Scattering on triply periodic minimal surfaces—the effect of the topology, Debye-Waller, and molecular form factors
Scattering on triply periodic minimal surfaces—the effect of the topology, Debye-Waller, and molecular form factors
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三周期最小表面上的散射——拓扑、德拜-沃勒和分子形状因子的影响
DOI：
10.1063/1.1287426
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发表时间：
2000
影响因子：
4.4
通讯作者：
R. Hołyst
中科院分区：
文献类型：
--
作者：
P. Garstecki;R. Hołyst
我们计算四个三重周期表面（TPS）的散射模式。三个最小施瓦茨P（Im 3 m）、施瓦茨D-菱形（Pn 3 m）、Schoen G-回转体（Ia 3 d）和一个结节S1（Ia 3 d）。采用简单的近似来研究分子形状因子和Debye-Waller因子对散射图案的影响。我们发现Debye-Waller因子对TPS的散射强度的影响比对由平行表面组成的层状结构的强度的影响小得多。这是由TPS的法向量的几乎球形分布引起的。我们给出了一个简单的公式，允许比较的实验散射数据与数据的P，D，G数学表面。最后比较了具有相同空间群对称性和不同拓扑结构的两个表面G和S1的光谱。发现在更复杂的S1结构的情况下，前两个峰的强度非常小。
We compute scattering patterns for four triply periodic surfaces (TPS). Three minimal—Schwarz P (Im3m), Schwarz D—diamond (Pn3m), Schoen G—gyroid (Ia3d), and one nodal S1 (Ia3d). Simple approximations are adopted to examine the influence of the molecular form factor, and the Debye–Waller factor on the scattering pattern. We find that the Debye–Waller factor has a much smaller influence on the scattering intensities of TPS than on the intensities of the lamellar structure consisting of parallel surfaces. This is caused by an almost spherelike distribution of normal vectors for TPS. We give a simple formula that allows a comparison of the experimental scattering data with the data for the P, D, G mathematical surfaces. Finally, the spectra of the two surfaces G and S1 of the same space group symmetry and different topologies are compared. It is found that in the case of the more complex S1 structure the intensities of the first two peaks are very small.