Stress analysis of polycrystalline thin films and surface regions by X-ray diffraction

Welzel, U.; Ligot, J.; Lamparter, P.; Vermeulen, A.C.; Mittemeijer, E.J.

doi:10.1107/S0021889804029516

Notes

¹The notion `direction-dependent grain interaction' signifies that different grain-interaction assumptions prevail along different directions in the specimen.

²Note that the components of the strain tensor $[\varepsilon _{ij}^{\rm S}]$ should be written as { $[\varepsilon _{ij}^{\rm S}]$ }^hkl. For the sake of simplicity, the curly brackets and the indication of the reflection are omitted.

³The notion texture without further specification refers to the occurrence of crystallographic, not morphological, texture in the following.

⁴Note that the symbols [alpha] , [beta] , [gamma] , [mu] and [nu] bear no relation to the same symbols used in earlier sections. These symbols are used here for consistency with the cited literature.

⁵Usually the arithmetic and not the geometric average is used. The geometrical average of n numbers is defined as the nth root of the product of the numbers. For Young's modulus, as an example, the geometric average of the moduli according to the Reuss (E_R) and Voigt (E_V) models E_GA is defined as (E_RE_V)^1/2.