Stability of Materials pp 37-52 | Cite as

# Continuum Diffuse-Interface Model for Modeling Microstructural Stability

## Abstract

The majority of advanced materials in practical applications are multiphase and/or polycrystalline, and their physical properties depend not only on the atomic structure and properties of each constituent phase, but also crucially on the nanoscale or microscale microstructure. A microstructure is characterized by (1) the number of phases and their volume fractions, and (2) the size, shape, distribution and orientation of each phase. Generally, a microstructure is thermodynamically unstable, or at most, metastable, and at a given temperature, it will evolve as a function of time towards equilibrium. The driving force for the temporal evolution of a microstructure usually consists of one or more of the following: (1) reduction in the bulk chemical free energy; (2) decrease of the total interfacial energy between different phases or between different orientation domains or grains of the same phase; (3) homogeneous and heterogeneous relaxation of the elastic strain energy generated by the lattice mismatch between different phases or different orientation domains; and (4) external fields such as applied stress, electrical, temperature and magnetic fields. The phase changes and resulted microstructural development driven by the decrease of the bulk chemical free energy is usually referred to as phase transformations whereas the microstructural evolution due to reduction in the total excess free energies associated with interfaces is called coarsening (or grain growth in polycrystalline materials). In coherent systems, however, elastic strain energy may play an important, and very often, a controlling role in the microstructural evolution during both phase transformations and coarsening.

### Keywords

Crystallization Migration Anisotropy Expense## Preview

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### References

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