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The theoretical model of fcc ultrathin film

机译：FCC超薄薄膜的理论模型

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A three-dimensional lattice model is constructed to theoretically study the size effects on the elastic properties of ultrathin films with face-center-cubic crystal structure. The lattice model directly takes the discrete nature in the thickness direction into account and treats the deformations along the film plane with continuum mechanics. Only the interactions between the nearest and second nearest atoms are considered in this model and represented as harmonic springs. The constitutive relation of the ultrathin film is then derived using the energy approach and the analytical expressions of the elastic moduli of ultrathin films, including in-plane, out-plane Young's modulus and Poisson's ratio, are obtained. Moreover, the analytical expressions of ultrathin films with different crystal orientations are also formulated. It is shown that the ultrathin film along in-plane directions may be stiffer or softer than its bulk counterpart, but it is always softer along the out-plane direction. (c) 2007 Elsevier Ltd. All rights reserved.
机译：构建了三维格子模型，从理论上构建了对具有面中心立方晶体结构的超薄膜的尺寸效应。晶格模型直接在厚度方向上取得离散性，考虑并用连续式机械处理沿胶片平面的变形。在该模型中仅考虑最近和第二最近原子之间的相互作用，并表示为谐波弹簧。然后使用能量方法来衍生超薄膜的本构关系，并获得超薄膜的弹性模量的分析表达，包括在内的外平面杨氏模量和泊松比。此外，还配制了具有不同晶体取向的超薄膜的分析表达。结果表明，沿面内方向的超薄膜可以比其体对应物更易于或更柔软，但是沿外平面方向总是更柔软。 （c）2007年elestvier有限公司保留所有权利。

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