Combustion for Material Synthesis 1482239515, 9781482239515

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Combustion for Material Synthesis

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Combustion for Material Synthesis Alexander S. Rogachev Alexander S. Mukasyan

CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2015 by CISP CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20141029 International Standard Book Number-13: 978-1-4822-3952-2 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

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For our teacher Alexander G. Merzhanov

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Contents 1.

Self-propagating High-temperature Synthesis: History and Present

1.1. 1.2. 1.3. 1.4. 1.5.

Discovery Gasless combustion synthesis Combustion synthesis with gasiication of the reagents Combustion synthesis in gas–solid systems Combustion synthesis with a reduction stage: the thermite type systems and nanothermites Combustion synthesis with inorganic compounds as precursors Thermal decomposition of complex compounds Solution combustion synthesis Mechanical activation of initial powder mixtures for SHS Reactive multilayer nanoilms (foils)

18 25 27 32 34 37

2.

Thermodynamics and Kinetics of SHS

44

2.1. 2.2.

Introduction Thermodynamics and driving force of SHS processes 2.2.1. Thermodynamics of SHS systems 2.2.1.1. General principles 2.2.1.2. Equilibrium, reversibility, stationary and stability of the SHS processes and products 2.2.1.3. The equilibrium composition of the SHS products and the adiabatic combustion temperature 2.2.1.4. Examples of thermodynamic calculations for SHS systems 2.2.2. Thermodynamics of the preheating–reaction zone 2.2.3. The thermodynamics of the reaction cell Kinetics of heterogeneous reactions 2.3.1. Solid-state reactions 2.3.2. Solid–gas reactions 2.3.3. Reactions with the liquid phase 2.3.4. Reactions with gasiication of the initial solid phase reagent 2.3.5. Methods of high-temperature kinetics of heterogeneous reactions

44 45 45 45

1.6. 1.7. 1.8. 1.9. 1.10.

2.3.

3.

3.1. 3.2.

Theory of Structural Macrokinetics

Introduction: The concept of structural macrokinetics Macrokinetics of thermal explosion

1 1 4 9 11

54 59 65 77 86 90 93 100 115 116 119

125

125 128

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Contents Combustion for Material Synthesis

3.3.

Macrokinetics of combustion 3.3.1. Homogeneous and quasi-homogeneous combustion models 3.3.2. Microheterogeneous combustion theory of gasless systems Theoretical models of structure formation in SHS 3.4.1. Structure formation in gasless combustion 3.4.1.1. General concepts 3.4.1.2. Mass transport of reagents in the reaction cell: melt spreading 3.4.1.3. Transport of reagents in the reaction cell: capillary impregnation 3.4.1.4. Transport of reagents in the reaction cell: coalescence of the droplets 3.4.1.5. Transport of reactants in a reaction cell: mass transfer in the gas phase 3.4.1.7. Evolution of the product microstructure in the post combustion zone (secondary structure formation) 3.4.2. Structure formation in hybrid solid–gas systems 3.4.2.1. Model of structure formation during combustion of metals with nitrogen 3.4.2.1. Models of structure formation during combustion of non-metals in nitrogen Conclusion

3.4.

3.5.

4. 4.1.

4.2.

Experimental Structural Macrokinetics of SHS Processes

Experimental methods 4.1.1. Basic principles of experimental diagnostics of SHS processes 4.1.2. Combustion wave velocity and temperature–time proiles 4.1.3. Preparation of samples with a quenched SHS wave 4.1.4. Experimental modelling of the reaction cell 4.1.5. Dynamic electron microscopy 4.1.6. Time-resolved X-ray diffraction (TRXRD) 4.1.7. Other methods Experimental results 4.2.1. Dynamics of phase and structural transformations during the thermal explosion mode 4.2.2. Macrostructure of reacting media and of combustion front in self-propagating mode 4.2.3. Gasless combustion: evolution of micro- and crystal structures 4.2.3.1. Primary structure formation 4.2.3.2. Post-combustion processes and secondary structure formation 4.2.4. Evolution of the microstructure and phase composition

136 136 149 168 168 168 169 173 176 178 190 191 194 199 203

205 205 205 208 210 213 216 217 221 221 221 230 243 243 262

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and crystal structure during iniltration combustion 4.2.4.1. Titanium–nitrogen system 4.2.4.2. Niobium–nitrogen system 4.2.4.3. Aluminium–nitrogen system 4.2.4.4. Silicon–nitrogen system 4.2.4.5. Boron–nitrogen system 4.2.5. Experimental data on the thermite-type systems 4.2.6. Experimental data on sol–gel systems 4.2.7. Experimental data on mechanically activated systems 4.2.8. Experimental data on the reactive multilayer nanoilms 4.2.9. Thermal microstructure of the combustion wave

268 268 275 281 285 294 298 310 315 321 327

5.

Commercialization and Industrial Applications of SHS Products

331

5.1. 5.2. 5.3. 5.4. 5.5. 5.6. 5.7.

Introduction Powders and cakes Ceramic materials Cermets and functionally graded materials Products of SHS metallurgy Application of multilayer reaction nanoilms Conclusion

331 332 342 349 351 352 354

Endnotes References Index

357 359 394

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Preface And they said one to another, let us make brick, and burn them. And they had brick for stone, and bitumen for mortar. And they said, let us build us a city and a tower, whose top may reach unto heaven, and let us make us a name, lest we be scattered abroad upon the face of the whole earth. Genesis: 11:3

Throughout the history, people have tried to understand what skills and abilities qualitatively separate them from other living beings. Philosophers have come up with many definitions, including the ability to use tools for labor, language, social organization, wearing clothing, etc. However, the close inspection of the lives of our “small brothers”, leads to the conclusion that all these capabilities could be found, in their infant stages, in animals. Indeed, many animals use tools, e.g. a stick to get a fruit, a stone – to break a nut; there are kinds of languages that exist for the majority of animals, and the dolphins even call each other by personal names; social organization of an ant-hill, a beehive or a wolf pack withstood the test for millions of years, i.e. much longer than human civilization. Clothes are not worn by all human tribes (what about young children and nudists?!), but some shellfish and octopus cleverly ‘dressed up’ in the “foreign” shells. And yet there is the ability that no one on Earth, except the human being, possesses. It is the ability to make fire and use it. The exclusivity of this skill was well understood by our ancestors, indeed, in many myths and legends the ownership of fire makes people rivals of the Gods. The ancient Greek philosopher Protagoras argued that the man exists only thanks to the three God’s gifts, i.e. the fire donated by Promethean, the wisdom (mind) bestowed by Athena, and the rules of social organization provided by Zeus. Note the sequence of importance: the fire – the mind – the society. The unique role of combustion in the development of technical civilization was outlined in 1940 by N. N. Semenov, a prominent

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Russian scientist, one of the founders of the combustion science [1]: “The discovery of the fire and the method for its initiation, made by people in early ages and imprinted in many ancient myths, is one of the most original and, in any case, the greatest achievement in the human history ... In the hands of the primitive man this powerful tool has become the source of their cultural growth, which led them in the search for new processes that improve lives. Using fire they learned to smelt and forge metals, bake clay and much more. The fire gave the initial impetus to the rational technical thinking. Thus it is one of the primary origins of the science in general. From these prehistoric times to the present day the fire has been and remains the greatest creative and destructive force in the hands of the mankind. The use of fire is the center line of the technological progress of mankind.” Since the time when these words were written, the value of combustion has increased even more: it is enough to mention the rocket and space technology, jet aircraft or general “motorization”. Even the development of electric and nuclear technologies has not reduced the value of combustion processes. Currently more than 80% of the energy consumed by humanity is generated by the burning of natural fuels. In the middle of 20 th century, it seemed that all kinds of combustion processes have been developed, studied, and accommodated to serve the people. However, in the later portion of the 1960s, a group of Russian scientists discovered a new class of combustion processes, which they called self-propagating hightemperature synthesis, abbreviated SHS [2]. The history of this discovery and development of its technological applications have been described in many books and reviews [3–9]. It is not necessary to reiterate these publications. We only note that the development of SHS has encountered both the hot enthusiasm and belief in the infinite possibilities of this method, and the complete negation of the idea to use ‘uncontrolled’ combustion processes for the direct synthesis of materials. This is vividly described in the memoirs of A.G. Merzhanov, who is one of the founders of SHS [10]. This book is dedicated to the physical and chemical principles of synthesis of materials in the combustion mode. Are they robust enough? Like a plant grows from a grain, the new technologies are based on fundamental scientific discoveries and innovative scientific ideas. Is there such a “grain” in the SHS, and what are its conceptual characteristics? To reply to these questions, it is necessary to critically overview the existing theoretical concepts

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and experimental evidences on the fundamental mechanisms of SHS, and to compare this approach with other methods of fabrication of advanced materials. And this is one of the goals of this book. More than a thousand new publications on SHS (or combustion synthesis, as this method is also often referred) appear every year. It is not a task to analyze in details each new result in this field, since this would lead to an unreasonably large book, which is interesting only to specialists. But we try to identify the main trends and outline the prospective directions of SHS development. The main task of this book is to present, in a concise form, the state-of art in R&D in the field of SHS, focusing on the combustion synthesis of novel materials. This book is intended for researchers, engineers and graduate students from different disciplines – everyone who wants to make their own opinions about the advantages and disadvantages, achievements and unsolved problems of heterogeneous combustion used for material synthesis. It is a multidiscipline field of science, which covers a wide range of knowledge from combustion theory to the fundamentals of materials science. Unfortunately, this combination of knowledge is uncommon. Indeed, typically one meets the outstanding professionals in combustion science, who do not consider it necessary to understand and use the modern capabilities to study the structure and properties of materials, even if these materials are combustion products. No less common are outstanding materials scientists, for whom the notions of combustion processes do not extend the high school programs in chemistry. If, after reading this book, at least some combustion-oriented scholars recognize that the knowledge of the real product structure and properties is necessary for the understanding of the combustion mechanisms, and materials scientists and chemists agree that combustion can be a reproducible and controlled process for the production of materials, the work of the authors will not be in vain. Finally, the authors hope that this book will also be of interest to specialists in the field of SHS. Upto-date issues of the development of this scientific and technical direction, part of which has been formulated above, while others are considered in the book, can be resolved only through the collective efforts of the experts of entire SHS community.

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SHS: History and Present

1

1 SELF-PROPAGATING HIGH-TEMPERATURE SYNTHESIS: HISTORY AND PRESENT All intelligent thoughts have already been thought; what is necessary is only to try to think them again J.W. Goethe

1.1. Discovery Discoveries do not arise out of nothing. Each new theory or experimental result has its own background and recognizing the achievements of predecessors is a sign of scientific professionalism. On the other hand, discoveries do not take place ‘according to plan’. They are always unexpected. For example, Christopher Columbus was looking for a new route to India and discovered America. This discovery would not have taken place if all previous history of naval engineering, navigation, combined with the courage and tenacity of Columbus and his companions did not pave the way across the ocean. When the new continent was ‘discovered’, the Europeans met people who had come there thousands of years before Columbus and even managed to create the civilizations. Perhaps the stories of many scientific discoveries have something akin to the discovery of America: based on the experience of predecessors, the researcher hunts for the predicted outcome and unexpectedly finds something new… And then it turns out that he is not the first ‘on this continent’. The history of the discovery of self-propagating high-temperature synthesis (SHS) is not an exception.

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In the 1960s, a group of researchers from the Institute of Chemical Physics, Academy of Sciences of the USSR, under the leadership of the young head of the laboratory Alexander G. Merzhanov looked for combustion systems, which would be burned without producing a gas flame [10, 11]. This was necessary in order to understand the role of reactions in the condensed phase during combustion of gunpowder and solid rocket propellants. It should be noted that the issue of the relationship of gas-phase and solid–liquid-phase processes during combustion of condensed fuels are still being discussed in scientific journals, so that A.G. Merzhanov and his colleagues did not manage to achieve the planned objectives. However, they discovered something that they did not plan – a new method for the synthesis of materials in the combustion mode. When this method gained world recognition, earlier studies, even of the 19th century, were found, where some similar phenomenon had been observed and described [12]. It is important to understand the history of the SHS to more clearly distinguish the novelties it brought to science and technology. But first, let us introduce some fundamental concepts. Considering the SHS as a variety of heterogeneous combustion, three stages of the process can be outlined: 1) mixing the components at room or slightly elevated temperature, when the chemical reaction does not yet take place; 2) the initiation of an exothermic chemical reaction (ignition or self-ignition); 3) a self-sustaining chemical reaction which occurs without external heat sources and leads to the formation of combustion products (in the case of SHS they are chemical compounds, powders, materials or net shape articles important from the practical viewpoint). The initiation of a chemical reaction is usually carried out by heating the reaction mixture and there are two entirely opposed methods of heating. The first way is to heat the whole sample slowly so that temperature has time to equalize over the entirety of its volume. In this case the reaction should develop simultaneously and uniformly at all points of the sample and at a specific temperature one should observe a sharp self-acceleration of the process – the whole sample evenly ‘self-ignites’. This SHS mode is called volume combustion or thermal explosion, it is illustrated in Fig. 1 a. SHS in the thermal explosion mode has much in common with reaction sintering in powder technology, but there is a fundamental difference. It consists in the fact that in reaction sintering it is necessary to

SHS: History and Present

3 a

time

temperature

Uniform heating of the initial sample

Final product

Propagation of the front of the combustion wave temperature

b

coordinate

Local initiation of the reaction

Thermal explosion

Initial sample

SHS

Final product

Fig. 1.1. Self-propagating high-temperature synthesis modes: a – volume combustion, b – auto-wave combustion (for the colour image please see the colour section in the middle of the book).

avoid spontaneous heating of the sample by chemical reaction, whereas in SHS this warm-up is utilized. The theory of thermal explosion was developed in the works of the outstanding Russian scientist and Nobel Prize winner N.N. Semenov and his followers. Some aspects of the theory and mechanism of this process will be discussed in chapter 3. The second way of ignition is optimal rapid heating of only a small volume of the sample (e.g. ~1 mm 3) that results in local reaction initiation of an exothermic reaction, which then selfpropagates to the rest of the sample in the form of a combustion wave. This SHS mode is called the wave or auto-wave combustion mode. Figure 1.1 b shows schematically such a process. Fast heating is needed to ensure that the heat from the local area of ignition has no time to spread to nearby areas and create an uneven temperature distribution in the sample. The point is that the route of the reaction and thus the properties of the combustion products depend on the initial temperature of the medium. Consequently, if the initial temperature is not uniform, the products of combustion synthesis are varied in the volume of the sample. Typically, the non-uniformity of

4

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the product is undesirable, except in special cases where the purpose of synthesis is to provide materials with a gradient structure and properties. The properly arranged volume and wave combustion modes are like two poles where the temperature is uniform throughout the sample at the time of initiation of the reaction. In the first case, the entire sample is evenly heated, and in the second – the entire sample, with the exception of a small area of a local ignition, is ‘cold’ at the time of the initiation of the reaction. Intermediate modes of reaction initiation, in which the sample has time to non-uniformly heat up, and then ignited at one end, are still often used in material science laboratories; however, the results thus obtained are unsuitable for investigations of combustion mechanisms. It is natural to ask whether the thermal explosion mode can be included in the group with the SHS processes, because in this mode there is no propagation of the combustion wave in space. We think that this is a question of just terminology, which will be resolved in the near future. If we use the alternative term for SHS, i.e. ‘combustion synthesis’ then such a problem does not arise. In any case, the key here is the term ‘synthesis’, not ‘self-propagation’, and therefore synthesis in the thermal explosion mode (volume combustion) is considered in this book together with the wave-type combustion modes. To conclude the definitions, we are ready to return to the history of the development of SHS. Since the concept of ‘SHS’ covers at present time a lot of different processes, each of which has its own history, we examine these processes gradually using the classification recognized by researchers.

