Leverage analysis of X-ray single crystal diffraction data from orthopyroxene and pigeonite

Abstract

Leverage analysis, a statistical procedure for calculating the influence of each reflection on the estimate of each refined variable, was applied to the structure refinement of a Pbca orthopyroxene (Wo 1 En 48 Fs 51 ) and that of a P 2 1 / c pigeonite (Wo 10 En 47 Fs 43 ). For both minerals this procedure was carried out on single-crystal X-ray diffraction data collected up to 55° 𝛉 and, for pigeonite, also on data collected in the 𝛉 range 2–28° during in situ annealing at 750 and 850°C. Leverage analysis revealed the role of certain groups of reflections in constraining some crucial variables of the structure refinement, such as atomic positions, atomic displacement parameters and site occupancies. The problem of which reflections to choose to achieve reliable results in terms of atomic coordinates and site population, and thus of Fe/Mg ordering degree, is discussed. The treatment of data collected on pigeonite during in situ annealing to induce P 2 1 / c ⟺ C 2/ c displacive phase transition is described in terms of leverage analysis. Some suggestions for correct data collection strategy and structure refinement are made.