2Γ(κ − 1) cos ϕ + (Γ + 1)2]0.5; Wn = |W| sin ϕ; Wt = |W| cos ϕ

[2.1]

where cos ϕ = −(1 + κ)/Γ determines the condition of a ball leaving the wall and where Wn and Wt are the normal and tangential components of the relative velocity, respectively. Now we shall characterize in brief the major direction of fundamental investigations into the theory of impact on solids. The most widely known is the elementary Newton’s theory of collisions based on the introduction of the collision coefficient at impact (Goldsmith, 1960). The wave theory of impact was first developed by Saint-Venant, Bernoulli, Poisson and Navier (Poisson, 1817; Kilchevsky, 1976; Kubenko, 1999). However, the methods



ω

A1

Thermocouples

ω1

A Motor

ω

Vials

ω1

Water

Water

Differential thermocouple battery

Planetary mill type AGO-2

Test object

Capsule

2.1 Modern vibratory (including SPEX 8000) and planetary (AGO-2) mills and schemes for temperature, intensity measurement and calculations used for planetary (Chattopadhyay et al., 2001; Pustov et al., 2001; Mio et al., 2002) and vibratory (Delogu et al., 2000) mills.

T

D

D1

SPEX 8000 or vibratory mill

12


ω1 D1

D

ω

W ϕ

2.2 Scheme for calculation of a planetary ball mill (AGO-2).

they used resulted in very slow convergence of the rows. A diametrically opposite theory was worked out by Hertz (1895). He assumed that the development of the impact process involves only small regions inside the bodies adjacent to the contact surface while other parts are not deformed during collision and move as absolutely rigid bodies. As a result, the problem of the collision of two elastic bodies was reduced to the problem of the collision of two material points, an elastic element being present between them (a spring or springs, Fig. 2.3). In the case of non-central collision of two elastic bodies, Routh’s ‘ξ-hypothesis’ was accepted (Routh, 1897; Maw et al., 1976; Keller, 1986; Stronge, 1990; Stoimenov, 1992). Accordingly, the connection between the tangential (It) and normal (In) momentums during the impact is formulated similarly to the Coulomb law of friction (Painlevé, 1895) It ≤ ξIn, where ξ is the dynamic friction coefficient (Fig. 2.4). The inequality sign is related to the cases when It is so small that slipping does not take place. If slipping occurs, the equality sign should be accepted. The essence of our approach to calculations in ball milling is best illustrated by the game of billiards. For example, to hit a ball into the right top billiard pocket under the Hertz theory it is necessary to strike the ball exactly at its centre (Fig. 2.4a). Clearly, the possibility of getting the balls


Mechanism and kinetics of mechanochemical processes Wt

ft

W

Wn

Xi

i Ri,ci,λi,ρi,θi Li = 1/Ri

0

fn

fij

εj

2rij

fn εi

Wt +

Lj = 1/Rj Rj,cj,λj,ρj,θj j

Xj

t=0

13

εij = εi + εj

ξ ij

Wt tij = 2rij

Wn tij = 2εij 0 ≤ t ≤ tij

2.3 Kinematics and dynamics of impact–friction contact of two elastic bodies (or particles) i and j, selected arbitrarily from the lined layer, in the region πr 2δ of impact action produced by a ball, see also Fig. 2.4b and Fig. 2.5.

(a)

(b)

In

It

δ∗

In

I

R′

θ′

I

It

D >> R′~R˝ >> δ∗~ δ >> Ri

1

2Ri

W Wt

I t ≤ ξ In

δ 3

W

Wt

L = 1/D ~ 0; θ wall

Wn

Wn θ˝

R˝ 2

2.4 Game in billiards, (a) illustrates Hertz theory and Routh’s ‘ξ-hypothesis’ (Coriolis, 1835; Delassus and Peres, 1923; Peres, 1923, 1924; Horák, 1948; Johnson, 1985; Persson, 2000; Popov et al., 2002, Schmitz et al., 2003; Ismail and Stronge, 2008) application to calculation of ball milling. (b) Impact–friction contact of lined (1, 2) or unlined (2, see Fig. 2.5) balls.

into the correct position and of having a player with the ability to hit the ball directly at its centre is rare. Therefore in ball mills, as in billiards, noncentral interactions prevail as shown by the direction of the ball in the top middle billiard pocket. In this case the normal interactions of balls are described by Hertz theory and the tangents are described by the Routh ξ-hypothesis. When the interactions are equal friction comes into force and the time taken by the frictional interaction is identical to the time taken by the normal interaction of the balls in Hertz theory. The same is true for impacts of a ball with a billiard table wall.


14


Moving on to mechanochemistry, it is sufficient to cover balls and billiard table walls with a treated material (Fig. 2.4b) according to the known property of self-lining of a surface by milling tools. The accuracy of the calculations of the parameters of collision by this procedure will depend on how precisely we manage to measure the altered elastic properties of self-lined balls and walls. The synthesis of the wave theory and Hertz theory is usually performed in two directions. One of them (Goldsmith, 1960; Harris and Piersol, 1961; Panovko, 1977; Brach, 1989; Zegzhda, 1997) implies the expedient fulfillment of the boundary conditions at the edge of colliding bodies. The second (Timoshenko, 1955; Brennan, 1957–58; Horák and Pacáková, 1961; Panovko, 1985) is based on the combination of the theory of transverse vibrations of a rod (a body) and Hertz’s theory of contact interaction. This is a modern approach (approaches) involving Hertz’s theory and wave theory, but like the theory presented by Timoshenko (1955), is only connected with the studies performed by Saint-Venant (Kilchevsky, 1976). It is curious that the experimental confirmation of these theories is only found in the cases of rather small relative velocities of collision (W ≤ 10 m s−1, billiards) or rather high ones (W ≥ 1 km s−1, shells), when the energy released is sufficient to change the aggregate state of colliding bodies. In this case, the problem is reduced to the solution of hydrodynamic equations of movement for a plastically deformed solid (liquid) in another liquid. Classical Newton’s theory does not take account of the physical properties of colliding bodies. Because of this, its application in the calculations of comminuting devices (mechanochemical reactors) gives the desired results only in the calculation of the kinematics and dynamics of the movement of particles under treatment in comminuting devices in combination with Hertz’s theory. On the other hand, the application of modern concepts of collisions in calculations for ball mills seems not to be feasible practically owing to the complexity of the mechanochemical processes occurring in them. This is possible only in the framework of non-linear elastic or elastoplastic Hertz’s theory with minimum (hypothetical) application of wave theory. The impact of balls with each other and of balls with a wall have been studied in detail and within 10% of the difference between the experimental measurements and the calculated data can be coordinated with Hertz’s theory if the relative velocity W of collision does not exceed 10 m s−1. Relative velocities of interaction of milling tools in ball mills are approximately 10 m s−1 also, therefore the Hertz–Routh theory is the best available for modeling MP. Therefore, its main statements and the results which will be used to construct the model and to calculate the comminuting devices are listed below.


Mechanism and kinetics of mechanochemical processes

2.2

15

General issues

Let us consider the collision of two solids, i and j (Fig. 2.3), without any connection to ball mills. In the framework of classical non-linear elastic Hertz theory, the connection between the impact force fij and the total deformation εij = εi + εj of the colliding bodies is accepted: fij = Bεij3/2. The coefficient B depends on the properties of materials of which the bodies are made and on the surface curvatures of the bodies Lk = 1/Rk, where Rk is the curvature radius at the contact point. The deviations in the calculations according to this theory increase with an increase in the relative normal velocity Wn of collisions, owing to the appearance of plastic deformations. More precise values (up to Wn = 30 m s−1) are obtained using the semi-empirical non-linear elastoplastic model (Batuev et al., 1969) in which it is accepted that fij = bεijn where b and n are constants determined experimentally. The results of calculations performed according to the non-linear elastic theory which is true up to Wn = 10 m s−1 are presented. The final results of calculations of the most important parameters have been presented in the most convenient form by Dinnik (1952) and Urakaev (2004) as follows: •

time tij of interaction of the two solids tij = (π/4)(10π)0.4{Wn−1(θi + θj)2(Li + Lj)[ρiρj/(ρiLj3 + ρjLi3)]2}0.2 [2.2]

•

maximum force fij of the interaction fij = (2/3)(10π)0.6{Wn6(θi + θj)−2(Li + Lj)−1 [ρiρj/(ρiLj3 + ρjLi3)]3}0.2

•

maximum stress σij in the centre of the contact area σij = 4(10/π4)0.2[Wn2(θi + θj)−4(Li + Lj)3ρiρj/(ρiLj3 + ρjLi3)]0.2

•

[2.5a]

maximum surface sij of the contact area, sij = πrij2 = (π/4)[(3/2) fij (θi + θj)/(Li + Lj)]2/3

•

[2.4b]

maximum radius rij of the contact area, rij = (1/2)[(3/2)fij(θi + θj)/(Li + Lj)]1/3

•

[2.4a]

mean mechanical stress at the contact point = 2σij/3 = (8/3π)(10π)0.2[Wn2(θi + θj)−4(Li + Lj)3 ρiρj/(ρiLj3 + ρjLi3)]0.2

•

[2.3]

[2.5b]

maximum total deformation εij of the bodies, εij = εi + εj = (1/4)[(9/4) fij2(θi + θj)2(Li + Lj)]1/3


[2.6a]

16

High-energy ball milling εiθj = εjθi

and from Equation [2.6a] εi = εijθi/(θi + θj);

εj = εijθj/(θi + θj)

[2.6b]

Here ρi and ρj are the densities, θi = 4(1 − νi2)/Ei and θj = 4(1 − νj2)/Ej are the values of compliance coefficients, νi and νj are the Poisson coefficients, Ei and Ej are the values of Young’s modules for the solids i and j.

2.3

Calculation of t–P–T conditions at point of contact of milling tools and treated particles

When building up a calculation model of ball mills, the following facts were used (Urakaev and Boldyrev, 1999a, 2000a; Urakaev, 2004). 1

2

3

4

5

6

One ball (N = 1; hypothetical choice) is present in the mill vial to comminute the material (the procedure for other numbers of balls N > 1 will be described below). The velocity W of the impact action of balls, with radius R, upon the treated material is determined by a set of dimensional and dimensionless parameters describing the rotation (vibration) frequencies ωk and the linear dimensions of the mill Dm so that |W| = W(N, ωk, Dm) and Dm >> R, for example, see Equation [2.1]. At the initial time interval of treatment, a quasi-equilibrium size distribution of the particles to be ground is achieved which is described by the mean radii Ri (i = 1, 2, . . . , j is the number of components of the material to be treated). For example (Schneider, 1968), in case i = 1 in the treatment of model materials (sodium chloride or quartz): R1(NaCl) = 16 × 10−5 cm and R1(SiO2) = 3 × 10−5 cm. A phenomenon involving self-lining (a layer of compact powder will be formed on the surface of milling tools) occurs (Kobayashi, 1995; Belyaev et al., 1998; Revesz and Takacs, 2007; Takacs and Torosyan, 2007), the thickness of the lining layer being δ (Fig. 2.4b and Fig. 2.5). In this case, Ri > 1/Dm = Lj = L, the inner wall layer can be treated in practical calculations of the collision with a ball with a density ρ = ρi, compliance θ = θi and radius R = 1/Li as a plane with curvature Lj = L = 0 and compliance θ = θj = θ. Using Equations [2.2]–[2.6] for the impact interaction of lined balls with a plane inner wall layer of the treated material, in accordance with point 4 above, one should accept the following values of the radius, density and compliance of the lined (*) balls: R* = 1/ Li ≈ R, ρ* = ρi ≈ ρ and θ* = θj = θ. For the impact of lined balls with each other, one should accept Li = Lj = L* = 1/R* ≈ 1/R, ρi = ρj = ρ* ≈ ρ and θi = θj = θ* ≈ θ in Equations [2.2]–[2.6]. The resulting equations are presented in Tables 2.1 and 2.2 where it is recommended that θ (Anderson, 1965) be described using the arithmetic means of compliances θi of the particles of different components of the treated mixture that make up the layer for compliance of the lined near-wall layers. For example, for a single-component substance, θ = θ1, for a twocomponent mixture, θ ≈ (θ1 + θ2)/2, and so on. Both during collision in milling tools (W) and under impulse pressure or stress wave propagation ( = P) at the conjunction of particles under treatment in the ball mills, the impact velocity W or force fij that acts at the point of contact between the milling tools and the particles can be resolved into normal (Wn, fn) and tangential (Wt, ft) constituents (Figs 2.3–2.5). As a result, during a characteristic time interval τ* of the action of the momen-



s12* = 1.8 (L1 + L2)−2ρ0.4θ−1.6(θ1 + θ2)2W0.8 r12* = 0.75 (L1 + L2)−1ρ0.2θ−0.8(θ1 + θ2)W0.4 f12* = 2.3 (L1 + L2)−2ρ0.6θ−2.4(θ1 + θ2)2W1.2 ε12* = 0.57 (L1 + L2)−1ρ0.4θ−1.6(θ1 + θ2)2W0.8 wn* = 0.28 [(ρ1L23 + ρ2L13)/ρ1ρ2(L1 + L2)3]0.5 × ρ0.5θ−2(θ1 + θ2)2W → (1300 cm s−1) t12* = 4.0[ρ1ρ2(L1 + L2)/(ρ1L23 + ρ2L13)]0.5 × ρ−0.1θ0.4W−0.2 → (1.4 × 10−9 s) wt* = 0.38 [(ρ1L23 + ρ2L13)/ρ1ρ2(L1 + L2)3]0.5 × ρ0.3θ−1.2(θ1 + θ2)W0.6 → (610 cm s−1) σn* = 1.5 ρ0.2θ−0.8W0.4 → (5.1 × 1010 dyn cm−2) σt* = 1.7 ρ0.12θ−0.48(θ1 + θ2)−0.4W0.24 σt* = 9.6 × 1010 dyn cm−2; ε12* = 6.8 × 10−7 cm; f12* = 1.4 dyn; r12* = 3.2 × 10−6 cm; s12* = 3.2 × 10−11 cm2.

t* = 3.6 Rρ0.4θ0.4W−0.2 → (1.54 × 10−5 s) f* = 2.3 R2ρ0.6θ−0.4W1.2 → (6.2 × 107 dyn) σ* = 1.9 ρ0.2θ−0.8W0.4 → (6.6 × 1010 dyn cm−2) = 1.3 ρ0.2θ−0.8W0.4 → (4.4 × 1010 dyn cm−2) r* = 0.75 Rρ0.2θ0.2W0.4 → (2.1 × 10−2 cm) s* = 1.8 R2ρ0.4θ0.4W0.8 → (1.4 × 10−3 cm2) ε* = 1.1 Rρ0.4θ0.4W0.8 → (4.36 × 10−3 cm)

Ball*–ball*

When studying the kinetics of reactions in mixtures of solids, we did not observe the lining of the balls made of WCo8 alloy. So, numerical values for different ΔT(x, t) sections are presented for the collisions of the unlined ball with the near-wall layer: ΔT(x, t) ≈ 1.0 ξ12W(c1c2λ1λ2ρ1ρ2)−0.25(θ + θ)−2(θ1 + θ2)[ρ(ρ1L23 + ρ2L13)/ρ1ρ2(L1 + L2)3]0.5 × {t0.5iErfc[x/2(a1a2)0.25t 0.5] − (t − t12)0.5iErfc[x/2(a1a2)0.25(t − t12)0.5]}; ΔT(x = 0; t = t12) ≈ 1300 K; ΔT(x = 0.5ε12; t = t12) ≈ 1100 K.

a

s12 = 3.1 (L1 + L2)−2ρ0.4(θ + θ)−1.6(θ1 + θ2)2W0.8 r12 = 1.0 (L1 + L2)−1ρ0.2(θ + θ)−0.8(θ1 + θ2)W0.4 f12 = 5.3 (L1 + L2)−2ρ0.6(θ + θ)−2.4(θ1 + θ2)2W1.2 ε12 = 1.0 (L1 + L2)−1ρ0.4(θ + θ)−1.6(θ1 + θ2)2W0.8 wn = 0.57 [(ρ1L23 + ρ2L13)/ρ1ρ2(L1 + L2)3]0.5 × ρ0.5(θ + θ)−2(θ1 + θ2)2W → (1600 cm s−1) t12 = 3.5 [ρ1ρ2(L1 + L2)/(ρ1L23 + ρ2L13)]0.5 × ρ−0.1(θ + θ)0.4W−0.2 → (1.0 × 10−9 s) wt = 0.57 [(ρ1L23 + ρ2L13)/ρ1ρ2(L1 + L2)3]0.5 × ρ0.3(θ + θ)−1.2(θ1 + θ2)W0.6 → (690 cm s−1) σn = 2.0 ρ0.2(θ + θ)−0.8W0.4 → (5.6 × 1010 dyn cm−2) σt = 2.0 ρ0.12(θ + θ)−0.48(θ1 + θ2)−0.4W0.24 σt = 10 × 1010 dyn cm−2; ε12 = 8.9 × 10−7 cm; f12 = 1.8 dyn; r12 = 3.5 × 10−6 cm; s12 = 3.8 × 10−11 cm2.

s12* = 1.0 (L1 + L2)−2ρ0.4θ−1.6(θ1 + θ2)2W0.8 r12* = 0.57 (L1 + L2)−1ρ0.2θ−0.8(θ1 + θ2)W0.4 f12* = 1.0 (L1 + L2)−2ρ0.6θ−2.4(θ1 + θ2)2W1.2 ε12*= 0.33 (L1 + L2)−1ρ0.4θ−1.6(θ1 + θ2)2W0.8 wn*= 0.14 [(ρ1L23 + ρ2L13)/ρ1ρ2(L1 + L2)3]0.5 × ρ0.5θ−2(θ1 + θ2)2W → (630 cm s−1) t12*= 4.6 [ρ1ρ2(L1 + L2)/(ρ1L23 + ρ2L13)]0.5 × ρ−0.1θ0.4W−0.2 → (1.6 × 10−9 s) wt* = 0.25 [(ρ1L23 + ρ2L13)/ρ1ρ2(L1 + L2)3]0.5 × ρ0.3θ−1.2(θ1 + θ2)W0.6 → (400 cm s−1) σn* = 1.2 ρ0.2θ−0.8W0.4 → (4.1 × 1010 dyn cm−2) σt* = 1.45 ρ0.12θ−0.48(θ1 + θ2)−0.4W0.24 σt* = 8.2 × 1010 dyn cm−2; ε12* = 3.9 × 10−7 cm; f12* = 0.6 dyn; r12* = 2.4 × 10−6 cm; s12* = 1.8 × 10−11 cm2.

t* = 4.1 Rρ0.4θ0.4W−0.2 → (1.76 × 10−5 s) f* = 4.0 R2ρ0.6θ−0.4W1.2 → (11 × 107 dyn) σ* = 1.5 ρ0.2θ−0.8W0.4 → (5.1 × 1010 dyn cm−2) = 1.0 ρ0.2θ−0.8W0.4 → (3.4 × 1010 dyn cm−2) r* = 1.1 Rρ0.2θ0.2W0.4 → (3.2 × 10−2 cm) s* = 4.1 R2ρ0.4θ0.4W0.8 → (3.2 × 10−3 cm2) ε* = 1.3 Rρ0.4θ0.4W0.8 → (5.15 × 10−3 cm)

t = 3.1 Rρ0.4(θ + θ)0.4W−0.2 → (1.46 × 10−5 s) f = 5.3 R2ρ0.6(θ + θ)−0.4W1.2 → (13 × 107 dyn) σ = 2.5 ρ0.2(θ + θ)−0.8W0.4 → (7.2 × 1010 dyn cm−2) = 1.7 ρ0.2(θ + θ)−0.8W0.4 → (4.8 × 1010 dyn cm−2) r = 1.0 Rρ0.2(θ + θ)0.2W0.4 → (2.9 × 10−2 cm) s = 3.1 R2ρ0.4(θ + θ)0.4W0.8 → (2.7 × 10−3 cm2) ε = 1.0 Rρ0.4(θ + θ)0.4W0.8 → (4.35 × 10−3 cm)

Particle interaction in near-wall lined layers

Ball*–flat layer

Ball–flat layer

Table 2.1 Calculating expressions. Numerical values for the treatment of an equimolar mixture of calcite and quartz in a KhK 871 mill (ω = 11 s−1, Wn = W = 9.2 m s−1, balls from WCo8 alloy are given in parentheses). An asterisk (*) corresponds to the lined ball loada


s1* = 1.8 R12ρ0.4θ10.4W0.8 → (9.5 × 10−10 cm2) r1* = 0.75 R1ρ0.2θ10.2W0.4 → (1.7 × 10−5 cm) f1* = 2.3 R12ρ0.6θ1−0.4W1.2 → (17 dyn) ε1* = 1.1 R1ρ0.4θ10.4W0.8 → (3.6 × 10−6 cm) wn* = 0.57 (ρ/ρ1)0.5W → (910 cm s−1) t1* = 4.0 R1ρ10.5ρ−0.1θ10.4W−0.2 → (8.1 × 10−9 s) wt* = 0.38 ρ1−0.5ρ0.3θ1−0.2θ1W0.6 → (4300 cm s−1) σn* = 1.5 ρ0.2θ1−0.8W0.4 → (2.1 × 1010 dyn cm−2) σt* = 1.3 ρ0.12θ1−0.88W0.2 → (4.0 × 1010 dyn cm−2) 2q1* = ξ1 wt → (6.3 × 1013 erg cm−2 s−1).

t* = 3.6 Rρ0.4θ10.4W−0.2 → (1.7 × 10−5 s) f * = 2.3 R2ρ0.6θ1−0.4W1.2 → (2.6 × 107 dyn) σ* = 1.9 ρ0.2θ1−0.8W0.4 → (2.7 × 1010 dyn cm−2) = 1.3 ρ0.2θ1−0.8W0.4 → (1.8 × 1010 dyn cm−2) r* = 0.75 Rρ0.2θ10.2W0.4 → (2.1 × 10−2 cm) s* = 1.8 R2ρ0.4θ10.4W0.8 → (1.4 × 10−3 cm2) ε* = 1.1 Rρ0.4θ10.4W0.8 → (4.5 × 10−3 cm)

Ball*–ball*

In the experiment on the treatment of NaCl particles, balls are lined only insignificantly, so the numerical values for different sections of temperature pulses are presented for the impact interaction of an unlined ball with the flat near-wall layer (T0 = 375 K): ΔT(x, t) ≈ 0.96 ξ1Wρ0.5(c1λ1ρ1)−0.5(θ + θ1)−2θ1{t0.5iErfc[x/2(a1t)0.5] − (t − t1)0.5iErfc[x/2(a1(t − t12)0.5]}. At the rise of ΔT: Tm − T0 = ΔTm = ΔT(x = 0; t = tm) = ΔT(x = xm; t = t1); tm ≈ 2.5 × 10−9 s; iErfc[xm/2(a1t)0.5] = 0.5642(tm/t1)0.5 and xm ≈ 8.7 × 10−6 cm. At the drop of ΔT: ΔTm = ΔT(x = 0; t = tm′); tm′ = (t1 + tm)2/4tm ≈ 1.0 × 10−8 s. ΔT(x = 0; t = t1) ≈ 1220 K; ΔT(x = 0.5ε1; t = t1) ≈ 1050 K; Δtm = tm′ − tm ≈ 8.0 × 10−9 s.

a

s1 = 3.1 R12ρ0.4(θ + θ1)−1.6θ12W0.8 → (1.3 × 10−10 cm2) r1 = 1.0 R1ρ0.2(θ + θ1)−0.8θ1W0.4 → (2.0 × 10−5 cm) f1 = 5.3 R12ρ0.6(θ + θ1)−2.4θ12W1.2 → (27 dyn) ε1 = 2.0 R1ρ0.4(θ + θ1)−1.6θ12W0.8 → (5.1 × 10−6 cm) wn = 1.1 (ρ/ρ1)0.5(θ + θ1)−2θ12W → (1000 cm s−1) t1 = 3.5 R1ρ10.5ρ−0.1(θ + θ1)0.4W−0.2 → (7.6 × 10−9 s) wt = 0.57 ρ1−0.5ρ0.3(θ + θ1)−1.2θ1W0.6 → (5400 cm s−1) σn = 2.0 ρ0.2(θ + θ1)−0.8W0.4 → (2.5 × 1010 dyn cm−2) σt = 1.5ρ0.12(θ + θ1)−0.48θ1−0.4W0.2→ 4.3 × 1010 dyn cm−2 2q1 = ξ1 wt → (9.1 × 1013 erg cm−2 s−1).

s1* = 1.0 R12ρ0.4θ10.4W0.8 → (5.3 × 10−10 cm2) r1* = 0.57 R1ρ0.2θ10.2W0.4 → (1.3 × 10−5 cm) f1* = 1.0 R12ρ0.6θ1−0.4W1.2 → (7.4 dyn) ε1* = 0.66 R1ρ0.4θ10.4W0.8 → (2.2 × 10−6 cm) wn* = 0.28 (ρ/ρ1)0.5W → (450 cm s−1) t1* = 4.6 R1ρ10.5ρ−0.1θ10.4W−0.2 → (9.3 × 10−9 s) wt* = 0.25 ρ1−0.5ρ0.3θ1−0.2θ1W0.6 → (2800 cm s−1) σn* = 1.2 ρ0.2θ1−0.8W0.4 → (1.7 × 1010 dyn cm−2) σt* = 1.1 ρ0.12θ1−0.88W0.2 → (3.4 × 1010 dyn cm−2) 2q1* = ξ1 wt → (3.1 × 1013 erg cm−2 s−1).

t* = 4.1 Rρ0.4θ10.4W−0.2 → (1.9 × 10−5 s) f* = 4.0 R2ρ0.6θ1−0.4W1.2 → (4.4 × 107 dyn) σ* = 1.5 ρ0.2θ1−0.8W0.4 → (2.1 × 1010 dyn cm−2) = 1.0 ρ0.2θ1−0.8W0.4 → (1.4 × 1010 dyn cm−2) r* = 1.1 Rρ0.2θ10.2W0.4 → (3.2 × 10−2 cm) s* = 4.1 R2ρ0.4θ10.4W0.8 → (3.3 × 10−3 cm2) ε* = 1.3 Rρ0.4θ10.4W0.8 → (5.2 × 10−3 cm)

t = 3.1 Rρ0.4(θ1 + θ2)0.4W−0.2 → (1.6 × 10−5 s) f = 5.3 R2ρ0.6(θ1 + θ2)−0.4W1.2 → (5.5 × 107 dyn) σ = 2.5 ρ0.2(θ1 + θ2)−0.8W0.4 → (3.1 × 1010 dyn cm−2) = 1.7 ρ0.2(θ1 + θ2)−0.8W0.4 → (2.1 × 1010 dyn cm−2) r = 1.0 Rρ0.2(θ1 + θ2)0.2W0.4 → (2.9 × 10−2 cm) s = 3.1 R2ρ0.4(θ1 + θ2)0.4W0.8 → (2.6 × 10−3 cm2) ε = 1.0 Rρ0.4(θ1 + θ2)0.4W0.8 → (4.2 × 10−3 cm)

Particle interaction in near-wall lined layers

Ball*–flat layer

Ball–flat layer

Table 2.2 Calculating expressions. Numerical values for the treatment of a model single-component material (sodium chloride) in a EI 2 × 150 mill (ω = 10 s−1, Wn = W = 8.4 m s−1, steel balls are given in parentheses). An asterisk (*) corresponds to the lined ball loada


21

tum, deformation of milling tools occurs with a shift which leads to an increase in temperature T at the point of contact (Fig. 2.4b and Fig. 2.5). For example, during impact–friction contact of the unlined ball with the lined layer wall (Fig. 2.5), the following expressions were obtained: •

time t of interaction of the milling tools (see Table 2.1, column 1, line 1) t = 3.1 Rρ0.4(θ + θ)0.4Wn−0.2

•

mean mechanical stress or pressure P at the contact point = P = 1.7 ρ0.2(θ + θ)−0.8Wn0.4

•

[2.7]

[2.8]

density of heat source 2Q and temperature impulse ΔT(X, t) in the vicinity of contact area X 2Q = ξPWt; ΔT(X, t) = 2Q (cc*λλ*ρρ*)−0.25 × {t0.5 iErfc[X/2(aa*)0.25t0.5] − (t − t)0.5 iErfc[X/2(aa*)0.25(t − t)0.5]}; ΔT(max) = ΔT(0, t); iErfc [0] = 0.5642

[2.9]

Here ξ is the dynamic friction coefficient, a = λ/cρ and a* = λ*/c*ρ*, λ and λ*, c and c* are thermal diffusivities, thermal conductivities and specific heat capacities of the ball and treated material in a ball mill, respectively. Thus, we have determined t–P–T conditions for the impact–friction contact of milling tools in a ball mills. During the collision of milling tools under the impact force f in a cylindrical volume πr2δ with the end face area s = πr2 (or a diameter of 2r) and a height δ (Fig. 2.5), a mean pressure impulse P = = f/s is realized, see Equation [2.8]. Because of this, when considering the interaction of the particles to be treated, selected from among those present in the given volume, mean values of these parameters are used. In this case, for a mean force characteristic of the interaction between any selected particles i and j in this volume (Fig. 2.3), fij = sij (f/s) = sij P is obtained. Independently, (see Equation [2.5a]) the expression for the impact contact area of the selected particles sij follows from the Hertz’s theory: sij = (π/4)[(3/2)Psij (θi + θi))/(Li + Lj)]2/3

[2.10]

Having determined the impact contact area of the selected particles sij from the Equation [2.10], fij, rij can be determined; the corresponding overall impact deformation (approach) of the particles εij can be found from Equation [2.6]. In order to determine separately the characteristic time (tij) and the normal constituent of the relative velocity (wn) describing the interaction of the selected particles i and j (Fig. 2.3), evident equation tij = 2εij/wn is used. An independent consequence of the Hertz’s theory, see Equation [2.2], gives the expression:


22


2εij/wn = (π/4)(10π)0.4{wn−1(θi + θi)2(Li + Lj)[ρiρj/(ρiLj3 + ρjLi3)]2}0.2

[2.11]

Having determined wn, tij, the tangential constituent of the relative velocity of particle interaction wt = 2rij/tij can be determined. Applying the Hertz’s theory, see Equation [2.4], the corresponding normal (σn) and shift (σt) maximum stresses which are developed at the impact contact of the selected particles i and j are calculated. For the temperature impulse ΔT(x, t) over the averaged distance x and time t in the vicinity of the impact−friction contact of the particles i and j (Fig. 2.3), the equation of thermal conductivity is solved ∂T(x, t)/∂t = (aiaj)0.5∂2T(x, t)/∂x2 with the boundary conditions (t ≥ 0; T(x, 0) = T0; λij [∂T(∞, t)/∂x] + qij = 0; 0 ≤ x ≤ ∞; T(∞, t) = T0; ∂T(∞, t)/∂x = 0) for semi-limited bodies with the heat source of the density 2qij = ξijσnwt symmetric on the sliding plane (Lykov, 1965, 1967): ΔT(x, t) = 2qij(cicjλiλjρiρj)−0.25{t0.5iErfc[x/2(aiaj)0.25t0.5] − (t − tij)0.5iErfc[x/2(aiaj)0.25(t − tij)0.5]}

[2.12]

Here ξij is the dynamic friction coefficient, ai and aj, λi and λj, ci and cj are thermal diffusivities, thermal conductivities and specific heat capacities of the particles, respectively (Fig. 2.3). Numerical values of the calculated parameters are presented in Tables 2.1 and 2.2 as examples of the conditions under which the mechanochemical reaction CaCO3 + SiO2 = CaSiO3 + CO2 proceeds and for the conditions under which a single-component model material (NaCl) is activated. The results are presented for different variants of the interaction between the milling bodies. The heat capacity and heat conductivity of the materials are listed for the temperature T = (T0 + Tm)/2 where Tm is the melting point of the compounds to be treated and T0 = 375 K is the background temperature in the operating mill. Thus, we have determined t–P–T conditions for the impact–friction contact of treated particles 1 and 2 (Fig. 2.7) in a ball mill. For the case NaCl treatment, both for time t and for distance x (up to xm > ε1/2), temperature impulse exceeds the melting point of NaCl, ΔTm ≈ 700 K, see points ΔT(x, t) in Fig. 2.8: ΔTm = ΔT(0, tm) = ΔT(0, tm′) = ΔT(xm, t1). However, contact melting of particles requires special consideration since the time during which the temperature impulse exists at a level above melting point is relatively small.

2.4

Mechanism of mechanochemical processes

The quantitative aspect of this problem includes numerical estimates of heat and mass transfer in the local regions of the particles under given t–P–T conditions aimed at the description of the possibilities and mechanisms of different physicochemical processes, namely, phase transitions and chemical reactions. Local processes of melting and the subsequent inevi-



23

x (cm) 10 1400

–4

10–5

10–6

0 1400

ε1/2

t1 = 7.6×10–9 s

1200

1200

xm

ΔT (0, t)

ΔT = ΔTm

800

800

ΔT (x, t 1)

1000

1000

600

600 tm

400

400

t′m

200

200

0

0 0

1

2

3 4 5 t (in t1 units)

6

7

2.8 Graph of the temperature impulse ΔT(x, t) at impact–friction contact of NaCl particles (R1 ≈ 1.63 × 10−4 cm, taking account of their contact melting) during treatment in a planetary mill EI 2 × 150 at ω = 10 s−1.

table solidification (crystallization or amorphization) of particles of substances treated in ball mills have consequences which are important for mechanochemistry generally, for example the effect of short-term melting is the formation of nanocrystals and amorphous nanoparticles. If we demonstrate the possibility of local contact melting of the treated particles, then the subsequent process of solidification will take place under very unusual conditions (Urakaev and Boldyrev, 1999b, 2000b). It has been shown by Landau (1950) that the propagation rate of the melting zone surface m′ is determined by a single parameter: h = π0.5c1ΔTm/2Hm

[2.13] −1

where Hm(NaCl) = 4.8 × 10 erg g is latent heat of fusion. The rate of fusion m′(t, h) increases with time and approaches to the stationary rate of fusion: 9

ms′ = q/ρ1(Hm + c1ΔTm)

[2.14]

where q is the density of the heat source at the boundary between the crystal and melt. Monograms of the ratio m′/ms′ = f(t, h) = f[y(t), h] have been presented as a function of a dimensionless parameter y(t) = (t/tm) − 1 for different


24


h values, where tm is time required to achieve the melting point of the initial crystal. In the case under consideration, from Table 2.2 and Fig. 2.8 it is easy to obtain the required parameters tm ≈ 2.5 × 10−9 s and tm′ ≈ 1.0 × 10−8 s is the time of ceasing fusion as determined by the condition ΔT(0; tm, tm′) − ΔTm = 0; y = (tm′/tm) − 1 ≈ 3 and h ≈ 1.3. Let us define q for the fused zone existing at the impact-friction contact of NaCl particles treated in the mill. The solution of this problem has been presented in (Schlichting, 1951; Bowden and Persson, 1961). A laminar flow of viscous film of a liquid between two parallel plane walls moving at a relative rate of wt is considered; in our case from Table 2.2, wt = 5400 cm s−1, if the viscosity of the melt is μ(NaCl, T = Tm) and the distance between the walls is 2d*(t), the density of heat source 2q (in the case of symmetry along the middle plane) will be: q = μwt2/d*

[2.15]

Using Equations [2.14] and [2.15], a graphic solution m′/ms′ = f(t) and the identity d*(t) = m′(t − tm), the following equations were obtained: m′ = wt[μf(t)/(t − tm)ρ1(Hm + c1ΔTm)]0.5 d* = wt[μf(t)(t − tm)/ρ1(Hm + c1ΔTm)]0.5

[2.16]

q = wt[μρ1(Hm + c1ΔTm)/f(t)(t − tm)]0.5 Since f(t = tm′) = f(3, 1.3) ≈ 0.55, it is easy to determine from Equation [2.16] the numerical values of the required parameters for fusion at t = tm′ before the reverse process (i.e. crystallization) starts, in the vicinity of the impact–friction contact of NaCl particles during MA: m′(tm′) ≈ 33 cm s−1; 2d*(tm′) ≈ 7 × 10−7 cm; 2q(tm′) ≈ 5 × 1012 erg cm−2 s−1, when the size of NaCl particles in contact R1 ≈ 1.63 × 10−4 cm. It is important to compare 2q with 2q1 ≈ 9.1 × 1013 erg cm−2 s−1 for ‘dry friction’ between NaCl particles, see Table 2.2. When both walls are kept at a constant temperature T(x = 0) = T(x = 2d*) = Tm, the temperature of the melt ΔTm follows the square law (the distance from one wall to another being x and a maximum is achieved at the medium plane of shift, x = d*): ΔTm′ = T − Tm = μwt2x[1 − (x/2d*)]/2λd*

[2.17]

Since for NaCl melt, λ(Tm = 1074 K) = 2.5 × 105 erg cm−1 K−1 s−1, a maximum temperature increase at x = d* in the middle zone of the melt is ΔTm′(x = d*) = μwt2/4λ ≈ 0.6 K. This indicates that local heating is limited above the melting point of particles treated in ball mills when the possibility of fusion is taken into account (Fig. 2.8). Proof of possible contact melting during MA has been obtained by Bowden and Persson (1961) and by Urakaev and Avvakumov (1978) studying of the rate exchange reaction


Mechanism and kinetics of mechanochemical processes (a)

25

(b)

0.8 0.8 α

α

0.6 0.4

0.4

0.2 0

0.6

0.2 0

4

8

12

16

τ / 60 = 8 s 0

τ / 60 (s)

2

4

6

8

10 12

ω (s–1)

2.9 Degree α of transformation for the reaction NaNO3 + KCl = KNO3 + NaCl depending on (Urakaev and Avvakumov, 1978): time τ (planetary mill EI 2 × 150 for ω = 7.1 s−1; ×, usual ball rotating mill) and frequency ω of rotation (for MA τ = 8 min in a planetary mill EI 2 × 150).

NaNO3 + KCl = KNO3 + NaCl executed in a ball planetary mill. It is noticeable (Fig. 2.9) that the reaction occurs at a high rate only when conditions for contact fusion at ω ≥ 5 s−1 have been achieved. The dependence of the thickness of crystallized layer d and overcooling ΔTc at the boundary between the phases on crystallization time tc are described by Equations [2.18] and [2.19] (Lyubov and Roytburd, 1962; Heertijes and Bouter, 1965): tc = ρ1Hm[d2 + (2λd/ρ1HmA)]/2λΔTs ≈ d/AΔTc

[2.18]

ΔTs/ΔTc = [1 + (2ρ1Hm A2ΔTstc/λ)]0.5 ≈ 1

[2.19]

where ΔTs = Tm − Ts (ΔTs is the substrate temperature). One can see that at the start of the crystallization process at small tc and d values, their interdependence is expressed in a linear form and ΔTs ≈ ΔTc. The value of the crystallization factor is A ≈ 0.1 cm K−1 s−1 for rapidly crystallized substances. Maximum overcooling is possible for the existing melt of NaCl at ΔTc* ≈ 170 K (Ubellohde, 1965). If this value is taken as ΔTc for crystallization in the region near the contacts between NaCl particles treated in a mill, the time for crystallization of a layer with a thickness of d = 2d* will be tc ≈ 4.1 × 10−8 s (see Equation [2.18]). This assumption can be shown to be correct both by the graphic representation shown in Fig. 2.8 or by Equation [2.12]. Even taking account of the released crystallization heat 2qc = 2d*ρ1Hm/tc ≈ 3.5 × 1011 erg cm−2 s−1 and 2qc < 2q < 2q1, overcooling of the melt by ΔTc = ΔTc* ≈ 170 K in the zone of contact between NaCl particles is achieved within the time interval Δt* ≈ 5 × 10−9 s which is much less than tc. Since crystallization and solidification are generally not identical processes (cf.


26


Chalmers, 1964; Strickland-Constable, 1968; Flemings, 1974), the very high cooling rate obtained for the fused contact zone of the treated particles explains the widely known process involving amorphization during their MA of substances that are difficult to crystallize. However, for any compound that undergoes crystallization, it is important to know the size of critical nuclei rcr at which new crystals are formed in the fused zone: 2rcr = 2σsTm/ρ1HmΔTc, where 2rcr is the diameter of a sphere or a side of a cube of the new phase (a crystal that has just formed) and σs is the surface tension at the boundary between the melt and the crystal (for NaCl, σs = 23–34 erg cm−2; Gorskii and Mikulich, 1964). In order to meet the demand rcr < d*, it is necessary for ΔTc > 17 K. As we have shown above, this ΔTc can easily be achieved in the fused zone of impact– friction contact between NaCl particles. It is clear that the size of new formed crystalline nuclei of NaCl on the surface of treated particles will remain in the order rcr ≈ 10−7 cm. So, we have shown that during impact– friction contact of NaCl particles treated in comminuting devices, the formation of nanocrystal particles of about 10−7 cm occurs owing to local short-time fusion-crystallization processes (∼10−7 s). It is known that the properties of nanocrystals can be substantially different from the properties of macrocrystals. Because of this, MA of the substances in comminuting devices can be considered to be the result of the formation of a nanocrystal or X-ray amorphous state of the particles during treatment at the submicrometre level. More generally, this is the result of quenching non-equilibrium defects and structures (dislocations, twinning and intergrain boundaries, nanocrystal or nanoamorphous submicrometre states) during crystallization (solidification) of the melt during rapid cooling (to be more exact, during the short pressure and temperature impulses). Contact fusion during impact–friction contact of particles of different types leads to a sharp increase in diffusion coefficients. As a consequence, the crystallization of the melted layer should also result in the formation of the nanocrystal products of different mechanochemical reactions, in accordance with thermodynamic and kinetic conditions in the fused zone. The proposed mechanism for the mechanochemical reaction can be used directly in other types of MP involving contact melting (i.e. mechanodestruction of individual compounds except those decomposing in the solid state below their melting temperature like Ag2C2O4 and many other compounds) (Brown et al., 1980). It can be used for the majority of reactions that occur during mechanical alloying of metals (Lü and Lai, 1998; Bhadeshia, 2000; El-Eskandarany, 2001) except for ones that fuse with difficulty. For example, the proposed mechanism provides an explanation for the very low decomposition rate of sodium nitrate and many other compounds in the mill because it is identical to the thermal decomposition at



27

their melting point (temperature impulse at contact between the particles is limited by the contact temperature at which the particles melt, as shown earlier). Thermal decomposition of sodium nitrate occurs at a noticeable rate only during fusion at temperatures much above its melting point Tm = 580 K. The kinetics of this type of process that occurs in comminuting devices, as well as the kinetics of processes with different mechanisms from the one described (solid state reactions including mechanical alloying of metals) will be considered in detail in the next section.

2.5

Kinetics of mechanochemical processes

The interaction of the particles of a compound that is being treated occurs in a coupled manner in the lining layer. Because of this, in order to build up a calculative kinetic model of ball milling, we shall select arbitrarily a pair of particles in contact, designated as 1 and 2 in Fig. 2.7. In order to obtain thermodynamic and kinetic parameters describing MP, it is sufficient to obtain the dependence of pressure σ and temperature T in some region x near the contact surface s12 of the particles 1 and 2 at the time t of impact– friction contact between these particles. In the general case for ball mills, the degree α of MP is a function of the frequencies ωk, the number of milling balls N, the ratio R/Dm of the ball size R to the linear dimension of the mill vial Dm, the properties of ball material and the compounds to be treated X and the time τ of MA; α(ωk, R/Dm, N, X, τ). Since any definite process in the mill is performed at some definite ωk, N, R/Dm, X values which are independent of τ, it is possible to separate the variables: α(ωk, R/Dm, N, X, τ) = K(ωk, R/Dm, N, X)α(τ) = K α(τ)

[2.20]

where K is the rate constant of the MP and α(τ) is described by the character of changes in the morphology of particles treated as a result of MP. The periodicity of action of loaded balls on particles of the substance being treated is one of the major characteristics of a ball mill of any type. In the general case, the impact of balls in the mill will be performed with a period of 1/ω′ or frequency ω′ = ω(ωk). Let us introduce a cycle of MA in ball mills: one period of impact of a ball load on the particles being treated is called the cycle of MA. The lined layers of the material being treated, which are formed at the mill vial walls and at the ball surface (Fig. 2.4a and Fig. 2.5), are composed of the contacting pairs of particles 1 and 2 (Fig. 2.3 and Fig. 2.7). Because of this, in order to describe the kinetics of the MP in general, it is sufficient to follow the changes in α that occur during the whole mill operation time τ for one pair of particles selected arbitrarily (Fig. 2.7). As a result of the impact interaction of particles 1 and 2 in a volume V*(σ, ΔT, τ) = d*(σ, ΔT)s12(τ) adjacent to the impact contact surface s12, conditions providing the possibility of MP arise. Let Φ*(U, σ, ΔT) describe the fraction


28


of reacted material in volume V* as a result of a single interaction (here U is the activation energy of the process). Let us assume that for only one ball present in the mill vial (Ν = 1), at some moment in time τ = τ′ in its operation, a selected pair of particles 1 and 2 has moved into the region of the impact of the ball πr2δ (Fig. 2.5). In this case, the degree to which MP runs will be α*(N = 1) = g(k1, k2)Φ*V*(τ′)/ V(τ′), where g(k1, k2) takes account of the identical impact–friction interactions of the selected particles 1 and 2, not only with each other, but also with the surrounding neighbours, see the regions marked in black on the circles in Fig. 2.7. Now, let us assume that the number of balls N > 1 and the particles 1 and 2 have moved into the region of the ball impact during a cycle. In this case α*(N > 1) = ζ(N)α*(N = 1), where ζ(N) is a dimensionless coefficient depicting the collective action of the ball load, ζ(N = 1) = 1 and ζ(N > 1) ∼ N (Urakaev and Boldyrev, 1999c, 2000a). Consequently, for N > 1, the α value of the MP within a single cycle of ball load action on the lined layers of particles being treated can be written as follows: α*(τ = τ′) = ζ(N)g(k1, k2)Φ*V*(τ = τ′)/V(τ = τ′)

[2.21]

Here V(τ = τ′) = V1 = V2 is the overall volume of the selected pair of particles 1 and 2 (Fig. 2.7) at some moment in time τ = τ′ of mill operation. As far as the function g(k1, k2) is concerned, it is not difficult to state that g(k1, k2) = k1 + k2 ≈ 24 for the treatment of an individual compound and g(k1, k2) = 2k1k2/(k1 + k2) ≈ 12 for the treatment of a mixture of two compounds (in further numerical estimations we will consider g = 10). The overall fictitious degree αf at any moment in time τ during the MA will be equal to αf(τ) = α*Ψτ, since these particles are repeatedly involved in collisions with balls with a definite probability, Ψ = η(N, R/Dm)ψω′. The geometric probability ψ is the ratio of the impact contact area (s) of an unlined ball or a lined ball with the lined near-wall layer or with another lined ball to the ‘dead’ surface of the lined layer covered by the colliding ball and therefore not approachable by other balls. For example, in the case of collision of unlined balls with a flat near-wall layer, it follows from Equation [2.5a] and Fig. 2.5 that: ψ = s/(2R)2 = 2−4(10π)0.4ρ0.4(θ + θ)0.4Wn0.8

[2.22]

where R, W, ρ and θ are the radius, velocity, density and compliance of the ball and θ is the compliance of the lined layer of material being treated. Now we shall define the η(N, R/Dm) function which is responsible for the influence of the number of balls on the probability Ψ that repeated impact interactions of the particles 1 and 2 will occur. One can note that for the case of a single ball (N = 1), the probability Ψ = ω′(s/Πv) = [π(2R)2/Πv]ψω′, so the minimum value is η(N, R/Dm) = η(1, R/Dm) = π(2R)2/Πv ∼ R2/D2, where Πv ≈ 4πD2 is the overall area of lined walls accessible to the impact



29

of a ball. Ideally, the maximum value η = 1 is achieved for a minimum number of balls Nmin ≈ D2/R2 providing a uniform treatment of the whole area Πv within unit time ω′. So, it has been shown that η(N, R/Dm) ≈ NR2/ D2 ∼ NR2. The product ζη ≈ (NR/D)2 ∼ (NR)2 can be estimated to be ∼1 with an accuracy of an order of magnitude, that is, ζη ≈ 0.1–10 (Urakaev and Boldyrev, 2000a). So, we have replaced the current time (τ) which has no physical sense by the real time (rpc) τrpc = τpcΨτ of the physicochemical (pc) interaction of the selected particles 1 and 2 with each other during MA. Here Ψ is the frequency of pulse interaction of the particles 1 and 2 with each other or 1/Ψ is the period at which the pulses follow each other and τpc is the time of the MP under consideration (Fig. 2.10), both during the impact–friction contact t12 of the particles and after the contact, under the conditions of σ and ΔT relaxation at the contacts. To sum up, for the transformation degree αf(τ), according to Equations [2.20]–[2.22], and at g(k1, k2)ζη ≈ 10: αf(τ) = α*Ψτ ≈ g(k1, k2)ζηψω′Φ*(V*/V)τ = K′τ

[2.23]

Equation [2.23] contains the value V*/V which is dependent on τ. The existence of this dependence is based on the completeness of the mechanochemical reaction which means the gradual disappearance of the initial particles (decrease of their size down to zero) during the formation of the final products of the reaction. Because of this, the assumption concerning the existence of some limiting quasi-equilibrium size of the treated particles R1 and R2 (see Section 2.3) can be true only for MA of the substance that

Δt(2)+Δt(1) Δt(1) = t′m – tm trpc (s)

= ~8×10–9 s

1/Ψ = ~ 20 s ΔT2

ΔT1 τ = τ0 τ (s)

2.10 Illustration of the dependence of real time (fixed) (trpc) of the activation process during contact between the particles 1 and 2 at the current time (τ) of the treatment in the mill vial, for melting NaCl particles as an example (τ0 is the time within which the first temperature impulse arises; 1/Ψ for ω = 10 s−1 is the period of the following ΔTi pulses).


30


involves changes in properties without changing the composition of the compounds. So, Equation [2.23] with its linear law for the degree of MA αf(τ) which changes with the time of mechanical treatment τ can be used to describe the kinetics of MA (K′, s−1). In order to determine the time dependence V*(τ)/V(τ), the existence of some function describing the changes of the specific surface S(τ) of the treated particles during the MP is assumed. Then, for spherical particles 1 and 2, assuming (L1 + L2)/2 = L(τ) = 1/R12, we find the mean curvature of the particles at the contact point L(τ) = ρ12S(τ)/3. On the other hand V(τ) = 8π/3L3(τ), and for V*(σ, ΔT, τ) = d*(σ, ΔT) s12(τ), since σ and ΔT are independent of L(τ), using Equation [2.7] for s12: V*(τ) = 2−4π(10π)0.4ρ0.4Wn0.8(θ + θ)−1.6(θ1 + θ2)2d*L−2(τ) = C1d*L−2(τ) [2.24] So, the equation which we wanted to obtain will be: V*(τ)/V(τ) = 8πC1d*L(τ)/3 = 8πC1d*S(τ)ρ12 = C1C2d*τ = Cd*τ

[2.25]

where C1 and C2 = C2′ρ12/8π are constants, and θ1, θ2 and R12 = 2R1R2/(R1 + R2), ρ12 = 2ρ1ρ2/(ρ1 + ρ2) are, respectively, compliances and the mean radius and density of the particles 1 and 2 during treatment. Usually (Fig. 2.11 and Fig. 2.12) a linear law for the changes in the specific surface area S of the reagents is used in practical applications, so it is accepted in Equation [2.25] that S(τ) = C2′τ. In order to take account of the influence of the final solid products on the kinetics of MP, we employ a universal principle (Barret, 1973, p.152) which says that the reaction rate is equal to the fictitious specific rate multiplied by the size of the effective uniform region within which the reaction is localized. This leads to the following correlation between the real and fictitious transformation degree: dα(τ) = (1 − α)pdαf(τ). Integrating this equation for different values of p (for explanation, see Delmon, 1969: 281, 414) and using Equations [2.23] and [2.25] makes Equations [2.20] and [2.21] more specific and leads to the following relations: Kτ2 = α

at p = 0

[2.26]

Kτ = −ln (1 − α)

at p = 1

[2.27]

Kτ2 = α/(1 − α)

at p = 2

[2.28]

2

Here Equation [2.26] should correspond to the kinetics of mechanochemical reactions without the formation of solid final products, for example: NH4NO3 = N2O + 2H2O, C + 2S = CS2, Ni + 6CO = Ni(CO)6 and possibly the kinetics of the MA (K, s−2). The case in Equation [2.27] is realized when the degree to which the new solid products formed during © Woodhead Publishing Limited, 2010


31

τ2 × 10–6 (s2) 1.0

12 14

0 1 2 3 4 5 6 7 8 9 10

16

18

20

22

24

–lg (1–α)

0.1 0.2

α/(1–α)

0.8

0.3 0.5

0.6

0.6 0.7 0.8

0.4

0.9

WCo8 ρ = 15.6 g cm–3 R = 0.2 cm N = 383 ω = 9 s–1

5 0.2

0.0 S0 = 0.035 0

1

2

3

4

5

6 –3

τ × 10

7

8

–lg (1 – α); α/(1 – α) ([2.27]) ([2.28])

0.4

α

S (m2 g–1)

15

10

0

1.0 1.1 1.2 9

10

11

12

(s)

2.11 Change in specific surface (S, m2 g−1) and conformity to the Equations [2.27] and [2.28] of the rate of mechanochemical decomposition of silver oxalate, Ag2C2O4 = 2Ag + 2CO2, in a planetary mill KhK 871 (Urakaev et al., 1982).

