Transformation Equations for Elastic Constants

The elastic properties of an ideally elastic crystal may be characterized corrrpletely by the nrrmerical valrres of either the elastic stiffnesses c,yw or cxfi or else of its compliartces syu or These nrrmerical values, however, are referred to a specific coordirrate system arrd are, therefore, dependent on its choice. Usually they are reproduced in tables as referred to a Cartesian coordinate system with axes parallel to irrrportartt crystallographic directiorrs. It is chosen in a way that makes the representation of crystal properties as sirrtple as possible, as was shown already in Chap. 2, and is called the crystal coordinate system. 

The transformation eqnations for the stiffnesses and the compliances then read  

Helpful tables for writing down the explicit matrix notation form of these relations for a general rotation of the coordinate system have been worked ont by Hearmon (1957) and can also be fonnd in Petrzilka et al. (1960). 

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