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Course11310210893 lectures

Crystals, Symmetry and Tensors

Prof. Rajesh Prasad · IIT Delhi

Start with lecture 1 At NPTEL

About

Crystallography is fundamental to physics, chemistry, metallurgy, materials science, mechanical engineering, chemical engineering, and any other disciplines dealing with solid state. Despite this importance, due to constraints in design of curriculua a full course is rarely available on this topic. The present course intends to fill this gap. It will begin with basic fundamentals and take the students to advanced concepts of point and space groups symmetry and vector and tensor applications in crystallography.

Intended audience: Students interested in solid state science and engineering will be benefited. UG and PG students of Physics, Chemistry, Metallurgy, Materials Science, Mechanical Engineering, Chemical Engineering will find the course useful.

Lectures

Week 1

  1. What is Crystal? YouTube
  2. Lattice and Motif YouTube
  3. Lattice Translation YouTube
  4. Unit Cell YouTube
  5. Voronoi Cell YouTube
  6. Unit cell, Basis, Fractional Coordinates YouTube
  7. Miller indices for direction YouTube

Week 2

  1. Miller indices for planes YouTube
  2. Line of intersection between two planes YouTube
  3. Plane normal of a plane for cubic crystal YouTube
  4. Weiss Zone Law YouTube
  5. Application of Weiss Zone Law YouTube
  6. Coordinate transformation YouTube
  7. Reciprocal Basis YouTube
  8. Reciprocal lattice vector (G*_hkl) is perpendicular to plane (hkl) YouTube

Week 3

  1. Length of G*_hkl is reciprocal of interplanar spacing (d_hkl) YouTube
  2. Metric tensor YouTube
  3. Review YouTube
  4. Some properties of metric tensor in real and reciprocal space YouTube
  5. Transformation of direction and planes YouTube
  6. Volume of a crystallographic unit cell YouTube
  7. Orthographic projection of crystals YouTube

Week 4

  1. Stereographic projection-I YouTube
  2. Stereographic projection-II YouTube
  3. Definition of symmetry YouTube
  4. What is a group? YouTube
  5. Matrix Representation of symmetry operation-I YouTube
  6. Matrix Representation of symmetry operation-II YouTube
  7. Trace of a rotation matrix YouTube
  8. Coordinate transformation of a matrix representing symmetry operation YouTube

Week 5

  1. Chirality YouTube
  2. Types of symmetry operation YouTube
  3. Relation between cube and tetrahedron YouTube
  4. 2-fold roto-inversion is a mirror: Proof using matrix method YouTube
  5. Invariance of a trace of symmetry operation during basis transformation YouTube
  6. Crystallographic restriction theorem YouTube
  7. Geometric proof of crystallographic restriction theorem YouTube
  8. Quasicrystals YouTube

Week 6

  1. Affine transformation and Seitz Operator YouTube
  2. Frieze group-I YouTube
  3. Frieze group-II YouTube
  4. 2D point group-I YouTube
  5. 2D point group-II YouTube
  6. The angle between mirrors is half the angle of rotation YouTube
  7. Different kinds of 2D lattices YouTube

Week 7

  1. 10- point groups associated with 5 lattices YouTube
  2. Plane group-I YouTube
  3. Plane group-II YouTube

Week 8

  1. 3D Point Groups I : Introduction YouTube
  2. 3D Point Groups II : Proper Monoaxial Groups YouTube
  3. 3D Point Groups III : Dihedral Groups YouTube
  4. 3D Point Groups IV : Proper cubic point groups YouTube
  5. 3D Point Groups V : Enantiomorphic Point Groups YouTube
  6. 3D Point Groups VI : Improper Monoaxial Point Groups YouTube
  7. 3D Point Groups VII : Combination of a mirror passing through an n-fold axis YouTube
  8. 3D Point Groups VIII : Combination of a mirror perpendicular to an n-fold axis YouTube

Week 9

  1. 3D Point Groups IX : Combination of a mirror perpendicular and parallel to an n-fold axis YouTube
  2. 3D Point Groups X : Mirror parallel to a rotoinversion axis YouTube
  3. 3D Point Groups XI : Improper Cubic Point Groups YouTube
  4. 3D Point Groups XII : Classification of Point Groups into 7 Crystal Systems YouTube
  5. 3D Point Groups XIII : Chirality Revisited YouTube
  6. 3D Point Groups XIV : Centrosymmetric Point Groups YouTube
  7. 3D Point Groups XV : Laue Classes YouTube
  8. 3D Point Groups XVI : Group-Subgroup Relations YouTube
  9. 3D Point Groups XVII : Polar Groups YouTube
  10. 3D Point Groups XVIII : Holohedral or Holosymmetric class YouTube

Week 10

  1. 3D Space Groups I : Introduction YouTube
  2. 3D Space Groups II : Trigonal / Rhombohedral / Hexagonal confusion YouTube
  3. 3D Space Groups III : Bravais Lattices in Trigonal Crystal System YouTube
  4. 3D Space Groups IV : Screw Axes and Screw Operations YouTube
  5. 3D Space Groups V : Glides in 3D YouTube
  6. 3D Space Groups VI : Symmorphic and Nonsymmorphic Space Groups YouTube
  7. 3D Space Groups VII : 73 Symmorphic Space Groups YouTube

Week 11

  1. 3D Space Groups VIII : Interpretation of International Table Page Part -1 : Headline YouTube
  2. 3D Space Groups IX : Interpretation of International Table Page Part -2 : Symmetry Diagrams YouTube
  3. 3D Space Groups X : Interpretation of International Table Page Part -3 : General Position Diagram YouTube
  4. 3D Space Groups XI : Interpretation of International Table Page Part -4 : Origin YouTube
  5. 3D Space Groups XII : Interpretation of International Table Page Part -5 : Asymmetric Unit YouTube
  6. 3D Space Groups XIII : Interpretation of International Table Page Part -6 : Symmetry Operations YouTube
  7. 3D Space Groups XIV : Interpretation of International Table Page Part -7 : Generators Selected YouTube
  8. 3D Space Groups XV : Interpretation of International Table Page Part -8 : Positions YouTube
  9. 3D Space Groups XVI : Interpretation of International Table Page Part -9 : General Position Coordinate Triplet YouTube

Week 12

  1. Representation of Physical Properties of Crystals by Tensors YouTube
  2. Index Notation YouTube
  3. Coordinate Transformation of Vectors YouTube
  4. Some properties of Coordinate Transformation matrix between two orthonormal bases YouTube
  5. Coordinate Transformation for a second rank tensor YouTube
  6. Coordinate Transformation of tensors of different rank YouTube
  7. Magnitude of a second rank tensor property in a given direction YouTube
  8. Neumann's Principle YouTube
  9. Physical properties represented by second rank tensors are CENTROSYMMETRIC YouTube
  10. Effect of symmetry on the components of tensor representing a physical property YouTube
  11. Cubic crystals are isotropic for second rank tensor properties YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Delhi
Department
Metallurgy and Material Science
Teacher
Prof. Rajesh Prasad
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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