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Simulating dislocation loop internal dynamics and collective diffusion using stochastic differential equations

机译：使用随机微分方程模拟位错环内部动力学和集体扩散

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Nanoscale prismatic loops are modeled via a partial stochastic differential equation that describes an overdamped continuum elastic string, with a view to describing both the internal and collective dynamics of the loop as a function of temperature. Within the framework of the Langevin equation, expressions are derived that relate the empirical parameters of the model, the friction per unit length, and the elastic stiffness per unit length, to observables that can be obtained directly via molecular-dynamics simulations of interstitial or vacancy prismatic loop mobility. The resulting expressions naturally exhibit the properties that the collective diffusion coefficient of the loop (I) scales inversely with the square root of the number of interstitials, a feature that has been observed in both atomistic simulation and in situ TEM investigations of loop mobility, and (ii) the collective diffusion coefficient is not at all dependent on the internal interactions within the loop, thus qualitatively rationalizing past simulation results showing that the characteristic migration energy barrier is comparable to that of a single interstitial, and cluster migration is a result of individual (but correlated) interstitial activity.
机译：纳米级棱柱形环通过描述随机阻尼的连续弹性线的偏随机微分方程建模，以描述环的内部和集体动力学随温度的变化。在Langevin方程的框架内，导出了一些表达式，这些表达式将模型的经验参数，每单位长度的摩擦力和每单位长度的弹性刚度与可以通过间隙或空位的分子动力学模拟直接获得的观测值相关联棱柱环流动性。所得表达式自然显示出环（I）的集体扩散系数与间隙数量的平方根成反比的特性，这种特性已在原子模拟和环迁移率的原位TEM研究中观察到，并且（ii）集体扩散系数完全不依赖于回路内的内部相互作用，因此定性地合理化了过去的模拟结果，表明特征迁移能垒与单个间隙的能垒相当，而簇迁移是个体的结果（但相关）间质活动。

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