Interatomic potential fitting study of Ag, Si and C based on first-principle calculations
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摘要: 为了实现Ag在SiC晶体中扩散的分子动力学模拟，根据第一性原理计算结果，采用“力匹配”方法对Ag、Si和C原子间相互作用势进行拟合，并用晶格常数、内聚能、体弹性模量、弹性常数和缺陷形成能等进行了势函数的验证.结果表明，拟合所得的势对Si、C和SiC晶体的内聚能、晶格常数和体弹性模量的计算非常准确，最大误差不超过0.6%；并且，该势对Si和C晶体中空位与间隙形成能及SiC晶体中Si与C空位形成能的计算值比采用J.Tersoff给出的势的计算值更精确；此外，该势对16种AgSiC三原子体系缺陷形成能的计算也比较精确.Abstract: In order to perform molecular dynamics simulations of Ag diffusion in SiC crystals, we use "force-matching" method to fit the interatomic interaction potentials of Ag, Si and C based on first-principle calculations. The effectiveness of our obtained potential functions are verified by the calculations of the lattice constants, cohesive energies, bulk modulus, elastic constants and defect formation energies, etc. The results show that the and interstitial formation energies of Si and C crystals and Si and C vacancy formation of SiC crystals calculated by our potentials are more accurate than that calculated by J. Tersoff's potentials. In addition, the formation energies of the 16 kinds of AgSiC three-atom defect systems can also be calculated accurately by our potentials. values of cohesive energies, lattice constants and bulk modulus can be calculated precisely by our potentials, and the maximum error does not exceed 0.6%. The values of vacancies
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Key words:
- Tersoff potential /
- force-matching /
- SiC /
- first-principle calculations
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图 1 TRISO包覆颗粒燃料结构示意图
Fig. 1 The structure of Tristructural-Isotropic-coated fuel particle
图 5 Si、C和SiC晶体在不同体积下内聚能的计算值及用Murnaghan方程拟合的结果
Fig. 5 The calculated values of cohesive energies at different volumes in Si, C and SiC crystals and the Murnaghan equation fitting results of these values
表 1 Si、C和SiC晶体中各物理量的计算值
Tab. 1 The calculated values of various physical quantities in Si, C and SiC crystals
(a) Si $a$ /Å E/(eV $\cdot$ atom $^{-1}$ ) $B$ /Mbar $C_{11}$ /Mbar $C_{12}$ /Mbar $C_{44}$ /Mbar Vac/Å Int/Å exp[34-36] 5.429 -4.63 0.99 1.7 0.6 0.8 Tersoff[21] 5.432 1 -4.629 0.98 1.3 0.9 0.4 3.7 3.6 This work 5.471 9 -4.545 0.94 1.4 0.7 0.7 3.6 3.4 DFT 5.468 8 -4.545 0.89 1.5 0.6 0.7 3.7 3.8 Refa[22] 1.5 0.8 0.7 3.7 3.8 Refb[37-39] 5.451 -4.67 0.98 (b) C $a$ /Å E/(eV $\cdot$ atom $^{-1}$ ) $B$ /Mbar $C_{11}$ /Mbar $C_{12}$ /Mbar $C_{44}$ /Mbar Vac/Å Int/Å exp [36,40-41] 3.567 -7.37 4.42 10.8 1.3 5.8 Tersoff[21] 3.566 8 -7.368 4.25 10.7 1.0 6.4 3.3 18.2 This work 3.573 7 -7.773 4.37 11.2 1.0 6.7 3.6 20.4 DFT 3.574 2 -7.773 4.33 10.4 1.2 5.6 7.1 21.3 Refa[20] 10.9 1.2 6.4 Refb[42] 3.560 -7.84 4.37 7.2 23.6 (c) SiC $a$ /Å E/(eV $\cdot$ atom $^{-1}$ ) $B$ /Mbar $C_{11}$ /Mbar $C_{12}$ /Mbar $C_{44}$ /Mbar Vsi/eV Vc/eV exp[43] 4.36 -6.34 2.2 3.90 1.42 2.56 Tersoff[21] 4.321 -6.164 2.24 4.25 1.09 2.52 3.1 3.9 This work 4.374 -6.432 2.11 3.51 1.42 2.98 7.5 4.2 DFT 4.379 -6.431 2.12 3.96 1.41 2.96 7.5 4.1 Refa[21] 4.32 2.2 4.2 1.2 2.6 Refb[15] 7.4 4.4 
