The Use of Reference Points in Measuring Unit Cell Parameters of Single Crystals on Current Diffractometers. X-Ray Diffraction Characterization of Bi12GeO20

Abstract

An original method is proposed for measuring the unit cell parameters of single crystals on commercial laboratory diffractometers using an external standard. At the first stage, a reference reflection of the standard and the 2θ_D detector position angle are selected. When a polycrystalline standard is used, data are collected in the Debye – Scherrer geometry, a plot of the intensity versus the X coordinate is constructed, and the position of the Kα₁ component is determined. In the case of a single crystal standard, its orientation is first determined relative to the goniometer axes (standard UB matrix), after which the φ and ω angles are calculated, which are required to bring the selected reflection to the equatorial circle, and ω scanning is performed. In both cases, the X and 2θ_D values, together with the theoretical reflection position, characterize the reference point. For the single crystal under study, its orientation is determined relative to the goniometer axes (standard UB matrices), and the φ and ω angles are calculated, which are required to bring the selected reflection to the equatorial circle. During the ω scanning, the detector is set at the 2θ_D angle such that the peak positions are brought as close as possible to the reference point. Then difference ΔX, along with difference in detector positions Δ2θ_D, are taken into account when calculating the diffraction angle. In all cases, the correction for sample eccentricity is applied. The proposed method is tested on a Si single crystal, using the polycrystalline certified reference material CeO₂ – SRM 674b as the external standard. The X-ray diffraction certification is performed for the promising single crystal standard Bi₁₂GeO₂₀: a= 10.1455(2) Å, space group I23, relative measurement error 1.7·10^–5.