Symmetry and Physical Properties of Crystals

Abstract

Crystals are everywhere, from natural crystals (minerals) through the semiconductors and magnetic materials in electronic devices and computers or piezoelectric resonators at the heart of our quartz watches to electro-optical devices. Understanding them in depth is essential both for pure research and for their applications. This book provides a clear, thorough presentation of their symmetry, both at the microscopic space-group level and the macroscopic point-group level. The implications of the symmetry of crystals for their physical properties are then presented, together with their mathematical description in terms of tensors. The conditions on the symmetry of a crystal for a given property to exist then become clear, as does the symmetry of the property. The geometrical representation of tensor quantities or properties is presented, and its use in determining important relationships emphasized. An original feature of this book is that most chapters include exercises with complete solutions. This allows readers to test and improve their understanding of the material. The intended readership includes undergraduate and graduate students in materials science and materials-related aspects of electrical and optical engineering; researchers involved in the investigation of the physical properties of crystals and the design of applications based on crystal properties such as piezoelectricity, electro-optics, optical activity and all those involved in the characterization of the structural properties of materials. Introduction -- Symmetry operations -- Crystal lattices -- Relationship between space groups and point groups -- Point groups -- Bravais lattices -- Space groups -- Chemical bonds and crystal structures -- Crystal anisotropy and tensors -- Second-rank tensors -- Stress tensor -- Deformation of a solid. The strain tensor -- Elasticity -- Elastic waves in crystals -- Crystal thermodynamics. Piezoelectricity -- Light propagation in crystals -- Polarization of light by crystals -- Optical activity, or rotatory power.