Mathematical Crystallography

Worked examples in the Geometry of Crystals, the 2nd edition, published in 2001 (updated 2006), is now available for free download from this site. The book deals with the mathematical crystallography of materials. It is intended for use by students and by anyone interested in phase transformations or interfaces. ISBN 0-904357-94-5, published by the Institute of Materials, 1 Carlton House Terrace, London SW1Y 5DB. Reviewed in Acta Crystallographica A57 (2001) 478. You can download the whole book: PDF file (6 Mb) Other free books Crystal Plasticity Bainite α'+αb Alloying Free download, published 2017

Introduction

• Definition of a Basis
• Co-ordinate transformations
• The reciprocal basis
• Homogeneous deformations
• Interfaces

Orientation Relationships

• Cementite in Steels
• Relations between FCC and BCC crystals
• Orientation relations between grains of identical structure
• The metric
• More about the vector cross product

Slip, Twinning and other Invariant-Plane Strains

• Deformation twins
• The concept of a Correspondence matrix
• Stepped interfaces
• Eigenvectors and eigenvalues
• Stretch and rotation
• Conjugate of an invariant-plane strain

Martensitic Transformations

• The diffusionless nature of martensitic transformations
• The interface between the parent and product phases
• Orientation relationships
• The shape deformation due to martensitic transformation
• The phenomenological theory of martensite crystallography

Interfaces in Crystalline Solids

• Symmetrical tilt boundary
• The interface between alpha and beta brass
• Coincidence site lattices
• Multitude of axis-angle pair representations
• The O-lattice
• Secondary dislocations
• The DSC lattice
• Some difficulties associated with interface theory

Appendices and References

• Vectors
• Matrices
• Transformation Texture
• References

Slide Presentations

• Vectors, coordinate transformations, reciprocal lattice
• Homogeneous deformations, orientation relationships
• Slip, twinning and other invariant-plane strains
• Martensite crystallography
• Texture calculations

Library of Relevant Computer Programs

Introduction to Crystallography

Crystallographic texture

Crystalline Trees

Click on image for movies illustrating the coincidence site lattice

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