Course11310107287 lectures
Phase Field Modelling: The Materials Science, Mathematics and Computational Aspects
Prof. M.P. Gururajan · IIT Bombay
About
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.
Intended audience: M Sc (materials science), BE/B.Tech (final year), ME / M.Tech (metallurgy), PhD
Prerequisites: Mathematical methods and materials thermodynamics; structure of materials, phase transformations, diffusion and computer programming are preferred.
Lectures
Week 1
- Module 1 - Lecture 1 : Solution models
- Module 1 - Lecture 2 : Summary of solution models
- Module 1 - Lecture 3 : G vs X diagrams
- Module 1 - Lecture 4 : Phase diagrams
- Module 1 - Lecture 5 : Bond breaking model
- Module 2 - Lecture 6 : Chemical potential
- Module 1 - Tutorial 1
- Module 1 - Tutorial 2
- Module 1 - Tutorial 3
- Module 1 - Tutorial 4
- Module 1 - Tutorial 5
- Module 2 - Tutorial 6
Week 2
- Module 2 - Lecture 7 : Diffusion and chemical potential
- Module 2 - Lecture 8 : Fick's law
- Module 2 - Lecture 9 : Failure of classical diffusion equation
- Module 2 - Lecture 10 : Some references
- Module 3 - Lecture 11 : Spinodal decomposition - some history
- Module 3 - Lecture 12 : Spinodal decomposition
- Module 3 - Lecture 13 : Stability
- Module 3 - Lecture 14 : Thermodynamic property : composition dependence
- Module 3 - Lecture 15 : Regions of stability
- Module 3 - Lecture 16 : Understanding spinodal region
- Module 2 - Tutorial 7
Week 3
- Module 4 - Lecture 17 : Solution to classical diffusion equation
- Module 4 - Lecture 18 : Diffusion and mobility I
- Module 4 - Lecture 19 : Diffusion and mobility II
- Module 4 - Lecture 20 : Failure of classical diffusion equation
- Module 4 - Lecture 21 : Non-classical diffusion equation
- Module 5 - Lecture 22 : GNU Octave : Introduction
- Module 5 - Lecture 23 : GNU Octave : interactive mode
Week 4
- Module 5 - Lecture 24 : GNU Octave : script mode
- Module 6 - Lecture 25 : Ideal solution using octave
- Module 6 - Lecture 26 : Regular solution using octave
- Module 6 - Lecture 27 : Constructing phase diagram
- Module 6 - Lecture 28 : Plotting spinodal
- Module 7 - Lecture 29 : Non-dimensionalisation of diffusion equation
- Module 7 - Lecture 30 : Diffusion and Fourier law of heat conduction
Week 5
- Module 8 - Lecture 31 : Diffusion equation : Analytical solution I
- Module 8 - Lecture 32 : Diffusion equation : Analytical solution II
- Module 8 - Lecture 33 : Diffusion equation : Error function solution I
- Module 8 - Lecture 34 : Diffusion equation: Error function solution II
Week 6
- Module 9 - Lecture 35 : Diffusion equation : finite difference method
- Module 9 - Lecture 36 : Diffusion equation : zero flux BC and explicit method
- Module 9 - Lecture 37 : Diffusion equation : zero flux BC and implicit method
- Module 9 - Lecture 38 : Diffusion equation : imposed concentration BC and explicit/implicit methods
- Module 10 - Lecture 39 : Periodic boundary conditions (PBC)
Week 7
- Module 10 - Lecture 40 : Expicit method with PBC
- Module 10 - Lecture 41 : Spectral techniques I
- Module 10 - Lecture 42 : Spectral techniques II
- Module 10 - Lecture 43 : Implicit spectral method
- Module 11 - Lecture 44 : Scalars, vectors and tensors
- Module 11 - Lecture 45 : Coordinate transformation
- Module 11 - Lecture 46 : Transformation laws
- Module 11 - Lecture 47 : II rank tensors and Neumann principle
- Module 12 - Lecture 48 : Group theory
Week 8
- Module 12 - Lecture 49 : Crystal: symmetry elements I
- Module 12 - Lecture 50 : Crystal: symmetry elements II
- Module 12 - Lecture 51 : Understanding Neumann's principle
- Module 12 - Lecture 52 : Representation quadric
- Module 13 - Lecture 53 : Variational calculus
- Module 13 - Lecture 54 : Optimization of functionals I
- Module 13 - Lecture 55 : Optimization of functional II
- Module 13 - Lecture 56 : Variational derivative
Week 9
- Module 13 - Lecture 57 : Free energy functional
- Module 14 - Lecture 58 : Derivation of Cahn-Hilliard (CH) equation I
- Module 14 - Lecture 59 : Derivation of Cahn-Hilliard (CH) equation II
- Module 14 - Lecture 60 : Free energy versus concentration curves
- Module 14 - Lecture 61 : Diffusion equation versus CH
- Module 15 - Lecture 62 : Numerical solution of CH: finite difference
- Module 15 - Lecture 63 : Numerical solution of CH: spectral method
Week 10
- Module 16 - Lecture 64 : Interfacial energy in CH
- Module 16 - Lecture 65 : CH: analytical solution
- Module 16 - Lecture 66 : Interfacial energy in CH: analytical calculation
- Module 16 - Lecture 67 : Interfacial energy: numerical versus analytical values
- Module 17 - Lecture 68 : Order-disorder transition and Allen-Cahn equation
- Module 17 - Lecture 69 : AC: numerical solution
Week 11
- Module 18 - Lecture 70 : Spinodal decomposition in 2D
- Module 18 - Lecture 71 : Order-disorder transformation
- Module 18 - Lecture 72 : Gibbs Thomson effect
- Module 18 - Lecture 73 : Grain growth
- Module 19 - Lecture 74 : Precipitate growth I
Week 12
- Module 19 - Lecture 75 : Precipitate growth II
- Module 20 - Lecture 76 : Grain growth: Fan-Chen model I
- Module 20 - Lecture 77 : Grain growth: Fan-Chen model II
- Module 21 - Lecture 78 : Grain boundary grooving I
- Module 21 - Lecture 79 : Grain boundary grooving II
- Module 22 - Lecture 80 : Overview of phase field modelling
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Bombay
- Department
- Metallurgy and Material Science
- Teacher
- Prof. M.P. Gururajan
- Level
- Undergraduate
- Language
- English
- Subjects
- Engineering
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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