Wave propagation in lattices based on Tersoff potential
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摘要: 在晶格间的Tersoff势作用下分别研究了单晶体系和多晶体系中的波动传播特性。首先，在微振动的情况下，分别基于晶格间线性作用、Tersoff势作用以及含缺陷的Tersoff势作用3种势能函数研究了单晶体系中格波的传播，得到了晶格中的色散关系以及格波波速的表达式。其次，分别以碳晶格和硅晶格为例，运用有限差分方法，研究了3种势能作用下单晶体系中的波动传播过程，对比了压缩和拉伸冲击下晶格的运动差异，并讨论了入射速度对位移峰值和受力峰值的影响，揭示了单晶体系中波动传播与连续介质中波动传播的差异。最后，分别以金刚石和碳化硅为例，采用分子动力学模拟方法，研究了多晶体系中的波动传播特性，讨论了不同空间位置原子的运动差异。结果表明：多晶体系中晶格结构更复杂，其中的波动传播特性与单晶体系存在差异；缺陷的存在对波动传播规律影响显著，这种影响在多晶体系中表现得更加突出。Abstract: The propagation characteristics of waves are the basis for studying the dynamic behavior of materials, and the theoretical study of waves in continuous media at the macro scale has been well developed. With the widespread application of materials and structures at the micro- and nano- scales, the study of wave propagation characteristics at the lattice scale is receiving increasing attention. In this article, the Tersoff potential interaction between lattices is applied to study the wave propagation characteristics in single-crystal and polycrystalline systems. Firstly, in the case of micro-vibration, the propagation of lattice waves in a single-crystal system is studied based on three potential energy functions between lattices: linear interaction, Tersoff potential, and Tersoff potential with defects. The dispersion relationship in the lattice and the expression of lattice wave velocity are obtained. Secondly, taking carbon lattice and silicon lattice as examples, the finite difference method is applied to study the wave propagation process in the single-crystal system under three potential energies. The differences in lattice motion under compressive and tensile impacts are compared, and the influence of incident velocity on the peak displacement and peak force is discussed, which reveals the difference in wave propagation between single-crystal systems and continuous media. Finally, taking diamond and silicon carbide as examples, molecular dynamics simulations are used to study the wave propagation characteristics in polycrystalline systems, and the differences in atomic motion at different spatial positions are discussed. The results indicate that the lattice structure in polycrystalline systems is more complex, and the wave propagation characteristics in polycrystalline systems are different from those in single-crystal systems. The existence of defects has a significant impact on the propagation law of waves, which is more prominent in polycrystalline systems. This study has good reference significance for the study of material dynamics performance at the micro- and nano- scales.
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Key words:
- lattice dynamics /
- micro-vibration /
- Tersoff potential /
- defect /
- molecular dynamics
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图 2 Tersoff势下角频率与波数的关系
Figure 2. Relationship between angular frequency and wavenumber under Tersoff potential
图 3 含缺陷的Tersoff势下角频率与波数的关系
Figure 3. Relationship between angular frequency and wavenumber under Tersoff potential with defects
图 4 碳晶格中势力与晶格间距的关系
Figure 4. Relationship between force and lattice spacing in carbon lattices
图 5 不同势作用下碳晶格中波的传播特性
Figure 5. Propagation characteristics of waves in carbon lattice under different potentials
图 6 压缩和拉伸过程中波形的对比
Figure 6. Comparison of waveforms during compression and stretching processes
图 7 含缺陷时压缩和拉伸过程中波形的对比
Figure 7. Comparison of waveforms during compression and stretching processes with defects
图 8 C晶格和Si晶格中波的传播特性
Figure 8. Propagation characteristics of waves in carbon lattice and silicon lattice
图 10 金刚石和碳化硅的分子动力学模型
Figure 10. Molecular dynamics models of diamond and silicon carbide
图 13 压缩和拉伸过程中金刚石中的波传播特性
Figure 13. Wave propagation characteristics of diamond during compression and stretching processes
图 14 金刚石与碳化硅中波传播过程的对比
Figure 14. Comparison of wave propagation processes in diamond and silicon carbide
图 15 多晶体系中入射速度对波传播的影响
Figure 15. Influences of incident velocity on wave propagation in polycrystalline systems
共价键种类 m1 γ λ3/Å–1 C d cosθ0 n1 C―C 3.0 1.0 0 38 049 4.348 4 –0.570 58 0.727 51 Si―Si 3.0 1.0 0 100 390 16.217 0 –0.598 25 0.787 34 共价键种类 β λ2/Å–1 B/eV R/Å D/Å λ1/Å–1 A1/eV C―C 1.572 4×10–7 2.211 90 346.70 1.95 0.15 3.487 9 1 393.6 Si―Si 1.100 0×10–6 1.732 22 471.18 2.85 0.15 2.479 9 1 830.8 
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表 2 2种晶格在平衡位置处的参数
Table 2. Parameters of two types of lattices at equilibrium positions
原子种类 摩尔质量/(g·mol−1) 平衡距离/Å 晶格常数/Å C 12 1.54 3.57 Si 28 2.35 5.43
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