# Phase Field Modelling: The Materials Science, Mathematics and Computational Aspects

- Institution: IIT Bombay
- Department: Metallurgy and Material Science
- Teacher: Prof. M.P. Gururajan
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/113101072)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/113101072)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

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

1. [Module 1 - Lecture 1 : Solution models](https://invisiblenetwork.ai/learn/nptel/113101072/acdd1b278068) (YouTube)
2. [Module 1 - Lecture 2 : Summary of solution models](https://invisiblenetwork.ai/learn/nptel/113101072/cb2390e56c5e) (YouTube)
3. [Module 1 - Lecture 3 : G vs X diagrams](https://invisiblenetwork.ai/learn/nptel/113101072/303f46e16b3d) (YouTube)
4. [Module 1 - Lecture 4 : Phase diagrams](https://invisiblenetwork.ai/learn/nptel/113101072/2ba9351f3d99) (YouTube)
5. [Module 1 - Lecture 5 : Bond breaking model](https://invisiblenetwork.ai/learn/nptel/113101072/9c42c1f7d1b1) (YouTube)
6. [Module 2 - Lecture 6 : Chemical potential](https://invisiblenetwork.ai/learn/nptel/113101072/41dc77c75845) (YouTube)
7. [Module 1 - Tutorial 1](https://invisiblenetwork.ai/learn/nptel/113101072/85fc1ef90c78) (YouTube)
8. [Module 1 - Tutorial 2](https://invisiblenetwork.ai/learn/nptel/113101072/8acd0904bf90) (YouTube)
9. [Module 1 - Tutorial 3](https://invisiblenetwork.ai/learn/nptel/113101072/f54faa119a27) (YouTube)
10. [Module 1 - Tutorial 4](https://invisiblenetwork.ai/learn/nptel/113101072/6fb9d4df40fa) (YouTube)
11. [Module 1 - Tutorial 5](https://invisiblenetwork.ai/learn/nptel/113101072/e082a210ece6) (YouTube)
12. [Module 2 - Tutorial 6](https://invisiblenetwork.ai/learn/nptel/113101072/7c3074ca149e) (YouTube)
13. [Module 2 - Lecture 7 : Diffusion and chemical potential](https://invisiblenetwork.ai/learn/nptel/113101072/dd384b62700b) (YouTube)
14. [Module 2 - Lecture 8 : Fick's law](https://invisiblenetwork.ai/learn/nptel/113101072/5dbecadd39fe) (YouTube)
15. [Module 2 - Lecture 9 : Failure of classical diffusion equation](https://invisiblenetwork.ai/learn/nptel/113101072/d71f0fa2861d) (YouTube)
16. [Module 2 - Lecture 10 : Some references](https://invisiblenetwork.ai/learn/nptel/113101072/3300586cd4d3) (YouTube)
17. [Module 3 - Lecture 11 : Spinodal decomposition - some history](https://invisiblenetwork.ai/learn/nptel/113101072/502e67dbfed4) (YouTube)
18. [Module 3 - Lecture 12 : Spinodal decomposition](https://invisiblenetwork.ai/learn/nptel/113101072/4c82dfaf99e1) (YouTube)
19. [Module 3 - Lecture 13 : Stability](https://invisiblenetwork.ai/learn/nptel/113101072/8a57c2813fb4) (YouTube)
20. [Module 3 - Lecture 14 : Thermodynamic property : composition dependence](https://invisiblenetwork.ai/learn/nptel/113101072/363da419fc58) (YouTube)
21. [Module 3 - Lecture 15 : Regions of stability](https://invisiblenetwork.ai/learn/nptel/113101072/0acf24fa70ea) (YouTube)
22. [Module 3 - Lecture 16 : Understanding spinodal region](https://invisiblenetwork.ai/learn/nptel/113101072/d31ad6fda082) (YouTube)
23. [Module 2 - Tutorial 7](https://invisiblenetwork.ai/learn/nptel/113101072/43b9a32bf195) (YouTube)
24. [Module 4 - Lecture 17 : Solution to classical diffusion equation](https://invisiblenetwork.ai/learn/nptel/113101072/83c398a3628e) (YouTube)
25. [Module 4 - Lecture 18 : Diffusion and mobility I](https://invisiblenetwork.ai/learn/nptel/113101072/03d3892dae12) (YouTube)
26. [Module 4 - Lecture 19 : Diffusion and mobility II](https://invisiblenetwork.ai/learn/nptel/113101072/e860c3464d87) (YouTube)
27. [Module 4 - Lecture 20 : Failure of classical diffusion equation](https://invisiblenetwork.ai/learn/nptel/113101072/28be26a20116) (YouTube)
28. [Module 4 - Lecture 21 : Non-classical diffusion equation](https://invisiblenetwork.ai/learn/nptel/113101072/763f9f37e3ef) (YouTube)
29. [Module 5 - Lecture 22 : GNU Octave : Introduction](https://invisiblenetwork.ai/learn/nptel/113101072/8984d9ed2e1d) (YouTube)
