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

Abstract

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 RbTi1−xZrxOPO4crystals (A,BandC) with KTiOPO4structure, at 295 and 105 K (five experimental data sets). Microprobe measurements yield compositionsxA,B= 0.034 (5) andxC= 0.022 (4). The corresponding site occupancy factors areQA,B= 0.932 (10) andQC= 0.956 (8). Using Anomalous-AniMMM and three independent refinements for the first and second samples, the initial occupancy factor ofQA,B= 0.963 (15) was improved toQA,B= 0.938 (7). Of the three room-temperature data sets, one was improved toQA,B= 0.934 (2). For the third sample and one data set, the initial occupancy factor ofQC= 1.000 was improved toQC= 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.