Time:10:00am, 6/10/2014—7/3/2014 (everyTuesday, Wednesday and Thursday）

Place:A306, 1 West Building

Speaker:Prof. Suliman Ahmed Dregia, Ohio State University, USA

Title of Talk:Crystal Symmetry and Domain Structures

Syllabus:

A. Review of Elementary Concepts

Crystals, lattices, and unit cells. Rational lattice planes and axes. The 14 Bravais lattices in 3-D Wigner-Seitz unit cell. The four crystal systems and 5 lattices in 2-D.

B. Crystallographic Calculations

Matrix representation of a vector relative to a basis. Cartesian, crystallographic bases, and the metric matrix. Bond lengths and angles. Lattice planes and the reciprocal lattice. Interplanar d and . Change of basis: Directi  Direct2, Direct  Reciprocal and the "circuit diagrams."

C. Symmetry

Symmetry as invariance under certain operations. Point symmetry, translational symmetry, and crystal (space) symmetry. Point operations, restrictions on combinations of symmetries. Graphical representation: stereograms. Analytical representation: Matrix methods. Active vs. passive linear operators. General positions vs. special positions, Symmetry operations vs. symmetry elements.

D. Crystal Classification by Minimum Symmetry

Characteristic/minimum point symmetries and the seven crystal systems in 3-D

E. External Symmetry: Point Groups

Algebraic definition of a group, from point operations to point groups, the 32 crystallographic point groups in 3-D.  The International notation for point groups. Matrix methods for finding equivalent points/directions and planes. Crystal forms and Neumann's principle.

F. Internal Symmetry

Combinations of point and translation operations: screw and glide operations. Sketchy development of crystallographic space groups. The point group of the space group, site symmetry and equivalent positions. International space group symbols and tables, use of tables for concise/precise description of crystal structures, examples of simple and complex structures.

G. Symmetry Dictated Polydomains

Orientation relationships. Symmetry breaking and polydomains in solid-solid transformatios and epitaxy. Orientation variants vs. Deformation variants in structural phase transformations. Euler’s law and topological properties of polydomains. Polydomain coarsening.

Invited by:Yunzhi Wang, CMS