Calculation of thermodynamic properties and transport coefficients of Ar-C-Si plasma

Zhu Cheng; Chen Xian-Hui; Wang Cheng; Song Ming; Xia Wei-Dong

doi:10.7498/aps.72.20222390

Abstract

The compositions, thermodynamic properties and transport coefficients of the argon-carbon-silicon plasma at local thermodynamic equilibrium and local chemical equilibrium in temperatures range of 300－30000 K and pressure range of 0.1 to 10 atm and are different mixture ratios are investigated in this work. The condensed phases and Debye-Hückel corrections are both taken into account. The equilibrium component in gas phase is calculated by mass action law (Saha’s law and Gulberg-Waage’s law), Dalton’s partial pressure law, conservation of the elements and charge quasi-neutral equation, and at the same time the condensed species is calculated under the assumption of local phase equilibrium. Thermodynamic properties including density, enthalpy and specific heat are evaluated through a classical statistical mechanics approach. The transport coefficient calculations including viscosity, electrical conductivity, and thermal conductivity are carried out by using a third-order approximation (second-order for viscosity) of the Chapman-Enskog method. Collision integrals are obtained by using the relatively new data. The results show that the concentration and ratio of blend of C vapor and Si vapor can greatly affect the properties of the Ar plasma owing to the introduced C and Si vapor’ s own properties and their new reactions. While the pressure influences those properties through the shift of chemical equilibrium and the change of total number density. In addition, the introduction of condensed species leads the thermodynamic properties and transport coefficients of the lower temperature plasma to become almost the same as those of pure argon, and causes discontinuous points at phase-transition temperature. The final calculation results are in good agreement with those in the literature, and the slight difference in transport coefficient between them can be explained by the different selection of interaction potentials. The results are expected to provide reliable basic data for the numerical simulation of argon-carbon-silicon plasma.

Keywords:

Authors and contacts

School of Engineering Science, University of Science and Technology of China, Hefei 230022, China

Corresponding author: Chen Xian-Hui, chenxian@mail.ustc.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12035015, 12075242) .

