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Course Co-ordinated by IIT Bombay
Coordinators
 
Dr. M.P. Gururajan
IIT Bombay

 

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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

8.

Symmetry, Group Theory and Variational Calculus

9.

Cahn-Hilliard Equation

10.

Interfacial Energy and Allen-Cahn Equation

11.

Applications I: Spinodal Decomposition, Order-disorder Transformation, Gibbs-Thomson, Grain and Precipitate Growth

12.

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.


  1. Porter and Easterling, Phase transformations in metals and alloys
  2. Kreyzig, Advanced Engineering Mathematics
  3. Quarteroni and Saleri, Scientific computing using Matlab and Octave


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