de Gelder R, Janner A
Institute for Molecules and Materials, Radboud University Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands.
Acta Crystallogr B. 2005 Jun;61(Pt 3):287-95. doi: 10.1107/S0108768105006968. Epub 2005 May 13.
The investigation of the lattice-parameter ratios of tetrahedral and hexagonal-rhombohedral inorganic compounds, as reported by Constant & Shlichta [(2003), Acta Cryst. A59, 281-282], has been extended to the structural data found for organic and metal-organic compounds (CSD), for bio-macromolecular crystals (PDB) and for inorganic materials (ICSD). In this first part of the series, the frequency distribution of orthorhombic, tetragonal and hexagonal crystals is presented. The results obtained confirm the existence of sharp peaks as a function of the ratios of lattice parameters and reveal additional exponential components, decaying for large and small values of these ratios. Practically all the important peaks occur at ratios which correspond to lattices having metric tensors with rational entries, the so-called integral lattices. The exponential component is interpreted as expressing a general statistical distribution which is valid for the generic crystal lattices, i.e. those normally considered. The exponential fraction dominates the peaked component in the organic and metal-organic cases, is less important for bio-macromolecular crystals and is much less important than the sharp peaks for inorganic crystals. Remarkable is the crystallographic relevance of the isometric hexagonal lattice, characterized by the axial ratio c/a = 1 and first observed in the molecular form of a protein. In the frequency distribution of 12 117 inorganic hexagonal crystals, the highest peak of 937 crystals occurs for c = a. In the hexagonal case of the bio-macromolecules the most important peak of 422 crystals is observed near the ideal h.c.p. (hexagonal closed packing) ratio of (8/3)(1/2).
如康斯坦特和施利希塔[（2003年），《晶体学报》A59卷，281 - 282页]所报道的，对四面体和六方 - 菱面体无机化合物晶格参数比的研究，已扩展至有机和金属有机化合物（剑桥晶体结构数据库）、生物大分子晶体（蛋白质数据库）以及无机材料（无机晶体结构数据库）的结构数据。在本系列的第一部分，给出了正交晶系、四方晶系和六方晶系晶体的频率分布。所得结果证实了作为晶格参数比函数的尖锐峰的存在，并揭示了额外的指数成分，这些成分在这些比值的大值和小值时衰减。实际上，所有重要的峰都出现在对应于具有有理数项度量张量的晶格的比值处，即所谓的整数晶格。指数成分被解释为表达了一种对一般晶格有效的通用统计分布，即通常所考虑的那些晶格。在有机和金属有机的情况下，指数部分在峰值成分中占主导，对于生物大分子晶体不太重要，而对于无机晶体则比尖锐峰重要得多。等轴六方晶格的晶体学相关性值得注意，其特征为轴比c/a = 1，首次在一种蛋白质的分子形式中观察到。在12117个无机六方晶体的频率分布中，937个晶体的最高峰出现在c = a时。在生物大分子的六方情况中，在理想的六方密堆积（h.c.p.）比(8/3)(1/2)附近观察到422个晶体的最重要峰。
