Crystal Symmetry, X-Ray Diffraction and Physical Properties

By Prof. Sandeep Sangal | IIT Kanpur

Learners enrolled: 245 | Exam registration: 3

ABOUT THE COURSE:

A thorough understanding of crystallographic symmetry: 2D/3D point groups and space groups. An understanding of the underlying symmetry as the basis of the 14 Bravais Lattices. Principles of X-Ray diffraction, relation of reflection conditions with crystal symmetry. Tensors and their uses in symmetry operations and representation of the physical properties of crystals. Applications to pyroelectricity, dielectric susceptibility, piezoelectricity, elasticity and other symmetry dependent properties, such as, optical properties, conductivity, ferroelectricity.

INTENDED AUDIENCE: Undergraduate and Postgraduate students of Metallurgy, Materials Science, Mechanical Engineering, Chemical Engineering, Chemistry, Physics

INDUSTRY SUPPORT: R&D divisions of materials development in industry, e.g., Tata Steel

Summary

Course Status :	Upcoming
Course Type :	Elective
Language for course content :	English
Duration :	12 weeks
Category :	Metallurgy and Material science & Mining Engineering Materials Characterization
Credit Points :	3
Level :	Undergraduate/Postgraduate
Start Date :	20 Jan 2025
End Date :	11 Apr 2025
Enrollment Ends :	27 Jan 2025
Exam Registration Ends :	14 Feb 2025
Exam Date :	04 May 2025 IST

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: Introduction to Crystallography: common misconceptions, lattice, motif and crystals; translation vectors; unit cells; Miller indices of planes and directions; interplanar spacing, angular relationships between planes and directions

Week 2: Symmetry elements in crystallographic patterns; symmetry restrictions; introduction to mathematical groups, specifically crystallographic point groups

Week 3: Combining 2D point symmetry operations through (i) geometrical and (ii) matrix representation; developing the 10 crystallographic point groups in 2D

Week 4: Classification of 2D lattices based on symmetry; adding translation to 2D point groups; combining rotation, reflection and translation using geometry and matrices

Week 5: Derivation of the 17 plane groups; Decoding the International Tables for Crystallography-I; Combination of rotation axes in 3D

Week 6: Development of 3D point groups; Derivation of the Bravais Lattices; Space Groups, Screw Axis, Glide Planes; Decoding the International Tables for Crystallography-II

Week 7: X-Ray Diffraction: Laue Conditions and Braggs Law; Structure Factor

Week 8: Reciprocal Lattice: use for deriving the equations for interplanar spacing; representation of diffraction conditions in reciprocal lattice space; Decoding the International Tables for Crystallography-III

Week 9: Experimental Techniques of X-Ray Diffraction: applications

Week 10: Physical properties of crystals: representation by tensors; transformation of tensors; extend to other second rank tensor properties:

Week 11: Electrical Conductivity of crystals: second-rank tensor property; extend to other second rank tensor properties, such as,:thermal conductivity, thermal expansion

Week 12: Third rank tensor property: piezoelectricity; Fourth rank tensor property: elastic stiffness and elastic compliance

Books and references

Elementary crystallography: an introduction to the fundamental geometrical features of crystals by M.J. Buerger, Wiley, 1956
Crystals and Crystal Structures by Richard J. D. Tilley, John Wiley and Sons, 2006 Elements of X-Ray Diffraction by B.D. Cullity S.R. Stoc, Third Edition, Pearson Education Limited 2014
Tensor Properties of Solids: Phenomenological Development of the Tensor Properties of Crystals by Richard F. Tinder, Morgan & Claypool Publishers, 2008
International Tables of Crystallography A, International Union of Crystallography
J. F. Nye, Physical Properties of Crystals (1995), Oxford Science Publications

Instructor bio

Prof. Sandeep Sangal

IIT Kanpur

Professor Sandeep Sangal did his B.Tech. from the then Department of Metallurgical Engineering at IIT Kanpur in 1982, followed by M.S. in 1985 and PhD in 1989 from University of Manitoba, Canada. He joined as Assistant Professor in IIT Kanpur in 1990. He has experience of over three decades of teaching metallurgy and materials science undergraduate and postgraduate courses. In 2016 he was chosen for the Distinguished Educator Award by the Indian Institute of Metals.

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:May 4, 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 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