30. [Module 5 - Lecture 23 : GNU Octave : interactive mode](https://invisiblenetwork.ai/learn/nptel/113101072/2f1ac207e71c) (YouTube)
31. [Module 5 - Lecture 24 : GNU Octave : script mode](https://invisiblenetwork.ai/learn/nptel/113101072/100355dc595d) (YouTube)
32. [Module 6 - Lecture 25 : Ideal solution using octave](https://invisiblenetwork.ai/learn/nptel/113101072/e302c9d7884d) (YouTube)
33. [Module 6 - Lecture 26 : Regular solution using octave](https://invisiblenetwork.ai/learn/nptel/113101072/3bfa15ab9575) (YouTube)
34. [Module 6 - Lecture 27 : Constructing phase diagram](https://invisiblenetwork.ai/learn/nptel/113101072/1415c64a4281) (YouTube)
35. [Module 6 - Lecture 28 : Plotting spinodal](https://invisiblenetwork.ai/learn/nptel/113101072/0401af4f60b6) (YouTube)
36. [Module 7 - Lecture 29 : Non-dimensionalisation of diffusion equation](https://invisiblenetwork.ai/learn/nptel/113101072/01f983ab854f) (YouTube)
37. [Module 7 - Lecture 30 : Diffusion and Fourier law of heat conduction](https://invisiblenetwork.ai/learn/nptel/113101072/6ebcb7a7568a) (YouTube)
38. [Module 8 - Lecture 31 : Diffusion equation : Analytical solution I](https://invisiblenetwork.ai/learn/nptel/113101072/d57e1055bc28) (YouTube)
39. [Module 8 - Lecture 32 : Diffusion equation : Analytical solution II](https://invisiblenetwork.ai/learn/nptel/113101072/23c9f7f91970) (YouTube)
40. [Module 8 - Lecture 33 : Diffusion equation : Error function solution I](https://invisiblenetwork.ai/learn/nptel/113101072/5fc243797375) (YouTube)
41. [Module 8 - Lecture 34 : Diffusion equation: Error function solution II](https://invisiblenetwork.ai/learn/nptel/113101072/3f8499d3b453) (YouTube)
42. [Module 9 - Lecture 35 : Diffusion equation : finite difference method](https://invisiblenetwork.ai/learn/nptel/113101072/00b630c46c55) (YouTube)
43. [Module 9 - Lecture 36 : Diffusion equation : zero flux BC and explicit method](https://invisiblenetwork.ai/learn/nptel/113101072/51a2fe304afe) (YouTube)
44. [Module 9 - Lecture 37 : Diffusion equation : zero flux BC and implicit method](https://invisiblenetwork.ai/learn/nptel/113101072/52f77b15387d) (YouTube)
45. [Module 9 - Lecture 38 : Diffusion equation : imposed concentration BC and explicit/implicit methods](https://invisiblenetwork.ai/learn/nptel/113101072/a44bf1aa4715) (YouTube)
46. [Module 10 - Lecture 39 : Periodic boundary conditions (PBC)](https://invisiblenetwork.ai/learn/nptel/113101072/134b5066f860) (YouTube)
47. [Module 10 - Lecture 40 : Expicit method with PBC](https://invisiblenetwork.ai/learn/nptel/113101072/5395b83746ec) (YouTube)
48. [Module 10 - Lecture 41 : Spectral techniques I](https://invisiblenetwork.ai/learn/nptel/113101072/076777aa27ee) (YouTube)
49. [Module 10 - Lecture 42 : Spectral techniques II](https://invisiblenetwork.ai/learn/nptel/113101072/b18751307c56) (YouTube)
50. [Module 10 - Lecture 43 : Implicit spectral method](https://invisiblenetwork.ai/learn/nptel/113101072/5875ec936590) (YouTube)
51. [Module 11 - Lecture 44 : Scalars, vectors and tensors](https://invisiblenetwork.ai/learn/nptel/113101072/4fb272d388e0) (YouTube)
52. [Module 11 - Lecture 45 : Coordinate transformation](https://invisiblenetwork.ai/learn/nptel/113101072/3e0ea076b7f8) (YouTube)
53. [Module 11 - Lecture 46 : Transformation laws](https://invisiblenetwork.ai/learn/nptel/113101072/f88559f919a9) (YouTube)
54. [Module 11 - Lecture 47 : II rank tensors and Neumann principle](https://invisiblenetwork.ai/learn/nptel/113101072/c641e34a8435) (YouTube)
55. [Module 12 - Lecture 48 : Group theory](https://invisiblenetwork.ai/learn/nptel/113101072/4d4e1f14fa76) (YouTube)
56. [Module 12 - Lecture 49 : Crystal: symmetry elements I](https://invisiblenetwork.ai/learn/nptel/113101072/46ab0dbe9b1d) (YouTube)
57. [Module 12 - Lecture 50 : Crystal: symmetry elements II](https://invisiblenetwork.ai/learn/nptel/113101072/b5ecd91f1f81) (YouTube)
58. [Module 12 - Lecture 51 : Understanding Neumann's principle](https://invisiblenetwork.ai/learn/nptel/113101072/8b999bf117e9) (YouTube)