S – S0 (m2 g–1)

40

WO3

30

WCo8 ρ = 15.6 g cm–3 R = 0.2 cm N = 228 ω = 14.3 s–1

20

BaCO3 10

0 0

4

8 τ / 60 (s)

12

2.12 Change in specific surface (S, m2 g−1) of barium carbonate (BaCO3) and tungsten oxide (WO3) in a planetary mill KhK 871 (Kopylov et al., 1978).


32


the MA of a substance affect the kinetics is proportional to the transformation degree α of the reaction, while Equation [2.28] is realized for nonlinear dependence of the kinetics upon the solid products formed. For rate constant K accompanied by changes in particle size, see Equations [2.26]– [2.28], using Equations [2.22]–[2.25]: K = 2−11(10π)0.8g(k1, k2)ζηρ0.8(θ + θ)−1.2(θ1 + θ2)2ωWn1.6ρ12Cd*Φ*

[2.29]

Numerical estimates of rate constants (K′, K) for MA and mechanochemical reactions in ball mills according to the Equations [2.21]–[2.29] will be performed in the next section.

2.6

Use of kinetic equations

Let us transform Equation [2.29] into a form which can be used to estimate K numerically. One can see from Tables 2.1 and 2.2 and Fig. 2.8 that ΔT(x, t12) is relatively constant at the depth x of the treated particles up to a distance x = x* = ε12/2. For example, in the case of NaCl treatment, the temperature impulse ΔT(x, t1) at the impact–friction contact point of particles can exceed their melting point ΔTm up to a distance 2xm* > ε1/2. Consequently, at some approximation, one can accept d*(σ, ΔT) = 2x* ≈ ε12, that is, the thickness of the reaction zone is equal to the total impact deformation of the particles 1 and 2 under consideration. Then, using the result obtained for ε12 in Equation [2.6] and [2.6a], the rate constant from Equation [2.29] becomes: K = 2−14(10π)1.2g(k1, k2)ζηρ1.2(θ + θ)−2.8(θ1 + θ2)4ωWn2.4ρ12R12CΦ*

[2.30]

A dimensionless parameter Φ*(U, σ, ΔT) can be determined by the mechanism of the chemical reaction under the prevailing conditions provided that calculated values of σ and ΔT impulses in the region of impact– friction contact of particles 1 and 2 are known. According to the definition, Φ*[U, σ(x, t) ΔT(x, t)] = n*[σ(x, t),ΔT(x, t)]/n0*, where n* is the number of reacted molecules and n0* is the total number of molecules (atoms) in the volume under consideration V* in which the pressure σ(x, t) and temperature ΔT(x, t) impulses are realized. The rate of the chemical reaction leading to the final products is d2n*/dxdt = n0*Kr[U, σ(x, t), ΔT(x, t)], where Kr is the reaction rate constant. It seems impossible to integrate the equation in this form, so, as a first approximation, under the conditions at which the chemical reaction occurs at the point of contact of the particles 1 and 2, the mean impulses can be σ(x, t) = σ and ΔT = 0.5[ΔT(0, t12) + ΔT(ε12/2, t12)] within the time interval. This means that we accept τrpc = t12. In this case, it follows that: Φ* = t12Kr = t12Kr0exp[−(U − χ12)/k(T0 + ΔT)]


[2.31]


33

where Kr0 is a pre-exponential factor, χ12 ∼ 10−23 cm3 (the structural factor, see Regel et al., 1974: 130) and k = 1.38 × 10−16 erg K−1 (the Boltzmann factor) are constants and T0 is the background temperature in the mill. Now we can present a more specific equation for K taking account of t12 from Equations [2.2] and [2.11]: K = 2−16(π/2)0.25(10π)2.6g(k1, k2)ζηρ1.1(θ + θ)−2.4 (θ1 + θ2)4ωWn2.2ρ121.5R122CKr

[2.32]

For Kr depending on the conditions of MA, only the most important parameters, that is, ρ and W of a ball, see Equation [2.1], at the next assumption about the known function Kr in Equation [2.31] are considered. The activation energy U of thermal solid phase processes controlled by diffusion and chemical transformations are usually much higher than χ12σ. If U >> χ12σ and ΔT >> T0, according to Equations [2.1], [2.12] and [2.32] it follows that: Wn = Aω, Kr ≈ Kr0exp(−U/kΔT) = Kr0exp(−Λ/ω0.9ρ0.45)

[2.33]

Λ ≈ 3(π/2) 2 (10π) iErfc[0](θ + θ) (c1c2λ1λ2ρ1ρ2ρ12) U/kA0.9R120.5ξ12(θ1 + θ2)

[2.34]

K ∼ (NR) Θ ρ ω exp(−Λ/ω ρ

[2.35]

1.625 1.5

2

1.6 1.1

0.2

3.2

1.8

0.9 0.45

)

0.25

where generalized compliance Θ1.6 = (θ + θ)−2.4(θ1 + θ2)4 depicts the dependence of K on the mechanical properties (compliances) of the material of both the balls, θ or θ = (θ1 + θ2)/2 for lined balls, and the particles being treated (θ1, θ2). Specific cases of application of the Equations [2.20]–[2.35] to various mechanochemical reactions (Figs 2.9, 2.11 and 2.13–2.17) occurring in ball mills are considered in the next sections.

2.6.1 Mechanical activation of substances Let us assume that the mechanism of MA of NaCl particles involves contact melting followed by hardening which is accompanied by the formation of non-equilibrium defects. The time interval within which ΔT ≥ ΔTm for NaCl particles is tpc = Δtm = t′m − tm ≈ 8 × 10−9 s (Figs 2.8 and 2.10). The possibility that NaCl particles will melt under these conditions and the determination of the thickness of fused layer d* ≈ 7 × 10−7 cm were presented above. Returning to the Equation [2.23] for the conditions under which NaCl particles are treated in the mill EI 2 × 150 at g(k1, k2) ≈ 10, ζη ≈ 1, R = 0.2 cm, ω = 10 s−1, Equation [2.22] or Table 2.2 are also used to find Ψ = Ψ = ψω ≈ 53 × 10−3 s−1 and 1/Ψ ≈ 20 s. This means that, in reality, NaCl particles with a size R1 ≈ 1.6 × 10−4 cm are subjected to the impact of balls about once every 20 s. The coefficient providing the transition to real time of treatment will be trpc/τ = tpcΨ = ΔtmΨ ≈ 4.2 × 10−10 (Fig. 2.10). To estimate


34

High-energy ball milling ω = 15.3 s–1 ω = 12.4 s–1 ω = 11.0, 9.7 s–1 ω = 9.0, 8.8 s–1

1.00

ω = 8.2 s–1

0.80

ω = 7.1 s–1 WCo8 ρ = 15.6 g cm–3 R = 0.2 cm N = 228

α

0.60 0.40

ω = 5.0 s–1

0.20 0.00

0

20

40

60

80 τ / 60 (s)

100

120

140

2.13 Degree α of transformation for the reaction BaCO3 + WO3 = BaWO4 + CO2 in a planetary mill KhK 871 depending on frequency ω of rotation (Avvakumov and Urakaev, 1982; Avvakumov et al., 1983).

WCo8 ρ = 15.6 g cm–3

1.00

Steel ρ = 7.9 g cm–3

Al2O3 ρ = 4.0 g cm–3

0.80

α

0.60

0.40

0.20

0.00 0

5

10

15

20

25

30

35

40

τ / 60 (s)

2.14 Degree α of transformation for the reaction BaCO3 + WO3 = BaWO4 + CO2 in a planetary mill KhK 871 depending on the density ρ of balls; R = 0.2 cm, N = 228, ω = 12.4 s−1 (Avvakumov and Urakaev, 1982).


Mechanism and kinetics of mechanochemical processes 1.00

35

R = 0.4 cm R = 0.25 cm

0.80

R = 0.15 cm

0.60 α

R = 0.11 cm R = 0.075 cm

0.40

0.20

0.00 0

5

10

15

20

25

30

τ / 60 (s)

2.15 Degree α of transformation for the reaction BaCO3 + WO3 = BaWO4 + CO2 in a mill KhK 871 depending on the radius R of balls; for steel ρ = 7.9 g cm−3, m = 209 g, ω = 12.4 s−1 (Avvakumov and Urakaev, 1982; Avvakumov et al., 1983). N = 467

1.00

N = 137

N = 262

0.80

N = 68

α

0.60

0.40

0.20

0.00 0

10

20

30

τ / 60 (s)

2.16 Degree α of transformation for the reaction BaCO3 + WO3 = BaWO4 + CO2 in a mill KhK 871 depending on the number N of balls; for steel ρ = 7.9 g cm−3, R = 0.2 cm, ω = 12.4 s−1 (Avvakumov and Urakaev, 1982).


36

High-energy ball milling WCo8 ρ = 15.6 g cm–3; R = 0.2 cm N = 228 ω = 12.4 s–1

1.00

BaCO3 β = 2.03 Mbar–1

0.80

SrCO3 β = 1.75 Mbar–1 MgCO3 β = 1.07 Mbar–1

CaCO3 β = 1.37 Mbar–1

α

0.60

0.40

0.20

0.00 0

1

2

3

4

5

6

7

8

9

10

τ / 60 (s)

2.17 Degree α of transformation for the reactions MeCO3 + WO3 = MeWO4 + CO2, where Me = Ba, Sr, Ca and Mg, in a mill KhK 871 depending on the compressibility β (Clark, 1966; Avvakumov and Urakaev, 1982) of the alkaline earth’s carbonates [β = 1/Ω (modulus of volume elasticity) ∼ 1/E (Young’s modulus) ∼ θ (compliance) ∼ Θ (generalized compliance)]. In τ (τ, s) 9

8

7

6

5

4

3

2

1

3

–6 –5

2

–4

1b

–3

3b

0

–2

2b

–1

–1

–2

2a

3a

0

1a

–3

1

–4

2

–5

3

–6

0

1

2

3

4 5 6 In τ (τ, s)

In [α /(1-α)]

1 In [–In (1-α)]

0

7

8

9

2.18 Experimental kinetic curves processed at the logarithmic coordinates of Equations [2.27] and [2.28]. The straight lines (a) correspond to Equation [2.27] and lines (b) to Equation [2.28]; 1 is related to the reaction NaNO3 + KCl = KNO3 + NaCl in a planetary mill EI 2 × 150 at ω = 10 s−1; 2 and 3 are related to the reactions BaCO3 + WO3 = BaWO4 + CO2 and Ag2C2O4 = 2Ag + CO2 in a planetary mill KhK 871 at ω = 11 s−1 and ω = 9 s−1, respectively. © Woodhead Publishing Limited, 2010


37

K′ in Equation [2.23], Φ* ≡ 1 as an identity should be taken into account since the accepted mechanism of NaCl particle activation is based on a process involving fusion and quenching. Let us determine (using Table 2.2) the ratio V*/V = 3d*s1/8πR13 ≈ 2.5 × 10−5; so the rate constant will be K′ ≈ 1.3 × 10−5 s−1. Because of this, the treatment time for complete fusion and quenching of all NaCl particles in a mill (αf = 1) will be, according to Equation [2.23], τ = 1/K′ ≈ 7.5 × 104 s or ∼21 h. Now we shall assume that for the same mechanism of NaCl activation (Φ* ≡ 1) the size of particles being treated changes. In this case, the MA kinetics will be described by Equation [2.26] with the constant from Equation [2.29]. According to Equation [2.29], K(ω = 10 s−1) ≈ 1.5 × 10−7 s−2 will be obtained. According to Equation [2.26], the corresponding time of MA (τ) necessary for NaCl particles to remelt completely (α = 1) will be τ = (1/K)0.5 ≈ 2600 s or only ∼0.7 h. One can see that a substantial difference is observed at the poles.

2.6.2 Reactions controlled by diffusion Now let us consider the kinetics of the reactions in a system of ionic salts (Fig. 2.9). It has been shown above that the rate of this exchange reaction is limited by mutual diffusion of ions in the fused layer. So, in Equation [2.29] we have d*Φ* ≈ 2.4 × 10−6 cm. Using relation [2.29], it is easy to obtain the calculated value of the rate constant for the reaction under consideration from Equations [2.26]–[2.28]: K(ω = 10 s−1) ≈ 2.2 × 10−6 s−2. Figure 2.18 presents the results of the treatment of kinetic curves at the coordinates determined by Equations [2.27] and [2.28] for a series of MA reactions. One can see that the experimental points agree well with the straight lines at the coordinates of Equation [2.27] within the whole range of α change. It can be concluded that the degree of ‘screening’ of a MP by the solid products of the reaction is proportional to the volume of the transformed substance. For the reaction being considered, an experimental value of the rate constant at the coordinates of Equation [2.27] is K1a ≈ 8.3 × 10−5 s−2 which is about 40 times higher than the calculated value. This difference will be discussed below when considering the dependence of K on the conditions of MA. An example of MP controlled by diffusion is a reaction BaCO3 + WO3 = BaWO4 + CO2. Kinetic curves α(τ) for this reaction were obtained by measuring the pressure of gaseous CO2 formed (see Figs 2.13–2.17). The thermal mechanism of this reaction involves the diffusion of tungsten into decomposing carbonate, the reaction rate being determined by the diffusion coefficient of tungsten. In order to estimate the rate constant of this MP, we shall use Equation [2.30] and the parameters calculated for a related reaction, see Table 2.1. It is shown that the key value Φ* ≈ 1. The constant for


38


the MA reaction under consideration will be estimated using Equation [2.30]: K(ω = 11 s−1) ≈ 0.6 × 10−6 s−2. The rate constant determined experimentally at the coordinates of Equation [2.27], see Fig. 2.18, is K2a ≈ 2.1 × 10−5 s−2 which exceeds the calculated value by a factor of 35. It is easy to note (Fig. 2.13) that when ω of mill rotation is decreased, owing to the decrease in the temperature pulse at the point of contact of particles, synthesis of BaWO4 should be transferred into the region controlled by the kinetics (see below).

2.6.3 Reactions controlled by the kinetics Decomposition of silver oxalate can be used as an example of MP controlled by kinetics (Fig. 2.11). Kinetic curves α(τ) for thermal and MA decomposition according to the scheme Ag2C2O4 = 2Ag + CO2 were also obtained by measuring the pressure of gaseous CO2 formed. The rate constants Kr and K of silver oxalate decomposition, under the pressure conditions and the temperature impulses that are realized at the point of impact–friction contact of the particles being treated can be estimated using Equations [2.31] and [2.32]. Using the calculation procedure described above when deducing Equation [2.31], we obtain Kr ≈ 2.0 × 10−7 s−1. This gives, see Equation [2.32], K(ω = 9 s−1) ≈ 4.0 × 10−9 s−2. The experimental value is K2a ≈ 3.5 × 10−8 s−2 (see Figs 2.11 and 2.18) which is about 10 times higher than the calculated value.

2.6.4 Effect of mechanochemical activation conditions on the kinetics In order to establish the dependence of K on the conditions of MA, see Equation [2.35], a complex investigation of the kinetics of MA reactions of the type BaCO3 + WO3 = BaWO4 + CO2 has been performed (Figs 2.13–2.17). Experimentally determined rate constants of the studied reactions, depending on the treatment conditions, should be straight lines at the coordinates shown in Fig. 2.19. It shows a result of this treatment which is in satisfactory agreement with the above considerations and assumptions. Using the slopes of the straight lines (1) and (2) in Fig. 2.19, ≈ 3.5 × 10−12 s cm−2, one can determine the value ζη ≈ 3.5 × 10−12 N2R2/K(N = 1; R) ≈ 15 where N = 137 and R = 0.2 cm can be determined, corresponding to the identical conditions of the experiment when studying the dependence of K on the number and size of balls where K(N = 1; R = 0.2 cm) ≈ 1.8 × 10−10 s−2. Using the slopes of the straight lines (3) and (5) we obtain the values lg K(ω = 1; ρ = 15.6) ≈ −17.8, lg K(ρ = 1; ω = 12.4) ≈ −6.65 and in Equations



39

(5) ← 3.2 lg ω – lg e/ω0.9 3.5

3.0

2.5

2.0

10 –3

(4)

6

–5

(3)

4

(1)

2 0

–4 lg K

K × 105 (s–2)

(2)

(5)

8

–6 –7

(3)

2

4

6

8

10 12 14

Θ1.6 × 1015

(4) 0.2 0.4 0.6 0.8 1.0 1.2 1.4

1.1 lg ρ – lg e/ρ0.45

(2)

N 2 × 10–4

(1)

4 2

8 4

6

12 8

16

20

10 12 14

R2 × 100 (cm2)

2.19 Experimental values of the rate constants K (s−2) for BaWO4 mechanochemical synthesis compared to the theoretical dependence [2.35] of K on the conditions of mechanical treatment in a mill KhK 871 (see also text): (1, 䊉) K − R 2, R in cm; (2, 䊊) K − N 2; (3, +) K − Θ1.6, Θ in cm2 dyn−1; (4, ⵧ) lg K − [(1.1 lg ρ − (lg e / ρ0.45)], ρ in g cm−3; (5, 䊏) lg K − [(3.2 lg ω − (lg e / ω0.9)], ω in s−1.

[2.32] and [2.33], Λ ≈ ω0.9ρ0.45[lg K(ω = 1) − lg K(ρ = 1) + 3.2 lg ω − 1.1 lg ρ]/ (ρ0.45 − ω0.9)lg e ≈ 110 g0.45 cm−1.35 s−0.9, where ρ = 15.6 g cm−3 and ω = 12.4 s−1 correspond to identical K when studying the dependence of K on the ball density and on the mill rotation frequency. It is interesting to compare the experimental value of Λ with the theoretical one (Λ = 84) for a related MA synthesis of calcium silicate (for parameters, see Table 2.1): Λ ≈ 103 g0.45 cm−1.35 s−0.9. In the case under consideration, the two values agree to an accuracy within an order of magnitude. It is important to note that for low ω, the diffusion regime of MA synthesis changes to the kinetic regime, see the fracture in curve (5) in Fig. 2.19. The final results of the comparison between the experimental and calculated rate constants of the MA reactions in planetary mills, taking account of the value ζη ≈ 15 determined experimentally, will be listed below. For the reaction NaNO3 + KCl = KNO3 + NaCl, K1a = 8.3 × 10−5 s−2 and the calculated value, K ≈ 1.5 × 10−5 s−2; for the synthesis of barium tungstate, K2a = 21 × 10−6 s−2 and the calculated value, K ≈ 9.0 × 10−6 s−2; for the mechanical destruction of silver oxalate, K3a = 3.5 × 10−8 s−2 and the calculated value, K ≈ 6 × 10−8 s−2. So one can see that the theory providing the calculation of


40


the kinetics of MA reactions is in quantitative agreement with the kinetic parameters determined experimentally, within an order of magnitude.

2.7

Conclusions

Using different ball mills as examples, it has been shown that, on the basis of the theory of glancing collision of rigid bodies, the theoretical calculation of t–P–T conditions and the kinetics of mechanochemical processes are possible for the reactors that are intended to perform different physicochemical processes during mechanical treatment of solids. According to the calculations, the ‘physicochemical’ effect of mechanochemical reactors is due to short-time impulses of pressure (ΔP = σ ∼ 1010–1011 dyn cm−2) with shift, and temperature ΔT(x, t). The highest temperature impulse ΔT ∼ 103 K are caused by the ‘dry friction’ phenomenon. Typical spatial and time parameters of the impact–friction interaction of the particles with a size R ∼ 10−4 cm are as follows: localization region, Δx ∼ 10−6 cm; time, Δt ∼ 10−8 s. On the basis of the obtained theoretical results, the effect of short-time contact fusion of particles treated in various comminuting devices can play a key role in the mechanism of activation and chemical reactions for wide range of mechanochemical processes. This role involves several aspects, that is, the very fact of contact fusion transforms the solid phase process onto another qualitative level, judging from the mass transfer coefficients. The spatial and time characteristics of the fused zone are such that quenching of non-equilibrium defects and intermediate products of chemical reactions occurs; solidification of the fused zone near the contact point results in the formation of a ‘nanocrystal or nanoamorphous state’. The calculation models considered above and the kinetic equations obtained using them allow quantitative ab initio estimates of rate constants to be performed for any specific processes of mechanical activation and chemical transformation of the substances in ball mills.

2.8

References

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gorskii fk and mikulich as (1964), ‘Size of interphase surface energy of sodium chloride on a border crystal-melt’, Crystallization Mechamism and Kinetics, Syrota NN (ed.), Nauka i tekhnika, Minsk, 71–8 (in Russian). harris cm and piersol ag (eds) (1961), Harris’ Shock and Vibration Handbook, McGraw-Hill, Toronto, in three volumes. heertijes pm and bouter ja (1965), ‘Subcooling effects in a crystallisation system’, Chem Proc Eng, 46, 654–8. hertz h (1895), Gesammelte Werke, J.A. Barth (Arthur Meiner), Leipzig, Vol. 1. horák z (1948), ‘Impact of a rough ball spinning round its vertical axis onto a horizontal plane’, Trans Dept Tech Univ Prague (Sb. CVUT Vys. Sk. Stroj. Inz., Prague), 1–16. horák z and pacáková i (1961), ‘The theory of the spinning impact of imperfectly elastic bodies’, Czechoslovak J Phys, 11, 46–65. ismail ka and stronge wj (2008), ‘Impact of viscoplastic bodies: dissipation and restitution’, J Appl Mech, 75, 061011 (5 pages). johnson kl (1985), Contact Mechanics, Cambridge University Press, Cambridge, UK. kajdas ck (2005), ‘Importance of the triboemission process for tribochemical reaction’, Tribol Int, 38, 337–53. keller jb (1986), ‘Impact with friction’, ASME J Appl Mech, 53, 1–4. kilchevsky na (1976), Dynamic Contact Stress of Solids. Impact, Naukova dumka, Kiev (in Russian). kobayashi k (1995), ‘Formation of coating film on milling balls for mechanical alloying’, JIM (Materials Trans), 36, 134–7. koch cc (2003), ‘Top-down synthesis of nanostructured materials: Mechanical and thermal processing methods’, Rev Adv Mater Sci, 5, 91–9. kopylov av, avvakumov eg and urakaev fkh (1978), ‘Mechanochemical reactions of barium carbonate with oxides of metals of IV, V, and VI group’, Izv Sib otd AN SSSR: Ser khim nauk, 9/4, 8–14 (in Russian). korchagin ma and lyakhov nz (2008), ‘Self-propagating high-temperature synthesis in mechanoactivated compositions’, Russian J Phys Chem B, 2, 77–82. kubenko vd (1999), ‘Local wave theory of the collision of elastic bodies. Noncentral impact – two-dimensional problem in the ideal-fluid approximation’, Int Appl Mech, 35, 1155–66. landau hg (1950), ‘Heat conduction in a melting solid’, Quart Appl Math, 8, 81–94. love aeh (1927), A Treatise on the Mathematical Theory of Elasticity, 4th edition, University Press, Cambridge. lü l and lai mo (1998), Mechanical Alloying, Springer, Berlin, 276 pp. lykov av (1965), Theory of Energy and Mass Transfer, Prentice Hall, New York, 392 pp. lykov av (1967), Teoriya teploprovodnosti, Moskva, Vysshaya shkola, 600 pp (in Russian). lyubov bya and roytburd al (1962), ‘About influence of overcooling on border of the unit of phases for speed of moving of front of crystallization in conditions directed heat transfer’, in Crystallization and Phase Transitions, Syrota NN (ed.), Minsk, AN BSSR, 226–34 (in Russian). maw n, barber jr and fawcet jn (1976), ‘The oblique impact of elastic spheres’, Wear, 38, 101–14.



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miani f and maurigh f (2004), ‘Mechanosynthesis of nanophase powders’, in Encyclopedia of Nanoscience and Nanotechnology, Marcel Dekker. mio h, kano j, saito f and kaneko k (2002), ‘Effects of rotational direction and rotation-to-revolution speed ratio in planetary ball milling’, Mater Sci Eng A, 332, 75–80. painlevé p (1895), Lec¸ons sur le Frottement, Paris. panovko yag (1977), Introduction to the Theory of Mechanical Impact, Nauka, Moscow (in Russian). panovko yag (1985), Mechanics of Deformable Solids. Modern Concepts, Mistakes and Paradoxes, Nauka, Moscow (in Russian). peres j (1923–24), ‘Choc en tenant compte de frottement’, Nouv Ann de Math, 2, 98–107. peres j (1923–24), ‘Choc de deux solides avec frottement’, Nouv Ann de Math, 2, 216–31. persson bnj (2000), Sliding Friction: Physical Principles and Applications, New York, Springer Verlag, New York. poisson sd (1817), Mechanics, Longman, London, in two volumes. popov vl, psakhie sg, shilko ev, dmitriev ai, knothe k, bucher f and ertz ì (2002), ‘Friction coefficient in “rail–wheel” contacts as a function of material and loading parameters’, Physical Mesomechanics, 5(3), 17–24. pustov lyu, kaloshkin sd, cherdyntsev vv, tomilin ia, shelekhov ev and salimon ai (2001), ‘Experimental measurement and theoretical computation of milling intensity and temperature for the purpose of mechanical alloying kinetics description’, Mater Sci Forum, 360–2, 373–8. regel vr, slutsker ai and tomashevsky ee (1974), Kinetic Nature of Solids Strength, Nauka, Moscow (in Russian). revesz a and takacs l (2007), ‘Coating metals by surface mechanical attrition treatment’, J Alloys Compounds, 441, 111–14. routh ej (1897), Dynamics of a System of Rigid Bodies, Macmillan and Co., London, vol. 1. schlichting h (1951), ‘Einige exakte Lösungen für die Temperaturverteilung in einer laminaren Strömung’, Zeitschrift für angewandte Mathematik und Mechanik, 31, 78–83. schmitz t, action j, ziegert j and sawyer w (2003), ‘Dynamic friction coefficient measurements: device and uncertainty analysis’, in Proceedings of the 18th ASPE Annual Meeting, October 26–31, Portland, OR (on CD). schneider u (1968), ‘Makroskopische und mikroskopische Eigenschaftsanderungen von Feststoffpulvern infolge starker mechanischer Beanspruchung in Mühlen’, Aufbereit Techn, 9, 567–73. stoimenov lg (1992), ‘Solution of the problem of oblique impact of bodies: Impact models for rough bodies’, Int Appl Mech, 28, 477–83. strickland-constable rf (1968), Kinetics and mechanism of crystallization from the fluid phase and of the condensation and evaporation of liquids, Academic Press, New York. stronge wj (1990), ‘Rigid body collisions with friction’, Proc Roy Soc London Ser A, 431, 169–81. suryanarayana c (2001), ‘Mechanical alloying and milling’, Progr Mater Sci, 46, 1–184.


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takacs l (2002), ‘Self-sustaining reactions induced by ball milling’, Prog Mater Sci, 47, 355–414. takacs l and torosyan ar (2007), ‘Surface mechanical alloying of an aluminum plate’, J Alloys and Compounds, 434, 686–8. timoshenko s (1955), Vibration Problems in Engineering, D. Van Nostrand, Toronto, 3rd edition in collaboration with Young DH. ubellohde ar (1965), Melting and Crystal Structure, Clarendon Press, Oxford. urakaev fkh (2004), ‘Theoretical bases of mechanochemical processes in ball milling’, Eurasian Chemico-Tech J, 6, 239–54. urakaev fkh (2007), ‘Mechanodestruction of minerals at the crack tip (overview): 1. Experiment’, Phys Chem Minerals, 34, 351–61. urakaev fkh (2008), ‘Mechanodestruction of minerals at the crack tip (overview): 1. Theory’, Phys Chem Minerals, 35, 231–9. urakaev fkh (2009), ‘Mineral processing by the abrasive-reactive wear’, Int J Mineral Processing, 92, 58–66. urakaev fkh and avvakumov vv (1978), ‘Mechanism of mechanochemical reactions in grinding apparatus’, Izv Sib otd AN SSS: Ser khim nauk, 3/7, 10–16 (in Russian). urakaev fkh and boldyrev vv (1999a), ‘Calculation of the physicochemical parameters of mechanochemical reactors’, Inorg Mat, 35, 189–96. urakaev fkh and boldyrev vv (1999b), ‘Formation of X-ray amorphous material during mechanical activation (by the example of NaCl)’, Inorg Mater, 35, 302–5. urakaev fkh and boldyrev vv (1999c), ‘Kinetics of mechanochemical processes in grinding machines’, Inorg Mater, 35, 405–12. urakaev fkh and boldyrev vv (2000a), ‘Mechanism and kinetics of mechanochemical processes in comminuting devices 1. Theory’, Powder Technol, 107, 93–107. urakaev fkh and boldyrev vv (2000b), ‘Mechanism and kinetics of mechanochemical processes in comminuting devices 2. Applications of the theory. Experiment’, Powder Technol, 107, 197–206. urakaev fkh and shevchenko vs (2007), ‘Phenomenology, kinetics and application of abrasive-reactive wear during comminution (Overview)’, KONA (Powder and Particle), 25, 162–79. urakaev fkh, avvakumov vv and jost h (1982), ‘Mechanodestruction of silver oxalate’, Izv Sib otd AN SSSR: Ser khim nauk, 7/3, 9–14 (in Russian). vasil’ev ls and lomaeva sf (2003), ‘Mechanism of saturation of nanocrystalline powders with interstitial impurities upon mechanical dispersion’, Colloid J, 65, 639–47. vick b and furey mj (2001), ‘A basic theoretical study of the temperature rise in sliding contact with multiple contacts’, Tribol Int, 34, 823–9. vick b and furey mj (2003), ‘An investigation into the influence of frictionally generated surface temperatures on thermionic emission’, Wear, 254, 1155–61. vick b, furey mj and iskandar k (2000), ‘Theoretical surface temperatures generated from sliding contact of pure metallic elements’, Tribol Int, 33, 265–72. zegzhda sa (1997), Collision of Elastic Solids, Saint Petersburg State University, 316 pp (in Russian).


3 Kinetic behaviour of mechanically induced structural and chemical transformations G. M U L A S, Università degli Studi di Sassari, Italy; and F. D E L O G U, Università degli Studi di Cagliari, Italy

Abstract: The kinetics of mechanically activated chemical reactions is an open field of investigation, with a number of mature problems that need to be dealt with in order to promote significant progress in mechanochemistry. Attention is here focused on the considerable efficiency exhibited by mechanochemical reactions when suitably referred to individual deformation events. Three different cases are covered in detail, which concern the degradation of toxic pollutants, the storage of hydrogen in hydride form and the enhancement of catalyst activity to produce hydrocarbons. All of these have been selected in view of their importance for future energetic scenarios and environmental policies, the emergence of which will modify the current assets of industrialized countries. Key words: mechanochemistry, kinetics, gas–solid reactions, pollutants degradation, catalysis.

3.1

Introduction

Concerns relating to the increasing demand for energy and to the impact of present technologies on environment and climate are forcing industrialized and developing countries to seek alternative solutions towards providing a sustainable future (Holdren, 2008). This is a tremendous challenge to science and engineering, which are called in to convert the unsustainable practices of industrialized countries to sustainable ones while improving the sustainability of living standards in developing countries (Holdren, 2008). The development of a fully sustainable future requires, on the one hand, more efficient utilization of resources and energy (Holdren, 2008). On the other, it implies a reduction in both wastes and in the environmental impact of human activities (Holdren, 2008). Both these issues have to cope with the needs of advancing fundamental and applied science (DOE, 2007). However, it must be noted that the demand for a sustainable future must necessarily pass across a number of intermediate scenarios in which the major role will be played by suitable rethinking of known methodologies 45 © Woodhead Publishing Limited, 2010

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(DOE, 2007). Within this framework, mechanochemistry has the opportunity to attract considerable interest. First, it is easy to apply and simple, even though its simplicity is only apparent. Second, under suitable conditions it allows very fast chemical processes. This chapter will focus precisely on these latter features, after a brief general introduction to mechanochemistry itself.

3.2

Mechanochemistry

Mechanochemistry is a form of chemistry activated by non-hydrostatic mechanical stresses (Heinicke, 1984; Levitas, 2004). In general terms, it results from the application of mechanical forces to solid phases and their consequent deformation (Heinicke, 1984; Butyagin, 1989; Gutman, 1998; Suryanarayana, 2001; Levitas, 2004). At the atomic level, the mechanical deformation of crystalline structural arrangements can be regarded as a distortion or modification of the coordination shells of individual atoms (Heinicke, 1984; Butyagin, 1989; Gutman, 1998; Suryanarayana, 2001; Levitas, 2004). In turn, the atomistic processes can be generically described as local structural excitations (Heinicke, 1984; Butyagin, 1989; Gutman, 1998; Suryanarayana, 2001; Levitas, 2004). These excitations pull the system away from thermodynamic equilibrium, which usually promotes a significant enhancement in the chemical reactivity (Gutman, 1998; Levitas and Zarechnyy, 2006; Delogu and Cocco, 2006). Local structural excitations are expected to have characteristic nature and lifetimes, which depend on a variety of intertwined factors including crystalline lattice geometry, intensity of mechanical stresses and temperature (Heinicke, 1984; Butyagin, 1989). Owing to the fast dynamics of relaxation processes in the solid phase (Delogu and Cocco, 2006), local excited states can be expected to have quite short lifetimes, roughly on the order of nanoseconds (Butyagin, 1989; Delogu and Cocco, 2006). In spite of this, promotional effects on the chemical reactivity can be expected whenever excited atoms involved in local structural excitations directly interact with other chemical species (Henicke, 1984; Butyagin, 1989). According to the brief description above, mechanochemical reactions rely substantially upon the response of any given solid phase to plastic mechanical deformation (Heinicke, 1984). In the most widespread methodology, mechanical deformation is operated by processing powders in socalled ball mills (Heinicke, 1984; Suryanarayana, 2001). Ball mills exhibit various geometries and mechanical actions (Suryanarayana, 2001). However, apart from the differences related to the design details, ball mills usually consist of stainless steel reactor chambers fixed either to platforms or to mechanical arms which are moved by electrical motors along eccentric trajectories (Suryanarayana, 2001). The powder charge is placed into the


Kinetic behaviour of structural and chemical transformations

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reactor chamber together with suitably chosen stainless steel balls. The reactors move along a selected trajectory such that the balls inside are forced to collide with each other and with the walls of the reactor chamber. When a powder charge is also present, a fraction of powder particles become trapped between the colliding surfaces of the milling tools. During the course of such events, relatively intense impulsive forces apply to the particles, inducing severe plastic deformation and a variety of correlated processes (Heinicke, 1984; Butyagin, 1989; Suryanarayana, 2001; Delogu et al., 2004). In turn, plastic deformation induces the accumulation of point, line and planar defects into the solid phase crystalline lattice (Heinicke, 1984; Honeycombe, 1984). Structural defects give rise to distorted local structures characterized by an intrinsic enhancement of chemical reactivity (Suryanarayana, 2001). The above-mentioned defective structures are static ones, that is, they refer to the content of lattice defects finally attained as a consequence of the relaxation processes following the mechanical deformation event. However, it can be reasonably expected that an enhancement in chemical reactivity could also be exhibited by atomic species involved in local deformation-induced rearrangements during the course of the deformation process and not only when the system has reached local equilibrium. The atoms undergoing rapid modifications of their local arrangement caused by the operating mechanical stresses necessarily exhibit different chemical properties from atoms at rest in a given structural configuration, whatever it is (Delogu, 2009). The local excited states connected with ongoing deformation processes are expected to trigger chemical transformations with possibly different kinetics and thermodynamics from relaxed defective systems, under conditions where the atoms participating in local excitations interact with chemical species in the surroundings (Delogu, 2009). The capability of mechanical activation to enhance chemical reactivity has already found various applications in areas of science and technology as different as powder metallurgy (Suryanarayana, 2001), mineral processing (Balaz, 2008) and organic synthesis (Rodriguez et al., 2007). Mechanical processing of powders has proved particularly valuable in the production of metastable phases such as amorphous alloys and nanostructured phases (Suryanarayana, 2001). However, it also attracts considerable interest within the framework of studies concerning hydrogen storage (DOE, 2003), pollutant abatement (Mulas et al., 1997, Loiselle et al., 1997, Monagheddu et al. 1999) and heterogeneous catalysis (DOE, 2007). Mechanical activation has only recently begun to exhibit all of its intrinsic potential despite being utilized in a variety of research activities for some time. There are a few main reasons for this (Heinicke, 1984; Butyagin, 1989; Gutman, 1998; Suryanarayana, 2001; Levitas, 2004). In the first place, the


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large amount of experimental data is extremely difficult to correlate owing to the variety of working conditions and experimental apparatuses. Second, solid phase structural transformations and interface processes exhibit a considerable degree of complexity, so that the characterization of the reactive behaviour is generally unsatisfactory. Finally, a suitable mathematical formalism to address properly thermodynamic and kinetic studies by taking account of the dynamics of powder processing in experimental devices is still lacking. Nevertheless, all of the above-mentioned points can be satisfactorily dealt with (Delogu et al., 2009; Delogu and Mulas, 2009). The emerging result provides striking experimental evidence common to all mechanically activated processes (Delogu et al., 2009; Delogu and Mulas, 2009). The rate of a given structural or chemical transformation induced by mechanical deformation is orders of magnitude higher than the one observed for the same transformation under thermal activation conditions (Delogu et al., 2009; Delogu and Mulas, 2009). This surprising evidence naturally comes from a detailed analysis of mechanically activated transformations as a function of local deformation events instead of time (Delogu et al., 2009; Delogu and Mulas, 2009). Focusing precisely on this latter issue, the present chapter aims to show the efficiency, and then the potential, of mechanical activation processes in the areas of hydrogen storage, toxic chemical degradation and catalytic transformations.

3.3

Outline of experimental methods

All of the mechanically activated transformations discussed below were carried out in a Mixer/Mill mod. 8000 from Spex CertiPrep Inc. (Metuchen, NJ, USA), which is one of the most popular commercial ball mills used in research. The milling device is equipped with a stainless steel cylindrical reactor, the internal chamber of which has radius and height of about 2 cm and 6 cm, respectively. Once the desired mass mp of powder and number of stainless steel balls are introduced, the chamber is sealed in the desired atmosphere and fixed on the clamping assembly of the mechanical arm. The arm is connected to the mill electrical motor through an eccentric fulcrum, which allows the reactor to move along a three-dimensional trajectory that can be described as a combination of rotations and translations. The frequency of such motion amounts to about 14.6 Hz (Delogu et al., 2004). As briefly mentioned earlier, the balls undergo a sequence of collisions with each other and with the reactor walls during the mill operation. At each collision, a small fraction of the powder charge is trapped between a pair of colliding surfaces and submitted to mechanical processing (Delogu et al., 2004).



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The fraction of powder charge trapped in individual collisions exhibits a dependence on the powder charge mp itself. In particular, the powder fraction trapped at collision increases on the average with the powder mass mp. A parallel increase in the inelasticity of collisions takes place. Almost perfectly inelastic collisions already occur when the powder charge occupies at least the 1% of the total volume of the reactor chamber (Manai et al., 2001; Delogu et al., 2004). For typical transition metal and transition metal oxide systems, such circumstances allow the processing of a mass m* of powders per collision roughly equal to 1 mg. This powder mass, relatively small when compared to typical powder charges mp of about 8 g, is processed at collision for a time interval that can be equalled to the time duration τ of the inelastic collision itself, which is roughly equal to 1 ms (Manai et al., 2001; Delogu et al., 2004). Owing to the particular dynamics of balls and powders inside the reactor chamber (Manai et al., 2001), both mp and τ are approximately insensitive to the exact amount mp of powder. Whereas the use of a relatively large amount of powders ensures an inelastic collision regime, the additional use of a single milling ball permits the establishment of regular milling dynamics (Manai et al., 2001). In fact, the ball can only undergo collisions with the internal reactor walls and with the base of the container in particular (Manai et al., 2001; Delogu et al., 2004). This allows the ball to follow periodic trajectories with two collisions per cycle of reactor displacement (Manai et al., 2001; Delogu et al., 2004). More specifically, collisions occur at a frequency N of about 29.2 Hz (Manai et al., 2001; Delogu et al., 2004). All the experimental trials were carried out with a powder charge mp of solid reactants or catalysts equal to 8 g. These powders were invariably manipulated under an inert argon atmosphere during the reactor chamber charge and discharge operations. With this aim in mind, a glove box with oxygen, nitrogen and water content below 2 ppm was used. When necessary, the atmosphere inside the reactor chamber was suitably modified by carrying out filling–emptying–refilling cycles with the desired pure gas or gaseous mixture. In these cases, a suitably manufactured cylindrical reactor was utilized, with the top and bottom caps equipped with valves for the inlet and outlet of gases. The reactor chamber can, in principle, be kept at any desired temperature, although within specific ranges depending on the leak-proof ‘O-ring’ systems. Suitable external jackets allow the circulation of heating and cooling fluids. In the absence of jackets, simple air jet cooling suffices to keep the average system temperature in the range between 300 and 330 K. The average temperature is measured by a thin lamella-shaped Ptresistance thermometer fixed on the external reactor wall or embedded in it. As for the local temperature experienced by powders, indirect clues


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suggest that the local rise caused by collisions amounts to about 100 K (Delogu and Cocco, 2008a). Analyses of solid phases were carried out by wide-angle X-ray diffraction (XRD), performed on powder sampled at selected times during mechanical treatment. XRD patterns were generally collected with a Rigaku D/Max diffractometer equipped with a Cu Kα radiation tube and a graphite monochromator in the diffracted beam. N2 adsorption was used to measure the specific surface area Sp of the different solid phases according to the BET method (Thomas and Thomas, 1997). Analytical tests employed a Fisons Sorptomatic 9600 apparatus. Liquid and gaseous phases were analysed by gas chromatography resorting to different detectors. In the former case, a Finnigam Tracker Mass Spectrometer GC/MS PE 8420 device was used. A Fisons 8000 apparatus equipped with a HWD detector was employed to monitor CO and H2 gases, whereas light hydrocarbons and other gaseous organic phases were analysed with a Perkin-Elmer 8600 apparatus equipped with a FID detector. High purity solid, liquid and gaseous reactants were invariably used.

3.4

Degradation of chlorinated aromatics

The behaviour of two different chlorinated aromatic compounds was selected for study in the presence of mechanically activated solid reactants, namely the chlorobenzene (C6H5Cl) and hexachlorobenzene (C6Cl6). At room temperature the former compound is in the liquid phase, whereas the latter is a solid. Degradation reactions were carried out over inorganic substrates such as MgO, CaO and CaH2. Reactants were mixed in order to have an atomic ratio of alkaline-earth metal to chlorine ratio equal to 15 : 1 (Mulas et al., 1997). The two toxic compounds exhibit markedly different reactivity. In particular, the mechanical treatment of C6Cl6 with CaH2 generally induces a very fast chemical conversion, mostly into benzene (C6H6) and CaCl2 with extremely large exothermic effects (Mulas et al., 1997). In contrast, the mechanical processing of C6H5Cl with CaH2 results in a gradual reaction, also yielding the same above-mentioned main products (Mulas et al., 1997, Loiselle et al., 1997). The chemical behaviour triggered by the mechanical activation of the reactant mixtures containing C6Cl6 is exemplified by the temperature profile shown in Fig. 3.1. Here, the temperature T of the mechanochemical reactor is reported as a function of the time t of mechanical processing. It can be seen that the reactor temperature T first undergoes a gradual increase connected with the thermal effects originated from the partial dissipation at impact of the kinetic energy of the single milling ball. The quantity of heat dissipated at collisions is a linear function of time t, so



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Temperature (K)

340 330 320 310 300 290 0

2000

4000 6000 Time, t (s)

8000

10000

3.1 The temperature (K) of the stainless steel reactor as a function of the time t of mechanical processing. Data refer to the reaction of CaH2 and hexachlorobenzene. The temperature spike marks the onset of the self-propagating high-temperature reaction.

that a rough estimate of this quantity can be obtained by the initial slope of the temperature curve. However, the process of heat generation at impact is soon counterbalanced by the heat dissipation process at the reactor external surfaces. The result is a curved trend that represents a compromise between heat generation and dissipation processes. After a certain milling time has elapsed, it is possible to observe a sharp thermal spike superposed on the gradual temperature rise and in a sense independent of it. The sudden temperature rise marks the onset of a very fast chemical reaction, the characteristics of which are only partially known. However, it is possible to state a few important features. First, the chemical process is self-propagating, that is, it does not need any further energy supply once triggered. Second, the chemical reaction occurs on very short timescales, roughly on the order of 1 s. Third, the exothermal effects perfectly correlate with the reaction enthalpy, so that no significant amount of intermediate species is present. Fourth, the reaction probably involves the formation of radical species, as suggested by the detection of negligible traces of chemical compounds, the formation of which relies upon radical condensation reactions. The evidence that mechanical processing succeeds in activating selfpropagating behaviour immediately points out the difference between mechanical activation and conventional thermally activated processes. In fact, no self-sustaining reaction takes place when the reactants are submitted to a progressive temperature increase, unless very high heating rates are imposed. On the contrary, the chemical reaction possibly proceeds at relatively low conversion rates. This does not mean that the self-propagating process cannot be triggered under purely thermal conditions. Nevertheless, such conditions must be quite severe in terms of heating rate and total


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energy transferred to reactants. More specifically, conditions must correspond to the ones generally met by self-sustaining high-temperature synthesis (Munir and Anselmi-Tamburini, 1989). It follows that mechanical activation is able to impose equally severe processing conditions on reactant powders (Takacs, 2002). In contrast to the previous case, the mechanical treatment of reactant mixtures containing C6H5Cl only results in a gradual conversion of reactants in the final main products. A typical kinetic curve is shown in Fig. 3.2, where the molar fraction of C6H5Cl reacted is reported as a function of the time t of mechanical processing. It can be seen that the conversion is described by a sigmoidal curve, which indicates that the reaction reaches completion on timescales on the order of 12 h. The gradual conversion curve can be used to gain insight into the reactive behaviour at individual collisions. Starting from evidence that the chemical reaction stops immediately when the mechanical processing is interrupted, the observed conversion rate can be connected with the frequency N of collisions. With this aim in mind, a necessary assumption is that the chemical events activated by individual deformation events at each collision are independent of each other. Correspondingly, the local chemical reaction initiated by a given collision is not influenced by the following one. In general terms, this assumption can appear quite arbitrary. However, it is based on evidence that local structural excitations induced by deformation events exhibit relaxation times on the order of 1 ns (Delogu, 2009) and involve small percentages of the powder charge, typically on the order of 0.1% (Delogu et al., 2004). Taking into account that successive collisions are separated by time intervals of about 30 ms (Delogu et al., 2004), it must be expected that any chemical reactivity triggered by mechanical deformation at a given collision is definitely quenched when the immediately successive collision occurs. Under these circumstances, the overall chemical reaction corresponds to the resultant of the whole sequence of discrete reactive events at individual collisions. Consequent to such assumption, the instantaneous conversion rate r at any selected point on the kinetic curve in Fig. 3.2 can be referred to individual collision events by dividing it by the frequency N of collisions. This provides a measure of the amount of reactants reacted at each collision. In the present case, the maximum conversion rate, referred to C6H5Cl, is attained at about 4 h and amounts to about 4.8 × 10−7 mol s−1. The frequency N of collisions being equal to about 29.2 Hz, the amount of C6H5Cl transformed at each collision is roughly equal to 1.6 × 10−8 mol. This value can be utilized to estimate the specific conversion rate of reactants at individual collision events. With this aim, the above-mentioned value must be referred to the mass m* ≈ 1 mg of powder trapped during the collision and to the time duration τ ≈ 1 ms of collisions, which represents a reasonable estimate



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Conversion α (%)

100 80 60 40 20 0 0

2

4

6

8

10

12

14

Time, t (h)

3.2 Fraction α of reacted chlorobenzene as a function of the time t of mechanical processing. Data refer to the reaction with CaH2.

of the time interval during which mechanical forces operate on powders. The resulting specific reaction rate amounts then to about 1.64 × 10−2 mol g−1 s−1. A way to interpret the above-mentioned result is by comparing the observed overall reaction rate and the possible overall reaction rate in the case in which negligible time intervals separate successive collisions. In the former case, the gradual degradation of C6H5Cl reaches 80% completion after about 8.5 × 105 collisions, that is, after 8 h. In the second case, provided that the same number of collisions is required, 80% conversion would be reached after only a few seconds of treatment. Therefore, the mechanochemical process in principle exhibits considerable efficiency, with very high specific rates of chemical reaction. In spite of the general observations above, it is worth noting here that this aspect can be adequately pointed out only through a suitable comparison of mechanochemical processes and thermal ones. This approach has not been possible in the present case, since the thermal activation of reactant powders does not produce any gradual conversion in the case of C6Cl6, whereas it induces the evaporation of C6H5Cl in the other. However, comparison of mechanically and thermally activated reactions will be the focus of the following sections.

