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Crystallography Orientation relationships Metric tensor

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Presentation on theme: "Crystallography Orientation relationships Metric tensor"— Presentation transcript:

1 Crystallography Orientation relationships Metric tensor
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

5 (110) ferrite (111) austenite

6 Kurdjumov-Sachs orientation

7

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9 The Kurdjumov-Sachs Orientation Relationship
X Y

10 X Y

11 Bagaryatski orientation relationship, cementite and ferrite

12

13

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15 Axis-Angle Pairs

16

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18 Symmetry related axis-angle pairs

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20

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22 Weiss Zone Rule proven!

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

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

25 The Metric Tensor

26 Orthorhombic

27 cementite

28 cubic tetragonal orthorhombic hexagonal trigonal triclinic monoclinic

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