Materials Science and Metallurgy Mathematical Crystallography

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Presentation transcript:

Materials Science and Metallurgy Mathematical Crystallography Professor Harry Bhadeshia Lecture 1: vectors, coordinate transformations, reciprocal lattice

coordinate transformation matrix J

each column of (B J A) represents the components of a basis vector of A with respect to B

The reciprocal basis A*

directions: refer to real space plane normals: refer to reciprocal space

to take a dot product between two vectors in any coordinate system, express one in the reciprocal basis and the other in real basis.