1.2. Gasless combustion synthesis Gasless combustion was the first variant of the new SHS method for synthesis of materials. This is understandable, since, as noted above, the discovery of the SHS was made when searching for systems that can burn without a gas flame. At that time it was shown that a mixture of two or more powders of refractory elements could be an ‘active’ medium in which the front of the reaction may self-propagate with formation, for example, of titanium carbide:

Ti + C = TiC + 310 kJ.

SHS: History and Present

5

The heat released in the process is so high that the temperature of solid and molten products may reach up to 2500–3500 K, so that the reaction does not depend on any external sources of heat and may spread like a combustion wave, which self-produces energy for its propagation. It is interesting that in many systems, despite the high temperature, the transition of any of the components of the mixture to the gas phase is extremely small and thus can be neglected. In the example mentioned above, i.e. during combustion of the Ti + C mixture, the total vapour pressure at a temperature of 3300 K is only 0.0058 atm, or about 4 mm Hg with the main contribution through evaporation of titanium. Also note that gases may be emitted not only by evaporation of the main reagents, but also due to gasification of impurities. For example, powders of transition metals (Ti, Zr, Hf) usually contain an appreciable amount of adsorbed hydrogen (2–3 wt.%) and also the fractions of a percent of CO, N 2, which transform to the gas phase during heating. Although these impurity gases may also affect the mode of the reaction wave propagation, they typically do not participate in the main combustion reaction and have no significant effect on the heat of reaction. The main precursors and combustion products (including intermediates) are in the solid or liquid (melt) state in such systems. Based on the above, it was decided to neglect the impurity gas evolution and assume that this type of combustion is a gasless process. The first product of gasless combustion mentioned in the literature was a molybdenum disilicide (MoSi2). A note was placed in 1959 in a scientific journal, which is now difficult to find, and consisted of 78 words in the German language and it is therefore appropriate to present it in its complete translation [13]: ‘‘molybdenum disilicide was obtained in a water-cooled closed container from elements. Argon was passed through the reaction space to create an inert (shielding) atmosphere, and the ignition of the reaction was carried out electrically by means of a molybdenum spiral. This method was selectively complemented by hot pressing at 1550–1750°C. The sample compacted at high temperature was immediately placed in an oven preheated to 1200°C and slowly cooled. The achieved density was equal to 6.15 against the theoretical value of 6.24. MoSi2 blends especially well with Al2O3. Such material has metallic conductivity to the Al2O3 content of 70%, after that the conductivity drops sharply.” A year later, the same author published a communication in the book [14] where he expanded on the description of the process, noting the uniformity of reaction propagation and that the product is strongly

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‘red-hot’. As we can see, these brief notes contain many features of gasless SHS: synthesis of a mixture of elementary powders, a watercooled reactor and the atmosphere of an inert gas to initiate locally the reaction with a heated electric spiral. Hot pressing and furnace annealing of the synthesized material were also tried. However, the author, a British materials scientist J.B. Huffadine was interested mainly in the final product and its properties; therefore he did not examine the process of synthesis and did not propose to use gasless combustion for the production of other materials. Perhaps the fact that he did not work in an academic institution, but in the laboratory of a private company Plessey in Caswell (Scotland), and thus was focused on getting new materials, primarily for the electronics industry, may explain why J.B. Huffadine missed the discovery of a new class of combustion processes. The next time gasless combustion was mentioned was in the works of A.G. Merzhanov and his co-workers, who very well understood the scientific importance and application capabilities of the new process, they synthesized dozens of compounds by SHS and secured the priority of this discovery by patents in several countries [15]. Among the first scientific studies, one should mention the proceedings by V.M. Shkiro on the Ti–C system at a conference of young scientists [16] in 1970, which have become now a bibliographic rarity, virtually inaccessible to the reader. The first publication in the generally available journal was the article by A.G. Merzhanov and I.P. Borovinskaya [17], which is cited today by most authors as a pioneering work in the field of SHS. This paper reported on two types of gasless SHS systems: metal–carbon and metal–boron. Around the same time, reports appeared about the possibility of gasless combustion in the metal–metal systems, first in the thermal explosion mode [18], and then in the mode of the self-propagating reaction wave [19]. The synthesis of silicides was also studied on a new scientific level [20]. Thus, from a chemical point of view, the process of gasless SHS includes four types of chemical reactions: –metals and non-metals with carbon producing carbides; –metals with boron to make borides; –metals with silicon, giving silicides; –metals with other metals to synthesize intermetallic compounds. In general, these reactions can be described by the chemical formula

SHS: History and Present

7

A + xB = AB x ,

(1.1)

Combustion temperature, K

A – the first reagent, usually a metal (Ti, Zr, Hf, Nb, Ta, Mo, Ni, Co, Fe, Cu, Si); B – the second reagent, mostly non-metals (C, B, Si, Al, Ni); x – stoichiometric ratio. Some element may play the role of both the first and second reagent, e.g. Ni + Al = NiAl and Ti + Ni = TiNi. The diagram in Fig. 1.2 shows the heat of formation from the elements and the adiabatic combustion temperature (i.e. the maximum temperature of the products of combustion in the absence of heat loss) of some of the compounds for the above four types of reactions. The diagram indicates the general pattern: all compounds with a large heat of formation can be synthesized in the gasless combustion mode. The compounds with moderate heat of formation can also be obtained by SHS but require additional external preheating. For the compounds with a relatively low heat of formation there are usually no reports on the synthesis in the combustion mode. For the overwhelming majority of gasless SHS compositions the combustion temperature exceeds the melting point of at least one of

Synthesis heat, kJ/mol Auto-wave SHS is proved No data on SHS from elements SHS with additional preheating

Fig. 1.2. The adiabatic combustion temperature and the heat of formation of elements for some two-component systems.

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Combustion for Material Synthesis

the reactants, products or exceeds the lowest eutectic temperature of the system. However, there are exothermic compositions for which even the adiabatic combustion temperature is below the minimum melting temperature in the system. The most striking example is the Ta + C composition which burns at the maximum temperature of 2734 K, while the eutectic temperature (Ta–Ta 2C eutectic) is equal to 3120 K. In other words, the gasless combustion in the Ta–C system should take place solely by means of solid state reactions. This fact played an important role in the development of SHS. The point is that the combustion processes with melting of the reactants have long been known, although it was not synthesis from the elements (e.g. burning of thermites, which will be considered in section 1.5). But the autowave combustion processes only by solid state reactions were not known at that time! This was the basis for registration in 1984 (with a priority of 05.06.1967) of the invention titled ‘The phenomenon of wave localization for auto-retarded solid-state reactions’. The essence of the invention is formulated as follows [21]: “Experiments established the previously unknown phenomenon of wave localization for self-retarded solid-state reactions, consisting in the fact that the chemical interaction between the solid dispersed components occurs without melting and gasification of the reactants and products, after thermal initiation is localized in a zone moving spontaneously in the space of the reagent in the form of a combustion wave’’. As will be shown below, the mechanism of solid-phase combustion is much more complicated than it was initially considered, but patenting the invention played a positive role in the development of SHS as a scientific and technological direction and attracted the attention of researchers in many countries. To date the mechanisms of gasless combustion and properties of the synthesized products were thoroughly investigated for dozens of simple compounds, indicated in Fig. 1.2. A large number of ternary and multicomponent systems, products and materials obtained thereof, are also being studied. As examples of practical applications it is worth noting the double carbide powder (Ti, Cr) C, is used for applying heat-resistant coating on metals, or ceramic material TiC– TiB2, has high hardness and wear resistance. Gasless systems remain also a popular target for experimental and theoretical research, which expands our understanding of the processes of heterogeneous combustion. These issues will be discussed in more detail in the subsequent chapters.

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1.3. Combustion synthesis with gasification of the reagents The overall chemical reaction for these processes can be described by the same equations as the gasless systems (1.1), with the only difference being that the reagent (B) is represented by the more volatile elements, such as S, Se, P, As, Sb. The number of the reagents (A) for these systems is even greater than the gasless systems since we may add metals from groups I–III of the periodic table (Na, Ca, Zn, Al, etc.) to the elements listed in section 1.2. Combustion reactions in such mixtures were discovered by the famous French chemist and pharmacist Henri Fonzes-Diacon, who reported it in 1900 in the scientific journal Comptes Rendus [22]. In the same year a brief overview of this article was published in Science, in a review of inorganic Chemistry, with the initials J.L.H. [23]: “Direct production of several double aluminium compounds described by Henri FonzesDiacon in Comptes Rendus. Sulphide, selenide, phosphide, gallium arsenide and stibid – they are obtained by the ignition of a fine powder mixture of alumina with the corresponding elements. In the case of sulphur and selenium, for igniting the mixture we need a small amount of burning magnesium; with antimony for the same purpose one can use sodium peroxide”. Recall that the ‘stibids’ in those days were called antimonites, i.e. a compound with antimony (Sb). H. Fonzie-Deacon died in 1935; he was Dean of the Faculty of Pharmacy at the University of Montpellier in southern France. His research interests were very broad, in particular, his name is mentioned in monographs with respect to the development of French wine making. However, he did not publish any further works on the synthesis of inorganic compounds by combustion. This class of chemical reactions was referred next after the discovery of SHS. Up until now, a variety of materials had been synthesized, including nickel [24, 25] and titanium [26] phosphides, zinc [27] and tungsten [28] selenides, as well as some ternary compounds, which are considered in subsequent chapters. However, the number of papers published for the SHS systems with gasifying components is a hundred times less than that for gasless chemical systems. There are several reasons for this. First, in this case the combustion synthesis process is complicated by the rapid evaporation of the reagents: for example, sulphur boils at 445 o C, selenium at 685 o C, white phosphorus at 257 o C, and black phosphorus (the most refractory compound) sublimes at

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Combustion for Material Synthesis

453 oC. Consequently, even if we ignore the fact that the vaporized reactant may exit the sample to the environment, the reaction in such systems does not proceed to the end. For example, according to thermodynamic calculations, synthesis in the combustion mode in the Zn–S system to obtain a compound ZnS (used as a luminophore) leads to the following result: Zn + S ≈ 0.69 ZnS (sol.) + 0.31 Zn (gas) + 0.15 S 2 (gas) with the adiabatic combustion temperature ~1860 K (1587 oC). Thus, due to gasification, instead of one mole of the product only 0.69 moles can form in the combustion wave. The second difficulty is the high toxicity of volatile reagents and compounds, which places stringent demands on synthesis equipment: it is necessary to keep all vapors within the reactor vessel to return them back into the reaction zone and avoid release into the atmosphere. The third reason is the existence of some compounds such as sulphides, as natural minerals. Well known and widely used are minerals cinnabar (HgS), pyrite (FeS 2), millerite (NiS), heazlewoodite (Ni3S2), godlewskite (Ni7S6), polydymite (Ni3S4), vaesite (NiS 2) and others. Should one extract elemental substances from mineral raw materials to prepare powder from them, and then mix and burn them to obtain compounds which were already present in the original minerals? This method is not always economically justified. Note that by this feature the considered compounds differ from the products of gasless combustion (see section 1.2). Indeed, for example, carbides have not been found among earth minerals, but only in meteorites. In 1889 the Austrian scientist E. Weinschenk discovered the cohenite mineral in meteorites which is complex carbide of iron, cobalt and nickel with the composition (FeNiCo) 3C. French chemist Henri Moissan found in 1904 in a meteorite from the Diablo Canyon (Arizona, USA) a dark green mineral representing silicon carbide SiC; this mineral was named moissanite. Finally, the fourth reason for the relatively small interest of scientists and engineers in combustion of such systems is because of the high combustibility of phosphorus, sulphur and other components in the air; their rapid inflammation on contact with water complicates the experimental research and, most importantly, the application of this class of processes in technology. It can be concluded that to date, due to a number of reasons, the SHS systems with gasifying agents

SHS: History and Present

11

have been studied insufficiently. The scientific and technological potentials of this group of SHS processes have yet to be uncovered

1.4. Combustion synthesis in gas–solid systems (infiltration combustion) Combustion synthesis in the systems involving a gas-phase reagent is one of the most important types of SHS. The process is described by the same chemical equation (1.1) as previously discussed processes, with the main difference being that reagent B is a gas. Attempts to find the origins of this class of reactions take us back to 16 th century. The famous alchemist, physician and expert in the occult sciences Phillippus Aureolus Theophrastus Bombastus von Hohenheim, better known as Paracelsus, showed that combustion requires air, and metals transforming to oxides increase in weight. One of the fathers of modern chemistry Antoine Lavoisier in 1775 explained the phenomenon of combustion and firing as a process of interaction of substances with oxygen. Great chemist Jens Jakob Berzelius first produced zirconium powder in 1824 and a year later reported that zirconium burns in air, turning to the oxide [29]. However, all these works of the great chemists can hardly be viewed as prototypes of SHS in the gas–solid systems. It is clear that in these classical papers there was no mention of the organization of the burning regime, since the theory of combustion and thermal explosion appeared much later. It should also be noted that the combustion of elementary reactants (metals and nonmetals) with oxygen is not used widely in SHS for the synthesis of materials. The reasons are the same as for the above-mentioned sulphides. Indeed, why, for example, burn zirconium in oxygen to obtain an oxide, if the mineral based on this oxide is present in nature, and it was the merit of Berzelius that he was able to separate metallic zirconium from the oxide? Note that an oxygen-containing atmosphere is more frequently used in the synthesis of complex oxide compounds, such as, for example, high-temperature superconducting ceramics YBa 2Cu 3O 7–x , as well as in the processes of synthesis in combustion of solutions, as discussed in section 1.8. Analysis of the literature suggests that the main gas reagent used in the SHS is nitrogen (N2)! Despite the fact that classical chemistry considered this major component of air incapable of supporting combustion (in contrast to oxygen), the reaction of metals with nitrogen taking place with intensive self-heating were known to

