Physical properties of crystals. Their representation by tensors and matrices / Физические свойства кристаллов. Их представление с помощью тензоров и матриц

Tne physical properties of crystals are defined by relations between measurable quantities. Density, for example, is defined from a relation between mass and volume. Now both mass and volume may be measured without reference to direction, and, accordingly, density is a property that does not depend on direction. On the other hand, a crystal property such as electrical conductivity is defined as a relation between two measurable quantities (the electric field and the current density) both of which have to be specified in direction as well as in magnitude. We therefore have to allow for the possibility that a physical property of this sort will depend upon the direction in which it is measured-and, as an experimental fact, the electrical conductivity of many crystals does indeed vary with direction. In such cases the crystals are said to be anisotropic for the property in question. The problem then arises of how to specify the value of a crystal property that can depend upon direction-clearly, a single number will not suffice. There is also the problem of how the specification, when we have it, is related to the symmetry of the crystal. The answers to these two questions, and some of their implications, form the subject of this book.