Determination of site occupancies by the intermeasurement minimization method. I. Anomalous scattering usage for noncentrosymmetric crystals

New methods for the determination of site occupancy factors are described. The methods are based on the analysis of differences between intensities of Friedel reflections in noncentrosymmetric crystals. In the first method (Anomalous-Expert) the site occupancy factor is determined by the condition that it is identical for two data sets: (1) initial data without averaging of Friedel intensities and (2) data that are averaged on Friedel pairs after the reduction of the anomalous scattering contribution. In the second method (anomalous anisotropic intermeasurement minimization method, Anomalous-AniMMM) the site occupancy factor is refined to satisfy the condition that the differences between the intensities of Friedel reflections that are reduced on the anomalous scattering contribution must be minimal. The methods were checked for three samples of RbTi_1-xZr_xOPO₄ crystals (A, B and C) with KTiOPO₄ structure, at 295 and 105 K (five experimental data sets). Microprobe measurements yield compositions x_A,B = 0.034 (5) and x_C = 0.022 (4). The corresponding site occupancy factors are Q_A,B = 0.932 (10) and Q_C = 0.956 (8). Using Anomalous-AniMMM and three independent refinements for the first and second samples, the initial occupancy factor of Q_A,B = 0.963 (15) was improved to Q_A,B = 0.938 (7). Of the three room-temperature data sets, one was improved to Q_A,B = 0.934 (2). For the third sample and one data set, the initial occupancy factor of Q_C = 1.000 was improved to Q_C = 0.956 (1). The methods improve the Hirshfeld rigid-bond test. It is discussed how the description of chemical bonding influences the site occupancy factor.