Fast grain boundary diffusion and rate-limiting surface exchange reactions in polycrystalline materials
Fast grain boundary diffusion and rate-limiting surface exchange reactions in polycrystalline materials
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DOI：
10.1063/1.1882770
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发表时间：
2005-04
影响因子：
3.2
通讯作者：
W. Preis;W. Sitte
中科院分区：
文献类型：
--
作者：
W. Preis;W. Sitte
本文给出了有限厚度多晶固体中由两个平行表面平面围成的快速晶界扩散方程的解析解。晶界扩散系数可能比体扩散系数高几个数量级。多晶样品的微观结构已被建模通过一个孤立的晶界以及平行晶界阵列。表面浓度已被假定为在扩散过程中不断变化，作为表面交换反应的扩散物种被认为是相当缓慢的和平衡之间的表面和恒定的扩散源（气相）没有达到。考虑了界面多晶样品/扩散源处的表面扩散的两种不同情况，即可忽略的和快速的表面扩散。相关的解析解允许计算薄膜中的二维扩散分布和半无限扩散系统的平均浓度分布。此外，扩散源和固体样品之间交换的扩散物种的总量的时间依赖性已被计算。的理论结果进行解释哈里森的分类的扩散制度。平行晶界模型能够计算A型和B型动力学的扩散分布。在A型动力学的情况下，提出的有效扩散系数以及有效的表面交换系数的表达式，这取决于相应的体积值，试样的微观结构，和各自的表面条件。
Analytical solutions to the diffusion equations for fast grain boundarydiffusion in polycrystalline solids of finite thickness bounded by two parallel surface planes are presented. The grain boundarydiffusion coefficient may be higher by several orders of magnitude than the bulk (volume) diffusion coefficient. The microstructure of the polycrystalline sample has been modeled by means of an isolated grain boundary as well as an array of parallel grain boundaries. The surface concentration has been assumed to vary continuously during the diffusion process, as the surfaceexchange reactions of the diffusing species are considered to be fairly slow and equilibrium between the surface and the constant diffusion source (gas phase) is not attained. Two different cases for surfacediffusion at the interfacepolycrystalline sample/diffusion source are taken into account, viz. negligible and fast surfacediffusion. The pertinent analytical solutions allow the calculation of two-dimensional diffusion profiles in thin films and average concentration profiles for semi-infinite diffusion systems. In addition, the time dependence of the total amount of diffusing species exchanged between the diffusion source and the solid sample has been calculated. The theoretical results are interpreted in terms of Harrison’s classification of diffusion regimes. The parallel grain boundary model enables the calculation of diffusion profiles for both type-A and type-B kinetics. In the case of type-A kinetics expressions for the effective diffusion coefficient as well as the effective surface exchange coefficient are proposed, which depend on the corresponding bulk values, the microstructure of the specimen, and the respective surface condition.