3.5

Hydrogen absorption on Mg2Ni/Ni composite

The H2 absorption processes were carried out on powder charges mp of 8 g of a Mg2Ni/Ni composite. A stainless steel ball of 8 g was used. The H2 pressure was kept constant at 0.4 MPa (Delogu and Mulas, 2009). The kinetics of the H2 absorption process is described by the curve shown in Fig. 3.3, where the number n of H2 moles absorbed is reported as a function of the time t of mechanical processing. The curve exhibits


High-energy ball milling H2 moles absorbed, n (mol)

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0.12 ns+d 0.08

Static Dynamic

ns 0.04

0.00 0

200

400

600

800

1000

Time, t (min)

3.3 Number n of H2 moles absorbed as a function of the time t of mechanical processing. The vertical dotted line separates the H2 absorption processes performed under static and dynamic conditions, whereas the horizontal dotted lines indicate their respective plateau values ns and ns+d.

two distinct portions relating to the H2 absorption processes carried out with the mechanochemical reactor, respectively, at rest and in motion. The two cases will be hereafter referred to as static and dynamic processing conditions. It can be seen that the number n of H2 moles absorbed under static conditions tends to reach a plateau value ns. The mechanical treatment was started at time t0, roughly 60 min before the number of hydrogen moles absorbed could reach the plateau value under static processing conditions, that is, when powders have already absorbed n0 ≈ 4.8 × 10−2 H2 moles. The mechanical processing induces a definite increase in the number n of H2 moles absorbed, which however tends to reach a plateau value ns+d larger than ns. The observed behaviour suggests that the H2 absorption reaction over Mg2Ni/Ni under static conditions is limited by some sort of thermodynamic or kinetic limitations. However, these are by-passed under dynamic conditions, which promote a significant absorption beyond the apparent asymptotic threshold ns. According to XRD analyses, the above-mentioned behaviour can be ascribed to a change in the H2 absorption kinetics. In fact, static processing conditions substantially induce the formation of the Mg2NiH0.3 hydride, which is relatively poor in H content. When the same powders have also been mechanically processed, the predominant phase is instead the Mg2NiH4 hydride, which is the hydride richest in H formed by Mg2Ni systems. Static and dynamic processing conditions produce, therefore, very different results. Under static conditions, H2 is absorbed according to an apparent secondorder rate equation: dn 2 = Ks ( ns − n) [3.1] dt the solution of which is © Woodhead Publishing Limited, 2010


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10

n/(ns–n)

8 6 4 2 0 0

20

40 Time, t (min)

60

80

3.4 n/(ns − n) as a function of the time t of mechanical processing. The line best-fit is also shown.

n = Ks ns t ns − n

[3.2]

Accordingly, the first portion of the curve in Fig. 3.3 can be linearized by reporting the quantity n/(ns − n) as a function of time t. The resulting plot is shown in Fig. 3.4. According to Equation [3.2], the slope of these linear trends is equal to Ksns, where Ks is the apparent rate constant of the H2 absorption process under static conditions. The best-fit of data in Fig. 3.4 indicates that ns and Ks amount to about 5.4 × 10−2 mol and 2.6 mol min−1, respectively. It immediately appears that ns is far from the value of 0.148 mol necessary for complete conversion into Mg2NiH4, but is about 5 times larger than the 1.1 × 10−2 mol necessary for the complete conversion into Mg2NiH0.3. Under dynamic conditions, the H2 absorption kinetics exhibits an exponential character. The scaled number n* = n − n0 of H2 moles absorbed under dynamic conditions and the scaled time t* = t − t0 were defined suitably to analyse the second portion of the curve in Fig. 3.3. As shown in Fig. 3.5, the quantity ln(n*s+d − n*), being n*s+d = ns+d − n0, changes linearly with t*. It follows that: ln(n*s+d − n*) = K*s+dt* + lnn*s+d

[3.3]

which is a solution of the rate equation: dn * = K*s+d (n*s+d − n*) dt *

[3.4]

The quantity K*s+d represents the apparent rate constant for the H2 absorption process performed under dynamic conditions on powders that have already absorbed n0 H2 moles after a time interval t0 under static conditions. The best-fit of data in Fig. 3.5 yields for n*s+d and K*s+d estimates of about 6.0 × 10−2 mol and 4.5 × 10−3 min−1, respectively. It is worth noting here that ns © Woodhead Publishing Limited, 2010

56

High-energy ball milling –2

ln(n*s+d –n*)

–3 –4 –5 –6 –7 –8 0

200

400

600

800

1000

1200

Time, t* (min)

3.5 ln(n*s+d − n*) as a function of the scaled time t*. The line of best-fit is also shown.

+ n*s+d ≈ 0.114 mol represents the total number of H2 moles absorbed. The above-mentioned experimental findings allow a quantitative comparison of experimental data obtained under static and dynamic conditions. Owing to the exponential character of the kinetic curve, the H2 absorption under dynamic conditions can be referred to independent reactive events taking place at individual collisions (Delogu and Cocco, 2007; Delogu and Cocco, 2008b). Under these conditions, the rate of mechanically activated processes only depends on the mass m* ≈ 1 mg of powders involved in individual collisions. In addition, H2 absorption at collision should take place for time periods roughly equal to the impact duration τ ≈ 1 ms. When the mechanical treatment starts, the scaled number n* of H2 moles absorbed under dynamic conditions is equal to zero. After the first collision has occurred, the number of H2 moles absorbed is approximately equal to K*s+dn*s+d, which then represents the initial rate rs+d of H2 absorption. This quantity amounts to about 4.5 × 10−6 mol s−1, which means that about 1.5 × 10−7 mol of H2 are absorbed at the first collision. This H2 amount is absorbed by roughly 1 mg of powders within time intervals of about 1 ms. Therefore, the specific H2 absorption rate at the first collision is equal to about 0.15 mol g−1 s−1. This value must be compared with the specific rate of H2 absorption under static conditions approximately after n0 H2 moles have been absorbed in a time period t0. It follows from Equation [3.1] that the rate rs of H2 absorption under static conditions is equal to Ks(ns − n0)2, which roughly amounts to 1.6 × 10−6 mol s−1. The specific H2 absorption rate under static conditions can now be obtained by dividing this rs value by the total powder mass mp = 8 g. The specific rate amounts to about 2.0 × 10−7 mol g−1 s−1. According to the above-mentioned specific rate values, H2 absorption under dynamic conditions is about six orders of magnitude faster than under static conditions. This difference cannot be explained in terms of



57

specific surface areas. In fact, the Mg2Ni/Ni powders interacting with H2 at individual collisions should exhibit a specific surface area S*p on the order of 1 × 105 m2 g−1, values characteristic of catalytic carbon or silica aerogels. In contrast, the BET specific surface area Sp is equal to only about 15 m2 g−1 before and after any mechanical treatment. In the light of calculations above, the enhanced H2 absorption capability of mechanically processed powders must find a different rationalization. This can be looked for in so-called mechanochemical effects, that is, in effects ascribable to the highly excited atomic structures that appear at the surface of powder particles as a consequence of deformation processes. More specifically, the extremely high specific rates of H2 absorption at individual collision events can be related to the increase of the surface density of reactive sites, to the enhancement of their chemisorption efficiency or to both these factors. Rough calculations carried out to pursue research further along these lines indicate that the activation energy Ea of the H2 chemisorption should drop from about 64 to 37 kJ mol−1. Alternatively, local temperatures should rise by about 400 K. Of course, no discrimination is possible between surface, temperature and energy effects. In contrast, it is highly probable that the enhanced H2 absorption capability of mechanically processed powders could result from a combination of all such effects.

3.6

Catalytic hydrogenation of carbon monoxide

The hydrogenation of carbon monoxide (CO) to produce methane (CH4) and other hydrocarbons was carried out over 8 g of a powder catalyst with a composition of (Co50Fe50)0.2(TiO2)99.8. A gaseous mixture of H2 and CO was introduced into the reactor chamber with a 1 : 3 CO:H2 ratio to maximize the reaction yield in CH4. The total pressure inside the reactor chamber was set at 0.3 MPa (Delogu et al., 2009). The conversion data for the CO hydrogenation process are given in Fig. 3.6, where the moles n of hydrocarbon produced are shown as a function of the time t of mechanical processing. Substantially, CO is selectively converted to CH4 with an initial rate of about 7.8 × 10−7 mol h−1. This conversion must be ascribed to the metallic Co-Fe phase, which, in 8 g of catalyst, is equal to 0.023 g. The amount r of CO converted on the average in individual impact events can be estimated by dividing the overall conversion rate by the frequency N of collisions, which is equal to about 29.2 Hz. Roughly 7.4 × 10−12 mol of CO are converted at each collision. Remembering that the time duration τ of collisions is equal to about 1 ms and that the mass m* of powder involved in each collision amounts roughly to 1 mg, the specific conversion rate r* = r τ−1m*−1 at individual collisions amounts to approximately 7.4 × 10−6 mol g−1 s−1. The specific


58

High-energy ball milling Moles of CH4, n (mmol)

80 60 40 20 0 0

30

60 Time, t (h)

90

120

3.6 n moles of hydrocarbon produced over the (Co50Fe50)0.2(TiO2)99.8 catalyst as a function of the time t of mechanical processing.

catalytic activity must be referred to the area s* of the catalytically active surface involved in individual collisions. This corresponds to a turnover frequency fmech, that is, the number of reactant moles reacted per time unit per active site of the catalytically active surface under mechanochemical −1 conditions. The quantity fmech is equal to rτ−1s*C−1 o Feρs , where ρs is the average surface atomic density of the Co50Fe50 solid solution. As s*CoFe = m*CoFeSp,CoFe, −1 the expression above is also equal to r*S*C−1 o Feρs , where Sp,CoFe is the specific surface area of only the Co50Fe50 solid solution, which is the catalytically active phase. The average surface atomic density ρs can be estimated by the arithmetic mean of the atomic densities of individual Co and Fe surfaces reported in the literature (Anderson, 1975). A ρs value of about 1.6 × 1019 at m−2 is obtained. The quantity s*CoFe can be estimated under the hypothesis that the Co50Fe50 domains supported on TiO2 correspond to individual crystallites. This hypothesis permits the estimation of the maximum specific surface area Sp,CoFe available to reaction by considering spherical Co50Fe50 domains with a diameter equal to the average crystallite size L. In this case, the maximum specific surface area Sp,CoFe is equal to 6ρ−1L−1, where ρ is the average density of the Co50Fe50 solid solution. Evaluating this quantity as the arithmetic average of Co and Fe densities, ρ amounts to about 8.5 g cm−3. As L is roughly equal to 20 nm, the maximum specific surface area Sp,CoFe amounts to about 35 m2 g−1. The total surface area s*CoFe of the Co50Fe50 domains available for reaction in individual collisions is therefore roughly equal to 9.8 × 10−5 m2, and the mass m*CoFe of Co50Fe50 phase involved in collisions equal to about 2.8 × 10−6 g. The mechanochemical turnover frequency fmech of the CO hydrogenation process is then equal to about 2.84 molecules atom−1 s−1. The fmech value obtained for the (Co50Fe50)0.2(TiO2)99.8 catalyst can be now compared with the value of turnover frequency fth obtained over a similar



59

catalyst under thermal activation conditions (Duvenhage and Coville, 1997). This catalyst has a (Co50Fe50)5(TiO2)95 chemical composition and was tested under flow conditions at a temperature of 493 K and a total pressure of a 1 : 2 CO : H2 mixture equal to 1 MPa (Duvenhage and Coville, 1997). The working conditions are therefore slightly different from the ones employed during the course of mechanical activation. The thermal turnover frequency fth for this catalyst amounts to about 1.4 × 10−2 molecules atom−1 s−1 (Duvenhage and Coville, 1997). Therefore, at least two orders of magnitude separate the above mentioned fth value from the mechanochemical turnover frequency fmech of about 2.84 molecules atom−1 s−1 obtained for the (Co50Fe50)0.2(TiO2)99.8 catalyst. The difference of two orders of magnitude represents only the minimum possible difference between the activity of the two catalysts. A few simple considerations suggest, in fact, that the difference in specific activity, or in turnover frequencies, must be larger. First, both temperature and pressure are higher in the case of thermal activation, which assures higher frequencies of collisions between gaseous species and catalyst surface. Second, the actual specific surface area Sp,CoFe value of the supported Co50Fe50 phase is expected to be smaller than the rough estimate based on the average crystallite size, since individual crystallites are expected to form nanostructured aggregates. Third, the time interval τ over which the chemical transformations are assumed to occur has been set equal to the time duration of an inelastic collision. However, such an estimate only represents an upper bound for the collision duration, since partially inelastic collisions often last only 0.1 ms (Manai et al., 2001). It follows that the mechanochemical turnover frequency fmech could be two to three orders of magnitude larger than the thermal fth one. Correspondingly, the mechanically activated catalytic process could be two or three orders of magnitude more efficient than the thermally activated one. This provides an indirect estimate of the importance of mechanochemical effects on the chemical behaviour of solid phases.

3.7

Future trends

The kinetics of mechanically activated processes is an area of research with a number of open questions. The brief overview presented here is specifically aimed at pointing out a few outstanding topics in mechanochemical kinetics, the investigation of which could promote significant advances in the field. According to the data and approaches discussed, there is a lack of fundamental knowledge about the mechanisms with which mechanically activated processes take place at individual collisions. In fact, the experimental evidence only refers to overall transformations observed on the macroscopic scale. Referring to individual collisions represents an important,


60


though still unsatisfactory, step toward the microscopic scale. There is a stringent need to perform careful investigations from both the experimental and theoretical points of view on the chemical response of materials embedded in a reactive environment while being submitted to ongoing mechanical deformations. The challenging objectives can be summarized in two main points of a middle-term programme: • •

set-up of experimental methodologies to investigate the chemical reactivity of solid, liquid and gaseous reactants at individual collisions; development of theoretical and numerical models able to address the fundamental issues intrinsically connected with a far-from-equilibrium chemistry.

Both these points imply considerable effort in tentative exploration of chemical reactivity under extreme conditions at the limit of application of present technologies. Which method can be applied to investigate the way a given amount of kinetic energy is distributed at individual collisions? How can reliable information be obtained at the very short timescales characteristic of collisions? How do portions of matter really behave when submitted to ongoing deformation during interaction with liquid and gaseous environments? These and a number of other questions regarding the intimate nature of mechanochemical processes clearly emphasize the unsatisfactory degree of knowledge in the field at present. There is a strong need for cooperation between research groups with different expertise, as well as to identify viable applications of current techniques to practical problems in mechanochemistry. New ideas are also needed that could permit a significant breakthrough in this field. And all of this must happen in the shortest possible time, if mechanochemistry has to play a role in the intermediate energetic scenarios that are becoming every day closer.

3.8

References

anderson j r (1975), Structure of Metallic Catalysts, Academic Press, London. balaz p (2008), Mechanochemistry in Nanoscience and Minerals Engineering, Springer, Berlin. butyagin p yu (1989), ‘Active states in mechanochemical reactions’, Sov Sci Rev Chem B, 14, 1–134. delogu f (2009), ‘Molecular dynamics of perturbed rearrangements at perturbed interfaces’, Phys Rev B, 80, 014115. delogu f and cocco g (2006), ‘Numerical simulations of atomic-scale disordering processes at impact between two rough crystalline surfaces’, Phys Rev B, 74, 035406. delogu f and cocco g (2007), ‘The size refinement of Cu crystallites under mechanical processing conditions: a phenomenological modeling approach’, J Mater Sci, 42, 4356–63.



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delogu f and cocco g (2008a), ‘Weakness of the “hot spots” approach to the kinetics of mechanically induced phase transformations’, J Alloys Compd, 465, 540–6. delogu f and cocco g (2008b), ‘Kinetics of amorphization processes by mechanical alloying: a modeling approach’, J Alloys Compd, 436, 233–40. delogu f and mulas g (2009), ‘Hydrogen absorption processes in Mg2Ni-based systems: thermal and mechanochemical kinetics’, Int J Hydrogen Energy, 34, 3026–31. delogu f, mulas g, schiffini l and cocco g (2004), ‘Mechanical work and conversion degree in mechanically induced processes’, Mater Sci Eng A, 382, 280–7. delogu f, mulas g, and garroni s (2009), ‘Hydrogenation of carbon monoxide under mechanical activation conditions’, Appl Catal A: Gen, 366, 201–5. doe report (2003), Basic Research Needs for the Hydrogen Economy, Report from the US Department of Energy (DOE) Basic Energy Sciences Workshop on Hydrogen Production, Storage, and Use, Argonne National Laboratory, Illinois (USA) May 13–15 (available at http://www.sc.doe.gov/bes/hydrogen.pdf). doe report (2007), Basic Energy Needs: Catalysis for Energy, Report from the US Department of Energy (DOE) Basic Energy Sciences Workshop, Bethesda, Maryland (USA), August 6–8 (available at http://www.sc.doe.gov/bes/reports/list. html). duvenhage d j and coville n j (1997), ‘Fe:Co/TiO2 bimetallic catalysts for the Fischer–Tropsch reaction. I. Characterization and reactor studies’, Appl Catal A: Gen, 153, 43–67. gutman e m (1998) Mechanochemistry of Materials, Cambridge International Science Publishing, Cambridge. heinicke g (1984), Tribochemistry, Akademie-Verlag, Berlin. holdren j p (2008), ‘Energy and sustainability’, Science, 315, 737. honeycombe r w k (1984), The Plastic Deformation of Metals, Edward Arnold, Baltimore. levitas v i (2004), ‘Continuum mechanical fundamentals of mechanochemistry’, in High Pressure Surface Science and Engineering, Gogotsi Y and Domnich V (eds), Institute of Physics, Bristol, 159–292. levitas v i and zarechnyy o m (2006), ‘Kinetics of strain-induced structural changes under high pressure’, J Phys Chem B, 110, 16035–46. loiselle s, branca m, mulas g, cocco g (1997), ‘Selective mechanochemical dehalogenation of chlorobenzenes over calcium hydride’, Environ Sci Technol, 31, 261–5. manai g, delogu f and rustici m (2001) ‘Onset of a chaotic dynamics in a ball mill: attractors merging and crisis induced intermittency’, Chaos, 12, 601–9. monagheddu m, mulas g, doppiu s, cocco g, raccanelli s (1999), ‘Reduction of polychlorinated dibenzodioxins and dibenzofurans in contaminated muds by mechanically induced combustion reactions’, Environ Sci Technol, 33, 2485–8. mulas g, loiselle, schiffini l, and cocco g (1997), ‘The mechanochemical selfpropagating reaction between hexachlorobenzene and calcium hydride’, J Sol State Chem, 129, 263–70. munir z a and anselmi-tamburini u (1989), ‘Self-propagating exothermic reactions: The synthesis of high-temperature materials by combustion’, Mater Sci Rep, 3, 277.


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rodriguez b, bruckmann a, rantanen t, and bolm c (2007), ‘Solvent-free carboncarbon bond formations in ball mills’, Adv Synth Catal, 349, 2213–33. suryanarayana c (2001), ‘Mechanical alloying and milling’, Prog Mater Sci, 46, 1–184. takacs l (2002), ‘Self-sustaining reactions induced by ball milling’, Prog Mater Sci, 47, 355–414. thomas j m and thomas w j (1997), Principles and Practice of Heterogeneous Catalysis, VCH, Weinheim.


4 Materials design through mechanochemical processing M A M O R U S E N N A, Keio University, Japan

Abstract: Controlled shear stressing on a dry solid mixture at ambient temperature enables charge transfer and short range interparticulate atomic transfer. They result in formation of hetero-bridging bonds, leading to nucleation of various composites or complexes, for example, perovskites or spinels. Similar phenomena could be applied to rationalizing organic syntheses or compounding of different materials in various genres. After surveying general and theoretical bases of materials design via solid state routes, case studies on electroceramics and novel organic synthesis by using moderate mechanical stressing are given using the concept of soft-mechanochemical processes, where the use of chemical spontaneity like self-organization or molecular recognition is emphasized. Key words: soft-mechanochemical processes, charge transfer, hetero-bridging bonds, perovskite ceramics, coordination compounds, Diels–Alder reaction.

4.1

Introduction

It is always a challenge to tailor materials pinpointed for particular applications. Since the characteristics of the materials are so diverse, the parameters that need to be controlled in materials design are necessarily numerous. One of the smartest methods in materials design is first to assemble atoms or molecules in a well-defined way in a given space. This is widely carried out by computer simulation.1–3 Although the concept is elegant and perfect, outcome of these studies cannot be applied to actual production processes. Various attempts have been made, to design materials and fabricate them, where atomic or molecular manipulation is regarded as an ultimate goal.4 Since this is extremely tedious, if possible at all, people have tried to let atoms self-organize themselves. This is realized to some extent in various thin film technologies.5 They can be stacked to give a three-dimensional (3D) structure, often called artificial lattices.6,7 On an industrial basis, however, the well-defined methodologies given above are mostly unaffordable. This is not just due to the very minute amount of thin film processing. Since most materials are handled in the 63 © Woodhead Publishing Limited, 2010

64


form of fine particulates, we need to start by designing particulates. This is far more complicated than for thin films, since fine particulate states cannot be prepared without introducing a significant amount of lattice defects and near-surface anomalies of solids, although the finely controlled technology of two-dimensional (2D) film formation can be smartly converted into socalled 3D films, which are actually an ensemble of fine particulates. When we go down to the level of several tens of nanometers, we need to regard them as an ensemble of surface anomalies without any stable parts in the bulk solid. In addition, we have to take huge number of extra parameters into account, that is, geometrical, physical and chemical ones, since we almost always have to deal with a large ensemble of particulate matters or grains. Thus, we have to abandon sophisticated beam technology and look into various methods of preparing fine particles with reasonable scalability. This chapter will discuss how the general concepts of materials design mentioned above could be associated with mechanochemistry. The structure of the chapter is as outlined below. •

• •

• •

The benefits of a mechanochemical route for materials design: after introducing the brief histories of mechanochemical processing for materials synthesis, the importance of microscopic phenomena at solid interfaces is emphasized. The theoretical aspects of modern mechanochemistry: anomalies in the near-surface region and nano-sized particles are briefly reviewed. Composite oxides for electromagnetic application: this is the main part of the chapter, explaining the concept of soft-mechanochemical processes with examples of several case studies for perovskite ceramic particles carried out in the author's laboratory. Organic synthesis and utilization of chemical spontaneity: the role of charge transfer complex on the solid state Diels–Alder reaction under mechanical stressing is introduced. Summarizing remarks and the future outlook.

4.2

Benefits of a mechanochemical route for materials design

First, the chemical implications of mechanical stressing on the solid state will be briefly reviewed. Traditional solid state processes are represented by crushing mountain rocks to acquire various natural resources, notably metals. Powder technology in mineral processing in its early stage includes size reduction, sorting or classification, among others, by floatation. Subsequent metallurgical processes are subdivided into wet and dry processes, called hydro- and pyro-metallurgy. Mechanical activation plays a particularly significant role in hydrometallurgy, which begins with a dissolution


Materials design through mechanochemical processing

65

process. The presence of finer particles with a larger specific surface area, together with higher reactivity at the solid/liquid interface prove to be beneficial. This is one of the origins of practical application of mechanochemistry.8,9 Thus, an enhanced rate of dissolution and apparent solubility is the main attraction in industry of using mechanical stressing on solids in a one phase system. Introduction of various lattice imperfections is key.10–12 This often leads to phase transformation13–15 and amorphization as well.16–18 While this kind of mechanical activation is of practical importance, it is not always directly associated with materials design, except in some special applications like pharmaceutics. A more interesting mechanochemical issue that is closely related to materials design is putting stress on a mixture of solids. One typical example is so-called mechanical alloying, where two or more metallic species in the form of powder are mixed in a mill, become quasi atomically homogeneous alloys,19–25 and could even exceed the solubility limits predicted by phase diagrams. Here, the process might seem quite simple, that is where different metallic species penetrate the boundary via a short-range transfer, called mechanical diffusion, as schematically illustrated in Fig. 4.1. Things are, however, not so straightforward when mixing coloured marble. Whether or not mixture really builds up is believed to be governed by the heat of mixing,26–29 although, the mechanical alloying state is far from thermodynamic equilibrium so that phase diagrams cannot be the sole measure of the phase availability of alloys. This illustrates another peculiarity of mechanical alloying, where the process goes in most cases through a multilayered structure and there is a large contact area for mechanical diffusion owing to the ductility of the ingredient metals.30,31 The concept of mechanical alloying was extended to the polymeric materials to give ‘polymer alloys’ under a more or less similar procedure,32–34 although the chemical procedure involved is quite different since the unit of species is a complicated molecule with high molecular weight. Polymer alloys, often called ‘polymer blends’ are formed by repeated breakage and (a)

(b)

(c)

4.1 Schematic illustration of forced diffusion at the contact point of dissimilar particles. This simple process explains the principle of mechanical diffusion, which is a basic process of mechanochemistry, along with charge transfer, explained below.


66


rebuilding of molecular chains with and without side chains via widely varying radical species. Finally, the concept of mechanical alloying has been further extended to more general compounds involving oxides or chalcogenides. These processes are then renamed as ‘mechanosynthesis’, where products are obtained straight from the milling pot, normally without any heating process.35–38 There are a number of outstanding books in this area.39–41 At this stage, it is worth emphasizing that the technological benefits of mechanical stressing relating with materials design are mainly associated with a cross-solid interaction, triggered by many different factors, including short-range diffusion. A typical attempt exerts mechanical stress on the solid mixture to obtain alloys or composite oxides outright from the milling devices. In the case of conventional alloying, we usually need vacuum furnace and temperature higher than the melting points of ingredient metallic species, or at least higher than the eutectic temperature. Melting of oxide mixtures is in most cases out of question owing to their extremely high melting points. Many of them tend to decompose prior to melting. Therefore, the apparent merits of mechanosynthesis are quite obvious. However, there are a number of disadvantages or pitfalls. First of all, mechanosyntheses are in most cases carried out in energy intensive milling devices after operating for a long time, often hundreds of hours. A direct consequence is high power consumption, as well as high cost of devices and their maintenance. At the same time, the level of contamination from abraded materials in the milling media or vessels is high, up to several percent, and hence not tolerable for many industrial products including electroceramics. The limited extent of scale up in energy intensive milling devices counts as another demerit. Meanwhile, as energy used in industrial processes became more important, a headwind developed against mechanosynthesis, since generally milling devices are notorious for their low energy efficiency. As the costly mechanochemical processes were applied to more high-value-added materials, another serious problem arose, contamination, which becomes more serious with increasing energy intensity. It is therefore important at this stage to re-examine the merit of mechanical stressing more critically to find out what kind of solid state reactions are really enhanced by exerting external mechanical energy on the reactants and whether materials processing under mechanical stress is the best method compared to other non-conventional methods like photochemical, sonochemical, magnetochemical, hydrothermal or high-pressure processes. Here, we must concentrate more scientific effort on considering how processes related to mechanochemistry can survive in the area of materials design and in an era where there is increasing emphasis on the energy cost and ecological burden. Homogenization of solid mixtures at the atomic or molecular level was believed to be possible only by heating to elevated temperatures where the



67

mobility of the transporting species are high enough. As we have used metal oxides in making ceramic products, a vast number of new technological processes have been developed with respect to materials design and syntheses. Mechanochemistry and mechanochemical processes are representative of these. Conventional ceramic processes, often called ‘shake-and-bake’, are regarded as old-fashioned, belonging to the 20th century. When we look at the solid–solid grain boundary, we recognize that charge transfer and electronic redistribution under mechanical stressing is unique. The change in the electronic states associated with cross-boundary charge transfer plays an important role in a number of functional materials. Intimate mixing under controlled shear stressing in a dry solid process at ambient temperature enables controlled charge transfer and short range atomic transfer across boundaries of solids, which no other methods, like photo-, magneto- or plasma chemical processes, could achieve. By the same token, seemingly more advanced processes of solution–chemical, colloid– chemical or sol–gel processes are not always capable of controlling the charge transfer or associated electronic band structure, even if they are superior with regard to homogeneity of mixing. It is also important to mention that these processes are developing parallel to solid state chemistry, or to be more exact, studies on the reactivity of solids. A conventional tumbling ball mill can certainly achieve intimate mixing of particles with simultaneous size reduction of individual particles, although only to a limited extent. The use of more intensive mills, such as vibromills or planetary mills, therefore became prevalent in the hope that much finer and more homogeneous starting mixtures for subsequent calcination processes could be obtained. Up until the end of the last century, energy intensive milling machines were developed for these purposes, including vibration and planetary mills. When it turned out that the technological development of milling devices with higher energy density was not always moving in the right direction, the problem was approached in reverse, that is, how can we use mechanical activation or mechanochemical processes with minimum external stressing, by combining with other processes, among them traditional chemical or thermal processes. This is the basis of soft-mechanochemistry,42–47 where charge transfer across the grain boundary of dissimilar particles enables bridging bond formation under mild conditions. This will be explained below in more detail after we have discussed the theoretical aspects of mechanochemistry.

4.3

Theoretical aspects of modern mechanochemistry

Another aspect of mechanochemical interest is the mechanism of solid-state processes under mechanical stressing. Physical chemists tend to


68


attribute a mechanochemical process to excitation of the electronic energy state to reduce the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Indeed, molecular distortion brings about energy excitation, understood as the inverse Jahn–Teller effect.48–50 This is just the reverse of the photochemical process where photo-induced excitation brings about molecular distortion. This is different from the simple route via a radical formation, which mechanochemists frequently observe.51–55 Mechanochemical processes are inevitably associated with grain downsizing, since milling processes are almost always involved. Classically, it is well known that brittle materials turn into plastic, under the concept of microplasticity.56,57 Primarily, downsizing of the solid particles becomes more difficult since the probability of pre-existing microcracks decreases with decreasing particle size. More important is the decrease in the energy efficiency for comminution with decreasing particle size. This was smartly demonstrated by Kapur et al.58 Similar phenomena must be observed more carefully when the downsizing of the solid particle proceeds into the nanometric regime. Gutkin and co-workers59,60 and Ovid’ko and Sheinerman61 suggested that the migration of the grain boundary changes significantly when a solid particle size is less than 10 nm. Inspired by stress-induced grain boundary migration, they extended their ideas to dislocation nucleation and nano-crack formation, which are attributable to the coexistence of dislocations and disclinations and their combined effects. A number of attempts have been made to explain anomalies in the nearsurface region of solids, where there are not only unusually highly concentrated lattice defects but also a loosening of chemical bonds, which are very significant in mechanochemical processes, particularly when we try to combine these concepts with nanostructured material. One of the most important things to be inferred is the charge transfer across the particulate boundary. The importance of cross boundary charge transfer cannot be overemphasized in rational solid state chemical processes, since this can be done at room temperature. Mechanical stressing is very appropriate for this purpose, as will be seen later on.

4.4

Composite oxides in electromagnetic applications

4.4.1 Principle of soft mechanochemical effects Some of the soft mechanochemical processes mentioned above were conducted in the author’s laboratory, as introduced in several review articles.46,47,62–69 Some case studies are briefly introduced below.


Materials design through mechanochemical processing (a)

(b) MS-0

TG

M-48

Weight loss 5%

Exothermic

Weight loss

M-1/2

M-24

TG

MS-1/12

M-0

M-8

DTA

MS-1/6 MS-1/2

Exothermic

DTA

5%

69

MS-1 MS-2 MS-3

300

400

500 800 900 Temperature (°C)

300

400


4.2 Change in the thermal gravimetry (TG)–DTA profiles of Mg(OH)2 (a) and an Mg(OH)2–SiO2 mixture (b) during milling. The milling time is indicated at the end of the sample names in hours.

One of the earliest works in this field was the base–acid system, Mg(OH)2– SiO2, where dehydration and amorphization of Mg(OH)2 during milling was found to take place much faster when they coexist with SiO2 fine particles.70 The differential thermal analysis (DTA) endothermic peak caused by dehydration of Mg(OH)2 persisted even after vibro-milling Mg(OH)2 alone for 48 h, as shown in Fig. 4.2(a). The same peak entirely disappeared after milling for 3 h with SiO2 coexisting in a stoichiometric amount with magnesium monosilicate, as shown in Fig. 4.2(b). What is actually taking place at the contact points between Mg(OH)2 and SiO2 is rather straightforward. Since Mg(OH)2 is highly basic, in contrast to the highly acidic SiO2, neutralization reaction takes place, as schematically shown in Fig. 4.3. An important consequence of this surface neutralization is the formation of a bridging bond between two metallic species, M-I and M-II, Si and Mg in this particular case, respectively, abridged by an oxygen atom, as shown in Fig. 4.3(b). Note that there are almost always OH groups on the surface of metal oxide, a silanol group, Si-OH, in the case of silica. Evidence of the formation of this kind of a hetero-bridging bond (HBB), or a hetero-metalloxane bond (HMB), is given in Fig. 4.4, where the intensity of the Si–O–Si symmetric


High-energy ball milling (a)

(b) Acidic (hydr)oxide M-I O M-II

M-I M-II

M-1 O H

Mechanical stressing

Basic (hydr)oxide

M-1 O H2O M-2

H O M-2

4.3 Schematic illustration of HBB formation during milling of (hydr)oxide mixture with charge transfer and consequent neutralization at the contact point of dissimilar particles.

Mg(OH)2–SiO2 Si–O–Si

MS-1/6

O–H

MS-1

Transmittance

70

MS-2

3500

2500

1000 600 1600 Wavenumber (cm–1)

4.4 Change in the FT-IR spectra of the Mg(OH)2–SiO2 mixture due to milling. The milling time is indicated at the end of the sample names in hours.



71

stretching vibration bond decreases with the milling time of the Mg(OH)2– SiO2 mixture. The same principle works for a number of mixed oxide systems. Comparative studies on a series of basic hydroxides combined with acidic oxides were carried out to study the effect of basicity on the trend of bridging bond formation.71,72 More detailed studies of the soft mechanochemical process were carried out for the system comprising Ca(OH)2 and SiO2.73–75 The mechanisms of HBB formation were examined by various methods, among others, in situ infrared (IR), X-ray photoelectron spectroscopy (XPS) and solid state proton nuclear magnetic resonance (NMR).73 The main outcome of these experimental studies shows the increase in the polarization of surface OH groups caused by mechanical stressing. This enables a proton formed from the surface silanol group to serve as a Brønsted acid. Thus, a liberated proton can jump into the electron rich oxygen of the OH group in Ca(OH)2. This was verified by a molecular orbital study,76 as shown in Fig. 4.5. The probability of this kind of proton jump, a typical cross-boundary charge transfer, inevitably increases under mechanochemical conditions because of the compressive stress exerted on the powder mass. It is also important to note that the consequent HBB, Si–O–Ca, is stabilized by the introduction of an oxygen vacancy around Ca, as shown in Fig. 4.6. This is again an explicit manifestation of a mechanochemical process, since introduction of an oxygen vacancy is more probable under mechanical stressing due to the microplasticity mentioned above.57 The probability of HBB formation could be generalized on the basis of the well-established concept of electronegativity equalization.77–80 In addition to the acid–base mechanisms, an alternative process via radical formation and recombination should not be overlooked.74

(a)

(b) SiO4

Si

0.2 nm

O

Z2

Ca Oxygen vacancy

H

Z1

CaOx (x = 4)

Si

Z

X

Si O

Z2Z1

O

Ca

O

Ca

Y Z2–Z1 = (i) 0.2

(ii) 0.0

(iii) 0.0

4.5 Molecular orbital calculation demonstrating the interfacial neutralization due to mechanical activation of the Ca(OH)2–SiO2 mixture. (a) Model cluster system employed; (b) detachment of H2O as a consequence of neutralization.


72

High-energy ball milling 0.95

0.14

Overlap population (–)

0.12

0.90

Ca–O

0.10

0.85

0.08

0.80

0.06

0.75

0.04

0.70 O–Si

0.02 0.00

5

2 4 3 Coordination number X (–)

0.65

1

0.60

4.6 Bond overlap population between Ca and O, and O and Si in Ca(OH)2 and SiO2, respectively.

4.4.2 Application to perovskite ceramics (1): BaTiO3 The next step in materials design is combined with the subsequent heating process, called ‘calcination’ in the community of ceramics. In the author’s laboratory, a series of studies have been carried out for Mg–O–Ti or Ba–O– Ti systems, leading to MgTiO381–83 or BaTiO3,84–89 respectively. On the basis of the schematic explanation given in Fig. 4.3, it might be almost instinctively understood that a soft mechanochemical method brings about a more ready reaction just because of the preformed nuclei. As a matter of fact, the temperature of reaction completion decreased significantly.86,88 A more explicit description is given below of the effect of the mechanical activation of the BaTiO3 starting mixture. Starting powders, BaCO3 and TiO2 were mixed in the molar ratio 1 : 1 and predispersed to obtain an aqueous slurry. Samples S and W, with and without agitation milling, respectively, were obtained by freeze drying the respective slurry. Sample S was further dry vibro-milled for 5 h to obtain sample Sb.84 The corresponding increase in the homogeneity is shown in Table 4.1 by taking the variation coefficient of local composition determined by electron probe microanalysis. As seen from thermogravimetry and the corresponding differential profiles given in Fig. 4.7, the initiation and termination temperature of CO2 evolution, which tallies fairly well with the process of BaTiO3 formation,88 shift significantly toward lower temperatures with better dispersion (W to



73

Table 4.1 Homogeneity of the starting mixtures for the preparation of BaTiO3

Sample

Coefficient of variation of X-ray intensity of Ti (σ/average)

W S Sb

0.324 0.074 0.063

100

TG (%)

80 60 W

40

Sb

20

S

0 W

DTG

S

Sb 200

400

600 Temperature (°C)

800

1000

4.7 TG (upper) and DTG (lower) profiles of the BaCO3 and TiO2 mixtures.

S) and subsequent vibro-milling (S to Sb). We further observed the mixture under high resolution transmission electron microscopy (HR-TEM) in an attempt to identify these particles. As shown in Fig. 4.8(a) and (b) for the sample S and Sb, individual particles above 100 nm with a high contrast are identified as BaCO3, while particles of 40–80 nm with smoother surface and lower contrast are identified as TiO2. When sample Sb is heated up to 650°C, the micrograph exhibits two categories of the particles, as shown in Fig. 4.8(c). The selected area diffraction pattern shown in Fig. 4.8(d)


74

High-energy ball milling S

BaCO3

Sb

TiO2

50 nm

50 nm (a)

(b)

Sb-650°C

S-750°C

80 nm (c) (e)

(d)

40 nm

9 nm (f)

4.8 TEM micrographs of the BaCO3 and TiO2 mixtures ((a) and (b)) with those of quenched samples ((c) and (d), and (e) and (f)).

identifies the larger particle as BaCO3, as we assigned the spot pattern to belong to the space group Pnma from the fitting under the lattice parameters, a = 0.6433 nm, b = 0.5315, and c = 0.8904 nm. On the other hand, assignment of the small particle in sample S heated up to 750°C, shown in Fig. 4.8(e), was less straightforward. While the size is similar to that of TiO2, the morphology is quite different. The crystallinity of the small particle is relatively low, as shown in Fig 4.8(f). Although we failed to obtain either a clear fringe pattern or diffractograms, the small particle observed in sample S, heated up to 750°C, is highly likely to be BaTiO3. This is also supported by the X-ray diffractogram shown in Fig. 4.9, where we observed a broad diffraction peak from BT, other than those of unreacted BaCO3 and TiO2. Note that we also observed BaCO3 in sample S heated up to 750°C, or conversely, similar small BT particles in the sample Sb heated up to 650°C. Scanning electron micrographs are shown in Fig. 4.10 for the samples S and Sb after heating at 1000°C for 2 h. From the cumulative volume distribution curves obtained by the image analyses, the median diameter, D50, was significantly smaller for sample Sb with a sharper size distribution, as shown in Table 4.2. The particles of the fired product after calcining at



75

Intensity (a.u.)

BT BaCO3 TiO2 anatase TiO2 rutile Sb-900°C Sb-750°C Sb-650°C S-900°C S-750°C 20

25

30 35 40 2q (CuK a) (deg)

45

S-650°C 50

4.9 XRD profiles of quenched samples. (a)

(b)

S

S

0.48 mm Sb

0.8 mm Sb

0.48 mm

0.8 mm

4.10 SEM micrographs of BaTiO3 obtained by calcining at 1000°C.

1000°C from sample S are the mixture of spherical and angled particles. In contrast, those from sample Sb are spherical with sharper size distribution. From these experiments, it is concluded that wet agitation milling deagglomerates the starting mixture and results in the clear separation of the first and second steps of BaTiO3 formation. Additional dry vibro-milling, on the other hand, disintegrates the primary particles of both ingredients significantly elevating the reactivity of the reactant mixture with the participation of the mechanochemical effects, favouring the smaller particle size with the narrower size distribution. We attribute these positive


76

High-energy ball milling Table 4.2 Granulometric properties of BaTiO3 obtained from starting mixtures S and Sb

Average particle size (μm) D50% (μm) Slope: M value

S

Sb

0.12 0.19 3.8

0.20 0.25 5.0

M is defined as an average slope of the cumulative distribution curve, i.e. M = 1/(log D80 − log D20), where D80 and D20 denote the cumulative particle diameter at 80% and 20%, respectively. Larger M means sharper particle size distribution. (a)

(b)

10 μm (c)

1 μm (d)

1 μm

10 μm

4.11 Scanning electron micrographs of the reaction mixture for PMN-xPT. Left and right columns: before and after mechanical homogenization, respectively. (a) and (b): x = 0. (c) and (d): x = 0.1.

effects to efficient mechanical activation without losing the state of high dispersion.

4.4.3 Application to perovskite ceramics (2): PMN and PZN In our case study on the complex perovskite, PbMg1/3Nb2/3O3 (PMN) with and without coexistence of PbTiO3 (PMN-xPT with x = 0, 0.1 or 0.2),90 we started from a stoichiometric mixture comprising respective oxides with the exception of Mg(OH)2, which is a stable hydroxide, instead of MgO. As shown in Fig. 4.11, the degree of agglomeration of the starting mixture substantially decreases after milling with a multi-ring mill91 for 60 min. While total deagglomeration by powder processing is generally not possi-



77

ble, the size distribution of the agglomerates always narrows toward homogenization in a 100 nm regime. Homogeneity in the nanometer regime was also quantified by using the standard deviation of the local atomic ratio from the overall nominal one determined by energy dispersive X-ray analysis (EDX) installed in the transmission electron microscope.90 It is, however, more important to notice that the mixture is chemically homogenized as well. As shown in Fig. 4.12, the oxygen 1s XPS spectra changes from being multimodal, reflecting the individual starting materials to that of the solid solution, that is, the end product. The increase in the relative intensity of Pb–O–multi component B-site ions by mechanical treatment is attributed to the formation of new chemical bonds as a result of chemical interactions between dissimilar components. When we calcined the mechanically homogenized mixtures mentioned in the previous section at 850°C for 4 h, we obtained always phase pure perovskite, as shown in Fig. 4.13. The morphology of the calcined powders is also much more uniform when we start from the homogenized mixture. The lattice constant decreases linearly with x, as shown in Fig. 4.14, indicating the formation of a uniform PMN-PT solid solution. As expected, the dielectric properties exhibit large differences, with typical characteristics of the relaxer in the case starting from the homogenized mixture, as shown in Fig. 4.15. The obvious superiority of the mechanically pre-

Oxygen 1s

(a)

x=0

(b)

(a)

x = 0.2

(b)

540

536 532 528 524 Binding energy (eV)

520

4.12 X-ray photoelectron spectra of the reaction mixture for PMN-xPT with x = 0 and 0.2; (a) before and (b) after milling for 60 min.


(111)

X=0

(110)

(100)

(311)

(400)

(311) (222) (110)


(100)

78

X = 0.1

X = 0.2

20

30 2q (CuK a) (deg) (a)

40 20

30 2q (CuK a) (deg) (b)

40

4.13 X-ray diffraction (XRD) profiles of PMN-xPT after firing at 850°C for 4 h; (a) and (b) correspond to the starting materials without and with mechanical homogenization, respectively.

8

0.4055

6

0.4050 4 0.4045 2

0.4040 0.4035

0

0.1 X

0.2

Average grain size, dm (mm)

Lattice parameter (nm)

0.4060

0

4.14 Lattice parameter, a, and average grain size of PMN-xPT after firing at 850°C for 4 h.

treated products is primarily attributed to the elimination of the second phase, pyrochlore. We were further challenged to apply a similar technique to PZN, where Mg in PMN is substituted by Zn. Difficulty is chiefly attributed to the thermodynamic instability of PZN, so that we expect kinetic stabilization to


Materials design through mechanochemical processing 25000

Dielectric constant

20000

1 kHz 10 100 500 1000

79

Milled

15000

10000

5000

0 –50

Intact

0

50 Temperature (°C)

100

150

4.15 Frequency dependence of the dielectric constant of PMN-0.1PT after sintering at 1200°C for 2 h.

reach the crystalline state as rapidly as possible and to quench before decomposition or further phase transformation takes place. Since the hurdle for pure PZN was too high, we tried to prepare PZN-PMN solid solution with a minimum proportion of PMN. We first mixed PbO, Mg(OH)2, Nb2O5 and 2ZnCO3⋅3Zn(OH)2⋅H2O in the desired stoichiometry.92 The compound 2ZnCO3⋅3Zn(OH)2⋅H2O possesses higher basicity than any other commercially available Zn salts in powdery form, favouring the principle of HBB formation. A set of new XRD peaks corresponding to perovskite appear at the early stages of milling. The relative intensity of perovskite peaks increases with milling time. On subsequent heating up to 400°C and air quenching, perovskite became the sole crystalline phase. As shown in Fig. 14.16, the percentage of perovskite decreases and again increases after showing a minimum at temperatures between 700°C and 800°C for the mixtures up to x = 0.8. We attributed the increase in the perovskite to the incorporation of PMN into PZN due to restabilization of the perovskite phase. No recovery of perovskite is observed for components with x = 0.9 and x = 1.0 (pure PZN). It has been theoretically calculated that substitution of Pb(II) at the A-site of the perovskite by Ba up to 10 mol% or Zn at the B-site by Mg up to 7.4 mol% will stabilize PZN. In actual fact, however, an additive concentration as high as 40 mol% Mg to PZN (PZxM1−xN for x = 0.6) was necessary for phase pure perovskite. The instability of perovskite PZxM1−xN is thus much higher than theoretically expected. Rapid formation of a


80

High-energy ball milling 100

% Perovskite

80

60

40

20

0

400

500


900

4.16 Plots of percentage perovskite against firing temperature for mixtures milled for 180 min. Different curves corresponding to different x values are shown from top to bottom: 0 (PMN), 0.2, 0.4, 0.6, 0.7, 0.8, 0.9 and 1.0 (PZN).

PZxM1-xN solid solution at relatively low temperatures, where the lattice strain is still accommodated in the perovskite structure, is the essence of a successful synthesis. A continuous increase in the X-ray diffraction peak breadth of perovskite was observed with the increasing fraction of PZN, x, as shown in Fig. 4.17.

4.5

Organic synthesis and utilization of spontaneous chemical reactions

4.5.1 Diels–Alder addition reaction The Diels–Alder (DA) reaction counts as one of the key steps in the total organic syntheses of complicated natural compounds and hence is examined in depth, together with the mechanisms of the syntheses.93–95 The reaction involves diene and dienophile, both having C=C bonds which form adducts with a six-membered ring to form two new C–C bonds. It is generally accepted that a smaller HOMO–LUMO gap (HLG) between the HOMO of the diene and the LUMO of the dienophile favours the reaction. Indeed, introduction of electron-accepting groups to the dieno-



81

Increase in FWHM (deg)

0.12 (110) (200) (211)

0.1 0.08 0.06 0.04 0.02 0

0

0.2

0.4

0.6

0.8

1

x

4.17 Increase in the full-width at half-maximum (FWHM) of XRD peaks with fraction of PZN, x, for mixtures milled for 180 min and fired at 1100°C for 1 h.

Table 4.3 Yields of Diels–Alder reaction under various conditions Entry

R1

R2

Condition

Time (h)

Yield (%)c

1 2 3 4 5 6 7

Br CH2Cl H Me Me Me Me

Br CH2Cl H H Me Me Me

Agate 2 mm ampa Agate 2 mm ampa Agate 2 mm ampa Agate 2 mm ampa Agate 2 mm ampa Mixingb Chloroform solution

5 5 5 5 5 48 5

0 0 0 8 26 Trace 40

a

Reactions were carried out under milling with Pulverisette 0. Mixing two powdered compounds in a rotary evaporator. c Yield determined by 1H-NMR (chloroform-d solution). b

phile and/or electron-donating groups to the diene enhances the DA reaction. The DA reaction can also take place in the solid state.96–98 In the latter case, we may enhance the reactivity via a mechanochemical route, that is by introducing molecular strain on the molecular crystals.99,100 This kind of solvent-free synthesis is increasingly explored in pursuit of green chemical concepts. Table 4.3 exhibits the yields of the mechanochemical DA reaction between anthracene (AN) derivatives and benzoquinone (BQ), determined by 1H-NMR. For the reaction we used a small vibro-mill.99 It is noteworthy that the yield was increased by introducing an electron-donating group to AN, in accordance with the principle of decreasing HLG mentioned above, even for the present mechanochemical processes, which in most cases are


82

High-energy ball milling O

Yield (%)

Me

100 90 80 70 60 50 40 30 20 10 0

+ O

Me

O Mechanical activation

Me

O R

With Binol, mechanochemical With Binol in chloroform at RT Chloroform solution at RT without additives Without additives

0

1

2 3 Reaction time (h)

4

5

4.18 Effect of alcohols on the rate of Diels–Alder reaction (in stoichiometric amounts). RT, room temperature.

non-Arrhenian.10 No appreciable reaction was observed in the physical mixture without milling. Poor mixing and hence a smaller number of contact points could also count for this, together with the HLG issue mentioned above. Upon addition of 1,1-bi-2-naphthol (Binol, BN) to the reaction system, dimethylanthracene (DMA) and BQ, the rate of the DA reaction increased remarkably toward completion, as shown in Fig. 4.18. It is known that a ladder-like molecular complex is formed between racemic BN and BQ. A more complicated complex is also reported to form, via a solid-state route, between BN, BQ and AN with the aid of mechanical stressing.101 Formation of this kind of charge transfer complex (CTC) serves as strong incentive for rational mechanochemical processes. To exploit the utilization of these charge transfer complexes further, we noted autogenous eutectic formation with automatic fusion during CTC formation between BQ and thymol (TM). As we conducted a mechanochemical DA reaction between DMA and BQ in the presence of the BQ-TM CTC, further acceleration of the mechanochemical DA reaction was confirmed.100 Immediately after adding TM to BQ, autogenous fusion was observed. When a small bit of crystalline DMA was attached to this mixture, it automatically fused and formed a CTC. The color of the entire mixture turned into that of the DA adducts and solidified again after 30 min, where the yield was 95%. Reaction kinetic curves for these CTC-aided mechanochemical DA reactions are given in Fig. 4.19. It should also to be mentioned that the intensity of mechanical stress needed for this kind of paste-like reaction mixture is much lower than those for dry powdered systems.



83

100 90 80 Yield (%)

70 60

Additives 200 mol% TM 10 mol% TM 5 mol% Binol None

50 40 30 20 10 0

0

0.5

1 Reaction time (h)

1.5

2

4.19 Diels–Alder reaction with a eutectic complex. TM, thymol.

4.5.2 Correlation between molecular distortion and change in the frontier orbitals It is well known that the symmetry of crystals and molecules is attributed basically to the symmetry of the electronic wave function, or more straightforwardly, to the spacial distribution of the electronic crowds. These symmetries are very specific to particular substances and those in gas or liquid phase cannot be altered in the usual manner. In the molecular solid state, however, the distorted state of molecules is quenchable through the plasticity of these crystals. In the case of transition metal complexes, a change in the electron orbitals upon mechanical stressing is observed by different analytical methods, for example, Mössbauer or XPS spectra.102–104 In addition, we also observed that by starting from the distorted crystals, the rate of complex formation increases. Furthermore, a mechanochemical process can produce a mono-coordinated Fe(II) complex with 1,10-phenanthroline (phen), when we mill Fe(II) oxalate with phen.105 The usual thermal process yields only bi-coordinates. Excitation of the electron energy states by mechanical activation can be explained by an inverse Jahn–Teller effect,106 also referred at the beginning of the Section 4.3. An explosive with a highly symmetrical molecule, hexahydro-1,3,5-trinitro 1,3,5-triadine, RDX, is analysed by initiating its fast reaction, with the loss of its molecular symmetry, by a shock wave,107 to explain the mechanisms of its mechanical detonation rationally. A similar discussion can take place for the solid state DA reactions mentioned previously. When two reacting molecules, AN and BQ, approach each other, the coplanar AN molecule folds along the symmetry axis C10– C11 so that the dihedral angle decreases, as shown in Fig. 4.20.108 The total energy of the system, as simultaneously plotted in Fig. 4.20 exhibits a


1000

190

900

180

800

170

700

160

600 500

150 r

140

400 300

130

θ

200

120

100

110

0

Dihedral angle, θ (deg)


Energy of system (kcal mol–1)

84

100 Intermolecular distance, r (Å)

4.20 Change in the energy of the system and dihedral angle of anthracene with decreasing intermolecular distance calculated using the AM1 method. The dihedral angle of anthracene at the state of activated complex is 150°. Note that the results given here refer to a model comprising two free molecules instead of those in an actual solid state reaction, where molecules are bound to the solid surface.

maximum, corresponding to the formation of the activated complex, at a dihedral angle of approximately 150°. When intermolecular HLG values for four derivatives of AN and BQ are plotted against the dihedral angle of the former, we recognize the decrease in HLG with increasing extent of folding of AN derivatives, as shown in Fig. 4.21.108 Although the computation is semi-empirical, using SPALTAN ’02, with relatively loose rigorousness, the results shown in Fig. 4.21 could be correct as a general trend. The reliability of the computation is evident for the point where the HLG takes the smallest value for DMA (curve c) compared at the same dihedral angle. It is thus verified that the mechanically derived molecular strain increases the reactivity of solids. Furthermore, charge transfer, often occurring autogenously, brings about a molecular complex or CTC. By utilizing these phenomena, mechanochemical processes can be rationalized and their application can also be extended deeper into the area of chemical syntheses of organic adducts and complexes with or without central metallic species. These processes are compatible with the world trend toward using green chemical processes.

