%0 Journal Article
%T 基于晶格动力学的硅单晶热学性质研究(IV)——数值计算与低温负热膨胀机制研究<br>Study on Thermal Properties of Silicon Single Crystal Based on Lattice Dynamics (IV)—Numerical Calculation and Study on Mechanics of Negative Thermal Expansion at Low Temperature
%A 贺业鹏
%A 黄建平
%J Applied Physics
%P 490-496
%@ 2160-7575
%D 2020
%I Hans Publishing
%R 10.12677/APP.2020.1012064
%X 本文先求解硅单晶的晶格动力学矩阵的本征值问题，得到和谐近似下的晶格振动频率和位移，然后在此基础上运用基于晶格动力学及量子力学推导得到的热膨胀系数公式进行数值计算。数值计算结果表明，硅单晶的热膨胀系数主要由两个部分构成，一部分与近邻原子间中心势能有关，提供正热膨胀系数的贡献；另一部分与近邻原子间的非中心势能有关，产生负热膨胀系数的贡献。当从温度0 K开始增加时，负热膨胀系数的增加快于正热膨胀系数的增加，因此总的热膨胀系数为负，并随温度增加负热膨胀性质更为显著；当温度超过80 K继续增加时，正热膨胀系数的增加快于负热膨胀的增加，此时虽然整体还呈现负热膨胀，但负热膨胀性质开始减弱；到约120 K温度时负热膨胀现象消失。本文还通过Rignanese等人计算得到的不同晶格常数下的线性力常数数据，发现硅单晶的三体势的三阶力常数为正，从而找到了支持我们早先提出的低温下硅单晶的负热膨胀的物理机制的直接证据。<br />
The lattice vibration frequency and displacement under harmonic approximation are obtained by solving the eigenvalue problem of lattice dynamics matrix of silicon single crystal, then the thermal expansion coefficients are calculated with the aid of the formula derived based on lattice dynamics and quantum mechanics. The numerical results show that the thermal expansion coefficient of silicon single crystal is mainly composed of two parts, one is positive, which is related to the central potential between the nearest atoms, and the other is negative, which is related to the non-central potential energy between the nearest atoms. When increasing temperature from 0K, the negative part increases faster than the positive part, so the total thermal expansion coefficient is negative and more significant with the increase of temperature; when temperature is exceeding80K, the positive part begins to increase faster than the negative part, so the negative thermal expansion property begins to weaken. At about 120 K, the negative thermal expansion disappears. With the aid of the linear force constants with different lattice constants calculated by Rignanese et al, it is found that the third order force constant of the three-body potential in silicon single crystal is positive. Thus, the direct evidence is found to support the physical mechanism of negative thermal expansion of silicon single crystal at low temperature suggested by us before.
%K 硅单晶，负热膨胀，晶格动力学，量子微扰论<br>Single Crystal Silicon
%K Negative Thermal Expansion
%K Lattice Dynamic
%K Perturbation Theory of Quantum Mechanics
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=39457