Li Liang, Wölfel Alexander, Schönleber Andreas, Mondal Swastik, Schreurs Antoine M M, Kroon-Batenburg Loes M J, van Smaalen Sander
Laboratory of Crystallography, University of Bayreuth, Germany.
Acta Crystallogr B. 2011 Jun;67(Pt 3):205-17. doi: 10.1107/S0108768111013814. Epub 2011 May 14.
A combination of structure refinements, analysis of the superspace MEM density and interpretation of difference-Fourier maps has been used to characterize the incommensurate modulation of rubidium tetrachlorozincate, Rb(2)ZnCl(4), at a temperature of T = 196 K, close to the lock-in transition at T(lock-in) = 192 K. The modulation is found to consist of a combination of displacement modulation functions, modulated atomic displacement parameters (ADPs) and modulated third-order anharmonic ADPs. Up to fifth-order Fourier coefficients could be refined against diffraction data containing up to fifth-order satellite reflections. The center-of-charge of the atomic basins of the MEM density and the displacive modulation functions of the structure model provide equivalent descriptions of the displacive modulation. Modulations of the ADPs and anharmonic ADPs are visible in the MEM density, but extracting quantitative information about these modulations appears to be difficult. In the structure refinements the modulation parameters of the ADPs form a dependent set, and ad hoc restrictions had to be introduced in the refinements. It is suggested that modulated harmonic ADPs and modulated third-order anharmonic ADPs form an intrinsic part, however small, of incommensurately modulated structures in general. Refinements of alternate models with and without parameters for modulated ADPs lead to significant differences between the parameters of the displacement modulation in these two types of models, thus showing the modulation of ADPs to be important for a correct description of the displacive modulation. The resulting functions do not provide evidence for an interpretation of the modulation by a soliton model.
通过结构精修、超空间MEM密度分析和差分傅里叶图解释相结合的方法，对四氯锌酸铷（Rb₂ZnCl₄）在T = 196 K温度下的非公度调制进行了表征，该温度接近T(锁定)= 192 K时的锁定转变。发现这种调制由位移调制函数、调制原子位移参数（ADPs）和调制三阶非谐ADPs的组合组成。高达五阶的傅里叶系数可针对包含高达五阶卫星反射的衍射数据进行精修。MEM密度的原子盆地电荷中心和结构模型的位移调制函数提供了位移调制的等效描述。ADPs和非谐ADPs的调制在MEM密度中可见，但提取有关这些调制的定量信息似乎很困难。在结构精修中，ADPs的调制参数形成一个相关集，并且在精修中必须引入临时限制。有人提出，调制谐波ADPs和调制三阶非谐ADPs通常构成非公度调制结构的一个固有部分，无论其多么小。对有无调制ADPs参数的交替模型进行精修，会导致这两种类型模型中位移调制参数之间存在显著差异，从而表明ADPs的调制对于正确描述位移调制很重要。所得函数没有为用孤子模型解释调制提供证据。
