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Garberoglio G, Harvey AH, Lang J, Przybytek M, Lesiuk M, Jeziorski B. Path-integral calculation of the third dielectric virial coefficient of helium based on ab initio three-body polarizability and dipole surfaces. J Chem Phys 2024; 161:144111. [PMID: 39387408 DOI: 10.1063/5.0232505] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2024] [Accepted: 09/23/2024] [Indexed: 10/15/2024] Open
Abstract
We develop a surface for the electric dipole moment of three interacting helium atoms and use it with state-of-the-art potential and polarizability surfaces to compute the third dielectric virial coefficient, Cɛ, for both 4He and 3He isotopes. Our results agree with previously published data computed using an approximated form for the three-body polarizability and are extended to the low-temperature regime by including exchange effects. In addition, the uncertainty of Cɛ is rigorously determined for the first time by propagating the uncertainties of the potential and polarizability surfaces; this uncertainty is much larger than the contribution from the dipole-moment surface to Cɛ. Our results compare reasonably well with the limited experimental data. The first-principles values of Cϵ computed in this work will enhance the accuracy of primary temperature and pressure metrology based on measurements of the dielectric constant of helium.
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Affiliation(s)
- Giovanni Garberoglio
- European Centre for Theoretical Studies in Nuclear Physics and Related Areas (FBK-ECT*), Trento I-38123, Italy
- Trento Institute for Fundamental Physics and Applications (INFN-TIFPA), via Sommarive 14, 38123 Trento, Italy
| | - Allan H Harvey
- Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - Jakub Lang
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Michał Przybytek
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Michał Lesiuk
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Bogumił Jeziorski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
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2
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Binosi D, Garberoglio G, Harvey AH. Third density and acoustic virial coefficients of helium isotopologues from ab initio calculations. J Chem Phys 2024; 160:244305. [PMID: 38912675 DOI: 10.1063/5.0217852] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2024] [Accepted: 05/31/2024] [Indexed: 06/25/2024] Open
Abstract
Improved two-body and three-body potentials for helium have been used to calculate from first principles the third density and acoustic virial coefficients for both 4He and 3He. For the third density virial coefficient C(T), uncertainties have been reduced by a factor of 4-5 compared to the previous state of the art; the accuracy of first-principles C(T) now exceeds that of the best experiments by more than two orders of magnitude. The range of calculations has been extended to temperatures as low as 0.5 K. For the third acoustic virial coefficient γa(T), we applied the Schlessinger point method, which can calculate γa and its uncertainty based on the C(T) data, overcoming some limitations of direct path-integral calculation. The resulting γa are calculated at temperatures down to 0.5 K; they are consistent with available experimental data but have much smaller uncertainties. The first-principles data presented here will enable improvement of primary temperature and pressure metrology based on gas properties.
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Affiliation(s)
- Daniele Binosi
- European Centre for Theoretical Studies in Nuclear Physics and Related Areas (FBK-ECT*), Trento I-38123, Italy
| | - Giovanni Garberoglio
- European Centre for Theoretical Studies in Nuclear Physics and Related Areas (FBK-ECT*), Trento I-38123, Italy
| | - Allan H Harvey
- Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
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Forssén C, Silander I, Zakrisson J, Amer E, Szabo D, Bock T, Kussike A, Rubin T, Mari D, Pasqualin S, Silvestri Z, Bentouati D, Axner O, Zelan M. Demonstration of a Transportable Fabry-Pérot Refractometer by a Ring-Type Comparison of Dead-Weight Pressure Balances at Four European National Metrology Institutes. SENSORS (BASEL, SWITZERLAND) 2023; 24:7. [PMID: 38202866 PMCID: PMC10780598 DOI: 10.3390/s24010007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Revised: 12/12/2023] [Accepted: 12/17/2023] [Indexed: 01/12/2024]
Abstract
Fabry-Pérot-based refractometry has demonstrated the ability to assess gas pressure with high accuracy and has been prophesized to be able to realize the SI unit for pressure, the pascal, based on quantum calculations of the molar polarizabilities of gases. So far, the technology has mostly been limited to well-controlled laboratories. However, recently, an easy-to-use transportable refractometer has been constructed. Although its performance has previously been assessed under well-controlled laboratory conditions, to assess its ability to serve as an actually transportable system, a ring-type comparison addressing various well-characterized pressure balances in the 10-90 kPa range at several European national metrology institutes is presented in this work. It was found that the transportable refractometer is capable of being transported and swiftly set up to be operational with retained performance in a variety of environments. The system could also verify that the pressure balances used within the ring-type comparison agree with each other. These results constitute an important step toward broadening the application areas of FP-based refractometry technology and bringing it within reach of various types of stakeholders, not least within industry.
