Journal of Applied Crystallography

Volume 39, Part 3 (June 2006)

research papers

J. Appl. Cryst. (2006). 39, 401-409 [ doi:10.1107/S0021889806011526 ]

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

B. Ortner

Abstract: It is shown that the so-called X-ray elasticity factors F_ij( [varphi] , [psi] , 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 of F tensors in textured polycrystalline materials; (ii) in some cases, F for one measurement direction can be calculated from F for another measurement direction; (iii) when the measurement direction r( [varphi] , [psi] ) is parallel to a symmetry axis or a mirror plane, some relationships among the entries of the F matrix exist, so the number of independent variables of F is reduced. Different equations are derived which could help in the calculation of the F tensors, be it for single crystals or polycrystalline materials with or without texture. It is also shown that many facts already known about F can be interpreted and proved in an elegant way by making use of the tensor character of F.

Keywords: elastic constants; stress factors; elasticity factors.