Skjærvø Sandra Helen, Karlsen Martin A, Comin Riccardo, Billinge Simon J L
Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA.
Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, 5230 Odense M, Denmark.
IUCrJ. 2022 Sep 1;9(Pt 5):705-712. doi: 10.1107/S2052252522007680.
Structural modelling of octahedral tilts in perovskites is typically carried out using the symmetry constraints of the resulting space group. In most cases, this introduces more degrees of freedom than those strictly necessary to describe only the octahedral tilts. It can therefore be a challenge to disentangle the octahedral tilts from other structural distortions such as cation displacements and octahedral distortions. This paper reports the development of constraints for modelling pure octahedral tilts and implementation of the constraints in , a powerful package to analyse pair distribution function (PDF) data. The model in the program allows features in the PDF that come from rigid tilts to be separated from non-rigid relaxations, providing an intuitive picture of the tilting. The model has many fewer refinable variables than the unconstrained space group fits and provides robust and stable refinements of the tilt components. It further demonstrates the use of the model on the canonical tilted perovskite CaTiO which has the known Glazer tilt system αββ. The Glazer model fits comparably to the corresponding space-group model below = 14 Å and becomes progressively worse than the space-group model at higher due to non-rigid distortions in the real material.
钙钛矿中八面体倾斜的结构建模通常利用所得空间群的对称性约束来进行。在大多数情况下，这引入的自由度比仅描述八面体倾斜严格所需的自由度更多。因此，要将八面体倾斜与其他结构畸变（如阳离子位移和八面体畸变）区分开来可能具有挑战性。本文报道了用于模拟纯八面体倾斜的约束条件的开发以及这些约束条件在 中的实现， 是一个用于分析对分布函数（PDF）数据的强大软件包。该程序中的模型允许将来自刚性倾斜的PDF特征与非刚性弛豫区分开来，从而提供倾斜的直观图像。该模型的可精修变量比无约束的空间群拟合少得多，并能对倾斜分量进行稳健且稳定的精修。它进一步展示了该模型在具有已知Glazer倾斜系统αββ的典型倾斜钙钛矿CaTiO 上的应用。在 = 14 Å以下，Glazer模型与相应的空间群模型拟合效果相当，而在更高的 时，由于实际材料中的非刚性畸变，其拟合效果逐渐比空间群模型差。
