Crystallography Orientation relationships Metric tensor

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Presentation transcript:

Crystallography Orientation relationships Metric tensor H. K. D. H. Bhadeshia Orientation relationships Metric tensor

coordinate transformation matrix derived by inspection

Kurdjumov-Sachs orientation how do we derive the coordinate transformation?

(110) ferrite (111) austenite

Kurdjumov-Sachs orientation

The Kurdjumov-Sachs Orientation Relationship X Y 

X Y 

Bagaryatski orientation relationship, cementite and ferrite

Axis-Angle Pairs

Symmetry related axis-angle pairs

Weiss Zone Rule proven!

generalised dot product express one vector in real space, other in 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.

The Metric Tensor

Orthorhombic

cementite

cubic tetragonal orthorhombic hexagonal trigonal triclinic monoclinic