A mean field theory for diffusion in a dilute multi-component alloy: a new model for the effect of solutes on self-diffusion
A mean field theory for diffusion in a dilute multi-component alloy: a new model for the effect of solutes on self-diffusion
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稀多组分合金中扩散的平均场理论：溶质对自扩散影响的新模型
DOI：
10.1080/14786430500228390
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发表时间：
2005
影响因子：
1.6
通讯作者：
M. Nastar
中科院分区：
文献类型：
--
作者：
M. Nastar
本文发展了一种新的扩展自洽平均场（SCMF）理论来描述稀合金中的扩散，特别注意溶质原子存在时的自扩散问题。我们从微观模型的原子空位交换频率，包括最近邻（nn）的相互作用，并从主方程推导动力学方程。非平衡态分布函数通过与时间相关的有效相互作用来表示。它们的相互作用范围控制了第一次交换后空位路径的描述水平。与以前的扩散模型集中的合金，本配方出现在最终结果几个交换频率相关的一个给定的原子取决于附近的原子的化学物种。限制到nn有效相互作用的第一近似产生的面心立方稀二元合金的输运系数的解析表达式。的唯象系数是等效的使用五频率模型内的第一壳近似。提出了一种新的自扩散系数的表达式，并与使用相同原子扩散模型的蒙特卡罗（MC）模拟进行了比较。SCMF理论再现MC模拟的主要趋势，特别是在随机合金区域内，最近的五频模型是不满意的。SCMF方法的局限性和未来的改进很容易与所考虑的有效相互作用的范围有关
A new extension of the self-consistent mean field (SCMF) theory is developed to describe diffusion in dilute alloys, special attention being paid to the problem of self-diffusion in the presence of solute atoms. We start from a microscopic model of the atom-vacancy exchange frequency including nearest neighbour (nn) interactions and derive kinetic equations from a Master equation. The non-equilibrium distribution function is expressed through time-dependent effective interactions. Their range of interaction is controlling the level of description of the paths of a vacancy after a first exchange. In contrast to the previous diffusion models devoted to concentrated alloys, the present formulation makes appear into the final result several exchange frequencies associated to a given atom depending on the chemical species of the atoms nearby. A first approximation restricted to nn effective interactions yields analytical expressions of the transport coefficients of a face centered cubic dilute binary alloy. The phenomenological coefficients are equivalent to the ones obtained using the five-frequency model within the first shell approximation. A new expression of the self-diffusion coefficient is proposed and compared to Monte Carlo (MC) simulations using the same atomic diffusion model. The SCMF theory reproduces the main tendencies of the MC simulations, in particular within the random alloy region where the recent five-frequency model was not satisfying. The limitations and future improvements of the SCMF approach are easily related to the range of the effective interactions considered