introduction and point groups stereographic projections low symmetry systems space groups

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Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships Martensitic transformations Crystallogra phy H. K. D. H. Bhadeshia

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Crystallography. H. K. D. H. Bhadeshia. Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships Martensitic transformations. 180° rotation about horizontal axis. Invert rotated image. - PowerPoint PPT Presentation

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Page 1: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Introduction and point groups

Stereographic projections

Low symmetry systems

Space groups

Deformation and texture

Interfaces, orientation relationships

Martensitic transformations

Crystallography

H. K. D. H. Bhadeshia

Page 2: Introduction and point groups Stereographic projections Low symmetry systems Space groups

180° rotation about horizontal axis

Page 3: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Invert rotated image

Page 4: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Invert rotated image

mirror+ =

Page 5: Introduction and point groups Stereographic projections Low symmetry systems Space groups

2 equivalent to mirror

Page 6: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Page 7: Introduction and point groups Stereographic projections Low symmetry systems Space groups

deformation of single crystals

crystal

axessample axes

Schmid and Boas

Page 8: Introduction and point groups Stereographic projections Low symmetry systems Space groups

properties as a function of sample axes

Page 9: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Page 10: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Orientation of grains in polycrystalline sample relative to sample axes

Page 11: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Diffraction phenomena

Page 12: Introduction and point groups Stereographic projections Low symmetry systems Space groups

2 equivalent to mirror

Page 13: Introduction and point groups Stereographic projections Low symmetry systems Space groups

great circles: diameter equal to that of sphere

sphere

sphere

Page 14: Introduction and point groups Stereographic projections Low symmetry systems Space groups

small circles: diameter less than that of sphere

small circle

small circle

sphere

sphere

Page 15: Introduction and point groups Stereographic projections Low symmetry systems Space groups

To represent angles and planes

010

100

001

Page 16: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Representing a plane normal

010

100

001

(north)

(south)

Page 17: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Representing a plane normal

010

100

001

(north)

(south)

Page 18: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Cubic stereogram

Page 19: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Representing a plane normal

010

100

001

(north)

(south)

Page 20: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Wulff net

Page 21: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Page 22: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Page 23: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Wulff net

Page 24: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Page 25: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Page 26: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Page 27: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Page 28: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Page 29: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Page 30: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Using small circles

• To locate a pole at angles 1 from p1 and 2 from p2 draw the two small circles with angular centres on the two poles.

• Solutions at intersections.

Page 31: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Angle between two planes

Page 32: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Cubic Symmetry

Page 33: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Cubic symmetry

Page 34: Introduction and point groups Stereographic projections Low symmetry systems Space groups

Full cubic stereogram

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