Diffusion in Multicomponent Solids

By Prof. Kaustubh Kulkarni   |   IIT Kanpur
Learners enrolled: 90
Diffusion is the fundamental process controlling most of the phase transformations and hence, is of great interest through both theoretical and application perspectives. Knowledge of diffusion behavior of materials is essential for control as well as design of new processes. Moreover, most of the industrially important systems are based on three or more components and thus, the understanding of diffusion in multicomponent systems is particularly of greater interest. This course will treat both the phenomenology and atomic theory of diffusion in multicomponent systems. In most of the first half, the course will cover the phenomenological aspect of diffusion, which is more important practically as it deals with usage of phenomenological diffusion coefficients for modeling various diffusion-driven processes as well as actual determination of these coefficients. Major part of the later half will focus on understanding the theoretical aspect of diffusion including atomic mechanisms of diffusion, fundamental driving forces for diffusion and dependence of phenomenological diffusion coefficients on atomic jump frequencies and thermodynamic factors. All the concepts and treatments will be explained in the context of both binary and multicomponent effects in diffusion. At the end of the course, the student should be able to describe diffusion in dilute as well as concentrated multicomponent alloys in terms of multicomponent diffusion coefficients, solve the diffusion equation for various processes, identify the various types of diffusion coefficients and select the appropriate type for a given model, understand the physical significance of these coefficients, evaluate these coefficients theoretically for some model systems and know the various methodologies of their experimental determination.

INTENDED AUDIENCE  : Metallurgical Engineering, Materials Science, Mechanical Engineering, Chemical Engineering
PRE REQUISITE : Preliminary knowledge of materials thermodynamics and structure of materials is desirable
INDUSTRY SUPPORT  : The industry working on design and development of alloys and processes may benefit from this course e.g. to name a few are General Electrics, General Motors, Tata Steel, Boing etc.
Course Status : Completed
Course Type : Elective
Duration : 12 weeks
Category :
  • Metallurgy and Material science & Mining Engineering
Credit Points : 3
Level : Undergraduate/Postgraduate
Start Date : 24 Jan 2022
End Date : 15 Apr 2022
Enrollment Ends : 07 Feb 2022
Exam Date : 24 Apr 2022 IST

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

Page Visits

Course layout

Week 1: Basics of thermodynamics: laws of thermodynamics, concept of chemical potentials and criteria for equilibrium
Week 2: Refresher on Solution Thermodynamics and Phase Stability
Week 3:   Phenomenology of multicomponent diffusion and various frames of reference used for measuring diffusion fluxes
Week 4: Solving diffusion equation for various boundary conditions including solution of multicomponent diffusion equation
Week 5: Self diffusion, impurity diffusion, interdiffusion and intrinsic diffusion; Experimental determination of interdiffusion and intrinsic diffusion coefficients
Week 6: Point defects in crystalline solids and mechanisms of diffusion
Week 7: Random walk, diffusivity and correlation effects in diffusion
Week 8: Derivation of correlation factors in some crystalline lattices
Week 9:  Derivation of fundamental driving forces for diffusion: chemical potential gradients and atomic mobilities; cross effects in multicomponent diffusion driven by defect mechanisms
Week 10: Interrelation between multicomponent diffusion coefficients, atomic jump frequencies and thermodynamic factors
Week 11: Multiphase diffusion, diffusion structures and phase diagrams
Week 12: Experimental determination of activation energies for diffusion; Fast diffusion paths: Grain boundary and pipe diffusion

Books and references

1. “Atom Movements: Diffusion and Mass Transport in Solids”, Jean Phillibert, les Editions de Physique 1991.
2. “Diffusion in Solids”; Paul Shewman, Publication of the Minerals, Metals and Materials Society; 1989
3. “Diffusion in Solids”; Helmut Mehrer; Springer; 2007
4. “Diffusion in Solids: Field Theory, Solid-State Principles and Application”; M. E. Glicksman; Johnson Wiley & Sons, INC
5. “Thermodynamics, Diffusion and the Kirkendall Effect in Solids”; Aloke Paul, Tomi Laurila, Vesa Vuorinen, Sergiy Divinski; Springer, 2014
6. “Phase Transformations in Metals and Alloys”; D. A. Porter and K. E. Easterling; CRC Press; 2004
7. “Advanced Engineering Mathematics”; E. Kreyszig; John Wiley and Sons, Inc.; 10th Edition; 2011 (For general mathematics)
8. “Thermodynamics of Materials”; David R. Gaskell; Taylor & Francis Group; 2008.

Instructor bio

Prof. Kaustubh Kulkarni

IIT Kanpur
I finished my PhD from Purdue University on the topic of multicomponent diffusion. Post my PhD, I worked in Industry for four years before joining IIT Kanpur in 2012. My research mainly focusses on understanding of multicomponent effects in diffusion kinetics and applying those for designing advanced materials and processes. The cross effects in diffusion mainly originate from thermodynamic interactions and hence, developing correlations between the multicomponent diffusion effects and thermodynamic properties is an integral part of my research. While working on this, I have developed a passion for teaching both Materials Thermodynamics and Diffusion in Solids. This course is an attempt to take the multicomponent effects in diffusion, which so far have been discussed only within restricted community of researchers working on diffusion, to the broader audience of metallurgical and materials engineering.

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: 24 April 2022 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.


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

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 Kanpur .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

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