The physical properties of crystals and their description by tensors

Abstract

Abstract The chapter starts with a general introduction of the topics covered here. If provides an ‘everyday’ example or analogy of a tensor property and a description of suffix notation. The chapter then gives consideration to symmetrical second rank tensors; principal axes (eigenvectors); the representation quadric; Neumann's principle, pyroelectricity and ferroelectricity; and second rank tensors which describe stress, strain, and atomic displacements. It provides the optical properties of crystals: the indicatrix, elliptically polarised light, and optical path differences. Finally, it looks at third rank tensors (the piezoelectric effect) and fourth rank tensors (elasticity, matrix notation, and elastic properties of cubic crystals).