59. [Module 12 - Lecture 52 : Representation quadric](https://invisiblenetwork.ai/learn/nptel/113101072/cd2a7bb895e2) (YouTube)
60. [Module 13 - Lecture 53 : Variational calculus](https://invisiblenetwork.ai/learn/nptel/113101072/fd9424be06ae) (YouTube)
61. [Module 13 - Lecture 54 : Optimization of functionals I](https://invisiblenetwork.ai/learn/nptel/113101072/a400de68cd2b) (YouTube)
62. [Module 13 - Lecture 55 : Optimization of functional II](https://invisiblenetwork.ai/learn/nptel/113101072/52a478424558) (YouTube)
63. [Module 13 - Lecture 56 : Variational derivative](https://invisiblenetwork.ai/learn/nptel/113101072/2ce04fbd0125) (YouTube)
64. [Module 13 - Lecture 57 : Free energy functional](https://invisiblenetwork.ai/learn/nptel/113101072/ab527eb9b731) (YouTube)
65. [Module 14 - Lecture 58 : Derivation of Cahn-Hilliard (CH) equation I](https://invisiblenetwork.ai/learn/nptel/113101072/0b23a368c687) (YouTube)
66. [Module 14 - Lecture 59 : Derivation of Cahn-Hilliard (CH) equation II](https://invisiblenetwork.ai/learn/nptel/113101072/cce638e29087) (YouTube)
67. [Module 14 - Lecture 60 : Free energy versus concentration curves](https://invisiblenetwork.ai/learn/nptel/113101072/638b181f6351) (YouTube)
68. [Module 14 - Lecture 61 : Diffusion equation versus CH](https://invisiblenetwork.ai/learn/nptel/113101072/f623e556dd89) (YouTube)
69. [Module 15 - Lecture 62 : Numerical solution of CH: finite difference](https://invisiblenetwork.ai/learn/nptel/113101072/8c945cf14b37) (YouTube)
70. [Module 15 - Lecture 63 : Numerical solution of CH: spectral method](https://invisiblenetwork.ai/learn/nptel/113101072/335176188aa4) (YouTube)
71. [Module 16 - Lecture 64 : Interfacial energy in CH](https://invisiblenetwork.ai/learn/nptel/113101072/41642fbfcbf0) (YouTube)
72. [Module 16 - Lecture 65 : CH: analytical solution](https://invisiblenetwork.ai/learn/nptel/113101072/b09e43ed397e) (YouTube)
73. [Module 16 - Lecture 66 : Interfacial energy in CH: analytical calculation](https://invisiblenetwork.ai/learn/nptel/113101072/ce8ced315d6c) (YouTube)
74. [Module 16 - Lecture 67 : Interfacial energy: numerical versus analytical values](https://invisiblenetwork.ai/learn/nptel/113101072/b189a4a78ea8) (YouTube)
75. [Module 17 - Lecture 68 : Order-disorder transition and Allen-Cahn equation](https://invisiblenetwork.ai/learn/nptel/113101072/28ddc677c3c4) (YouTube)
76. [Module 17 - Lecture 69 : AC: numerical solution](https://invisiblenetwork.ai/learn/nptel/113101072/a98b5dea002a) (YouTube)
77. [Module 18 - Lecture 70 : Spinodal decomposition in 2D](https://invisiblenetwork.ai/learn/nptel/113101072/1183c55a2a1d) (YouTube)
78. [Module 18 - Lecture 71 : Order-disorder transformation](https://invisiblenetwork.ai/learn/nptel/113101072/bfbafe8dfe54) (YouTube)
79. [Module 18 - Lecture 72 : Gibbs Thomson effect](https://invisiblenetwork.ai/learn/nptel/113101072/d85657c03fec) (YouTube)
80. [Module 18 - Lecture 73 : Grain growth](https://invisiblenetwork.ai/learn/nptel/113101072/afa5f017fd5f) (YouTube)
81. [Module 19 - Lecture 74 : Precipitate growth I](https://invisiblenetwork.ai/learn/nptel/113101072/f2f684f27ee9) (YouTube)
82. [Module 19 - Lecture 75 : Precipitate growth II](https://invisiblenetwork.ai/learn/nptel/113101072/63a8858f0537) (YouTube)
83. [Module 20 - Lecture 76 : Grain growth: Fan-Chen model I](https://invisiblenetwork.ai/learn/nptel/113101072/f45f1ff80a7c) (YouTube)
84. [Module 20 - Lecture 77 : Grain growth: Fan-Chen model II](https://invisiblenetwork.ai/learn/nptel/113101072/d4a384c3b04c) (YouTube)
85. [Module 21 - Lecture 78 : Grain boundary grooving I](https://invisiblenetwork.ai/learn/nptel/113101072/1addf570e43a) (YouTube)
86. [Module 21 - Lecture 79 : Grain boundary grooving II](https://invisiblenetwork.ai/learn/nptel/113101072/7ee09d99eba4) (YouTube)
87. [Module 22 - Lecture 80 : Overview of phase field modelling](https://invisiblenetwork.ai/learn/nptel/113101072/d491b2c53f59) (YouTube)