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Affiliation(s)
- Clayton Forssén
- Department of Physics, Umeå University, SE-901 87 Umeå, Sweden; (C.F.); (I.S.); (J.Z.); (O.A.)
- Measurement Science and Technology, RISE Research Institutes of Sweden, SE-501 15 Borås, Sweden; (E.A.); (D.S.)
| | - Isak Silander
- Department of Physics, Umeå University, SE-901 87 Umeå, Sweden; (C.F.); (I.S.); (J.Z.); (O.A.)
| | - Johan Zakrisson
- Department of Physics, Umeå University, SE-901 87 Umeå, Sweden; (C.F.); (I.S.); (J.Z.); (O.A.)
| | - Eynas Amer
- Measurement Science and Technology, RISE Research Institutes of Sweden, SE-501 15 Borås, Sweden; (E.A.); (D.S.)
| | - David Szabo
- Measurement Science and Technology, RISE Research Institutes of Sweden, SE-501 15 Borås, Sweden; (E.A.); (D.S.)
| | - Thomas Bock
- Physikalisch-Technische Bundesanstalt (PTB), Abbestr 2-12, 10587 Berlin, Germany (A.K.); (T.R.)
| | - André Kussike
- Physikalisch-Technische Bundesanstalt (PTB), Abbestr 2-12, 10587 Berlin, Germany (A.K.); (T.R.)
| | - Tom Rubin
- Physikalisch-Technische Bundesanstalt (PTB), Abbestr 2-12, 10587 Berlin, Germany (A.K.); (T.R.)
| | - Domenico Mari
- Istituto Nazionale di Ricerca Metrologica (INRiM), Strada delle Cacce 91, 10135 Turin, Italy; (D.M.); (S.P.)
| | - Stefano Pasqualin
- Istituto Nazionale di Ricerca Metrologica (INRiM), Strada delle Cacce 91, 10135 Turin, Italy; (D.M.); (S.P.)
| | - Zaccaria Silvestri
- Conservatoire National des Arts et Métiers, Laboratoire Commun de Métrologie (LNE-CNAM), 1 Rue Gaston Boissier, 75015 Paris, France;
| | - Djilali Bentouati
- Laboratoire National de Métrologie et d’Essais (LNE), 1 Rue Gaston Boissier, 75015 Paris, France;
| | - Ove Axner
- Department of Physics, Umeå University, SE-901 87 Umeå, Sweden; (C.F.); (I.S.); (J.Z.); (O.A.)
| | - Martin Zelan
- Measurement Science and Technology, RISE Research Institutes of Sweden, SE-501 15 Borås, Sweden; (E.A.); (D.S.)
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4
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Lang J, Przybytek M, Lesiuk M, Jeziorski B. Collision-induced three-body polarizability of helium. J Chem Phys 2023; 158:114303. [PMID: 36948830 DOI: 10.1063/5.0137879] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/23/2023] Open
Abstract
We present the first-principles determination of the three-body polarizability and the third dielectric virial coefficient of helium. Coupled-cluster and full configuration interaction methods were used to perform electronic structure calculations. The mean absolute relative uncertainty of the trace of the polarizability tensor, resulting from the incompleteness of the orbital basis set, was found to be 4.7%. Additional uncertainty due to the approximate treatment of triple and the neglect of higher excitations was estimated at 5.7%. An analytic function was developed to describe the short-range behavior of the polarizability and its asymptotics in all fragmentation channels. We calculated the third dielectric virial coefficient and its uncertainty using the classical and semiclassical Feynman-Hibbs approaches. The results of our calculations were compared with experimental data and with recent Path-Integral Monte Carlo (PIMC) calculations [Garberoglio et al., J. Chem. Phys. 155, 234103 (2021)] employing the so-called superposition approximation of the three-body polarizability. For temperatures above 200 K, we observed a significant discrepancy between the classical results obtained using superposition approximation and the ab initio computed polarizability. For temperatures from 10 K up to 200 K, the differences between PIMC and semiclassical calculations are several times smaller than the uncertainties of our results. Except at low temperatures, our results agree very well with the available experimental data but have much smaller uncertainties. The data reported in this work eliminate the main accuracy bottleneck in the optical pressure standard [Gaiser et al., Ann. Phys. 534, 2200336 (2022)] and facilitate further progress in the field of quantum metrology.
