This work develops an analytical model to estimate the effective interfacial thermal and electrical resistances of an interface with an array of periodic microcracks between two dissimilar materials. The theoretical model and the numerical results for a Bi₂Te₃/PbTe bimaterial system indicate that the interfacial thermal and electrical resistances increase linearly with increasing crack length when the crack length per unit interface length (specific crack length) is fixed. The interfacial resistances depend strongly on the specific crack length and go to infinity when the specific crack length approaches unity. Moreover, higher thermal and electrical conductivities of the bulk dissimilar materials lead to lower interfacial resistances. Based on the developed interfacial resistance model, it is found that the influence of the microcracks at the interface between the two segments on the energy efficiency of a segmented Bi₂Te₃/PbTe thermoelectric material is insignificant when the specific crack length is not close to 1. The effects of the microcracks become pronounced when the specific crack length is close to 1.

中文翻译：

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微裂纹界面的有效界面热电阻和热电学应用

这项工作建立了一个分析模型，以估计两种异种材料之间具有周期性微裂纹阵列的界面的有效界面热阻和电阻。Bi ₂ Te ₃的理论模型和数值结果/ PbTe双材料系统表明，当每单位界面长度的裂纹长度（特定裂纹长度）固定时，界面热阻和电阻随裂纹长度的增加而线性增加。界面电阻在很大程度上取决于特定的裂纹长度，并且当特定的裂纹长度接近于一时，界面电阻将变为无穷大。而且，块状异种材料的较高的热导率和电导率导致较低的界面电阻。基于已开发的界面电阻模型，发现两段界面处的微裂纹对分段Bi ₂ Te ₃的能量效率的影响/ PbTe热电材料在比裂纹长度不接近1时微不足道。当比裂纹长度接近1时，微裂纹的影响变得明显。