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表 2 Ag、Si和C的化学势
Tab. 2 Chemical potentials for Ag、Si and C
Case μSi/eV μC/eV μAg/eV γSi/eV γC/eV Si rich -5.44 -9.65 0 -0.44 Ref. [15] C rich -5.89 -9.20 -0.44 0 γSi=γC -5.76 -9.43 -0.22 -0.22 Si rich -4.545 -8.046 -2.662 0 -0.545 2 This work C rich -5.090 -7.773 -2.662 -0.545 2 0 γSi=γC -4.818 -8.046 -2.662 -0.272 6 -0.272 6
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表 3 16种缺陷体系缺陷形成能的计算值
Tab. 3 The calculated formation energies of 16 kinds of defect systems
Defect 缺陷形成能/(eV $\cdot$ atom-1) $\gamma _\mathrm {Si}=\gamma _\mathrm {C}$ Si rich C rich Ref. [15] DFT This work Ref. [15] DFT This work Ref. [15] DFT This work error Ag $_\mathrm{C}$ 7.65 7.73 7.39 7.89 7.97 7.83 7.35 7.42 0.07 Ag $_\mathrm{C}V_\mathrm{Si}$ 5.31 6.07 5.28 6.04 5.28 6.04 0.76 Ag $_\mathrm{C}2V_\mathrm{Si}$ 11.14 10.29 11.40 10.84 10.00 10.96 11.38 10.54 0.84 Ag $_\mathrm{C}V_\mathrm{Si}V_\mathrm{C}$ 8.30 6.18 8.54 6.42 8.00 5.87 2.12 Ag $_\mathrm{C}V_\mathrm{Si}$ C $_\mathrm{Si}$ 8.00 8.08 7.42 7.49 8.51 8.59 0.08 Ag $_\mathrm{C}V_\mathrm{Si}$ Si $_\mathrm{C}$ 7.54 5.23 8.06 5.74 6.97 4.65 2.31 Ag $_\mathrm{C}V_\mathrm{C}$ 8.14 12.98 8.66 13.49 7.56 12.4 4.83 Ag $T_\mathrm{C}$ 11.18 11.00 10.49 11.15 10.96 10.49 11.15 10.96 0.18 Ag $_\mathrm{Si}$ 6.35 6.49 6.60 6.05 6.18 6.16 6.59 6.73 0.14 Ag $_\mathrm{Si}V_\mathrm{C}$ 5.31 6.07 5.32 5.27 6.04 5.32 5.28 6.04 0.76 Ag $_\mathrm{Si}2V_\mathrm{C}$ 6.81 7.00 6.44 7.05 7.24 6.88 6.51 6.69 0.19 Ag $_\mathrm{Si}V_\mathrm{C}V_\mathrm{Si}$ 10.72 11.09 10.97 10.4 10.79 10.52 10.96 11.34 0.37 Ag $_\mathrm{Si}V_\mathrm{C}$ Si $_\mathrm{C}$ 7.54 5.23 7.05 8.06 5.74 7.93 6.97 4.65 2.31 Ag $_\mathrm{Si}V_\mathrm{C}$ C $_\mathrm{Si}$ 8.00 8.08 8.56 7.42 7.50 7.67 8.51 8.59 0.08 Ag $_\mathrm{Si}V_\mathrm{Si}$ 7.92 7.46 13.53 7.34 6.88 12.65 8.43 7.97 0.46 Ag $T_\mathrm{Si}$ 12.09 12.61 11.38 12.06 12.57 11.38 12.06 12.57 0.52
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表 4 Si、C和Ag原子间相互作用势参数表
Tab. 4 Interatomic potential parameters of Si, C and Ag
A/eV B/eV λ/Å-1 μ/Å-1 β n c d h S/Å R/Å Si-Si 1 830.8 471.69 2.467 2 1.726 1 1.1×10-6 0.787 34 100 390 16.217 -0.598 25 3.0 2.7 C-C 1 393.6 351.93 3.448 9 2.183 2 1.6×10-7 0.727 51 38 049 4.348 4 -0.570 58 2.1 1.8 Si-C 1 413.38 388.706 2.806 9 1.918 0 1.393×10-5 3.363 35 68 706.3 12.952 7 -0.594 85 2.51 2.21 Si-Ag 521.25 99 913.56 50.696 9 3.097 71 1.0 1.0 64 851.36 54.53 -0.374 60 3.65 3.00 C-Ag 99 173.95 99 480.55 4.330 4 1.068 3 1.0 1.0 22.64 0.089 -0.292 48 3.0 2.0 Ag-Ag 0 0 3.808 1 1.082 1 1.0 1.0 309.62 4.347 1 -0.885 72 3.1 2.7
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