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首页> 外文期刊>Acta Crystallographica, Section B. Structural Science >Towards a More Comprehensive Crystallography
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Towards a More Comprehensive Crystallography

机译：走向更全面的晶体学

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摘要

Despite the intrinsic difference from the point of view of structure of various types of crystals, such as commensurate, incommensurately modulated, inter-growth crystals and quasicrystals, a common approach to their symmetry seems to be possible which eventually will lead to a more comprehensive crystallography. The unifying elements become apparent through treatments which, at first, seem to be contradictory with the geometry of the crystal structures involved. Examples are the description of aperiodic crystals in terms of lattice-periodic structures (going beyond three-dimensionality), the investigation of scaling symmetry in quasicrystals by means of a H-module of translations generating a dense set of translationally equivalent atomic positions (going beyond discreteness) and finally the characterization of Euclidean properties of normal crystals through non-Euclidean symmetries (going beyond Euclidean metric). These changing approaches do not modify, however, the fundamental nature of crystals to be three-dimensional, discrete and Euclidean. They only allow implicit symmetry groups like the superspace groups (unifying the crystallography of incommensurate and commensurate crystals) and the multimetrical space groups (unifying the possible symmetries of quasicrystals and normal crystals) to be made explicit. Aspects of crystal diffraction, morphology and crystal structure are presented from this unifying point of view, without intending to cover the whole crystallography.
机译：尽管从各种类型的晶体（例如相称，不相称调制，生长间晶体和准晶体）的结构来看存在本质差异，但似乎有可能采用一种通用的对称方法，最终将导致更全面的晶体学。起初，通过似乎与所涉及的晶体结构的几何形状矛盾的处理，统一元素变得显而易见。例子是用晶格周期结构（超越三维）描述非周期性晶体，借助产生密集的平移等效原子位置的平移H-模，研究准晶体的定标对称性（超越离散性），最后通过非欧几里得对称性（超过欧几里得度量）来表征正常晶体的欧几里得性质。但是，这些不断变化的方法并没有将晶体的基本性质修改为三维，离散和欧几里得。它们仅允许明确隐含的对称组，例如超空间组（统一不相称和相称晶体的晶体学）和多度量空间组（统一准晶体和法向晶体的可能对称性）。从这种统一的观点介绍了晶体衍射，形态和晶体结构的各个方面，而无意覆盖整个晶体学。

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