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arXiv 2202.06743cond-mat.mtrl-sci
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过渡金属双硫族化合物单层膜的原子有限变形连续膜模型

An Atomistic-based Finite Deformation Continuum Membrane Model for Monolayer Transition Metal Dichalcogenides

Upendra Yadav, Susanta Ghosh

摘要:

提出了过渡金属二硫属化物(TMD)单分子膜的有限变形晶体弹性膜模型。单层TMD是具有排列在三个平行表面中的原子的多原子厚的二维(2D)结晶膜。在本公式中,TMD膜的变形配置通过其中间表面的变形图和垂直于中间表面的两个拉伸来表示。基于晶体弹性的运动学规则被用来表达的连续应变的变形键长和键角的TMD。由原子间相互作用势导出了TMD薄膜的连续超弹性应变能。在本构关系中还考虑了两个简单的TMD晶格之间的相对位移。一个光滑的有限元框架,使用B样条数值实现目前的连续膜模型。所提出的模型将纯2D膜(如石墨烯)的基于晶体弹性的膜理论推广到多原子厚的TMD晶体膜。数值结果表明了相对位移和两个正常拉伸的重要性。所提出的基于原子的连续体模型准确地匹配材料模量,复杂的后屈曲变形,和平衡能量预测的纯原子模拟。它还准确地再现了包含数千万个原子的大面积TMD样品的实验结果。

英文摘要:

A finite-deformation crystal-elasticity membrane model for Transition Metal Dichalcogenide (TMD) monolayers is presented. Monolayer TMDs are multi-atom-thick two-dimensional (2D) crystalline membranes having atoms arranged in three parallel surfaces. In the present formulation, the deformed configuration of a TMD-membrane is represented through the deformation map of its middle surface and two stretches normal to the middle surface. Crystal-elasticity based kinematic rules are employed to express the deformed bond lengths and bond angles of TMDs in terms of the continuum strains. The continuum hyper-elastic strain energy of the TMD membrane is formulated from its inter-atomic potential. The relative shifts between two simple lattices of TMDs are also considered in the constitutive relation. A smooth finite element framework using B-splines is developed to numerically implement the present continuum membrane model. The proposed model generalizes the crystal-elasticity-based membrane theory of purely 2D membranes, such as graphene, to the multi-atom-thick TMD crystalline membranes. The significance of relative shifts and two normal stretches are demonstrated through numerical results. The proposed atomistic-based continuum model accurately matches the material moduli, complex post-buckling deformations, and the equilibrium energies predicted by the purely atomistic simulations. It also accurately reproduces the experimental results for large-area TMD samples containing tens of millions of atoms.

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