Tensor properties of crystals

著者

書誌事項

Tensor properties of crystals

D.R. Lovett

Institute of Physics, 1994, c1989

  • : pbk.

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注記

"Reprinted with minor corrections 1994 (pbk)."--T.p. verso

Includes bibliographical references (p. [129]-130) and index

内容説明・目次

内容説明

As the use of single crystals in scientific and technological applications has become increasingly important, so has an understanding of the variation of physical properties with crystalline direction. Such knowledge is needed to maximize the performance of solid state devices and many useful effects can be produced only in materials of the correct orientation. Tensor Properties of Crystals demonstrates how the application of tensors to a study of crystalline materials fulfils this need. This concise introduction to the subject is written from a physical, rather than mathematical, approach, although the reader needs some prior knowledge of vectors. After a discussion of crystal symmetry and an introduction to the uses of and differences in tensors, Tensor Properties of Crystals discusses applications to such areas as conductivity, elasticity and crystal optics. Each application illustrates particular features of the use of tensors, equipping the reader with principles that can be applied to any physical situation. Extensive use of diagrams, worked examples and problems with answers completes this useful textbook for undergraduate and graduate students of physics, materials science, chemistry, electronic engineering, optoelectronics and geophysics. Scientists investigating or utilising the properties of single crystals will also find this book of value. The Author After carrying out research in the Materials Section of the Electrical Engineering Department of Imperial College, David Lovett was appointed lecturer at Essex University in 1966. His teaching has moved from chemical to mainstream physics and his research interests have included the electrical and thermal properties of semiconductors and the x-ray topography of materials. At present his research is mainly in the area of thin films prepared by the Langmuir-Blodgett technique. other_titles

目次

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. blurb As the use of single crystals in scientific and technological applications has become increasingly important, so has an understanding of the variation of physical properties with crystalline direction. Such knowledge is needed to maximize the performance of solid state devices and many useful effects can be produced only in materials of the correct orientation. Tensor Properties of Crystals demonstrates how the application of tensors to a study of crystalline materials fulfils this need. This concise introduction to the subject is written from a physical, rather than mathematical, approach, although the reader needs some prior knowledge of vectors. After a discussion of crystal symmetry and an introduction to the uses of and differences in tensors, Tensor Properties of Crystals discusses applications to such areas as conductivity, elasticity and crystal optics. Each application illustrates particular features of the use of tensors, equipping the reader with principles that can be applied to any physical situation. Extensive use of diagrams, worked examples and problems with answers completes this useful textbook for undergraduate and graduate students of physics, materials science, chemistry, electronic engineering, optoelectronics and geophysics. Scientists investigating or utilising the properties of single crystals will also find this book of value. The Author After carrying out research in the Materials Section of the Electrical Engineering Department of Imperial College, David Lovett was appointed lecturer at Essex University in 1966. His teaching has moved from chemical to mainstream physics and his research interests have included the electrical and thermal properties of semiconductors and the x-ray topography of materials. At present his research is mainly in the area of thin films prepared by the Langmuir-Blodgett technique.

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