Crystallization in the hexagonal lattice for ionic dimers

Author:

Friedrich Manuel1,Kreutz Leonard1

Affiliation:

1. Applied Mathematics Münster, University of Münster, Einsteinstrasse 62, 48149 Münster, Germany

Abstract

We consider finite discrete systems consisting of two different atomic types and investigate ground-state configurations for configurational energies featuring two-body short-ranged particle interactions. The atomic potentials favor some reference distance between different atomic types and include repulsive terms for atoms of the same type, which are typical assumptions in models for ionic dimers. Our goal is to show a two-dimensional crystallization result. More precisely, we give conditions in order to prove that energy minimizers are connected subsets of the hexagonal lattice where the two atomic types are alternately arranged in the crystal lattice. We also provide explicit formulas for the ground-state energy. Finally, we characterize the net charge, i.e. the difference of the number of the two atomic types. Analyzing the deviation of configurations from the hexagonal Wulff shape, we prove that for ground states consisting of [Formula: see text] particles the net charge is at most of order [Formula: see text] where the scaling is sharp.

Funder

Austrian Science Fund

Vienna Science and Technology Fund

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

Cited by 11 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A Proof of Finite Crystallization via Stratification;Journal of Statistical Physics;2023-12-12

2. The double-bubble problem on the square lattice;Interfaces and Free Boundaries;2023-11-26

3. Emergence of Wulff-Crystals from Atomistic Systems on the FCC and HCP Lattices;Communications in Mathematical Physics;2023-07-10

4. Crystallinity of the Homogenized Energy Density of Periodic Lattice Systems;Multiscale Modeling & Simulation;2023-01-28

5. Effect of Periodic Arrays of Defects on Lattice Energy Minimizers;Annales Henri Poincaré;2021-03-27

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3