Abstract

Using asymptotic methods in the theory of differential equations, an analytical approximate solution to the problem of diffusion of interstitial atoms in a restricted medium under the condition of a constant temperature gradient is obtained. As follows from the analysis, this solution is applicable to plate samples undergoing thermal and ionic modification of one of the surfaces, whose thickness does not exceed the diffusion penetration depth of impurities, provided that a stationary temperature distribution over the thickness is established. For the certification of the proposed method, a comparison of the approximate solution with the numerical solution of the thermal diffusion problem is carried out. Conditions are obtained under which the contribution of thermal diffusion effects to the total diffusion mass transfer of the impurity is significant.

中文翻译：

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允许热扩散效应的材料表面改性过程中扩散区形成的理论

摘要

利用微分方程理论中的渐近方法，获得了在恒定温度梯度条件下间隙原子在受限介质中扩散问题的解析近似解。根据分析，该解决方案适用于对其中一个表面进行热和离子改性的板状样品，只要在该厚度上建立了固定的温度分布，其厚度就不会超过杂质的扩散渗透深度。为了验证所提出的方法，将近似解与热扩散问题的数值解进行了比较。