Abstract The paper presents a two-dimensional model of grain-boundary diffusion with consideration for triple junctions. A diffusant is assumed to come from an amorphous film containing an active component. In heating, the diffusant is transferred from the film into the crystalline material, which is composed of the two phases: grain (volume) phase and grain-boundary phase. The material structure is specified explicitly, which allows an investigation of the influence of the phase size and triple junctions on diffusion dynamics. Boundary conditions suggest a perfect contact between the phases. Consideration is given to a temperature dependence of the diffusion coefficient. A variation in temperature with time is specified explicitly. The problem is solved numerically. We plot concentration-time dependences at points of the computational domain as well as the diffusant concentration distribution over the phases to illustrate the effect of grain size on diffusion. The diffusant is found to behave nonmonotonously, accumulating and consuming, at the triple junction during diffusion. The higher the diffusion coefficient ratio between the phases and the smaller the grain, the faster the concentration variation at the triple junction.

中文翻译：

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微结构材料中的晶界扩散建模

摘要 本文提出了考虑三重结的晶界扩散二维模型。假设扩散剂来自含有活性成分的非晶膜。在加热过程中，扩散剂从薄膜转移到结晶材料中，结晶材料由两相组成：晶粒（体积）相和晶界相。材料结构被明确指定，这允许研究相尺寸和三重结对扩散动力学的影响。边界条件表明相之间的完美接触。考虑了扩散系数的温度依赖性。明确规定了温度随时间的变化。这个问题是用数值解决的。我们绘制了计算域点处的浓度-时间依赖性以及各相上的扩散剂浓度分布，以说明晶粒尺寸对扩散的影响。发现扩散剂在扩散过程中的三联结处表现为非单调、累积和消耗。相之间的扩散系数比越高且晶粒越小，三重结处的浓度变化越快。