Phase equilibria in alloys displaying diffusional and displacive characteristics
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I.
INTRODUCTION
P H A S E transformations in alloys are sometimes classified as either diffusional (replacive) or displacive (martensitic). Displacive transitions usually involve a change in crystal symmetry or dimensions of the unit cell and occur without a change in concentration, m The thermodynamic variables usually associated with a displacive transition are temperature, stress, and strain. ~2"31Diffusional phase transformations, which involve concentration changes over long distances, are usually characterized by such thermodynamic variables as temperature and concentration (chemical potential). However, diffusional phase transformations in the solid state almost always lead to changes in the dimensions of the unit cell (lattice parameter or angles between planes) and sometimes to changes in crystal symmetry. Thus, deformation, or stress and strain, must also be a relevant thermodynamic variable for solid-state diffusional phase transformations as well as for displacive transitions. Since diffusional transformations give rise to stresses and strains, even when the system is free from external load, it can be expected that "purely diffusional" phase transformations will display some microstructural characteristics similar to those of displacive transitions (e.g., see References 4 and 5 and references quoted therein). However, which similarities result from kinetic aspects of the phase transformation and which are equilibrium features is not at all clear owing to the complexity of the phase transformation process. Up to now, most analyses considering the coupling between displacive and diffusive phase transformations have focused on the kinetic aspects of the problem, t4-Tj The intent of this article is to examine some equilibrium characteristics of alloy systems that can undergo both diffusional and displacive phase transitions. O f particular interest is how these equilibrium characteristics
In honor of Professor Hubert I. Aaronson on the occasion of his 65th birthday. W I L L I A M C. J O H N S O N , Professor, is with the Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, Pittsburgh, PA 15213-3890. Manuscript submitted February 6, 1991. METALLURGICAL TRANSACTIONS A
can be displayed in a series of phase diagrams or free energy diagrams. The difficulties and complexities of the kinetics of coupled diffusional and displacive phase transformations, including the mechanism of the transformation, ~4-7] premartensitic effects, ]8,91 and plastic deformation, ~~ are not considered. However, it is hoped that an understanding of thermodynamic equilibria in these systems will assist in the future development of kinetic theories. In Section II, the thermodynamic basis of the model system is presented. The resulting equilibrium conditions are applied in Sections III and IV to two types of displacive transformations that can be characterized by a Landau-type expansion of the free energy in terms of the deformation. Some resulting phase diagrams and corresponding free energy curv
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