Latin squares as a model of perfect mixing of high-entropy alloys
Abstract
The structure of high-entropy alloys, which include 5 or more components in equimolar proportions, is proposed to be described in the mathematical language of Latin squares. This model is fundamentally discrete and allows for a quantitative description of ideal mixing, in which any given alloy element is guaranteed not to have an identical element as its nearest neighbor. For the two-dimensional case, the model possesses four axes of translational symmetry, which makes it possible to tile the plane with a single Latin square and, based on the properties of this square, describe the properties of macroscopic material samples. The model makes it possible to make quantitative estimates of the suitability of a particular atomic structure (configuration) for implementation in a perfectly mixed high-entropy alloy with maximum mixing entropy. A condition has been obtained for acceptable fluctuations in the concentration of components at which the thermodynamic stability of the alloy is maintained. The possibility of identifying superstructures in high-entropy alloys based on group theory, as applied to the description and construction of Latin squares, is discussed. Based on the proposed model, the probability of forming a multicomponent alloy with ideal mixing is estimated. For a five-component alloy, this probability is no more than 2.6*10^{-10}.
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BibTeX
@misc{grinchuk2026latin,
title = {{Latin squares as a model of perfect mixing of high-entropy alloys}},
author = {P. S. Grinchuk},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13519},
eprint = {2610.13519},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13519},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Latin squares as a model of perfect mixing of high-entropy alloys
AU - P. S. Grinchuk
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13519
UR - https://arxiv.org/abs/2610.13519
AB - The structure of high-entropy alloys, which include 5 or more components in equimolar proportions, is proposed to be described in the mathematical language of Latin squares. This model is fundamentally discrete and allows for a quantitative description of ideal mixing, in which any given alloy element is guaranteed not to have an identical element as its nearest neighbor. For the two-dimensional case, the model possesses four axes of translational symmetry, which makes it possible to tile the plane with a single Latin square and, based on the properties of this square, describe the properties of macroscopic material samples. The model makes it possible to make quantitative estimates of the suitability of a particular atomic structure (configuration) for implementation in a perfectly mixed high-entropy alloy with maximum mixing entropy. A condition has been obtained for acceptable fluctuations in the concentration of components at which the thermodynamic stability of the alloy is maintained. The possibility of identifying superstructures in high-entropy alloys based on group theory, as applied to the description and construction of Latin squares, is discussed. Based on the proposed model, the probability of forming a multicomponent alloy with ideal mixing is estimated. For a five-component alloy, this probability is no more than 2.6*10^{-10}.
ER -