Algorithm and program for precise determination of unit-cell parameters of single crystal taking into account the sample eccentricity

Abstract

A technique has been developed to refine the unit-cell parameters of single crystals with minimization of the influence of instrumental errors on the result. The corresponding computational procedure HuberUB is added to the software package of Huber-5042 diffractometer with a point detector and closedcycle helium cryostat Displex DE-202. The parameters of unit cell, its orientation, the goniometer zero angles, the sample eccentricity, the distances in the goniometer, and the radiation wavelength were refined by the nonlinear least-squares method, which allows imposition of constraints on the unit-cell parameters, depending on the crystal symmetry. The technique is approved on a LuB₁₂ single crystal. The unit-cell parameters are determined in a temperature range of 20–295 K, with an absolute error not larger than 0.0004 Å (the relative error is of ~5 × 10^–5). The estimates of the unit-cell parameters obtained by the proposed method are evidenced to be unbiased. Some specific features of the behavior of parameters in the ranges of 120–140 and 20–50 K are revealed, which correlate with the anomalies of the physical properties of the crystal.