圆柱微波谐振法测量氩气折射率
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摘要
氩气等单原子气体的折射率,是检验量子力学从头算理论的重要参数。基于圆柱微波谐振法,精确测量了234～303 K、0～750 k Pa范围内氩气的折射率。测量了圆柱腔内不同压力下4种横磁(TM)模式的微波谐振频率,对谐振频率进行非理想因素修正后,结合真空下的微波谐振频率获得氩气的折射率。圆柱腔内微波谐振频率测量不确定度为2×10-8,4种模式获得的氩气折射率的相对标准偏差小于1×10-6。通过氩气的折射率计算获得了氩气的第一介电维里系数,与国际上已发表的结果具有良好的一致性。基于建立的实验系统,后续可开展其他气体的折射率测量。
The refractive index of monatomic gases such as argon is an important parameter for the verification of the ab initio calculations based on quantum mechanics. The refractive index of argon from 234 K to 303 K and 0 k Pa to 750 k Pa was measured accurately using a cylindrical microwave resonator. Microwave resonance frequencies of four TM modes at different pressures in a cylindrical cavity were measured. After the correction of the non-ideal factors,the refractive index of argon was obtained by the comparison of the microwave resonance frequencies in vacuum and in gases. The uncertainty of microwave resonance frequency in the cylindrical cavity is 2 × 10-8,and the inconsistence between the argon refractive index from four modes is less than 1 × 10-6. The first dielectric virial coefficients of argon are obtained by calculating the refractive index of argon,and the results show a good agreement with the published results. The refractive index measurement of other gases can be carried out in the future using the experimental apparatus.
The refractive index of monatomic gases such as argon is an important parameter for the verification of the ab initio calculations based on quantum mechanics. The refractive index of argon from 234 K to 303 K and 0 k Pa to 750 k Pa was measured accurately using a cylindrical microwave resonator. Microwave resonance frequencies of four TM modes at different pressures in a cylindrical cavity were measured. After the correction of the non-ideal factors,the refractive index of argon was obtained by the comparison of the microwave resonance frequencies in vacuum and in gases. The uncertainty of microwave resonance frequency in the cylindrical cavity is 2 × 10-8,and the inconsistence between the argon refractive index from four modes is less than 1 × 10-6. The first dielectric virial coefficients of argon are obtained by calculating the refractive index of argon,and the results show a good agreement with the published results. The refractive index measurement of other gases can be carried out in the future using the experimental apparatus.
引文
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[19] Moldover M R,Trusler J P M,Edwards T J,et al.Measurement of the universal gas constant R using a spherical acoustic resonator[J]. Journal of Research of the National Institute of Standards and Technology,1988,93(2):85-144.
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[21] Ewing M B,Royal D D. Relative permittivities and dielectric virial coefficients of nitrogen at T=283. 401 K and T=303. 409 K determined using a cylindrical microwave cavity resonator[J]. Journal of Chemical Thermodynamics,2002,34(12):1985-1999.
[22] Goodwin A R H. Thermophysical properties from the speed of sound[D]. London:University of London,1988.
[23] Orcutt R H,Cole R H. Dielectric constants and pair interactions in argon,carbon dioxide and ethylene[J].Physica,1965,31(12):1779-1791.
[24] Moldover M R,Buckley T J. Reference Values of the Dielectric Constant of Natural Gas Components Determined with a Cross Capacitor[J]. International Journal of Thermophysics,2001,22(3):859-885.
[25] Bose T K,Cole R H. Dielectric and Pressure Virial Coefficients of Imperfect Gases. II. CO2–Argon Mixtures[J]. Journal of Chemical Physics,1970,52(1):140-147.
[26] Vidal D,Lallemand M. Evolution of the Clausius–Mossotti function of noble gases and nitrogen, at moderate and high density,near room temperature[J].Journal of Chemical Physics,1976,64(11):4293-4302.
[2]陈强华,罗会甫,王素梅,等.基于相位测量的角漂移自适应结构表面等离子体共振气体折射率测量系统[J].光学学报,2012,32(12):165-171.Chen Q H,Luo H P,Wang S M,et al. Gas Refractive Index Measurement System Based on a Surface Plasmon Resonance Sensor with Self-Adaptive Structure for Angle Shift and Phase Detection[J]. Journal of Optics,2012,32(12):165-171.
[3] Faulkner D R,Rutter E H. Comparisons of water and argon permeability in natural clay-bearing fault gouge under high pressure at 20℃[J]. Journal of Geophysical Research Solid Earth,2000,105(B7):16415-16426.
[4]徐彦德,王政平,梁艺军.用光纤测量气体折射率的研究[J].光学仪器,1994,(2):1-4.Xu Y D,Wang Z P,Ling Y J. Research on Using Optical Fiber to Measure the Refractive Index of Gas[J]. Optical Instruments,1994,(2):1-4.
