硅晶体原子间相互作用力常数的计算与负热膨胀机制的研究

Calculations of the Interatomic Force Constants and Study on the Mechanism of Negative Thermal Expansion of Silicon Crystal

摘要: 本文根据Rignanese等人基于第一性原理得到的硅晶体中原子间的力常数矩阵元，计算了两体和三体线性力常数，再将这些线性力常数对原子间距求导数得两体和三体非线性力常数，在此基础上运用硅晶体的热膨胀系数公式计算了其热膨胀系数。计算结果与实验结果很好地吻合，这表明硅晶体的各个线性和非线性力常数是正确的。计算结果还表明，硅晶体的两体非线性力常数为负，两体势引起了正热膨胀，而三体非线性力常数为正，三体势引起负热膨胀，且低温时负热膨胀效应大于正热膨胀效应，因而总体上呈现低温负热膨性质。

Abstract: The two-body and three-body linear force constants in silicon crystal were calculated based on the interatomic force constant matrix elements obtained by Rignanese with the ab initio method, and then the two-body and three-body non-linear force constants were obtained by derivate the corresponding linear force constants with respect to bond length. Finally, the thermal expansion coefficients of silicon crystal were calculated based on these force constants and formula for thermal expansion coefficients of silicon crystal, and the calculated results are in good agreement with experimental results, it means that the results of all the linear and non-linear force constants are correct. It is also found that the thermal expansion caused by two-body potential is positive because of the negative two-body non-linear force constant, the thermal expansion caused by three-body potential is negative because of the positive three-body non-linear force constant, and at low temperature the total thermal expansion is negative because the absolute value of thermal expansion caused by three-body potential is greater than thermal expansion caused by two-body potential.