12

Combustion for Material Synthesis

chemists for a long time. For example, the reaction of titanium with nitrogen taking place from an intense glow and the formation of a nitride was reported by Henri Moissan [30]. However, this outstanding chemist who got the Nobel Prize in 1906 for his invention of the electric arc furnace and for his work on the chemistry of fluorine did not attempt to arrange the combustion process either in the auto-wave mode or in the bulk combustion mode: he simply heated the titanium powder in a flow of nitrogen. The same conclusion can be related to the early work on the combustion of cerium in nitrogen [31]. Thus, the first experiments in which the combustion of metallic powders in a nitrogen atmosphere was organized as the auto-wave process represent early stages of SHS development. A pioneering article on the synthesis of nitrides of transition metals (Zr, Ti, Nb, Ta) was published in 1972 [32]. The next fundamentally important steps were the combustion synthesis of silicon nitride Si3N4, [33, 34], boron nitride [35] and aluminium nitride [36], which are the basis of many advanced ceramic materials. At present, all binary refractory nitrides, as well as many ternary and multicomponent materials based on nitrides, which have practical value, have been produced by SHS. The second most important gas phase precursor for the SHS processes is hydrogen. Combustion of metals in hydrogen in the SHS mode to form hydrides was first reported in [37]. Recently, interest in this direction has increased due to the development of prospects of hydrogen energetics: hydrides of some metals and alloys can be effective for hydrogen storage. Metals, as is well known in chemistry, also readily burn in gases such as chlorine and fluorine, but these reactions cannot be used for SHS because of the extreme aggressiveness and toxicity of these gases. Besides the elementary gaseous reactants, many transition metals can burn in an atmosphere of gaseous hydrocarbons, e.g. C 2 H 2 or CH 4 (thus obtaining metal carbides and releasing hydrogen), as well as in CO and CO 2 (to form carbides and oxycarbides), but these systems have not been studied in details. All SHS processes that involve a gas reagent are considered to be an infiltration type of combustion. Infiltration combustion (IC) is the phenomenon of propagation of the combustion wave (front of a chemical reaction) in porous media with ‘feeding’ (infiltrating) of the gas to the reaction front. Generally speaking, IC may occur both in the self-propagating and the thermal explosion regimes. The auto-wave regime is schematically presented in Fig. 1.3, which shows a sample of compacted metal (or non-metal) powder placed

SHS: History and Present

Vf

Vf

13

B – gas

Vf

Vf A(sol) + xB(gas) = ABx(sol)

Filtration of gas through the porous frame

Fig. 1.3. Auto-wave mode of infiltration combustion (for the colour image please see the colour section in the middle of the book).

in a chemical reactor of constant pressure (its volume is much higher than the sample volume). The sample has a relative density Δ (thus relative porosity of the medium is Π = 1 – Δ). For example, if the titanium powder (Ti theoretical density ρ t = 4.5 g/cm 3 ) is compacted to the actual density ρ = 2.25 g/cm 3 then Δ = ρ/ρt ≈ 0.5, which means that half the volume of the sample is occupied by the pores. The porosity can be open, providing gas access from the external environment, and closed. The pressure of the reaction gas (e.g. nitrogen) in the reactor power is equal to P and coincides with the initial gas pressure in the pores of the sample. Initiation of the reaction leads to the propagation of the combustion wave front with velocity U owing to interaction between the initially solid phase of porous skeleton (A) and the gas (B) according to the reaction (1.1). The combustion wave is followed by the formation of the solid-phase product (AB x). It is necessary to distinguish between the gas initially contained in the pores of the sample (internal reagent) and in the environment (external agent). At relatively low pressures in the reactor, the amount of internal nitrogen may be insufficient to ensure adequate heat required for the propagation of the wave. In this case, combustion wave propagation maybe due to infiltration of nitrogen from the environment to the combustion front through pores of the solid reaction media. Infiltration takes place due to the pressure difference arising between the combustion zone, in which nitrogen is absorbed (P = 0), and the surrounding atmosphere with constant pressure

14

Combustion for Material Synthesis

(P 0 ). Indeed, the gas contained in the pores is quickly absorbed in the front of the combustion wave due to the reaction with the solid particles. As a result, the gas pressure in the pores sharply decreases (in the limit to zero), while the external pressure in the reactor remains constant and equal to P0. There is a pressure gradient ΔP/Δx (where Δx is the characteristic scale, such as the radius of the sample), which is a driving force in the supply of the gas-phase reactant from the outside to the reaction front. This process can be compared to the effect of a chemical pump, which supplies the gas from the environment to the reaction surface in the sample volume. The question naturally arises: is the infiltration of gas from the outside necessary for the existence of the self-sustained combustion wave? Is it possible to ensure that the gas, initially located inside the pores of the sample, is sufficient for the synthesis process? Obviously, this gas must be at high pressure, but what is the magnitude of this pressure? One can make some simple estimates. Consider the same reaction (1.1) with respect to systems with a single gas reagent: A(sol) + 0.5 xB2 (gas) = AB x (sol) Here it is taken into account that the most commonly used gas reagents, i.e. N2 and H2, are diatomic molecules. The relative porosity of the medium (Π) is the total pore volume divided by the total sample volume. If the mass of the gas in this volume (pore) is such that per mole of solid reactant A we have 0.5x mole of the reactant gas B 2, the reaction will be complete without the participation of the gas from the outside, but solely by the gas stored in the pores. It is easy to show that to fulfill this condition the density of the gas in the pores must be equal to the critical value ρ B: rB =

xM B 1 − P rA , MA P

(1.2)

where ρ A and ρ B are the densities of the solid reactant A and gas reactant B2, respectively; M A, M B are the molecular (mole) weights of the reagents. The results of calculation by formula (4.15) for the ‘solid reagent – N 2’ systems are shown in Fig. 1.4. Typically, the relative porosity of the sample does not exceed 0.5–0.6 (samples with greater porosity crumble when handled), but the samples with a porosity of less than 0.35–0.4 are also rarely used in the combustion mode. As can be seen from Fig. 1.4, in

Density of nitrogen, g/cm 3

SHS: History and Present

15

Solid nitrogen

Liquid nitrogen

Porosity Fig. 1.4. The critical density of nitrogen in the pores of the sample, sufficient for 100% conversion of the solid reactant to the corresponding nitride.

the range of actually used porosities (0.35 to 0.6) the value of the critical density of nitrogen is very high. For most systems, it is higher than the density of liquid nitrogen and for some is higher than the density of solid nitrogen! It is difficult to estimate how much pressure is required to compress the nitrogen to such a density. The van der Waals equation for real gases, of course, does not apply to this density range. A highly rough estimate can be made, perhaps, with the help of the so-called virial equation of state, but even this equation does not work when approaching the density of the liquid and the gas becomes difficult to compress [38]. Figure 1.5 shows the results of estimates of the critical pressure of nitrogen by using the virial equation: PB =

RT  C D + 1 + , VB  VB VB2 

(1.3)

where VB = MB/ρB – molar volume of the reactant gas; T = 298 K – initial room temperature; virial coefficients for nitrogen C = –5.47 cm3/mol, D = 1437 cm6/mol 2. It can be seen that the critical pressures are in the range of tens and hundreds of thousands of atmospheres for the Zr–N 2 and Hf–N 2 systems, while for other systems the critical gas density is higher than the density of liquid nitrogen. Thus, calculations show that it is

Combustion for Material Synthesis

Nitrogen pressure, MPa

16

Density of liquid nitrogen Density of solid nitrogen

Nitrogen density, g/cm 3 Fig. 1.5. The critical pressure of nitrogen stored in the pores at room temperature, required for complete conversion of the solid reactant to a nitride. Porosity P = 0.6.

impossible to store the reactant gas inside the sample in an amount necessary for 100% completion of the reaction. But is it always necessary to complete the reaction for the propagation of combustion wave? For example, in the Ti–N 2 system reaction heat is so high that the adiabatic combustion temperature reaches 3446 K, when the reaction product TiN melts completely and partially dissociates. Thermodynamic calculations show that if only one tenth of titanium reacts with nitrogen, the temperature in the reaction zone may already exceed 1300 K, and if one-fifth of titanium reacts, the temperature is over 2000 K. And it is shown that the combustion wave can already self-propagate at these temperatures. Although these critical densities and gas pressures still remain pretty high (hundreds or thousands of atmospheres), they can be achieved in high-pressure reactors. Thus the SHS wave with a single gas phase reactant may in principle propagate due to the gas stored in the pores. However, to complete the reaction during post-combustion stage it is required to ensure infiltration supply of the gas reagent from the external atmosphere. And, as it is shown in section 4, this is the typical route for the final SHS-product formation in the gassolid (hybrid) reaction systems. There is another method to increase the degree of conversion in the reaction front of the combustion wave. Assume that in addition to solid reactant (A) and pores, filled with reagent gas (B), the original sample already contains some amount of final solid AB x, i.e. the reaction equation is as follows:

SHS: History and Present

A(sol) + 0.5 xB2 (gas) + yAB x (sol) = (1+ y )AB x (sol).

17

(1.4)

For fixed pressure and porosity, the greater the amount of ABx in the initial mixture, the more gas per solid reactant in the pores of the skeleton of the sample. In this case equation (4.15) for the critical density of the gas takes the form rB =

xM B 1− P rA rAB , M A rAB + yM ABrA P

where ρ AB is the density of the product AB x. Dilution of the initial mixture by the reaction product is a very effective way to increase the ratio of gaseous and solid reactants inside the sample and is often applied in practice. Its advantage is that incomplete combustion is reduced to a minimum, i.e. the combustion product does not retain any initial component A, and the entire phase consists of the desired phase AB x. On the other hand, in this case some amount of released energy is used for preheating of the inert additive, which does not participate in the reaction; therefore, this approach is applicable only to systems with large energy generation. For example, for the Ti–N 2 system for y = 8 (Eq. 1.4) the adiabatic combustion temperature is ~1610 K, and for y = 9 it decreases to 990 K, and the combustion mode becomes unobtainable. Thus, in most cases, infiltration of the reactant gas from the environment into the porous sample is essential for the synthesis of the single-phase product by SHS in the solid–gas systems. It turns out that in such systems there are typically two stages of the chemical interaction. During the first stage, the reaction proceeds with a degree of conversion that is significantly less than 100%, however this stage controls the velocity and temperature of the combustion wave. The second stage, the so-called volume postcombustion stage, under optimal conditions may lead to complete conversion of the solid phase reactant to the final product with the desired composition. In concluding this section, it is worth noting that the concept of ‘infiltration combustion’ refers not only to the SHS processes. Some examples are: infiltration combustion of gases in chemically inert porous media [39]; propagation of the reaction wave during infiltration of the reaction gas mixture through the bed of a solid catalyst [40]; infiltration combustion of oil- and gas-bearing fields [41]; burning of debris in infiltration combustion reactors with super-

18

Combustion for Material Synthesis

adiabatic heating [42], and others. Infiltration combustion is also a favourite object of study in the field of combustion theory.

1.5. Combustion synthesis with a reduction stage: the thermite type systems and nanothermites A simple chemical scheme for the synthesis of inorganic compounds and materials involving the reduction stage is described by the equation AB x + yC + zD = AD z + B x C y .

(1.5)

where A – the first element, usually a metal: Fe, Ni, Co, Cr, Cu, W, Mo, Bi, Ti, Ta, etc., but may be a non-metal, such as boron or silicon; B – a second element, usually oxygen (O); C – a third element is a metal – reducing agent, typically Al or Mg, less often Ti or Zr. D – a fourth element which can react with component A, after the latter is reduced from compound, is often represented by carbon; x, y, z – stoichiometric coefficients. A typical example of the reaction (1.5) is the process: 3Cr2 O3 + 6A1+ 4C = 2Cr3 C 2 + 3A12 O3 ,

that may occur in the combustion mode, with the temperature reaching 2320 K, which is above the melting point of the carbide Cr 3C 2 (2100 K) and is equal to the melting point of the oxide Al 2O 3 (2320 K). The combustion products are in the molten state, so the process is often referred to as SHS metallurgy [43]. Another popular name is the thermite type system that indicates the relationship of the reaction with the metallothermic processes. The boiling points of aluminium and magnesium are 2773 K and 1380 K respectively, and many aluminium and magnesium thermite reactions occur at a temperature above 3500 K, therefore, the thermite type processes are obviously not gas-free. The thermite mixtures are most often referred to in the literature as prototypes of SHS systems, and an opinion exists that the synthesis of materials by SHS is not a new scientific and technological direction, but only the further development of the thermite area. In Russian literature, it is believed that metallothermy was developed by N.N. Beketov in 1859–1865, and in the foreign literature it is stated that metallothermy was invented by G. Goldschmidt in 1895 or in 1898. Let us try to analyze the case.

SHS: History and Present

19

N.N. Beketov was professor at the Universities in Khar’kiv and Moscow, Academician of the St. Petersburg Imperial Academy of Sciences. He was an enthusiastic, versatile scientist, one of the founders of physical chemistry. The lectures, which he gave not only for students, caused great public interest. As recalled by one of his students A.M. Il’ev [44]: “He often mentioned the fact that for a whole hour he could not stop discussing the issues that had, apparently, no large value to its program. The audience was amazingly affected by this, there were no bored people, and the most indifferent people became interested… His lectures were given the best evidence of the benefits of live speech in comparison with the book”. Selected papers and lectures of N.N. Beketov were published in 1955 [45], but there was no report on the discovery of metallothermy! The first indications of the reduction reactions of oxides with aluminium and magnesium were found in the Bulletin of Annual Meetings of the Chemical Society in Paris (1859) [46], and in the doctoral thesis of N.N. Beketov [47] published in 1865 in Khar’kiv. These works have become a bibliographic rarity, but fragments of them are cited in the book of A.I. Belyaev [48]. So, what did N.N. Beketov accomplish? In the thesis [47] there are two important conclusions: first is that aluminium reduces barium and potassium from their oxides, and, secondly, magnesium reduces aluminium from its fluoride (cryolite). These findings were the result of both theoretical analysis and experiments. Here is what N.N. Beketov wrote [47]: “For the experiment, I took a calcined and milled to powder barium chloride and put it with pieces of aluminium in a coal crucible; thus prepared crucible was placed for protection against oxidation in the other clay crucible and covered by coal powder; this all was then annealed for several hours. In the cooled down crucible I found a fused metal bead, which was clean not affected aluminium without any barium contamination. So it is clear that the aluminium does not dissolve barium chloride. For special reasons, however, I was convinced that although the aluminium does not reduced barium from barium chloride and possibly also bromide and iodide, it does reduce it from oxygen compounds, i.e. oxide. To verify this experiment, I took the anhydrous barium oxide, and adding to it a certain amount of barium chloride as a fluxing agent, put this mixture together with a piece of aluminium in a coal crucible and in the same way heated it for several hours. After cooling the crucible I found in it a metal alloy with an entirely different appearance

20

Combustion for Material Synthesis

and physical properties than aluminium. This alloy had a coarse crystalline structure, was very brittle, the fresh fracture surface had a faint yellow glow; analysis showed that it consists in 100 parts of 33.3 parts of barium and 66.7 parts of aluminium or otherwise, for one part of barium it contained two parts of aluminium… If aluminium reduces barium from the oxide, then one could expect such an effect of aluminium on potassium oxide; I performed an experiment in a bent rifle barrel with the closed end of the barrel containing pieces of potassium hydroxide and aluminium; potassium vapors appeared at a fairly high temperature most of which were concentrated in the coldest part of the barrel, from which I extracted a few pieces of soft metal, floating on the water and burning with a violet flame that thus had, all characteristic properties of pure metallic potassium. I did not repeat this experiment on a large scale, and maybe it would be convenient for practice, as the cost of aluminium is low, and the reduction is, apparently, much easier and occurs at a lower temperature than the reduction of potassium oxide by iron.” Later N.N. Beketov often returned to the high-temperature reactions with the reduction stage. In 1888 and 1889, he published papers dealing with the reducing production of metallic rubidium [49, 50]: “…I applied to rubidium the method that I discovered on purely theoretical grounds many years ago (1859), namely the effect of aluminium on the hydrate… According to my considerations, rubidium should also be easily precipitated by aluminium; this assumption was justified by the results, and I already produced several times by this method a relatively large amount of metal – from 31 to 27 g at once. The reaction is performed in an iron cylinder with an iron gas-conducting tube, which is connected with a glass vessel. The cylinder in an upright position is heated in a gas furnace to bright red-hot; the reaction proceeds rapidly at first with a high degree of separation of gas, but then slows down and rubidium gradually floating down, like mercury, and even keeping its metal luster due to the fact that the whole shell is filled with hydrogen during the process.” In 1889, together with A.D. Chirikov, N.N. Beketov published results on the reduction of silicon oxide by magnesium [51], and in 1890 – a note dealing with the reduction of the oxides of lithium, sodium, potassium, rubidium and cesium by magnesium. [52]