FullText HTML : translate this paragraph

References

[1]	Kim T H, Oh J H, Kim M, Hong S H, Choi S 2020 Appl. Sci. Converg. Technol. 29 117 Google Scholar
[2]	Wang C, Zhou J, Song M, Chen X, Zheng Y, Yang C, Xia W, Xia W 2022 Ceram. Int. 48 632 Google Scholar
[3]	Zhou J W, Wang C, Song M, Chen X H, Xia W D 2021 Mater. Lett. 299 130072 Google Scholar
[4]	Choi S, Lee H, Park D W 2016 J. Nanomater. 2016 5849041 Google Scholar
[5]	Okuyama H, Saito S, Uda M, Nakata T, Sakka Y 2012 J. Alloys Compd. 520 127 Google Scholar
[6]	Qadri S B, Imam M A, Feng C R, Rath B B, Yousuf M, Singh S K 2003 Appl. Phys. Lett. 83 548 Google Scholar
[7]	Rai P, Kim Y S, Kang S K, Yu Y T 2012 Plasma Chem. Plasma Process. 32 211 Google Scholar
[8]	Wan X H, Fan Y K, Ma W H, Li S Y, Huang X, Yu J 2018 Mater. Lett. 220 144 Google Scholar
[9]	Zhang X Y, Hayashida R, Tanaka M, Watanabe T 2020 Powder Technol. 371 26 Google Scholar
[10]	Zhang X Y, Liu Z S, Tanaka M, Watanabe T 2021 Chem. Eng. Sci. 230 116217 Google Scholar
[11]	Mendoza Gonzalez N Y, El Morsli M, Proulx P 2008 J. Therm. Spray Technol. 17 533 Google Scholar
[12]	Kim K S, Moradian A, Mostaghimi J, Soucy G 2009 Plasma Chem. Plasma Process. 30 91 Google Scholar
[13]	Atsuchi N, Shigeta M, Watanabe T 2006 Int. J. Heat Mass Transf. 49 1073 Google Scholar
[14]	Pan Z H, Chen X H, Yuan X, Wang C, Xia W D 2021 Plasma Chem. Plasma Process. 41 1183 Google Scholar
[15]	Colombo V, Ghedini E, Gherardi M, Sanibondi P 2013 Plasma Sources Sci. Technol. 22 035010 Google Scholar
[16]	Wang W Z, Rong M Z, Murphy A B, Wu Y, Spencer J W, Yan J D, Fang M T C 2011 J. Phys. D Appl. Phys. 44 355207 Google Scholar
[17]	Wang W Z, Yan J D, Rong M Z, Murphy A B, Spencer J W 2012 Plasma Chem. Plasma Process. 32 495 Google Scholar
[18]	Wu Y, Chen Z X, Rong M Z, Cressault Y, Yang F, Niu C P, Sun H 2016 J. Phys. D Appl. Phys. 49 405203 Google Scholar
[19]	王海兴, 孙素蓉, 陈士强 2012 61 195203 Google Scholar Wang H X, Sun S R, Chen S Q 2012 Acta Phys. Sin. 61 195203 Google Scholar
[20]	Akashi K, Tanaka Y, Nakano Y, Furukawa R, Ishijima T, Sueyasu S, Watanabe S, Nakamura K 2021 Plasma Chem. Plasma Process. 41 1121 Google Scholar
[21]	Colonna G 2019 Rend. Lincei Sci. Fis. Nat. 30 537 Google Scholar
[22]	Colonna G, D'Angola A, Pietanza L D, Capitelli M, Pirani F, Stevanato E, Laricchiuta A 2018 Plasma Sources Sci. Technol. 27 015007 Google Scholar
[23]	Devoto R S 1966 Phys. Fluids 9 1230 Google Scholar
[24]	Devoto R S 1967 Phys. Fluids 10 2105 Google Scholar
[25]	Godin D, Trepanier J Y 2004 Plasma Chem. Plasma Process. 24 447 Google Scholar
[26]	Kramida A, Ralchenko Y, Reader J, NIST ASD Team https://www.nist.gov/pml/atomic-spectra-database [2022-12-1]
[27]	Chase M W, Davies C A, Downey J R, Frurip D J, McDonald R A, Syverud A N https://janaf.nist.gov/ [2022-12-1]
[28]	André P, Bussière W, Rochette D 2007 Plasma Chem. Plasma Process. 27 381 Google Scholar
[29]	André P, Brunet L, Bussière W, Caillard J, Lombard J M, Picard J P 2004 Eur. Phys. J. Appl. Phys. 25 169 Google Scholar
[30]	Capitelli M, Cappelletti D, Colonna G, Gorse C, Laricchiuta A, Liuti G, Longo S, Pirani F 2007 Chem. Phys. 338 62 Google Scholar
[31]	Colonna G, Laricchiuta A 2008 Comput. Phys. Commun. 178 809 Google Scholar
[32]	Stallcop J R, Partridge H, Pradhan A, Levin E 2000 J. Thermophys Heat Transfer 14 480 Google Scholar
[33]	Aubreton J, Bonnefoi C, Mexmain J M 1986 Phys. Appl. Rev. 21 365 Google Scholar
[34]	Laricchiuta A, Bruno D, Capitelli M, Catalfamo C, Celiberto R, Colonna G, Diomede P, Giordano D, Gorse C, Longo S, Pagano D, Pirani F 2009 Eur. Phys. J. D 54 607 Google Scholar
[35]	Sourd B, Aubreton J, Elchinger M F, Labrot M, Michon U 2006 J. Phys. D Appl. Phys. 39 1105 Google Scholar

Cited By

图 1 不考虑凝聚态碳, 1 atm下50%Ar与50%C平衡组分随温度变化　(a) 300—8000 K; (b) 8000—30000 K

Figure 1. Temperature dependence of equilibrium composition of 50%C and 50%Ar at 1 atm, neglecting condensed carbon: (a) 300–8000 K; (b) 8000–30000 K.

