Gusev A.I., Rempel A.A., Magerl A.J. Disorder and Order in Strongly Nonstoichiometric Compounds: Transition Metal Carbides, Nitrides and Oxides (Materials Science, Vol. 47) (monograph)

One of the topical problems in many provinces of modern science is that of order and disorder. It is well known that in the various different physical systems (solids and liquids, classical and quantum systems) ordered structures arise at the macroscopic level. However, the formation of these structures cannot be predicted proceeding from only the microscopic properties of matter. Indeed, the occurence of ordering is not associated with a specific kind of interparticle interection but is of a nature common to different objects, a nature that is determined by the statistical properties of the many-particle system. Only by using, developing and refining the concept of order and disorder is it possible to construct a bridge between the macroscopic and the microscopic levels and to effectively describe complicated material systems.
The present book provides an exhaustive account of the phenomena of non-stoichiometry, disorder and order in solid. Ordering and disordering in solids, that is, the redistribution of different species (or atoms and vacancies) in crystal lattice sites, can occur in all systems with substitutional disorder. Such systems include non-stoichiometric carbides, nitrides and oxides, substitutional solutions of these compounds, and metallic alloys - all of them are treated in this book. Of particular interest are the non-stoichiometric compounds, whose composition can very wide range with the basis crystal structure remaining unchanged.
Order and disorder in solid are intimately related to structure. Therefore, the first and second chapters of the book deal with the fundamental concepts of crystal symmetry, with a description of the regions of homogeneity and of the crystal structures of disordered and ordered non-stoichiometric compounds. Chapter 2 considers the concepts of the structural vacancy and of the region of homogeneity and shows the difference between a structural vacancy and other types of defects (thermal vacancy, Schottky defects, Frenkel defects, etc.). A method is proposed which permits determinig the structural stability boundaries of the non-stoichiometric compounds.
Ideal disorder is attained seldom, because correlation between neighboring atoms exist in the lattice and a short-range order can arise. The concept of short-range order and its parameters, the methods and results of observations of the short-range order in non-stoichiometric compounds, solid solutions and alloys are discussed in Chapter 3.
Chapter 4 is devoted to the long-range order. This chapter provides a brief summary of the major methods of introducing long-range order parameters and gives a detailed discussion of fundamental concepts as the disorder-order transition channel and the atomic distribution function in the crystal. In this context, chapter 4 considers in detail the problem of the theoretical determination of the diffraction picture on the basis of data on the disorder-order transition channel and describes various types of substitutional and interstitial structures and the corresponding distribution functions and diffraction spectra. The same chapter shows for the first time that the variation of long-range order parameters is restricted to a certain region of allowed values.
By intuition, it is clear that a close relation exists between short-range order and long-range order. However, in spite of the apparent simplicity, the problem of interrelation between short-range and long-range order has not yet been resolved. Chapter 5 gives predominant treatment to the cluster-variational method of analyzing this relation. The correlation between short-range and long-range order is shown to determine the type of disorder-order phase transitions. Two short-range order com-ponents are singled out in superstructures: the correlational and the superstructural short-range order.
The disordered state of solids is reached at a sufficiently high temperature, when the evaporation of their constituents becomes noticiable. The evaporation kinetics and the thermodynamics of disordered compounds that posses extended regions of homogeneity exhibit a number of peculiarities. An understanding of correct use of these features are a clue to controling the properties of the non-stoichiometric compounds and alloys at high temperatures and at high pressures. This subject is taken up in Chapter 6.
The next chapter provides a brief overview of the major directions of phase transition theory with focus on the methods and the models that are most efficient in describing disorder-order transitions.
Chapter 8 is entirely devoted to the order parameter functional method and the practical applications of it in the calculation of conditions for the order-disorder and the order-order transitions to occur in various systems with substitutional disorder (non-stoichiometric compounds MXy with NaCl structure, AyB1-y alloys with body-centred cubic and face-centred cubic structures, A2B3-type semiconductors with ZnS structure, etc.). It is shown how one can, from a knowledge of some thermodynamic characteristics of a disordered compound or alloy, calculate the phase diagram with allowance for ordering, predict the possibility of the formation of particular superstructures and the regions in which these exist, and the properties of ordered phases. For the first time, phase diagrams are presented for the M - C and M - N systems (M - Ti, Zr, Hf, Nb, and Ta).
The effect of ordering on the magnetic, electrokinetic, superconducting, thermodynamic, and mechanical properties of the non-stoichiometric compounds is considered in detail in Chapter 9. Models are described which explain the alteration of different properties as the short-range or the long-range order arises. Currently, the major methods for altering the properties of a different materials are alloying and the introduction of various additives, that is, changing the composition. Chapter 9 describes a novel method of finely controling the properties of non-stoichiometric compounds by altering their structural state while keeping the chemical composition unchanged. This chapter will be helpful to those who are concerned with the practical utilization of the novel structural and the tool materials in modern engineering, ranging from electronics to metal working and power engineering.
Solid solution possess, as a rule, higher service properties compared to those of the individual compounds that form these solutions. In this context, the last chapters of the book discuss factors (crystal structure, non-stoichiometry, electronic structure, elastic properties, etc.) affecting the formation and breakdown of solid solutions and propose quantitative methods of assessing the chapter of the mutial solubility of the non-stoichiometric compounds. A detailed description is given of an efficient method for calculating phase diagrams of the pseudobinary systems. Phase diagrams of over twenty carbide systems M1C - M2C are presented. Considerable attention is given to the magnetic, electrokinetic, superconducting, thermodynamic, and mechanical properties of the carbide solid solutions and the metallic alloys.
The present monograph embraces the entire range of the problems associated with disorder, order and non-stoichiometry in solids. The methods and models presented are applicable to all physical systems with substitutional disorder and permit the structure, phase diagrams and properties of these systems to be considered in terms of unified approch. The book contains a wealth of facts, over a hundred tables and about two hundred figures. In its contents, the book will appeal to and be useful to specialists in phase transition theory, in solid state physics and chemistry, to materials science engineers, as well as to students of physical and chemical faculties and all readers wishing to understand the relation of chaos and order in nature.
607 pp. References 1041. Figures 205. Tables 107.