Master Crystal Symmetry & X-Ray Diffraction | IIT Kanpur Course Guide
Course Details
| Exam Registration | 88 |
|---|---|
| Course Status | Ongoing |
| Course Type | Elective |
| Language | English |
| Duration | 12 weeks |
| Categories | Metallurgy and Material science & Mining Engineering, Materials Characterization |
| Credit Points | 3 |
| Level | Undergraduate/Postgraduate |
| Start Date | 19 Jan 2026 |
| End Date | 10 Apr 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 20 Feb 2026 |
| Exam Date | 19 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Crystal Symmetry, X-Ray Diffraction and Physical Properties: A 12-Week Masterclass
Welcome to a deep dive into the fundamental principles that govern the structure and behavior of materials. This detailed guide outlines the comprehensive 12-week course, "Crystal Symmetry, X-Ray Diffraction and Physical Properties," instructed by the esteemed Prof. Sandeep Sangal of IIT Kanpur. Designed for undergraduate and postgraduate students, this course bridges theoretical crystallography with practical applications critical to advanced materials development.
Meet Your Instructor: Prof. Sandeep Sangal
Prof. Sandeep Sangal brings over three decades of dedicated teaching and research experience in metallurgy and materials science. An alumnus of IIT Kanpur (B.Tech, 1982) and the University of Manitoba, Canada (M.S., 1985; PhD, 1989), he joined IIT Kanpur as an Assistant Professor in 1990. His exceptional contributions to education were recognized with the Distinguished Educator Award by the Indian Institute of Metals in 2016. His expertise ensures that the course content is both profound and pedagogically excellent.
About the Course
This course offers a rigorous exploration of the symmetry principles that underpin the crystalline state of matter and the techniques used to probe them. You will develop a thorough understanding of crystallographic symmetry, including 2D/3D point groups and space groups, and see how this symmetry dictates the 14 Bravais Lattices. The curriculum seamlessly connects these concepts to the principles of X-Ray Diffraction, explaining how reflection conditions are related to crystal symmetry.
A significant portion of the course is dedicated to the application of tensor mathematics to describe the physical properties of crystals. You will learn how symmetry governs properties like pyroelectricity, dielectric susceptibility, piezoelectricity, elasticity, optical behavior, and electrical conductivity.
Who Should Enroll?
INTENDED AUDIENCE:
- Undergraduate and Postgraduate students of Metallurgy, Materials Science, Mechanical Engineering, Chemical Engineering, Chemistry, and Physics.
INDUSTRY SUPPORT:
- This course is highly relevant for R&D divisions in industries focused on materials development, such as Tata Steel and other advanced manufacturing sectors.
Detailed 12-Week Course Layout
Weeks 1-3: Foundations of Crystallography & Symmetry
- Week 1: Introduction to Crystallography: Lattice, motif, unit cells, Miller indices, interplanar spacing.
- Week 2: Symmetry elements, restrictions, and an introduction to crystallographic point groups.
- Week 3: Combining 2D point symmetry operations geometrically and via matrices, deriving the 10 crystallographic point groups in 2D.
Weeks 4-6: From 2D Patterns to 3D Space Groups
- Week 4: Classifying 2D lattices by symmetry; adding translation to point groups.
- Week 5: Derivation of the 17 plane groups; using the International Tables for Crystallography.
- Week 6: Developing 3D point groups, deriving the Bravais Lattices, and understanding Space Groups with Screw Axes and Glide Planes.
Weeks 7-9: Principles and Practice of X-Ray Diffraction
- Week 7: X-Ray Diffraction fundamentals: Laue Conditions, Bragg's Law, and Structure Factor.
- Week 8: The power of the Reciprocal Lattice for understanding diffraction conditions.
- Week 9: Experimental X-Ray Diffraction techniques and their applications.
Weeks 10-12: Tensor Properties of Crystals
- Week 10: Representing physical properties with tensors and their transformations.
- Week 11: Second-rank tensor properties: Electrical Conductivity, Thermal Conductivity, Thermal Expansion.
- Week 12: Higher-order tensor properties: Piezoelectricity (3rd rank) and Elasticity (4th rank).
Recommended Textbooks & Resources
| Book Title | Author(s) | Publisher |
|---|---|---|
| Elementary Crystallography | M.J. Buerger | Wiley |
| Crystals and Crystal Structures | Richard J. D. Tilley | John Wiley and Sons |
| Elements of X-Ray Diffraction | B.D. Cullity & S.R. Stock | Pearson Education |
| Tensor Properties of Solids | Richard F. Tinder | Morgan & Claypool |
| International Tables for Crystallography A | International Union of Crystallography | IUCr |
| Physical Properties of Crystals | J. F. Nye | Oxford Science Publications |
Why This Course is Essential
Understanding the intrinsic link between a crystal's symmetry, its diffraction pattern, and its macroscopic properties is not just academic—it's the cornerstone of modern materials design. Whether you aim to develop stronger alloys, more efficient semiconductors, or novel piezoelectric devices, the concepts covered in this course provide the essential toolkit. Under the guidance of Prof. Sangal, you will gain the clarity and depth needed to excel in both academic research and industrial R&D.
Duration: 12 Weeks | Level: Undergraduate/Postgraduate | Categories: Metallurgy, Material Science, Mining Engineering, Materials Characterization
Enroll Now →