DownLoad: Full-Size Img PowerPoint

图 2 不考虑凝聚态硅, 1 atm下50%Ar与50%Si平衡组分随温度变化　(a) 300—8000 K; (b) 8000—30000 K

Figure 2. Temperature dependence of equilibrium composition of 50%Ar and 50%Si at 1 atm, neglecting condensed silicon: (a) 300–8000 K; (b) 8000–30000 K.

DownLoad: Full-Size Img PowerPoint

图 3 不考虑凝聚态物种, 1 atm下50%Ar与50%SiC平衡组分随温度变化　(a) 300—8000 K; (b) 8000—30000 K

Figure 3. Temperature dependence of equilibrium composition of 50%Ar and 50%SiC at 1 atm, neglecting condensed species: (a) 300–8000 K; (b) 8000–30000 K.

DownLoad: Full-Size Img PowerPoint

图 4 考虑凝聚态物种, 1 atm下的平衡组分随温度变化　(a) 50%Ar与50%C; (b) 50%Ar与50%Si; (c) 50%Ar和50%SiC

Figure 4. Influence of condensed species on the equilibrium composition of mixtures at 1 atm: (a) 50%Ar and 50%C; (b) 50%Ar and 50%Si; (c) 50%Ar and 50%SiC.

DownLoad: Full-Size Img PowerPoint

图 5 1 atm下, 带有不同SiC浓度的Ar-SiC等离子体的焓值　(a) 300—5000 K的焓值, 考虑凝聚态物种(折线图), 忽略凝聚态物种(散点图); (b) 300—30000 K下的焓值(不考虑凝聚态物种)

Figure 5. Enthalpy of Ar-SiC plasma with different SiC concentrations at 1 atm: (a) Enthalpy at 300–30000 K, (solid lines) considering condensed species, (dotted lines) neglecting condensed species; (b) results at 300–30000 K (neglecting condensed species).

DownLoad: Full-Size Img PowerPoint

图 10 1 atm下, 50%Ar和50%不同碳硅比混合物的等离子体的定压比热　(a) 300—5000 K的焓值, 考虑凝聚态物种(折线图), 忽略凝聚态物种(散点图); (b) 300—30000 K下的结果(不考虑凝聚态物种)

Figure 10. Specific heat at constant pressure of 50%Ar and 50% mixture with different C/Si ratios at 1 atm: (a) Results at 300–5000 K, (solid lines) considering condensed species, (dotted lines) neglecting condensed species; (b) results at 300–30000 K (neglecting condensed species).

DownLoad: Full-Size Img PowerPoint

图 6 1 atm下, 带有不同SiC浓度的Ar-SiC等离子体的定压比热　(a) 300—5000 K的定压比热, 考虑凝聚态物种(折线图), 忽略凝聚态物种(散点图); (b) 300—30000 K下的结果(不考虑凝聚态物种)

Figure 6. Specific heat at constant pressure of Ar-SiC plasma with different SiC concentrations at 1 atm: (a) Results at 300–5000 K, (solid lines) considering condensed species, (dotted lines) neglecting condensed species; (b) results at 300–30000 K (neglecting condensed species).

DownLoad: Full-Size Img PowerPoint

图 7 不同气压下50%Ar-50%SiC等离子体的焓值变化曲线　(a) 300—5000 K的焓值, 考虑凝聚态物种(折线图), 忽略凝聚态物种(散点图); (b) 300—30000 K下的焓值(不考虑凝聚态物种)

Figure 7. Enthalpy of 50%Ar-50%SiC plasma at different pressures: (a) Results at 300–5000 K, (solid lines) considering condensed species, (dotted lines) neglecting condensed species; (b) results at 300–30000 K (neglecting condensed species).