[5] Rourke P M C,Hill K D. Progress toward development of low-temperature microwave refractive index gas thermometry at NRC[J]. International Journal of Thermophysics,2014,36(2-3):205-228.
[6] Aziz R A, Janzen A R, Moldover M R. Ab initio calculations for helium:A standard for transport property measurements[J]. Physical Review Letters,1995,74(9):1586-1589.
[7] Feng X J,Zhang J T,Lin H,et al. Determination of the Boltzmann constant with cylindrical acoustic gas thermometry:new and previous results combined[J].Metrologia,2017,54:748-762
[8]张凯.定程圆柱基准声学温度计研制与热力学温度测量[D].北京:清华大学,2017.
[9]崔劲,冯晓娟,林鸿,等.单圆柱微波谐振法测量热力学温度的研究[J].计量学报,2018,39(2):255-261.Cui J, Feng X J, Lin H, et al. Thermodynamic Temperature Measurement Using Single Cylindrical Microwave Resonator[J]. Acta Metrologica Sinica,2018,39(2):255-261.
[10]郑荣伟,冯晓娟,伍肆,等.近临界区二氧化碳声速的精密测量研究[J].计量学报,2017,38(1):1-6.Zheng R W,Feng X J,Wu S,et al. Sound Speed Measurement for Carbon Dioxide Near the Critical Region[J]. Acta Metrologica Sinica, 2017, 38(1):1-6.
[11] Mahmoud S F. Electromagnetic Waveguides:theory and applications[M]. London:IET Digital Library,1991.
[12] Ewing M B,Royal D D. A highly stable cylindrical microwave cavity resonator for the measurement of the relative permittivities of gases[J]. J Chem Thermodyn2002,34(7):1073-1088.
[13] Underwood R J,Mehl J B,Pitre L,et al. Waveguide effects on quasispherical microwave cavity resonators[J]. Measurement Science and Technology,2010,21(7):075103.
[14] Royal D D. Dielectric constants of simple gases determined using microwave cavity resonators[D].London:University College London,2000.
[15] Zhang K,Feng X J,Zhang J T,et al. Microwave measurements of the length and thermal expansion of a cylindrical resonator for primary acoustic gas thermometry[J]. Measurement Science and Technology,2017,28(1):6-15.
[16] Migliori A,Sarrao J L,Visscher W M,et al. Resonant ultrasound spectroscopic techniques for measurement of the elastic moduli of solids[J]. Physica B,1993,183:1-24
[17]鲍静,冯晓娟,林鸿,等.可变温的固体材料弹性参数测量系统研究[J].计量学报,2015,36(5):449-454.Bao J,Feng X J,Lin H,et al. Study on the Setup for Measurement of Temperature-dependent Elastic Properties of Solids[J]. Acta Metrologica Sinica,2015,36(5):449-454.
[18]张凯,冯晓娟,张金涛,等.声学温度计中共鸣腔精密控温技术研究[C]//第七届全国温度测量与控制技术学术会议.杭州,2015:17-20.
[19] Moldover M R,Trusler J P M,Edwards T J,et al.Measurement of the universal gas constant R using a spherical acoustic resonator[J]. Journal of Research of the National Institute of Standards and Technology,1988,93(2):85-144.
[20] Lemmon E W,Span R. Correlations Short Fundamental Equations of State for 20 Industrial Fluids[J]. Journal of Chemical&Engineering Data,2006,51(3):785-850.
[21] Ewing M B,Royal D D. Relative permittivities and dielectric virial coefficients of nitrogen at T=283. 401 K and T=303. 409 K determined using a cylindrical microwave cavity resonator[J]. Journal of Chemical Thermodynamics,2002,34(12):1985-1999.
[22] Goodwin A R H. Thermophysical properties from the speed of sound[D]. London:University of London,1988.
[23] Orcutt R H,Cole R H. Dielectric constants and pair interactions in argon,carbon dioxide and ethylene[J].Physica,1965,31(12):1779-1791.
[24] Moldover M R,Buckley T J. Reference Values of the Dielectric Constant of Natural Gas Components Determined with a Cross Capacitor[J]. International Journal of Thermophysics,2001,22(3):859-885.
[25] Bose T K,Cole R H. Dielectric and Pressure Virial Coefficients of Imperfect Gases. II. CO2–Argon Mixtures[J]. Journal of Chemical Physics,1970,52(1):140-147.
[26] Vidal D,Lallemand M. Evolution of the Clausius–Mossotti function of noble gases and nitrogen, at moderate and high density,near room temperature[J].Journal of Chemical Physics,1976,64(11):4293-4302.