SHS: History and Present

21

Thus, the above analysis of the works by N.N. Beketov leads to the following conclusions: 1. N.N. Beketov had discovered the reduction reactions of oxides and other compounds by aluminium and magnesium, which later became the basis of metallothermy. 2. He did not set the task to carry out these reactions in the combustion mode, and heated pieces of aluminium together with the oxide in a crucible for a long time. Since he used pieces of aluminium rather than powder, we can hardly talk about the thermal explosion mode. 3. N.N. Beketov saw the possible prospects of practical application of this type of reaction, but did not take patents and did not try to organize industrial production or somehow ‘advertise’ his process to attract the attention of industrialists. He limited himself to academic publications and reports. Let us now turn to the works of H. Goldschmidt. Hans Goldschmidt worked in Berlin at the factory Chemische Fabrik Th. Goldschmidt, which was founded in 1847 by his father, Theodore Goldschmidt. Did H. Goldschmidt know of the works of N.N. Beketov? He did! In their pioneering papers in 1898 in German [53] and English [54] Goldschmidt mentions Beketov’s studies of the reduction of barium oxide by aluminium. But he was interested in something else – industrial production of pure metals without carbon impurities. He mastered a method of producing granulated aluminium, and in his experiments he used granulated metal (i.e. virtually coarse powder) and not aluminium pieces. In 1892–1893, H. Goldschmidt worked on the reduction of metals by aluminium from sulphides, and then moved to oxides. As a co-owner of the plant, which was run by his older brother Carl, he had all the necessary facilities for chemical and metallurgical experiments. In a very short time H. Goldschmidt confirmed by experiments that aluminium reduces the oxides of metals: Cr, Mn, Fe, Cu, Ti, W, Mo, Ni, Co, Zr, V, Nb, Ta, Ce, Th, Ba, Ca, Na, R, Pb, Sn [54]. But the major results were the discovery of burning of thermites. Initially Goldschmidt heated a mixture of the oxide with aluminium in a crucible, as everybody did before him. However, he noticed that when the crucible is heated to a bright red glow, the reaction starts to proceed so rapidly that the temperature rises quickly up to 3000°C according to his estimates. He then made a revolutionary step: decided to completely abandon the stage of crucible heating. Here is how he described it [54]:

22

Combustion for Material Synthesis

“It has been proved by experiment that it is unnecessary to heat the whole of the mixture from which the metal is to be obtained to the temperature at which reaction takes place; that is to say, it is only necessary to start the reaction at one point of a given charge as the local heat produced is sufficient to cause the whole charge to re-act, the beat passing gradually through the entire mass. In the reduction of chromic oxide by aluminium the temperature to which it is necessary to heat one point of the charge before the reaction takes place is about 1050°C, or a bright red heat. At first, however, it was found very difficult to cause the mixture to ignite at one point without external beating, but this trouble was overcome by using a “fuse" of a highly inflammable nature which was capable of setting up an initial impulse which subsequently caused the combustion of the whole charge.” The most efficient ‘fuse’, which is also called ‘cartridge’, was made of a mixture of barium peroxide, aluminium and a cementing material in the form of a paste from which ignition cartridges were made after hardening. Each cartridge was fitted with a piece of magnesium ribbon, which makes ignition simple and reliable. In 1895, H. Goldschmidt took out a patent for his process [55], which he called metallothermy and later actively promoted its use [53, 54, 56, 57]. The process was rapidly introduced into practice and began to be used primarily for welding of rails. The first commercial use of aluminothermy for welding rails was done in Essen (Germany) in 1899. Figure 1.6 shows the metallothermic welding of rails which was performed at the beginning of the 20th century (a) and at present (b). As one can see, the Goldschmidt technology has remained nearly the same for a hundred years! The company ‘Goldschmidt AG’ a

b

Fig. 1.6. Metallothermic welding of rails: a – in Graz, Austria, 1914 (http://history. evonik.com/sites/geschichte/en/chemicals/history/goldschmidt); b – allTEC Engineering Service, Austria 2011 (http://www.alltec-eng.com.au).

SHS: History and Present

23

still exists today, but produces other products. The world’s largest manufacturer of thermites for welding is the company Evonik, the successor of the Degussa company founded by H. Goldschmidt. In Russia metallothermic welding was applied in 1915 in Moscow, when 126 rail joints were welded. In 1918, another 151 joints were welded. Since 1923, the Moscow tramway tracks have been welded regularly by thermic welding. Prior to 1925 the joints were welded using an imported composition. In 1925, M.S. Karasev organized industrial production of thermite compositions at the Moscow thermite-switch plant. Further uses of thermites have a long history, which includes: welding, production of metals and alloys, military applications (for example, in the famous Katusha rocket mortar shells, etc). However, the history of thermite processes is not the task of this book and there is a large amount of literature on this topic (see, e.g. [58, 59]). Let’s go back to the SHS processes with the reduction (metallothermic) stage. So the thermite process, the scientific foundations of which were laid in the works of N.N. Beketov and which has been put into practice by H. Goldschmidt, has the basic features of the synthesis in the combustion mode: local ignition, self-heating and self-acceleration of the reaction, propagation of the reaction wave, and formation of a useful product as a result of combustion. But the development of SHS has brought many new advances in the field of metallothermy. The search for gasless flammable compounds, referred to in section 1.1, was first based on the use of iron–aluminium thermite heavily diluted by alumina in order to lower combustion temperature and suppress evaporation of the components [60]. In this work, as well as in a preceding work [61], the metallothermic process was studied using the methodology, which had been developed to study the combustion of gunpowder. This approach involves the organization of the plane front of the combustion wave propagating in one direction; recording the linear velocity of reaction front propagation; the study of the thermal structure of the wave; the identification of controlling experimental parameters and patterns of burning. Thus, the novelty was already in that metallothermy was not studied as a process of metallurgy, but as a process of combustion. With expansion of research in the field of SHS, the ‘SHS metallurgy’ systems form a separate research area [62]. An important contribution in the field of thermite reactions was the development of the use of centrifugal force to control the separation of immiscible melts (metallic melts and slag) formed in the processes of SHS metallurgy [63]. Based on

24

Combustion for Material Synthesis

this approach, methods were developed for centrifugal SHS-casting [64, 65] for manufacturing of steel pipes with an inner ceramic coating [66–69]. Currently, the SHS thermite type processes are among the most ‘advanced’ in practical application, as is discussed in more details in chapter 5. At the same time, the mechanisms of combustion and formation (microstructure formation) of products in these systems have been studied insufficiently, despite a long history of thermite reactions. In recent years, the thermite subject received a new impetus, due to the developments of nanothermites. The development of various nanotechnologies, including metals and their oxides, allowed the preparation of the reaction heterogeneous structures with nanostructured reagents. The range of available nanopowders is now quite large (aluminium, boron, carbon, silicon, nickel, many oxides). Thermite compositions prepared using nanopowders are called nanothermites or superthermites [70]. The metal reducing agent in the superthermites is primarily nanoaluminium and the latest results in the production of nanoaluminium described in recent monographs [71, 72]. Despite the availability of nanopowders, in preparation of reaction mixtures from them it is necessary to overcome some specific problems, including the difficulty of uniformly mixing the very fine components, aging (passivation) of nanopowders in storage and an abnormally high sensitivity of nanoheterogeneous compositions to ignition. As shown, for example, in [73], the optimal methods of storage and handling of nanopowders of metals are important not only in terms of safety but also the accuracy and reliability of the scientific results. The metal powders with a large specific surface area exposed to rapid oxidation in an oxygen-containing environment leading to changes in their reactivity (aging). Therefore using the same raw nanopowders but contained and mixed under different conditions usually leads to different results for the characteristics of the ignition and combustion of such systems. The data on the chemical composition and particle size of some reagents of the studied superthermites systems are summarized in Table 1.1. Superthermite mixtures are highly sensitive to ignition and have an unusually high rate of combustion (according to some data more than a kilometer per second!). These systems will be discussed in more detail in chapter 4.

SHS: History and Present

25

Table 1.1. Some characteristics of superthermite systems

System

Al–MoO3

Al–WO3 Al–Bi2O3 Al–CuO2 Al–Fe2O3

Metal particle size, nm

Oxide particle size

Reference

17, 25, 30, 40, 53, 76, 100, 108, 160, 200 50, 80, 120 44, 80, 120 44 30, 45, 140, 170 80 80 80 40, 100 80 52

Sheets 10 × 10 μm × 10 nm 10 × 10 μm 1 × 1 μm × 20 nm 15.5 nm Ssp. = 66 m 2/g 200 × 200 × 30 nm 100 × 100 × 20 nm filaments – 25 × 2 μm 40, 108, 321, 416 nm 100 × 100 × 20 nm Ssp. = 50 – 300 m2/g

[74, 75] [76] [77] [78] [79] [80] [81] [81] [82] [81] [83]

1.6. Combustion synthesis with inorganic compounds as precursors Never say “never again” I. Fleming

Above, the combustion synthesis of complex compounds by using chemical elements as initial reagents is primarily considered. While discussing the thermite type reactions, we first encountered using a compound (oxide) as a precursor. It is logical to assume that the chemical routes of self-sustaining exothermic reactions are not limited to these examples. Indeed, the literature analysis shows that there exists a wide variety of combinations of chemical elements and compounds, which can react in the combustion regime. One of the first among such processes was the combustion synthesis of complex oxides from binary oxides as initial reagents [84], for example: PbO 2 + WO 2 = PbWO 4 .

It is interesting that this type of combustion reactions occurs in the gasless regime, despite the presence of oxygen, which remains in a bound state over the entire process. When high temperature superconducting oxide ceramics were discovered in the 1980s, synthesis schemes for such materials in the combustion mode were rapidly developed [85, 86]. For example, the following reaction

26

Combustion for Material Synthesis

was used for the synthesis of the high temperature superconducting ceramic YBa 2Cu 3O 7–x 3Cu + 2BaO 2 + 0.5Y2O3 + ( 0.75 − 0.5 x ) O 2 (gas) = YBa 2Cu 3O7− x ,

in which oxygen is involved in both the solid and gaseous state. Another example of using compounds as a precursor is synthesis of nitrides with azides as nitrogen containing reagents [87–90]. Azides are the salts of hydrazoic acid (HN3) and best known among them are sodium NaN3, potassium KN3, lithium LiN3, and ammonium NH 4 N 3 azides. At room temperature the azides are in the solid state, but they are easily decomposed during heating. Using such compounds to synthesize nitrides in preparation for an initial powder mixture, which contain enough bounded nitrogen in azides, allows completely eliminate the need for infiltration supply of nitrogen gas from the outside. For example, in the reaction 4Ti + NH 4 N 3 = 4TiN + 2H 2 (gas)

all the necessary nitrogen is present in the initial mixture (although it is necessary for removal of the hydrogen, formed during the decomposition of the azide, from the sample). Sometimes the azides are used in conjunction with thermite type reactions, for example: 3TiO 2 + 6Mg + NaN 3 = 3TiN + 6MgO + Na(gas).

Widespread use of azide-based technologies is mainly constrained by the explosion hazards posed by these compounds. In addition to the azides, there are other nitrogen containing compounds that exist, for example, nitrides which are absolutely safe from the viewpoint of combustion and explosion. So ‘safe’ that for a long time they were not even considered as possible reactants for SHS. Indeed, as was shown in section 1.4, the nitrides are products of combustion in nitrogen. Is it possible to burn what has already been burnt? Is it possible to use the ashes of yesterday’s firewood to heat the house today? Amazingly by the thermodynamic calculations, and then by experiments it was shown that nitrides, e.g. BN, AlN, Si 3 N 4 can be used as precursors for the combustion synthesis of materials [91, 92], for example: 3Ti + 2BN = TiB2 + 2TiN; 9Ti + Si3 N 4 = 4TiN + Ti5Si3 .

SHS: History and Present

27

Initiation of such reactions should be carried out by using hightemperature exothermic mixtures, e.g. Ti + 2B, but after ignition, the reaction propagates steadily, with constant speed along the whole reactive media. It is worth noting that the loss of nitrogen due to its filtration from the sample is either completely absent or negligible. Thus, the use of metallic nitrides as solid nitrogencontaining reagents for SHS overcomes the difficulties associated with the need for the use of an additional supply of the gaseous reagent in the synthesis of certain materials based on metal nitrides. Some non-metallic carbides, such as B 4C [93] and SiC [94] can also be used as starting reactants, for example: 3Ti + B4C = 2TiB2 + TiC.

At first glance, this reaction route does not seem justified, since the carbon can be easily placed in the reaction mixture in the form a low-cost carbon black or graphite powder. However, in some cases, the use of compounds instead of chemical elements can affect the formation of the desired phases of the produced material. In particular, the use of SiC as a precursor in Ti–Si–C system proved to be useful for the formation of the so-called MAX-phase Ti 3SiC 2, representing practical interest [95]. Silicon carbide can react with nitrogen in SHS mode forming silicon nitride and carbon, which in turn may form a carbide with another element, such as boron. This principle is the basis of the preparation of certain composite ceramics, including the so-called black ceramic, which is discussed in section 5 [96]. Thus, many inorganic compounds, including those produced in the combustion mode, may be re-used as fuel components in combination with, e.g. strong oxidizing agents. Products of such ‘repeated’ combustion should have a strong chemical bond and a greater heat of formation from chemical elements, as compared to that for the compound used as a precursor. Such two-stage organization of the synthesis process extends the possibilities of controlling the phase composition, microstructure and thus properties of the synthesized materials.

1.7. Thermal decomposition of complex compounds The previous sections examined the combustion of heterogeneous powder mixtures with a micron-scale level of heterogeneity (e.g.