DownLoad: Full-Size Img PowerPoint

图 8 在不同气压下50%Ar-50%SiC等离子体的定压比热C_p　(a) 300—5000 K的定压比热, 考虑凝聚态物种(折线图), 忽略凝聚态物种(散点图); (b) 300—30000 K下的结果(不考虑凝聚态物种)

Figure 8. Specific heat of 50%Ar-50%SiC plasma at different constant pressure: (a) Results at 300–000 K, (solid lines) considering condensed species, (dotted lines) neglecting condensed species; (b) results at 300–30000 K (neglecting condensed species).

DownLoad: Full-Size Img PowerPoint

图 9 1 atm下, 50%Ar和50%不同碳硅比混合物的等离子体的焓值　(a)300—5000 K的焓值, 考虑凝聚态物种(折线图), 忽略凝聚态物种(散点图); (b) 300—30000 K下的结果(不考虑凝聚态物种)

Figure 9. Enthalpy of 50%Ar and 50% mixture with different C/Si ratios at 1 atm: (a) Results at 300–5000 K, (solid lines) considering condensed species, (dotted lines) neglecting condensed species; (b) results at 300–30000 K (neglecting condensed species).

DownLoad: Full-Size Img PowerPoint

图 11 电导率随温度变化曲线　(a)不同压力下50%Ar+50%SiC的曲线; (b) 1 atm下不同SiC浓度的曲线; (c) 50%Ar和50%不同碳硅比混合物的曲线

Figure 11. Temperature dependence of electrical conductivity: (a) Curves of 50%Ar and 50%SiC under different pressures; (b) curves of different SiC concentrations at 1 atm; (c) curves of 50%Ar and 50% mixtures with different C/Si ratios

DownLoad: Full-Size Img PowerPoint

图 12 黏度随温度变化曲线　(a)不同压力下50%Ar+50%SiC的曲线; (b) 1 atm下不同SiC浓度的曲线; (c) 50%Ar和50%不同碳硅比混合物的曲线

Figure 12. Temperature dependence of viscosity: (a) curves of 50%Ar and 50%SiC under different pressures; (b) curves of different SiC concentrations at 1 atm; (c) curves of 50%Ar and 50% mixtures with different C/Si ratios.

DownLoad: Full-Size Img PowerPoint

图 13 热导率随温度变化曲线　(a)不同压力下50%Ar+50%SiC的曲线; (b) 1 atm下不同SiC浓度的曲线; (c) 50%Ar和50%不同碳硅比混合物的曲线; (d)总热导率(total λ)、电子平动热导率(λ_tre)、重粒子平动热导率(λ_trh)、总平动热导率(total λ_tr)、反应热导率(λ_r)随温度变化曲线

Figure 13. Temperature dependence of thermal conductivity: (a) Curves of 50%Ar and 50%SiC under different pressures; (b) curves of different SiC concentrations at 1 atm; (c) curves of 50%Ar and 50% mixtures with different C/Si ratios; (d) curves of Temperature dependence of total thermal conductivity (total λ), electron translational thermal conductivity (λ_tre), heavy species translational thermal conductivity (λ_trh), total translational thermal conductivity (total λ_tr) and reactive thermal conductivity (λ_r).

DownLoad: Full-Size Img PowerPoint

图 14 纯物质热导率随温度变化曲线

Figure 14. Temperature dependence of reactive thermal conductivity of pure substance.

DownLoad: Full-Size Img PowerPoint

表 1 计算考虑的物种

Table 1. Species considered in calculations.

元素物种

Ar Ar, Ar⁺, Ar²⁺, Ar³⁺
C C(g), C⁺, C²⁺, C³⁺, C₂, C₃, C₄, C₅, C(c)
Si Si(g), Si⁺, Si²⁺, Si³⁺, Si₂, Si₃, Si(c)
C, Si SiC(g), SiC₂, Si₂C, SiC(c)

DownLoad: CSV

表 2 部分二体相互作用势选取

Table 2. Partial selection of interaction.

