On the selection of measurement directions in second-rank tensor (e.g. elastic strain) determination of single crystals

The components of a symmetric second-rank tensor (e.g. the strain tensor) can be calculated from measurements of that tensor property in at least six directions. A system of simultaneous equations (t(m) = Σ6i = 1 amiti) must be solved. The coefficient matrix ami is determined by the measurement directions, and therefore it is of great importance to choose these directions properly. Part 1 deals with the necessary condition: rank (ami)<> 0. Rules are given by which it is easy to decide whether rank (ami) = 0 or rank (ami) ≷0 without calculating the rank. In part 2 methods are developed to find optimized sets of measurement directions. An optimized set is one for which the inevitable measurement errors will give errors of the calculated tensor components as small as possible. Special attention is given to the case of X-ray strain measurement of single crystals.