Course Modules
Lecture 1: Symmetry Operations
Exploring the foundations of bonds, mathematical symmetry, and group theory in materials. Interactive visualizations included.
Lecture 2: Inversion & Roto-Reflection
Delving into improper rotations and exploring the comprehensive symmetry elements of complex molecules like Staggered Ethane.
Lecture 3: From Symmetry Operations to Point Groups
Analyzing the successive applications of roto-reflections in Staggered Ethane and formalizing collections of symmetry operations into Point Groups.
Lecture 4: Complex Point Groups & Thorocene Symmetry
Moving beyond simple rotations and reflections to build multi-element groups like $C_{nh}$, $C_{nv}$, $D_n$, and $D_{nh}$.
Lecture 4: Applications
Discover how abstract algebra (subgroups, transforms, and SALCs) directly engineers ferroelectric memory and chemical bonding.
Lecture 5: Symmetry Classes & Platonic Solids
Exploring symmetry classes, high-symmetry point groups like $T_d$, and the geometry of Platonic solids.
Lecture 6: High Symmetry & Projections
Delving into the symmetry of dual polyhedra, a systematic flowchart for point group identification, and stereographic projections.
Lecture 6: Applications
Explore how stereographic projections, flowcharts, and translations dictate metallurgical textures, pharmacology, and XRD patterns.
Lecture 7: Hermann-Mauguin Notations
Understanding standard crystallographic point group nomenclatures using proper and improper rotations, and directional hierarchies.
Lecture 8: 2D Lattices & Plane Groups
Deriving the fundamental 2D Bravais Lattices and methodically constructing the 17 unique 2D Plane Groups using symmetry elements.
Lecture 9: 3D Crystallography & Bravais Lattices
Discover how systematically extruding the 17 unique 2D plane groups into the third dimension enforces strict geometric constraints, yielding exactly 14 unique 3D lattice types.
"The universe is built on a plan, the profound symmetry of which is somehow present in the inner structure of our intellect."
— Paul Valéry
Why study Structure of Materials?
Understanding the interplay between a material's internal structure and its properties is the cornerstone of Materials Science and Engineering.
The MSE Tetrahedron
The foundation of materials engineering relies on four interconnected pillars. As depicted in the schematic, Structure (at all length scales) dictates a material's Properties.
These structures are achieved through specific Processing techniques, and ultimately determine the material's final Performance in real-world applications.
Reference: The Structure of Materials by Allen and Thomas, MIT Series in Materials Science.
Course Syllabus
A comprehensive journey from basic symmetry to complex crystallographic defects.
1 Pre-Midsemester
- Fundamentals: Types of bonds, coordination number, packing fraction, order and disorder.
- Symmetry & Group Theory: Crystalline state, symmetry operations, and Schönflies (Schoenflies) notations.
- Point Groups: Platonic solids (e.g., Tetrahedron, Icosahedron) and their point groups; Stereographic projection.
- Crystallography Intro: Hermann-Mauguin (International) notations.
- Lattices: 2D lattices & plane groups (analytical representation); 3D structures (Derivation of 14 Bravais lattices and space groups).
2 Post-Midsemester
- Advanced Tools: Introduction to International Tables for Crystallography (ITC).
- Diffraction: Reciprocal lattices, Miller indices, systemic absences, and structure determination using XRD.
- Common Structures: Metals (fcc, bcc, hcp) and Ceramics (rock salt, zinc blende, wurtzite, spinel, perovskite). Ordered structures, close-sphere packing & Pauling’s rules.
- Defects: Point (vacancies, solutes, Kroger Vink notations), Line (dislocations, partials), Planar (stacking faults, twins, grain boundaries) and 3D defects (precipitates, voids).
- Relations: Crystal Structure-Physical Property & Microstructure-Property relations.
Textbooks & References
Structure of Materials
De Graef and McHenry
Chemical Applications of Group Theory
F. Albert Cotton
Structure of Materials
Allen and Thomas
International Tables for Crystallography (ITC)
Vols. A, A1
The definitive resource for rigorous crystallography.
Crystallography and Crystal Defects
Kelly and Knowles
Structure of Metals
C S Barrett
Imperfections in Crystalline Solids
W Cai and W D Nix
Software Tools
VESTA (Visualization for Electronic and STructural Analysis)
Essential for visualising 3D structures.
Grading & Evaluation
A clear breakdown of how your final grade will be calculated.
Attendance
5/5 marks for those having ≥ 80% attendance. 0/5 for all others.
Quizzes
~10 online quizzes (~5 mins) every Thursday in class. Bring devices. Best ~5 out of ~10 considered (absolute marks).
Mid-Sem
Marks normalized with respect to the highest scorer will be considered towards the final score.
End-Sem
Marks normalized with respect to the highest scorer will be considered towards the final score.
Term Project
Groups of 8. Presentations in last week. Topics floated by end of August. Normalized scoring.