弹性碰撞来源非弹性碰撞来源

C-C [32] Ar-Ar⁺ [33]
Si-C [22] Ar-Ar⁺⁺ [34]
Si-C⁺ [22] C-C⁺ [16]
Si-Si [22] C-C⁺⁺ [34]
Si-Si⁺ [22] Si-Si⁺ [22]
C⁺-C [35] Si-Si⁺⁺ [22]

DownLoad: CSV

map

[1]	Kim T H, Oh J H, Kim M, Hong S H, Choi S 2020 Appl. Sci. Converg. Technol. 29 117 Google Scholar
[2]	Wang C, Zhou J, Song M, Chen X, Zheng Y, Yang C, Xia W, Xia W 2022 Ceram. Int. 48 632 Google Scholar
[3]	Zhou J W, Wang C, Song M, Chen X H, Xia W D 2021 Mater. Lett. 299 130072 Google Scholar
[4]	Choi S, Lee H, Park D W 2016 J. Nanomater. 2016 5849041 Google Scholar
[5]	Okuyama H, Saito S, Uda M, Nakata T, Sakka Y 2012 J. Alloys Compd. 520 127 Google Scholar
[6]	Qadri S B, Imam M A, Feng C R, Rath B B, Yousuf M, Singh S K 2003 Appl. Phys. Lett. 83 548 Google Scholar
[7]	Rai P, Kim Y S, Kang S K, Yu Y T 2012 Plasma Chem. Plasma Process. 32 211 Google Scholar
[8]	Wan X H, Fan Y K, Ma W H, Li S Y, Huang X, Yu J 2018 Mater. Lett. 220 144 Google Scholar
[9]	Zhang X Y, Hayashida R, Tanaka M, Watanabe T 2020 Powder Technol. 371 26 Google Scholar
[10]	Zhang X Y, Liu Z S, Tanaka M, Watanabe T 2021 Chem. Eng. Sci. 230 116217 Google Scholar
[11]	Mendoza Gonzalez N Y, El Morsli M, Proulx P 2008 J. Therm. Spray Technol. 17 533 Google Scholar
[12]	Kim K S, Moradian A, Mostaghimi J, Soucy G 2009 Plasma Chem. Plasma Process. 30 91 Google Scholar
[13]	Atsuchi N, Shigeta M, Watanabe T 2006 Int. J. Heat Mass Transf. 49 1073 Google Scholar
[14]	Pan Z H, Chen X H, Yuan X, Wang C, Xia W D 2021 Plasma Chem. Plasma Process. 41 1183 Google Scholar
[15]	Colombo V, Ghedini E, Gherardi M, Sanibondi P 2013 Plasma Sources Sci. Technol. 22 035010 Google Scholar
[16]	Wang W Z, Rong M Z, Murphy A B, Wu Y, Spencer J W, Yan J D, Fang M T C 2011 J. Phys. D Appl. Phys. 44 355207 Google Scholar
[17]	Wang W Z, Yan J D, Rong M Z, Murphy A B, Spencer J W 2012 Plasma Chem. Plasma Process. 32 495 Google Scholar