4.6

Conclusions and future trends

An overview is given above of some possible applications of mechanochemical principles in materials design with technical affordability.



HOMO–LUMO gap (eV)

6.6

85

d

6.5

e

6.4 a

6.3 6.2

b

6.1

c

6 145

150

155 160 170 165 Dihedral angle, θ (deg)

175

180

4.21 The intermolecular HOMO–LUMO gap of (a) anthracene, (b) 9-methyl anthracene, (c) 9,10-dimethyl anthracene, (d) 9,10-bis(chloromethyl)anthracene, and (e) 9,10-bis(bromomethyl) anthracene.

Mechanical stressing on the large scale is quite costly and contamination by the equipment is unavoidable. The process is often stochastic and localized. Care should, therefore, be taken not try to apply a mechanochemical process unless there is an absolute merit and necessity. Charge transfer across a boundary of dissimilar solids with simultaneous polarization, size reduction and homogenization without external heating are the main merits of applying mechanochemistry to various functional materials including metal coordination compounds or molecular complexes via smart or even autogenous charge transfer. This could lead to innovation in organic syntheses starting from the solid state, involving solvent-free and hence green chemical processes. Since mechanical stress often brings about unusually excited states, it could enable some noble metals that have been unavoidable in catalysis to be replaced with less expensive metals. Mechanochemical processes or mechanically aided charge transfer is expected to be applied further to biocompatible complexes109,110 and pharmaceutics.111,112

4.7

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5 Kinetic processes and mechanisms of mechanical alloying F. D E L O G U, Università degli Studi di Cagliari, Italy; and G. M U L A S, Università degli Studi di Sassari, Italy

Abstract: This chapter focuses on the study of the kinetics of mechanically activated alloying processes. This is a difficult area of study that has great importance for any substantial progress in the field from both the fundamental and applied points of view. Various questions arise when a rationalization of experimental evidence is attempted. These concern aspects as different as the dynamics of the apparatuses used for mechanical activation on the macroscopic level and the intimate features of individual reactive events induced by mechanical stresses on the microscopic level. A brief overview of such intertwined questions is given together with a possible line of approach to the characterization of mechanical alloying mechanisms operating on the atomic scale (atomistic). Key words: mechanical alloying, phase transformation, kinetics, atomistic mechanisms.

5.1

Introduction

Mechanical alloying (MA) is a powder metallurgy methodology widely employed to synthesize metallic alloys starting from pure elements (Heinicke, 1984; Butyagin, 1989; Suryanarayana, 2001). MA is usually performed in suitably designed ball mills, inside which milling tools undergo a series of collisions with each other (Heinicke, 1984; Butyagin, 1989; Suryanarayana, 2001). MA is generally thought to proceed through the accumulation of structural defects in crystalline lattices and the intimate mixing of elemental species at interfaces consequent on the mechanical deformation of powder particles trapped between the surfaces of colliding milling tools (Suryanarayana, 2001). However, any agreement is lost as soon as attention is focused on the mechanisms that may underlie the MA process on the atomic scale. Hypotheses regarding the mechanisms range from the oldest scenarios of hot spot theory (Benjamin, 1992; Koch, 1992) and defect-enhanced diffusion (Schwarz and Johnson, 1983; Johnson, 1986; Hellstern and Schultz, 1986; Cahn and Greer, 1996) to the most recent ones of shear-induced 92

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mixing, interface roughening and contact melting (Martin, 1984; Bellon and Averback, 1995; Hammerberg et al., 1998; Urakaev and Boldyrev, 2000; Vick et al., 2000; Fu et al., 2001; Lund and Schuh, 2003; Delogu and Cocco, 2005a,b; Odunuga et al., 2005). While passing from the former approach to the latter ones, the emphasis gradually shifts from inherently thermal processes to coupled thermally and mechanically induced phenomena. Along these lines, MA reactions can be tentatively connected to local rearrangements at sliding interfaces that originate from the action of non-hydrostatic mechanical stresses operating on the atomic scale (Levitas, 2004; Martin, 1984; Bellon and Averback, 1995; Hammerberg et al., 1998; Urakaev and Boldyrev, 2000; Vick et al., 2000; Fu et al., 2001; Lund and Schuh, 2003; Delogu and Cocco, 2005a,b; Odunuga et al., 2005). In fact, relative sliding events are accompanied by the local generation of frictional heat, which can easily result in far-from-equilibrium conditions promoting a transient enhancement of chemical reactivity (Martin, 1984; Bellon and Averback, 1995; Hammerberg et al., 1998; Urakaev and Boldyrev, 2000; Vick et al., 2000; Fu et al., 2001; Lund and Schuh, 2003; Delogu and Cocco, 2005a,b; Odunuga et al., 2005). Owing to the lack of direct experimental evidence on the microscopic MA mechanisms, the above-mentioned scenarios are substantially based on conjecture or numerical findings. Of course, this is not the best way to pursue the research farther. Yet, valuable insight into the mechanisms of MA processes in ball mills can be still gained by investigating the apparent kinetics of phase transformations and relating the macroscopic evidence obtained to individual local deformation events. This chapter describes an attempt in this direction.

5.2

Fundamentals of mechanical alloying processes in ball mills

A ball mill is a relatively simple apparatus in which the motion of the reactor, or of a part of it, induces a series of collisions of balls with each other and with the reactor walls (Suryanarayana, 2001). At each collision, a fraction of the powder inside the reactor is trapped between the colliding surfaces of the milling tools and submitted to a mechanical load at relatively high strain rates (Suryanarayana, 2001). This load generates a local nonhydrostatic mechanical stress at every point of contact between any pair of powder particles. The specific features of the deformation processes induced by these stresses depend on the intensity of the mechanical stresses themselves, on the details of the powder particle arrangement, that is on the topology of the contact network, and on the physical and chemical properties of powders (Martin et al., 2003; Delogu, 2008a). At the end of any given collision event, the powder that has been trapped is remixed with the


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powder that has not undergone this process. Correspondingly, at any instant in the mechanical processing, the whole powder charge includes fractions of powder that have undergone a different number of collisions. The individual reactive processes at the perturbed interface between metallic elements are expected to occur on timescales that are, at most, comparable with the collision duration (Hammerberg et al., 1998; Urakaev and Boldyrev, 2000; Lund and Schuh, 2003; Delogu and Cocco, 2005a,b). Therefore, unless the ball mill is characterized by unusually high rates of powder mixing and frequency of collisions, reactive events initiated by local deformation processes at a given collision are not affected by a successive collision. Indeed, the time interval between successive collisions is significantly longer than the time period required by local structural perturbations for full relaxation (Hammerberg et al., 1998; Urakaev and Boldyrev, 2000; Lund and Schuh, 2003; Delogu and Cocco, 2005a,b). These few considerations suffice to point out the two fundamental features of powder processing by ball milling, which in turn govern the MA processes in ball mills. First, mechanical processing by ball milling is a discrete processing method. Second, it has statistical character. All of this has important consequences for the study of the kinetics of MA processes. The fact that local deformation events are connected to individual collisions suggests that absolute time is not an appropriate reference quantity to describe mechanically induced phase transformations. Such a description should rather be made as a function of the number of collisions (Delogu et al., 2004). A satisfactory description of the MA kinetics must also account for the intrinsic statistical character of powder processing by ball milling. The amount of powder trapped in any given collision, at the end of collision is indeed substantially remixed with the other powder in the reactor. It follows that the same amount, or a fraction of it, could at least in principle be trapped again in the successive collision. This is undoubtedly a difficult aspect to take into account in a mathematical description of MA kinetics. There are at least two extreme cases to consider. On the one hand, it could be assumed that the powder trapped in a given collision cannot be trapped in the successive one. On the other, it could be assumed that powder mixing is ideal and that the amount of powder trapped at a given collision has the same probability of being processed in the successive collision. Both these cases allow the development of a mathematical model able to describe the relationship between apparent kinetics and individual collision events. However, the latter assumption seems to be more reliable than the former one, at least for commercial mills characterized by relatively complex displacement in the reactor (Manai et al., 2001, 2004). A further obvious condition for the successful development of a mathematical description of MA processes is the one related to the uniformity



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of collision regimes. More specifically, it is highly desirable that the powders trapped at impact always experience the same conditions. This requires the control of the ball dynamics inside the reactor, which can be approximately obtained by using a single milling ball and an amount of powder large enough to assure inelastic impact conditions (Manai et al., 2001, 2004; Delogu et al., 2004). In fact, the use of a single milling ball avoids impacts between balls, which have a remarkable disordering effect on the ball dynamics, whereas inelastic impact conditions permit the establishment of regular and periodic ball dynamics (Manai et al., 2001, 2004; Delogu et al., 2004). All of the above assumptions and observations represent the basis and guidelines for the development of the mathematical model briefly outlined in the following. It has been successfully applied to the case of a Spex Mixer/ Mill mod. 8000, but the same approach can, in principle, be used for other ball mills.

5.3

A phenomenological model of mechanical alloying kinetics

During MA reactions by ball milling, powder particles undergo fracturing and coalescence processes so that their number changes (Heinicke, 1984; Butyagin, 1989; Suryanarayana, 2001). At the same time, complex morphological, microstructural and chemical transformations that affect each other take place (Heinicke, 1984; Butyagin, 1989; Suryanarayana, 2001). In contrast, the volume of powder trapped at each collision keeps approximately constant (Manai et al., 2004; Delogu et al., 2004). Indeed, the amount of powder trapped between the surfaces of colliding milling tools depends on the total amount of powder within the vial, on the ball size and on the relative impact velocity (Courtney, 1995; Maurice and Courtney, 1996). Therefore, the volume of powder trapped at individual collisions can be regarded as a key reference quantity in describing MA kinetics. It should be noted regarding this point that the mechanical load at collision is not uniformly distributed within this volume. On the contrary, as briefly mentioned before, it is distributed in the network formed by the points of contact between different particles (Martin et al., 2003; Delogu, 2008a). The extent to which chemical modifications occur depend on the intensity of the non-hydrostatic mechanical stresses generated at these points. Therefore, the rate of MA processes is related to the volume fraction of powder trapped at collision during which a mixing of elemental species actually takes place. Of course, whether or not such mixing could take place depends on whether the mechanical stresses in the volume of trapped powders reach the necessary intensity.


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Numerous questions arise in connection with the aforementioned observations. For example, how large must be the fraction of powder trapped in a given individual collision, if that collision is involved in deformation events severe enough to start the interfacial mixing of elemental species? How many individual collisions are necessary for this process to proceed? As the number of loading events experienced by a given quantity of powder is different from the total number of collisions, what is the relationship between the number of loading events undergone by a certain quantity of powder and the total number of collisions? As will be shown below, an approximate response to such questions can be given, provided that a few critical assumptions are made. Let us assume that the volume vimp of powders trapped at each individual collision remains constant during the course of the MA process. For the sake of simplicity, the average density ρ of the powders is also considered constant. It follows that the mass mimp of powder trapped on the average at each collision is equal to vimpρ. Therefore, the volume fraction ximp of powder trapped at individual collisions is equal to vimpv−1 p , where vp is the total powder volume mpρ−1 and mp is the total powder mass inside the reactor. The rate at which a given MA reaction proceeds will be necessarily proportional to the fraction ximp. Let us also assume that mixing chemical species at perturbed interfaces will occur only in the fraction of powder that has experienced critical loading conditions (CLCs) a number I of times. CLCs can be defined as the conditions under which a certain amount of powder experiences a mechanical stress σ higher than a critical threshold value σ0. The critical threshold value σ0 which allows a given MA process to occur is in turn defined as the lowest mechanical stress necessary to induce the mixing of elemental species at perturbed interfaces. A further necessary assumption is that at each individual collision, a fraction k of the powder charge mp in which σ is higher than σ0 can be found. Of course, k must be smaller than ximp. Finally, let us assume that the powders are perfectly remixed after each collision event, so that the powder mass inside the reactor is kept homogeneous and that each volume fraction k in which the powder mass mp can be ideally subdivided has the same probability of being involved in a collision event as any other. Let us define now χ0 as the volume fraction of powder charge that never experienced CLCs. Of course, χ0 is equal to 1 before the first collision has occurred. After it has taken place, a volume fraction χ1 of the powder trapped at collision has been submitted for the first time to CLCs. According to the above mentioned assumptions, χ1 corresponds to k. It follows that the fraction of powder charge never submitted to CLCs after the first collision has occurred is equal to χ0(1) = 1 − k.



97

After the second collision has taken place, the fraction of powder never submitted to CLCs becomes equal to χ0(2) = 1 − k − k(1 − k) = (1 − k)2. The fraction of powder submitted to CLCs once is equal to χ1(2) = k + k(1 − k) − k2 = 2k(1 − k) and the fraction of powder submitted to CLCs for two times is equal to χ2(2) = k2. The process briefly sketched above continues as the number n of collisions increases. The fraction of powder χ0(n) never submitted to CLCs after n impacts is equal to: χ0(n + 1) = χ0(n) − kχ0(n)

[5.1]

The fraction of powder submitted to i CLCs after n impacts is instead equal to: χi(n + 1) = χi(n) − kχi(n) + kχi−1(n)

[5.2]

In fact, at the nth collision, a fraction kχi(n) of powder experiences CLCs for the (i + 1)th time, thus becoming part of the fraction χi+1(n). Conversely, a fraction kχi−1(n) experiences CLCs for the ith time and becomes part of the fraction χi(n). It is now worth noticing that usually the fraction k of powder that is submitted to CLCs at each collision is small with respect to the total amount of powder (Benjamin, 1992; Delogu et al., 2004; Delogu and Cocco, 2006, 2007). Under these conditions, Equations [5.1] and [5.2] can be written in the continuous form shown below: dχ0(n) = −kχ0(n)dn

[5.3]

dχ0(n) = −kχi(n)dn + kχi−1(n)dn

[5.4]

Equation [5.3] is solved by: χ0(n) = e−kn

[5.5]

whereas the solution to Equation [5.4] is (Szabò, 1969): χ i ( n) =

(kn)i i!

e- kn

[5.6]

As the total amount of powder in the reactor is constant, Equations [5.5] ∞

and [5.6] satisfy the constraint

∑ χ ( n) = 1 . i

i=0

Equations [5.5] and [5.6] represent the starting set of mathematical functions that must be combined in order to obtain a rough description of MA kinetics. With this aim, let us define j as the minimum number of CLCs that powders must experience to undergo MA. The total volume fraction α(n) of powders involved in MA processes at the nth collision is then equal to:


98

High-energy ball milling n

α(n) = ∑ χi ( n) ≅ 1 − kne− kn … − i= j

( kn ) j − 1 ( j − 1)!

e- kn

[5.7]

provided that the number n of collisions that have taken place is so large that it tends to infinity. Of course, the kinetic curves can also be obtained by considering the mass fraction αm(n) of powders involved in MA processes at the nth collision event. This quantity can be expressed as: n

α m (n) = ∑ χi ( n) ≅ 1 − km ne− km n … − i= j

(km n) j − 1 ( j − 1)!

e- km n

[5.8]

where km represents the apparent rate constant of the MA process referred to the mass fraction of powder involved in individual collision events. Accordingly, if a single CLC is necessary to induce the MA process, and then j is equal to 1, the mathematical function describing the evolution of the volume fraction of alloyed phase as a function of the total number n of collisions is α(n) = 1 − e−kn. Should two CLCs be required, j would be equal to 2 and the volume fraction of alloyed phase would be α(n) = 1 − (1 + kn)e−kn. The volume fraction k, which measures the fraction of trapped powder that experiences CLCs at collision and then undergoes the MA process, can also be regarded as an apparent rate constant for the MA reaction (Szabò, 1969). Effectively, the volume fraction of powders experiencing CLCs at collision events determines the rate of the MA process. Provided that all the above-mentioned assumptions can be made, the mathematical model discussed here has the remarkable merit of providing the possibility of plotting best-fitting experimental kinetic curves and thus estimating the number j of CLCs necessary to induce the MA process and the apparent rate constant k. It is precisely the shape of kinetic curves that permits discrimination between different cases. However, this possibility is to a large extent dependent on the accuracy of the experimental data. Only refined experimental measurements of the relative amount of alloyed phases can indeed be used profitably to further this aim. A few practical examples of the usefulness of Equations [5.7] and [5.8] are given in the following section, where experimental data concerning different MA reactions under different conditions are considered.

5.4

Collecting and analysing experimental data on the kinetics of mechanical alloying reactions

The necessary conditions for obtaining a satisfactory quantification of the kinetics of MA processes are given by accurate characterization of the solid



99

phases formed during the mechanical treatment and by the evaluation of their relative quantities. Any experimental technique able to give information on such aspects can, in principle, be used to quantify the kinetics, but X-ray diffraction (XRD) methods are not the most widespread ones (Klug and Alexander, 1974). Their fundamentals will not be dealt with here. It suffices to remember that obtaining quantitative information on the phase transformation modelling of solid phases is not easy. Long data acquisition times and optimized procedures and equipment are required, the best choice being represented by intense synchrotron radiation facilities (Enzo, 1998). Once accurate data have been acquired, a suitable analysis of XRD patterns must be carried out (Enzo, 1998). This is generally done through a numerical reconstruction of experimental XRD profiles based on a set of mathematical functions with adjustable parameters (Lutterotti et al., 1998). The method, usually referred to as the Rietveld method (Lutterotti et al., 1998), essentially consists of a least-square best-fitting. The different adjustable parameters have a physical meaning such that their value can be used to gain information on the relative amount of a given phase, on its composition and on its microstructural features (Lutterotti et al., 1998). The data obtained are affected by error bars, the size of which depends on the accuracy of data collection and XRD pattern analysis. Under the condition where the error bars are quite small, the data concerning the mass fraction of the different phases can be used to describe the kinetics of the mechanically induced phase transformations. A few examples of the way Equations [5.7] and [5.8] can be employed to gain information on microscopic events governing MA processes are given below. Although mechanically induced phase transformations of pure substances cannot be considered MA processes, it is nevertheless instructive to see what happens in this case. The first example discussed concerns the transition of Co powders from the hexagonal close-packed (hcp) lattice to the face-centred cubic (fcc) one, which has been studied in detail in previous work (Delogu, 2008b). The stable crystallographic phase for Co at room temperature is the hcp one. When it is submitted to mechanical treatment, a transition to the fcc crystallographic phase takes place. The experimental data describing the kinetic modelling of pure Co powders are shown in Fig. 5.1, where the mass fractions αm(n) of hcp and fcc Co phases are reported as a function of the number n of collisions. It can be seen that the hcp phase undergoes an exponential decrease, whereas the fcc one undergoes a complementary exponential increase. The set of data corresponding to the mass fraction of fcc phase is satisfactorily best-fit by Equation [5.8] provided that j is set equal to 1. In other words, a single collision event suffices for Co powders to trigger the transition from the hcp to the fcc phase. The best-fit curve exhibits a km value approximately equal to 1.2 × 10−6 when collisions involve a stainless steel ball of 12 g and take place with an impact energy of about


High-energy ball milling Mass fraction, a m (n)

100

1.0 0.8 0.6 0.4 0.2 0.0

0

3

6

9

12

15

18

5

Number of collisions, n (10 )

Mass fraction, a m (n)

5.1 The mass fractions αm(n) of hcp (䊐) and fcc (䊊) Co phases as a function of the number n of collisions. The set of data representing the mass fraction of the fcc phase is best-fitted by Equation [5.8].

1.0 0.8 0.6 0.4 0.2 0.0

0

1

2

3

4

5

6

7

Number of collisions, n (106)

5.2 The mass fractions αm(n) of crystalline (䊐) and amorphous (䊊) NiTi2 phases as a function of the number n of collisions. The set of data representing the mass fraction of the amorphous phase is bestfitted by Equation [5.8].

0.1 J (Delogu, 2008b). This means that, as the powder charge mp is equal to 8 g, only 9 μg of powder experiences CLCs at individual collisions. Analogous behaviour is exhibited by NiTi2 intermetallic powders (Delogu and Cocco, 2003). In this case, the mechanical treatment of NiTi2 powders induces a transition from the ordered crystalline fcc phase to an amorphous one in which long-range crystalline order is completely lost. As shown in Fig. 5.2, where the mass fractions αm(n) of crystalline and amorphous NiTi2 phases are reported as a function of the number n of collisions, the kinetics has a clear exponential character. The modelling is strictly similar to that of the Co powders cited above and, correspondingly, the increase of the mass fraction of the amorphous phase is satisfactorily reproduced by Equation [5.8] with j equal to 1. Although impact energy and ball mass are the same as in the previous case, the apparent kinetic constant km is nevertheless smaller, taking a value of about 0.3 × 10−6 (Delogu and Cocco, 2003). Correspondingly, the mass of powder involved in amorphization processes


Mass fraction, a m (n)


101

1.0 0.8 0.6 0.4 0.2 0.0 0.0

0.5

1.0

1.5

2.0

2.5

6

Number of collisions, n (10 )

5.3 Mass fraction αm(n) of the amorphous Ni40Ti60 binary alloy as a function of the number n of collisions. The set of data is best-fitted by Equation [5.8].

at individual collisions amounts roughly to 2 μg of a total of 8 g inside the reactor. The case of binary mixtures, that is of true MA processes, exhibits remarkably different features. For example, let us consider the case of Ni40Ti60 powder mixtures, which have been studied in detail in previous work (Cocco et al., 2000; Delogu et al., 2004). Data obtained for an impact energy of about 0.1 J and with a stainless steel ball 12 g in mass are shown in Fig. 5.3, where the mass fraction αm(n) of the amorphous phase is reported as a function of the number n of collisions. It can be seen that the kinetics no longer exhibits an exponential character. On the contrary, data are arranged according to a sigmoidal trend, which points to the existence of some intermediate stage between reactant powders and final amorphous alloy (Szabò, 1969). The experimental points in Fig. 5.3 can be satisfactorily interpolated by Equation [5.8] provided that the parameter j is set equal to 2. It follows that powders must undergo CLCs at least twice before an amorphous phase could be generated. The best-fitting procedure indicates that the apparent kinetic constant km of the MA process amounts roughly to 1.5 × 10−6 (Cocco et al., 2000). Therefore, once the second individual collision has occurred, the powder charge contains approximately 18 pg of amorphous phase. The experimentally obtained km values are very small, so that the amount of powder transformed at individual collisions is correspondingly very small. This suggests that the mechanical stresses at impact are not uniformly distributed within the volume of powders trapped at collisions. On the contrary, a highly inhomogeneous distribution of the mechanical loads can be expected, so that only limited regions around the points of contact between powder particles are actually involved in phase transformation processes, and not all of them are under the same conditions. A very similar modelling is observed for all the binary mixtures composed by Ni and the elements of the Ti group in the periodic table. In all


102


cases, two CLCs are needed to induce the formation of a binary amorphous alloy (Cocco et al., 2000). The same is observed for binary mixtures containing Ti and a transition metal belonging to the fourth period of the periodic table (Delogu, 1999). Of course, the nature of the final product changes with the chemical nature of the binary mixture. In particular, whereas Fe–Ti, Co–Ti, Ni–Ti and Cu–Ti mixtures give rise to amorphous alloys, V–Ti and Cr–Ti ones exhibit the formation of metastable crystalline solid solutions (Delogu, 1999). Again, only two CLCs are required for the final phase to appear. The conceptual framework behind the experimental kinetic evidence and the theoretical interpretation discussed above is, however, much more complex than the approximate description based on a few key parameters such as j and km. First, it should be noted that km strongly depends on the impact energy, that is on the amount of kinetic energy transferred to powders at individual collisions (Delogu, 1999; Cocco et al., 2000; Delogu et al., 2004; Delogu and Cocco, 2007; Delogu, 2008a,b). This dependence is typically linear and points to the existence of a threshold energy below which no structural transformation can take place (Delogu, 1999; Cocco et al., 2000; Delogu et al., 2004; Delogu and Cocco, 2007; Delogu, 2008a,b). Second, and much more interesting, j also depends on the energy of individual collisions (Delogu and Cocco, 2007). This means that the number of CLCs to which the powder must be submitted to undergo a MA process depends on the energy transferred to the powder at impact. In turn, this again suggests that the extent to which elemental species alloy at collision depends on the intensity of mechanical stresses at the points of contact between surfaces. Unfortunately, this is not amenable to direct experimental investigation. It is, however, the area in which numerical simulation methods can be most fruitfully employed. These will be dealt with in some detail in the next section. Before doing this, it is worth mentioning a particular kinetic regime observed in a few systems consisting of a cyclic mixing–demixing process that takes place under mechanical treatment conditions. As broadly discussed in previous work (Johnson et al., 2006; Lee, 2008), the mechanical treatment occasionally gives rise to cyclic modelling in microstructural and phase transformations. This is the case, for example, in the cyclic amorphization of Co-based systems (El-Eskandarany et al., 1997, 2002; ElEskandarany and Inoue, 2007). Previous investigations have shown that the occurrence of cyclic MA processes critically depends on the interplay of various mechanical processing parameters, including impact energy, temperature and powder mixture composition (Johnson et al., 2006; Lee, 2008). All of this clearly suggests that a simple and comprehensive description of MA kinetics is unlikely to be obtained on the basis of the current knowledge. On the contrary, considerable efforts should be devoted to clarifying



103

various fundamental aspects of MA processes. Among these, their atomistic features are probably the most important.

5.5

Mechanisms of chemical mixing on the atomic scale

As briefly mentioned in the Introduction, relatively few studies have been carried out that shed light on the intimate details of mechanically induced processes taking place on the atomic scale. All of them consist substantially of numerical investigations (Martin, 1984; Bellon and Averback, 1995; Hammerberg et al., 1998; Urakaev and Boldyrev, 2000; Vick et al., 2000; Fu et al., 2001; Lund and Schuh, 2003; Delogu and Cocco, 2005a,b; Odunuga et al., 2005; Vo et al., 2009). Phenomenological approaches have laid emphasis in the past on the capability of shear stresses of inducing stochastic atomic displacements to be able to withstand, at least under suitable conditions, opposite thermodynamic forces (Martin, 1984; Martin and Gaffet, 1990). However, the mechanisms according to which such displacements take place remained for a long time completely obscure. A very elegant experimental study based on electron microscopy and atom probe tomography techniques recently allowed insight to be gained into the atomistic processes governing MA in immiscible binary systems (Zgahl et al., 2002a,b; Wu et al., 2006). It was shown that the particular nanostructure of immiscible alloys arises as a consequence of a relatively complex interplay between the tendency to phase separation, which is a consequence of the thermodynamic driving force operating in the system, and the disordering phenomena due to forced mixing. The mechanistic details of such forced mixing were further investigated in successive works based on numerical simulation methods (Odunuga et al., 2005; Delogu, 2008c; Vo et al., 2009). These have shown that intense plastic deformation regimes can generate unusual atomic flows, mediated by dislocation motion, reminiscent of the ones observed in turbulent fluids. The occurrence of disordered atomic displacements and rearrangements has been also pointed out in two- and three-dimensional molecular dynamics simulations aimed at studying the atomistic processes at sliding interfaces (Hammerberg et al., 1998; Fu et al., 2001; Delogu and Cocco, 2005a,b). In particular, numerical findings suggested the existence of a hierarchy of processes involving the creation of defective atoms, that is atoms with defective coordination. These assure the attainment of a relatively high degree of local mobility and allow the occurrence of mixing phenomena, which represent the fundamental mechanistic step for obtaining a so-called driven alloy. Finally, once the mechanical load has been removed, or has locally ceased its action, the clusters of defective atoms progressively relax, without


104


Square of layer thickness, Δ2 (nm2)

necessarily completely disappearing. All of these processes must be regarded as a relatively complex sequence of intertwined phenomena dependent on a number of parameters, including the intensity of interatomic forces, the intensity of the mechanical stress and the duration of the deformation event (Hammerberg et al., 1998; Fu et al., 2001; Delogu and Cocco, 2005a,b). Interestingly, simulations pointed out that the time dependence of the volume of crystalline phase involved in chemical mixing and disordering processes is analogous to the one exhibited by isothermal vacancy-mediated diffusion mechanisms (Fu et al., 2001; Delogu and Cocco, 2005a). An example relevant to the case of amorphization reactions is shown in Fig. 5.4, where the square of the thickness Δ of the layer of crystalline phase that underwent disordering upon mechanical loading is reported as a function of the time t for the case of a Ni–Zr sliding interface (Delogu and Cocco, 2005a,b). It can be seen that the data are arranged according to a linear plot despite the conditions for the growth of the amorphous interfacial layer being far from similar to the ones of isothermal diffusion. Rather, the displacement of atoms is mediated by the clusters of defective atoms and the formation of particular rotating structures, such as the one shown in Fig. 5.5. These groups of atoms, submitted to local torques, are able to displace individual atoms at relatively high rates, enabling them to overcome the ideal interface and alloy into the other elements. Of course, the continuous nucleation and propagation of dislocations and partial dislocations permit these atoms to migrate successively far from the interface region (Delogu and Cocco, 2005a,b). Mixing and disordering processes during deformation are accompanied by continuous, though inhomogeneous, transfer of mechanical energy to the system. This can produce significant local rises of temperature. As shown in Fig. 5.6, temperatures as high as 1500 K can be reached. However, local heat is rapidly dissipated owing to the very steep temperature gradients operating in relatively small volumes. For example, data in Fig. 5.7 indicate that 30 20 10 0 0.0

0.5

1.0

1.5 2.0 Time, t (ns)

2.5

3.0

5.4 Square of the thickness Δ of the amorphous layer, formed upon mechanical loading at a Ni–Zr sliding interface, as a function of the time t. The line of best-fit is also shown.



105

Local temperature, T (K)

5.5 Cluster of atoms undergoes rotation, as indicated by the large white arrows. Small arrows indicate the direction of displacement of the individual atoms. White and grey indicate, respectively, Ni and Zr atoms. The dashed horizontal line ideally marks the interface between Ni and Zr crystals. The small cross indicates the instantaneous axis of rotation of the cluster.

2000 1500 1000 500 0.2

0.3

0.4 Time, t (ns)

0.5

0.6

5.6 Local temperature T as a function of time t. Data refer to a square domain with sides about 1.7 nm long at the interface between Ni and Zr crystals.

temperatures as different as about 700 and 1000 K are present in a small square region with sides about 1.7 nm long (Delogu and Cocco, 2005a,b). Further numerical studies have also shown that the topology of colliding surfaces and the geometry of their collision can significantly affect the resulting chemical mixing and disordering processes, as well as the local distribution of temperature (Delogu and Cocco, 2006). In particular, it was


106

High-energy ball milling 750.0 875.0 950.0 1025 1100

5.7 Map of instantaneous temperature (in K) for a square domain with sides about 1.7 nm long at the interface between Ni and Zr crystals.

shown that the collision between rough surfaces, more effectively than smooth surfaces, results in a local disordering and temperature increase. The displacement of atomic species is mediated by the formation of force chains along which repulsive forces preferentially operate, thus determining the occurrence of atomic rearrangements through the possible path at lowest potential energy. Despite the considerable efforts devoted to the field and the small advances achieved, the intimate mechanisms governing mechanically induced processes remain a matter of debate. The role of localized mechanical stresses as well as of local structural perturbations need suitable clarification. Owing to the complicated nature of mechanochemical transformations, which are governed by intertwined hierarchies of elementary events on the atomic scale, numerical simulations are expected to play an increasingly important role in the definition of detailed mechanistic scenarios.

5.6

Future trends

In the light of the considerable work carried out recently by different research groups around the world, it is astonishing that the view given in a paper published about 14 years ago (Khina and Froes, 1996) can still stand. The large gap between macroscopic kinetic evidence and microscopic transformation mechanisms must be filled. Similarly, the thermodynamic description of MA processes must be improved in order to include the nonequilibrium features typical of atomic rearrangement processes taking place at mechanical loading events. Despite apparently well defined objectives, a great deal of work remains to be done from both the experimental and theoretical points of view.



107

With regard specifically to the kinetic and mechanistic aspects of MA processes, at least four main topics can be clearly pointed out that need particularly urgent attention in order to attain a significant advance in the field. 1. Refinement of global models linking the operation of milling devices to the dynamics of powders inside the reactor. 2. Refinement of local models describing the relationship between the mechanical action exerted by milling tools at impact events and the corresponding behaviour of powders. 3. Integration of suitably improved kinetic models based on a statistical approach to the description of phase evolution with phenomenological kinetic laws accounting for the phase transformation behaviour on a microscopic level. 4. Rationalization of phenomenological kinetic evidence on the basis of atomistic models of mechanically induced atomic rearrangement processes. Each and every one of the above-mentioned areas of investigation requires the dedication of intense research effort. Effectively, all of them define a complex and variegated conceptual framework extending from the dynamics of milling devices to the displacement of atomic species. Between these extreme boundaries, there is the evident need to relate the motion of milling tools to the regime of impacts inside the reactor, to shed light on the behaviour of powder particles submitted to high strain rate compaction at impact, and to connect the topology of the net formed by the points of contact between the powder particles to the local mechanical stresses operating on them. In turn, this would allow realistic studies to be carried out on the local deformation processes and the corresponding response of interfaces between both neighbouring particles and inside the same particles to be carried out, in order to rationalize the cold-welding and fragmentation behaviour of powder particles and to gain insight into the stress and temperature conditions under which MA reactions take place at the atomistic levels. Finally, it should be possible to link the mechanical response of the materials to the local alloying behaviour, eventually identifying the finest aspects of atomistic mechanisms. The above-mentioned considerations clearly define a series of complementary studies aimed at creating deeper and better connections between the different scales involved in MA processes. The briefly sketched plan of research activity outlined here may permit a deepening of the current knowledge on MA. It also invites more intense and frequent collaboration between the different researchers involved in the field. It is with the sincere wish that such collaborations can be realized in the near future that this chapter ends.


108


5.7

References

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6 Mechanochemical synthesis of complex ceramic oxides T. R O JAC and M. K O S E C, Jozˇef Stefan Institute, Slovenia

Abstract: Mechanochemical synthesis has recently been recognized as a promising method for synthesizing a variety of technologically important ceramic oxides with complex compositions. This chapter begins by presenting some recent results related to the mechanisms and kinetics of mechanochemical reactions in oxide systems. In the second part of the chapter, attention is turned to the literature data on direct mechanochemical synthesis and the mechanochemical activation-based synthesis of a variety of complex oxides having different properties. This includes ferroelectric oxides and related materials, magnetic oxides and oxides with semiconducting and catalytic properties. Key words: mechanochemical synthesis, mechanochemical activation, high-energy milling, complex ceramic oxides, reaction mechanisms.

6.1

Introduction

Mechanochemical synthesis has recently received a lot of interest for processing ceramic powders, opening up new ways of producing technologically important oxides with complex compositions. One of the most important research areas is the study of the mechanisms and kinetics of mechanochemical reactions, which form the basis of the further development of mechanochemical synthesis. The first part of the chapter is devoted to this subject and discusses various topics, including the relation between milling conditions and phase formation, the course of mechanochemical reactions including amorphization and nucleation phenomena triggered by high-energy milling, the formation of intermediate phases during a reaction, the evolution of the crystallite size and the particularities of the nanocrystalline products obtained. In general, complex ceramic oxides exhibit a variety of properties, making them attractive for a range of different applications. The second part of the chapter highlights the main results related to both direct mechanochemical synthesis (referring to the formation of the final product directly during milling) and the mechanochemical activation-based synthesis (referring to high-energy milling, used to increase the reactivity of powders, 113 © Woodhead Publishing Limited, 2010

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which is followed by an annealing step to induce the formation of the final product) of complex oxides with a variety of properties. This section includes ferroelectric, antiferroelectric, piezoelectric, relaxor and multiferroic oxides as well as oxides with magnetic, semiconducting and catalytic properties. From the extensive literature data available some key points are highlighted, in particular the influence of mechanochemical activation on both the phase formation during subsequent annealing and the preparation of the final ceramics, the influence of milling conditions, such as humidity, and the effect of the hydration state of the reagents on the course of the mechanochemical reaction as well as the issue of contamination during milling.

6.2

Mechanisms and kinetics of mechanochemical reactions in complex oxide systems

One of the main tasks when exploring the basics of the mechanochemical synthesis is to correlate the parameters that describe the milling operation with the formation of the final product during milling. Rojac et al. (2006b) were the first to apply the concept of the milling map, which was originally developed for metal systems, to the synthesis of ceramic oxide powders. They chose the mechanochemical reaction between Na2CO3 and Nb2O5, which yields NaNbO3, as a model system. The reaction was carried out under different milling conditions. From the milling parameters characteristic of a planetary mill (Fig. 6.1a) the authors calculated the ball-impact energy (ΔEb) (amount of kinetic energy of a milling ball released to the powder during a collision, in J) and the ball-impact frequency (νt) (number of ball impacts per unit time, in s−1) applied in each milling experiment using the Equations [6.1] and [6.2], respectively: ⎛ ⎛ W ⎞ D − db ⎞ 2 ⎛ W ⎞ 1 ⎛ π d3 ⎞ ΔEb = ⋅ ⎜ ρb b ⎟ ⋅ Wp2 ⎜ ⎜ v ⎟ ⎛ v ⋅⎜ 1 − 2 v ⎟ − ⎝ ⎠ ⎝ ⎠ ⎝ Wp ⎠ 2 6 2 ⎝ ⎝ Wp ⎠ 2

⎛ W ⎞ D − db ⎞ ⎛ Wv ⎞ ⎛ Dv − db ⎞ 2 ⎞ − 2 Rp ⎜ v ⎟ ⋅ ⎛ v ⎟ ⎝ Wp ⎠ ⎝ 2 ⎠ ⎜⎝ Wp ⎟⎠ ⎝ 2 ⎠ ⎠ 2

νt = NbK(Wp − Wv)

[6.1]

[6.2]

where K is a constant depending on the geometry and on the ball diameter (Rojac et al., 2006b). The mechanochemical formation of NaNbO3 under specific energy and frequency conditions was followed using X-ray diffraction (XRD) analysis. This allowed the authors to construct the milling map shown in Fig. 6.1b. Their results suggested that a minimum or critical cumulative kinetic energy


Mechanochemical synthesis of complex ceramic oxides

115

(a) Diameter db

Diameter Dv

Number Nb

Height Hv Milling balls

Milling vial

Density rb

Powder weight mp

Milling parameters

Operation Disc (plate) rotational speed Wp

Mill Distance between rotational axes Rp

Vial rotational speed Wv

(b) 200 10 min DEb∗ (mJ per hit)

150 15 min 100

30 min

50

60 min

0 1

10

100

1000

–1

Ecum (kJ g )

6.1 (a) Milling parameters for the case of a planetary mill and a cylindrical milling vial and (b) the milling map of NaNbO3. Notation: ΔE*b ball-impact energy, Ecum cumulative kinetic energy, 䊊 no NaNbO3 is detected in the mixture, 䊉 NaNbO3 is detected in the mixture according to XRD analysis; the milling times of the first appearance of NaNbO3 according to XRD analysis are given on the figure (from Rojac et al., 2006b).

(the weight-normalized product of the ball-impact energy, the ball-impact frequency and the milling time) of between 7 and 12 kJ g−1, which does not depend on the ball-impact energy applied, is needed to trigger the formation of the NaNbO3. Milling for a duration equivalent to a cumulative kinetic energy lower than this critical value, however, will not result in the


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formation of NaNbO3. In addition, by comparing several oxide systems on the basis of the experimental data available in the literature the authors also stressed the importance of the critical ball-impact energy, which determines, in a similar manner, whether a certain product will form or not under specific milling conditions. The mathematical model used to construct the milling maps described above assumes that collisions are the prevailing mechanism by which the energy is transferred from the milling balls to the powders, while friction is neglected. However, in some circumstances the friction component might play a crucial role in the reaction kinetics, as was explained by Jean and Nachbaur (2008) for their mechanochemical synthesis of ZnFe2O4. They used a Fritsch Pulverisette 4 planetary mill, which allows independent adjustment of the rotational frequency of the supporting disc and that of the grinding vials. On the basis of the extent of the mechanochemical reaction between ZnO and α-Fe2O3 they estimated the milling efficiency for various ratios of the two frequencies, denoted as k in Equation [6.3]. The results are shown in Fig. 6.2:

600 550

Disc rotation speed (r.p.m.)

500 450 400

+ A No efficient milling

350

+ B High-efficiency milling

+ C High-efficiency milling

Pure ZnFe2O4 after 18 h


+ E Low-efficiency milling

+ F High-efficiency milling

Trace of ZnFe2O4 after 18 h


300 250 200 150

+ D No efficient milling

100 50 0 200

300

400

500

600

700 –1

Vial rotation speed, x

800

900

1000

(r.p.m.)

6.2 Graphical representation of the milling efficiency estimated for various ratios of disc and vial rotational frequencies (mechanochemical synthesis of ZnFe2O4). The end products of the milling experiments performed at different frequency ratios are given on the graph (from Jean and Nachbaur, 2008).


Mechanochemical synthesis of complex ceramic oxides k=−

Wv Wp

117 [6.3]

In Equation [6.3], Wp and Wv are the rotational frequencies of the supporting disc and of a grinding vial of the planetary mill, respectively. The negative sign indicates that the rotations of the disc and the vial are in opposite directions. Abdellaoui and Gaffet (1995), in their work on metal systems, reported that the end product obtained by milling depends on the injected mechanical power, defined as the product of ball-impact energy and ball-impact frequency. Because the injected mechanical power increases as a function of the rotational frequencies of the disc and the vial, Jean and Nachbaur (2008) were able to explain the increasing milling efficiency in experiments A to C or D to F (Fig. 6.2), with increasing injected power. However, this did not explain, for example, the low milling efficiency in the case of experiment A, where no reaction occurred, during which more injected power was used than in experiment F, where the spinel phase was obtained. This observation meant that it was also necessary to include a friction component in the discussion. Based on literature data, which show that the tangential component of the impact force during a collision event is nearly zero for |k| < 1, while its absolute value increases rapidly for |k| > 1 (Chattopadhyay et al., 2001), the authors related the high milling efficiency of experiment F (|k| = 3.6) to the large frictional force during milling, while the low milling efficiency in experiment A (|k| = 0.5) is due to a low friction component. The results clearly showed that the injected power and the friction phenomenon have to be considered simultaneously, especially if the k-ratio is varied over a broad range. The importance of the milling conditions during the synthesis of a target oxide is best demonstrated by the example of BaTiO3. It was shown that single-phase BaTiO3 can be synthesized mechanochemically from a mixture of BaO and TiO2 by milling in a vacuum (Welham, 1998) or a nitrogen atmosphere (Xue et al., 2000a). However, several authors have reported their inability to synthesize BaTiO3 from a mixture of BaCO3 and TiO2 (Stojanovic´ et al., 1999; Gomez-Yanez et al., 2000; Brzozowski and Castro, 2000, 2003; Berbenni et al., 2001a; Pavlovic´ et al., 2002; Kong et al., 2002a; Goes et al., 2008). Xue et al. (2000a) claimed that it was impossible to prepare BaTiO3 by milling BaO and TiO2 in a shaker mill in air owing to the formation of BaCO3 from the BaO and atmospheric CO2. This point was discussed in the work of Welham (1998), who explained, using thermodynamic calculations, the high stability of BaCO3 in the reaction with TiO2 in comparison with BaO or Ba(OH)2. A positive free energy was calculated for the reaction between BaCO3 and TiO2 (ΔG298 = 60.3 kJ mol−1), in contrast to the negative


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free energies of the reactions between BaO and TiO2 (ΔG298 = −158 kJ mol−1) and Ba(OH)2 and TiO2 (ΔG298 = −60.7 kJ mol−1). However, as was mentioned in the paper, the influence of the milling conditions on the reaction should not be overlooked. As a matter of fact, in a later investigation, Stojanovic´ et al. (2005) showed that BaTiO3 can be synthesized from a BaO– TiO2 mixture in air using a planetary mill, even if a substantial amount of BaCO3 had already been observed in the initial stage of milling. In addition, a recent publication of Ohara et al. (2008a) demonstrates that single-phase BaTiO3 can be synthesized in just 12 min from a BaCO3–TiO2 mixture using a highly efficient attrition-type mill operating at a rotational frequency of 4000 min−1 (Fig. 6.3). In the past few years great efforts have been made to understand the basic mechanisms that govern the mechanochemical reaction. The mechanistic aspect of reactions of mixtures of oxides, which are, according to the literature, the most frequently used reagents in the mechanochemical synthesis of complex ceramic oxides, has been studied by Wang, Xue and coworkers (Wang et al., 2000a). Their work involves the synthesis of several materials, including ferroelectrics, relaxors and relaxor-ferroelectrics, such as PbTiO3 (PT) (Xue et al., 1998), Pb(Zr0.52Ti0.48)O3 (PZT) (Wang et al., 2000a), Pb(Mg1/3Nb2/3)O3 (PMN) (Wang et al., 1999, 2000a; Xue et al., 2002), Pb(Zn1/3Nb2/3)O3 (PZN) (Wang et al., 2000b), 0.36Pb(Mg1/3Nb2/3) (a)

(b) BaTiO3 BaCO3 TiO2

Powders

Intensity (a.u.)

After

Chamber Rotor Before

20

30

40

50

60

70

2θ (deg)

6.3 (a) XRD patterns of BaCO3–TiO2 powder mixture before and after 12 min of high-energy milling (from Ohara et al., 2008a) and (b) schematic view of the attrition-type mill employed (from Sato et al., 2006).



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O3–0.54Pb(Zn1/3Nb2/3)O3–0.1PbTiO3 (0.36PMN–0.54PZN–0.1PT) (Wan et al., 1999; Wang et al., 2000a, 2000b; Xue et al., 2002), 0.9Pb(Zn1/3Nb2/3) O3–0.1BaTiO3 (0.9PZN–0.1BT) (Xue et al., 1999a) and SrBi4Ti4O15 (SBIT) (Ng et al., 2002a). Wang et al. (2000a) explained the mechanochemical synthesis of PMN from a PbO–MgO–Nb2O5 mixture by dividing the process into different stages. In the initial part of the mechanochemical treatment they first observed a crystallite-size refinement of the initial oxides coupled with a partial amorphization of the mixture. At this stage the PMN phase formed from the activated mixture and, with further milling, the amount of PMN increased. According to XRD analysis, a single nanocrystalline PMN phase was obtained after 20 hours of milling. They also observed a sharpening of the XRD peaks of the PMN during its formation and estimated, using the Scherrer equation, an increase in the size of the PMN crystallites from 9 nm to 15 nm when extending the milling time from 5 hours to 20 hours. This suggested that the perovskite nanocrystallites underwent a steady growth during the mechanochemical treatment. The authors claimed that pyrochlore phases, such as Pb3Nb4O13 and Pb2Nb2O7, which are typically encountered as intermediate reaction products during the temperaturedriven solid-state reaction, were not involved in the process. They believe that the formation of the PMN occurs via nucleation from an activated amorphous matrix involving all three oxides, rather than being a result of an interfacial ‘reaction and diffusion’ mechanism, which is characteristic for thermally activated reactions and results in the formation of transitional pyrochlore phases. On the basis of similar observations in other systems, the authors explained the mechanochemical synthesis as a ‘nucleation and growth’ process in which the product nanocrystallites nucleate from a highly activated amorphous matrix and grow with continued milling. In Fig. 6.4 we indicate schematically the stages involved in the reaction mechanism. The mechanism proposed by Wang et al. (2000a) was partially put into question after the work of Kuscer et al. (2006, 2007). As a matter of fact, they observed the formation of pyrochlore phases during the mechanochemical synthesis of Pb(Mg1/3Nb2/3)O3 (PMN) and 0.65Pb(Mg1/3Nb2/3) O3–0.35PbTiO3 (PMN–PT) solid solutions. In the initial stage of the mechanochemical synthesis of PMN from a PbO–MgO–Nb2O5 powder mixture, a lead-niobate pyrochlore was formed first (Kuscer et al., 2006). Based on the results of a Rietveld refinement analysis coupled with an internal standard method, which was used to determine the amount of amorphous phase from the XRD background, a change in the pyrochlore’s lattice parameter, as well as the consumption of MgO from the crystalline and amorphous phases, were observed with further milling. This suggested that a lead–magnesium–niobate pyrochlore, that is Pb1.86Mg0.24Nb1.76O6.5,


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Mixture of oxides

Mechanochemical treatment

Reduction of crystallite size and amorphization


Growth of product nanocrystallites


Nucleation of the product from the amorphous phase

6.4 Schematic view of the ‘nucleation and growth’ mechanism proposed by Wang, Xue and co-workers (Wang et al., 2000a).

was also formed subsequently owing to the incorporation of the MgO into the pyrochlore structure. At the same time, the PMN perovskite phase appeared in the mixture. The amount of pyrochlore phase reached a maximum during milling, while the amount of perovskite phase increased almost linearly. Since the quantity and the composition of the amorphous phase changed in the course of milling, it was suggested that it takes part in reactions related to the formation of both perovskite and pyrochlore phases. As in the case of the PMN synthesis, Kuscer et al. (2007) showed that the formation of the PMN–PT solid solution in the initial stage of milling is characterized by nucleation from the amorphous phase. This is consistent with the previously discussed mechanism of Wang et al. (2000a) (Fig. 6.4). However, after a certain milling time, when the PbO, TiO2 and Nb2O5 were no longer identified in a crystalline form and MgO had disappeared from the amorphous phase, a significant decrease in the formation rate of PMN– PT was observed (Fig. 6.5). As there was no MgO in the amorphous phase, the authors assumed that the perovskite could not simply nucleate from the amorphous phase. The amount of pyrochlore decreased even though the amount and the composition of the amorphous phase did not change significantly with increasing milling time from 32 to 64 hours (see Fig. 6.5b, c). Based on this, the authors supposed that the formation mechanism of the perovskite phase changed to a pyrochlore-to-perovskite transformation, which is predominant after prolonged milling and occurs in a way similar to conventional solid-state synthesis. When comparing the mechanisms proposed by Kuscer et al. (2006, 2007) and Wang et al. (2000a) it should be mentioned that the latter put together their explanation on the basis of not observing any pyrochlore phases being formed during the mechanochemical synthesis of PMN and


Mechanochemical synthesis of complex ceramic oxides (a) 70 18 16 14 12 10 8 6 4 2 0

121

Mass (%)

PbO TiO2 Nb2O5 MgO 0

10

20

30 40 50 Milling time (h)

(b) 70

60

70

Per

60 Mass (%)

50 AF

40 30 20 10

PY

0 0

10

20

30 40 50 Milling time (h)

60

70

Amorphous phase (mol)

(c) 0.35 0.3 PbO

0.25 0.2 0.15

NbO2.5

0.1

TiO2

MgO

0.05 0 0

10

20 30 40 50 Milling time (h)

60

70

6.5 Quantitative phase composition of high-energy milled PbO–MgO– Nb2O5–TiO2 powder mixture as a function of milling time. (a) Fraction of PbO, MgO, Nb2O5 and TiO2 in crystalline form; (b) fraction of perovskite PMN–PT (Per), pyrochlore (PY) and amorphous (AF) phases; and (c) calculated composition of the amorphous phase (from Kuscer et al., 2007).