28

Combustion for Material Synthesis

a

b

Fig. 1.7. Eruption of volcanoes: a – Etna (Sicily, Italy), b – school experiment (for the colour image please see the colour section in the middle of the book).

micron size of the particle of the initial reagents). Intuitively it is clear that to obtain nanosized products (powders, nanomaterials) it is better to have a system with an extremely small initial scale of heterogeneity. The question arises whether there is such solid phase system in which the reagents are mixed, for example, on the molecular level and they are exothermic enough for the reaction to proceed in the self-sustaining mode to provide the solid product? Recall the famous school experiment ‘the volcano eruption’. The ammonium dichromate [(NH 4) 2Cr 2O 7] single-phase powder contains both fuel and oxidant that are ‘mixed’ at the molecular level. The decomposition of this compound to form a trivalent chromium oxide powder occurs by the reaction

( NH 4 )2 Cr2O7 (sol) → Cr2O3 (sol) + N 2 (gas) + 4H 2O (gas) +1790 J which is an exothermic process which under certain conditions (for example, at T > 225°C) takes place in the self-sustaining mode (Fig. 1.7). The temperature in this case reaches 500°C. Consequently, this process has characteristics of combustion: release of heat and selfacceleration of the reaction during heating; of course, instead of the synthesis reaction, the reverse process takes place – the decomposition of a complex compound into simpler ones. Thus, the ‘school volcano’ is a homogeneous reaction system which is capable of burning with the formation of a solid product – a fine chromium oxide powder. It would seem that the process with one initial reactant should be very easy from the standpoint of the reaction mechanism. Since the melting point of the only

SHS: History and Present

29

solid product, Cr 2O 3 (2435°C), is much higher than the adiabatic combustion temperature (decomposition) of (NH 4 ) 2 Cr 2O 7 , it was concluded in 1958 that the decomposition mechanism of the direct transformation of solid ammonium dichromate to the solid trivalent chromium oxide with the release of a large amount of gaseous products is solely a solid phase process [97]. However, 25 years later, scientists from Queen’s University (Belfast, Ireland), investigated the decomposition of [(NH4)2Cr2O7] using, as they state, “... a microscope with a sufficiently large magnification...” and found clear evidence of the presence of the liquid phase during the decomposition of this substance [98]. Based on the data on changes in the microstructure of the reaction medium, as well as studies of the kinetics of gasphase products formation, the authors came to the conclusion that the first stage of the reaction produces hexavalent chromium oxide (CrO 3). The melting point of this phase is only 197°C so that at the decomposition temperature, which exceeds 200°C, the intermediate product is in the liquid state. About 10 years later, in 1992, a new publication with the unusual name ‘Reinvestigation of decomposition products of (NH 4 ) 2 CrO 4 and (NH 4 ) 2 Cr 2O 7 ’ appeared [99]. In this article it was shown that depending on the rate of heating of the medium the reaction mechanism may be different. With rapid heating the reaction begins to take place rapidly (burst) at 225°C, and the only detected solid-phase product is Cr 2O 3. With slow heating to temperatures of about 340°C no explosion is observed, and the authors of [99] detected a series of intermediate solid products, including CrO 3 . This example is a predecessor of a new class of processes based on the combustion of virtually homogeneous raw materials (size of the heterogeneity does not exceed nanometers) developed over the past 15–20 years to synthesize the nanopowders of various compounds, mainly oxides. A detailed description of the methods and products for such type of combustion systems can be found in a recent monograph [100]. In this section we shall consider only some typical examples. Synthesis of binary oxides. Metallic complexes which exothermically decomposed to yield fine powders of binary metal oxides can be obtained by adding hydrazine hydrate (N2 H 4 )·H 2 O to an aqueous solution of metal salts of various acids, such as oxalic, acetic and formic acids and, simultaneous saturation of the solution with carbon dioxide (CO 2). For example, an aqueous acetic acid solution of ferric salt (CH3COO) 3Fe·xH 2O is mixed with (N 2H 4)·H 2O in the presence of dry ice. After drying, we obtain the

Combustion for Material Synthesis

30

hydrazinecarboxylate of iron hydrazine N2H5Fe(N2H3COO)3·H2O. This bluish powder, after local preheating in air by a hot coil, burns in the self-propagating mode, forming a red-brown iron oxide powder (so-called Pharaoh’s snake). Formally, the combustion reaction can be represented as follows: 2 2N 2 H 5 Fe(N 2 H 3 COO)3 ⋅ H 2 O(sol) 2.50  → Fe 2 O3 (sol) +

+ 8NH 3 (gas) + 2H 2 (gas) + 4N 2 (gas)

(1.6)

Study of the kinetics of the reaction by thermogravimetric (TGA) and differential thermal (DTA) analyses show that this reaction is initiated at a temperature of 165°C, and quickly leads to a 76% reduction in the weight of the sample, which is very close to the amount of gaseous products produced according to the reaction (1.6). X-ray phase analysis, the measurement of the specific surface (SBET) of the particles, and study of the microstructure of the product by transmission electron microscopy showed that the reaction leads to the formation of fine ( 1 (< 1) – fuel rich (lean) systems, respectively. In the absence of water the adiabatic combustion temperature for the stoichiometric mixture exceeds 2200 K and during combustion a large amount of gaseous products form, which increases as the parameter φ increases. Local initiation of the reaction in these solutions, similarly to gasless systems, leads to the propagation of the self-sustained combustion wave. All above, i.e. molecular mixing of the reagents and intensive release of gaseous species, result in formation of solid products with very fine nanostructure. The solution combustion synthesis (SCS) is a rapidly growing direction in material science, however the mechanisms of nanopowders formation are still not well understood. The currently available results on SCS in different reaction systems are discussed in chapter 4.

1.9. Mechanical activation of initial powder mixtures for SHS Another rapidly developing direction in the field of combustion synthesis of materials is the mechanical activation of SHS green mixtures. Mechanical activation (or simply activation) of combustible mixtures is a treatment in high-speed planetary ball mills, vibratory mills, and other devices in which the particles in the mixture are subjected to mechanical effects with the force sufficient for cracking of brittle and plastic deformation of ductile components [105]. Brittle reagents are ground to finer particles and ductile reagents (usually metals) are subjected to multiple flattening deformations forming laminated composites, in which the layer thickness decreases with increasing duration of activation. Often fine pieces of brittle components of the mixture are inside the particles of the ductile reactants. Activation not only reduces the size of the reactants but also increases the contact area between them, cleans the contact surface from oxide layers and other impurities, accumulates the crystal defects and all these increase the chemical activity of the reactive mixture [106, 107]. Already at the stage of activation there may be partial or

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35

complete dissolving of one reagent in the other (mechanical alloying), and even a chemical reaction between the components of the mixture to form a new compound (mechanosynthesis) may take place. In some cases, mixture auto-ignition occurs directly during activation. The question arises: what is the degree of heterogeneity of the reactive mixture that can be achieved before the reactants start to interact with each other? Many papers present direct evidence (electron microscopic images, etc.) that by such mechanical treatment it is possible to produce nanostructured reactive composites, with the size structural components (phases) of the order of 10–100 nm. But even in cases where such direct evidence is not provided, mechanical activation has resulted in a sharp change in the properties of the reaction mixtures, for example, a significant decrease (by hundreds of degrees) of its selfignition temperature. In particular, an abrupt change in the properties of substances is considered by many scholars to indicate the presence of a nanostructured state, and not some ‘numerical’ boundary in 1, 10 or 100 nm [108, 109]. Based on this, in this section we discuss the specific features of the mechanical activation of SHS compositions. Over the last decade, a vast number of publications have been devoted to the mechanical activation of flammable mixtures. Comparison of the results of different authors is difficult because of the fact that the mechanical activation process depends on many parameters, including speed, acceleration, mass, size and shape of the grinding media, geometrical dimensions of the unit, the ratio of the mass of milling bodies (balls) to the mass of the activated mixture, the environment in which the activation takes place (air, inert gas, vacuum, liquid) and many others. However, we can distinguish three parameters, which most obvious express the physical (not technical) aspect of the process: the energy of an impact, (collision between the balls or of balls with the wall), the frequency of collisions and the total activation time. If we multiply all three parameters, we obtain the amount of total energy that is spent on activation. Of course, this does not mean that all this energy is ‘stored’ in the activated mixture, since most of it is converted into heat, however, the three parameters and their product can serve as a physical basis for comparing the results. The published data can be divided into two distinct groups on the basis of the impact energy. The first group can be called low-energy activation, the energy of collision is 0.1–0.2 J and the activation time – from minutes to tens of hours [110–114], the second group of results is related to high-energy

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activation when the impact energy is 1–2 J and the activation lasts from a few seconds to minutes [115–118]. For gasless type systems (section 1.2) it is reported that the velocity of the combustion front generally increases with an increase of impact energy. Combustion temperature may also increase, but never exceeds the adiabatic combustion temperature. The combustion characteristics of mechanically activated gasless compositions will be discussed in chapter 4. Mechanical activation of powder mixtures, such as thermite, was discussed in a recent review [119]. Typically, the thermite systems burn fairly rapidly, with high heat and do not require additional activation for a self-sustaining reaction. The purpose of mechanical activation in these systems is either getting nanocrystalline products, e.g. nanocomposite Al 3Ni/Al 2O 3 [120], or forming the ‘superactive’ thermite compositions. The latter is closely associated with the above-mentioned nanothermites (superthermites), and mechanical activation is a method for obtaining of such nanothermites [121– 124]. To accomplish this task, one should determine the critical time of mechanical treatment for the Me 1 + Me 2O x system, which is necessary for self-ignition of the mixture during high-energy ball mixing (typically tens of minutes). Mechanical treatment is then arrested (arrested reactive milling) before the critical time to produce a product in the form of composite particles of the micron size, but with a small (a few nanometers) crystallite size, which depends on the treatment conditions. An increase in the combustion velocity for mechanically activated thermite compositions was reported, but rather moderate velocity values were given (about 0.5 m/s for Al–Fe 2O 3, [122]). The activation energies of ignition were also determined for different nanothermites, which appear high, e.g. 152±19 kJ/mol for the Al–MoO3 and 170±25 kJ/mol for Al–Fe2O3 systems. These values are close to the energies of activation of the ignition of conventional thermites, such as 167 kJ/mol for the non-activated Al–Fe 2O 3 [125]. Another group of mechanically activated reactive compounds are hybrid systems ‘solid fuel – gaseous oxidizer – solid product’, which react in filtration combustion regime. Mechanical activation for several hours of Si and α-Si 3N 4 powder mixture with addition of 4–5% NH 2 Cl allowed preparing the mixture which burns in nitrogen at a pressure of 1–3 MPa, which is much less than that required for SHS of non-activated silicon in nitrogen [126, 127]. It is worth noting that α-Si 3N 4 phase was obtained as the product, while α-Si 3 N 4 typically forms during conventional SHS in the

SHS: History and Present

37

Si–N 2 system. A similar approach was developed for the synthesis of β-sialon (Si6AlzOzN8–z, 0 < z ≤ 4.2). In this case, the activation in a planetary ball mill was carried out on a mixture of silicon, aluminium and aluminium oxide, and combustion took place in a nitrogen atmosphere at a pressure of 1 MPa [128, 129]. In [130] it is reported that the mechanical activation of mixtures Y2O3, Si, Al, SiO2, α-Si3N4 and stearic acid (CH 3 (CH 2 ) 16 COOH) produced a compound that burns in air at normal pressure forming α-sialon. Another approach comprises the mechanical activation of metal fuel (e.g. titanium powder) in a gaseous oxidant (nitrogen) until auto-ignition occurs. By this method nanodispersed TiN [131] and TiC xN 1–x cermets were successfully synthesized [132]. The combustion mechanisms in mechano-activated hybrid systems and combustion directly during activation process are still not understood well. To sum up this section, it may be concluded that almost all researchers agree that high-energy ball milling reduces the ignition temperature of various combustible systems, expands their combustion limits, promotes more complete reactions, and typically leads to an increase in the velocity of combustion wave propagation.

1.10. Reactive multilayer nanofilms (foils) Finally, let us consider one more type of SHS systems, which are based on nanoscale reagents. Reactive multilayer nanofilms (RMNs) that consist of alternating nanoscale layers of specific reagents capable of exothermic reactions are new and unusual combustible objects. At present there are several methods for obtaining RMNs. The most often used approach is a magnetron sputtering. It allows one to deposit reagents of uniform composition over a long period of time with a constant growth rate, which is important in the deposition of hundreds or thousands of alternating layers. This method for deposition of reactive multilayer nanofilms [133, 134] is similar to that previously developed [135, 136] for the production of multilayer coatings. The scheme of the method is shown in Fig. 1.8. Reagents are sputtered from two or more simultaneously operating sources (magnetron targets); the substrates are mounted on a rotating holder and alternately exposed to the flow of the deposited substance from one or the other target. The number of layers is equal to the number of revolutions of the holder, and the thickness of each layer is determined by exposure time (speed of rotation), the power of the source and the distance from the source to the substrate. The

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Rotating substrate

Source of atoms A

Source of atoms B Separating diaphragm

Fig. 1.8. Scheme for production of multilayer nanofilms by the magnetron sputtering method (for the colour image please see the colour section in the middle of the book).

process is typically carried out in high purity argon at pressures of about several tens of Pascal (the sputtering chamber is preliminary evacuated to a high vacuum). A necessary condition is to maintain the substrate at low temperature to prevent the reaction between the layers and to suppress their mutual diffusion during the deposition. Typically, the substrate temperature is close to room temperature during the deposition process. Figure 1.9 shows examples of the cross-sections of the reactive nanofoils [137, 138]. The images indicate that the layers are flat and do not lose continuity with decreasing thickness. The RMF system has an excess of chemical energy, the energy of elastic stress of the layers, and the free energy of the phase boundaries. This energy excess provides a thermodynamic driving force that can disrupt layers, e.g. lead to their intermixing or even discontinuation (formation of separate islands of phases). Furthermore, each layer is polycrystalline, i.e. consists of a mosaic of grain with the boundaries between them directed perpendicular to the interface between the layers. As shown by the stability analysis of multilayer films from the viewpoint of the excess energy of the boundaries, the layers are more flat, if the specific (per unit square) energy of the boundary between the grains is much less than the energy of the boundary between the layers. At the opposite case, the characteristic grooves

SHS: History and Present

39

a d = 333 nm d = 143 nm d = 72 nm d = 54.5 nm d = 23.2 nm d = 10 nm d = 100 nm 200 nm c

b

100 nm

10 nm

Fig. 1.9. TEM images of nanostructures of different RMNs: a – Nb/Al film with variable thickness of layers d [137], b – Ti/Al film [138], c – Ni/Al.

appear at the grain and layer boundaries intersections, which may lead to rupture of the layers. The presence of the irregularities of the layers, caused by grain boundaries, can be clearly seen in Fig. 1.10 obtained in a scanning tunneling microscope [139]. An excess of energy at the grain boundaries leads to the effect that the center of the grain grows faster than its periphery, resulting in the grain surface being domeshaped. As seen in Fig. 1.10, the height of the dome is 5–10 nm and

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Combustion for Material Synthesis

Z, nm

1 μm X, nm Fig. 1.10. The surface and surface profile of the Ti/Al film (layer thickness 60 nm). Scanning tunneling microscopy [139].

the diameter of the grains is about 500 nm. The characteristics of the roughness of the layers vary depending on the system, the thickness of the layer, the properties of the substrate, and other parameters. It is not possible to exactly predict in advance the microstructure of the layer; every time it is necessary to determine it experimentally for each system. Finally, a special feature of the layers which are deposited using a magnetron sputtering method is the texture. It means that in the crystalline structure of different grains, which form the polycrystalline film, the specific atomic planes are oriented preferably along the layers. This phenomenon is well known from the practice of thin films deposition. Thus, despite the apparent simple geometry of the multilayer films, they have a complex microstructure, or considering the size of the layers, a complex nanostructure. The most important characteristics of this nanostructure, which appears in almost all the works in this area, is the period of the structure, i.e. the total thickness of the two adjacent layers (we will henceforth refer to this value d) and the total film thickness (denoted by Latin H). The influence of the nanostructure on the reaction mechanisms is discussed in chapter 4 of this book. Magnetron sputtering has been used to produce the reaction films in the following systems: Ni–Al [140, 141], Ti–Al [139, 142–148], Nb–Al [137, 149, 150], Ta–Al [150], Cu–Al [150], Nb–Si [133, 151], CuO–Al [152, 153], and some others. The number of the investigated systems is still relatively low, and the main reason

