Distances in the face-centered cubic crystalline structure applying operational research.

IF 1.9 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2023-09-01 DOI:10.1107/S2053273323004837

Gergely Stomfai, Gergely Kovács, Benedek Nagy, Neşet Deniz Turgay, Béla Vizvári

引用次数: 0

Abstract

The f.c.c. (face-centered cubic) grid is the structure of many crystals and minerals. It consists of four cubic lattices. It is supposed that there are two types of steps between two grid points. It is possible to step to one of the nearest neighbors of the same cubic lattice (type 1) or to step to one of the nearest neighbors of another cubic lattice (type 2). Steps belonging to the same type have the same length (weight). However, the two types have different lengths and thus may have different weights. This paper discusses the minimal path between any two points of the f.c.c. grid. The minimal paths are explicitly given, i.e. to obtain a minimal path one is required to perform only O(1) computations. The mathematical problem can be the model of different spreading phenomena in crystals having the f.c.c. structure.

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面心立方晶体结构中距离的应用运筹学研究。

面心立方网格是许多晶体和矿物的结构。它由四个立方晶格组成。假设两个网格点之间有两种步长。可以步进到同一立方体晶格的最近邻居之一(类型1)或步进到另一个立方体晶格的最近邻居之一(类型2)。属于同一类型的步具有相同的长度(权重)。然而，这两种类型具有不同的长度，因此可能具有不同的权重。本文讨论了fcc网格任意两点之间的最小路径。最小路径是显式给出的，即要获得最小路径，只需进行O(1)次计算。数学问题可以是具有fcc结构的晶体中不同扩散现象的模型。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Crystallographica Section A: Foundations and Advances CHEMISTRY, MULTIDISCIPLINARYCRYSTALLOGRAPH-CRYSTALLOGRAPHY

CiteScore

2.60

自引率

11.10%

发文量

419

期刊介绍： Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials. The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial. The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.