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0.36PMN–0.54PZN–0.1PT. This observation was made primarily on the basis of an XRD analysis, where a peak overlapping with PbO makes identification of the pyrochlore less than straightforward. Secondly, the authors used a shaker mill for the synthesis, whereas a planetary mill was used in the work of Kuscer et al. (2006, 2007); this could result in some differences in the formation of pyrochlore phases. In order to elucidate this point, further studies should be more focused on the relation between the milling conditions and the formation of transitional pyrochlore phases during the mechanochemical synthesis of PMN and related solid solutions. Zdujic´ et al. (2006) studied the mechanochemical synthesis of Bi4Ti3O12, determining the amount of amorphous phase formed during milling and following the crystallite size as a function of the milling time. In addition to the stoichiometric Bi2O3–TiO2 mixture, a preformed Bi4Ti3O12 powder was also subjected to mechanochemical treatment. First, they found that the amorphization of the Bi4Ti3O12 compound was realized only when its average crystallite size decreased below 40 nm. The amorphization mechanism was therefore explained as a collapse of the crystal structure after a certain critical crystallite size was reached, with a subsequent dissolution of the nanocrystallites into the amorphous matrix. On the other hand, milling the Bi2O3–TiO2 mixture resulted first in the formation of Bi2(CO3)O2 as an intermediate product (due to the reaction of the Bi2O3 with atmospheric CO2), which reacted subsequently with the TiO2, finally forming the Bi4Ti3O12. In both cases, however, they found that the form of the Bi4Ti3O12 obtained by milling, that is amorphous or nanocrystalline, depends strongly upon the milling conditions applied. While a higher injected mechanical power (the product of the ball-impact energy and the ball-impact frequency) favours a nanocrystalline phase, a lower power results in an amorphous one. For example, by increasing the power during a milling experiment, the processed powder responded to the change in the milling conditions in such a way that the amorphous phase crystallized, to some extent, in the form of Bi4Ti3O12, while decreasing the power during the same milling experiment resulted in complete amorphization. The milling power was modified by changing both the ball-impact energy and the frequency. Therefore, the direction of the nanocrystalline-to-amorphous transition is determined most probably by the ball-impact energy itself since it is reasonable to expect that the change in the frequency can influence at most the kinetics of the transformation but not its course. A detailed study and identification of the intermediate phases formed during a mechanochemical synthesis was carried out by Rojac et al. (2006a), who focused on the reaction between Na2CO3 and Nb2O5. After milling the mixture, they observed a complete loss of the long-range periodicity of the Na2CO3 structure in the first 40 hours, before NaNbO3 was formed. However, this did not occur if the Na2CO3 was milled separately, without the presence of Nb2O5. The results suggested that the two reagents interacted during © Woodhead Publishing Limited, 2010


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milling, resulting in the amorphization of the Na2CO3. The coordination state of the carbonate ions (CO32−) was further examined by infrared spectroscopy. Simultaneously with the amorphization of Na2CO3, a lowering of the point-group symmetry of the CO32− ions was observed, which was attributed to the coordination of these ions into a carbonato complex. The amorphization of the Na2CO3 in the mixture with Nb2O5 was therefore explained in terms of complex formation, during which the CO32− ions must be rearranged from their original structure. The carbonato complex, which was found to be amorphous or eventually nanocrystalline, was considered to be an intermediate phase in the mechanochemical synthesis of NaNbO3. Further studies of the reaction mechanism in the Na2CO3–Nb2O5 system were focused on the second part of the reaction, the formation of NaNbO3 (Rojac et al., 2007, 2008a). In one investigation the formation of the niobate was studied by applying different ball-impact energies (Rojac et al., 2008a). Using a Rietveld refinement analysis complemented by an internal standard method and X-ray line-broadening analysis, the quantitative phase composition (the amounts of Na2CO3, Nb2O5, NaNbO3 and XRD amorphous phase) as well as the crystallite size and the quantity of microstrains in the Nb2O5 and NaNbO3 were determined as a function of the milling time. In addition, the amount of carbonate was followed using thermogravimetric analysis. The results showed that the NaNbO3 forms through an intermediate XRD amorphous phase, which is in agreement with the mechanism proposed by Wang et al. (2000a) and Kuscer et al. (2006, 2007) for systems involving oxides as reagents. The investigation of the mechanochemical synthesis of NaNbO3 by Rojac et al. (2007, 2008a) showed that after prolonged milling a constant ratio between the mass fractions of the NaNbO3 and the XRD amorphous phase was established, which did not change with increasing milling time. At this stage the mixture contained about 50% (in terms of mass fraction) of XRD amorphous phase. This suggested that a quasi-equilibrium condition is reached during the milling, like that observed by Zdujic´ et al. (2006) during the mechanochemical synthesis of Bi4Ti3O12. In a similar manner, the NaNbO3 crystallite size and the quantity of microstrains reached constant values, 17–18 nm and 1.0%, respectively, and did not differ significantly even if the milling experiments were performed under very different milling conditions. In contrast to the work of Wang et al. (2000a), who reported on the growth of PMN nanocrystallites during milling, there was no such tendency observed during the mechanochemical synthesis of NaNbO3. Namely, at low ball-impact energy (15 mJ per hit) a decrease of the perovskite crystallite size was observed with increasing milling time, while it remained constant throughout the experiment at higher ball-impact energy (370 mJ per hit). In addition, the final conversion of Na2CO3 in the mechanochemical reaction with Nb2O5 in terms of its decomposition was found to be lower © Woodhead Publishing Limited, 2010

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(around 70%) than usually obtained in a thermally activated reaction, where a nearly complete decomposition of the Na2CO3 is typically achieved. This suggests that, in terms of thermodynamics, there exists a difference between a mechanochemically induced and a thermally induced reaction. Kosova et al. (1999, 2000, 2001) compared the mechanochemical synthesis of LiMn2O4 starting from mixtures of LiOH–MnO2 or Li2CO3–MnO2. In one of their investigations, the purpose was to identify the intermediate state formed at the very beginning of the mechanochemical interaction between the reagents (Kosova et al., 1999). They observed a considerable difference in the reaction course depending on whether the lithium hydroxide or the carbonate was used in the initial mixture. In the case of the LiOH–MnO2 mixture it was shown that the valence state of the surface manganese ions, determined by X-ray photoelectron spectroscopy (XPS), changed from Mn4+ to a mixed state of Mn3+ and Mn4+ after 10 min activation. At the same time, the Li/Mn concentration ratio on the surface decreased. However, after 10 min of milling this ratio was found to be still 1.6 times higher than in the spinel LiMn2O4, indicating that the surface layer of the particles was enriched with amorphous LiOH. Based on these data, the authors reconstructed the changes occurring on the surface of the LiOH–MnO2 mixture in the following way: during the initial stage of milling LiOH, having a layered structure and exhibiting good plasticity, covers the MnO2 particles, forming an amorphous layer. A similar mechanism, which takes into account the difference in the mechanical properties of the reagents, was also suggested by Streletskii et al. (1995), in their case for the reaction between PbO and Nb2O5. The subsequent chemical interaction is associated with an electron transfer from the OH− ions of LiOH to the Mn4+ ions, partially reducing them to Mn3+ (Equations [6.4], [6.5] and [6.6]). At the same time, the lithium ions diffuse into the interior of the particle, resulting in a decrease of the lithium concentration on the surface. 4LiOH + 8MnO2 → 4Li(Mn3+,Mn4+)O4 + 2H2O + O2 −

[6.4]

−

4OH − 4e → 2H2O + O2

[6.5]

4Mn4+ + 4e− → 4Mn3+

[6.6]

A different picture was observed in the case of the Li2CO3–MnO2 mixture. No reduction of Mn4+ occurred and the Li concentration on the surface of the particles increased during activation from 1 min to 10 min. It was suggested that Li2CO3, being more brittle than LiOH, does not behave in the same way as the hydroxide. The authors proposed that a defect spinel-like phase Li2O⋅yMnO2 (2.5 ≤ y ≤ 4), with a Li content higher than in LiMn2O4, forms on the surface in this case, where the redox stage is absent and only brittle fracture occurs, Equation [6.7]: Li2CO3 + yMnO2 → Li2O⋅yMnO2 + CO2


[6.7]


125

The reaction between LiOH and MnO2 was identified as a new, more complex type of reaction. The particularity of the so-called ‘soft mechanochemical reactions’ consists of the high reactivity of surface functional groups, notably, OH groups (Avvakumov et al., 2001). Details of these kinds of reactions are given in Chapter 14. It is well known that mechanochemical reactions can produce nanocrystalline products, for which specific properties are expected. Sˇepelák et al. (2007a) studied the reaction between NiO and α-Fe2O3 giving special attention to the structural particularities of the synthesized NiFe2O4. It was found that the ferrite nanoparticles exhibit a core-shell structure consisting of an ordered inner core surrounded by a disordered surface-shell region with a thickness of about 1 nm (Fig. 6.6). The size of the nanoparticles was estimated to be in the range 6–13 nm. Using Mössbauer spectroscopy, Sˇepelák and co-workers (2007a) showed that the bulk NiFe2O4 exhibits a fully inverse spinel structure with a collinear spin alignment or (Fe↓)[NiFe↑]O4 (for illustration see core in Fig. 6.6). In contrast, the mechanochemically synthesized nanoparticles Shell

Core

t = 1.0 nm

Core: (Fe ) [NiFe ] O4; λc = 1.00; Ψ[A]s = 0°; Ψ[B]s = 0° Shell: (Ni0.33 Fe0.67

) [Ni0.67 Fe1.33

] O4; λs = 0.67; Ψ[A]s = 28°; Ψ[B]s = 40°

6.6 Non-uniform core/shell structure of mechanochemically synthesized nanocrystalline NiFe2O4. The chemical formulae denote the atomic site occupancy and the spin alignment (Ψ[A]s, and Ψ[B]s, where A and B subscripts refer to A and B sites of the spinel structure, respectively) within the particle’s core and shell. λc denotes the degree of inversion defined as the fraction of A sites occupied by Fe3+ ions in 3+ ˇ the spinel structure (M12+−λFeλ3+)(M2+ λ Fe2−λ)O4, where M is Ni (from Sepelák et al., 2007a).


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showed different structural and magnetic features. While the core was considered to possess the same structure and magnetic spin alignment as the bulk ferrite, the shell was shown to be structurally disordered with a nearly random distribution of cations and a canted spin arrangement (see Fig. 6.6). The authors showed that this configuration influences the macroscopic magnetic properties of the ferrite, that is the saturation magnetization and the coercivity. Interestingly, a non-uniform core-shell nanoparticle structure was also observed in high-energy-milled LiNbO3 (Heitjans et al., 2007) and mechanochemically synthesized MgFe2O4 (Sˇepelák et al., 2006), MnFe2O4 (Muroi et al., 2001), PbTiO3 (Szafraniak et al., 2006) and BiFeO3 (Szafraniak et al., 2007).

6.3

Mechanochemical synthesis of complex oxides with various properties

6.3.1 Ferroelectric and related oxides Traditionally, ferroelectric oxides have been synthesized via a conventional solid-state synthesis route, which requires multiple calcinations at elevated temperatures with intermediate milling steps. In addition to the large number of processing steps, a homogeneous powder is difficult to obtain by this method, especially when complex compositions are being synthesized. Furthermore, owing to the coarse particles and low specific surface area, resulting in a poor sinterability of the obtained powders, increased sintering temperatures are required to obtain ferroelectric ceramics with the desired performance. For lead- and alkaline-containing ferroelectrics, for example, high temperatures can lead to an increased loss of highly volatile PbO or alkali oxides giving rise to stoichiometry variations and, eventually, the formation of secondary phases, which have a negative effect on the functional properties of the final ceramics. Because of these problems, extensive research has been done in recent decades to develop alternative synthesis routes. Recently, it has been realized that the main potential of the mechanochemical method lies in its ability to prepare highly homogeneous nanopowders, making it especially attractive for the preparation of materials with a rather complex chemical composition, which is the case for ferroelectric and related oxides. The method has several advantages over other processing routes. First, it uses cost effective and widely available starting compounds (typically, oxides, carbonates or hydroxides) in contrast to the often expensive and moisture-sensitive precursors used in wet chemistry-based methods, such as the sol–gel process. Second, by synthesizing the oxide directly using high-energy milling, the repeated calcination steps, encountered in conventional solid-state synthesis, can be skipped, leading to a simpler process. Furthermore, the mechanochemical reactions are believed © Woodhead Publishing Limited, 2010


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to take place at lower temperatures, which can reduce the loss of volatile components. This is particularly important since most ferroelectric oxides contain lead, bismuth or alkali elements (K, Na and Li). In the past few years, a large number of technologically important complex oxides with different structures (perovskite, Aurivillius, tungsten bronze) and properties (ferroelectric, antiferroelectric, piezoelectric, relaxor, multiferroic) have been prepared either directly by mechanochemical synthesis or by annealing mechanochemically activated powders. These oxides are collected in Table 6.1. Table 6.1 Complex oxides with various structures and properties prepared directly by mechanochemical synthesis or by annealing mechanochemically activated powders Ferroelectric and antiferroelectric oxides with perovskite structure

• BaTiO3, (Ba1−xSrx)TiO3 • PbTiO3, PbZrO3, Pb(ZrxTi1−x)O3, (Pb1−3x/2Lax)TiO3, (Pb1−yLay)(ZrxTi1−x)1−y/4O3, (Pb1−xZnx)(Zr0.53Ti0.47)O3,1 (Pb1−xGdx)(Zr0.53Ti0.47)1−x/4O3,2 (Pb0.97La0.02) (Zr0.62Sn0.31Ti0.04)O3, (Pb0.99Nb0.02)(Zr0.85Sn0.13Ti0.02)0.98O3, (Pb0.99La0.01)(Fe0.01Nb0.02Li0.007Ti0.453Zr0.53)O3.3 • LiNbO3, NaNbO3, (Na0.95Li0.05)NbO3,4 (K0.5Na0.5)NbO3.5 • (Na0.5Bi0.5)TiO3.6

Ferroelectric oxides with Aurivillius structure

• • • • • •

Ferroelectric oxides with tungstenbronze-type structure

• Ba2ANb5O15 (A = K,Na,Li).8

Relaxors and relaxorferroelectrics with perovskite structure

• PMN, PMN–PT, PMN–PZN • PZN, PZN–PT, PZN–BT, PZN–PFW, PZN–PMN–PT, PZN–PFN–PFW • PST

Multiferroic oxides

• BiFeO3,9 Bi(Fe1−xMnx)O3,10 0.7BiFeO3–0.3PbTiO3.11 • Pb(Fe1/2Nb1/2)O3, (Pb1−xBax)(Fe1/2Nb1/2)O3,12 0.8Pb(Fe1/2Nb1/2)O3–0.2Pb(Mg1/2W1/2)O3.13 • Pb(Fe2/3W1/3)O3

Bi4Ti3O12 Bi4Srn−3Ti4O3n+3 (n = 4,5),7 CaBi4Ti4O15 Bi3TiNbO9, (1 − x)Bi2SrNb2O9–xBi3TiNbO9 Bi2MoO6, Bi2(Mo0.25W0.75)O6 Bi2VO5.5 SrBi2Ta2O9

The table was constructed by updating the literature data given in the review of Kong et al. (2008). The reader can refer to the review article for references that are not given in the table. Notations: PMN is Pb(Mg1/3Nb2/3)O3, PZN is Pb(Zn1/3Nb2/3)O3, PST is Pb(Sc1/2Ta1/2) O3, PFN is Pb(Fe1/2Nb1/2)O3, PFW is Pb(Fe2/3W1/3)O3, PT is PbTiO3, BT is BaTiO3. References: 1 Parashar et al., 2005; 2 Parashar et al., 2004; 3 Miclea et al., 2004; 4 Pardo et al., 2004; 5 Rojac et al., 2005b; 6 Van Hal et al., 2001; 7 Ferrer et al., 2005; 8 Van Hal et al., 2001; Khachane et al., 2006; 9 Santos et al., 2006a; Szafraniak et al., 2007; 10 Santos et al., 2006a, 2006b; 11 Khan et al., 2005; 12 Varshney et al., 2007; 13 Levstik et al., 2007.


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The mechanochemical synthesis of a great majority of the oxides listed in Table 6.1 is discussed in the review by Kong et al. (2008). In the following section, some of the main results will be presented for selected materials or groups of materials, that is BaTiO3, Pb(Zr,Ti)O3, alkaline niobates, Bi4Ti3O12, Pb-based relaxor-ferroelectrics and multiferroic BiFeO3. Barium titanate (BaTiO3) is one of the most important materials among the ferroelectric oxides, with a variety of possible applications (Haertling, 1999). A lot of work has been done on its preparation, including mechanochemical synthesis. There are a large number of reports explaining the difficulties associated with synthesizing BaTiO3 directly by milling from a mixture of BaCO3 and TiO2 (Stojanovic´ et al., 1999; Gomez-Yanez et al., 2000; Brzozowski and Castro, 2000, 2003; Berbenni et al., 2001a; Pavlovic´ et al., 2002; Kong et al., 2002a; Goes et al., 2008). As explained by Berbenni et al. (2001a), and in agreement with the results obtained by other researchers (Gomez-Yanez et al., 2000; Brzozowski and Castro, 2000; Kong et al., 2002a; Pavlovic´ et al., 2002), the activation of the BaCO3–TiO2 mixture enhances its reactivity, resulting in a lowering of the temperature of BaTiO3 formation upon subsequent annealing in comparison with the non-activated mixture. However, in all cases, Ba2TiO4 formed as a transitional phase during the heating of the activated powders (Fig. 6.7). The formation of Ba2TiO4 is typically encountered in thermally activated synthesis as a result of the diffusion-controlled reaction between the initially formed BaTiO3 and the BaCO3 (Brzozowski and Castro, 2000; Pavlovic´ et al., 2002). This indicates that under the experimental conditions used in these studies the basic formation mechanism of BaTiO3 upon annealing was not changed by preactivating the BaCO3–TiO2 mixture. However, the amount of secondary phase formed upon annealing can be reduced by increasing the rotational frequency of a planetary mill and/or the activation time (Brzozowski and Castro, 2000). Lead zirconate titanate (Pb(ZrxTi1−x)O3 or PZT) is a technologically important material in electronics and microelectronics, owing to its outstanding ferroelectric, piezoelectric and other properties (Haertling, 1999). The mechanochemical synthesis of nano-sized PZT powders and the fabrication of PZT ceramics from these powders have been reported by several groups using different milling conditions (Lee et al., 1999; Xue et al., 1999b; Kong et al., 2000, 2001a, 2001b, 2002b; Brankovic´ et al., 2003; Beitollahi and Moravej, 2004). A combined approach consisting of mechanochemically activating a co-precipitated precursor has also been proposed (Xue et al., 2000b; Liu et al., 2005). Kong et al. (2001a) combined a mechanochemical synthesis with reaction sintering, using a partially mechanochemically reacted mixture comprising PZT (nominal composition: Pb(Zr0.52Ti0.48)O3), crystalline PbO and an amorphous phase, according to X-ray diffraction (XRD) analysis. Nearly



(211)

(210)

(111) (d)

(200)

(110)

BaCO3 TiO2 Ba2TiO4 BaTiO3

(100)

Intensity (a.u.)

129

(c) (b) (a) 20

30

40 2θ (deg)

50

60

6.7 XRD patterns of mechanochemically activated BaCO3–TiO2 powder mixture annealed for 2 hours at different temperatures: (a) 600°C, (b) 700°C, (c) 800°C and (d) 900°C (from Kong et al., 2002a). The Miller indices in (d) refer to BaTiO3.

fully dense PZT ceramics (99.2% of theoretical density) sintered at 1100°C for 1 hour were obtained with dielectric and ferroelectric properties comparable to the values reported using other processing techniques. Similar results were also obtained from a mechanochemically synthesized PZT, which did not contain unreacted crystalline oxides (Lee et al., 1999; Xue et al., 1999b). Brankovic´ et al. (2003) synthesized PZT using a planetary mill in a much shorter time (1 hour) in comparison with the results reported by other authors, who typically report on the formation of almost pure PZT after several tens of hours (Kong et al., 2000; Lee et al., 1999; Xue et al., 1999b). The increased rate of PZT formation was attributed mainly to the higher rotational frequency of the disc (317 min−1) and the higher ball-to-powder mass ratio (40 : 1) than was used in other investigations. This could also cause increased contamination during milling, which was not discussed. In addition, the authors observed an interesting phenomenon related to the stability of PZT under high-energy impacts; with prolonged milling the newly formed PZT started to transform into an amorphous phase. However, no explanation was given for this. Alkaline niobates are of a particular interest as they are one of the most promising groups of materials that could replace Pb-containing piezoelectric oxides, such as, for example, PZT. Most of the work relating to


130


the mechanochemical synthesis of alkaline niobates has been done on the antiferroelectric NaNbO3. Castro et al. (2004) reported on the mechanochemical synthesis of NaNbO3 using a starting mixture of Na2CO3 and Nb2O5. After 30 days of activation in a vibration mill, a powder mixture with increased reactivity was achieved. Single-phase NaNbO3 was obtained only after subsequent annealing at a lower temperature than usually required by conventional solid-state synthesis, that is 600°C. In order to decrease the activation time, more reactive sodium reagents were used, such as NaOH and Na2O (Hungría et al., 2005). However, because of its high sensitivity to moisture and, therefore, the difficulty of handling Na2O, an off-stoichiometry resulted and a secondary phase was formed upon heating the activated precursor. In addition, they showed that using a planetary mill instead of a vibration mill, which supplies more energy to the reagents, the milling time necessary for the activation of the powder mixture could be reduced to two days. In order to improve the synthesis of NaNbO3 further, a combined wet chemistry and mechanochemical activation technique was also proposed. In this case, single-phase NaNbO3 was prepared by heating the two-days-activated mixture at 700°C. In contrast, Rojac et al. (2005a) managed to prepare NaNbO3 with a crystallite size in the range of a few nanometres to 25 nm directly by a mechanochemical reaction between Na2CO3 and Nb2O5 using a planetary mill. Other studies related to alkaline niobates include the mechanochemical synthesis and activation of LiNbO3 (Figueiredo et al., 1998; Heitjans et al., 2007) and the synthesis of (Na0.95Li0.05)NbO3 (Pardo et al., 2004), which was prepared by annealing a mechanochemically activated powder mixture of alkali carbonates and Nb2O5. To the best of our knowledge there is only one publication on the synthesis of a (K0.5Na0.5)NbO3 (KNN) solid solution, in which the authors report the amorphization of the initial alkali carbonates (K2CO3 and Na2CO3) during milling, while the KNN formation was not realized under the milling conditions applied (Rojac et al., 2005b). A similar behaviour was observed for the synthesis of KNbO3 from a K2CO3–Nb2O5 mixture. Finally, mechanochemical activation was recently applied to the synthesis of a Li- and Ta-modified KNN solid solution (Rojac et al., 2008b). In general, however, poor literature data exist on the mechanochemical synthesis of alkaline niobates and further work is necessary. Bismuth titanate (Bi4Ti3O12) is the most famous Aurivillius-type ferroelectric material. It is distinguished by its high Curie temperature (675°C) and considered a good candidate for high-temperature piezoelectric applications (Subbarao, 1961; Megriche et al., 1999). In the work of Lisoni et al. (2001) it was shown that the mechanochemical activation of a Bi2O3–TiO2 mixture, leading to the formation of an amorphous phase, results in a lowering of the temperature of Bi4Ti3O12 formation upon subsequent annealing



131

by about 300°C with respect to the traditional ceramic procedure (850°C). However, upon heating the powders activated in a vibration mill for a total of 72 and 168 hours or in a planetary mill for 19 hours they observed the formation of intermediate phases, that is, Bi12TiO20 and a fluorite-like Bi– Ti–O compound. In contrast, by increasing the activation time in the planetary mill from 19 to 72 hours, apparently, direct crystallization of Bi4Ti3O12, without the appearance of any intermediate phase, took place upon heating the amorphous precursor. This was explained by the increased homogeneity of the mixture, which was achieved by prolonging the activation time. Kong et al. (2001c) showed the feasibility of the synthesis of Bi4Ti3O12 directly by high-energy milling using a planetary mill and tungsten carbide milling media. By sintering the nanopowder, they obtained a dense ceramic (96% of theoretical density) at 750°C within 1 hour. According to the comparison made by the authors, the Bi4Ti3O12 powder obtained exhibited better sinterability than the one prepared by other synthesis methods, such as solid-state reaction and wet chemistry-based processes. Several other studies were published subsequently, reporting on the mechanochemical synthesis of Bi4Ti3O12 and its structural and electrical characterization (Zdujic´ et al., 2006; Stojanovic´ et al., 2006a, 2006b, 2008; Lazarevic´ et al., 2007a, 2007b, 2008). Mechanochemical synthesis also offers the possibility of synthesizing compositions with a rather complex nature, such as, for example, 0.54Pb(Zn1/3Nb2/3)O3–0.36Pb(Mg1/3Nb2/3)O3–0.1PbTiO3 (0.54PZN–0.36PMN– 0.1PT) (Wan et al., 1999). The mechanochemical reaction starting from PbO, ZnO, MgO, Nb2O5, and TiO2 resulted in the formation of the perovskite phase after 20 hours of milling in a shaker mill. The powder exhibited a surface area of 10.9 m2 g−1 and consisted of crystallites that were 10–15 nm in size. A dense single-phase ceramic (>95% of theoretical density) was obtained after sintering at temperatures as low as 900°C, which is considerably lower than those (in the range of 1200°C) generally required for Pb-based relaxors prepared by conventional solid-state synthesis. These powders could be used, for example, in the production of thick films, as proposed by Kosec et al. (2007). They used a mechanochemically synthesized 0.65PMN–0.35PT nanopowder together with the addition of 2 mol% of excess PbO to enable liquid-phase sintering and demonstrated that a homogeneous and single-phase PMN–PT thick film can be obtained after sintering at temperatures as low as 950°C with dielectric, ferroelectric and piezoelectric properties comparable to bulk ceramics (Fig. 6.8). BiFeO3 belongs to a rare group of materials, the multiferroics, in which ferroelectric and magnetic ordering coexist in a single phase. Among the multiferroic oxides, BiFeO3 is distinguished by its high Curie temperature (TC = 830°C) and Néel temperature (TN = 370°C) (Jian and JunHao, 2008). Because of the many problems related to the conventional solid-state


132

High-energy ball milling (a)

950°C 900°C 850°C 10

20

30

40 2θ (deg)

50

60

70

(b)

PMN–PT

Pt

10 μm

6.8 (a) XRD patterns of 0.65PMN–0.35PT thick films, prepared using a mechanochemically processed powder, after sintering at 850, 900 and 950°C and (b) cross-section of the thick film on Pt/Al2O3 substrate sintered at 950°C for 2 hours (from Kosec et al., 2007).

synthesis of BiFeO3, such as the formation of undesirable secondary phases and the volatilization of Bi2O3 at higher temperatures, there is a need to develop alternative processing routes. The first steps towards the mechanochemical synthesis of BiFeO3 have already been taken. Santos et al. (2006a) report on the partial amorphization of a Bi2O3–Fe2O3 mixture after 24 hours of high-energy milling in a planetary mill. Annealing the activated mixture



133

led to the formation of BiFeO3 together with Bi12Fe4O9 and Bi25FeO40 as secondary phases. In contrast, a successful mechanochemical synthesis of nanocrystalline BiFeO3 by prolonged milling (70 hours) in a shaker mill was achieved by Szafraniak et al. (2007). The impact of the mechanochemical synthesis on the final electrical and magnetic properties of the ferrite remains the subject of future studies.

6.3.2 Magnetic oxides Among various topics in the research on spinel ferrites of type MFe2O4 (M is a divalent metal cation), the magnetic properties of nanoparticles have recently attracted a lot of attention from a fundamental point of view, where an understanding of the basics of nanomagnetism is of major interest, as well as being of considerable practical interest. Because of this, much interest has been shown in mechanochemical synthesis as a way to synthesize ferrite nanoparticles. The idea of using mechanochemistry in order to prepare spinel ferrites dates back to the 1960s, when Kimura (1963) prepared zinc ferrite from ZnO and Fe2O3 by explosive compression. Later, several articles were published on the mechanochemical synthesis of various ferrites, such as ZnFe2O4 (Sˇepelák et al., 1999; Yang et al., 2004a; Verdier et al., 2005; Jean and Nachbaur, 2008), NiFe2O4 (Jovalekic´ et al., 1995; Yang et al., 2004b; Sˇepelák et al., 2005a, 2007a, 2007b), MgFe2O4 (Sˇepelák et al., 2005a, 2006; Bergmann et al., 2006), CoFe2O4 (Shi et al., 2000), MnFe2O4 (Muroi et al., 2001; Osmokrovic´ et al., 2006) and Mn1−xZnxFe2O4 (Arcos et al., 1998; Fatemi et al., 1999; Mozaffari et al., 2008). More data relating to this topic can be found in the review of the mechanochemical synthesis and mechanical activation of ferrites written by Sˇepelák et al. (2005b). Mechanochemical synthesis offers several advantages over traditional processing routes. Besides the low temperature retained during synthesis and the reduced number of processing steps, the method allows the production of nanocrystalline ferrites with particular structural and magnetic properties, as described at the end of Section 6.2. These properties can be tailored by controlling the crystallite size of the obtained mechanosynthesized ferrite, as shown by the example of NiFe2O4 in Fig. 6.9 (Sˇepelák et al., 2005b, 2007a, 2007b). Increasing the crystallite size by annealing at elevated temperatures (up to 1000°C) brings about a gradual increase in the magnetization and a decrease in the coercivity. A magnetic softening is observed and the hysteresis loop saturates at a larger crystallite size. On heating, the metastable mechanosynthesized NiFe2O4 relaxes to a structural and magnetic state similar to that of the bulk. While nanocrystalline mechanosynthesized NiFe2O4 showed a lower magnetization than the bulk ferrite (Fig. 6.9; compare ‘as-prepared’ with ‘1273 K’), the reverse effect was observed for MgFe2O4 (Sˇepelák et al.,



M (emu g–1)

134

60

1273 K

40

1073 K

20

973 K As-prepared

0 8.6 nm –20 16.7 nm

T=3K

–40 38.9 nm –60 82.8 nm –5 –4 –3 –2 –1 0

1

2

3

4

5

H (T)

6.9 Magnetization (M)–magnetic field (H) hysteresis loops for mechanosynthesized and subsequently annealed NiFe2O4. The annealing temperature and the corresponding crystallite size, determined by Rietveld refinement analysis, are shown (from ˇ epelák et al., 2007a). S

2006). This was explained in terms of a competition between two effects coming from the disordered shell of the mechanosynthesized nanoparticles (see Fig. 6.6): (1) spin canting, which tends to reduce the magnetization, and (2) site exchange of cations, resulting in an enhanced magnetization. It seems that the two effects play a crucial role in the macroscopic magnetic properties of the ferrite and, interestingly, give different results for NiFe2O4 and MgFe2O4. Recently, besides mechanochemical synthesis, the mechanical activation of spinel ferrites, prepared by a conventional ceramic method, has also become of interest (Sˇepelák et al., 2005b). Similar particularities as in the case of the mechanochemically synthesized ferrites were identified, that is structural disordering reflected in the cation redistribution in the spinel structure and magnetic disordering caused by spin canting (see also Fig. 6.6). Based on the literature data, it should be emphasized that the extent of structural disordering is influenced by the milling conditions applied, since the same nanomaterials from different laboratories exhibited different degrees of cation redistribution (represented by the degree of inversion). In addition, it has also been found that the degree of magnetic disordering (characterized by the spin-canting angle) increases with increasing milling time. These observations seem promising in view of the control of the magnetic properties of ferrites by mechanical activation.

6.3.3 Oxides with semiconducting and catalytic properties LaMnO3 and related perovskites, such as, for example, La1−xSrxMnO3, LaCrO3 and LaCoO3, have been studied primarily for utilization in solid oxide fuel cells (SOFCs) owing to their high electrical conductivity (Minh, © Woodhead Publishing Limited, 2010


135

1993) and as catalysts for oxidation and reduction reactions associated with the regulation of waste-gas emissions from vehicles (Voorhoeve et al., 1977). A traditional way to synthesize such materials is by the solid-state reaction from constituent oxides, for which high temperatures are required, typically of the order of 1000°C (Shu et al., 2005; Cheikh-Rouhou Koubaa et al., 2008; Tseggai et al., 2008; Ito et al., 2004). This method results in a large particle size and a limited degree of chemical homogeneity. In order to decrease the synthesis temperature and to obtain fine powders with high specific surface areas, which is important with respect to catalytic applications, mechanochemical synthesis has been considered as a possible preparation method. Zhang and Saito (2000) reported the mechanochemical synthesis of LaMnO3 from a powder mixture of La2O3 and Mn2O3. According to the XRD data, the mechanochemical reaction, yielding LaMnO3, was realized in a planetary mill after just 3 hours of high-energy milling. The final LaMnO3 powder exhibited a specific surface area of 10 m2 g−1. However, the powder consisted of agglomerates with a size up to several micrometers, composed of nanoparticles ( 290 nm

Light off

(b) (c)

80.0

(d)

(a)

(e)

60.0 40.0 Vis-light

UV-light

20.0 0.0

0

2

4

6

8

0

2

4

6

8 0 2 4 Time (min)

6

8

0

2

4

6

8 10

13.8 Relationship between light wavelength and the photocatalytic ability for oxidation of nitrogen monoxide in the prepared samples. (a) 䉬, P25 titania; (b) 䊉, planetary milled P25–10 wt% urea mixture at 700 rpm for 1 hour; (c) 䊊, calcined (b) in air at 400°C for 1 hour; (d) 䉱, planetary milled P25–5 wt% HMT mixture at 700 rpm for 1 hour; (e) 䉭, calcined (d) in air at 400°C for 1 hour. Adapted from Yin et al.39

titania–5% HMT mixture followed by calcination in air at 400°C. The powder prepared by planetary milling the P25 titania–10% urea mixture showed lower activity than that with 5% HMT. On the other hand, the photocatalytic activity under visible-light irradiation of the as-prepared powders without calcination was negligible. This is due to the depression of NO adsorption by the remaining reaction products such as CO2, NH3, carbon, organic molecules, and so on. In addition, as expected, no photocatalytic activity was observed for P25 because of its large band gap energy of 3.1 eV. In the case of irradiation by light of wavelength >400 nm, similar results were observed. The activities of the powders after calcination ((c) and (e)) were at almost the same level as that of P25 TiO2 but higher than those before calcination ((b) and (d)). When the light was turned off, the nitrogen concentration at the outlet of the reactor returned to the initial concentration of 1 ppm within 10 min, indicating that light energy is essential for the oxidation of nitrogen monoxide. It is thought that the chemical reaction between titania and HMT or urea occurs together with the phase transformation of titania. Usually, HMT/ urea hydrolyses to form ammonia and formaldehyde/CO2; however, it was found that many carbon/related compounds, such as biuret and cyanuric acid, were generated by the mechanochemical reaction of HMT or urea, as shown by Equations [13.12] and [13.13], owing to the lack of H2O.


Photocatalyst synthesis by mechanochemical doping C6H12N4 → 6C + 4NH3

(mechanochemical reaction)

317 [13.11]

2(NH2)2CO → NH3 + NH2CONHCONH2 (biuret) (mechanochemical reaction)

[13.12]

3(NH2)2CO → 3NH3 + C3H3N3O3 (cyanuric acid) (mechanochemical reaction)

[13.13]

This is the reason why the as-prepared powders showed low photocatalytic activity. The intermediate products or residual nitrogen sources depressed the adsorption of irradiated light on the surface of the photocatalyst. As shown in Fig. 13.8, the photocatalytic activity could be promoted by calcination at 400°C. Recently, it was also found that nitrogen-doped titania loaded with metallic ions (such as Fe or Pt) on the surface led to a great improvement in the photocatalytic activity and quantum yield. It was confirmed that NOx could be continuously removed successfully, not only under UV light irradiation but also under solar light and even some long-wavelength monochrome LED light (red LED: λ > 627 nm; green LED: λ > 530 nm; blue LED: λ > 445 nm, with light intensity of 2 mW).47

13.3.3 Carbon-doped titanium dioxide and its photocatalytic activity In addition to nitrogen-doped titania, carbon-doped titania has also attracted the attention of researchers. Asahi et al.24 predicted that other anions, such as C, S, and F, would possess a similar effect to nitrogen. In 2002, Khan et al.26 synthesized chemically modified TiO2−xCx by flame pyrolysis of a Ti metal sheet at 850°C in a natural gas flame with a controlled amount of oxygen. Irie et al.27 also prepared C-doped TiO2 by oxidative annealing of a TiC precursor in air/O2 at 600°C. Janus et al.48 pointed out that the photocatalytic ability of C-doped TiO2 could be improved by decreasing the recombination rate in a photogenerated electron–hole pair using electron scavenger carbon doped into TiO2. The nature of the carbon-induced modifications of the TiO2 electronic band structure remained unclear and the enhancement of photocatalytic activity was attributed either to the band gap narrowing or to the formation of a localized mid-gap state in the TiO2 band gap. In principle, any element could be doped into a discretionary matrix material by the aforementioned mechanochemical doping process. Greycolored carbon-doped titania was successfully and easily prepared by grinding TiO2 with ethanol and applying heat treatment.49 Anatase titania powder supplied by Wako Pure Chemical Industry (Osaka, Japan) was mixed with ethanol in 5% by mass and introduced into a planetary ball


318


NO decomposition rate (%)

50 40 30

(c) (d)

(c) (d) (b)

(b)

(c) (a)

20 10

(a)

(a) Raw (b) As prepared (c) 200°C (d) 400°C

(b)

(d)

(a)

0 > 510 nm

> 400 nm

> 290 nm

13.9 DeNOx activity of the carbon doped titania treated by postmechanochemical heating; (a) raw-TiO2, (b) without heating (as prepared product), heated at (c) 200°C and (d) 400°C for 1 hour in air. Adapted from Kang et al.49

mill with a partially stabilized zirconia pot and grinding was then carried out at 700 rpm for various periods of time, followed by heat treatment in air to remove impurities from the ground products. Figure 13.9 illustrates the NOx gas decomposition activity of carbon-doped titania. This result also confirmed that surface impurities on the as-prepared samples prevented optical irradiation of the surface of the TiO2 in a redox reaction. The best photocatalytic activity of the C-doped TiO2 in the visible irradiation region was achieved by grinding for 2 hours followed by heating in air at 200°C. It was confirmed that grinding TiO2 with ethanol caused the formation of Ti–C and C–O bonds in the ground product. Both the Ti–C and C–O bonds remained after heating at 200°C. Further heating the product at 400°C caused the dissociation of Ti–C bonds in the product, whilst the C–O bonds still remained. This result induced a decrease in photocatalytic activity of the product when heated at 400°C. Using adamantine (ADM) instead of ethanol as the carbon source also led to carbon doping in the titania lattice. Details will be given in Section 13.3.5.

13.3.4 Sulfur-doped titanium dioxide and its photocatalytic activity In general, it is particularly difficult to dope sulfur, which has a large ionic size, into the lattice of titania. It has been reported that sulfur-doped titania could be synthesized by heating TiO2 at a high temperature under a gas


Photocatalyst synthesis by mechanochemical doping

319

flow of NH3 and H2S. However, calcination of TiO2 under H2S gas flow does not give satisfactory results.50 Heating TiS2 in air has been proposed for preparing sulfur-doped TiO2; however, use of the expensive TiS2 precursor could not be avoided.28,29 Ohno et al.30 also prepared yellowish S-doped TiO2 by mixing titanium isopropoxide with thiourea and ethanol, followed by evaporation and calcination in air at 400–700°C. Zhang et al.51 provided the basic information for easy-to-perform sulfur doping of TiO2 by mechanochemical treatment, where an inexpensive sulfur sample could be used as the doping agent. Commercial titania powder supplied by Wako Pure Chemical Industry was mixed with 10 wt% sulfur and 2 g of the mixture were put in a zirconia pot (45 cm3 inner volume) with seven zirconia balls (15 mm in diameter) and subjected to grinding using a planetary ball mill at a rotation speed of 700 rpm in air for different periods of time. Because the sulfur element was easy to oxidize in high-temperature air, the ground samples were calcined at 673 K for 60 min in an argon flow. Figure 13.10 shows the S 2p X-ray photoelectron spectroscopy (XPS) spectra of the mixtures ground for 20 min and 120 min. The S 2p state has a broad peak because of the limited amounts of sulfur doped, as well as an overlap of the split sublevels, the 2p3/2 and 2p1/2 states, with separation of 1.2 eV by spin-orbit coupling.29,52,53 A distinct difference in the peak position was observed for spectra of two samples ground for different periods of time. The peak of the sample ground for 20 min was located at 165–163 eV, whereas that of the one

Absorbed SO2 120 min

20 min

172 170 168 166 164 162 160 158 Binding energy (eV)

13.10 XPS spectra of S 2p of the samples ground for 20 min and 120 min. Adapted from Zhang et al.51


320


ground for 120 min was positioned at 163–161 eV. The peak positioned at 169 eV was related to the absorbed SO2 molecules on the TiO2 surface,16,17 while the peak at 162 eV resulted from bonding between sulfur and titanium atoms, and sulfur itself usually exhibits a peak position at 164 eV. The S–S bond remained as the main component in the product ground for a short time (20 min). Prolonged mechanochemical treatment is crucial to ensure the formation of S–Ti bonds in the titania lattice.

13.3.5 Co-doping effect on titanium dioxide photocatalysis Instead of hexamethylenetetramine, (NH4)2CO3 (denoted as NHC) could also be used as a nitrogen source to prepare nitrogen-doped titania; while adamantine (denoted as ADM), which has the same basic structure as that of HMT, could be used as a carbon source to prepare carbon-doped titania samples, respectively.54 Figure 13.11 shows the N 1s and C 1s XPS spectra of P25 and the TiO2−xAy (A = N, C) products prepared by mechanochemical doping. No peaks for N–Ti and C–Ti bonding were observed in the commercial P25 powders, indicating that no nitrogen or carbon was doped in the P25 powders. The binding energy around 396 eV, which relates to the existence of N–Ti, was

(a)

(b) C 1s

C

N 1s

C–Ti

With HMT

N–N N–Ti N–C N–O

Intensity (a.u.)

Intensity (a.u.)

With HMT With ADM With NHC

P25

298

With ADM With NHC

P25

294 290 286 282 Binding energy (eV)

278

408 406 404 402 400 398 396 394 392 Binding energy (eV)

13.11 (a) C 1s, and (b) N 1s XPS spectra of P25, the commercial powder, and the powders prepared by the planetary ball milling of P25 with 10 wt% NHC, ADM and HMT, followed by calcination in air at 400°C. The measurement was carried out after Ar+ ion sputtering for 3 min. Adapted from Yin et al.54



321

confirmed in the TiO2−xNy samples prepared by using NHC and HMT, indicating that Ti–N bonds were actually formed in the lattice of the titania crystal during the mechanochemical treatment. It is known that the peak around 400 eV is related to the N–N, N–O or N–C bonds and the one around 402 eV is related to the N–H bonds.24,25 According to the integral intensity of the peaks around 396 and 400 eV, it was estimated that about 63% and 58% of the nitrogen atoms in the samples were actually incorporated into the TiO2 lattices (peak at 396 eV) by using HMT and (NH4)2CO3. It was also found that the binding energy around 282 eV, relating to the existence of C–Ti, was confirmed in the titania samples prepared using ADM and HMT. It is obvious that both nitrogen and carbon were actually co-doped in the lattice of the titania crystal during the mechanochemical treatment using HMT as a reaction reagent. Figure 13.12 shows the relationship between the wavelength of light irradiated and the photocatalytic ability for the oxidative destruction of nitrogen monoxide. The photocatalytic deNOx ability was calculated by Equation [13.14]: deNOx ability (%) = [(C − C0)/C0] × 100%

[13.14]

where C0 is the initial NOx concentration and C is the NOx concentration after photocatalytic reaction.

20 10 0

With ADM

Blank

30

Blank

With HMT

40

With HMT

(b) P25 P25-milled With NHC

(a)

P25 P25-milled With NHC With ADM

NO degradation ability (%)

50

>510 nm

>400 nm Wavelength (nm)

13.12 DeNOx ability of the titania powders prepared by a mechanochemical doping process using NHC, ADM and HMT as reaction reagents. Open dotted bars: as-prepared by mechanochemical doping; solid bars: calcined at 400°C for 1 hour. Diagonal lines: commercial titania P25. The photocatalytic activity is carried out under light irradiation of λ > 510 nm (a) and 400 nm (b). For comparison, the results of P25 before and after ball milling are also plotted. Adapted from Yin et al.54


322


The photocatalytic activity of P25 decreased by c. 10–20% after milling without any additive at 700 rpm. This may have been due to the introduction of crystal defects or the phase transformation from anatase to rutile. It is obvious that nitrogen or carbon-doped titania prepared with NHC and ADM possessed relatively higher photocatalytic activity than non-doped titania under visible light >510 nm. The powder prepared with HMT showed photocatalytic activity about twice as high as that prepared with NHC and ADM, that is nearly 37% of nitrogen monoxide could be continuously removed by the nitrogen/carbon co-doped titania prepared with a 10 wt% HMT mixture. The activity was c. 6–7 times higher than that of P25, estimated by taking the blank result into consideration. This result indicated that nitrogen and carbon co-doping had multiple effects on the improvement of visible light photocatalytic activity. Similar results were observed for a wavelength >400 nm, although the differences between the samples were not so clear. The nitrogen-doped amount is controlled by optimizing the reaction conditions.

13.3.6 Titanium dioxide-based binary composite photocatalyst It has been found that the photocatalytic activity of classical TiO2 in the purification of polluted effluents containing volatile organic compounds can be greatly improved using coupling semiconductors and oxides, such as WO3/SiC–TiO2, TiO2–V2O5,55 SnO/TiO2,56 WO3–TiO2, ZnO–TiO2,57–59 SiO2/TiO2.60 The results indicate that this combination can result in an enhancement of photocatalytic activity. The efficiency of the binary composite system strongly depends on its composition. The increase and synergy in photo-oxidation activity are related to retarding the electron– hole recombination process by an electron-trapping effect and to the modification of surface acidity compared to that of pure TiO2. In titania-based photocatalytic research, it is well known that commercial photocatalyst Degussa P25 shows excellent photocatalytic activity because of its mixed structure of anatase and rutile at the nano level. The rutile phase acts as a hole acceptor and the anatase phase operates as the electron acceptor, resulting in a long lifespan for the photoinduced electron and hole and leading to effective separation of the photoinduced electron–hole.61,62 In principle, similar to Degussa P25 titania, the visible-light-induced photocatalytic activity of titania could be improved by the addition of nitrogendoped titiania. Figure 13.13 shows the mechanism of the electron–hole separation in TiO2−xNy/TiO2 composition during visible light-irradiated photocatalysis. In the case of the commercial Degussa P25 titania sample, rutile TiO2 has 3.0 eV band gap energy, so its photoactivity under visible light is less sensi-


Photocatalyst synthesis by mechanochemical doping B

B– Light e–

323

e–

CB

CB

TiO2

Light e–

TiO2–xNx h+

h+ VB

A+

VB h+ A

13.13 Mechanism of electron-hole separation in TiO2−xNy /TiO2 composition during photocatalysis. Adapted from Kang et al.63

tive. Therefore, if a photocatalyst that is more sensitive to visible light replaces rutile, a photocatalyst that is more reactive to visible light may be obtained. Based on these results, it is reasonable to use nitrogen-doped TiO2 instead of the pure rutile phase. N-doped TiO2/anatase–TiO2 (TiO2−xNy/ TiO2) composites were prepared in ethanol with various weight ratios of TiO2−xNy/TiO2 (from 10 : 0 to 0 : 10) under relatively mild mechanochemical conditions. A 2.0 g sample was mixed with 30 ml ethanol and introduced into the mill pot with 40 g balls 5 mm in diameter, then the mechanochemical treatment was carried out at 200 rpm for 15 min. Finally, the residual solvent was removed by heating at around 80°C with magnetic stirring, followed by drying in an oven at 80°C for 12 hours.63,64 Figure 13.14 shows the acetaldehyde photodegradation ability of the TiO2−xNy/TiO2 composite samples under irradiation by black light at wavelength 352 nm. The CO2 concentration increased linearly with the light irradiation time. The commercial titania nanoparticles showed an obviously higher acetaldehyde photodestruction ability than those of TiO2−xNy under UV light irradiation. Furthermore, the acetaldehyde degradation activity of the composite samples was also higher than that expected by the additive property (dotted lines), that is the activity increased up to a mixture ratio of TiO2−xNy :TiO2 of 1 : 9–2 : 8. When the TiO2−xNy :TiO2 ratio = 2 : 8, the acetaldehyde decomposition activity of the composite was about 1.4 times higher than that of titania alone. In addition, the CO2 generation activity also increased up to TiO2−xNy :TiO2 = 1 : 9–2 : 8. These results also supported the idea that the photocatalytic activity of TiO2 was improved by mixing it with TiO2−xNy owing to the depression of electron-hole recombination by the heterogeneous transfer of photoinduced holes from TiO2 to TiO2−xNy.


324

High-energy ball milling (b) 8 7 6 5 4 3 2 0.0

0.2

0.4

0.6

0.8

TiO2–xNy content (wt%)

1.0

CO2 generation rate (ppm min–1)

CH3CHO decomposition rate (ppm min–1)

(a)

6 5 4 3 2 1 0 0.0

0.2

0.4

0.6

0.8

1.0

TiO2–xNy content (wt%)

13.14 Acetaldehyde photo degradations ability of TiO2−xNy/TiO2 composites under the irradiation by black light (light wavelength 352 nm). The influence of TiO2−xNy/TiO2 mix ratio on the acetaldehyde degradation rate (a), and CO2 generation rate (b) is shown. Adapted from Liu et al.64

13.3.7 Fluorine doping and multiple-element co-doped photocatalysts Besides titania powders, SrTiO3 is also an important titania-based photocatalyst matrix and widely studied by many researchers because it has a similar band structure to that of titania. It was found that nitrogen could be doped into the lattice of SrTiO3 by the same mechanochemical method as for nitrogen-doped titania.65 It was also found that not only nitrogen, but also other elements such as fluorine could be doped by the mechanochemical treatment method. Saito66 synthesized lanthanum oxyfluoride (LaOF) by using polytetrafluoroethylene (PTFE, [-CF2-]n), as the fluoride source. Benziada-Taibi et al.67 reported that SrF2 and LiF could be used as fluorine co-doping sources in SrTiO3 ceramics containing fluorine by a solid-state reaction process. Wang et al.40,41 successfully synthesized fluorine-doped SrTiO3 using polytetrafluoroethylene, SrF2 and LiF as doping fluorine sources during the mechanochemical treatment process. From the XPS spectra of the prepared fluorine-doped SrTiO3 sample and that of commercially available SrF2 (Fig. 13.15), it is clear that the peak at 684.1 eV in SrF2-doped SrTiO3 can be attributed to the doping state of fluorine being shifted to 0.8 eV lower energy compared to that of the starting material SrF2 (684.9 eV), indicating that chemical bonds between the titanium and fluorine in the lattice of SrTiO3 were formed. The fluorine-doped SrTiO3 showed higher photocatalytic activity compared with that before doping, although the doped SrTiO3 samples had lower activity than that of the titania samples.



