Morphological Stability during Electrodeposition I. Steady States and Stability Analysis
Morphological Stability during Electrodeposition I. Steady States and Stability Analysis
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电沉积过程中的形态稳定性 I. 稳态和稳定性分析
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
A. Bocarsly
中科院分区：
文献类型：
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作者：
M. Haataja;D. Srolovitz;A. Bocarsly
我们开发了一种形式体系，用于预测电沉积过程中形态演变作为沉积参数、电解质组成和沉积物质的函数。我们的模型明确地将静电场与任意浓度的金属阳离子和观察者离子耦合起来。我们首先进行混合渐近分析来预测自洽、均匀、稳态静电场和浓度场。形态演化是在微扰理论的框架内进行分析的，我们围绕均匀的稳态场进行线性化。我们发现，由于扩散不稳定性，表面在长尺度上不稳定，这与之前的结果一致。此外，我们发现在固定沉积速率下增加沉积速率和电解质内的旁观者离子浓度都会增加表面粗糙度，这也与常见经验一致。我们提供了作为观察者离子浓度函数的扰动增长率的近似分析公式。这里开发的形式主义提供了一个严格的、自洽的基础，在此基础上，在配套论文中分析了添加剂对表面形态的影响。
We develop a formalism for predicting morphology evolution during electrodeposition as a function of the deposition parameters, composition of the electrolyte, and the species being deposited. Our model explicitly couples the electrostatic fields and the metal cations and spectator ions of arbitrary concentrations. We first perform a mixed asymptotics analysis to predict the self-consistent, uniform, steady-state electrostatic, and concentration fields. Morphology evolution is analyzed within the framework of perturbation theory, where we linearize around the uniform, steady-state fields. We find that the surface is unstable at long length scales due to a diffusional instability, in agreement with previous results. Furthermore, we find that both increasing the deposition rate and the spectator ion concentration within the electrolyte at fixed deposition rate increases surface roughness, also in agreement with common experience. We provide an approximate analytical formula for the perturbation growth rates as a function of the spectator ion concentration. The formalism developed here provides a rigorous, self-consistent foundation upon which the effects of additives on surface morphology are analyzed in a companion paper.