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

By Prof. M P Gururajan | IIT Bombay

Learners enrolled: 171 | Exam registration: 7

ABOUT THE COURSE:
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.

INDUSTRY SUPPORT: GE, Tata Steel, TRDDC, National labs (BARC, DMRL, ...)

Summary

Course Status :	Upcoming
Course Type :	Elective
Language for course content :	English
Duration :	12 weeks
Category :	Metallurgy and Material science & Mining Engineering
Credit Points :	3
Level :	Undergraduate/Postgraduate
Start Date :	21 Jul 2025
End Date :	10 Oct 2025
Enrollment Ends :	04 Aug 2025
Exam Registration Ends :	15 Aug 2025
Exam Date :	25 Oct 2025 IST
NCrF Level	4.5 — 8.0

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Thermodynamics: Some Basics

Week 2: Diffusion and Spinodal Decomposition: Some Basics

Week 3: Solving Classical Diffusion Equation and Failure of Classical Diffusion Equation

Week 4: GNU Octave: Some Preliminaries

Week 5: Analytical Solution of Diffusion Equation

Week 6: Numerical Solution to the Diffusion Equation I

Week 7: Numerical Solution to the Diffusion Equation II and Introduction to Symmetry and Group Theory

Week 8: Symmetry, Group Theory and Variational Calculus

Week 9: Cahn-Hilliard Equation

Week 10: Interfacial Energy and Allen-Cahn Equation

Week 11: Applications I: Spinodal Decomposition, Order-disorder Transformation, Gibbs-Thomson, Grain and Precipitate Growth

Week 12: Applications II: Precipitate Growth, Grain Growth in Multi-grain Systems and Grain Boundary Grooving

Books and references

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

Instructor bio

Prof. M P Gururajan

IIT Bombay

Prof. M P Gururajan research interests are in modelling microstructural evolution. My teaching interests, among other things, include physical metallurgy, phase transformations, computational methods, simulation and optimization, modelling, mathematical methods and data analysis and interpretation. I am also interested in using mathematical and computational techniques to solve materials problems of academic interest and industrial importance as well as introducing open source software to materials scientists / metallurgists.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams: October 25, 2025 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Bombay .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team