325

(a) F-SrTiO3

(b) SrF2 675

680

685

690

695

Binding energy (eV)

13.15 XPS spectra of F1s of SrF2-doped SrTiO3 sample and commercially available SrF2 powder: (a) SrF2-doped SrTiO3, (b) pure SrF2. Adapted from Wang et al.40

As mentioned above, because of the narrowing of the band gap, nitrogendoped titania possessed excellent photocatalytic activity. However, replacing O2− with N3− would result in the formation of anion defects in the charge compensation and the anion defects would act as electron–hole recombination centres, which would limit improvement in the photocatalytic activity. It is expected that the charge compensation would be satisfied if O2− was replaced with N3− together with F−, without producing a large lattice strain. In a similar mechanochemical manner, SrTiO3 with nitrogen/fluorine codoping was successfully synthesized and showed higher photocatalytic activity than that synthesized by the heat treatment method.68

13.4

Future trends

Photocatalysis appears to be a promising technology which has various applications in environmental systems such as air and water purification. It can be demonstrated that an environmentally friendly, low-temperature mechanochemical process is effective for the synthesis of well-crystallized nanosize photocatalyst materials, which possess high UV and visible light activity. Besides nitrogen-doped titania, other anion-doped photocatalysts such as carbon, sulfur and fluorine were successfully prepared. Developments in the synthesis of highly active photocatalysts continue to be made. For example, a reformative complete low-temperature mechanochemical treatment method has been developed. In this process, a post-mechanochemical reaction washing process was applied instead of calcination treatment. Where soluble nitrogen reagents such as urea and/or (NH4)2CO3 were used, the effect was obvious. Compared with the samples treated with a post-mechanochemical reaction calcination process, the samples prepared by water-washing showed similar or higher deNOx activity (Fig. 13.16).


326


DeNOx ability (%)

60 50 40 30

(c) (d)

20 10

(f) (g)

(b) (a)

(e)

(h)

0 510 Wavelength (nm)

13.16 Effect of washing process on the photocatalytic activity of TiO2−xNy prepared by mechanochemical doping. (a) P25, (b) as-prepared by using urea, (c) calcined at 400°C for 60 min, (d) washed with distilled water followed by drying at 80°C, (e) as-prepared by using (NH4)2CO3, (f) calcined (e) at 400°C for 60 min, (g) washed with distilled water followed by drying at 80°C, (h) blank (without catalyst).

These results also indicated that nitrogen doping was carried out during the mechanochemical treatment but not caused by the post-mechanochemical reaction calcination. In principle, cation doping, anion/cation co-doping in titania, in other oxides and in other composites could be achieved by mechanochemical treatment. Some successful examples such as nitrogen-doped ZnO, nitrogen and lanthanum co-doped SrTiO3 have already been reported.69–71 The mechanochemical doping process combined with another low-temperature process, such as O2 plasma treatment, is also an effective way to remove intermediate or unreacted organic compounds and to produce the photocatalyst at room temperature.72 In addition to photocatalytic applications, other advanced functional materials are expected to be synthesized by the mechanochemical doping process.

13.5

Acknowledgement

The authors would like to acknowledge AAAS and Elsevier for permission to use material from their published sources.

13.6

References

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14 Soft mechanochemical synthesis of materials for lithium-ion batteries: principles and applications N. V. K O S O VA, Institute of Solid State Chemistry and Mechanochemical SB RAS, Russia

Abstract: A soft mechanochemical synthesis approach was applied to prepare some fine particulate lithium-containing compounds with a spinel (LiMn2−xMxO4, Li4Ti5O12), layered (LiNi1−x−yCoxMnyO2, LiV3O8) and framework structure (LiFePO4, Li2FeSiO4, LiTi2(PO4)3). It consists of the fast formation of amorphous or low-crystalline precursors during mechanical activation of LiOH (or Li2CO3) with corresponding anhydrous oxides of d-metals, solid hydroxides, crystal hydrates and acidic salts in highly energetic planetary mills and transformation of these precursors into nanostructured final products under ‘soft’ heating conditions (lower temperatures and shorter time of treatment) after removal of water molecules, hydroxide groups and other volatile compounds. Most of as-prepared materials show good electrochemical properties as cathodes, anodes or solid electrolytes for lithium-ion batteries. Key words: soft mechanochemical synthesis, materials for lithium-ion batteries.

14.1

Introduction: principles of soft mechanochemical synthesis of solid inorganic compounds

Recently, nanostructured materials have attracted a great deal of attention. They have noticeable advantages over micrometre-sized materials. For instance, the advantages of nanostructured active electrode materials used in lithium-ion batteries can be summarized as follows: •

a larger electrode/electrolyte contact area leads to higher charge/ discharge rates; • short path length for both electronic and Li-ion transport permits operation of materials even with low electronic or low Li-ion conductivity; • significantly reduced specific current density owing to very large surface area effectively stabilizes an electrode and preserves its capacity at high charge/discharge rates; • stability to large volume expansion/contraction conserves the integrity of the electrode and leads to stable cycle performance. 331 © Woodhead Publishing Limited, 2010

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As a rule, manufacturing nanomaterials requires more complex synthesis process, generally based on solutions, including metallorganics, and is accompanied by large amounts of waste products. Therefore, the development of new facile synthesis methods for large-scale production of such materials is highlighted. The idea of performing the reactions directly between solids, excluding the dissolution stage, has been always attractive. Mechanical activation (MA) is a promising solid state method for preparing highly dispersed materials. It is a time-saving, energy efficient, economically convenient, ecologically clean and capable to scale-up method providing reduction of material cost. MA of mixtures involves the dispersion of solids and their plastic deformation. These processes generate defects in solids, accelerate the migration of defects in the bulk, increase the number of contacts between particles and renew the contacts, providing chemical interaction between solids. MA taking place in highly energetic planetary mills allows final products to be obtained either directly at close to room temperature or after a short-time one-step thermal treatment of activated mixtures at moderate temperatures, thus increasing phase homogeneity and decreasing particle size. It was revealed that hydroxides are usually more reactive in solid state synthesis compared with anhydrous oxides. They yield only water as a byproduct, giving a much ‘cleaner’ decomposition in contrast to metallorganic precursors, such as acetates or citrates (Pechini process) which produce large amounts of volatile organics on pyrolysis. According to Avvakumov et al.,1 hydroxides along with other solids containing oxygen and hydrogen groups (solid acids, acidic and basic salts, crystal hydrates, etc.) appear to be more reactive in mechanochemical reactions owing to the high reactivity of their surface oxide/hydroxide groups in proton and electron transfer and bond formation. This type of acid–base reaction has been called ‘soft mechanochemical synthesis’. The acid–base reaction is realized when more than two types of M–O(H) bond with differing acid–base properties are brought into contact. When using hydrated compounds with a hardness three to four times lower than that of anhydrous oxides, the level of mechanical loading and contamination decreases. The method consists of fast formation of amorphous or low-crystalline precursors during MA and their transformation into nanostructured final products under ‘soft’ heating conditions (lower temperatures and shorter time of treatment) after removal of water molecules, hydroxide groups and other volatile compounds. The present short review contains recent experimental results on mechanochemical interactions of LiOH (or Li2CO3) with anhydrous oxides, hydroxides, crystal hydrates of d-metals and acidic salts revealing the formation of precursors after a short time MA (1–10 min). The final products of these reactions – complex oxides with layered, spinel and framework structured compounds with polyanions – were prepared after a short-time


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heat treatment (1–4 hours) at moderate temperature. The experiments were performed using AGO-2 planetary mills with stainless steel, titanium or corundum milling bodies (830 rpm). The results might be interesting for the scientists who have been developing new methods of preparation of cathode, anode and electrolyte materials for rechargeable lithium batteries.

14.2

Reactions of LiOH with anhydrous oxides

14.2.1 Synthesis of LiMn2O4 LiMn2O4 is an inexpensive and environmentally benign cathode material used for lithium-ion batteries with a practical capacity of about 120 mA h g−1 in the 4 V range. An important problem that prevents LiMn2O4 from wider use as a cathode is its unstable rechargeability, that is the amount of reversibly inserted lithium decreases gradually during cycling. At room temperature, LiMn2O4 has a cubic spinel-type structure, space group Fd3¯ m. The structure can be described as ideally consisting of closepacked arrangements of oxygen ions in 32e sites. Li+ ions occupy tetrahedral 8a sites, while Mn3+ and Mn4+ ions occupy octahedral 16d sites. The intercalation properties of LiMn2O4 have been widely studied.2,3 The extraction/ insertion of two lithium ions from/into the Li[Mn2]O4 spinel framework proceeds in two distinct steps. Lithium extraction/insertion from/into 8a tetrahedral sites occurs at around 4 V with maintenance of the initial cubic spinel symmetry, while that from/into the 16c octahedral sites occurs at around 3 V by a two-phase mechanism involving the cubic spinel Li[Mn2] O4 and the tetragonal lithiated spinel Li2[Mn2]O4. The cubic to tetragonal transition is due to Jahn–Teller distortion associated with Mn3+ (t2g3eg1) ions and is the origin of poor cycleability in the 3 V range. LiMn2O4 tends to exhibit capacity fade in the 4 V region as well, particularly at elevated temperatures (50°C). Several factors have been suggested to be the source of capacity fade, such as Jahn–Teller distortion occurring on the surface of the particles, manganese dissolution into the electrolyte, formation of two cubic phases, loss of crystallinity and the development of micro-strain during cycling. Electrochemical properties strongly depend on the method and conditions of synthesis, crystal and electronic structure, particle size, and so on. Soft mechanochemical synthesis of submicrometre LiMn2O4 was performed starting from LiOH and manganese oxides with different oxidation states of manganese ions (MnO2, Mn2O3, MnO).4,5 The interaction of lithium hydroxide with manganese oxides can be considered as acid–base reactions. According to Lewis classification, lithium hydroxide is a base whereas manganese oxides are acids with different strengths. Acid–base properties of


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14.1 X-ray patterns of activated mixtures of LiOH with different manganese oxides: (1) MnO, (2) Mn2O3, (3) MnO2. 䊉, LiMn2O4; 䉬, Mn2O3; 䉲, MnO; +, Mn3O4.

oxides significantly depend on the oxidation degree of the cation. The acidity increases along the series: MnO (2+) < Mn2O3 (3+) < MnO2 (4+). Reflections of LiOH are present in the background on X-ray diffraction (XRD) patterns of activated mixtures. No observable interaction occurs in the mixtures of LiOH with Mn2O3 or MnO (Fig. 14.1). The reflections of Mn2O3 remain practically unchanged after MA while a significant transformation of MnO to Mn3O4, an oxidation process, occurs. In contrast, MnO2 reacts almost completely forming cubic lithium–manganese spinel (probably, with a defective structure) after 10 min of MA without heating. The pattern can be indexed in the Fd3¯ m space group. The broadening of reflections is associated with reduced particle size and residual strain. On differential analysis (DTA) curves of the LiOH+MnO2 non-activated mixture, endothermic peaks corresponding to phase transitions of the reagents (TLiOH = 440°C, TMnO2 = 540°C) are present (Fig. 14.2). These effects practically disappear when the mixture was activated for 1 min. Moreover, on the DTA curve of the mixture activated for 10 min, a sharp exothermic peak at 485°C appears associated with crystallization of the final product, LiMn2O4. Thermogravimetric (TG) curves of activated mixtures have a



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14.2 DTA heating curves of initial (1) and activated mixtures of LiOH with MnO2 for 1 min (2) and 10 min (3).

sloping form. Mass loss, induced by elimination of gaseous products according to reaction [14.1] 4LiOH + 8MnO2 = 4LiMn2O4 + 2H2O + O2

[14.1]

becomes significantly lower than the theoretical one and is complete at a lower temperature (∼550°C) compared with a non-activated mixture. Solid state 7Li NMR (nuclear magnetic resonance) was used to study interaction in the LiOH+MnO2 mixtures activated by corundum milling bodies for 1–10 min. Strong shifts of 7Li lines to weaker magnetic fields appear in the NMR spectra, although no reflection of LiMn2O4 was observed in the X-ray patterns of these mixtures (Fig. 14.3). The value of the shift increases with the time of activation and does not coincide with that of the final paramagnetic crystalline product, LiMn2O4 (470 ppm).6 Such a shift was attributed to the appearance of paramagnetic Mn3+ and Mn4+ ions in the second coordination sphere of Li+ ions indicating the occurrence of intimate mixing of reagents (at the atomic level) and the beginning of spinel formation. According to photoelectron spectroscopy (XPS),6 the Li/Mn ratio on the surface of particles of the MnO2+LiOH mixture activated for 1 and 10 min is equal to 3.2 and 1.6, respectively, compared to 0.5 in the


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14.3 Li NMR spectra of the LiOH+MnO2 activated mixture. (—) 1 min MA, (—) 10 min MA, (---) spectrum of initial LiOH.

final spinel LiMn2O4, indicating that the surface layer of particles obtained is enriched with amorphous LiOH. As-prepared precursor accelerates the formation of crystalline LiMn2O4 with subsequent heat treatment. Spinels prepared at moderate temperatures (400–600°C) are characterized by high dispersion (secondary particles of about 50–100 nm) and a low cell parameter owing to increased numbers of Mn4+ ions in their structure. This results in high capacity and good structural stability of spinel when cycling in the 3 V range. As the temperature of heating increases to 750–800°C, the cell parameter of spinel increases to 8.24Å, indicating the average oxidation state of Mn ions to be +3.5, while particle size does not noticeably change. The electrochemical performance of these spinels at 4 V is similar to that of the ceramically prepared spinel.

14.2.2 Synthesis of LiNi0.5Mn1.5O4 Recently it has been shown that substitution of Mn ions for the other d-ions in LiMn2O4 results in the appearance of a 5 V plateau on the charge/ discharge curves. Among others, LiNi0.5Mn1.5O4 is of the most interest, since all nickel ions are in the 2+ oxidation state, while all manganese ions are in the 4+ state. Thus, a 5 V plateau is associated with the two-electron oxidation process Ni2+ → Ni4+, whereas Mn4+ ions remain electrochemically inactive. According to XRD, LiNi0.5Mn1.5O4 has a spinel-type structure (space group Fd3¯m) similar to LiMn2O4.7,8 However, its IR spectrum has a complex


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14.4 DTA and TG curves of initial (---) and activated (—) mixture of LiOH with NiO and MnO2.

form indicating a more ordered structure described by the P4332 space group.9 Preparation of LiNi0.5Mn1.5O4 with this crystal and electronic structure, high discharge capacity and cycling stability will require the development of new synthesis methods. Earlier, using solution (sol–gel and combustion) methods, it was shown that fine particles are preferable for better LiNi0.5Mn1.5O4 electrochemistry. In this study, high-dispersed LiNi0.5Mn1.5O4 was prepared using soft mechanochemical synthesis. Figure 14.4 shows DTA and TG curves of non-activated and mechanically activated mixtures of LiOH, NiO and MnO2. Removal of adsorbed water occurs below 400°C for both mixtures. The corresponding mass loss for an activated mixture in this region exceeds that for a non-activated one. However, it stops as the temperature increases; moreover, one can observe a small mass gain, probably associated with oxidation of some Mn3+ ions, which appears during MA. For a non-activated mixture, in contrast, mass loss continues up to 565°C. New reflections appear on the X-ray pattern of the mixture activated for 10 min, which were assigned to lithium-rich manganese spinel (e.g. Li4Mn5O12), similar to results described above for the LiOH+MnO2 activated mixture (Fig. 14.5). However, the reflections of NiO remain, become less intensive and slightly wider. The formation of lithiated NiO with a cell parameter close to NiO is not excluded. The final product, LiNi0.5Mn1.5O4, with a submicrometre particle size is formed after heat treatment of the precursor at 900°C via interaction of lithium–manganese spinel with NiO. It has been shown that the structural and electrochemical properties of LiNi0.5Mn1.5O4 used as 5 V cathode material strongly depend on the regime of subsequent heat treatment: cooling rate, gas atmosphere, and so on.


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LiNi0.5Mn1.5O4 NiO Li4Mn5O12

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14.5 X-ray patterns of the LiOH + NiO + MnO2 mixture activated for 10 min (1) and after heat treatment at 900°C (2).

14.2.3 Synthesis of Li4Ti5O12 Recently, the quest to find a substitute for the graphite anode has received much attention. Lithium–titanium oxide Li4Ti5O12 or Li1.33Ti1.67O4 is one of the best candidates. It is a partly inverse spinel with a Fd3¯m space group, in which Li+ ions occupy both tetrahedral 8a and octahedral 16d sites: LiTd[Ti5/3Li1/3]OhO4.10–12 Li4Ti5O12 has a working voltage of 1.5 V and shows no volume changes during intercalation/deintercalation of lithium ions (‘zero strain’ material) providing a significant structural stability at cycling. It has been shown that the theoretical capacity can be achieved using fine particulate material. Below, the results of soft mechanochemical synthesis of Li4Ti5O12 are presented.


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14.6 DTA and TG curves of initial (---) and activated (—) mixture of LiOH with TiO2.

Two endothermic peaks at 100 and 400°C are observed on DTA curves of non-activated mixture of LiOH with TiO2 (anatase). They are induced by removal of absorbed water and melting of LiOH, respectively (Fig. 14.6). In the case of a mixture activated for 10 min, the first peak becomes less intensive whereas the second one disappears evidencing the consumption of all LiOH below 400°C. Instead of a stepped mass loss (at 20–100°C, 100–350°C and 350–650°C) for the non-activated mixture, the TG curve of the activated mixture has a smooth form. Mass loss is already complete at ∼350°C. Its value considerably decreases, evidencing a significant degree of interaction, associated with water elimination during MA. According to X-ray data, MA of the LiOH and TiO2 mixture is accompanied by full and partial amorphization of LiOH and TiO2, respectively (Fig. 14.7). New reflections were assigned to monoclinic Li2TiO3 (space group C2/c). The final single-phase product, Li4Ti5O12, is formed after a short-time heating of as-prepared precursor at 800°C. Li4Ti5O12 anode material with enhanced properties was prepared after additional short-time grinding, especially in the presence of carbon as an electron-conductive additive, thus forming Li4Ti5O12/C composite material.13

14.2.4 Synthesis of Li1+xV3O8 Li1+xV3O8 has been widely studied as a promising 3 V cathode material because of its high discharge capacity (up to 250 mA h g−1), facile preparation and stability in air. Li1+xV3O8 is a bronze-type compound in which some of the V5+ ions are reduced to V4+. Li1+xV3O8 crystallizes in a monoclinic


340


TiO2, anatase TiO2, rutile Li2TiO3, cubic

3 ? 2 ? 1 20

30

40 50 2θ (degree)

60

70

14.7 X-ray patterns of the LiOH + TiO2 activated for 10 min (1) and subsequently heated at 400°C (2) and 800°C (3).

system (space group P21/m). The structure of Li1+xV3O8 consists of double and single zigzag octahedral strings arranged to provide interlayer sites (tetrahedral and octahedral) for Li ions. It is achieved by expanding the framework of vanadium polyhedrons.14–17 The synthesis conditions were shown to induce important differences in the reversible capacity and cycling behaviour of Li1+xV3O8. Enhanced electrochemical characteristics were observed for low-crystalline materials with increased specific surface area and expanded interlayer spacing which causes an increase in Li-ion mobility. In this study, LiOH and V2O5 were used as initial reagents to prepare Li1.07V3O8. Mechanical activation was carried out for 30 s to 10 min with corundum jars and balls in air.18,19 The thermal effects of phase transfor-


100

350

Exo

98 96 94

160

88

590

90

Endo

400

92

ΔT

335

Mass loss (%)

341

286


86 100

200


600

700

14.8 DTA and TG curves of the LiOH + V2O5 mixture activated for 10 min.

mations of reagents (TLiOH = 445°C, TV2O5 = 690°C) are absent on DTA curves of the LiOH + V2O5 mixture activated for 10 min (Fig. 14.8). Instead, an endothermic peak appears at 20–250°C accompanied by release of weakly bonded H2O and CO2. It transforms into a strong exothermic peak, associated with crystallization of the final product. The next endothermic effect at 590°C is due to melting of Li1+xV3O8. It is accompanied by mass gain (∼0.5 mass %) as a result of oxidation process of some of the V4+ ions. Figure 14.9 shows X-ray patterns of precursors formed after activation of the LiOH + V2O5 mixture for 30 s to 10 min and heat treated at 400°C. It is seen that the intensity of V2O5 reflections decreases if the milling time increases. Reflections of the initial LiOH are present in the background owing to its amorphization and weak scattering ability of Li atoms. One can see the appearance of new weak reflections assigned to lithium–vanadium bronzes after MA for only 1 min. After 10 min, the reflections of the final product, Li1+xV3O8, are present in the pattern, indicating that chemical interaction and crystallization occur at the early stage of MA. In infrared (IR) spectra of the LiOH + V2O5 activated mixtures, the intensity of absorption band at 1020 cm−1, corresponding to stretching vibrations of double vanadyl bonds ν (V苷O) in V2O5, decreases versus time of MA (Fig. 14.10). New bands characteristic of Li1+xV3O8 appear in the 900– 1000 cm−1 range. After heating the activated mixtures at 400°C, all reflections on the X-ray patterns belong to Li1+xV3O8. Note that only partial interaction occurs when


342


6

5

4

3

2

1 5

10

15 θ (degree)

20

25

14.9 X-ray patterns of the LiOH + V2O5 mixtures activated for 30 s (1), 1 min (2), 5 min (3), 10 min (4), 10 min followed by annealing to 400°C (5), 5 min followed by ageing for 6 months (6). 䊉, V2O5; 䉬, LiV3O8; 䉲, Li–V bronzes.

a non-activated mixture was heated to temperatures below the melting point of V2O5. Thus, MA of mild and basic LiOH with hard and acidic V2O5 results in fast deformation mixing of reagents at atomic level and chemical interaction caused by mechanical and chemical forces. LiOH probably also acts as a surfactant towards V2O5, accelerating its comminution. Surprisingly, X-ray patterns and IR spectra of the sample, activated for 5 min, significantly change after ageing the sample for 6 months at room temperature (without heating). X-ray reflections of V2O5 sharply decrease, while those of Li1+xV3O8 increase, evidencing the occurrence of chemical reactions


Soft mechanochemical synthesis for Li-ion batteries ν(V O) 950 995 920

995

595

745

6

Absorbance

545

740

545

νs(V O)

595

νas(V O)

343

5

3 1020

920 955

810

600

490

4

2

1

200

400

600

800

1000

Wavenumber (cm–1)

14.10 IR spectra of the LiOH + V2O5 mixtures activated for 30 s (1), 1 min (2), 5 min (3), 10 min (4), 10 min followed by annealing at 400°C (5), 5 min followed by ageing for 6 months (6).

by the relaxation of accumulated mechanical energy and diffusion processes in the solid state at room temperature (Fig. 14.9). Simultaneously, the intensity of the IR bands, corresponding to Li1+xV3O8, increases; a complex line in the 900–1050 cm−1 range become narrow; a clear maximum at 950 cm−1 with a shoulder at 970 cm−1 appears. The reduction process V5+ → V4+ during MA and ageing of activated mixture was confirmed by EPR spectroscopy.18 The final product Li1+xV3O8 was prepared by heat treatment of the precursor at 400–600°C. Its electrochemical capacity was about 300 mA h g−1 when discharging to 1.5 V; discharge curves have no distinct plateaus like ceramically prepared samples.


344


14.3

Reactions of LiOH with solid hydroxides

14.3.1 Synthesis of LiCoO2 LiCoO2 is the most suitable lithium intercalation material for today’s high density and long life lithium-ion batteries. However, it is also the most expensive. High-temperature fabrication processes result in significant costs in terms of energy usage. This has led many researchers to seek lower temperature fabrication routes, resulting in fine particulate material. LiCoO2 can be prepared in two modifications: a high-temperature (HT) and a low-temperature (LT) one.20–23 The structure of HT-LiCoO2 is related to the trigonal space group R-3m with oxygen anions occupying 6c sites and Li and Co ions occupying 3a and 3b octahedral sites, respectively. Li layers alternate with Co ones between layers of oxygen. LT-LiCoO2 is believed to adopt a spinel-like structure, consisting of a cubic close packed oxygen network with alternating cation layers with compositions 0.75 Co, 0.25 Li and 0.75 Li, 0.25 Co perpendicular to each of the cubic (111) directions. The space group is Fd3¯m; Li and Co ions are in 16c and 16d sites, respectively and O ions are in 32e sites. Unfortunately, only 50% of the theoretical capacity of Li1−xCoO2 could be practically utilized. This corresponds to a reversible extraction/insertion of 0.5 lithium ions per cobalt and a practical capacity of 120–140 mA h g−1. Capacity fade occurs at (1 − x) < 0.5. The limitation of practical capacity has been attributed to an ordering of lithium ions and consequent structural distortion around x = 0.5. LiCoO2 was prepared using preliminary MA of LiOH with Co(OH)2.24,25 The time of MA varied from 1 to 10 min. In reaction with LiOH, cobalt hydroxide exhibits its amphotheric (acidic) properties. Moreover, the synthesis of layered LiCoO2, using Co(OH)2, is more efficient compared with Co3O4 owing to the structural similarity of the initial hydroxide and final LiCoO2 and the large specific surface area of the hydroxide. Interaction of LiOH with Co(OH)2 to prepare LiCoO2 should be accompanied by oxidation of Co2+ to Co3+ ions. Therefore, additional oxygen is needed to provide reaction [14.2]: 4LiOH + 4Co(OH)2 + O2 = 4LiCoO2 + 6H2O.

[14.2]

TG–DTA data highlight an appreciable difference in the thermal behaviour of the activated and non-activated mixtures. Heating the non-activated LiOH+Co(OH)2 mixture is accompanied by three endothermic peaks: two peaks in the low-temperature region (below 300°C) and one peak at 400– 500°C. They were assigned: (i) to the removal of adsorbed water from LiOH in the course of the sample preparation; (ii) to the dehydration of the initial cobalt hydroxide; and (iii) to LiOH melting, respectively. In



345

contrast, the DTA curve of the activated mixture is less busy presenting a single endothermic peak at 50–200°C, associated with the removal of gaseous products. Thermal effects associated with the formation and crystallization of LiCoO2 were absent in both cases. Only broadened reflections of Co(OH)2 are observed on the X-ray patterns of activated mixtures, while the reflections of LiOH are absent, probably owing to its amorphization and weak scattering ability of Li ions (Fig. 14.11). Partial oxidation of Co(OH)2 with the formation of CoOOH occurs. In the IR spectrum of the LiOH + Co(OH)2 activated mixture, the intensity of the bands at 307 and 490 cm−1, corresponding to stretching vibrations of Co2+—O bonds in the Co2+O6 octahedra of the Co(OH)2 structure, as well as those of hydroxide groups of the initial reagents at 3630 and 3680 cm−1, sharply decreases (Fig. 14.12). New bands in the 500–700 cm−1 range, corresponding to stretching vibrations of Co3+—O bonds in the Co3+O6 octahedra appear, evidencing the beginning of LiCoO2 formation. Correspondingly, in electronic diffuse reflectance spectra (EDRS) of the LiOH + Co(OH)2 activated mixture, the overall absorption above 15000 cm−1 increases as a result of strong distortion of the Co(OH)2 structure (Fig. 14.13). A new band at 25000 cm−1, corresponding to low-spin [Co3+]Oh ions, appears, indicating partial oxidation of Co2+ to Co3+ followed by transformation of Co(OH)2 to CoOOH (but not to Co3O4). As-prepared precursors were subsequently annealed at 400°C, 600°C and 800°C for 1–4 hours in air. The annealing results in fast chemical interaction with the formation of homogeneous product, LiCoO2. The width of X-ray reflections decreases and their intensity increases with respect to the temp-

3 2

1 10

15

20 25 2θ (degree)

30

35

14.11 X-ray patterns of LiOH + Co(OH)2 mixtures activated for 1 min (2) and 10 min (3) compared with initial Co(OH)2 (1). 䊉, Co(OH)2; 䉬, CoOOH; 䊏, LiCoO2.



ν(CO32–)

ν(OH–)

865

575

346

3 3630

2

490

307

Absorbance

ν(Co2+ O6)

1 200

400

600

800

3200

3400

3600

3800

Wavenumber (cm–1)

14.12 IR spectra of the LiOH + Co(OH)2 mixture activated for 1 min (2) and 10 min (3) compared with initial Co(OH)2 (1).

25 20

F (R)

15 10 1 2 3

5 0 10000

20000

30000

40000

50000

Wavenumber (cm–1)

14.13 Diffuse reflectance spectra of LiOH + Co(OH)2 mixtures activated for 1 min (2) and 10 min (3) compared with initial Co(OH)2 (1). F(R) is the Kubelka–Munk function.

erature of heat treatment as a result of the processes of crystallization and particle growth. Splitting of 006 and 012 and 018 and 110 reflections, as well as the value of c/a ratio equal to 4.99, are evidence of the formation of HT-LiCoO2 even at 400°C. Note that annealing the non-activated mixture at 400°C leads to formation of the mixture of HT- and LT-LiCoO2. The electrochemical performance of LiCoO2 cathode material prepared using



347

MA and heat treatment at high temperatures is similar to materials prepared by the ceramic method, although its synthetic process is more facile, time- and energy-conserving.

14.2.2 Synthesis of LiNi1−x−yCoxMnyO2 Cathode materials based on solid solutions of LiNi1−yCoyO2 are less expensive than LiCoO2 and show a larger discharge capacity at 4 V. Their discharge curves have a sloping form. It has been found that Ni3+ ions are oxidized first on charging LixNi1−yCoyO2 (in the 0.85 < x < 1 range), while Co3+ ions are oxidized at a higher voltage. In the LiCoO2–LiNiO2 system, a continuous row of solid solutions is formed. Depending on the temperature of synthesis, they can adopt either a HT- or a LT-structure, similar to LiCoO2.26–28 Introduction of Mn in LiNi1−yCoyO2 was proposed to improve further the electrochemical and thermal stability. LiNi1−x−y CoxMnyO2 materials are viewed as candidates for large-scale batteries for electric vehicles. LiNi1−x−yCoxMnyO2 materials are usually considered to be solid solutions in the LiCoO2–LiNi0.5Mn1.5O2 system with Ni2+, Co3+ and Mn4+ ions.30,31 The synthesis conditions are important in determining the metal ordering in the LiNi1−yCoyO2 and LiNi1−x−yCoxMnyO2 layered structure and in the subsequent electrochemistry. Thus, these compounds are best formed by mixing Ni, Co and Mn salts in aqueous solution, precipitation by LiOH and corresponding firing. In this study MA was applied as an alternative to the solution method. Solid solutions of LiNi1−yCoyO2 (y = 0.2, 0.4, 0.6 and 0.8) were prepared by MA of mixtures of LiOH with double Ni1−yCoy-hydroxides.29 Figure 14.14 shows DTA and TG curves of activated and non-activated mixtures as well as of the double Ni0.8Co0.2-hydroxide alone. This hydroxide loses water in two steps accompanied by endothermic effects at 100°C and at 220–290°C (with minimum at 275°C) owing to removal of absorbed and structural water, respectively. When heated in a mixture with LiOH, the temperature of the latter effect decreases by ∼30°C in the initial mixture and by ∼80°C in the activated mixture. The TG curve of the activated mixture has a smoother form; mass loss is completed at lower temperature. The endothermic peak associated with melting of non-reacted LiOH (∼400°C) significantly decreases. A similar effect was observed for the mixtures of LiOH with Ni1−x−y CoxMny hydroxides. Triple hydroxides lose water in the 100–400°C temperature range accompanied by two endothermic effects at 100°C and 290°C and a stepped mass loss.32 In both non activated and activated mixtures, these effects shift by ∼20° to the lower temperature region, while the effect associated with LiOH melting disappears.


348

High-energy ball milling 2.0

1.0 197 245 275

90

0.5 0.0

80

–0.5

70

0

100

DSC (μV mg–1)

1.5

101

Mass loss (%)

100

–1.0 200

300

400

500

600

700

–1.5 800

Temperature (°C)

14.14 DTA and TG curves for initial (---) and activated (—) mixtures of LiOH with Ni0.8Co0.2(OH)2 compared with the double hydroxide (......).

Since the average oxidation state of d-ions in the final products is higher than in initial hydroxides, the process of LiNi1−yCoyO2 and LiNi1−x−yCox MnyO2 synthesis should be accompanied by oxidation of d-ions. However, we did not observe exothermic effects on the DTA curves associated with oxidation or with the crystallization of final products. It should be noted that the total mass loss for both mixtures is practically identical. The water eliminated in the course of dehydration of d-metal hydroxides, probably, enters intermediate products. According to X-ray analysis, formation of the final products is observed after heating these precursors to 400°C, however their crystallinity is poor (Fig. 14.15). Final crystallization occurs at 750°C for LiNi1−yCoyO2 and at 850°C for LiNi1−2yCoyMnyO2 independently of y.33 All as-prepared materials are defined as single-phase HT-modifications. They are characterized by a specific discharge capacity of 170 mA h g−1 for LiNi0.8Co0.2O2 and LiNi0.6Co0.2Mn0.2O2 and good rechargeability.

14.4

Reactions of LiOH and Li2CO3 with crystal hydrates and acidic salts

14.4.1 Synthesis of LiFePO4 Lithium metal phosphates are among the most promising cathode materials for high capacity lithium-ion batteries. Their promise is due to the ‘inductive effect’ of the PO4 polyanion, which elevates the M2+/M3+ redox couple by about 1.5–2 V. A redox potential of 3.45 V vs. Li/Li+ results in the case of LiFePO4, making it a particularly appealing material for hybrid energy


349

003


018 110 113

107

105

104

101 006, 102

Li2Ni8O10 [ASTM 23-362]

1 2 3 4 5 20

30

40 50 2θ (degree)

60

70

14.15 X-ray patterns of LiNi1−yCoyO2, prepared by annealing activated mixtures at 750°C: y = 0.2 (1), 0.4 (2), 0.6 (3) and 0.8 (4). Trace (5) is the LiOH + Ni0.8Co0.2(OH)2 mixture activated for 5 min and annealed at 400°C.

systems where cost and safety are of major concern. LiFePO4 adopts an olivine-type structure, built on an oxygen hexagonal packing in which Li+ and Fe2+ ions occupy half of the octahedral sites and P5+ ions occupy 1/8 of the tetrahedral sites (space group Pmnb). The peculiar distribution of Li+ and Fe2+ within the octahedral sites generates MO6 layers.34–36 Owing to the inherently low electronic conductivity of LiFePO4, it is essential to optimize its properties: to minimize the defect concentration and crystalline size (down to submicron level), control morphology, and so on. MA is one of the most convenient methods of preparing LiFePO4 with enhanced electrochemical performance. Four endothermic peaks at 108°C, 188°C, 223°C and 402°C are present on a DTA curve of non-activated mixture of LiOH with FeC2O4⋅2H2O and NH4H2PO4 heated in Ar atmosphere, associated with dehydration and decomposition of FeC2O4⋅2H2O and NH4H2PO4 and melting of LiOH, respectively (Fig. 14.16). The same peaks are observed for the mixture, activated in Ar for 5 min, however, the peak at 188°C is less intensive and the peak at 402°C practically disappears. A new low-intensive endothermic peak is present at ∼255°C. The TG curve adopts a smooth form. Whereas the crystallization of the final product in the non-activated mixture occurs at about 500°C followed by a low intensive exothermic peak, a distinct peak at 443°C is observed for the activated mixture. A decrease in the crystallization temperature of LiFePO4 is an important factor in preparing cathode material with a smaller grain size.37


350


The reflections of FeC2O4⋅2H2O and NH4H2PO4 on the X-ray pattern of the activated mixture become broader and less intensive, while the reflections of LiOH completely disappear (Fig. 14.17). New weak reflections assigned to Li3PO4 as an intermediate product are present. This indicates that the initial interaction occurs during MA according to Reaction [14.3]: NH4H2PO4 + 3LiOH → Li3PO4 + NH3 + 3H2O

[14.3]

Figure 14.18 shows the Mössbauer spectrum of the activated mixture. The experimental curve can be decomposed into two components: FeC2O4⋅2H2O and Fe3O4. This correlates with the scheme for thermal decomposition of FeC2O4⋅2H2O proposed by Hermanek:38 FeC2O4⋅2H2O → FeC2O4 + 2H2O (170–230°C)

[14.4]

3FeC2O4 → Fe3O4 + 4CO + 2CO2 (230–390°C)

[14.5]

3FeC2O4 + 2CO → Fe3C + 7CO2 (360–410°C)

[14.6]

Fe3C → 3Fe + C (410–530°C)

[14.7]

443

Accordingly, LiFePO4 is formed under subsequent heating via interaction of Li3PO4 with Fe3O4. Crystallization of LiFePO4 occurs after heat treatment of the activated mixture at 450°C. The crystallinity of the final product does not noticeably change up to 600°C, while its crystallinity increases sharply after heating to 700°C. According to Mössbauer spectroscopy, as the temperature increases, the amount of Fe3+ impurities in LiFePO4 decreases. The specific discharge capacity of as-prepared LiFePO4

110

3.0

100

2.0

402

70 ~255

50

20

1.0 0.5

188 223

40 30

1.5

185

108 127

60

79 105

Mass loss (%)

80

0.0

10 0

0

100

200

DSC (μV mg–1)

2.5

90

300

400

500

600

–0.5 700

Temperature (°C)

14.16 DTA and TG curves of initial (---) and activated (—) mixtures of LiOH with FeC2O4⋅2H2O and NH4H2PO4.



(112)

(131) (211) (140) (012) (221, 041)

(031)

(200)

(120) (101)

(020)

(011)

(111)

NH4H2PO4 [ASTM 37-1479] FeC2O4 2H2O [ASTM 23-293] Li3PO4 [ASTM 15-760]

351

6

5

4

3

2

1 15

20

25 30 2θ (degree)

35

40

14.17 X-ray patterns of activated mixture LiOH with FeC2O4⋅2H2O and NH4H2PO4 (1) and after heat treatment at different temperatures: (2) 450°C, (3) 500°C, (4) 550°C, (5) 600°C, (6) 700°C.

is about 125–130 mA h g−1, while that of mechanochemically prepared composite cathode of LiFePO4 with carbon as an electronic conductive agent is more than 150 mA h g−1.

14.4.2 Synthesis of Li2FeSiO4 In the on-going search for alternative cathode materials, the Li–Fe–Si–O system holds great promise since one can expect the same lattice stabilization effect (‘inductive effect’) as in LiFePO4 through the presence of strong Si–O bonds. The lower electronegativity of Si versus P will result in a lowering of the Fe3+/Fe2+ redox couple. Such materials should therefore have a lower electronic band gap and therefore a higher electronic conductivity. A


352

High-energy ball milling –10

–5

MA 5 min (Ar)

0

5

10

Experimental spectrum Fe2+ + Fe3+ Fe2+ Fe3+

Component

% Width Chemical Quadrupole shift splitting 1.768 FeC2O4•2H2O 58 0.299 1.187 31 0.383 0.530 0.264 Fe3O4 11 0.370 0.080 Fe

14.18 Mössbauer spectrum of the Li2CO3, FeC2O4⋅2H2O and NH4H2PO4 mixture activated for 5 min in Ar atmosphere and its decomposition.

material based on Fe and Si would also be potentially low cost in terms of raw material costs. Indeed, Fe- and Si-oxides represent >10% of the Earth’s crust. Iron orthosilicate Li2FeSiO4 has been reported to crystallize in the orthorhombic system with a Pmn21 space group, isostructural to Li3PO4. Li, Fe and Si atoms are tetrahedrally coordinated to four oxygen atoms.39–41 Reducing the particle size and optimizing its distribution will certainly improve the electrochemical performance of this cathode material. Compared with other methods, MA is very attractive in this case. Li2FeSiO4 is usually prepared starting from Li2SiO3 and FeC2O4⋅2H2O. We used a mixture of Li2CO3, SiO2⋅xH2O (silica gel) and FeC2O4⋅2H2O. Four endothermic peaks are present on DTA curves of a non-activated mixture heated in Ar atmosphere, associated with dehydration and decomposition of SiO2⋅xH2O and FeC2O4⋅2H2O (at 100°C, 195°C and 397°C), and melting of Li2CO3 (at 716°C) followed by three-step mass loss (in the RT– 200°C, 200–400°C and 400–720°C regions), while only two peaks are observed for the activated mixture (in the RT–150°C and 350–450°C regions) followed by two steps on the TG curves (in the RT–250°C and 250–500°C regions) (Fig. 14.19). The total mass loss for the activated mixture is slightly lower. According to X-ray analysis, amorphization of the initial reagents is observed after 2.5 min of MA. When as-prepared precursor was heated at 600°C for 4 hours, the synthesis was completed and crystallization of the final product occurred,



353

110 2.0

1.0

80

0.5

70

–0.5

195

60 50

0.0

0

200

DSC (μV mg–1)

716

352 397 433

90

1.5

102.5

Mass loss (%)

100

400

600

800

–1.0

Temperature (°C)

14.19 DTA curves of initial (---) and activated (—) mixtures of Li2CO3 with FeC2O4⋅2H2O and SiO2⋅0.1H2O.

while ≥20 hours were needed when low-energy ball milling is used. Thus, preliminary MA, resulting in intimate mixing and amorphization of reagents significantly accelerates formation of Li2FeSiO4 under further heating, keeping the small particle size.

14.4.3 Synthesis of LiTi2(PO4)3 Recently, high energy density and long life all solid state lithium-ion batteries using solid lithium-ion electrolytes have been requested. NASICONtype materials (isostructural with NaZr2(PO4)3) are good ionic conductors with negligible electronic conductivity and are stable in air. Among them, LiTi2(PO4)3 is one of the most promising electrolytes. The structure of LiTi2(PO4)3 (space group R-3c) consists of a three-dimensional network made up of TiO6 octahedra sharing all their corners with PO4 tetrahedra and vice versa to form so-called ‘lantern’ units, all oriented in the same direction (along the c-axis).42,43 It has been shown that conduction at grain boundaries is the rate determining step for the lithium-ion migration at room temperature and significantly depends on the method of synthesis, as well as on the nature and the number of dielectric impurities. In order to prepare LiTi2(PO4)3, a stoichiometric mixture of LiOH, TiO2 and NH4H2PO4 was initially preheated at 400°C to decompose NH4H2PO4. As-prepared precursor was then activated for 5 min with Ti milling bodies. Two endothermic peaks are present on the DTA curve of the non-activated mixture. They were assigned to decomposition of NH4H2PO4 (200°C) and to melting of LiOH (400°C) accompanied by mass loss up to 600°C (Fig. 14.20). In contrast, these peaks disappear on the DTA curves of the



100

1.5

95

92 ~104

90 85

1.0 0.5 0.0

80

–0.5 204

Mass loss (%)

2.0

403

105

75 70

0

100

200

DSC (μV mg–1)

354

–1.0 300

400

500

600

700

800

–1.5

Temperature (°C)

14.20 DTA and TG curves of initial (---) and activated (—) LiOH + TiO2 + NH4H2PO4 mixture.

activated precursor; mass loss significantly decreases indicating the occurrence of the reaction. Figure 14.21 shows X-ray patterns of the preheated mixture and the products of its activation and heat treatment at 800°C. When heat treated at 400°C, the reflections of LiOH disappear, while the reflections of TiO2 become less intensive and broaden out. Besides, the reflections of a new phase – TiP2O7 – are present as a result of interaction of TiO2 with NH4H2PO4. After MA of the preheated mixture, the reflections of the final product – LiTi2(PO4)3 – appear. It crystallizes during annealing at elevated temperatures (800–1000°C). While TiP2O7 is the main impurity for ceramically prepared LiTi2(PO4)3, only tiny amounts of TiO2 were observed for that prepared using MA.44,45 Thus, as-prepared ceramic and MA samples of LiTi2(PO4)3 are different in nature and in the number of dielectric admixtures they form. It has been shown that lithium ionic conductivity of mechanochemically prepared LiTi2(PO4)3 is characterized by a significant reduction in grain boundary resistance compared with the ceramically prepared sample, while the bulk conductivity remains unchanged.

14.5

Conclusions

The peculiarities of soft mechanochemical reactions in mixtures of LiOH (or Li2CO3) with anhydrous oxides of d-metals (MnO, Mn2O3, MnO2, NiO, TiO2, V2O5), solid hydroxides (Co(OH)2, Ni1−x−yCoxMny(OH)2), crystal hydrates (FeC2O4⋅2H2O) and acidic salts (NH4H2PO4) can be summarized as follows.



355

LiTi2(PO4)3 TiO2, anatase TiP2O7

3

2

1 20

30

40

50

60

2θ (degree)

14.21 X-ray patterns of the LiOH + TiO2 + NH4H2PO4 mixture preheated at 400°C (1), activated (2) and heated at 800°C (3).

1. All mechanochemical reactions are characterized by fast formation of amorphous or low-crystalline nanostructured precursors. These precursors are shown to consist of intimately mixed mechano(nano)composites of LiOH with another component. In the presence of the other component fast and almost complete amorphization of composites of LiOH (or Li2CO3) occurs. The structure of solid hydroxides, crystal hydrates and acidic salts being activated in the mixtures with LiOH (or Li2CO3) undergo significant distortion followed by a decrease in the dehydration and decomposition temperature. 2. Highly reactive precursors accelerate the formation of low-crystalline final (LiMn2O4 in the LiOH + MnO2 mixture; LiV3O8 in the LiOH + V2O5 mixture) or intermediate (e.g. Li3PO4 in the LiOH + FeC2O4⋅2H2O + NH4H2PO4 mixture; Li2TiO3 in the LiOH + TiO2 mixture) products


356


during MA. Moreover, in some cases (e.g. LiOH + V2O5), the accumulated mechanical energy relaxes in chemical energy with formation of the product even during aging at room temperature due to fast diffusion processes. 3. Fast chemical interactions in the above mixtures are provided by intimate mixing of reagents and high reactivity of surface functional groups, notably, OH groups. They can be considered as acid–base reactions. Although most metal oxides absorb water molecules at their surface, replacing anhydrous oxides by hydroxides or crystal hydrates results in much higher OH density per surface area. The bond energy of Me–O and O–H is a measure of the acidity of the OH-group. The acid–base reaction is realized when more than two types of Me–O(H) bonds with differing acid–base properties are brought into contact. Thus, the efficiency of chemical interaction in mixtures of LiOH with d-metal compounds depends on their acidic properties. It is evident that the highest output might be expected in mixtures exhibiting a maximum difference in the acid–base properties of the compounds. The strength of solid acids and bases can be characterized by proton affinity (PA). Paukschtis46 has developed a method to determine PA based on IR spectroscopy of adsorbed molecules. In general, the changes in the acidity of OH groups on the oxide surface follow the regularities governed by the Periodic law: the higher the position occupied by an element in the Mendeleev’ periodic table (for each group), the higher is the proton donor ability of the surface. For each period, the acidity of groups increases with the element number. Acidic properties of d-metal oxides significantly increase with the degree of oxidation of the cation. Indeed, the highest acidity of MnO2, compared to MnO and Mn2O3, results in its noticeable efficiency in reaction with LiOH during MA leading to the formation of a low-crystalline final product, lithium– manganese spinel. On the other hand, when LiOH is activated with TiO2, the Li4Ti5O12 spinel is not formed because of the lower acidity of TiO2. The acidity of V2O5 is comparable with that of MnO2; therefore MA of V2O5 with LiOH results in the formation of LiV3O8 with a monoclinic structure. Thus, acid–base properties of reagents are more significant in soft mechenochemical reactions than the structure of the final product. 4. Crystalline nanostructured and homogeneous Li-containing final products are formed via transformation of as-obtained amorphous or lowcrystalline precursors under ‘soft’ heating conditions (lower temperatures and a shorter treatment time) after removal of water molecules, hydroxide groups and other volatile compounds. These groups inhibit the growth of particles under subsequent heat treatment of precursors. Therefore, grain growth is less significant than in conventional solid state synthesis.



357

5. All Li-containing compounds obtained by the reactions described above show good electrochemical properties as cathode, anode or solid electrolyte materials for lithium-ion batteries. In addition, as an energysaving fabrication route, soft mechanochemical synthesis results in a significant reduction of material cost.

14.6

Future trends

This short review reveals the principles of ‘soft mechanochemical synthesis’, generally based on the acid–base properties of the reagents. The method can be widely used for the synthesis of different functional inorganic materials. Making a choice of reagents and tuning conditions of MA one can vary the particle size and morphology, crystal and electronic structure, transport properties and, as a result, functional properties of the asprepared materials. In any case, this method has noticeable advantages over other methods of preparing high-dispersed materials, including simplicity and accessibility and should find successful industrial application in the field of materials science in the near future.

14.7

Acknowledgements

The author would like to thank E. Devyatkina, I. Asanov, S. Kozlova, S. Gabuda, V. Anufrienko, V. Kaichev, A. Slobodyuk, A. Titov, N. Uvarov, A. Stepanov and A. Buzlukov for their contribution to this study.

14.8

References

1. avvakumov e, senna m and kosova n (2001), Soft Mechanochemical Synthesis. A Basics for New Chemical Technologies, Kluwer, Dordrecht. 2. tarascon jm and guyomard d (1991), ‘Li Metal-free rechargeable batteries based on Li1+xMn2O4 cathodes (0 ≤ x ≤ 1)’, J. Electrochem. Soc., 138, 2864–8. 3. thackeray mm, de kock a, rossouw mh, liles d, bittihn r and hoge d (1992), ‘Spinel electrodes from the Li–Mn–O system for rechargeable lithium battery applications’, J. Electrochem. Soc., 139, 363–6. 4. kosova nv, uvarov nf, devyatkina et and avvakumov eg (2000), ‘Mechanochemical synthesis of LiMn2O4 cathode material for lithium batteries’, Solid State Ionics, 135, 107–14. 5. kosova nv, devyatkina et and kozlova sg (2001), ‘Mechanochemical way for preparation of disordered lithium-manganese spinel compounds’, J. Power Sources, 97–8, 406–11. 6. kosova nv, asanov ip, devyatkina et and avvakumov eg (1999), ‘State of manganese atoms during the mechanochemical synthesis of LiMn2O4’, J. Solid State Chem., 146, 184–8. 7. ohzuku t, takeda s and iwanaga m (1999), ‘Solid-state potentials for Li[Me1/2Mn3/2]O4 (Me: 3d-transition metal) having spinel-framework structures:


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26. rougier a, saadoune i, gravereau p, willmann p and delmas c (1996), ‘Effect of cobalt substitution on cationic distribution in LiNi1−yCoyO2 electrode materials’, Solid State Ionics, 90, 83–90. 27. delmas c, menetrier m, croguennec l, saadoune i, rougier a, poillerie c, prado g, grune m and fournes l (1999), ‘An overview of the Li(Ni,M)O2 systems: synthesis, structures and properties’, Electrochim. Acta., 45, 243–53. 28. zhecheva e and stoyanova r (1993), ‘Stabilization of the layered crystal structure of LiNiO2 by Co-substitution’, Solid State Ionics, 66, 143–9. 29. kosova nv, devyatkina et and slobodyuk ab (2008), ‘Structure and electrochemical properties of LiNi1−yCoyO2 solid solutions, prepared using mechanical activation’, Chem. Sustainable Development, 17, 141–9. 30. yabuuchi n and ohzuku t (2003), ‘Novel lithium insertion material of LiCo1/3Ni1/3Mn1/3O2 for advanced lithium-ion batteries’, J. Power Sources, 119–21, 171–4. 31. koyama y, makimura y, tanaka i, adachi h and ohzuku t (2004), ‘Systematic research on insertion materials based on superlattice models in a phase triangle of LiCoO2–LiNiO2–LiMnO2. I. First-principles calculation on electronic and crystal structures, phase stability and new LiNi1/2Mn1/2O2 material’, J. Electrochem. Soc., 151, A1499–A1506. 32. kosova nv, devyatkina et and kaichev vv (2007), ‘Mixed layered Ni–Co–Mn hydroxides: crystal structure, electronic state of ions, and thermal decomposition’, J. Power Sources, 174, 735–40. 33. kosova nv, devyatkina et and kaichev vv (2007), ‘Optimization of Ni2+/Ni3+ ratio in layered Li(Ni,Mn,Co)O2 cathodes for better electrochemistry’, J. Power Sources, 174, 965–9. 34. padhi k, nanjundaswamy ks and goodenough jb (1997), ‘Phospho-olivins as positive-electrode materials for rechargeable lithium batteries’, J. Electrochem. Soc., 144, 1188–94. 35. andersson as and thomas jo (2001), ‘The source of first-cycle capacity loss in LiFePO4’, J. Power Sources, 97–8, 498–502. 36. yamada a, chung sc and hinokuma k (2001), ‘Optimized LiFePO4 for lithium battery cathodes’, J. Electrochem Soc., 148, A224–A229. 37. kosova nv and devyatkina et (2004), ‘On mechanochemical preparation of materials with enhanced characteristics for lithium batteries’, Solid State Ionics, 172, 181–4. 38. hermanek m, zboril r, mashlan m, machala l and schneeweiss o (2006), ‘Thermal behaviour of iron(II) oxalate dihydrate in the atmosphere of its conversion gases’, J. Mater. Chem., 16, 1273–80. 39. nytén a, abouimrane a, armand m, gustafsson t and thomas jo (2005), ‘Electrochemical performance of Li2FeSiO4 as a new Li-battery cathode material’, Electrochem. Comm., 7, 156–60. 40. nytén a, kamali s, häggström l, gustafsson t and thomas jo (2006), ‘The lithium extraction/insertion mechanism in Li2FeSiO4’, J. Mater. Chem., 16, 2266–72. 41. zaghib k, salah aa, ravet n, mauger a, gendron f and julian c (2006), ‘Structural, magnetic and electrochemical properties of lithium iron orthosilicate’, J. Power Sources, 160, 1381–6. 42. aono h, sugimoto e, sadaoka y, imanaka n and adachi g (1989), ‘Ionic conductivity of the lithium titanium phosphate (Li1+xMxTi2−x(PO4)3, M = Al, Sc, Y, and La) systems’, J. Electrochem. Soc., 136, 590–1.


