دانلود کتاب Tensor Properties of Crystals

فهرست مطالب :

CRYSTALS AND CRYSTAL SYMMETRY

Structure of solids. Close-packing structures. Two-dimensional lattices. Three-dimensional lattices. Crystallographic indices for planes-Miller indices. Crystallographic direction indices. Worked examples on symmetry problems. Problems.

INTRODUCING TENSORS

Introduction to the notation. Reducing the number of components. Transformation of axes. Transformation of a vector. Transformation of the coordinates of a point. Transformation and definition of a tensor. Second-rank symmetrical tensors-the representation quadric. Neumann`s principle. Some examples of tensors. Worked examples showing change of axes for a tensor. Problem.

SECOND-RANK TENSORS-CONDUCTIVITY

Thermal conductivity and thermal resistivity. Heat flow in crystal samples. The radius-normal property of the representation quadric. Electrical conductivity and electrical resistivity. Diffusion. Some worked examples of second-rank tensor properties. Problems.

FOURTH-RANK TENSORS-ELASTICITY

Introduction. Strain. Symmetrical and antisymmetrical tensors. The strain tensor. Stress. Elasticity. The matrix notation. Effect of crystal symmetry-equating components by inspection. Elasticity components in cubic crystals and polycrystalline samples. Elasticity components in other crystal systems. Worked examples on stress, strain and elasticity. Problems.

CRYSTAL OPTICS

Introduction. The indicatrix. The wave surface. Biaxial crystals. Double refraction (birefringence) at a boundary. Worked examples on polarization and birefringence. Problems.

AXIAL TENSORS

Definition of an axial tensor. Transformation of axial vectors. Transformation of axial tensors. Optical activity. Optical activity in the presence of birefringence. The gyration tensor-second-rank axial tensor. The Hall effect-third-rank axial tensor. The Hall effect- relationship to symmetry. Magnetoresistance and other effects. Problems.

FURTHER TENSOR APPLICATIONS

Introduction. Thermal expansion. The pyroelectric effect. Piezoelectricity. Photoelasticity. The linear electro-optic effect (the Pockels effect). The quadratic electro-optic effect (the Kerr effect). Some concluding comments. Problems.

APPENDICES

REFERENCES AND FURTHER READING

ANSWERS TO PROBLEMS

INDEX