Spontaneous evolution of microstructure in materials
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Spontaneous Evolution of Microstructure in Materials
J.S. KIRKALDY R.F. Mehl Medalist
Microstructures which evolve spontaneously from random solutions in near isolation often exhibit patterns of remarkable symmetry which can only in part be explained by boundary and crystallographic effects. With reference to the detailed experimental record, we seek the source of causality in this natural tendency to constructive autonomy, usually designated as a principle of pattern or wavenumber selection in a flee boundary problem. The phasefield approach which incorporates detailed boundary structure and global rate equations has enjoyed some currency in removing internal degrees of freedom, and this will be examined critically in reference to the migration of phase-antiphase boundaries produced in an order-disorder transformation. Analogous problems for singular interfaces including solute trapping are explored. The microscopic solvability hypothesis has received much attention, particularly in relation to dendrite morphology and the Saffman-Taylor fingering problem in hydrodynamics. A weak form of this will be illustrated in relation to local equilibrium binary solidification cells which renders the free boundary problem unique. However, the main thrust of this article concerns dynamic configurations at anisotropic singular interfaces and the related patterns of eutectoid(ic)s, nonequilibrium cells, cellular dendrites, and Liesegang figures where there is a recognizable macroscopic phase space of pattern fluctuations and/or solitons. These possess a weakly defective stability point and thereby submit to a statistical principle of maximum path probability and to a variety of corollary dissipation principles in the determination of a unique average patterning behavior. A theoretical development of the principle based on Hamilton's principle for frictional systems is presented in an Appendix. Elements of the principles of scaling, universality, and deterministic chaos are illustrated. J.S. KIRKALDY, Professor, is with the Institute for Materials Research, McMaster University, Hamilton, ON, Canada L8S 4M1. John S. Kirkaldy is Professor Emeritus of Materials Science and Engineering and Engineering Physics at McMaster University. He received his Ph.D. in nuclear physics at McGill in 1953 and joined the Metallurgy Department in 1954. He moved to McMaster in 1957 to help establish Metallurgy in that University. He has held the Stelco Professorship and chaired both the Departments of Metallurgy and Materials Science and Engineering Physics. Dr. K i r k a l d y ' s p r i m a r y r e s e a r c h i n t e r e s t s have b e e n in multicomponent diffusion, phase transformations in steel, and pattern formation. He has published 180 papers and is co-author or co-editor of eight volumes. His recent Institute of Metals monograph "Diffusion in the Condensed State" with J.D. Young is the definitive treatment of multicomponent diffusion in materials. His commercial software package, "Computerized Alloy Steels Information System METALLURGICAL
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