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arXiv 1004.1202cond-mat.mtrl-scicond-mat.mes-hallphysics.comp-ph
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在原子尺度上定义接触

Defining Contact at the Atomic Scale

Shengfeng Cheng, Mark O. Robbins

摘要:

分子动力学模拟被用来研究在原子尺度上接触的不同定义。对于简单的几何形状,温度,粘附相互作用和原子结构的作用进行了研究。一种弹性的晶体衬底接触一个刚性的原子级平坦表面或球形尖端。刚性表面由相称或不相称晶体或非晶态固体形成。球形尖端是通过弯曲晶面或去除球体外的材料制成的。在连续介质理论中,当施加载荷时,原子级平面接触的比例从零急剧上升到1。这个简单的行为很难用原子尺度的接触定义来重现。由于热波动,在任何时刻接触的原子数量在很宽的负载范围内随负载线性上升。在典型温度下,需要与理想硬度相当的压力来实现完全接触。简谐平均场论提供了这种行为的定量描述,并解释了为什么原子上的瞬时力具有普遍的指数形式。接触面积也通过计算具有时间平均排斥力的原子的数量来获得。对于粘合剂相互作用,所得到的面积几乎与温度和平均间隔无关,但通常在与理想硬度相当的压力范围内从零上升到一。唯一的例外是两个相同的相称表面的情况。对于非粘性表面,如果在平均间隔$Δt$内有任何接触,则平均压力为排斥力。相关区域对$Δt$非常敏感,并且单调增长。在定义球形尖端的接触面积时遇到类似的复杂情况。

英文摘要:

Molecular dynamics simulations are used to study different definitions of contact at the atomic scale. The roles of temperature, adhesive interactions and atomic structure are studied for simple geometries. An elastic, crystalline substrate contacts a rigid, atomically flat surface or a spherical tip. The rigid surface is formed from a commensurate or incommensurate crystal or an amorphous solid. Spherical tips are made by bending crystalline planes or removing material outside a sphere. In continuum theory the fraction of atomically flat surfaces that is in contact rises sharply from zero to unity when a load is applied. This simple behavior is surprisingly difficult to reproduce with atomic scale definitions of contact. Due to thermal fluctuations, the number of atoms making contact at any instant rises linearly with load over a wide range of loads. Pressures comparable to the ideal hardness are needed to achieve full contact at typical temperatures. A simple harmonic mean-field theory provides a quantitative description of this behavior and explains why the instantaneous forces on atoms have a universal exponential form. Contact areas are also obtained by counting the number of atoms with a time-averaged repulsive force. For adhesive interactions, the resulting area is nearly independent of temperature and averaging interval, but usually rises from zero to unity over a range of pressures that is comparable to the ideal hardness. The only exception is the case of two identical commensurate surfaces. For nonadhesive surfaces, the mean pressure is repulsive if there is any contact during the averaging interval $Δt$. The associated area is very sensitive to $Δt$ and grows monotonically. Similar complications are encountered in defining contact areas for spherical tips.

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