低温下替代无序合金电阻率的统计计算

Statistical Calculation of Resistivity of Substitutional Disordered Alloys at a Low Temperature

由于合金是由排列无序的两种离子所组成,每个离子的移动互相不关联,并且只具有两个稳平衡点:最稳平衡点和亚稳平衡点.本文只考虑邻近离子的相互作用,采用双能级隧道模型理论,利用通常统计方法得到了合金电阻率对离子位置的平均和对温度的热力学平均的公式.运用一定的近似处理,计算了在低温(KT1)下替代无序合金的电阻率,得到合金电阻率可表示为ρ=A+BT,即温度的一次方函数,与已有的实验结果一致.

A Model of disorder channeling is adopted in this paper. It considers that the alloy is formed by two ions that arrange in disorder,under the assumption that each ion has only two equilibrium points： the most stable equilibrium point and the metastable equilibrium point and it only considers the near-ion interaction and the movement of all ions is not associated with each other. Using the two-levels model,formula of the alloy resistivity,the statistical mean expectation for the position of ions and the thermodynamic mean expectation for temperature are obtained by statistical method. With some approximate treatment,resistivity of substitutional disordered alloys ρ,which is expressed as ρ=A＋BT,that is,which is the linear function of temperature T,is calculated at a low temperature. This result is equal that has been measured in experiment.