Phase-field modelling of microstructural evolution and properties

As one of the most powerful techniques in computational materials science, the diffuse-interface phase-field model has been widely employed for simulating various meso-scale microstructural evolution processes. The main purpose of this thesis is to develop a quantitative phase-field model for predicting microstructures and properties in real alloy systems which can be linked to existing thermodynamic/kinetic databases and parameters obtained from experimental measurements or first-principle calculations. To achieve this goal; many factors involved in complicated real systems are investigated, many of which are often simplified or ignored in existing models, e.g. the dependence of diffusional atomic mobility and elastic constants on composition.; Efficient numerical techniques must be developed to solve those partial differential equations that are involved in modelling microstructural evolutions and properties. In this thesis, different spectral methods were proposed for the time-dependent phase-field kinetic equations and diffusion equations. For solving the elastic equilibrium equation with the consideration of elastic inhomogeneity, a conjugate gradient method was utilized. The numerical approaches developed were generally found to be more accurate and efficient than conventional approach such as finite difference method.; A composition-dependent Cahn-Hilliard equation was solved by using a semi-implicit Fourier-spectral method. It was shown that the morphological evolutions in bulk-diffusion-controlled coarsening and interface-diffusion-controlled developed similar patterns and scaling behaviors. For bulk-diffusion-controlled coarsening, a cubic growth law was obeyed in the scaling regime, whereas a fourth power growth law was observed for interface-diffusion-controlled coarsening.; The characteristics of a microstructure under the influence of elastic energy depend on elastic properties such as elastic anisotropy, lattice mismatch, elastic inhomogeneity and externally applied strain. Specifically the effects of elastic inhomogeneity on the coarsening of a two-phase microstructure were investigated. It was generally found that the hard phase tends to form precipitates surrounded by the soft matrix phase to reduce the elastic energy, in agreement with prior studies using first-order approximations. Increasing the elastic inhomogeneity will reduce the growth exponent.; A three-dimensional phase-field model was developed which can be linked with the CALPHAD method through the local free energy construction as a function of field variables. The model takes most important thermodynamic and kinetic parameters, such as lattice parameters, interfacial energy and elastic constants, from either a database or independent experimental measurements. The Ni ₃Al precipitate shape evolution in a binary Ni-Al system was studied as an example. Depending on the balance between interfacial energy and elastic energy relaxation, the simulated microstructures developed different shapes at different sizes.; The diffuse-interface model can also be employed for modelling temporal mass diffusion transport through an arbitrary microstructure as well as the corresponding effective properties. From the comparison results in a wide variety of examples including the three kinetic regimes of grain boundary diffusion, the effective property prediction obtained by the diffuse-interface model was in good agreement with that obtained by using a conventional sharp-interface model.