Theory of Structural Transformation in Solids (Anglais) Relié – 9 novembre 1983
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To the curious minds of today and tomorrow:
Those who are not well versed in Fourier Analysis, Matrix Algebra, and are not skilled in the use of Elasticity Theory and Statistical Thermodynamics might be very well shocked upon taking a first glance at the book. However, if the contrary is the case, you will soon discover that the entire book is nothing but a stroke of brilliance of a very creative mind. And you will also discover that text reads like poetry (no kidding)!
In this book, Prof. Khachaturyan discusses essentially all aspects of structural phase transitions in solids, i.e. diffusion kinetics, equilibrium & stability, transformations involving diffusion (nucleation & growth as well as spinodal decomposition), displacive transitions, and effects of elastic strain on microstructure development in multiphase systems. While the book is primarly focused on metallic systems, the approach presented therein is of universal validity and use, making the book very valuable.
The book most impressively introduces the reader to the concept of "superposition of static plane concentration waves" in the treatment of diffusional phase transformations and shows how Fourier analysis can be so powerfully used in studying such phase transformations.
Displacive phase transitions, on the other hand, are treated with hermitian matrices which provides a lucid method for analyzing the crystallographic changes accompanying such phase transitions. It also sets the stage to examine microstructural evolution of multiphase systems, and comprises the foundation for elastic strain effects. And in the following chapters, elastic strain effects is masterfully presented.
As someone who learned about phase transitions from classical physical metallurgy books such as Christian, Reed-Hill, Haasen,
Verhoven (still good books but...), I need to admit that the traditional presentations of these topics turn out to be very pedestrian as compared to Prof. Khachaturyan's.
This book is certainly not for the novice. Yet, I believe that graduate students in solid state physics, solid state chemistry, and materials science as well as professionals conducting research in phase transformations will find this book very useful. I highly recommend it.
1. Crystallography of Phase transformations
2. Stability of Homogeneous Solid Solutions
3. Ordering in Alloys
4. Decomposition in Alloys
5. Diffusion Kinetics in Solid Solutions
6. Diffusionless Transformation in Solids
7. Elastic Strain Caused by Crystal Lattice Rearrangement
8. Morphology of a Single Coherent Inclusion
9. Habit Plane and Orientation Relations in Precipitates
10. Strain-Induced Coarsening
11. Morphology of coherent cubic and tetragonal phases
12. Simulation of crystal phase transformations
13. Microscopic theory of homogeneous solid solutions
14. Microscopic elasticity theory as applied to phase transformations
This is a mathematically-sophisticated treatment of phase transformations which employs a wide range of theoretical tools, ranging from elasticity theory to Fourier transforms. The author also makes good use of experimental results in order to provide a proper context for the many aspects of theory of phase transformations. He makes particular good use of the wealth of information gleaned from transmission electron microscopy (TEM). Many electron micrographs are provided, including those by such luminaries as Illinois’ C. M. “Marv” Wayman (p.321), Berkeley’s Gareth Thomas (p.356), and J. van Landuyt (p.404).
I had first learned of Khchaturyan’s work 40 years ago when I was a study taking a graduate course in metallurgical kinetics. The focus of the course was spinodal decomposition with regard to phase separation (Chapters 2, 4, 5) as well as spinodal ordering (Chapter 3).
I found chapter 7 (pp.198-212) to be particularly valuable. Although many journal articles address the strain induced by phase transformations, such treatments, are generally very difficult to follow. Khachturyan provides a much more complete mathematical treatment of this phenomenon, by including steps in the calculation that other authors leave out completely or merely implicitly imply. I greatly appreciated his explicit implementation of Gauss’ Theorem in applying the boundary condition that the variation in displacement vanishes at the body surface (p.206, Eqs. 7.2.28 & 7.2.29).