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15 Materials for lithium-ion batteries by mechanochemical methods L. C. YA N G, Q. T. Q U, Y. S H I, and Y. P. W U, Fudan University, China; and T. VA N R E E, University of Venda, South Africa

Abstract: Lithium-ion batteries have many advantages over traditional rechargeable batteries and their development has been very rapid. In this chapter, preparation and electrochemical performance of their key materials including cathode materials such as LiCoO2 and LiMn2O4, anode materials such as carbon, alloys and nitrides, and electrolytes such as oxides and sulfides by mechanochemical (MC) methods are primarily summarized. Compared with conventional solid state reactions at high temperature, the MC methods appear to accelerate and simplify the synthesis process and decrease the energy expenses as well as the cost of the material. In addition, the prepared materials present good electrochemical performance. When MC methods are combined with other techniques, their advantages can be more fully displayed. In the meanwhile, MC reactions will have some unfavourable actions to some materials which should be avoided. Finally, some further aplications for MC methods in lithium-ion batteries are pointed out. Key words: mechanochemical method, lithium-ion battery, anode, cathode, electrolyte, electrochemical performance, capacity, cycling behaviour.

15.1

Introduction

After several decades of research and development, lithium-ion batteries came into use in the late 1980s and early 1990s (Wu et al., 2004). Since then their development has been very rapid owing to their evident advantages over traditional rechargeable batteries: • • • • • • • •

high output voltage (average 3.6–3.7 V or 3.2–3.3 V) and power high energy density (>180 Wh kg−1) low self discharge (1000 times) high rate capability (1 C) high coulomb efficiency (near 100% after the 1st cycle) easy measurement of the residual capacity 361 © Woodhead Publishing Limited, 2010

362 • • •


maintenance free no environmental pollution (green battery) wide working temperature range (−25 to +45°C, extended to −40 to 70°C).

Lithium-ion batteries have now become the major power sources for mobile electronics such as cellular phones, portable computers, digital cameras/videos and portable multimedia players. As competition in the market increases, lithium-ion batteries are required to have low cost and high performance, properties which are known to be dependent on the materials in the batteries including cathodes, anodes and electrolytes. Recently, many methods for preparing materials for lithium-ion batteries have been widely explored, for example incorporation of heteroatoms (Wu et al., 2002a), composite technology (Ning et al., 2004), soft chemistry routes (Manthiram and Kim, 1999) and some non-classical methods such as template methods, pulsed laser deposition, plasma-enhanced chemical vapour deposition, radio-frequency magnetron sputtering (Ning et al., 2004) and sol–gel methods (Fu et al., 2005). Several mechanochemical (MC) methods have also been tried. A MC method is one that can achieve its goal via chemical reactions in the solid state by various mechanical methods, mainly including grinding and milling such as ball milling, colloidal milling and jet milling. During milling or grinding, the mechanical energy is transferred to the particles of the reactants, causing many changes to the particles such as deformation, friction, fracture, amorphization, quenching and so on. After grinding or milling, a product phase(s) at the interfaces of the reactant particles is (are) formed. The main advantage of the MC method is its simplicity in the synthesis process, effective mixing accompanying a breaking of chemical bonds and their recombination, and a decrease in energy expenses as well as the cost of the materials (Ning et al., 2004). As a result, MC methods show some promise in the preparation of materials with low cost and good performance in lithium-ion batteries.

15.2

Lithium-ion batteries

15.2.1 The principle of lithium-ion batteries Originally, rechargeable batteries were found to function based on pure redox reactions. Later, rechargeable batteries were based on doping and undoping performance with a gain and loss of electrons (Novak et al., 1997, Wu et al., 2002b). Lithium-ion batteries are based on intercalation and deintercalation of lithium ions accompanying gain and loss of electrons or redox behaviour with the reaction shown in Equations [15.1]–[15.3], which is schematically shown in Fig. 15.1 (Wu et al., 2004).


Materials for lithium-ion batteries by mechanochemical methods

363

Li+/e Discharge Li+/e Charge

: Li

: C

: O

: Co

: Li

15.1 Principle of lithium-ion batteries. Adapted from Wu et al. (2002b).

During the charge process, lithium ions deintercalate from the cathode which is oxidized after losing electrons. The lithium ions deintercalated from the cathode pass through the electrolyte and intercalate into the anode. In this process, the anode gains electrons and is reduced. Prior to intercalation of lithium ions into the anode, a solid electrolyte interface (SEI) should be formed via the reduction of the electrolytes so that the anode will be stable upon contact with organic electrolytes. During the discharge process, the reverse happens. Lithium ions deintercalate from the anode which is oxidized after losing electrons. The deintercalated lithium ions from the anode pass through the electrolyte and then intercalate into the cathode. In this process, the cathode gains electrons and is reduced. Since the intercalation compounds for the anode are much less reactive than lithium metal, lithium-ion batteries present stable cycling performance and satisfactory safety. The reactions of the electrodes are: Discharge Cathode: LinMyXz X Lin−xMyXz + xLi+ + xe−

[15.1]

Charge Discharge +

Anode: A + xLi + xe− X LixA

[15.2]

Charge Discharge Total reaction: A + LinMyXz X Lin−xMyXz + LixA Charge


[15.3]

364


15.2.2 Requirements for materials In lithium-ion batteries, cathode, anode and electrolyte are three key components (Wu et al., 2004). As they perform various roles they must be manufactured from different materials in order to meet different requirements. In order to obtain a high output voltage, the intercalation compounds for the cathode should meet the following requirements: • • • • • • • •

to have a high redox potential for the intercalation of Li+ in the intercalation compound LixMyXz, providing a high output voltage; to have a large value of x for the reversible intercalation and deintercalation of Li+ in the intercalation compound Lin−xMyXz so that high reversible capacity can be achieved; to show little or no change in the host structure of [MyXz] during the repeated intercalation and deintercalation of Li+ so that the best cycling behaviour can be obtained; to show little or no change in the redox potential with varying x so that charge and discharge voltages remain stable; to have good electronic (σe) and ionic (σLi+) conductivities for LinMyXz so that the overpotential is small and the rate capability at large current density remains satisfactory; to have a high chemical stability for LinMyXz during the total charge and discharge process and no reaction between LinMyXz and the electrolyte; to have a large diffusion coefficient of Li+ in LinMyXz would be favourable for rapid charge and discharge; the manufacturing process for LinMyXz should be easily realized, at low cost and presenting no unfavourable environmental effects.

In the case of the anode materials, the requirements, almost similar to those for the cathode materials, are as follows: • • • • •

a low redox potential for the intercalation of Li+ in the intercalation compound LixA, providing a high output voltage; a large x value for the reversible intercalation and deintercalation of Li+ in the intercalation compound LixA so that high reversible capacity can be achieved; little or no change in the host structure of [A] during the repeated intercalation and deintercalation of Li+ so that optimum cycling behaviour can be obtained; little or no change in the redox potential with varying x, so that charge and discharge voltages will remain stable; good electronic (σe) and ionic (σLi+) conductivities for LixA so that the overpotential is small and the rate capability at large current density is satisfactory;


Materials for lithium-ion batteries by mechanochemical methods • • • •

365

a good surface structure so that an excellent solid–electrolyte interface (SEI) film can be formed during the initial charge process; a high chemical stability for LixA during the total charge and discharge process and no reaction between LixA and electrolyte after the formation of the SEI film; a large diffusion coefficient of Li+ in the host [A] so that the LixA complex can favour rapid charge and discharge; the manufacturing process for A should be easily realized, at low cost and with no unfavourable environmental effects.

As far as the electrolyte state is concerned, liquid electrolyte, gel electrolyte and solid electrolyte are possible. For application in lithium-ion batteries, the ideal solid electrolyte should have the following properties: • • • •

a high ionic conductivity (σLi+) especially at room temperature and low electronic conductivity (σe) to avoid or reduce self discharge; a stable phase structure even during the charge and discharge processes; recrystallization should be prevented especially in the case of glassy solid electrolytes; high chemical stability during the total charge and discharge process and no redox reaction upon contact with Li metal and electrode materials; good electrochemical stability and a wide electrochemical window above 4.2 V.

15.2.3 Materials for cathode, anode and electrolyte From the above requirements, it can be seen that powdered materials like layered LiCoO2 and LiNiO2, spinel LiMn2O4 and olivine LiFePO4 can be good cathode materials. Anode materials include carbon materials, alloybased materials including silicon, tin and antimony, and nitrides. There are mainly two kinds of solid electrolyte: solid polymer electrolyte and solid inorganic electrolyte (e.g. oxides- and sulfides-based electrolyte). Usually, most of the above-mentioned materials are prepared via high temperature heat treatment, which requires high energy consumption. Using MC methods, however, they can be prepared at room temperature, which makes them promising for practical applications.

15.3

Mechanochemical preparation of cathode materials

15.3.1 Lithium cobalt oxides (LiCoO2) As early as 1987, it was reported that a layered phase LiCoO2 was achieved using MC methods by ball milling mixtures of lithium and cobalt hydroxides


366


(Fernandez-Rodriguez et al., 1987). However, since the mobility of lithium is increased by mechanical activation, spinel Co3O4, which is not favourable, will appear after an extension of the milling time. During the ball milling process, Co(OH)2 decomposes at first into CoOOH and then reacts with LiOH to form LiCoO2 (Jeong and Lee, 2001). Consequently, CoOOH and LiOH can be used to prepare LiCoO2 with a cubic spinel-related structure by ball milling for a shorter time (Kosova et al., 2002). However, the LiCoO2 prepared by the mechanical activation is characterized by high dispersion, structural disorder and different electronic states of the transition metal ions. MC treatment can be used to decrease the heat treatment temperature required to achieve the desired crystal structure and to shorten the heat treatment time (Jeong and Lee, 2002). If the ratio of ball to powder weight is increased, the MC reaction will be promoted owing to the increased number of collisions and greater collision energy per particle. In order to improve the safety and electrochemical performance of LiCoO2, an inert layer is coated on the surface of LiCoO2 particles so as to decrease their contact with the electrolyte. As a result, dissolution of Co4+ will be prevented (Li et al., 2006a). The most simple, economical and convenient way to coat LiCoO2 particles is by mechanical milling. In the case of 1.0 wt% silica-coated LiCoO2, the silica species can partially diffuse into the bulk and form a solid solution LiSiyCo1−yO2+0.5y on the surface, which is evident from the diminished lattice parameter c upon coating (Fey et al., 2004). In addition, other kinds of nano oxides such as Al2O3, TiO2, Li4Ti5O12, ZrO2, or their mixed oxide ZrTiO4 can also be coated on the surface of LiCoO2 by mechanical milling (Fey et al., 2005, 2006, 2007). For example, in the case of an Al2O3 coating derived from methoxyethoxy acetate-alumoxane (MEA-alumoxane) by a MC process followed by calcination at 723 K in air for 10 hours, a thin layer forms on the surface of the core material with an average thickness of 20 nm, which can prevent direct contact of LiCoO2 with electrolytes (Fey et al., 2006). This process is summarized in Table 15.1 and it is clear that MC methods provide a good method of preparing good quality LiCoO2 material with less energy consumption.

15.3.2 Spinel lithium manganese oxides (LiMn2O4) There are several kinds of lithium manganese oxides (Wu et al., 2004). Spinel LiMn2O4 is the most widely used in the application of lithium-ion batteries. MC methods can be used to synthesize highly dispersed LiMn2O4 spinel starting from different manganese oxides (MnO2, Mn2O3, MnO) and lithium compounds (Li2O, LiOH, LiOH⋅H2O, Li2CO3) (Ning et al.,



Milling/40 hours

Ball milling + 600°C/2 hours Milling + 600°C/4 hours Milling Ball milling + 850°C/24 hours Ball milling

LiOH + Co(OH)2

LiOH⋅H2O + Co(OH)2

LiCoO2 + silica, TiO2 and ZrO2

HT-LiCoO2

Li2O + CoO LiOH⋅H2O + Co(OH)2

Milling

Milling/10 hours

LiOH + Co(OH)2

LiOH + Co(OH)2(CoOOH)

Process

Raw materials

LiCoO2 + disordered LixM1−xO Coated LiCoO2

Disordered, dispersed HT-LiCoO2 Spinel LiCoO2 HT-LiCoO2

–

HT-LiCoO2 + spinel Co3O4 LiCoO2

Excellent

Poor

Poor Good

Intermediate

–

–

Electrochemical performance

HT-LiCoO2

Structure

Table 15.1 Some LiCoO2 materials prepared by mechanochemical processes

Fey et al., 2004, 2005, 2006, 2007

Obrovac et al., 1998

You et al., 1998 Jeong and Lee, 2002

Kosova et al., 2002

Fernandez-Rodriguez et al., 1987 Fernandez-Rodriguez et al., 1987 Jeong and Lee, 2001

References

368


2004). On the one hand, the oxidation state of manganese greatly influences the kinetics of MC reactions, for example, MnO2 reacts almost completely with Li2CO3 to produce LiMn2O4. However, there is no evident interaction between Mn2O3 or MnO with Li2CO3. On the other hand, different crystal structures and mechanical properties of the initial lithium compounds result in different mechanisms of MC action on the activated mixtures. LiOH has a layered structure and exhibits good plasticity; the chemical interaction during MC processing between MnO2 and LiOH is preceded by a stage of molecular-dense aggregates (mechanocomposites) formation through the action of adhesive forces and thus the surface of the mechanocomposite particle is covered by an amorphous LiOH layer. In the case of Li2CO3, which is a typical ionic compound but more brittle, the chemical interaction is preceded by a process of brittle fracture of the components of MnO2 and Li2CO3 (Kosova et al., 2000). A longer milling time results in amorphization and further decomposition of the spinel LiMn2O4 into Mn2O3 and Li–Mn–O (Soiron et al., 2001). The spinel LiMn2O4 resulting from ball milling the mixture of Li2O and MnO2 is highly disordered, with nanocrystalline sizes of less than 25 nm, and has much strain variance or defects (Choi et al., 2001; Soiron et al., 2001). The existence of the highly disordered structure could accommodate the Jahn–Teller distortion, which comes from the transition of Mn4+ into Mn3+ in the spinel structure during Li+ intercalation around the 3 V region (Choi et al., 2001). In addition, Li-doped LixMn2O4 (x > 1) spinels can also be prepared by MC activation since doping lithium can further improve the cycling performance of this cathode material (Kosova et al., 2000). The composition and lattice constants of the final products are affected by the lithium content. The intergrain resistance rather than the bulk properties of the spinels, including the starting reagents and molding pressure, determines their conductivity. The activation energy of conductivity (Ea) of LixMn2O4 does not depend on x over a wide composition range (0.21 ≤ x ≤ 1.21) and is 0.36 ± 0.04 eV (Kosova et al., 2000). Instead, Li doping increases the valence of Mn above 3.5, which will be good way of inhibiting the Jahn–Teller distortion. When micrometre LiMn2O4 powder is ball milled, the particles are broken into nano particles. On further milling, the nano particles stick back together again as hard agglomerates and many nanocrystallites (20–40 nm) are generated within a large crystallite by the action of defects such as dislocation and strain at the grain boundaries. Partial oxidation of manganese ions also occurs during ball milling for less than 120 min (Kang et al., 2001). Of course, the Jahn–Teller effect associated with the spinel structure still exists during lithium deintercalation and intercalation.



369

Table 15.2 Some LiMn2O4 materials prepared by mechanochemical processes

Raw materials

Process

LiOH (LiOH⋅H2O, Li2CO3) + MnO2 LiOH + Mn2O3 (MnO) Li2O + MnO2

Milling

LiMn2O4 from solid state reaction LiMn2O4 + carbon

Ball milling

Milling Grinding

Ball milling

Features of structure


Nanocrystalline LiMn2O4 Disordered LiMn2O4 Disordered nano spinel LiMn2O4 with strain or defects Nanodomains, strains, defects Nanocomposite of LiMn2O4 with carbon

4 V, good – 3 V, 4 V plateaus, good cycling

References Kosova et al., 2000 Kosova et al., 2000 Choi et al., 2001; Soiron et al., 2001

3 V, good cycling

Kang et al., 2001

High reversible capacity of 200 mAh g−1, excellent cycling

Im and Manthiram, 2003

However, the net deformation of a particle consisting of small grains is less anisotropic than a particle with large grains and the possibility of particle fracture caused by the tetragonal distortion will be lower. In addition, the strain from the tetragonal distortion is expected to be accommodated by the already existing strain in the particles. Some selected results are summarized in Table 15.2 and it is clear that MC methods provide an easy way of preparing nanocrystalline LiMn2O4 with good accommodation of strains.

15.3.3 Other kinds of cathode materials Reports on the preparation of LiNiO2 using MC methods are rare (Obrovac et al., 1998). However, the mixing of primary materials such as Ni(OH)2 and Li2CO3 usually utilizes MC methods like ball milling (Wu et al., 2002a). The surface stability with electrolytes can be improved by coating, for example, LiNi0.8Co0.2O2 can be coated with ZrO2 by simple grinding (Lee et al., 2006). Layered LiNi1/3Co1/3Mn1/3O2 presents better safety performance and higher reversible capacity than LiCoO2, and has become another popular cathode material after LiCoO2. It can be prepared by ball milling, which favours solid state metathesis reactions. For example, in the case of the mixture of LiAc⋅2H2O, Ni(Ac)2⋅4H2O, Co(Ac)2⋅4H2O, Mn(Ac)2⋅4H2O (Ac = acetate) and excess H2C2O4⋅2H2O without any solvent, after ball-milling and a fol-


370


lowing heat treatment, layered LiNi1/3Co1/3Mn1/3O2 is prepared (He et al., 2007a). Of course, F can be doped by adding LiF during this process to obtain layered LiNi1/3Co1/3Mn1/3O2−zFz (0 ≤ z ≤ 0.12) cathode material. The primary particle size of LiNi1/3Co1/3Mn1/3O2−zFz gradually increases with the fluorine content (He et al., 2007b) so that a better cycling performance is expected. Olivine LiFePO4 has an advantage over other cathode materials since sources of iron raw materials in the Earth are very rich. Its preparation requires heat treatment in an inert atmosphere to ensure that the iron exists in the 2+ form. Its preparation by ball milling alone has not been reported since the primary material usually exists in the ferric (+3) state. Consequently, ball milling of FePO4 and Li3PO4 is combined with heat treatment, for example microwave heating. In addition, during the preparation process, the addition of conductive carbon as a coating after the heat treatment is necessary since the electronic conductivity of LiFePO4 is very low. The existence of Fe2P after heat treatment enhances the electronic conductivity of the LiFePO4/C composite. Of course, when the amount of Fe2P is too high, it blocks the one-dimensional pathways for Li+ in LiFePO4 and might hinder Li+ movement in LiFePO4 (Song et al., 2008). Other cathode materials, such as LiMnO2, can also be prepared by ball milling a mixture of transition metal and lithium oxides; short-range ordering of cations such as Li+ and Mn3+ in the crystal structure still occurs even after extended milling (Obrovac et al., 1998). When lithium manganese oxide (LixMnOz) is ball milled with conductive carbon, nanocomposite powder particles in which the components are intimately mixed on a nanometer level are prepared. Although nanostructured oxide particles may be intrinsically prone to poor electronic conductivity arising from high grain boundary areas and side surface reactions arising from the high surface area, results show that ball milling with carbon is an effective and simple way to avoid these problems owing to the presence of conductive carbon (Im and Manthiram, 2003). Layered LiNi0.5Mn0.5O2, another promising cathode material, can also be produced by ball milling LiOH, NiO and MnO2 (Xia et al., 2008a). LiMnPO4 and Li3Fe2−2xTixMnx(PO4)3 (NASICON-type structure) can be separately treated by ball milling to reduce the particle size (Drezen et al., 2007; Ning et al., 2004; Sun et al., 2009). For example, as shown in Fig. 15.2, the particle size of Li3Fe2−2xTixMnx(PO4)3 can be reduced from 10–20 μm to 100–500 nm by ball milling at a rotation speed of 220 rpm for 10 hours (Sun et al., 2009). In addition, conductive carbon can be further introduced by ball milling with acetylene carbon at a rotation speed of 220 rpm for 10 hours to increase the electrical conductivity of the powders (Sun et al., 2009).


Materials for lithium-ion batteries by mechanochemical methods (a)

371

(b)

10 μm

100 nm

15.2 Scanning electron micrographs of (a) Li3Fe1.8Ti0.1Mn0.1(PO4)3 and (b) ball milled Li3Fe1.8Ti0.1Mn0.1(PO4)3/carbon mixture (reprinted from Sun et al., 2009 with permission from Elsevier BV).

15.3.5 Electrochemical performance of cathode materials produced using mechanochemical methods As mentioned above, after ball milling there are distortions and defects in the crystal lattice, so that the prepared LiCoO2 powder does not give a good electrochemical performance. Only in combination with subsequent firing or heat treatment at 850°C, will a well-ordered LiCoO2 achieving good electrochemical performance be obtained. When LiCoO2 particles are coated, the reactivity of Co4+ with liquid electrolytes is reduced. As a result, the cycling behaviour is greatly improved (Li et al., 2006a). For example, the cycling life of LiCoO2 with a coating level of 1.0 wt% Al2O3 was improved three and nine times, respectively, for two different commercial LiCoO2 samples (Fey et al., 2004). Impedance spectra of the coated cathode powder suggest that the surface coating on LiCoO2 reduces changes in the surface film during electrochemical cycling, resulting in a longer cycle life. The results are complemented by slow scan cyclic voltammetric profiles, which show that the alumina nano coatings lead to a suppression of the cycle-limiting phase transitions from hexagonal to monoclinic to hexagonal (Fey et al., 2006, 2007), which is due to slower impedance growth and increased resistance to Co dissolution into the electrolyte during the (de)intercalation processes. The above-mentioned coating technology is also effective for LiNiO2. For example, ZrO2 coating on the LiNi0.8Co0.2O2 cathode improves its cycling stability considerably owing to the suppression of the impedance growth during charge–discharge cycling (Lee et al., 2006). Milling time influences the charge and discharge curves of LiMn2O4 since mechanical energy input during milling is comparable to treatment at high temperature, which will influence its crystal structure. After an intermediate milling time of about 8 hours, the resultant LiMn2O4 spinel powder shows the charge and discharge curves typical of spinel LiMn2O4 prepared by solid


372


state reaction at 800°C for 1 hour, that is plateaus at 3 V and 4 V (Soiron et al., 2001). Milling can produce highly disordered structures, which can alleviate the Jahn–Teller distortion around the 3 V region that always exists during lithium deintercalation and intercalation. The intercalation of Li+ takes place with an initial capacity of up to 167 mAh g−1 in the 2.5–4.3 V range with a steady slope instead of two plateaus at around 3 V and 4 V in spinel structure. In addition, the cycling behaviour is much improved compared to the well-ordered crystalline LiMn2O4 powders (Kang et al., 2001; Choi et al., 2001). As shown in Fig. 15.3, in a 50-cycle test at 0.5 mA cm−2, a sample ball milled for 1 hour gives a constant capacity of 122 mAh g−1 between 2.4–3.4 V versus lithium and the cycling behaviour at elevated temperatures is also satisfactory. In addition, polarization during cycling is also greatly decreased (Choi et al., 2001). In the case of nano LiMn2O4 powder obtained from ball milling, excellent capacity retention in the 3 V range at room temperature has been achieved. The main reason for this capacity retention is that the net deformation of a particle with small crystallites is less anisotropic than deformation with the large ones and there is less possibility of fracture of particles caused by the tetragonal distortion. In addition, the strain imposed by the formation of the tetragonal phase can be accommodated by the already existing strain in particles. Incidentally, ball milling provides intimate mixing that improves the electrical contact between spinel particles and carbon (Kang et al., 2001).

(b)

180

Capacity (mAh g–1)

Capacity (mAh g–1)

(a)

150 120 90 Cut-off voltage: 2.4–3.4V Current density: 0.5 mA cm–2

60 0

10

20 30 40 Cycle number

175 150 125 100

Room temperature 60°C 80°C

75 50

50

0

10

20 30 40 Cycle number

50

15.3 (a) Effects of ball-milling time on cycling behaviour of LiMn2O4; 䊊, n = 5 h; 䊉, n = 15 h; ⵧ, n = 30 h; 䊏, n = 60 h; 䉭, n = 120 h. (b) Cycling behaviour of one LiMn2O4 sample after 1 h milling at different temperatures; 䊉: room temperature; 䉭, 60°C; 䊊, 80°C – both with a voltage range of 2.4–3.4 V and a current density of 0.5 mA cm−2 (reprinted from Kang et al., 2001 with permission from the American Chemical Society).



373

Good electrochemical performance is provided by LiMnO2 obtained by ball milling (Obrovac et al., 1998). The nanocomposite particles obtained by ball milling of nanostructured lithium manganese oxide (LixMnOz) with acetylene black exhibit high capacity of over 200 mAh g−1 with excellent cyclability and charge efficiency, which are attributed to increased electronic conductivity and decreased surface area (Im and Manthiram, 2003). Layered LiNi0.5Mn0.5O2 obtained from ball milling can present a reversible capacity of 120 mAh g−1 over the range of 2.5–4.3 V (versus Li+/Li) (Xia et al., 2008a). The electrochemical performance of LiNi1/3Co1/3Mn1/3O2 obtained by ball milling is excellent. A steady discharge capacity of about 140 mAh g−1 after 100 cycles at a rate of 1 C (160 mA g−1) in the voltage range 3–4.5 V (versus Li+/Li) is achieved and the capacity retention is about 87% at the 350th cycle (He et al., 2007a). When F is doped in the ball milling process, the fluorine-substituted LiNi1/3Co1/3Mn1/3O2−zFz (0 ≤ z ≤ 0.12) presents a lower initial discharge capacity. In the case of a small amount of fluorinesubstituted LiNi1/3Co1/3Mn1/3O2−zFz (z = 0.04 and 0.08), this material exhibits excellent cycling and better rate capability compared with fluorine-free LiNi1/3Co1/3Mn1/3O2 (He et al., 2007b). LiFePO4/C composite with Fe2P below a critical concentration provides a very high discharge capacity of 165 mAh g−1, excellent rate capability (85.4% of C/50-rate discharge capacity at 2C) and stable capacity retention for 250 cycles. Above the critical concentration, the electrochemical performance deteriorates. In order to obtain a LiFePO4/C composite with good electrochemical performance, the amount of Fe2P should be carefully controlled (Song et al., 2008). After ball milling the initial LiMnPO4 powder, reversible capacities of 156 mAh g−1 at C/100 and 134 mAh g−1 at C/10 have been obtained, which are 92% and 79% of the theoretical values, respectively. At higher charging rates, the electrochemical performance is also improved since the particle size of LiMnPO4 is reduced compared to that without ball-milling (Drezen et al., 2007). Improved cycling behaviour is achieved if LiMnPO4 powder particles are coated by carbon via the milling process (Sun et al., 2009). In summary, compared with conventional solid state reactions at high temperature, MC methods appear to accelerate and simplify the synthesis process and decrease the energy expenses as well as the cost of the final product. Consequently, based on the latest developments in the technology to prepare cathode materials, further improvements can be expected. Obviously, when combined with some other methods such as high temperature heat treatment and adding a solvent such as water during milling (Kakuda et al., 2007), different cathode materials with even better electrochemical performance will become available (Ning et al., 2004).


374


15.4

Mechanochemical preparation of anode materials

Various kinds of anode materials such as carbonaceous and alloy-based powders have become available (Wu et al., 2002a). Some have been prepared or modified by MC methods and these present some interesting changes and properties.

15.4.1 Carbonaceous materials Carbonaceous materials were the first available and major anode materials to come on the market. Since the highest reversible capacity of graphite is 372 mAh g−1, many methods have been tried to break through this limit, for example doping with heteroatoms (Wu et al., 2002a). Recently, it was found that milling or grinding was a good way to modify the electrochemical performance of carbon materials. The structure changes of carbonaceous materials are dependent on the ball milling period and mode. These changes mainly include the following aspects as shown in Table 15.3: particle size, surface area, surface structure, electronic self-spinning of radicals, microstructure such as defects and nanocavities or voids – and crystal structure. The effects of milling and grinding mainly on the structure and electrochemical performance of graphite are shown in Table 15.3. During milling, the graphite particle size will change. In general, bondbreaking of graphene layers leads to smaller particles (Disma et al., 1996). For example, after 150 hours ball milling, well-graphitized graphite is pulverized into small particles with a size of about 50 nm. Owing to the large surface energy, the merging of single particles is favoured and results in the formation of agglomerates with an average size of about 1 μm. In the case of impact or shock type ball milling, interactions vertical to the graphite cleavage planes are so strong that graphite particles are torn into pieces of disordered carbons. Although jet milling and turbo milling are soft and mild techniques, they also cut graphite particles into smaller ones in directions both perpendicular and parallel to the basal planes (Wang et al., 1999). Since the graphite particle size becomes smaller during milling, the specific surface area of the material increases with milling, although the degree depends on the milling mode (Disma et al., 1996; Natarajan et al., 2001). The surface structure especially the composition of surface groups is greatly changed. Different ambient atmospheres, for example air, high purity argon, nitrogen, and CO2 produce different effects. The active surface sites formed by milling react readily with active gases or vapours, for example O2, CO2 and H2O, to produce oxygen-containing highly reactive surface groups (Aurbach et al., 2002). Reactive milling can be used to develop bonding between carbon and lithium atoms and to form a lithiated surface which decreases the irreversible capacity of carbon in the first cycle.



Torn into pieces of disordered carbon

Impact/shock-type mechanical milling/ grinding

Cut into smaller particles

Particle

Nano agglomerates

Drastic, strong

Soft, mild

Type of milling action

Ball milling

Jet- and turbo-milling

Mechanochemical methods

Increase

Increase

Increase

Specific surface area

O-terminated carbon

Surface structure

Localized spins, smaller g-value

Localized spins, larger g-value

Radicals

Large ratio of disorder such as vacancies, microcavities, and voids

Microstructure

Changes in structure parameters

Increase or little change in d002, and decrease in content of hexagonal phase Decrease in La and Lc

Little change in d002, decrease in Lc

Crystal structure

Increased reversible capacity mainly associated with the charge slope >1.0 V, increase in irreversible capacity, capacity fading

Decrease in irreversible capacity, increase in coulomb efficiency under optimal conditions Increase in reversible capacity and coulomb efficiency, improved cycling


Disma et al., 1996, Wang et al., 1999, SalverDisma et al., 1997, 1999

Natarajan et al., 2001

Wang et al., 1999, SalverDisma et al., 1997

References

Table 15.3 Selected results of the effects of mechanochemical reactions on structure and electrochemical performance of graphite


Decrease in particle size

Increase

Oxygencontaining groups

Slight increase

O2, CO2, H2O

Reactive atmosphere

Jet milling

Lithiated surface

Increase

Graphite + lithium

Reactive milling

O-terminated carbon

No evident change

Shear force

Surface structure

Shear-type grinding

Particle

Specific surface area

Type of milling action Radicals

Disorder present

Less disorder or disorganization such as vacancies, microcavities

Microstructure

Changes in structure parameters

Mechanochemical methods

Table 15.3 Continued

Increase in rhombohedral (3R) phase

Little change in d002 and crystal size

Little change in crystal size and d002

Crystal structure

Spontaneous formation of surface passivating film, high reversible capacity, lower hysteresis Loose surface passivating film, exfoliation of graphite, capacity fading, slight increase of reversible capacity High initial capacity

Increase in reversible and irreversible capacity


Herstedt et al., 2003

Aurbach et al., 2002

Tossici et al., 2003

Salver-Disma et al., 1997, 1999

References


377

ESR spectra of natural graphite derived powder vary with grinding methods. The line width which is due to conduction electron spins broadens for all ball milled specimens except for those ground by a ball mill down to 1 μm diameter. The contribution of localized spins produced in the mechanical grinding process becomes predominant over that of conduction electron spins in the range of T < 50 K (Salver-Disma et al., 1997). On the other hand, the absorption intensity of ball milled material satisfies the Curie law. Samples ground by jet milling have larger g-values compared with those prepared by ball and colloidal milling (Ning et al., 2004). However, for each grinding mode, the change is totally independent of the nature of the precursors used (graphite, mesocarbon microbead, coke) and/or its morphology (layers, microbeads or fibres) (Salver-Disma et al., 1997). The microstructure is also affected by the MC treatment. For example, shock-type mechanical milling generates a large ratio of disorder within the powder and small stacks of 2–3 parallel fringes of less than 1 nm are formed. These disordered domains are misoriented and distributed at random to form mesopores and no single layer is observed. Shear-type grinding generates a weaker mechanical strain than the shock mode and the carbon material is much less damaged, with fewer defects in the directions both perpendicular and parallel to the basal planes (Wang et al., 1999). Depending on the type of grinding, energetic interactions of different intensity are generated resulting in disorder or disorganization of the carbonaceous materials (Disma et al., 1996; Natarajan et al., 2001; Salver-Disma et al., 1999), observed by transmission electron microscopy (Salver-Disma et al., 1999). In addition, many vacancies, microcavities (or voids) and metastable carbon interstitial phases with sizes around 1.3 nm are formed among the agglomerated particles. Different atmospheric conditions also result in different microstructures. For example, in the case of a planetary mill where the deformation forces are mainly shear in nature, mechanically induced oxidation on the surface, probably along the edges of the graphene planes, suppresses the fracture rate and preserves the crystallinity of natural graphite milled in oxygen (Ning et al., 2004). Generally, after milling, the crystal structure of carbonaceous materials will be changed in the same way as it is after MC treatment and this is mainly reflected in disordering of the structure, changes in the interlayer distance d002, and the content of crystal phases (Wu et al., 2002a; Disma et al., 1996; Wang et al., 1999; Natarajan et al., 2001). The interlayer distance d002 usually increases with milling time owing to the introduction of voids and vacancies. However, in the case of mild milling such as turbo and jet milling, little change in d002 of the milled carbons is observed owing to the less destructive effect on graphite particles (Wang et al., 1999). The graphite lattices become thinner owing to expansion of graphite layer interspacing (Disma et al., 1996). As a result, the content of the hexagonal phase


378


decreases and that of the rhombohedral phase (3R) increases (Wu et al., 2002a). However, there is a conflicting report that the rhombohedral phase fraction decreases with the milling time and then stabilizes at about 10% (Natarajan et al., 2001). Perhaps this depends on the species of graphite used. Similarly, in the case of other kinds of carbons such as non-graphitic carbon, the milling affects the particle size distribution, BET specific surface area, interlayer distance and other structural characteristics (Ning et al., 2004).

15.4.2 Alloy-based anode materials The first alloy-based powders for anode materials were produced by ball milling in the late 1970s. However, the problem associated with the growth of dendrite, which can easily lead to short circuit of the batteries, has not been completely overcome. As a result, alloy-based materials gave way to graphitic carbons in the early 1990s (Wu et al., 2002b). Recently, however, it was found that introduction of a conductive or inactive agent as a buffer could lead to an improvement in electrochemical performance of alloybased anodes. Consequently, the focus has again moved to novel alloybased anode materials, which mainly include tin-based, silicon-based and antimony-based alloy anode materials. Some selected results are summarized in Table 15.4. In the case of pure tin, since it can form alloys with Li up to Li22Sn4, the volume change can be up to 376%, resulting in serious cracking or crumbling of Li–Sn alloys and rapid capacity fading (Wu et al., 2002b). As a result, some buffering components, such as Li2O, conductive metals or graphite should be added to prevent or buffer the drastic volume change. Composites consisting of Sn and Li2O clusters can be prepared directly by ball milling tin and Li2O (Ning et al., 2004) or SnO and lithium metal as precursors (Wang et al., 2008b). In these clusters, tin particles are uniformly distributed within a lithium oxide matrix with the majority size of the tin particles in the order of 100 nm or less, which can be seen clearly from the transmission electron micrograph shown in Fig. 15.4. Besides Li2O, Al2O3 can also be used as a matrix. Finely dispersed tin alloy/oxide composites have been synthesized via the reduction of SnO by aluminium employing high-energy ball milling (Al powder and Co or Ni powder as precursors in a molar ratio of SnO :Al : Co = 1 : 0.878 : 0.333 or SnO :Al : Ni = 1 : 0.878 : 0.75). During milling process, the following reactions take place: 3SnO + 2Al → 3Sn + Al2O3

[15.4]

3Sn + Co → Sn3Co

[15.5]

4Sn + 3Ni → Sn4Ni3

[15.6]



Ni3Sn4 Composite such as C0.9Sn0.1 or C0.8Sn0.2 SnMn3C

Sn31Co28C41 Sn3Co/Al2O3 Ag4Sn coated graphite Si Si/Li4SiO4 + Li2O

Mixture of SiO and graphite Si + Si3N4

Si core + amorphous carbon

Sn + Ni Sn + graphite

Sn + Co + C SnO + Co + Al Sn + Ag + graphite

SiO + graphite

Si + C

Si + Si3N4

SiBr4 + Mg SiO + Li

Sn + Mn + C

Cu6Sn5 Mg2Sn

Sn/Li2O

SnO + Li

Sn + Cu Sn + Mg

Composition

Precursors

Nano sized Monoclinic Li4SiO4 + nano Si Decrease in crystal size of graphite Nano crystal or amorphous Si Core-shell

Crystal Sn + amorphous Li2O Hexagonal structure Cubic + orthorhombic phase Nanocrystalline Amorphous graphite + nanocrystalline Sn Perovskite, nano particles Crystal Nano crystal of Sn3Co Amorphous graphite

Structure

Good

Good

>320 1000

Good

Fair to good Good

Good Good Fair to good

Good

Good Good

Improved but fair Good Good

Cycling

696

1375 770

500 540 >600

150

125–200 400–600

200 460

>500

Reversible capacity (mAh g−1)


Table 15.4 Selected results of alloy-based anode materials prepared by mechanochemical methods

Liu et al., 2004b

Zhang et al., 2007b

Doh et al., 2008

Sandu et al., 2007 Yang et al., 2007

Hassoun et al., 2007 Zheng et al., 2007a Wang et al., 2008a

Beaulieu et al., 2000

Lee et al., 2002 Wang et al., 2001

Xia et al., 2001 Kim et al., 2001

Wang et al., 2008a

References


Co + Sb Zn4Sb3 + graphite

β-Zn4Sb3

Si + Sn + graphite

Fe80Si20 + graphite Si + Ni + graphite

Si + graphite

Si + copper(II) D-gluconate Si + Ni (Fe)

Si + TiN

85C–15[Si0.66Sn0.34] composite ZnSb + unknown structure CoSb3 Composite

Composite such as C0.8Si0.2 Composite Si/C alloy

NiSi (FeSi)

Si + Cu3Si + Carbon

Composite of Si and PPy

SiAg

Si + Ag

Si + PPy

Composition

Precursors

Table 15.4 Continued

Fine powder, 500 Increased to 566

Good Excellent

Satisfactory

Poor

Good

Good

Fair

Good

Cycling

ca. 600 780

1039

600–1000

1000

ca. 300

>1000

ca. 280

Reversible capacity (mAh g−1)


Zhang et al., 2002 Zhao et al., 2001

Rock and Kumta, 2007 Cao et al., 2001

Lee and Lee, 2002 Park et al., 2005

Wang et al., 1998

Wang et al., 2000

Yoon et al., 2006

Kim et al., 2000

Guo et al., 2005a

Hwang et al., 2001

References


381

0.2 μm

15.4 Transmission electron micrograph of Sn and Li2O composite particles (reprinted from Wang et al., 2008b with permission from Elsevier BV).

As a result, Sn3Co/Al2O3 and Sn4Ni3/Al2O3 composite powders were formed (Zheng et al., 2007a). Cu–Sn is the first reported novel alloy anode material (Wu et al., 2002b). It was found that Cu–Sn alloys could be prepared by MC methods with flake sizes below 1 μm (Xia et al., 2001). Mechanochemical reaction of Mg and Sn powders produces another tinbased alloy, Mg2Sn. The structure obtained changes with milling time and a mixture of cubic and orthorhombic phases of Mg2Sn is achieved, which provides some interstitial space that can accommodate possible stress during electrochemical reactions. In the case of cubic Mg2Sn, although some intercalation sites do exist, they appear to be too narrow. However, the orthorhombic phase has a layered structure and the distance between the layers is sufficient to accommodate Li atoms, so that lithium can insert into the layers (Ning et al., 2004). Apart from Cu and Mg, Ni can also form alloys with Sn and a nanocrystalline Ni3Sn4 alloy can be prepared by high energy ball milling (Lee et al., 2002). In addition to conductive metals such as Mg and Ni used as buffer or additive, graphite, which is an active material for lithium-ion insertion, can also be mixed with Sn. After intensive ball milling, composite particles of graphite and tin are obtained, with Sn encapsulated in the ductile graphite matrix at the nanometre scale, which can be seen in Fig. 15.5. During milling, graphite becomes amorphous and tin becomes nanocrystalline. In contrast with the ball milling of graphite alone, the graphite in this composite con-


382


C

Sn

5 nm

15.5 High-resolution electron micrograph of ball milled C0.8Sn0.2 composite (reprinted from Wang et al., 2001 with permission from Elsevier BV).

tains fewer interstitial carbon atoms owing to the existence of the soft Sn particles. Tin particles are broken down to 15–20 nm and still attain an ordered crystalline state. Also in this material there are some interstitial sites such as vacancies and disorganized regions (Wang et al., 2001). On the basis of the composite of Sn with graphite, further additives such as metallic Mn, Fe, Co and Ag can be introduced into Sn particles. In the case of Mn, an intermetallic compound, SnMn3C, which has a perovskite structure, is obtained. After ball milling, the resultant SnMn3C powder comprises nanostructured particles with different crystallographic orientations and grain boundaries (Beaulieu et al., 2000). As for SnFe3C, its structure is similar to SnMn3C after ball milling. The Sn–Co–C composites are prepared by ball milling commercially available micrometresized powders of Sn, Co and C (graphite). The Sn : Co : C molar ratio can be varied, such as 0.31 : 0.28 : 0.41, 0.3 : 0.3 : 0.4 or 0.36 : 0.41 : 0.23. Composites of Sn30Co30C40 or Sn36Co41C23 with the same nanostructure from cosputtering can also be prepared by high energy ball milling and vertical-axis attritor milling (Hassoun et al., 2007; Ferguson et al., 2008). The tin–graphite–silver (Sn–G–Ag) composite powder obtained from high-energy mechanical milling comprises electrochemically active Sn and graphite, as well as Ag4Sn phases which are uniformly distributed on the surface of the graphite particles (Wang et al., 2008a). New tetragonal phases such as those of Ni, Sn and P can also be directly prepared via MC reactions (Xia et al., 2008b).



383

Silicon, similar to tin, can form alloys up to Li22Si4 (Wu et al., 2002b). As a result, Si-based alloy anode materials are also promising owing to their high reversible capacity. However, the volume change during the charge/ discharge process is also very large, even more than that of Sn and capacity fades very quickly. Consequently, some measures are used to buffer or alleviate the drastic volume change. The first measure is to introduce inert oxides into Si in order to decrease volume expansion. Composite particles consisting of nanosized silicon, Li4SiO4 and other lithium-rich components are synthesized using reactive milling of SiO amorphous powder with lithium metal, resulting in the oxidation of lithium and silicon and the reduction of SiO to Si (Yang et al., 2007). Nanosized silicon particles have been obtained by reaction between SiBr4 solution and Mg granules during a ball milling process. After the MC reaction, crystallized silicon was obtained together with MgBr2, non-reacted Mg and probably amorphous SiOx. When the residual products were removed by cleaning processes, silicon powder consisting of nanosized Si particles with a limited oxidized fraction in regard to its high surface area was obtained (Sandu et al., 2007). Instead of Li and Mg, Al can be used as a reducing agent. By milling a mixture of amorphous SiO (325 mesh) and aluminium (100–200 mesh) powders with a molar ratio of SiO :Al = 1 : 1 at a speed of 400 rpm for 15 hours in an argon atmosphere, a Si/Al2O3 composite was prepared. The composite was added slowly to hydrochloric acid while stirring to remove Al2O3 and nano-porous Si powder particles were formed together with a thin layer of oxides. On the basis of the nanoporous Si particles, carbon can be further incorporated by using an approach such as ball milling to obtain nanoporous Si/graphite composite powder (Zheng et al., 2007b). Ballmilling of SiO can lead to a reduction in particle size (Doh et al., 2008). Of course, graphite or pyrolyzed carbon can also be added (Kim et al., 2007). The second way to reduce volume expansion is by adding some electrochemically inactive or inert compounds such as TiN, TiC or Si3N4. Nanocomposite particles of silicon and TiN from high-energy mechanical milling are composed of nanosized TiN containing a uniform dispersion of Si independent of the composition. The very small size of the Si crystals prevents the formation of a distinct phase boundary between Si and TiN. As a result, the volume changes continuously rather than abruptly and discretely (Kim et al., 2000). The nanocomposite particles of silicon/titanium carbide (TiC) obtained by high-energy ball milling consist of amorphous silicon and nanocrystalline titanium carbide (Guo et al., 2005b). In the case of the composites of silicon/Si3N4 nanoparticles, the amorphous Si3N4 particles could be the inactive buffer matrix supporting Si particles, which could prohibit further agglomeration of Si particles during cycling and ensure cycling stability (Zhang et al., 2007b).


384


The third approach is to add some metals such as Mg, Ni, Fe, Mn, Ag, or alloy compounds (Wu et al., 2002a; Hwang et al., 2001) in order to decrease the volume expansion. In the case of Ni, Fe and Mn, they form nanosized intermetallic alloy powders with Si such as NiSi and FeSi, FeSi2 and MnSi after MC reactions, with Si still acting as an active material for lithium storage (Wang et al., 2000; Zuo et al., 2006). SiAg powder particles formed by the mechanical alloying process appear to contain a uniform dispersion of Si in the ductile Ag particle matrix. Ag not only provides a buffering environment for nanocrystalline Si but also serves as a conducting matrix. Of course, longer milling time leads to better dispersion of Si in the Ag matrix (Hwang et al., 2001). In the case of alloy compounds, a typical example is AB5 (e.g. MmNi3.6Co0.7Al0.3Mn0.4). In the Si–AB5 composites, Si nanocrystals are distributed homogeneously on the surface of the AB5 matrix and the inactive AB5 alloy can accommodate the large volume changes in the Si nanocrystals (Zhang et al., 2007a). The fourth technique is to add conductive agents such as carbon and polypyrrole. During the mechanical milling of Si and graphite powders, the crystal size of graphite increases and that of silicon decreases with the reducing silicon content (Wang et al., 1998). Ball milling of silicon powder with single wall carbon nanotubes (SWCNTs) functionalized by LiOH can provide good electrical contact between the electrochemically active particles (Wang and Kumta, 2007). In the composite powders of silicon with polypyrrole obtained by high-energy mechanical milling, polypyrrole acts as a good matrix to hold the active silicon grains and buffer the possible volume change, which is schematically shown in Fig. 15.6 (Guo et al., 2005a). Of course, the above approaches can be combined to obtain better composites of Si powder particles (Yan et al., 2008). For example, graphite can be ball milled with alloys of Si such as Fe20Si80, FeSi6 and MnSi to prepare composite powders (Lee and Lee, 2002; Li et al., 2008; Zuo et al., 2006). Electrochemically active Si0.66Sn0.34 (SiSn) composite alloys can be dispersed in a carbon (graphite) matrix using both wet and dry high-energy mechanical milling (HEMM). The resultant composite powder particles consist of amorphous carbon (in the case of dry HEMM) or crystalline carbon (in the case of wet HEMM) and crystalline silicon and tin (in both cases) (Rock and Kumta, 2007). Si–M–C (C is disordered carbon, and M is a hard comilling component like TiB2, TiN or Ni) composite powders can be prepared by the HEMM process. A large number of pores are produced, which can accommodate volume changes effectively and are essential to prevent the formation of inactive secondary phases between Si and M. In the case of Si/Ni alloy-C composites, inactive secondary phases such as NiSi and NiSi2 produced during the arc-melting process act as buffers to reduce pulverization of the



385

PPy

Si

15.6 Schematic diagram of the Si/PPy composite particle: Si crystals act as the active phase and PPy as the inactive phase to buffer volume change (reprinted from Guo et al., 2005a with permission from Elsevier BV).

electrode (Park et al., 2006b). A Si–Zn–C composite powder is prepared by mechanical ball-milling using Zn as third element (Yoon et al., 2007). When the above processes are combined with heat treatment, new composite anode materials based on Si can be prepared. For example, a carbon–Si–Cu3Si composite powder was prepared using silicon and copper(ii) d-gluconate powders as precursors via a MC reaction and subsequent pyrolysis. In this process, Cu3Si and pyrolysed carbon uniformly adhere to the surface of the silicon particles (Yoon et al., 2006). Combination of HEMM with thermal pyrolysis may provide silicon-disordered carbon composite particles, in which multiphase Si–C cores are homogeneously distributed within the pyrolysed carbonaceous matrix (Liu et al., 2004c). In the Si/Ni alloy and graphite composites obtained by arc-melting followed by HEMM, alloy particles consisting of NiSi2, NiSi and Si phases are distributed finely and uniformly on the graphite surface. Fourier transform infrared spectroscopic (FTIR) analysis confirmed that some bonds were formed between alloy and graphite after HEMM, which appear to retain the electrical connection between alloy and graphite (Park et al., 2005). Si/G/PAN-C composite powders can be prepared by mechanically milling mixtures of elemental powders of synthetic graphite (1–2 μm), Si (−325 mesh) and PAN with a high energy shaker mill for up to 15 hours in a stainless steel (SS) vial using 20 SS balls of 2 mm diameter (total ball mass 20 g) with a ball to powder weight ratio 10 : 1 (Datta and Kumta, 2006).


