基于晶格动力学的硅单晶热学性质研究(I)——晶格动力学与比热
Study on Thermal Properties of Silicon Single Crystal Based on Lattice Dynamics (I)—Lattice Dynamics and Specific Heat
摘要: 为探究硅单晶在低温下的热学性质，本文提出了用晶格动力学进行硅单晶热学性质计算的思路，并运用他人计算得到的最近邻和次近邻原子间个数有限的相互作用力常数，推导了完整的晶格动力学力常数矩阵和晶格动力学矩阵，并求解晶格动力学矩阵的本征值问题，得到了比热与温度的关系的数值计算结果。结果表明，本文计算得到的比热与他人通过实验得到的数据吻合，因此我们推导得到的晶格动力学矩阵是正确的，从而也能用于硅单晶的其它热学性质的计算。
Abstract: In order to study the thermal properties of silicon single crystal at low temperature, this paper puts forward the idea of calculating the thermal properties of silicon single crystal by lattice dynamics. The complete lattice dynamic force constant matrix and lattice dynamic matrix are derived by using the finite number of interaction forces between the nearest neighbor atoms and the next-nearest neighbor atoms calculated by others; then the eigenvalue problem of lattice dynamics matrix is solved; and the relationship between specific heat and temperature is calculated. It is found that the specific heat calculated by us coincides with those experimental results obtained by others, so the lattice dynamic matrix derived by us is correct, and can be used to calculate the other thermal properties of silicon single crystal.
文章引用：贺业鹏, 黄建平. 基于晶格动力学的硅单晶热学性质研究(I)——晶格动力学与比热[J]. 应用物理, 2020, 10(11): 459-466. https://doi.org/10.12677/APP.2020.1011060

参考文献

[1] Hashimoto, T. and Morito, Y. (2006) Synthesis of Large Amount of Negative Thermal Expansion Oxide and Application to Controlling the Thermal Expansion of Materials. NetsuSokutei, 33, 66-73.
[2] Bauer, E. and Wu, T.Y. (1956) Thermal Expansion of a Linear Chain. Physical Review, 104, 914-915. [Google Scholar] [CrossRef] 
[3] Pishkenari, H.N., Mohagheghian, E. and Rasouli, A. (2016) Mo-lecular Dynamics Study of the Thermal Expansion Coefficient of Silicon. Physics Letters A, 380, 4039-4043. [Google Scholar] [CrossRef] 
[4] Xu, C.H., Wang, C.Z., Chan, C.T., et al. (1991) Theory of the Thermal Expansion of Si and Diamond. Physical Review B, 43, 5024-5027. [Google Scholar] [CrossRef] 
[5] Rignanese, G.M., Michenaud, J.P. and Gonze, X. (1996) Ab Initio Study of the Volume Dependence of Dynamical and Thermodynamical Properties of Silicon. Physical Review B, 53, 4488-4497. [Google Scholar] [CrossRef] 
[6] 黄建平, 胡诗一. 基于原子间相互作用的低温硅单晶负热膨胀机制的研究[J]. 原子与分子物理学报, 2014, 31(5): 851-854.
[7] 黄建平, 唐婧. 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[J]. 自然科学, 2017, 5(4): 398-403.
[8] Huang, J., Wu, X. and Li, S. (2005) Thermal Expansion Coefficients of Thin Crystal Films. Communications in Theoretical Physics, 44, 921-924. [Google Scholar] [CrossRef] 
[9] Herman, F. (1959) Lattice Vibrational Spectrum of Germanium. Journal of Physics & Chemistry of Solids, 8, 405-418. [Google Scholar] [CrossRef] 
[10] Bottger, H. (1983) Principles of the Theory of Lattice Dy-namics. Physik-Verlag, Weinheim, 15-20.
[11] Shanks, H.R., Maycock, P.D., Sidles, P.H., et al. (1963) Thermal Conductivity of Silicon from 300 to 1400˚K. Physical Review, 130, 1743-1747. [Google Scholar] [CrossRef] 
[12] Anderson, C.T. (1930) The Heat Capacity of Siliconat Low Temperature. Journal of the American Chemical Society, 52, 267-270. [Google Scholar] [CrossRef] 

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