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arXiv 1701.07413cond-mat.mtrl-sci
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多面固体表面台阶自由能:Cu(111)表面台阶的理论和原子计算

Step free energies at faceted solid surfaces: Theory and atomistic calculations for steps on the Cu(111) surface

Rodrigo Freitas, Timofey Frolov, Mark Asta

摘要:

本文提出了一个关于多面晶体表面台阶热力学性质的理论。形式主义导致的步骤多余量的定义,包括一个多余的步骤应力,这是一个步骤的表面应力的模拟。该方法是用来开发的步骤自由能($γ^\mathrm{st}$)和步骤多余的能量和应力,可以很容易地计算出原子模拟的量的温度依赖性之间的关系。我们证明了这种形式主义的应用程序中的台阶自由能的积分(TI)计算,基于分子动力学模拟,考虑$\left< 110 \right>$步骤上的$\{111\}$表面的经典潜在模型元素铜。在本申请中,我们采用Frenkel-Ladd方法来计算TI计算的$γ^\mathrm{st}$参考值。多余的能量和应力的计算结果显示出相对较弱的温度依赖性的同源温度约为0.6,以上这些数量强烈增加,步骤应力变得更加各向同性。从计算的过量,我们计算从零到熔点($T_\mathrm{m}$)的温度范围内的$γ^\mathrm{st}$。我们发现,$γ^\mathrm{st}$保持有限的$T_\mathrm{m}$,这表明没有一个粗糙化温度为这个$\{111\}$表面刻面,但从零温度值下降了大约百分之五十。最强的温度依赖性发生以上的同源温度约0.6,其中的步骤变得构型无序,由于形成的点缺陷和明显的毛细管波动。

英文摘要:

A theory for the thermodynamic properties of steps on faceted crystalline surfaces is presented. The formalism leads to the definition of step excess quantities, including an excess step stress that is the step analogy of surface stress. The approach is used to develop a relationship between the temperature dependence of the step free energy ($γ^\mathrm{st}$) and step excess quantities for energy and stress that can be readily calculated by atomistic simulations. We demonstrate the application of this formalism in thermodynamic-integration (TI) calculations of the step free energy, based on molecular-dynamics simulations, considering $\left< 110 \right>$ steps on the $\{111\}$ surface of a classical potential model for elemental Cu. In this application we employ the Frenkel-Ladd approach to compute the reference value of $γ^\mathrm{st}$ for the TI calculations. Calculated results for excess energy and stress show relatively weak temperature dependencies up to a homologous temperature of approximately 0.6, above which these quantities increase strongly and the step stress becomes more isotropic. From the calculated excess quantities we compute $γ^\mathrm{st}$ over the temperature range from zero up to the melting point ($T_\mathrm{m}$). We find that $γ^\mathrm{st}$ remains finite up to $T_\mathrm{m}$, indicating the absence of a roughening temperature for this $\{111\}$ surface facet, but decreases by roughly fifty percent from the zero-temperature value. The strongest temperature dependence occurs above homologous temperatures of approximately 0.6, where the step becomes configurationally disordered due to the formation of point defects and appreciable capillary fluctuations.

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