Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853-1301, USA.
Chemistry. 2013 Jul 29;19(31):10244-70. doi: 10.1002/chem.201203758. Epub 2013 Jun 18.
We review the way in which atomic tetrahedra composed of metallic elements pack naturally into fused icosahedra. Orthorhombic, hexagonal, and cubic intermetallic crystals based on this packing are all shown to be united in having pseudo-fivefold rotational diffraction symmetry. A unified geometric model involving the 600-cell is presented: the model accounts for the observed pseudo-fivefold symmetries among the different Bravais lattice types. The model accounts for vertex-, edge-, polygon-, and cell-centered fused-icosahedral clusters. Vertex-centered and edge-centered types correspond to the well-known pseudo-fivefold symmetries in Ih and D5h quasicrystalline approximants. The concept of a tetrahedrally-packed reciprocal space cluster is introduced, the vectors between sites in this cluster corresponding to the principal diffraction peaks of fused-icosahedrally-packed crystals. This reciprocal-space cluster is a direct result of the pseudosymmetry and, just as the real-space clusters, can be rationalized by the 600-cell. The reciprocal space cluster provides insights for the Jones model of metal stability. For tetrahedrally-packed crystals, Jones zone faces prove to be pseudosymmetric with one another. Lower and upper electron per atom bounds calculated for this pseudosymmetry-based Jones model are shown to accord with the observed electron counts for a variety of Group 10-12 tetrahedrally-packed structures, among which are the four known Cu/Cd intermetallic compounds: CdCu2, Cd3Cu4, Cu5Cd8, and Cu3Cd10. The rationale behind the Jones lower and upper bounds is reviewed. The crystal structure of Zn11Au15Cd23, an example of a 1:1 MacKay cubic quasicrystalline approximant based solely on Groups 10-12 elements is presented. This compound crystallizes in Im3 (space group no. 204) with a = 13.842(2) Å. The structure was solved with R1 = 3.53 %, I > 2σ; = 5.33 %, all data with 1282/0/38 data/restraints/parameters.
我们回顾了由金属元素组成的原子四面体自然堆积成熔融二十面体的方式。基于这种堆积的正交、六方和立方金属间化合物晶体都被证明具有拟五重旋转衍射对称性。提出了一个涉及 600 胞的统一几何模型：该模型解释了不同布拉维晶格类型之间观察到的拟五重对称性。该模型解释了顶点、边、多边形和胞心熔融二十面体团簇。顶点和边团簇对应于 Ih 和 D5h 准晶近晶相中熟知的拟五重对称性。引入了一个四面体堆积倒易空间团簇的概念，该团簇中的原子间矢量对应于熔融二十面体堆积晶体的主要衍射峰。这个倒易空间团簇是伪对称性的直接结果，就像实空间团簇一样，可以用 600 胞来合理化。倒易空间团簇为金属稳定性的琼斯模型提供了启示。对于四面体堆积的晶体，琼斯区面彼此证明是拟对称的。对于基于该拟对称琼斯模型的计算，每个原子的电子数下限和上限与各种 10-12 族四面体堆积结构的观察到的电子计数相符，其中包括四种已知的 Cu/Cd 金属间化合物：CdCu2、Cd3Cu4、Cu5Cd8 和 Cu3Cd10。回顾了琼斯下限和上限的原理。提出了一个仅基于 10-12 族元素的 1:1 MacKay 立方准晶近晶相 Zn11Au15Cd23 的晶体结构。该化合物在 Im3（空间群 No.204）中结晶，a = 13.842(2) ⁇ 。结构用 R1 = 3.53%、I > 2σ；= 5.33%，所有数据为 1282/0/38 数据/约束/参数。
