Kerman Sean, Campbell Branton J, Satyavarapu Kiran K, Stokes Harold T, Perselli Francesca, Evans John S O
Brigham Young University, Department of Physics and Astronomy, Provo, Utah 84602, USA.
Acta Crystallogr A. 2012 Mar;68(Pt 2):222-34. doi: 10.1107/S0108767311046241. Epub 2012 Jan 5.
For any crystal structure that can be viewed as a low-symmetry distortion of some higher-symmetry parent structure, one can represent the details of the distorted structure in terms of symmetry-adapted distortion modes of the parent structure rather than the traditional list of atomic xyz coordinates. Because most symmetry modes tend to be inactive, and only a relatively small number of mode amplitudes are dominant in producing the observed distortion, symmetry-mode analysis can greatly simplify the determination of a displacively distorted structure from powder diffraction data. This is an important capability when peak splittings are small, superlattice intensities are weak or systematic absences fail to distinguish between candidate symmetries. Here, the symmetry-mode basis is treated as a binary (on/off) parameter set that spans the space of all possible P1 symmetry distortions within the experimentally determined supercell. Using the average R(wp) over repeated local minimizations from random starting points as a cost function for a given mode set, global search strategies are employed to identify the active modes of the distortion. This procedure automatically yields the amplitudes of the active modes and the associated atomic coordinates. The active modes are then used to detect the space-group symmetry of the distorted phase (i.e. the type and location of each of the parent symmetry elements that remain within the distorted supercell). Once a handful of active modes are identified, traditional refinement methods readily yield their amplitudes and the resulting atomic coordinates. A final symmetry-mode refinement is then performed in the correct space-group symmetry to improve the sensitivity to any secondary modes present.
对于任何可被视为某种高对称性母结构的低对称性畸变的晶体结构，人们可以用母结构的对称适配畸变模式来表示畸变结构的细节，而不是传统的原子xyz坐标列表。由于大多数对称模式往往是不活跃的，并且在产生观测到的畸变时只有相对较少数量的模式振幅起主导作用，对称模式分析可以极大地简化从粉末衍射数据确定位移畸变结构的过程。当峰分裂小、超晶格强度弱或系统消光无法区分候选对称性时，这是一项重要的能力。在这里，对称模式基被视为一个二进制（开/关）参数集，它跨越了实验确定的超晶胞内所有可能的P1对称畸变的空间。使用从随机起始点重复局部最小化得到的平均R(wp)作为给定模式集的代价函数，采用全局搜索策略来识别畸变的活跃模式。这个过程会自动得出活跃模式的振幅和相关的原子坐标。然后，活跃模式被用于检测畸变相的空间群对称性（即畸变超晶胞内保留的每个母对称元素的类型和位置）。一旦识别出少数活跃模式，传统的精修方法很容易得出它们的振幅和由此产生的原子坐标。然后在正确的空间群对称性中进行最终的对称模式精修，以提高对任何存在的次要模式的灵敏度。