[18]	Wu Y, Chen Z X, Rong M Z, Cressault Y, Yang F, Niu C P, Sun H 2016 J. Phys. D Appl. Phys. 49 405203 Google Scholar
[19]	王海兴, 孙素蓉, 陈士强 2012 61 195203 Google Scholar Wang H X, Sun S R, Chen S Q 2012 Acta Phys. Sin. 61 195203 Google Scholar
[20]	Akashi K, Tanaka Y, Nakano Y, Furukawa R, Ishijima T, Sueyasu S, Watanabe S, Nakamura K 2021 Plasma Chem. Plasma Process. 41 1121 Google Scholar
[21]	Colonna G 2019 Rend. Lincei Sci. Fis. Nat. 30 537 Google Scholar
[22]	Colonna G, D'Angola A, Pietanza L D, Capitelli M, Pirani F, Stevanato E, Laricchiuta A 2018 Plasma Sources Sci. Technol. 27 015007 Google Scholar
[23]	Devoto R S 1966 Phys. Fluids 9 1230 Google Scholar
[24]	Devoto R S 1967 Phys. Fluids 10 2105 Google Scholar
[25]	Godin D, Trepanier J Y 2004 Plasma Chem. Plasma Process. 24 447 Google Scholar
[26]	Kramida A, Ralchenko Y, Reader J, NIST ASD Team https://www.nist.gov/pml/atomic-spectra-database [2022-12-1]
[27]	Chase M W, Davies C A, Downey J R, Frurip D J, McDonald R A, Syverud A N https://janaf.nist.gov/ [2022-12-1]
[28]	André P, Bussière W, Rochette D 2007 Plasma Chem. Plasma Process. 27 381 Google Scholar
[29]	André P, Brunet L, Bussière W, Caillard J, Lombard J M, Picard J P 2004 Eur. Phys. J. Appl. Phys. 25 169 Google Scholar
[30]	Capitelli M, Cappelletti D, Colonna G, Gorse C, Laricchiuta A, Liuti G, Longo S, Pirani F 2007 Chem. Phys. 338 62 Google Scholar
[31]	Colonna G, Laricchiuta A 2008 Comput. Phys. Commun. 178 809 Google Scholar
[32]	Stallcop J R, Partridge H, Pradhan A, Levin E 2000 J. Thermophys Heat Transfer 14 480 Google Scholar
[33]	Aubreton J, Bonnefoi C, Mexmain J M 1986 Phys. Appl. Rev. 21 365 Google Scholar
[34]	Laricchiuta A, Bruno D, Capitelli M, Catalfamo C, Celiberto R, Colonna G, Diomede P, Giordano D, Gorse C, Longo S, Pagano D, Pirani F 2009 Eur. Phys. J. D 54 607 Google Scholar
[35]	Sourd B, Aubreton J, Elchinger M F, Labrot M, Michon U 2006 J. Phys. D Appl. Phys. 39 1105 Google Scholar

