Lattice constant determination by grazing incidence diffraction in thin cubic films under thermal strain

Abstract

If thermal strain ε th exists in a thin film, then the lattice constant a is dependent on the orientation of the crystallites within the film due to the elastic anisotropy of the crystallites. For this case, in X-ray diffraction the lattice constant α is a function of the Miller indices ( hkl) and of the measurement direction. Assuming the film to have cubic structure, a theoretical expression for the relative strain ε( hkl)ε th is derived. The expression is valid for the usual Bragg-Brentano geometry and for grazing incidence diffraction. As an application, from the measured a(hkl) of a thin copper film, the film's strain-free lattice constant a 0 and ε th are estimated.