Oishi-Tomiyasu R
High Energy Accelerator Research Organization, Tsukuba, Ibaraki, Japan.
Acta Crystallogr A. 2012 Sep;68(Pt 5):525-35. doi: 10.1107/S0108767312024579. Epub 2012 Jul 20.
A new Bravais-lattice determination algorithm is introduced herein. For error-stable Bravais-lattice determination, Andrews & Bernstein [Acta Cryst. (1988), A44, 1009-1018] proposed the use of operations to search for nearly Buerger-reduced cells. Although these operations play an essential role in their method, they increase the computation time, in particular when lattice parameters obtained in (powder) auto-indexing are supposed to contain large errors. The new algorithm requires only several permutation matrices in addition to the operations that are necessary when the lattice parameters have exact values. As a result, the computational efficiency of error-stable Bravais-lattice determination is improved considerably. Furthermore, the new method is proved to be error stable under a very general assumption. The detailed algorithms and the set of matrices sufficient for error-stable determination are presented.
本文介绍了一种新的布拉菲点阵确定算法。为了实现误差稳定的布拉菲点阵确定，安德鲁斯和伯恩斯坦[《晶体学报》(1988年)，A44，1009 - 1018]提出使用一些操作来搜索接近布尔格约化的晶胞。尽管这些操作在他们的方法中起着至关重要的作用，但它们会增加计算时间，特别是当(粉末)自动指标化中获得的晶格参数被认为包含较大误差时。新算法除了在晶格参数具有精确值时所需的操作外，只需要几个置换矩阵。因此，误差稳定的布拉菲点阵确定的计算效率得到了显著提高。此外，在非常一般的假设下，新方法被证明是误差稳定的。文中给出了详细的算法以及足以实现误差稳定确定的矩阵集。
