Discontinuous modulation functions and their application for analysis of modulated structures with the computing system JANA2006
Discontinuous modulation functions and their application for analysis of modulated structures with the computing system JANA2006
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DOI：
10.1515/zkri-2015-1913
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发表时间：
2016-05-01
影响因子：
1.2
通讯作者：
Cejchan, Antonin
中科院分区：
文献类型：
--
作者：
Petricek, Vaclav;Eigner, Vaclav;Cejchan, Antonin
提出了一种称为Crenel和锯齿形的不连续调制函数，用于描述调制参数突然变化的强调制晶体结构。虽然用于许多调制结构的精细化，并在关于非周期晶体的书籍中提到，但这种精细化的技术细节从未公布过，并且隐藏在精细化程序Jana2006的源代码中。在这篇文章中，我们解释了如何识别傅里叶映射中的不连续调制，以及如何改进其中Crenel或锯齿函数与附加二次调制相结合的结构。提出了三组适合于这种组合的函数：传统的正弦函数，以及新发展的勒让德多项式和x-调和函数集。使用模拟的和现有的调制结构演示了基于特定函数集的精化之间的微小差异。
Discontinuous modulation functions called crenel and saw-tooth have been developed for description and refinement of strongly modulated crystal structures with abrupt changes of modulation parameters. Although used for refinement of many modulated structures and mentioned in books on aperiodic crystals, technical details of such refinements have never been published and remained hidden in the source code of the refinement program Jana2006. In this article we explain how to recognize discontinuous modulations in a Fourier map and how to refine structures where crenel or saw-tooth functions are combined with additional secondary modulation. Three sets of functions suitable for such combination are presented: the traditional ortho-harmonics, and newly developed sets of Legendre polynomials and x-harmonics. Tiny differences between refinements based on particular function sets are demonstrated using simulated as well as existing modulated structures.