Modelling of diffraction from fibre texture gradients in thin polycrystalline films

Crystallographic textures in thin polycrystalline films typically exhibit a rotational symmetry, i.e. they occur as a fibre texture with the texture pole being orientated in the direction of the substrate normal. As a further characteristic of thin-film textures, it was often observed that the degree of preferred orientation increases with increasing thickness. It is shown in this work how a fibre texture gradient may be modelled in kinematical X-ray diffraction and which effects it has on the intensity mapping of the I_HKL reflection, when the HKL pole is the fibre axis. A general expression for I_HKL is derived for a depth-dependent fibre texture that is based on the finite Laplace transform of the texture distribution. The concept is outlined for the cosⁿψ function to model the tilt-angle dependence of intensity, with the parameter n denoting the degree of texture. It is found that the measured intensity distribution sensitively depends on the ratio of texture gradient over X-ray attenuation coefficient. For particular cases, it is found that the maximum intensity may occur for non-zero tilt angles and thus arise at a different tilt angle from the pole of the fibre texture.