Modeling Solid-State Phase Transformations and Microstructure Evolution
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Modeling Solid-
State Phase Transformations and Microstructure Evolution
L.Q. Chen, C. Wolverton, V.Vaithyanathan, and Z.K. Liu Introduction The last decade or so has seen exciting developments in the field of modeling solidstate phase equilibria and phase transformations. In this article, we highlight three areas where such significant advancements have taken place, and demonstrate that linking these three approaches may yield an even more powerful tool for modeling solid-state phase transformations and microstructure evolution during the processing of multicomponent commercial materials: (1) first-principles atomistic calculations, (2) phase-field modeling of the temporal microstructure evolution, and (3) computational thermodynamics. First-principles atomistic calculations, based on density-functional theory, do not rely on empirical input and hence are predictive in nature. These methods yield quantities related to the electronic structure and total energy of a given system, and may be used to accurately predict zerotemperature phase stabilities of alloys and compounds. By combining first-principles techniques with statistical mechanics methods (e.g., as discussed in the next section), one opens the possibility of exploring, without any fitting parameters, thermodynamics phenomena such as phasetransformation temperatures and phase diagrams,1,2 short-range order,3,4 and antiphase and interphase boundary energetics.5 Furthermore, these approaches are amenable to any phases of a given alloy system, not only the equilibrium phases.
MRS BULLETIN/MARCH 2001
Hence, first-principles techniques can provide a method to obtain properties of metastable phases, which are often crucial to mechanical properties (e.g., strengthening precipitates) but can be difficult to isolate and study experimentally. Phase-field modeling, based on fundamental principles of thermodynamics and kinetics, has recently been established as a powerful method for predicting the temporal microstructure evolution during solid-state phase transformations6,7 (for applications of phase-field modeling to solidification microstructures, see the recent review by Boettinger et al.8). In a phase-field model, the nature of a phase transformation as well as the microstructures that are produced is described by a set of continuous order-parameter fields. The temporal microstructure evolution is obtained by solving field kinetics equations that govern the time-dependence of the spatially inhomogeneous orderparameter fields. This model does not make any a priori assumptions about the transient morphologies and microstructures that may appear during a phasetransformation path. The phenomenological nature of the phase-field model allows one to model the microstructure evolution for a wide variety of diffusional and diffusionless phase transformations such as precipitation reactions,9 ferroelectric transformations,10,11 martensitic transformations,12 phase transformations under an applied stress,12–15 and phase transformations in
the presence of structural defe
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