Resolution of the diffusional paradox predicting infinitely fast kinetics on the nanoscale
Resolution of the diffusional paradox predicting infinitely fast kinetics on the nanoscale
复制标题
扩散悖论的解决预测纳米级无限快的动力学
DOI：
10.1103/physrevb.73.035426
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发表时间：
2006
影响因子：
3.7
通讯作者：
Z. Erdélyi
中科院分区：
文献类型：
--
作者：
D. Beke;Z. Erdélyi
在我们的论文中，我们为扩散中长期存在的悖论提供了一个自然的解决方案。我们表明，扩散区（反应层）的增长率不应该随着时间的减少而达到无穷大（如 $1∕\sqrt{t}$），因为界面的扩散渗透率是有限的。相分离二元 $A(B)$ 系统中界面位移的线性和抛物线区域之间的转换厚度 ${X}^{*}$ 的表达式是在扩散的确定性原子模型框架中导出的。 ${X}^{*}$ 通常介于 $0.01$ 和 $300\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ 之间，具体取决于扩散系数的成分依赖性和合金的相分离趋势。虽然在具有与成分无关的扩散率的理想二元合金中，实际上无法观察到与抛物线定律的偏差，但在实际系统中（其中扩散系数可以随成分变化几个数量级），预计会出现可测量的偏差，正如最近在 $\mathrm{Ni}∕\mathrm{Cu}$ 和 $\mathrm{Au}∕\mathrm{Ni}$ 系统中通过实验观察到的那样。我们还为现象学界面传递系数 $K$ 提供了原子论解释。它测量有限界面磁导率（与界面上的跳跃频率成正比），从而控制界面在短时间内的移动（扩散距离）。尽管文献中几乎完全接受线性生长动力学是界面反应控制的结果，但我们的结果表明纳米级反应层的线性或非抛物线生长不能由界面反应自动解释。
In our paper, we offer a natural resolution for a long-standing paradox in diffusion. We show that the growth rate of the diffusion zone (reaction layer) should not go to infinity with decreasing time (as $1∕\sqrt{t}$), just because the diffusion permeability of the interface is finite. Expression for the changeover thickness ${X}^{*}$ between the linear and parabolic regimes of the interface shift in phase separating binary $A(B)$ systems is derived in the framework of a deterministic atomistic model for diffusion. ${X}^{*}$ lies typically between $0.01$ and $300\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, depending on the composition dependence of the diffusion coefficient and the phase separation tendency of the alloy. While in ideal binary alloys with composition independent diffusivity, the deviation from the parabolic law practically cannot be observed, in real systems (where the diffusion coefficient can change several orders of magnitude with the composition), measurable deviations are expected as it was experimentally observed very recently in the $\mathrm{Ni}∕\mathrm{Cu}$ and $\mathrm{Au}∕\mathrm{Ni}$ systems. We also offer an atomistic explanation for the phenomenological interface transfer coefficient $K$. It measures the finite interface permeability (proportional to the jump frequency across the interface) and thus it controls the shift of the interface at short times (diffusion distances). Although it is almost exclusively accepted in the literature that linear growth kinetics are the result of interface reaction control, our results suggest that the linear or nonparabolic growth of a reaction layer on the nanoscale cannot be automatically interpreted by an interface reaction.