Symmetry properties and transformation behaviour of the X-ray stress factors

Abstract

It is shown that the so-called X-ray elasticity factorsFij(φ, ψ, hkl) are second-rank tensors. The advantages that can be drawn from that fact are revealed: (i) it is possible to find the best strategies for the measurement ofFtensors in textured polycrystalline materials; (ii) in some cases,Ffor one measurement direction can be calculated fromFfor another measurement direction; (iii) when the measurement directionr(φ, ψ) is parallel to a symmetry axis or a mirror plane, some relationships among the entries of theFmatrix exist, so the number of independent variables ofFis reduced. Different equations are derived which could help in the calculation of theFtensors, be it for single crystals or polycrystalline materials with or without texture. It is also shown that many facts already known aboutFcan be interpreted and proved in an elegant way by making use of the tensor character ofF.