论文标题
晶格的二维七维差异细胞表征
An Invertible Seven-Dimensional Dirichlet Cell Characterization of Lattices
论文作者
论文摘要
晶体学晶格的表征是结构解决方案，晶体数据库搜索和衍射图像在串行晶体学中的聚类的重要工具。通常使用Niggli还原细胞（基于三个最短的非跨晶格边缘载体）或Delaunay还原的细胞（基于四个边缘向量求和到零，所有以钝角或正确的角度的汇合）来表征晶格。 Niggli细胞源自Minkowski的减少。 Delaunay细胞来自销售减少。所有这些都与晶格的Wigner-Seitz（或Dirichlet或Voronoi）单元有关，该晶体至少由这些点组成，至少与其他晶格点相比，这些点至少接近所选的晶格点。 Starting from a Niggli-reduced cell, the Dirichlet cell is characterized by the planes determined by thirteen lattice half-edges: the midpoints of the three Niggli cell edges, the six Niggli cell face diagonals and the four body-diagonals, but seven of the edge lengths are sufficient: three edge lengths, the three shorter of each pair of face-diagonal lengths and the shortest可以回收黑色的细胞长度，从中恢复了斑点。
Characterization of crystallographic lattices is an important tool in structure solution, crystallographic database searches and clustering of diffraction images in serial crystallography. Characterization of lattices by Niggli-reduced cells (based on the three shortest non-coplanar lattice edge vectors) or by Delaunay-reduced cells (based on four edge vectors summing to zero and all meeting at obtuse or right angles) are commonly used. The Niggli cell derives from Minkowski reduction. The Delaunay cell derives from Selling reduction. All are related to the Wigner-Seitz (or Dirichlet, or Voronoi) cell of the lattice, which consists of the points at least as close to a chosen lattice point than they are to any other lattice point. Starting from a Niggli-reduced cell, the Dirichlet cell is characterized by the planes determined by thirteen lattice half-edges: the midpoints of the three Niggli cell edges, the six Niggli cell face diagonals and the four body-diagonals, but seven of the edge lengths are sufficient: three edge lengths, the three shorter of each pair of face-diagonal lengths and the shortest body-diagonal length, from which the Niggli-reduced cell may be recovered.