[1]	Fan Jun-Yu, Gao Nan, Wang Peng-Ju, Su Yan. Intermolecular interactions and thermodynamic properties of LLM-105. Acta Physica Sinica, 2024, 73(4): 046501. doi: 10.7498/aps.73.20231696
[2]	Hu Min-Li, Fang Fan, Fan Qun-Chao, Fan Zhi-Xiang, Li Hui-Dong, Fu Jia, Xie Feng. Theoretical study on macroscopic thermodynamic properties of NO⁺ ion system. Acta Physica Sinica, 2023, 72(16): 165101. doi: 10.7498/aps.72.20230541
[3]	Jian Jun, Lei Jiao, Fan Qun-Chao, Fan Zhi-Xiang, Ma Jie, Fu Jia, Li Hui-Dong, Xu Yong-Gen. Theoretical study on thermodynamic properties of NO gas. Acta Physica Sinica, 2020, 69(5): 053301. doi: 10.7498/aps.69.20191723
[4]	Zhao Yu-Na, Cong Hong-Lu, Cheng Shuang, Yu Na, Gao Tao, Ma Jun-Gang. First-principles study of lattice dynamical and thermodynamic properties of Li₂NH. Acta Physica Sinica, 2019, 68(13): 137102. doi: 10.7498/aps.68.20190139
[5]	Deng Shi-Jie, Zhao Yu-Hong, Hou Hua, Wen Zhi-Qin, Han Pei-De. Structural, mechanical and thermodynamic properties of Ti2AlX (X= C, N) at high pressure. Acta Physica Sinica, 2017, 66(14): 146101. doi: 10.7498/aps.66.146101
[6]	Tang Wen-Hui, Xu Bin-Bin, Ran Xian-Wen, Xu Zhi-Hong. Equations of state and thermodynamic properties of hot plasma. Acta Physica Sinica, 2017, 66(3): 030505. doi: 10.7498/aps.66.030505
[7]	Wu Ruo-Xi, Liu Dai-Jun, Yu Yang, Yang Tao. First-principles investigations on structure and thermodynamic properties of CaS under high pressures. Acta Physica Sinica, 2016, 65(2): 027101. doi: 10.7498/aps.65.027101
[8]	Men Fu-Dian, Wang Bing-Fu, He Xiao-Gang, Wei Qun-Mei. Thermodynamic properties of a weakly interacting Fermi gas in a strong magnetic field. Acta Physica Sinica, 2011, 60(8): 080501. doi: 10.7498/aps.60.080501
[9]	Li Xiao-Feng, Liu Zhong-Li, Peng Wei-Min, Zhao A-Ke. Elastic and thermodynamic properties of CaPo under pressure via first-principles calculations. Acta Physica Sinica, 2011, 60(7): 076501. doi: 10.7498/aps.60.076501
[10]	Chen Xiang-Rong, Fu Zhi-Jian, Chen Qi-Feng. Transport properties of titanium and silver plasmas in the region of partial ionization. Acta Physica Sinica, 2011, 60(5): 055202. doi: 10.7498/aps.60.055202
[11]	Li Shi-Na, Liu Yong. First-principles calculation of elastic and thermodynamic properties of copper nitride. Acta Physica Sinica, 2010, 59(10): 6882-6888. doi: 10.7498/aps.59.6882
[12]	Chen Yi, Shen Jiang. Structural and thermodynamic properties of Fe based compounds with NaZn13-type. Acta Physica Sinica, 2009, 58(13): 141-S145. doi: 10.7498/aps.58.141
[13]	Li Quan, Zhu Zheng-He. The potential energy function and thermodynamic properties of AuZn and AuAl for the ground states and low-lying excited states. Acta Physica Sinica, 2008, 57(6): 3419-3424. doi: 10.7498/aps.57.3419
[14]	Liu Na-Na, Song Ren-Bo, Sun Han-Ying, Du Da-Wei. The electronic structure and thermodynamic properties of Mg2Sn from first-principles calculations. Acta Physica Sinica, 2008, 57(11): 7145-7150. doi: 10.7498/aps.57.7145
[15]	Song Hai-Feng, Liu Hai-Feng. Theoretical study of thermodynamic properties of metal Be. Acta Physica Sinica, 2007, 56(5): 2833-2837. doi: 10.7498/aps.56.2833
[16]	Yuan Du-Qi. The influence of weak interaction on thermodynamic properties and the stability of imperfect Bose gas. Acta Physica Sinica, 2006, 55(4): 1634-1638. doi: 10.7498/aps.55.1634
[17]	Men Fu-Dian. Thermodynamic properties of a weakly interacting Fermi gas in weak magnetic field. Acta Physica Sinica, 2006, 55(4): 1622-1627. doi: 10.7498/aps.55.1622
[18]	Su Guo-Zhen, Chen Li-Xuan. Thermodynamic properties of a weakly interacting Fermi gas. Acta Physica Sinica, 2004, 53(4): 984-990. doi: 10.7498/aps.53.984
[19]	Zhang Ya-Nan, Yan Shi-Lei. Thermodynamic properties of random transverse mixed Ising spin system with cryst al field. Acta Physica Sinica, 2003, 52(11): 2890-2895. doi: 10.7498/aps.52.2890
[20]	Guo Jian-Jun. . Acta Physica Sinica, 2002, 51(3): 497-500. doi: 10.7498/aps.51.497

Catalog

Vol. 72, Issue 12 - 2023-06-20

Metrics

Abstract views: 3273
PDF Downloads: 69
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板