Residual stress measurement in textured thin film by grazing-incidence X-ray diffraction

Abstract

Measurements of residual stresses in textured thin films have always been problematic. In this article, a new experimental method using grazing-incidence X-ray diffraction is presented with its principles based upon the conventional sin 2ψ method. Instead of using the Bragg–Brentano (B-B) or Seemann–Bohlin geometry, the proposed method utilizes an asymmetrical diffraction geometry for which the X-ray beam is incident at a grazing angle γ to the sample surface, while the angle ψ is the tilt angle of the sample surface as defined by the conventional sin 2ψ method. Basic equations involved in the X-ray residual stress analysis are described, along with exemplified experimental data. Analysis shows that, for an isotropic medium, strain measured using this grazing-incidence geometry assumes a linear relationship with the geometrical parameter cos 2α sin 2ψ, where the angle α is a constant and is defined as the Bragg angle at ψ=0°, θ o, minus the grazing incidence angle γ, i.e. α=θ o−γ. The grazing-incidence diffraction geometry effectively increases the irradiation volume from a thin-film specimen, thereby giving rise to higher intensity for high-angle Bragg peaks than the conventional B-B geometry. The proposed analysis has another advantage, in that the inhomogeneous sample casts little effect on the residual stress results when compared to the traditional sin 2ψ method.