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41

for this lies in the technological complexities of obtaining regular multilayer reaction structures. If for conventional powder reagents it is sufficient to mix them to obtain the initial reaction composition, then for manufacturing RMNs it is essential to carefully select the sputtering conditions for each reagent, the adequate magnetron targets, and substrates. Also, not every pair of reagents has acceptable structure and mechanical properties for producing multilayer films. Mismatches in crystallographic structures or in thermal expansion coefficients could lead to the destruction of the layers, the entire film during the deposition, or in attempts to initiate combustion. For example, multilayer films of the Ti–C system with a thickness of approximately 1 μm can be obtained by magnetron sputtering, but locally heating the film causes it to breakup immediately and roll ‘into a tube’, so that it is not possible to ensure the propagation of the combustion wave over macroscopic distances of at least several millimeters. For another common SHS system, Ti–B, multilayer films were not produced because of the difficulties in magnetron sputtering and deposition of boron. Nevertheless, the method of magnetron sputtering is the main method for studying self-sustaining reactions in nanofilms and it was used to prepare films with continuous alternating layers with a thickness from 3–4 nm and up, and with the number of the layers in the film exceeding 5000 [147]. The second most common method of producing the RMNs is the vacuum deposition method. Physical vapour deposition (PVD) in a high vacuum allows one to obtain very thin (down to a few angstroms) layers of a given composition. However, in this method it is difficult to achieve a constant rate of evaporation for a long time, which is necessary for the deposition of hundreds or thousands of layers. Apparently, for this reason this method has found use only for films with a relatively small number of layers. The propagation of reaction waves in two-layer films [154, 155] of the Al–Ni, Al–Fe, Al–Co systems with a thickness of each layer within 30– 100 nm was studied, with the thickness of the whole film not higher than 200 nm. The layers were deposited by evaporation–deposition in vacuum of 10 –4 Pa. In earlier work [156] on the combustion of films of the Ni–Al system, several dozen layers were prepared by electron beam evaporation and deposition in a vacuum of 10 –6 Pa; the total film thickness was typically 300 μm. Vacuum deposition was also used to produce multilayer Pt–Co films [157] comprising of 60 to 90 pairs of layers with a thickness of 0.40–0.45 nm for the Co layer and 0.50–0.55 nm for Pt. Electron beam evaporation under

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high vacuum (10 –6 Pa) was also used to produce multilayer films in the Ti–Si reaction system [158], with the Ti layer thickness of 15 to 20 nm and Si 15–40 nm; the number of layers in this case was usually ~10 (5 layers of each reagent). Note that often, the layers deposited in vacuum are amorphous. The main drawback of both methods discussed above is their low productivity and high cost. Work is being carried out on developing alternative, more efficient and low-cost methods for making the multilayer nanofilms. Of greatest interest is the method of multiple rolling. For example, using this approach in the Ag–Ni system allows obtaining films with a thickness of the double layer of 2.6 nm, containing more than 5000 layers [159]. Fine silver (9 μm) and nickel (14 μm) foils were stacked in alternating order (250 foils) and subjected to annealing in the compressed state at a temperature of 1073 K for 1 hr. The resulting multilayer sample was rolled to a thickness of 0.2 mm and followed by forming a pile of 21 of identically rolled samples, which was again subjected to hot pressing and rolling. A similar technique was used to produce multilayer films in the Ni–Al reaction system [160], with up to 70 rolling cycles. The prepared film with aluminium and nickel layers with the thickness less than 100 nm is shown in Fig. 1.11 a. A more regularly layered nanostructure was prepared by rolling of Pt and Al foils (Fig. 1.11 b) [161]. It can be seen that at large degree of reduction of the foils thickness by rolling, the layers become undulated, and less plastic layers often break. A difficult, and sometimes impossible, task is the joint rolling of foils with very different mechanical properties (tensile strength, elastic modulus, Poisson’s ratio). To overcome these difficulties, it was recently proposed to carry out rolling using multilayer composite particles obtained by mechanical activation of a mixture of powders [162, 163]. Mechanical activation of the SHS compositions (discussed a

b

5 μm

1 μm

Fig. 1.11. The microstructure of the multilayer films obtained by rolling alternating foils: a – Ni and Al after 70 rolling cycles (white phase – Ni, dark – Al) [160]; b – Pt and Al (white layer – Pt) [161]. Scanning electron microscopy, reflected electrons.

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in section 1.9) produces multilayer composite particles with a layer thickness of 100–200 nm or less. By cold rolling of such particles, it was easier to prepare multilayer nanofilms than from foils or particles of individual reactants. It is also interesting to note the approach suggested in [164], where Nb/Al multilayer nanofilms were prepared by magnetron sputtering, and then subjected to rolling. The goal of this work was to study the mechanical properties of multilayer nanofilms, but it is also possible that such a ‘hybrid’ approach can be used to produce certain types of reactive nanofilms. A review of the methods of production of multilayer nanofilms shows that it is still a lot of work to do. On the one hand, it is necessary to improve productivity and reduce the cost of magnetron and vacuum deposition, on the other hand it is critical to improve rolling-based methods to obtain a film with a more regular and perfect structure. Based on the analysis of literature, it can be also concluded that methods such as chemical and electrochemical depositions have not yet attracted the attention of researchers in the field of multilayer nanofilms, although work on the electrodeposition of nanocomposites with a granular structure can be found [165–167]. It could be promising, for example, to combine layer chemical (electrochemical) deposition with subsequent rolling. Apparently, a rapid development of methods for the production of reaction nanofilms can be expected in near future. The combustion process in multilayer nanofilms was discovered and patented for the first time in 1996 [133]. It turned out that by locally heating the RMN with an electrical spark, a laser pulse, or a hot filament, it is possible to trigger a reaction wave, which rapidly self-propagates throughout the film. The self-sustaining nature of the process; the presence of the wave front, which is clearly indicated by the incandescent glow of solid reaction products, an abrupt temperature rise in the front by 1000–1500 degrees, and very rapid formation of solid products behind the combustion wave front; classify this phenomenon as gasless combustion (see section 1.1). The parameters of the RMN combustion waves differ much from those for conventional systems of a similar composition obtained by mixing powders. For example, the velocity of the combustion front propagation in the RMN may exceed the combustion velocity in the powder mixtures of similar chemical composition by 2–3 orders. Main features of combustion of the multilayer nanofilms are discussed in details in chapter 4.

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2 THERMODYNAMICS AND KINETICS OF SHS Whoever, in the pursuit of science, seeks after immediate practical utility, may generally rest assured that he will seek in vain. Hermann von Helmholtz

2.1. Introduction For all the diversity of SHS systems, presented in the first chapter, there are common fundamental principles of materials synthesis in the combustion mode. Consideration of these principles is the focus of this chapter. The literature on combustion synthesis of materials regularly uses terms such as stationary, equilibrium, reversibility, and stability, which are applied to both the reaction systems and the process, and sometimes to the products of synthesis. It is often assumed that these concepts are well known and their definitions are not necessary. Also many thermodynamic functions and values, such as internal energy, enthalpy, thermodynamic potentials, chemical potentials, the heat of reaction, and so on are widely used without explanations of their meanings. No wonder one gets lost in all these complexities, because even in different books on thermodynamics one can find different definitions of basic concepts and thermodynamic quantities. An even more difficult case is the kinetics of heterogeneous combustion: what is the rate of reaction in a multiphase system or what is the effective activation energy of the heterogeneous process. These and many other questions require separate discussion and analysis before the corresponding concepts can be correctly used.

Thermodynamics and Kinetics of SHS

45

The task of the second chapter is to identify clear physical meanings of the fundamental thermodynamic and kinetic characteristics in relation to combustion synthesis of materials. Although this chapter focuses on the fundamental aspects of the SHS, their analysis provides answers to the some important practical questions: for example, what products and materials can or cannot be synthesized in the combustion mode, whether the products of SHS are equilibrium or metastable phases and others

2.2. Thermodynamics and driving force of SHS processes 2.2.1. Thermodynamics of SHS systems 2.2.1.1. General principles After initiation, the SHS process proceeds self-sufficiently without any external energy sources. Consequently, the driving force of the process should be sought in the SHS system itself. What is this driving force? The simplest and most obvious answer is that the driving force of the process is to reduce the internal energy of the system, more precisely, by conversion of its chemical potential into heat. In general this is true, but it does not reflect all the specifics of the thermodynamics of the SHS. To understand these particular features, one needs to analyze the different structural levels of reactive systems. Let us first consider the SHS system as a whole, on a macroscopic scale, under the assumption that the interaction with the surrounding environment can be neglected. Conditions in which there is no exchange of heat between the considered system and the environment are called adiabatic conditions. If in addition the amount of matter in the system remains constant, the system is called the isolated system. So, assume that a reaction mixture consisting of the powder particles of the solid reagents is placed in a sealed adiabatic vessel (optionally the vessel may also contain a gaseous or liquid reagent). It is experimentally confirmed that at room temperature such an initial mixture can typically exist indefinitely long, without noticeable changes in composition, microstructure, temperature or pressure. The condition in which the system does not change its characteristics over time is called the stationary state. However, such an initial stationary state of the SHS system is ‘deceptive’. If the temperature of the system is raised to the point at which the mutual diffusion of the reagents could occur at an appreciable rate, a chemical reaction with heat generation starts in the vessel. As a result of the exothermic reaction, the temperature in the vessel increases even more, which

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in turn leads to an increase in the reaction rate, i.e. the process becomes self-accelerating. This process stops when the reagents are completely transformed into the reaction products and the system reaches a new steady state. It is natural to ask how the new state is different from the initial stationary state. Since any exchange with the environment is excluded (isolated adiabatic system), then from the energy conservation law it follows that the total energy of the system remains unchanged. At the same time, the reaction has been completed and common sense suggests that the system does not spontaneously return to its original state. Which characteristic of the system has undergone irreversible changes? In thermodynamics, this characteristic is called the Gibbs free energy and can be presented as follows [1]: G = U + PV − TS ,

(2.1)

where U and S are the internal energy and the entropy of the system respectively, P is pressure, V is volume, and T is temperature. Josiah Willard Gibbs (1839–1903) was a great American scientist with a broad range of scientific interest, one of the founders of chemical thermodynamics and statistical mechanics. He was also the first Doctor of Philosophy (PhD) in engineering sciences and the first professor of mathematics in the United States; perhaps the role of J.W. Gibbs for the science in the U.S. is similar to the role of M.V. Lomonosov in Russian science. In the second half of the 19th century, J.W. Gibbs proved that any spontaneous irreversible process occurs with a decrease in free energy G. And this decrease in free energy is the driving force of the process. Since this statement is fundamental for the SHS, including both auto-wave and thermal explosion modes, we discuss it in more details. First of all, it should be noted that the free energy G is not energy in a physical sense; otherwise its decrease in an isolated system would contradict the law of conservation of energy. In our view, it is a matter of terminology, and if one is confused by the term ‘energy’, other terms, such as ‘isobaric–isothermal potential’ or ‘Gibbs potential’ can be used. For a system with a single type of particles, if G is divided by the number of particles in the system, N (or moles), a quantity called the chemical potential (µ) can be obtained: µ=

G . (2.2) N Let us consider the physical meaning of each term in equation

Thermodynamics and Kinetics of SHS

47

(2.1). The internal energy, U, is the total energy contained by a thermodynamic system. This concept is fundamental, like the concept of energy over-all, so it is not possible to derive its definition from some general principles. Classical thermodynamics does not raise the question of the nature of internal energy [2]. Based on current knowledge about the structure of matter, one can only specify the types of energy that make up the internal energy: the potential energy of the interaction of atoms and molecules, their kinetic energy of translational, rotational and vibrational motions, the energy of the electron shells of atoms, the interaction energy of the particles in the atomic nucleus, the rest mass energy of elementary particles (the famous E = mc2) and so on. One may want to include a hypothetical ‘dark energy’, which is believed to account for most of the latent energy of the universe, or the energy of vibration of ‘superstrings’, or the energy of the physical vacuum. These list is just illustrates that, generally speaking, it is impossible to determine the absolute value of the internal energy of the system. In real physical and chemical processes one can measure only the change in internal energy (ΔU), which occurs when the system transfers from one state to another. To measure ΔU the concepts of heat (Q) and the work (A) should be used. The second term on the right-hand side of equation (2.1) is just a measure of mechanical work: for example, at a constant pressure the work done by the system (or with the system) is equal to A = P∆V ,

(2.3)

where ΔV is the change of the volume of the system. In the analysis of SHS processes, the mechanical work is almost always negligible. It is undoubtedly true for gasless chemical systems, since the volume change of the liquid or solid phases during the reaction is insignificantly small. But even in solid–gas systems, in which the volume of the gas reagent due to the reaction varies considerably, mechanical work can be neglected compared to the heat of the chemical reaction. Consider, for example, the reaction

A ( sol ) + xB2 (gas) = AB2 x (sol), where the solid reactant A bonds with the diatomic gas B 2 at a constant pressure P (constant pressure condition means that the initial volume of gas in the vessel is much larger than that required

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Combustion for Material Synthesis

for the completion of the reaction). Due to the formation of solid product AB 2x the amount of the reactant gas is reduced by x moles, i.e. the corresponding change of the gas volume can be estimated in accordance with the Mendeleev–Clapeyron equation: ∆Vr =

xRT , P

and the work is done Ar = P∆Vr = xRT

(2.4)

(R = 8.314 J/mol·K is the universal gas constant). Here we have neglected a change in the solid product volume compared to that for the gas phase and also used the ideal gas approximation, due to which the A r in the expression (2.4) does not depend on pressure. For approximate evaluation these assumptions are well justified. According to the formula (2.4) we can calculate, for example, that the work done during the reaction Ti + 0.5N2 = TiN is 1.25 kJ/mol. Comparing this value with the energy of formation of TiN from the elements, which is equal to 383 kJ/mol, one may conclude that for engineering calculations the mechanical work of the reaction can be neglected. Another important thermodynamic function, which for a system with a constant number of particles can be written as F = U − TS ,

(2.5)

is called the Helmholtz free energy (Hermann Ludwig Ferdinand von Helmholtz, 1821–1894, was a German physicist and physiologist) or the isochoric–isothermal potential. Change of this function, ΔF, in any process, shows the maximum work which the system may carry out over the other bodies. Classical thermodynamics has historically developed, responding to the needs of creating heat engines (steam and internal combustion engines), which convert the internal energy to work. Therefore, the fundamental differences of the G and F functions in conventional thermodynamic processes are essential. However, as it is mentioned above, the mechanical work in the SHS processes is negligible, therefore the change of the free energy at constant volume, ΔF, and the change in free energy at constant pressure, ΔG, tend to have similar values. The other thermodynamic function

Thermodynamics and Kinetics of SHS

H = U + PV ,

49

(2.6)

is called enthalpy (from the Greek ενθαλπα – heating). The enthalpy is of great importance for the analysis of combustion and thermal explosion processes including SHS. The change of this function, ΔH, when the system moves from one state to another, shows the amount of internal energy and work that can be transformed into heat (note again that since the mechanical work in SHS processes is small, it is mainly the internal energy of the system that is converted to heat). The absolute value of the enthalpy is unknown, and, in any process only the enthalpy change is important (sees above about the internal energy). To facilitate practical calculations, an arbitrary selected ‘zero’ reference point, which is called the standard molar enthalpy of formation from elements ΔH, or simply the standard enthalpy is usually introduced. It is considered that the standard enthalpy of elemental substances, consisting of identical atoms, is zero under normal conditions, i.e. at temperature of 298 K and a pressure of 1 atmosphere. If a substance exists under normal conditions in several crystalline modifications (polymorphism), the zero standard enthalpy is attributed to the most stable modification (typically, this modification is most common in nature). For example, for carbon the graphite has a zero standard enthalpy ΔH (graphite) = 0 kJ/mol, and for diamond ΔH (diamond) = 1.828 kJ/mol. A similar approach is used for molecules and gases; for example, for molecular oxygen ΔH (O 2) = 0, and for ozone ΔH (O 3) = 142.3 kJ/mol. In contrast to the G and F functions, which remain unchanged only in equilibrium states, the enthalpy H remains unchanged in the isolated system, no matter what type of processes take place. This follows from the first law (the first origin) of thermodynamics. The wording of the first thermodynamic law differs, depending on to which system it is applied, but in any formulation this law is a consequence of the fundamental law of conservation of energy. For an open system, which exchanges heat and work with the environment, the formulation is as follows: the quantity of heat Q transmitted to the system (or taken away from it), is used for changing the internal energy of the system ΔU and for carrying out work A against external forces, i.e. Q = ∆U + A.

