基于原子间相互作用的低温硅单晶负热膨胀机制的研究

运用晶格热膨胀的微扰理论，推导了硅晶体的热膨胀系数与原子间两体作用和三体作用的三阶力常数之间的关系公式，在此基础上对热膨胀系数的实验数据进行拟合，计算了硅晶体内的原子间两体和三体的三阶力常数，发现三体作用的三阶力常数为正数，是硅晶体在低温下具有负热膨胀性质的根本原因。计算与分析的结果表明，运用Stillinger-Weber模型得到的三阶力常数为负数，据此不可能计算得到低温下的负热膨胀系数，因此应该对该模型进行修正。

Study on the mechanism of negative thermal expansion of silicon crystal base on the interatomic interaction

The formula to describe thermal expansion coefficient of silicon crystal in terms of the third order two-body and three-body interatomic force constants are derived based on the perturbation theory of thermal expansion, and then these interatomic force constants are obtained by fitting thermal expansion coefficients of silicon crystal with this formula. It is found that the third order three-body interatomic force constant is positive, and this is the main reason why the thermal expansion coefficient of silicon crystal is negative at low temperature. As the analysis and calculation results show, the Stillinger-Weber model for silicon crystal must be revised because the third order three-body interatomic force constant derived with this potential model is negative and the negative thermal expansion coefficient can not be obtained with this third order three-body interatomic force constant.