X-ray strain analysis of {111} fiber-textured thin films independent of grain-interaction models

The anisotropic elastic response of supported thin films with a {111} fiber texture has been studied using an in-situ micro-tensile tester and X-ray diffractometry. It is shown which specific X-ray diffraction measurement geometries can be used to analyze the elastic strains in thin films without requiring any assumptions regarding elastic interactions between grains. It is evidenced (theoretically and experimentally) that the combination of two specific geometries leads to a simple linear relationship between the measured strains and the geometrical variable sin²ψ, avoiding the transition scale models. The linear fit of the experimental data allows a direct determination of the relationship between the three single-crystal elastic compliances or a direct determination of the S₄₄ single-crystal elastic compliance and the combination of S₁₁ + 2S₁₂ if the macroscopic stress is known. This methodology has been applied to a model system, i.e. gold film for which no size effect is expected, deposited on polyimide substrate, and it was found that S₄₄ = 23.2 TPa⁻¹ and S₁₁ + 2S₁₂ = 1.9 TPa⁻¹, in good accordance with values for large crystals of gold.