(2.7)

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Combustion for Material Synthesis

For an isolated system Q = 0, and therefore, ΔU + A = 0. If the process takes place in an isolated system at constant pressure, it is obvious that ∆U + A = ∆U + P∆V = ∆H = 0, i.e. the first law of thermodynamics in this case takes the form of the law of conservation of enthalpy. The standard enthalpies of formation from elements were measured for essentially all known chemical compounds using different calorimetric approaches and can be found in handbooks. Therefore, based on the first law of thermodynamics and knowing the composition of the starting components and reaction products, one can calculate the amount of heat generated during the reaction and thus the temperature of the products. The practical use of such calculations will be discussed below, but now let us return to the formula (2.1) and consider the third and final term of the right-hand side of this equation. The product TS in expression (2.1) characterizes the part of the free energy which the system lost when transferring from one state to another and cannot be used for any useful work or to increase the temperature of the system. The concept of entropy (from the Greek εντρoπα – turning, transformation) was introduced in 1865 by the German physicist and mathematician Rudolf Julius Emmanuel Clausius (1822–1888) to determine the measures for irreversible dissipation of energy, the measure of the deviation of the real process from the ideal one. From a macroscopic standpoint for reversible processes, entropy (DS) is introduced as a state function, where changes (DS) are determined by the ratio of the amount of heat (Q) transferred to or out of the system at constant temperature T, to this temperature ∆S =

Q . T

(2.8)

Clear understanding of the physical meaning for this thermodynamic function came later, with the development of statistical physics and the theory of the structure of matter. It was found that the entropy is a measure of disorder of the system, or a measure of the number of specific ways in which a thermodynamic system may be arranged. If the system receives a constant amount of heat at constant temperature, all the heat goes into increasing of chaotic, random motion of particles, i.e. an increase of entropy. This takes

Thermodynamics and Kinetics of SHS

51

place during melting of matter or its evaporation under isothermal conditions, for example during boiling. On the contrary, increasing the system order, e.g. by crystallization of the liquid, the entropy of the system decreases and the latent heat of fusion is released. The concept of entropy is essential for the analysis of the reversibility or irreversibility of the processes that occur in nature and technology. It is the basis of the second law of thermodynamics, which states that in an isolated system only such processes can spontaneously proceed that lead to an increase of disorder of the system, i.e. increase of its entropy. This principle is fundamental, like the law of conservation of energy, as it is a generalization of scientific experience and cannot be derived from any other laws. At the same time, statistical physics makes it possible to consider some of the physical aspects of this principle. Let the number of different ways by which the given state of the system can form be W; obviously, for macroscopic systems, this number is very large. The value of W is called the thermodynamic probability. In statistical physics it is shown that the entropy S is proportional to the natural logarithm of the thermodynamic probability of the system: S = k ln W .

(2.9)

Note that in principle the constant k can be any value, because the absolute value of the entropy is not defined and in any process only the change of this function is important (similar to the functions U and H discussed previously). However, to ensure that the statistical definition (2.9) is consistent with the thermodynamic one (2.8), it is that k is equal to the Boltzmann constant (k B = 1.38·10 –23 J/K). For practical calculations of S and G values of fundamental importance is the third law of thermodynamics. It is also called the Nernst theorem, in honor of Walter Hermann Nernst (1864–1941), a German chemist who received a Nobel Prize in 1920 for his work on thermodynamics. This law states that the entropy of perfect crystal approaches zero as the temperature approaches absolute zero (0 K). This law shows, in particular, that near 0 K the specific heat of any perfect crystal lattice approaches zero. From the statistical physics point of view (equation (2.9), the zero entropy means that W = 1, provided that its ground state is unique, Based on established benchmarks for the enthalpy and entropy, and using the results of measurements of some thermophysical properties, it is possible to calculate the change of free energy (ΔG)

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in any chemical process at any temperature T. There are several ways for such calculations: 1. Calculation according to the Gibbs–Helmholtz equation: ∆GT = ∆H T − T ∆ST ,

(2.10)

with the value ΔH T obtained by solving the Kirchhoff equation d ∆H = ∆c P , dT

(2.11)

and ΔS T is calculated from the formula: ∆S = cP

∆T , T

(2.12)

where c P is the heat capacity of the system at constant pressure, and Δc P is the heat capacity difference between the reaction products and the precursors determined from the calorimetric measurements. Heat capacity, by definition, is the amount of heat that must be transferred to system to raise its temperature by one degree. Usually, the specific heat per gram or one mole of constant pressure (c P) or constant volume (c P ) is determined. For solids and melts the difference between cP and cP is insignificant, so that the heat capacity of solid bodies is often denoted just by letter c. 2. Calculations by the Temkin–Schwartzman method are carried out by integration of the expression in the range from 298 K to T: ∆H T  ∆G  d  = − 2 dT T  T 

(2.13)

this gives: 0 ∆GT = ∆H 298 − T ⋅ ∑ i =0 ∆ai M i . N

(2.14)

To calculate ΔG T by this formula, it is sufficient to know the heat of the reaction, the standard enthalpies of formation at 298.15 K for all substances, and the coefficients A, B, C in terms of the temperature dependence of heat capacity c(T ) = A + BT + CT 2 .

(2.15)

These values, as well as the integrals designated M i can be found in thermodynamic reference books

Thermodynamics and Kinetics of SHS

53

Table 2.1. Criteria for spontaneous occurrence of a chemical process and the establishment of equilibrium Constant parameters

Criterion for occurrence of direct process

U and V

ΔS > 0; S → max ΔS = 0

Adiabatic combustion in a constant volume reactor (the volume of the reaction mixture is comparable with the volume of the reactor), combustion of hybrid SHS systems solid–gas

H and P

ΔS > 0; S → max ΔS = 0

Adiabatic combustion in the constant pressure volume or with expansion to constant pressure (in a rocket engine, in a furnace of power equipment), combustion of gasless SHS systems

T and P

ΔG < 0; G → min ΔG = 0

Isothermal reaction at constant pressure, for example, reactive sintering in the absence of thermal explosion

T and V

ΔF < 0; F → min ΔF = 0

Isothermal reaction at constant volume, for example, slow reaction inside a thermostatically controlled hermetic vessel, filled with the reaction mixture

S and P

ΔH < 0; H → min ΔH = 0

Isoentropic compression or expansion of gases

S and V

ΔU < 0; U → min ΔU = 0

Isoentropic heating or cooling of the gas in a constant volume vessel

Equilibrium criterion

Process examples

3. Calculations using the reduced isobaric potentials: Φ′ =

0 ∆GT0 − ∆H 298 , T

(2.16)

which are also given in the thermodynamic handbooks. Combining the tabulated values of Φ′ for the initial reagents and products, ΔG T can be determined as follows 0 ∆GT0 = −T ∆Φ′ + ∆H 298 .

(2.17)

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All spontaneous reactions occur with a decrease in free energy, which reaches the minimum at equilibrium, and under constant conditions remains further unchanged. Depending on the nature of the processes, the criterion for equilibrium is defined by the extreme value of one of the thermodynamic functions (see Table 2.1). As can be seen from the table, the first two cases are related directly to the combustion processes. Note that some above defined values, such as G, U, F, H and S are functions of the state, i.e. for the given parameters of the system – the component concentrations, temperature, pressure, volume – they are uniquely determined. During transition from one state to another the difference of their values in the initial and final states is independent of the pathway between the states (this rule, known as Hess’s law, which is another specific case of the law of conservation of energy): ΔG = G2 – G1; ΔU = U2 – U1; ΔH = H2 – H1; ΔF = F2 – F1; ΔS = S2 – S1. At the same time the concepts of heat (Q) and work (A) do not relate to the system but relate to the processes. They are not energies but the forms of energy transfer [2]. Since the work in the considered combustion processes is negligibly small, the energy is transferred in the system only in the form of heat, which leads to high temperature of the products.

2.2.1.2. Equilibrium, reversibility, stationary and stability of the SHS processes and products With the required thermodynamic values defined, we are ready to discuss the concepts of equilibrium, reversibility, stationary and the stability of the real SHS processes and products on a macroscopic scale. Can we consider the combusting sample to be an isolated system (Fig. 2.1)? The answer depends on the specific times of reactions and product formation, as well as the rate of heat exchange with the environment. The time of chemical transformation in the combustion wave is in the range of treact = 0.001–0.1 s. The total time required for the process to be completed along the whole sample depends on the sample size and the velocity of combustion wave propagation; for the most common laboratory conditions this time is of the order t comb = 1–10 s. The heat generated by the exothermic reaction in the sample is transferred to the environment by radiation, heat conduction along the contact surface with the solid parts of the reaction chamber, and by convective heat transfer in the surrounding gas atmosphere (Fig. 2.1, b, c). Due to these heat losses the sample

Thermodynamics and Kinetics of SHS

a

55

Reaction chamber Igniting pulse Initial sample Substrate

b Combustion wave

c Hot products

d Cooled products

Fig. 2.1. SHS sample as a thermodynamic system at different stages of the process (for the colour image please see the colour section in the middle of the book).

cools down to ambient temperature with typical cooling time t cool = 100–1000 s (the larger the sample and smaller the heat loss, the longer the cooling time). Thus, treact 2000 K), hence we should expect the successful implementation of synthesis in the self-sustained combustion mode. Experimental verification of thermodynamic calculations, similar to those discussed above, in many cases showed an exact match of the theoretical predictions and experimental results [13]. These and many other examples [14–18] show that the thermodynamic calculations in the theory and practice of SHS have become a powerful infallible research method. This approach not only predicts the conditions (temperature, composition of the products) of the SHS process, but is also a tool for analysis of possible mechanisms of combustion and structure formation in heterogeneous chemical reactions.

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To conclude this section, we list the questions which can be answered by the thermodynamic analysis of the SHS system as a whole. 1. Is it possible in this system to synthesize the given compound in the SHS mode? Recognizing that the kinetic parameters of a reactive system, ultimately, determine the possibility of propagation of the reaction in the wave regime, yet one cannot neglect the thermodynamic information. It was even proposed to assume that if the adiabatic combustion temperature is less than 1800°C, the reaction in the SHS mode cannot be accomplished [19]. To date, there are many methods allowing SHS synthesis at lower temperatures, however, if the adiabatic temperature is low, we can expect difficulties in the implementation of the SHS. 2. What are the optimal synthesis parameters, including the composition of the initial mixture, the initial temperature, pressure of inert or reaction gases, the volume of the reactor, that must be used to synthesize the product of the given phase composition? As demonstrated above, thermodynamic evaluations are very useful for determining the optimal synthesis conditions for products of a given composition, which is a non-trivial task in multi-component systems. 3. Is it possible to get rid of the impurities present in the starting reagents and contaminating the final product? Thermodynamics shows (and this is confirmed by experiment) that due to the very high combustion temperatures many contaminants are transferred into the gas phase, which can be removed from the reaction volume (SHS-self-cleaning effect). But if this does not take place, then the thermodynamics can tell which supplements and in what quantity should be added to the system for such cleaning to take place. In this case, all the contaminants and additives will be in the gaseous phase in the SHS wave and will be easily removed from reactor ensuring the required purity of the synthesis product. 4. Are the SHS products equilibrium? SHS products have lower free energy, i.e. they are closer to equilibrium than the original mixture. The distance of the products from equilibrium depends on the temperature conditions during sample cooling. Rapid cooling may lead to

Temperature

Reaction zone

Initial reaction mixture

Preheating zone

Thermodynamics and Kinetics of SHS

77

Hot combustion products

Preheating and reaction zone Fig. 2.9. Preheating–reaction zone as an open thermodynamic system (for the colour image please see the colour section in the middle of the book).

the formation of metastable ‘quenched’ phases. Under slow cooling conditions the SHS products are in an equilibrium state similar to that from materials produced by conventional sintering.

