This course is a tutorial introduction to phase field modelling. Phase field models are used to model microstructure evolution in a wide variety of systems; for example, they can be used to study microstructural evolution during solidification, solid-solid phase transformations and plastic deformation. In this course, we will primarily concentrate on modelling solid-solid transformations using phase field models. Specifically, we will discuss the materials science, mathematical and computational aspects of phase field modelling. The computations will be carried out using GNU Octave, a freeware for scientific computations.
Week
Topics
1.
Thermodynamics: Some Basics
2.
Diffusion and Spinodal Decomposition: Some Basics
3.
Solving Classical Diffusion Equation and Failure of Classical Diffusion Equation
4.
GNU Octave: Some Preliminaries
5.
Analytical Solution of Diffusion Equation
6.
Numerical Solution to the Diffusion Equation I
7.
Numerical Solution to the Diffusion Equation II and Introduction to Symmetry and Group Theory
Applications II: Precipitate Growth, Grain Growth in Multi-grain Systems and Grain Boundary Grooving
Mathematical methods and materials thermodynamics; structure of materials, phase transformations, diffusion and computer programming are preferred.
Porter and Easterling, Phase transformations in metals and alloys
Kreyzig, Advanced Engineering Mathematics
Quarteroni and Saleri, Scientific computing using Matlab and Octave
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