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Since the chemical properties of Sb are similar to those of Si and Sn, and lithium insertion can reach the level of Li3Sb, Sb-based alloys can also potentially be used as the anode for lithium-ion batteries including β-Zn4Sb3, CoSb3 and InSb, when they are prepared using MC methods, as shown in Table 15.4. β-Zn4Sb3 has a rhombohedric crystal structure with a = 1.2231 nm and c = 1.2428 nm; its density (6.077 g cm−3) is lower than that of Zn (7.14 g cm−3) or Sb (6.684 g cm−3), suggesting that there is some space available in the structure for lithium storage. After high-energy ball milling, β-Zn4Sb3 alloy powders change into a ZnSb structure together with another unknown structure (Cao et al., 2001). CoSb3 powder with different particle sizes can also be prepared by ball milling Co and Sb. As can be expected, the particle size decreases with an increase in the ball milling time (Zhang et al., 2002). Heteroatoms such as Fe can be incorporated by high-energy ball milling to obtain ultrafine CoFe3Sb12 (Zhao et al., 2001). InSb can be prepared by ball milling In and Sb, the purpose of which is similar to that of the introduction of inert components in Si (Hewitt et al., 2001). Like Sn and Si, conductive agents acting as a buffer, and a conductive matrix such as graphite or carbon can also be introduced (Wang et al., 2001; Lee and Lee, 2002; Zhang et al., 2005a). For example, composites such as CoFe3Sb12–C16 (Zhao et al., 2001) and Zn4Sb3–C7 (Cao et al., 2001) have been successfully prepared. Of course, other metals may also be used to form alloys with Sb by MC reactions if they present good conductivity and good stability during cycling.

15.4.3 Anode materials from nitrides The application of nitrides as anode materials is due to the high ionic conductivity of Li3N. After the introduction of transition metals (TM) to partially substitute Li, Li–TM–N has shown promise as anode materials (Wu et al., 2002a). Partial results of mechanochemical reactions to prepare anode materials by using nitrides are summarized in Table 15.5. Li3N reacts with SnO during the milling process according to Equation [15.7] (Foster et al., 2000): 2Li3N + 3SnO → 3Li2O + 3Sn + N2↑

[15.7]

Ball milling SnO with Li3N produces composite particles of Li2O and Sn, wherein Sn is homogeneously distributed, with a particle size of about 100 nm or less. During the first charge–discharge cycle, the irreversible capacity is greatly decreased owing to oxidation of Li3N. Lithium-rich silicon nitride composites can be prepared by ball milling a mixture of Si powder (1.0 V (Salver-Disma et al., 1999). During charge–discharge cycles, the reversible capacity above 1 V decreases rapidly. Another report mentions that the charge slope at >1.0 V converts to a plateau at 0.27, the following reaction will take place: 3Li + InSb → Li3Sb + In

[15.10]

The voltage plateau of this process is above 0.65 V and the cycling behaviour is good. At a lower potential, the In produced reacts with Li and forms alloys with a composition InLix, resulting in poor cyclability (Hewitt et al., 2001). Perhaps at the first stage, In can act as a buffer to resist cracking or volume expansion. The composites of Sb-based alloys with carbon lead to better cycling behaviour in comparison with virginal alloys. For example, composite material CoFe3Sb12–C16 obtained via ball milling shows superior cycling even at a large current density of 100 mA g−1 (Zhao et al., 2001). Compared with Zn4Sb3 powder, composite Zn4Sb3–C7 powder prepared by ball milling possesses higher initial reversible capacity (580 mAh g−1), smaller voltage hysteresis and better capacity retention, indicating another promising anode material (Cao et al., 2001). Anode materials from nitrides In the product obtained by ball milling SnO with Li3N, the irreversible capacity is greatly decreased and the cycling behaviour is improved. The main reason for the improvement seems to be the existence of Li2O as a buffer and the disappearance of SnO (Foster et al., 2000).


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Lithium-rich silicon nitride composite particles possess a reversible capacity of about 500 mAh g−1 and the retained capacity after 50 cycles is above 400 mAh g−1, which is 80% of the reversible capacity of the second cycle. The structure of the composite particle is stable even at a high lithium extraction state and can still maintain excellent cycling performance (Wen et al., 2006). The lithium silicon oxynitride composite powder obtained via ball milling presents capacity retention of 488 mAh g−1 (95% of the second cycle) after 50 cycles. It is superior to many other high capacity anode materials for lithium-ion batteries. The capability for charging–discharging within a wide voltage cut-off window makes it suitable to compensate lithium-ion sources for different electrode systems of either cathode or anode (Wen et al., 2008). In Li–TM–N composites with carbonaceous materials obtained by mixing or ball milling, both Li–TM–N and the carbonaceous materials are electrochemically active within the potential window of 0–1.4 V versus Li/Li+. The charge and discharge behaviour of the composite powder reflects the mixed electrochemical characteristics of the two active hosts. Additionally, the carbonaceous hosts can function as conducting materials, leading to an improvement in the charge rate of Li–TM–N. High cycling stability is feasible owing to the low volume effects upon Li insertion and extraction. However, voltage hysteresis was found during charge and discharge in the electrode owing to the different reactive potentials of the two active hosts (Hanai et al., 2008). This research indicates that ball milling with nitrides such as Li3N and Li–TM–N is a good way to decrease the irreversible capacity. Doping of Li–TM–N powders by metals such as Cu and Fe leads to a slight decrease in capacity, an improvement in electrochemical kinetics associated with the modification of morphology characteristics of the active particles and a reduction in the potential hysteresis between the charge and discharge process (Liu et al., 2004b, c). The lithium transition metal nitrides therefore appear to be promising anode materials for lithium-ion batteries. Other kinds of anode materials The SnO–B2O3–P2O5 system prepared by the MC method has a discharge capacity in the first cycle of more than 500 mAh g−1 at a constant current of 1.5 mA cm−2. The charge–discharge curves of these materials from the MC method are similar to those for the glassy powders in the SnO–B2O3– P2O5 system prepared by a melt quenching procedure (Morimoto et al., 1999). By selecting the cutoff voltage, good cycling performance is achieved. The amorphous 50SiO⋅50SnO (mol%) obtained through ball milling the composite shows a high capacity of over 800 mAh g−1 in the potential range of 0–2.0 V versus Li+/Li with a current density of 1.5 mA cm−2. Its first dis-



397

charge capacity is much larger than that of the amorphous SnO–B2O3–P2O5 materials obtained via mechanical milling. In addition, its irreversible capacity is also smaller (Morimoto et al., 2001). In the case of SnO2 doped with metal oxides, for example Sn1−xMoxO2, the metal oxides additives present two favourable effects, namely: (i) an increase of the discharge capacity and (ii) an improvement of capacity retention during cycling owing to the Li–M–O oxide conductive matrix (Martos et al., 2002). The electrochemical performance of nanosized SnS particles is dependent on the particle size, inactive buffer phase of Li2S and S and the ratio of Li2S to S. The irreversible capacity loss in the first discharge is attributed to the formation of Li2S, which plays an important role in the following discharge–charge cycles in preventing volume expansion and stabilizing the electrode structure. Li2S is more appropriate for buffering the volume change than S. In the following cycles, the nanosized SnS anode material synthesized via ball milling delivers high discharge capacity and exhibits good cycling stability (Li Y, et al., 2006b). Composite powders of SiO with porous carbons prepared via mechanical milling present high reversible capacity, excellent cycling behaviour and excellent high-rate discharge capability even at a discharge current density of 600 mA g−1. The main reason for this seems to be the embedding of Si–SiO in the continuous porous structure of carbon (Yuan et al., 2007; Chao et al., 2008). In the case of α-Fe2O3 powder obtained by mechanical milling, the material displays a high insertion capacity of over 1000 mAh g−1 (Morimoto et al., 2005). The electrochemical performance of the phosphides MPx obtained by mechanical milling, especially the initial capacity and capacity retention, is strongly related to the powder morphology: small particle size favours high capacity and the operational scan rate affects the capacity depending on the degree of crystallinity of the powder. On the other hand, capacity retention is better than that of microsized powders (Bichat et al., 2004). In the case of CoPx (CoP3 + CoP) prepared by ball milling, the resulting coulombic efficiency in the first cycle is increased from about 74% to 95%, along with a sacrifice of part of the reversible capacity. In contrast, the lithiated product by thermoreaction results in poor electrochemical performance (Zhang et al., 2005b).

15.5

Solid electrolytes from mechanochemical methods

Solid electrolyte is divided into inorganic electrolyte and solid polymer electrolyte (Wu et al., 2002a). Although solid polymer electrolyte is usually prepared by polymerization, MC methods are also applied in its prepara-


398


tion, such as the addition of nanofillers (Wu et al., 2002b). However, it is not the main or determining process and this aspect will not be expounded here. Inorganic electrolyte usually includes oxide and sulfide powders. In the application to lithium-ion batteries, it should be amorphous or noncrystalline. As a result, MC methods using milling or grinding are promising ways to prepare inorganic solid electrolytes such as oxides, sulfides and oxysulfides (Wu et al., 2002b). Amorphous oxide electrolyte powders can be prepared via MC reactions between Li2O and SiO2, or P2O5 and GeO2 owing to the amorphization effect during the milling process. Other oxides such as B2O3 and lithium salts such as Li3PO4 can be added (Wu et al., 2002a). Nanosized amorphous Li1.4Al0.4Ti1.6(PO4)3 powders can be prepared by mechanical milling, which will be converted into glass ceramics after heat-treatment at 700–1000°C (Xu et al., 2006). Lithium-ion conducting amorphous solid electrolytes based on sulfides are first prepared from SiS2 and other sulfides. For example, grinding crystal Li2S with SiS2, P2S5 or P2S3 produces an amorphous glass. The amorphousforming region is extended in comparison with that obtained by meltquenching, and the molar ratio of Li2S in amorphous xLi2S⋅(1 − x)P2S5 can be as high as 0.80 (Tatsumisago et al., 2002). During the formation of Li2S– P2S5-based glass ceramics, softening of the glass occurs concurrently, which must be used to form close solid/solid contact between electrolyte and electrode powders without any chemical reactions because of low heattreatment temperature (Tatsumisago, 2004). Superionic crystals, a series of sulfide crystalline solid electrolytes such as Li4GeS4–Li3PS4, have been successfully formed by the crystallization of mechanically milled Li2S–P2S5 glasses and GeS2 (Hayashi et al., 2003). Amorphous composite 75Li2S⋅xP2S3⋅ (25 − x)P2S5 (mol%) can be obtained in the range of x = 0–5. In composites with x ≥ 8.3, a crystalline Li2S phase remains after ball milling for 50 hours (Machida et al., 2005). Considering the experience with sulfides, oxides such as LixMOy (M = Si, P or Ge) and P2O5 can be further incorporated by ball milling (Hayashi et al., 2002; Ohtomo et al., 2005). The glassy composite powders obtained are pelletized and heated to various temperatures over their crystallization temperatures to form the glass–ceramic materials (Hayashi et al., 2002; Tatsumisago and Hayashi, 2008). During milling, the particle size at first decreases with milling time and later increases because the particles aggregate with each other. The local structure of the mechanically milled amorphous materials containing Li4SiO4 is similar to that of the corresponding melt-quenched glasses, in which SiS4 and SiOS3 tetrahedral units are mainly present. SiOnS4−n (n = 1, 2, 3) tetrahedral units are formed when adding Li4SiO4 and Li4GeO4 to the sulfide system, however these units are not present when Li3PO4 is added. The reactivity of LixMOy derived from its



399

basicity affects the structure and formation process of the oxysulfide materials obtained by mechanical milling (Hayashi et al., 2002). As well as oxides, lithium compounds such as Li2S, Li3N, Li2O, Li3PO4, LiOH, LiCl and LiI can be added to sulfides and solid electrolytes are obtained through mechanical milling (Hayashi et al., 2004; Ning et al., 2004). Too long a grinding time will lead to partial crystallization (Ning et al., 2004). The electrochemical properties of the prepared solid electrolytes vary according to the materials and ball milling treatment employed. In the case of the Li2O–B2O3–P2O5 composite oxides, the total ionic conductivity can be as high as 9 × 10−5 S cm−1 (Wu et al., 2002a). The ionic conductivity of the glass–ceramic Li1.4Al0.4Ti1.6(PO4)3 increases with the increasing amount of crystalline phase and the reduction in grain size. The highest bulk conductivity (σb) is 1.09 × 10−3 S cm−1 at room temperature with an activation energy as low as 0.28 eV (Xu et al., 2006). Amorphous sulfide composites such as 60Li2S⋅40SiS2 (mol%) prepared via ball milling show ionic conductivities up to 10−4 S cm−1 at room temperature, comparable with those obtained by melt quenching, and the transport number of Li+ is nearly 1.0. When these composites are heated to suitable temperatures to obtain glass ceramics, the ionic conductivity will be further increased. For example, as shown in Fig. 15.11, the Li2S–P2S5 glass ceramic

0

Log (conductivity / S cm–1)

–1

Glass–ceramics

–2 –3 –4 Glass

–5 –6 –7 Solid-state reaction

–8 –9 1.8

2

2.2

2.4

2.6 2.8 1000 / T

3

3.2

3.4

15.11 Temperature dependence of the conductivities of the 70Li2S– 30SiS2 glass and glass–ceramics prepared by the MC method. The conductivity data for the sample prepared by solid state reaction are also shown for comparison (reprinted from Tatsumisago and Hayashi, 2008 with permission from Elsevier BV).


400


shows ionic conductivity as high as 3.2 × 10−3 S cm−1 at room temperature (Tatsumisago and Hayashi, 2008). After the addition of oxides by the MC method, the prepared amorphous oxysulfide materials of (100 − x)(0.6Li2S⋅0.4SiS2)⋅xLi4SiO4 show an ionic conductivity above 10−4 S cm−1 and an electrochemical window up to 10 V (Hayashi et al., 2002). The addition of a small amount of P2O5 to the Li2S–P2S5 sulfide system in the ball milling process lowers the ionic conductivity, but enhances the electrochemical stability of the glass– ceramic electrolytes (Ohtomo et al., 2005). Amorphous solid electrolytes from SiS2 and various kinds of lithium compounds such as Li2S, Li3N and Li2O exhibit high conductivities of 10−5–10−4 S cm−1 at room temperature, while those obtained using Li3PO4, LiOH and LiCl present conductivities lower than 10−6 S cm−1. The conductivity of the 50Li2O⋅50SiS2 (mol%) composite drastically increases with the milling time from 0 to 5 hours. The enhancement is due to the formation of corner-shared and isolated SiS4 and SiOS3 tetrahedral units in the solid electrolyte, leading to lower activation energy for the movement of lithium ions (Hayashi et al., 2004). When these kinds of amorphous sulfides and oxysulfides are used as electrolytes and assembled into solid-state lithium-ion batteries, they exhibit excellent cycling performance (Hayashi et al., 2002; Machida et al., 2005). For example, an all-solid-state battery fabricated with LiCoO2 fine powder as cathode material, the glass ceramic 80Li2S⋅20P2S5 (mol%) as solid electrolyte and a metallic indium foil as anode shows a rechargeable capacity of 100 mAh g−1 based on the cathode material, and its cycle efficiency is almost 100% after the second cycle, with no capacity fading for 500 cycles (Machida et al., 2005).

15.6

Conclusions

In conclusion, MC methods are promising methods for preparing materials for lithium-ion batteries. Compared with conventional solid state reactions at high temperature, the MC methods appear to accelerate and simplify the synthesis process and decrease the energy expenses as well as the cost of the material. Furthermore, the prepared materials present good electrochemical performance. For example, cathode materials such as LiMn2O4 spinels present better cycling behaviour in comparison to those from solid state reactions because the highly disordered nanocrystalline particles can accommodate the Jahn–Teller distortion. Carbonaceous anode materials such as graphite show very high capacity due to the introduction of many defects, such as voids/nanocavities and the change into nanoparticles (Kosova and Devyatkina, 2004). In the case of alloy-based anode materials, their cycling behaviour is also improved since heteroatoms can be homo-



401

geneously incorporated into the prepared nanocomposites and they buffer the drastic volume change. The prepared solid glass electrolytes show high conductivity (>10−4 S cm−1) and the fabricated all-solid state lithium-ion battery presents good cycling behaviour. In addition, MC methods can be combined with other techniques to prepare materials for lithium-ion batteries. As mentioned above, when MC methods are combined with heat treatment, glass–ceramic electrolytes can be prepared with high ionic conductivity, around 10−3 S cm−1 at ambient temperature (Tatsumisago et al., 2002; Akitoshi et al., 2003). Grinding in combination with subsequent firing at 400°C or higher can enable high purity spinel Li4Mn5O12 to be prepared which is difficult to obtain by heat treatment alone (Tanaka et al., 2003). Combining with electric discharge, which favours the formation of crystal structure, will lead to preparation of versatile electrode materials for lithium-ion batteries such as LiFePO4 (Needham et al., 2006). MC reactions cannot induce every material to display the best electrochemical performance since some actions are not favoured by ball milling. For example, during the mechanical milling process, sometimes the structure change will lead to poor cycling performance (Wang and Kumta 2007; Zhang et al., 2005a). One main reason for the deteriorated performance is the resulting amorphization. Another one is perhaps related to the change in morphology (Bichat et al., 2004). In the case of the composite of Si with graphite, a diffusion barrier such as polymethacrylonitrile must be added to suppress the possible MC reaction between silicon and graphite particles to form SiC and further to prevent the amorphization of graphite during extended milling (Wang and Kumta 2007). The agglomeration of the composite particles during the high energy mechanical milling process and low coulombic efficiency in the initial cycle still remain to be solved (Wang et al. 2008a). In some situations, good crystallinity could not be achieved since the ball-milling could not provide energies sufficient to arrive at a temperature above 400°C (Gillot et al., 2007). Furthermore, there is still much development expected from further research into the effects of MC methods on the materials for lithium-ion batteries. With further research and development, the application of MC reactions can be expected to expand even more (Myung et al., 2006).

15.7

Acknowledgement

Financial support from the National Basic Research Program of China (973 Program No: 2007CB209702), the Shanghai Committee of Science and Technology (09QH1400400) and the South African National Research Foundation (UID No. 67295) is gratefully acknowledged.


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15.8

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Index

acetylene black, 373 acetylsalicylic acid, 230 acylation reactions, 226 adamantine, 318, 320 adhesion, 243 AGO-2, 11 Akashi Hardness Testing Machine, 270 Al7Cu2Fe, 155 Al13Cu4Fe3, 155 Al8Fe2Si, 155 alkaline niobates, 129, 130 aluminium plates, 261 Al sample with hammered Ti particles, 259 entirely coated Al surface with Ti particles, 262 ammonia, 316 amorphisation, 234 anastase, 305–6, 311 anchoring, 269 anode materials alloy-based anode materials, 378–86 ball milled C0.8Sn0.2 composite, 382 selected results, 379–80 Si/PPy composite particle, 385 Sn and Li2O composite particles, 381 carbonaceous materials, 374–8 cycling performance discharge/charge profiles of Si/C/ PAN–C composite electrode, 394 efficiency of Sn3Co/Al2O3, 391

nanoporous anode materials based on silicon, 393 electrochemical performance, 389–97 anode materials from nitrides, 395–6 antimony-based anode materials, 395 carbonaceous anode materials, 389–91 other kinds of anode materials, 396–7 silicon-based anode materials, 392–4 tin-based anode materials, 391–2 mechanochemical preparation, 374–97 from nitrides, 386–7 ball milling effects, 387 other kinds of anode materials, 387–9 carbon xerogel and CX–SiO, 388 anthracene, 81 arabinogalactan, 236, 237, 239 arc-melting process, 384–5 Archimedes method, 282 armoured surface, 260 artificial lattices, 63 ascorbic acid, 242 attritor mill, 137, 139, 186 β-cyclodextrin, 235, 236 β-sialon, 187

409 © Woodhead Publishing Limited, 2010

410

Index

β-SiC, 177 β-Zn4Sb3 powder, 395 ball-impact energy, 114 ball-impact frequency, 114 ball milling, 10, 12, 94, 149, 252, 275 devices and summary of conditions investigated, 280 ball mills, 16, 46–7, 93 ball to powder mass ratio, 275 barium titanate, 117, 128 BaTiO3 see barium titanate benzoquinone, 81, 82 bicarbonate, 241 biexponential kinetics, 238 BiFeO3, 131–2 binary alloy systems, 152–5 Fe–X (X = Sn, Zn, Sb, Al) systems, 153 Ni–X (X = Sn, Sb, Zn, Al) systems, 153–4 other systems, 154–5 binary composite system, 322 Binol, 82 bismuth titanate, 122, 130–1 biuret, 304 Boltzmann factor, 33 borides, 292 Bragg diffraction peaks, 388 Bridgman’s anvils, 225, 226 brookite, 305–6 bulk composites, 193 calcination, 72 calcium carbonate, 243 carbide powders, 173 carbides, 173–9, 292 carbon, 384 carbon cryogel, 388 carbon monoxide, 57–9 carbon xerogel, 388 carbonaceous materials, 374–8 carbonato complex, 123 carbothermal reaction, 185 carbothermal reduction, 185–7 carboxylic acids, 244 catalytic hydrogenation, 57–9

cathode materials ball-milling time effects on LiMn2O4 cycling behaviour, 372 electrochemical performance, 371–3 Li3Fe1.8Ti0.1Mn0.1(PO4)3 and ball milled Li3Fe1.8Ti0.1Mn0.1(PO4)3/ carbon mixture, 371 lithium cobalt oxides, 365–6 mechanochemical preparation, 365–73 other kinds of cathode materials, 369–70 spinel lithium manganese oxides, 366–9 cellulose, 235 ceramic method, 347 ceramic oxides, 113–40 complex oxides with various properties, 126–39 future trends, 139–40 mechanisms and kinetics, 114–26 ceramics, 194 cermetals, 194, 217 charge transfer complex, 82 Chirchik Plant, 2 chitosan, 236 chlorinated aromatics, 50–3 chlorobenzene, 50 citric acid, 242 cobalt, 99 CoFe3Sb12, 386 (Co50Fe50)0.2(TiO2)99.8 catalyst, 58–9 combustion synthesis, 169 composite powder, 194–203 conductive carbon, 370 copper, 217 Coulomb interaction, 239 Coulomb law of friction, 12 coulombic efficiency, 397 covalent bonds, 167 critical loading conditions, 96, 97, 102 critical nuclei, 26 critical threshold value, 96 Cr3O3, 135 cryomilling technique, 297 CSEM Revest, 271 Cu/Al2O3, 219


Index Cu–Al/Al2O3 composite powder lamellar structure, 197 mechanosynthesis GTM results, 200 SHS GTM results, 201 structure homogeneity, 199 CuO–Al system Al2O3 particles embedded in Cu–Al matrix, 213 effects of mechanosynthesis, 211–13 XRD patterns after different treatment times, 212 Cu2(OH)2CO3–Al system after different treatment times, 209 after mechanochemical synthesis, 206 DTA curve, 202 effects of mechanosynthesis, 208–11 TG–DTA curves, 211 Curie law, 377 Curie temperature, 131 cyanuric acid, 316 cyclisation, 326 cyclodextin, 243 degree α, 27 Degussa P25, 311, 322 densification, 168 diamagnetic imidazoline, 229 Diels–Alder reaction, 64, 80–2 effect of alcohols on rate, 82 with a eutectic complex, 83 yields under various conditions, 81 differential scanning calorimetry, 234 differential thermal analysis, 69, 201 diffuse reflectance spectroscopy, 314–15 dimethylanthracene, 82 effervescent tablet, 241 El 2 × 150 mill, 20 electric current activated sintering, 276 electrochemical photolysis, 305 electron-hole separation, 322–3 electron probe microanalysis, 261, 262 electron-trapping effect, 322 electronic diffuse reflectance spectra, 345

411

ethanol, 318 etherification, 226 extractive metallurgy, 1 extruders, 225 Fermi level, 306 ferroelectric oxides, 126–33 Fe20Si80 alloy–graphite composite, 394 Finnigam Tracker Mass Spectrometer GC/MS PE 8420, 50 Fisons 8000, 50 Fisons Sorptomatic 9600, 50 flame pyrolysis, 317 flash point, 202 fluorides, 228 Fourier transform infrared spectroscopy, 385 Fritsch Pulverisette 4, 116 gas-atomising, 392 gas pressure–temperature measuring system, 204 Gibbs energy, 177 glass–ceramic electrolytes, 400 GN-2 ball mill, 175 grain boundary migration, 68 graphene, 374 graphite, 374, 400 mechanochemical reactions effect on structure and electrochemical performance, 375–6 particle size effect on their reversible lithium capacity, 390 GTM see gas pressure–temperature measuring system Halder–Wagner method, 281 hammering effect, 258 HBB see hetero-bridging bond Hertz–Routh theory, 14 Hertz theory, 12, 14, 16, 21–2 illustration, 13 hetero-bridging bond, 69, 71 hetero-metalloxane bond, 69 heteroatoms, 374, 386, 400 hexachlorobenzene, 50, 228, 229


412

Index

hexamethylenetetramine, 311, 316, 320 high-energy ball milling, 160, 195 see also mechanical alloying vs solid–liquid reaction ball milling, 163–4 high-energy mechanical milling, 384, 385 highest occupied molecular orbital, 68 HOMO see highest occupied molecular orbital hydrogen, 53 absorption on Mg2Ni/Ni composite, 53–7 hydrogen bond, 239 hydrometallurgy, 64–5

hydrogen moles absorbed as a function of time, 54 mechanically induced structural and chemical transformations, 45–60 mechanochemistry, 46–8 outline of experimental methods, 48–50 quantity as a function of scaled time, 56 as a function of time, 55 stainless steel reactor temperature, 51 Kyence Color 3D Laser Confocal Microscope VK9700, 270

ignition temperature, 199 ignition time, 198–9 INCO laboratories, 2 induction effect, 351 ingot metallurgy, 158 injected mechanical power, 117 inorganic compounds, 331–3 intermetallic compounds, 150 ion-plating technique, 271 iron, 153, 386

LA132 binder, 391 La-monazite coatings, 251, 253, 272–3 LaCoO3, 137 LaCrO3, 135 LaMnO3, 134, 135, 136 lantern units, 353 lanthanophosphate coatings characterisation, 264, 266–7 cross-section deposited at different levels, 265 stainless steel surface, 263 degree of coverage and coating microstructure, 261–4 EPMA mapping of coated samples, 263 microhardness and peeling force, 266 on stainless steel plates, 261–7 lanthanum oxyfluoride, 324 LaOF see lanthanum oxyfluoride LaPO4 coatings see lanthanophosphate coatings lead zirconate titanate, 128–9, 129 Lewis classification, 333 LiCoO2 see lithium cobalt oxides LiFePO4, 348–51 Li2FeSiO4, 351–3 LiMn2O4, 124, 333–6 LiNi0.5Mn1.5O4, 336–7 LiNi1–x–yCoxMnyO2, 347–8

Jahn–Teller distortion, 68, 83, 333, 368, 400 JEOL Cross Section Polisher SM-09010, 262–3, 270 jet milling, 374 JXA-8200, 262 K-type thermocouple, 256 KhK 871 mill, 19 kinetic behaviour carbon monoxide catalytic hydrogenation, 57–9 conversion data, 58 chlorinated aromatics degradation, 50–3 fraction α of reacted chlorobenzene, 53 future trends, 59–60 hydrogen absorption on Mg2Ni/Ni composite, 53–7


Index liquid-phase oxidation, 230 liquid reactants, 154 lithium cobalt oxides, 344–7, 365–6 materials prepared by mechanochemical processes, 367 lithium-ion batteries anode materials mechanochemical preparation, 374–97 alloy-based anode materials, 378–86 anode materials from nitrides, 386–7 carbonaceous materials, 374–8 electrochemical performance, 389–97 other kinds of anode materials, 387–9 cathode materials mechanochemical preparation, 365–73 electrochemical performance, 371–3 lithium cobalt oxides, 365–6 other kinds of cathode materials, 369–70 spinel lithium manganese oxides, 366–9 DTA curves of initial and activated mixtures Li2CO3 with FeC2O4·2H2O and SiO2·0.1 H2O, 353 LiOH with MnO2, 335 IR spectra LiOH + Co(OH)2 activated mixture, 346 LiOH + V2O5 activated mixtures, 343 Li NMR spectra of LiOH + MnO2 activated mixture, 336 LiOH + Co(OH)2 activated mixtures diffuse reflectance spectrum, 346 LiOH and Li2CO3 reactions with crystal hydrates and acidic salts, 348–54 LiFePO4 synthesis, 348–51

413

Li2FeSiO4 synthesis, 351–3 LiTi2(PO4)3 synthesis, 353–4 LiOH reactions with anhydrous oxides, 333–43 LiMn2O4 synthesis, 333–6 LiNi0.5Mn1.5O4 synthesis, 336–7 Li4Ti5O12 synthesis, 338–9 Li1+xV3O8 synthesis, 339–43 LiOH reactions with solid hydroxides, 344–8 LiCoO2 synthesis, 344–7 LiNi1–x–yCoxMnyO2 synthesis, 347–8 70 Li2S–30SiS2 glass and glass– ceramics conductivities temperature dependence, 399 materials for cathode, anode and electrolyte, 365 mechanochemical methods, 361–401 Mössbauer spectrum of Li2CO3, FeC2O4·2H2O and NH4H2PO4, 352 principle, 362–3 requirements for materials, 364–5 soft mechanochemical synthesis of materials future trends, 357 principles of solid inorganic compounds synthesis, 331–3 solid electrolytes from mechanochemical methods, 397–400 TG and DTA curves of initial and activated mixtures LiOH + TiO2 + NH4H2PO4, 354 LiOH + V2O5, 341 LiOH and TiO2, 339 LiOH with FeC2O4· 2H2O and NH4H2PO4, 350 LiOH with Ni0.8Co0.2(OH)2, 348 LiOH with NiO and MnO2, 337 X-ray patterns LiNi1-yCoyO2, 349 LiOH + Co (OH)2 activated mixtures, 345 LiOH + FeC2O4·2H2O and NH4H2PO4, 351


414

Index

LiOH + NiO + MnO2 activated mixture, 338 LiOH + TiO2, 340 LiOH + TiO2 + NH4H2PO4 mixture, 355 LiOH + V2O5 activated mixture, 342 LiOH activated mixtures with different manganese oxides, 334 lithium manganese oxide, 370, 373 lithium silicon oxynitride composite, 387, 396 lithium transition metal nitrides, 386–7, 396 Li4Ti5O12, 338–9 LiTi2(PO4)3, 353–4 Li–TM–N see lithium transition metal nitrides LixMnOz see lithium manganese oxide Li1+xV3O8, 339–43 lowest unoccupied molecular orbital, 68 LUMO see lowest unoccupied molecular orbital magnesium carbonate, 243 magnetic oxides, 133–4 malachite green oxalate, 314 matrix-isolated imidazoline radicals, 229 mechanical activation, 47–8, 134, 195–6, 275, 332 mechanical alloying, 65, 66, 149–50, 196, 252 cycle, 27 kinetic processes and mechanisms, 92–107 chemical mixing mechanisms, 103–6 collecting and analysing experimental data, 98–103 fundamentals of processes in ball mills, 93–5 future trends, 106–7

instantaneous temperature map for square domain, 106 local temperature time, 105 mass fractions as a function of the number of collisions, 100 Ni40Ti60 mass fraction, 101 NiTi2 phases mass fractions, 100 phenomenological model kinetics, 95–8 rotating atoms cluster, 105 square of thickness of amorphous layer, 104 vs solid–liquid reaction ball milling, 161–3, 163–4 mechanical diffusion, 65 mechanical doping synthesis anion-doped, titanium dioxide, visible-light induced photocatalysts, 310–25 photocatalysts synthesis, 304–26 mechanical energy, 2 mechanical stressing, 66 mechanically induced self-propagating reaction, 174 mechanochemical activation, 113–14 mechanochemical alloying, 1–2 mechanochemical processing, 1–4 composite oxides in electromagnetic applications, 68–80 bond overlap population, 72 HBB formation during milling, 70 homogeneity of starting mixtures for BaTiO3 preparation, 73 Mg(OH)2 and Mg(OH)2-SiO2 change in thermal gravimetryDTA profiles, 69 Mg(OH)2-SiO2 change in FT-IR spectra, 70 molecular orbital calculation, 71 percent perovskite against firing temperature, 80 PMN and PZN perovskite ceramics application, 76–80 quenched samples XRD profiles, 75 reaction mixture for PMN-xPT SEM micrographs, 76


Index soft mechanochemical effects principle, 68–71 definition, 1 degree α of transformation for BaCO3 + WO3 = BaWO4 + CO2 density of balls, 34 frequency of rotation, 34 number of balls, 35 radius of balls, 35 departure from equilibrium achieved from various processes, 3 effects on graphite structure and electrochemical performance, 375–6 manufacturing non-oxide powders, 169–80 ball size effect on milled powder lattice strain and crystallite size, 178 carbides, 173–9 milled and heat-treated powders, 180 milled silicon and graphite powders XRD patterns, 177 nitrides, 170–3 silicides, 179–80 silicon-based mixture maximum combustion temperature, 171 Ti-C powder TEM micrographs, 176 titanium and activated carbon reaction progress, 175 materials design, 63–85 forced diffusion schematic illustration, 65 future trends, 84–5 mechanochemical route benefits, 64–7 modern mechanochemistry theoretical aspects, 67–8 materials for lithium-ion batteries, 361–401 anode materials preparation, 374–97 cathode materials preparation, 365–73

415

lithium-ion batteries, 362–5 solid electrolytes, 397–400 mechanism and kinetics, 9–40 calculating expressions, 19–20 change in specific surface of barium carbonate and tungsten oxide, 31 dependence of real time of activation process, 29 general issues, 15–16 Hertz theory and Routh’s Ω-hypothesis illustration, 13 impact-friction contact kinematics and dynamics, 13 impact-friction contact of two particles, 18 kinetics, 27–32 mechanism, 22–7 milling tools impact on particle layers and lining, 17 modern vibratory and planetary mills, 11 NaNO3 + KCl = KNO3 + NaCl degree α of transformation, 25 planetary ball mill scheme for calculation, 12 silver oxalate change in specific surface and conformity, 31 stress wave propagation, 17 temperature impulse at impactfriction contact, 23 t–P–T conditions calculation, 16–22 non-oxide systems with highly covalent bonds, 167–88 basic properties, 169 reactive systems, 180–7 α-Si3N4 unit cell volume vs milling time, 184 carbothermal reduction, 185–7 defective β-Si3N4 particle TEM image, 184 gas-pressured sintered β-sialon microstructure, 186 precursor activation in subsequent densification, 181–5


416

Index

sialon precursor powder specific surface area vs milling time, 183 spontaneous chemical reactions organic synthesis and utilisation, 80–4 change in energy of system and dihedral angle of anthracene, 84 Diels–Alder addition reaction, 80–2 increase in XRD peaks with fraction of PZN, 81 intermolecular HOMO-LUMO gap, 85 molecular distortion and change in frontier orbitals, 83–4 use of kinetic equations, 32–40 BaWO4 experimental values for mechanical synthesis, 39 degree of transformation based on compressibility, 36 experimental kinetic curves, 36 mechanochemical activation conditions effect on kinetics, 38–40 reactions controlled by diffusion, 37–8 reactions controlled by kinetics, 38 substances mechanical activation, 33, 37 mechanochemical synthesis complex ceramic oxides, 113–40 BaCO3–TiO2 powder mixture XRD patterns, 118 mechanochemical reactions mechanisms and kinetics, 114–26 milling efficiency graphical representation, 116 milling parameters, 115 NiFe2O4 non-uniform core/shell structure, 125 nucleation and growth mechanism schematic, 120

PbO–MgO–Nb2O5–TiO2 quantitative phase composition, 121 complex oxides with various properties, 126–39 BaCO3–TiO2 powder XRD patterns, 129 complex oxides with various structures and properties, 127 Cr(OH)3-nH2O XRD patterns, 136 ferroelectric and related oxides, 126–33 La2O3–Mn3O4 XRD patterns, 137 magnetic oxides, 133–4 oxides with semiconducting and catalytic properties, 134–9 PMN–PT thick films XRD patterns, 132 Zn–Fe–O sorbents sulphur absorption capacity, 138 composite powder formation, 194–203 Cu2(OH)2CO3–Al mixture DTA curve, 202 Cu2(OH)2CO3–AL2O3 synthesised composite powder elemental microanalysis results, 198 mechanical activation, mechanical alloying, reactive milling, 195–203 mechanical treatment, 195 SHS mechanochemical reactions induction time intervals, 203 copper-based composite powders with Al2O3, 207–13 CuO–Al reagent system, 211–13 Cu2(OH)2CO3–Al reagent system, 208–11 metal oxides formation enthalpy values, 208 Cu–Al–O and Ni–Al–O elemental systems, 217–19 low-molecular organic compounds solid-state mechanochemical synthesis, 227


Index main sequence and products, 226 metallic–ceramic composite powders, 193–200 applied high-energy milling, 205–6 Cu2(OH)2CO3–Al system after mechanochemical synthesis, 206 nickel-based composite powders with Al2O3, 214–16 combustion aluminothermic reaction product structure, 218 NiO–Al reagent systems, 216 Ni(OH)2CO3·xH2O–Al reagent system, 214–16 organic compounds and rapidly soluble materials, 224–45 mechanochemically activated powders, 281–2 mechanochemistry, 1, 46–8, 65, 149, 195 theoretical aspects, 67–8 mechanosynthesis, 66 melt-spinning techniques, 392 melts, 150 Mendeleev periodic table, 356 metal carbonates, 241, 244 metallic–ceramic composite powders mechanochemical synthesis, 193–220 applied high-energy milling, 205–6 composite powder formation, 194–203 copper-based composite powders with Al2O3, 207–13 Cu–Al–O and Ni–Al–O elemental systems, 217–19 monitoring mechanochemical processes, 203–5 nickel-based composite powders with Al2O3, 214–16 metallothermic reactions, 206 metallothermic reduction, 206 methane, 57 methanol, 307 MFe2O4, 133 Mg2Ni/Ni composite, 53 Mg2NiH4, 53 Mg2Sn alloy, 392 microhardness, 264

417

milling map, 114 milling medium, 153, 154 milling parameters, 115 Mixer/Mill mod. 8000, 48 molecular mass distribution, 237 molybdenum, 179 molybdenum disilicide system, 187, 281, 282–7, 293 milling time and charge ratio effect on product formation, 285 Mo crystallite size dependence on milling time, 283 temperature and sample displacement, 286 XRD patterns co-milled Mo + 2 Si powders, 284 Mo as function of milling time, 283 starting mixture and final product, 287 monazite-type lanthanum phosphate, 260 MoSi2 see molybdenum disilicide Mössbauer spectroscopy, 350 Na2CO3, 122–3 NaNbO3, 114, 123, 130 nanocoatings, 267–72 characterisation, 270–2 nanofillers, 398 NASICON, 353 NbAl3 system, 293–5 milling time effect on composition of samples obtained by SPS, 294 temperature and mechanical load temporal profiles, 295 XRD patterns of reactants as function of milling time, 293 Néel temperature, 131 neutralisation, 326 Newton’s theory of collisions, 10 (NH4)2CO3, 325 NiAl, 214 Ni3Al, 214 Ni2Al/Al2O3, 216 nickel, 153, 214, 217 Nikolsky Plant, 2


418

Index

NiO–Al system effects of mechanosynthesis, 216 XRD patterns after mechanochemical treatment, 217 niobium aluminides, 277 Ni2(OH)2CO3·xH2O–Al system effects of mechanosynthesis, 215–16 XRD patterns after mechanochemical treatment, 216 NiTi2, 100 nitrides, 170–3 anode materials preparation, 386–7 nitrogen monoxide, 308, 315 non-linear elastic theory, 15–16 non-oxide systems compounds basic properties, 169 with highly covalent bonds mechanochemical processing, 167–88 powder manufacturing by mechanochemical processing, 169–80 reactive systems mechanochemical processing, 180–7 O2 plasma treatment, 326 O-ring systems, 49 octachloronaphthalene, 228 Olivine LiFePO4, 370 organic acid–metal carbonate, 231 organic compounds benzoic acid/BaSO4 DSC thermograms, 235 break area of aggregated particle sample, 233 changes in morphology of reagents particles, 231 citric acid/CaCO3 mixture microphotographs, 232 fluorinated products yields after 20 hours autoclave treatment, 229 low-molecular organic compounds solid-state mechanochemical synthesis, 225–9, 227 possibilities in various types of reactions, 225–8

solid reagents preliminary activation for subsequent heterophase reactions, 228–9 mechanochemical synthesis, 224–45 future trends, 244–5 solid particles aggregation on reactivity carbon acids neutralisation, 230–5 stable iminoxyl radicals formation, 229–30 solid particles aggregation on reactivity in mechanochemical reactions, 229–35 synthesis for pharmaceutical applications, 235–44 low molecular organic compounds and polysaccharide adducts, 235–41 pharmaceutical substances solubility in water solutions, 238 rapidly soluble composite materials mechanochemical preparation, 241–4 oxidation–reduction, 326 oxide-dispersion strengthening, 1, 2 oxygen, 262 oxysulfides, 400 particle-reinforced surface, 260 PCA see process control agent Pechini process, 332 pentachloropyridine, 228 Periodic law, 356 Perkin-Elmer 8600, 50 perovskite, 382 perovskite ceramics BaTiO3, 72–6 granulometric properties, 76 obtained by calcining, 75 perovskite ceramics application, 72–6 PMN and PZN, 76–80 PMN-0.1PT dielectric constant frequency dependence, 79


Index PMN-xPT lattice parameter and average grains size, 78 PMN-xPT reaction mixture x-ray photoelectron spectra, 77 PMN-xPT XRD profiles, 78 petroleum cokes, 391 phenol, 308 Phillips X’Pert diffractometer Cu K α, 208 phosphide CoP3, 389 phosphides MPx, 389, 397 photocatalysis, 325 photocatalysts environment purification system by photocatalytic reaction, 309 mechanical doping synthesis, 304–26 anion-doped, titanium-dioxide, visible-light induced, 310–25 future trends, 325–6 titanium dioxide and its photocatalytic applications, 305–10 photocatalytic system, 304 pilling force, 264 piroxicam, 236 planetary ball milling, 314, 315 planetary mills, 10, 67, 116, 118, 128, 130, 131, 139, 177, 182, 186, 225, 226, 236, 377 milling parameters, 115 scheme for calculation, 12 PMN, 119 PMN–PT, 119, 120 polyethylene glycol, 235, 243 polymer alloys, 65–6 polymorphism, 234 polypyrrole, 384 polysaccharide, 239 polysaccharide–arabinogalactan systems, 240–1 polytetrafluoroethylene, 178, 324 polyvinylpyrrolidone, 235, 243 potassium bicarbonate, 242 potassium fluoride, 229 potassium persulphate, 229 powder charge, 49, 96 powder mass, 49, 96

419

powder processing, 94 powder technology, 64 precoating, 261 process control agent, 157–8 proton affinity, 356 pulsed mechanical action, 225 Pulverissette 6, 208 pyrometallurgy, 64 pyrometer, 281 PZT see lead zirconate titanate rapidly soluble materials mechanochemical synthesis, 224–45 future trends, 244–5 pharmaceutical applications, 235–44 low-molecular-weight organic compounds and polysaccharide adducts, 235–41 rapidly soluble composite materials mechanochemical preparation, 241–4 possible components, 242 reactant, 152 reactive milling, 149–50, 150, 160, 198 reactor chamber, 49 Rietveld method, 99 Rietveld refinement analysis, 119 Rigaku D/Max diffractometer, 50 roll mills, 225 Routh’s ξ-hypothesis, 12 illustration, 13 rutile, 305–6, 311 Scion Image software, 256 self-propagating high-temperature synthesis, 169, 199, 204 shaker mill, 117, 122, 131, 133, 139 Sherrer’s formula, 183 shock-attrition mills, 225 SHS see self-propagating hightemperature synthesis Si/C/PAN–C composites, 394 sialon ceramics, 182–3 sialon powders, 172 Siberian larch, 236 silicides, 179–80 silicon, 383


420

Index

silicon carbide, 176–9 silicon monoxide–carbon composite powder, 393 silicon nitride, 170 silicon nitride ceramics, 181–2 silver oxalate, 38 single wall carbon nanotubes, 384 Si–Zn–C composite, 385 Sn–Co–C composite, 382 Sn31Co28C41 composite, 392 SnO–B2O3–P2O5, 388, 396–7 sodium bicarbonate, 242 soft heating conditions, 356 soft mechanochemical synthesis, 125 future trends, 357 materials for lithium-ion batteries, 331–57 principles of solid inorganic compounds synthesis, 331–3 LiOH and Li2CO3 reactions with crystal hydrates and acidic salts, 348–54 LiOH reactions with anhydrous oxides, 333–43 LiOH reactions with solid hydroxides, 344–8 soft-mechanochemistry, 67 solid activation, 202 solid electrolyte interface, 363, 390 solid–liquid reaction ball milling as-milled products obtained, 152–8 binary alloy systems, 152–5 Fe1.3Sn powder particle SEM and TEM images, 154 milled product with addition of different PCAs, 158–9 nano-size intermetallic compound powder formation mechanism, 160 process control agents effect, 157–8 ternary alloy powders TEM images, 156 ternary alloy systems, 155–7 XRD results, 157

intermetallic compound powders production, 149–64 equipment schematic diagram, 151 experiment equipment and methods, 151–2 reaction mechanism, 158–4 comparison with high-energy ball milling, 161–3 main advantages vs mechanical alloying, 163 solid-state mechanochemical synthesis low-molecular organic compounds, 225–9 illustration, 227 possibilities in various types of reactions, 225–6, 228 solid reagents preliminary activation for subsequent heterophase reactions, 228–9 SPALTAN ’02, 84 spark plasma sintering process, 275–97 apparatuses and summary of consolidation of conditions investigated, 281 future trends, 296–7 mechanochemically activated powders, 281–2 MoSi2 system, 282–7 NbAl3 system, 293–5 schematic representation, 276 selected systems investigated, 278–9 starting powders used, 280 starting reactants mechanochemical activation, 277, 280–1 TiC–TiB2 system, 287–93 Spex 8000, 11, 175 Spex CertiPrep Inc., 48 Spex Mixer/Mill mod. 8000, 95 spin-orbit coupling, 319 spinel ferrites, 133, 134 spinel lithium manganese oxides, 366–9 materials prepared by mechanochemical processes, 369 spin–spin relaxation, 238 SPS see spark plasma sintering process srilankite, 311 stainless steel plates, 261–7


Index start material, 152 substrate temperature, 25 sulphides, 400 supersaturation, 234 surface atomic density, 58 tartaric acid, 242 temperature impulse, 22 ternary alloy systems, 155–7 thermal decomposition, 350 thermoreaction, 397 thymol, 82 TiC–TiB2 system, 281, 287–93 effect of milling time crystallite sizes in SPS samples, 292 SPS samples density, 291 sample shrinkage and temperature time profiles, 289 SPS sample when starting from unmilled and milled reactants, 290 XRD patterns of reactants as function of milling time, 288 TiN nanocoating, 270 characterisation, 271 cross-sectional view on Al and steel substrates, 268 interface between TiN coating and Al substrate, 270 original particles TEM image, 269 tin–graphite–silver composite, 382 Ti3SiC2, 179 titanate, 304–5 titania, 305, 316 DeNOx ability, 321 diffuse reflectance spectra, 315 light wavelength and photocatalytic ability relationship, 316 milling time effect on rutile phase mole fraction, 312 NOx gas decomposition activity, 318 particle size distribution and medium diameter, 313 S 2p XPS spectra of mixtures ground for 20 and 120 minutes, 319 titanium, 259, 267

421

titanium carbide, 173–6, 179 titanium coatings, 261, 262 titanium dioxide, 304–5, 304–26 acetaldehyde photo degradations ability, 323 and BaCO3 mixtures TEM micrographs, 74 TG and DTG profiles, 73 C 1s and N 1s XPS spectra of P25, 320 doped TiO2 total densities, 310 electron-hole separation mechanism during photocatalysis, 323 energy diagram and photoinduced charge transfer process, 307 F1s of SrF2-doped SrTiO3 sample and SrF2 powder XPS spectra, 325 malachite green oxalate sorption and degradation, 314 photocatalytic applications, 305–10 highly active visible-light induced TiO2 and its applications, 308–10 photocatalytic reaction mechanism, 306–8 structure, 305–6 polymorphs with distinct structure, 306 synthesis by mechanochemical doping, 310–25 binary composite photocatalyst, 322–3 carbon-doped and its photocatalytic activity, 317–18 co-doping effect on TiO2 photocatalysis, 320–2 effect on structure, sorption, and physicochemical properties, 311–14 fluorine doping and multipleelement co-doped photocatalysts, 324–5 nitrogen-doped and its photocatalytic activity, 314–17


422

Index

sulfur-doped and its photocatalytic activity, 318–20 TiO2-xNy/TiO2 composite acetaldehyde photodegradation ability, 324 washing process effect on photocatalytic activity, 326 t–P–T conditions, 10, 16–22 transition metals, 386 transmission electron microscopy, 205 tumbler milling, 160 tungsten, 179 turbo milling, 374 ultrasonic mechanical coating and armouring, 253 future trends, 272–3 key concepts, 253–5 representation, 254 ultrasonic vibration future trends, 272–3 key concepts, 253–5 mechanochemical plating and surface modification, 251–73 nanostructured coatings production, 267–72 nanocoatings characterisation, 270–2 surface morphology and coating nanostructure after treatment, 268–70 treatment conditions, 267

precoated substrates surface treatment, 260–7 LaPO4 coatings on stainless steel plates, 261–7 material systems and treatment conditions, 260–1 Ti coatings on Al plates, 261 surface modification and coating treatment, 255–60 Al surface armoured with Ti particles, 257 degree of coverage, 256–8 experimental, 255–6 particle sizes distribution, 258 set-up, 255 surface morphology and coating microstructure after treatment, 258–60 ultraviolet, 305 Uni-Ball-Mill, 170, 175 urea, 316, 325 Vegard’s law, 210 vibration mill, 130, 131, 139, 180 vibromills, 67 visible light irradiation, 305 Wako Pure Chemical Industry, 317, 319 wave theory, 14 Williamson–Hall method, 281, 284 zinc, 385 ZnFe2O4, 138 ZrO2 balls, 261


High-Energy Ball Milling

Mechanical Alloying and Milling

Vampire's Ball

Margaret Ball

Margaret Ball

Vampire's Ball

Witch Ball

Opal Ball

Bride Ball

Jingle Ball

Dead Ball

Summer Ball

Charity Ball

Jingle Ball

Kusudama Ball

Bride Ball

Jingle Ball

High Ball

Opal Ball

Opal Ball

Billiard Ball

9 Ball

Bride Ball

Witch Ball

Dead Ball

Vertical Milling in the Home Workshop

Milling Operations In The Lathe 5

Playing Without the Ball

Power The Ball Plateward

Ball and Surface Arithmetics

High-Energy Ball Milling

Mechanical Alloying and Milling

Vampire's Ball

Margaret Ball

Margaret Ball

Vampire's Ball

Witch Ball

Opal Ball

Bride Ball

Jingle Ball

Dead Ball

Summer Ball

Charity Ball

Jingle Ball

Kusudama Ball

Bride Ball

Jingle Ball

High Ball

Opal Ball

Opal Ball

Billiard Ball

9 Ball

Bride Ball

Witch Ball

Dead Ball

Vertical Milling in the Home Workshop

Milling Operations In The Lathe 5

Playing Without the Ball

Power The Ball Plateward

Ball and Surface Arithmetics

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