X-ray residual stress measurement in films with crystallographic texture and grain shape

X-ray diffraction provides an easy and powerful method for measuring residual stress in thin films. However, nonlinearity of the d vs. sin²ψ relation can lead to the misinterpretation of results, especially when one of the measurements is made at low values of ψ. It is shown that anisotropy from either crystallographic texture or grain shape will cause serious nonlinearity. Calculations of the d vs. sin²ψ relation for different combinations of ideal crystallographic textures and grain shapes are given. In all cases, a high ψ angle range exists where the d vs. sin²ψ relation is linear and the residual stress can be determined from easily calculated Reuss and Voigt model elastic constants. This is despite the fact that more complicated models are necessary to predict the d vs. sin²ψ relation in the low ψ angle range.