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Crystallography: Kurdjumov-Sachs Orientation Relationship & Metric Tensor in Material Transformation

Explore the Kurdjumov-Sachs Orientation Relationship Y-gamma-X and the Metric Tensor, related to coordinate transformation in crystallography. Learn how to derive the transformation matrix through inspection in ferrite and austenite structures, with insights on Bagaryatski and Axis-Angle Pairs relationships. Discover the Weiss Zone Rule and the use of generalized dot product to express vectors in different coordinate systems. Delve into the Metric Tensor applications in orthorhombic, cubic, tetragonal, hexagonal, trigonal, triclinic, and monoclinic structures.

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Crystallography: Kurdjumov-Sachs Orientation Relationship & Metric Tensor in Material Transformation

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

  2. coordinate transformation matrix derived by inspection

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

  4. (110) ferrite (111) austenite

  5. Kurdjumov-Sachs orientation

  6. Y  X The Kurdjumov-Sachs Orientation Relationship

  7. Y  X

  8. Bagaryatski orientation relationship, cementite and ferrite

  9. Axis-Angle Pairs

  10. Symmetry related axis-angle pairs

  11. Weiss Zone Rule proven!

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

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

  14. The Metric Tensor

  15. Orthorhombic

  16. cementite

  17. cubic tetragonal orthorhombic hexagonal trigonal triclinic monoclinic

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