Implementation of Bond’s Scheme in a Single Crystal Diffractometer. Study of the Homogeneity of (Y1–xEux)2O3 Single Crystals

Abstract

An original procedure is proposed to refine unit cell parameters (UCPs) of single crystals in Bond’s scheme. The procedure involves the use of a modern laboratory diffractometer equipped with a 2D detector and a three-circle goniometer. At the first stage, preliminary UCPs, diffraction class, and crystal orientation relative to goniometer axes are determined. Then φ and ω angles are calculated to bring an appropriate (occurrence of a well-resolved doublet, intensity) reflection hkl on the equatorial plane. The measurement in Bond’s scheme is carried out at two symmetric positions of the detector ±2θ_D ≈ 2θ_hkl. The principal difference from the measurement on a single crystal spectrometer consists in refusing to plot the reflection profile I(ω) and passing to ω-scans with a width of 3-4°, which allows the measurement of the Kα₁/Kα₂ doublet profile. After its processing by two independent 2D functions, coordinates of the maxima are determined, and then the 4θ_hkl. Angle is found based on angular sizes of the detector pixel and the difference in the coordinates of X Kα₁-component reflections obtained in symmetric positions. In this approach, measurement errors are related to the accuracy of placing the detector in two symmetric positions and the correctness of processing 2D reflection profiles. In the study of reference Si and Ge single crystals in the range of 2θ_D angles close to 100°, UCP deviations from the theoretical values are found to not exceed 0.0004 Å, and the relative measurement accuracy is 6·10^–5. The refinement of UCPs of single crystals grown in the Y₂O₃–Eu₂O₃ system by the melt-solution technique indicates the formation of the (Y_1–xEu_x)₂O₃ solid solution with the x value range of 0.27-0.40. A scheme is proposed to improve the measurement accuracy when the procedure is transferred to the diffractometer with synchrotron radiation.