2.2.2. Thermodynamics of the preheating–reaction zone Assume that the combustion wave propagates through the infinite reaction medium, as shown in Fig. 2.9. In this case, there are no heat losses, since the medium is infinite. The combustion products are in a steady-state equilibrium condition at a constant temperature Tad. The initial mixture is in a non-equilibrium quasi-stationary state, as its chemical and phase composition, as well as pressure and volume remain unchanged at the initial (room) temperature T 0 for a long time, as compared to the characteristic time of the process. All physical and chemical changes, including changes in temperature, phase composition, etc., occur in a region between the cold initial mixture and the hot combustion products. In the combustion theory this region should be subdivided into the preheating zone in which chemical transformations do not occur (or are ignored), and the reaction zone (Fig. 2.9). This division will be discussed in the next chapter, and now we consider the region, where the substance is heated and phase and chemical transformations take place, as a single thermodynamic system. To analyze this zone from the thermodynamics point of view, let us use the coordinate system associated with this zone. In this coordinate system, the preheating–reaction zone is stationary. The flux of the initial cold reaction mixture enters the zone through the left boundary A with velocity U, and the flux of the hot reaction

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products leaves it through the right boundary C. For simplicity, we assume that the density of the medium is constant along the zone, and thus the velocity of the outgoing flux also equals U. The upcoming flux of the initial reactive mixture carries internal chemical energy; this energy is released during the reaction and is converted into heat, which is carried out by the hot products of the reaction. Thus, the preheating–reaction zone exchanges both matter and energy (heat) with the environment, and can be considered as a thermodynamically open system in which irreversible physical and chemical processes occur. The study of open systems is a relatively new field of thermodynamics, which appeared in the mid-20th century and has been actively developed so far. It is called the thermodynamics of irreversible processes [20–22] or sometimes referred to as nonequilibrium thermodynamics. Let us discuss some principles and approaches of the thermodynamics of irreversible processes, which are specifically related to the analysis of combustion processes Thermodynamic functions and values at different points in the preheating–reaction zone have different values. Therefore, for each characteristic (e.g. P,V,T) of this open thermodynamic system one cannot use a single value (as it was done for the homogeneous systems in section 2.2.1), but local values of these parameters, which depend on the spatial coordinates, should be introduced. This is possible only in the case when the thermodynamic functions and parameters can be defined in small volumes, i.e. they are in a local equilibrium. The concept of local equilibrium means that the system can be divided into a number of cells, which are large enough to treat them as macroscopic systems, but small enough to be considered in equilibrium state, i.e. previously discussed equilibrium thermodynamic relations are valid for each cell. In this case, variables such as temperature and pressure become functions of the spatial coordinates and time, and the thermodynamic functions – internal energy, enthalpy, entropy – are replaced by their densities. For example, if we consider entropy S of a single cell and divide it by the volume of this cell V, we obtain the local density of entropy in the given microscopic region of the system:

s=

S . V

Similarly, we can set the density of enthalpy

(2.31)

Thermodynamics and Kinetics of SHS

h=

79

H , V

(2.32)

G , V

(2.33)

the Gibbs energy density g=

and densities of other thermodynamic functions. In the example of combustion wave (Fig. 2.9), the local values of the variables and densities are assumed to be continuous functions of the spatial coordinates and such systems are called continuous. The differences between the local values of the thermodynamic variables at different points leads to the formation of fluxes of matter and energy: heat flows from hotter areas of the system to colder ones, the substance moves as a diffusion flux into the region of its lower concentration (the flux refers to the amount of some physical quantity – mass, energy, charge etc., transferred in unit time through an unit area in the direction normal to the area). In many cases, fluxes are linearly proportional to the gradients of some physical quantity. For example, the mass flux of the j-th component is proportional to its concentration gradient (1 st Fick’s law): m j = − D j ∇c j ,

where ∇ =

(2.34)

∂ ∂ ∂ is the Hamilton differential operator, which + + ∂x ∂y ∂z

allows one to calculate the gradient of a physical quantity; c is the concentration of the component (in g/cm 3). In the one-dimensional case this law can be presented as follows m j = −Dj

∂c j ∂x

,

where D j is the diffusion coefficient which is essentially constant at constant temperature. In turn the heat flux is proportional to the temperature gradient (Fourier’s law): ∂T q = −λ∇T , or in the one-dimensional case q = −λ , ∂x (2.35) λ is the coefficient of thermal conductivity. The fluxes (2.34) and

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(2.35) play the most important role in the combustion of SHS compositions. The so-called cross-processes – diffusion fluxes of matter due to the temperature gradient (thermal diffusion) and the heat flux under the influence of the concentration gradient (Dufour effect) are much weaker and typically can be neglected. The gradients of physical quantities of the type (2.34), (2.35) are called the generalized thermodynamic forces. A generalized linear dependence between the flux and the force causing this flux is called the linear Onsager’s law (Lars Onsager, 1903–1976, Norwegian–American physical chemist, Nobel Prize in Chemistry in 1968 for his work on the thermodynamics of irreversible processes) and can be presented as

J i = ∑ Lij  , j

(2.36)

where L ij are the Onsager coefficients that depend on the local state parameters (temperature, pressure, etc.),  is the generalized force. For example, the diffusion mass flux the equation (2.36) can be written as follows:

w j = − D j ∇c j + DTj ∇T + D Pj ∇P. The first term on the right-hand side represents conventional diffusion (Fick’s law), the second – thermal diffusion, the third – baro-diffusion; respective driving forces are the concentration, temperature and pressure gradients, and the corresponding Onsager coefficients are: the diffusion coefficient D, the thermal diffusion coefficient D Tj and the baro-diffusion coefficient D Pj. If all fluxes in the thermodynamic system can be expressed by linear laws (2.36), this system is called linear and can be analyzed by the methods of linear irreversible thermodynamics. In the diffusion-type flows the substance or heat are transferred as a result of the random motion (or vibration) of individual atoms and molecules and such flows are called conductive. The physical quantities can be also carried by the macroscopic movements of matter, and this type of transfer is called convective. In the considered case the flux (m j) of the j-th component of the mixture through the heating and reaction zone, which moves with the velocity U, is:

w j = Uc j .

(2.37)

Each local volume (cell) of the substance contains certain amounts of internal energy and enthalpy, thus, together with the flow of

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81

substance there are fluxes of enthalpy () and entropy (S) = Uh,

(2.38)

S = Us,

(2.39)

where h and s are the local densities of enthalpy and entropy, respectively, given by the formulas (2.32) and (2.31). The considered open system is characterized by a spontaneous chemical reaction, which converts the starting reagents into products and the internal energy of the system into heat. The chemical reaction rate W can be expressed as the amount of the initial reagent converted to the product in the unit volume of the medium per unit time. More details on this value can be found in section 2.3 which is dedicated to the kinetics of the chemical reaction. In this case, the local rate of heat release can be expressed as qr = QrW ,

(2.40)

where Qr is the specific heat of the reaction (see 2.2.1.3). The rate of the non-equilibrium chemical reaction W and hence the heat release rate q r cannot be expressed as a linear function of some generalized thermodynamic force (difference between the chemical potentials, temperature, etc.). This circumstance makes our open system nonlinear, and it must be considered in the framework of non-linear irreversible thermodynamics. Thus, the preheating–reacytion zone is a non-linear open thermodynamic system that exchanges matter, entropy and energy with the external environment, and involves both conductive and convective fluxes, as well as chemical reactions. The main question to be answered by the non-equilibrium thermodynamics is: can such system be in a stationary state? If the answer is yes, than what this state is and how can it be reached? The fundamental ability to use combustion processes for the synthesis of materials depends so much on the answers to these questions. Indeed, the preheating–reaction zone can be considered as a reactor, wherein the product with desired chemical, phase compositions and microstructure is produced from the initial mixture. If the fields of temperature, density and concentration distribution within the reactor uncontrollably and unpredictably vary with time, the properties of the output reactor product will also be unpredictable. For a reliable, reproducible technology it is essential to establish a stationary distribution of temperature and other physical parameters in the reactor which

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are independent of time. Can such conditions be accomplished? One can strictly define the boundary conditions at the inlet of the reactor, the chemical composition, density and the initial temperature of the initial mixture, but cannot directly set the temperature and concentration distribution within the reactor. The system itself has to ‘choose’ and ‘tune’ the stationary mode of transformation. Nonequilibrium thermodynamics implies that such ‘tuning’, which is called self-organization, could and should occur in open systems. In 1947, the Russian-born Belgian–American physicist and chemist Ilya Prigogine (1917–2003, the Nobel Prize in Chemistry in 1977), based on the works of L. Onsager, proved a theorem of Minimum Entropy Production [20], the essence of which is as follows: the stationary state of an open continuous linear system under the nonequilibrium corresponds to the minimum entropy production, i.e. the minimum amount of entropy produced in the system per unit time as a result of non-equilibrium processes occurring in the system. Entropy production per unit volume is called local. If the system is in a stationary state, it will change as long as the production of entropy in the system reaches the lowest values. If there are no external obstacles to reach equilibrium (closed system), the entropy production reaches its absolute minimum – zero (and the entropy itself reaches a maximum value at the same time, in accordance with the second law of thermodynamics). The physical meaning of Prigogine’s theorem is that in the stationary state, to which the linear thermodynamic system irreversibly approaches, the entropy transfer to the environment is as small as allowed by the boundary conditions. The equilibrium state corresponds to the extreme case when the boundary conditions allow an infinitely small entropy production. If the boundary conditions prevent the system from reaching the state of thermodynamic equilibrium, the system tends to a state as close to the equilibrium as it is allowed by the exchange of matter and energy with the environment. Prigogine’s theorem shows that the steady state exists in an open system, and the system goes into this state spontaneously. However, it does not answer the question as to which distribution of physical quantities (temperature, density, concentration, energy, enthalpy, etc.) corresponds to the steady state. The answer to this question must be sought from the analysis of flows, the balance of energy, entropy, and other variables, taking into account the boundary conditions for each case. Furthermore, as mentioned above, the systems with chemical reactions are non-linear so that

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Prigogine’s theorem is applicable to them only approximately. The behaviour of non-linear systems is quite unusual and as yet poorly understood. The non-linear thermodynamics of irreversible processes is being actively developed at present, and one of the impressive results in this area was the discovery of the so-called dissipative structures. These structures are rather complex spatial structures and processes that occur spontaneously in an open system far from equilibrium condition and stably exist for a long time. At first glance, the appearance of dissipative structures contradicts the second law of thermodynamics – entropy increase in the irreversible process, because the emergence of ordered structures means that the entropy of the system has decreased! In fact, there is no contradiction. The second law is valid for isolated systems, but in the open (especially in non-linear) system, which involves fluxes of energy, the selforganization processes occurs, leading to a local entropy decrease. A classic example of dissipative structures are structures, first described by French physicist Henri Bénard (1874–1939) back in 1900 and named after him – Bénard cells. When a layer of a viscous fluid is poured into a flat container (such as a Petri dish) and then heated from below, then when the temperature difference between the upper and lower liquid layers is sufficiently large, convection cells of regular hexagonal shape appear in the liquid, and the liquid rises in the center and falls along the edges of the cell [23]. (Henri Bénard carried out his experiments with thin (not more than 0.5 mm) horizontal layers of cachalot wax – spermaceti, poured onto a steel plate). In Prigogine’s theory, Bénard cells are considered as huge fluctuations stabilized by energy exchange with the environment [24]. Other examples of spontaneous ordering in open systems include oscillatory Belousov–Zhabotinsky reactions [25], and lasers. Are there any dissipative structures in the heating- reaction zone of the combustion wave? Well-known is the self-oscillating combustion mode of SHS systems [26], and these fluctuations can, with certain assumptions, be interpreted as a dissipative process of the Belousov–Zhabotinsky reaction type [27]. However, there are many other reasons for the occurrence of oscillations in the SHS, in addition to self-organization of the heating and reaction zone. The spontaneous formation of cellular structures in gas flames has also been observed [28]. Experimental study of the spatial ordered structures in the combustion wave of powder mixtures is difficult because the surface of the combustion front in such systems cannot be directly observed, since the medium is opaque. Therefore, the

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spatial structure of the front should be judged by what is seen on the surface of the sample. Sometimes, instead of a solid line marking the intersection of the combustion front with the cylindrical surface of the sample, the stable local hot spots are observed which move along a spiral trajectory. This mode is called spin combustion [26]. All of these modes are discussed in more detail in chapters 3 and 4. Consider the quantitative enthalpy balance in any very small volume (cell) of the preheating–reaction zone as an open thermodynamic system in the one-dimensional case (Fig. 2.9). If the conductive heat flows, entering and leaving this volume and defined by the Fourier formula (2.35), are not equal to each other (i.e. the derivative of the conductive heat flow in the spatial coordinate is not equal to zero), then during the time dt the local density of enthalpy (2.32) changes by the value ∂  ∂T  (2.41) λ  dt. ∂x  ∂x  The reaction occurring in the same microscopic volume also changes in the enthalpy density: dhT =

dhR = QW dt.

(2.42)

Consequently, the overall enthalpy density change per unit time (i.e. the rate of change of enthalpy) will be ∂h ∂  ∂T = λ ∂t ∂x  ∂x

  + QW . 

(2.43)

Using the relation between enthalpy and specific heat (see (2.11) – in fact, this formula is a definition of a specific heat) – expression (2.43) can be rewritten in the well-known form of the heat conductivity equation with a heat source: cP ρ

∂T ∂  ∂T  = λ  + QW . dt ∂x  ∂x 

(2.44)

Thus, the heat conductivity equation is a direct consequence of the law of conservation of enthalpy, which in turn, is a special case of the first law of thermodynamics. Assume that the preheating– reaction zone has reached the steady (but non-equilibrium!) state in a coordinate system associated with this zone (Fig. 2.8). Then the time derivative in the left-hand side of equation (2.44) is equal to zero,

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but instead the additional convective flow of the enthalpy density appears (3.38), and the rate of enthalpy change in this microvolume is

∂h ∂T ∂h ∂ . = c p ρU = (Uh ) = U ∂x ∂x ∂t ∂x

(2.45)

To satisfy the stationary condition, i.e. local enthalpy values do not change with time, the enthalpy change due to the heat conduction and the reaction (2.43) should be completely compensated by the convection flow (2.45), so that the resulting rate of enthalpy change is equal to zero:

d  ∂T  dT + QW = 0.  − c p ρU λ dx  ∂x  dx

(2.46)

Note that since the local temperature does not depend on time, and is only a function of the coordinates, one use full derivatives along the coordinate x. Equation (2.46) is the classical combustion equation, which is usually solved with boundary conditions: x = −∞, T = T0 ; x = + ∞, T = Tad .

(2.47)

In the third chapter, the problem (2.46), (2.47) will be discussed in details for the various kinetic functions of the reaction rate W. Solution of this problem, if it is exist, should provide a specific stationary temperature profile, as well as the concentration distribution of the product and the value of the constant velocity of combustion wave U, to which the open system spontaneously tends, according to the thermodynamics of irreversible processes. Let us return to the problem of the enthalpy balance in the preheating–reaction zone. The enthalpy of the initial substance entering this zone H 0 should be equal to the enthalpy of the output reaction product H f, which is required by the first law of thermodynamics. However, within the zone there is a local maximum of enthalpy as illustrated in Fig. 2.8. In the left part of the zone (preheating zone) the initial substances are heated by the conductive heat flow but the rate of chemical reaction in this zone is still negligible and, therefore, the internal energy of the reactive media remains constant. Thus, the excess heat is added to internal energy of the media, which leads to a local maximum of enthalpy (or more precisely, enthalpy density). But the local enthalpy density should return to its initial value. This occurs in the right part of

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the system – in the reaction zone. For the enthalpy density in this zone to decrease, the amount of heat removed by heat conductivity must be greater than the heat generated by the chemical reaction. If this condition cannot be satisfied, the steady-state combustion mode cannot be accomplished. This condition imposes limitations on the rate of reaction heat generation in the stationary combustion mode of homogeneous (or quasi-homogeneous) media that is discussed in chapter 3. The local excess of enthalpy is ‘placed’ in the preheated layer during ignition and then moves with the combustion wave. Interestingly, the enthalpy excess may not occur during combustion of gases. The point is that the diffusion coefficient of combustion products D in gas flames is approximately equal to the coefficient of thermal diffusivity a = λ/cρ, i.e. the so-called Lewis number is close to unity: Le = D/a ≈ 1. Consequently, simultaneously with the heat flow the flow of inert reaction products enter the initial mixture, diluting it and reducing its heat content. Effects of heating and dilution are mutually balanced, so there is no enthalpy excess in the gas flames [29, 30]. This circumstance is called the similarity of concentration and temperature fields. In condensed homogeneous systems such similarity does not occur, because D