Interpretation of displacement-caused diffuse scattering using the Taylor expansion

The suitability is considered of employing a Taylor expansion of the kinematic scattering equation for analysing and interpreting diffuse diffraction intensities induced by atomic displacements. The diffuse scattering caused by static atomic displacements in yttria-stabilized cubic zirconium oxide is used as a test of the method because a computer model of the local atomic structure exists that satisfactorily reproduces the measured diffraction data. By concentration on the computer model, it was possible to calculate the diffuse intensity using expansions to various orders and test the results against an exact computation of the diffuse diffraction pattern. In this example, where the r.m.s, atomic displacements are approximately 3%, it was found that the usual second-order expansion could not account for many diffraction features. Most notable was the inability of an expansion to second order to describe an observed asymmetry across certain reciprocal planes. Expansion to a minimum of three orders is necessary to describe such features qualitatively and an accurate quantitative fit of the diffraction pattern at moderate diffraction angles requires the use of a fourth-order expansion.