Statistical approaches for the treatment of anharmonic motion in crystals. I. A comparison of the most frequently used formalisms of anharmonic thermal vibrations
Statistical approaches for the treatment of anharmonic motion in crystals. I. A comparison of the most frequently used formalisms of anharmonic thermal vibrations
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DOI：
10.1107/s0567739482001211
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发表时间：
1982-09
期刊：
影响因子：
--
通讯作者：
U. Zucker;H. Schulz
中科院分区：
文献类型：
--
作者：
U. Zucker;H. Schulz
已知几种非简谐运动的统计方法，但不同形式之间不存在比较。因此，本系列论文的第一部分对最常见的形式主义（势、Edgeworth 和 Gram-Charlier 展开式以及 α 形式主义）进行了相互比较。势和埃奇沃斯展开的数学缺陷可能会导致对相应概率密度和势的可疑解释。在传统的晶体学精修程序中，形式主义的效率很低。它往往收敛得很差并且计算非常耗时。其中最好的结果是 Gram-Charlier 展开式获得的，它可以很容易地扩展到六阶张量。
Several statistical approaches to anharmonic motion are known, but there exists no comparison between different formalisms. Therefore the most common formalisms (potential, Edgeworth and Gram-Charlier expansions and α formalism) are compared with each other in part I of this series of papers. Mathematical shortcomings of the potential and Edgeworth expansions may lead to doubtful interpretations of the corresponding probability densities and the potentials. The a formalism works inefficiently in conventional crystallographic refinement programs; it tends to converge badly and its computation is very time consuming. The best results of all are obtained for the Gram-Charlier expansion, which can be easily expanded to tensors up to sixth rank.