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Affiliation(s)
- J Lang
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - M Przybytek
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - M Lesiuk
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - B Jeziorski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
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Gambette P, Gavioso RM, Madonna Ripa D, Plimmer MD, Sparasci F, Pitre L. Toward the realization of a primary low-pressure standard using a superconducting microwave resonator. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2023; 94:035112. [PMID: 37012751 DOI: 10.1063/5.0136857] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 03/04/2023] [Indexed: 06/19/2023]
Abstract
We describe a primary gas pressure standard based on the measurement of the refractive index of helium gas using a microwave resonant cavity in the range between 500 Pa and 20 kPa. To operate in this range, the sensitivity of the microwave refractive gas manometer (MRGM) to low-pressure variations is substantially enhanced by a niobium coating of the resonator surface, which becomes superconducting at temperatures below 9 K, allowing one to achieve a frequency resolution of about 0.3 Hz at 5.2 GHz, corresponding to a pressure resolution below 3 mPa at 20 Pa. The determination of helium pressure requires precise thermometry but is favored by the remarkable accuracy achieved by ab initio calculations of the thermodynamic and electromagnetic properties of the gas. The overall standard uncertainty of the MRGM is estimated to be of the order of 0.04%, corresponding to 0.2 Pa at 500 and 8.1 Pa at 20 kPa, with major contributions from thermometry and the repeatability of microwave frequency measurements. A direct comparison of the pressures realized by the MRGM with the reference provided by a traceable quartz transducer shows relative pressure differences between 0.025% at 20 kPa and -1.4% at 500 Pa.
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Affiliation(s)
- P Gambette
- LNE-Cnam, 61 Rue du Landy, F93210 La Plaine-Saint Denis, France
| | - R M Gavioso
- Joint Research Laboratory for Fluid Metrology Evangelista Torricelli Between LNE and INRiM, France and Italy
| | - D Madonna Ripa
- Joint Research Laboratory for Fluid Metrology Evangelista Torricelli Between LNE and INRiM, France and Italy
| | - M D Plimmer
- LNE-Cnam, 61 Rue du Landy, F93210 La Plaine-Saint Denis, France
| | - F Sparasci
- LNE-Cnam, 61 Rue du Landy, F93210 La Plaine-Saint Denis, France
| | - L Pitre
- LNE-Cnam, 61 Rue du Landy, F93210 La Plaine-Saint Denis, France
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Garberoglio G, Harvey AH, Jeziorski B. Path-integral calculation of the third dielectric virial coefficient of noble gases. J Chem Phys 2021; 155:234103. [PMID: 34937356 DOI: 10.1063/5.0077684] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a rigorous framework for fully quantum calculation of the third dielectric virial coefficient Cɛ(T) of noble gases, including exchange effects. The quantum effects are taken into account with the path-integral Monte Carlo method. Calculations employing state-of-the-art pair and three-body potentials and pair polarizabilities yield results generally consistent with the few scattered experimental data available for helium, neon, and argon, but rigorous calculations with well-described uncertainties will require the development of surfaces for the three-body nonadditive polarizability and the three-body dipole moment. The framework, developed here for the first time, will enable new approaches to primary temperature and pressure metrology based on first-principles calculations of gas properties.
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Affiliation(s)
- Giovanni Garberoglio
- European Centre for Theoretical Studies in Nuclear Physics and Related Areas (FBK-ECT*), Trento I-38123, Italy
| | - Allan H Harvey
- Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - Bogumił Jeziorski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
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Garberoglio G, Harvey AH. Path-integral calculation of the fourth virial coefficient of helium isotopes. J Chem Phys 2021; 154:104107. [PMID: 33722004 PMCID: PMC8358982 DOI: 10.1063/5.0043446] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
We use the path-integral Monte Carlo (PIMC) method and state-of-the-art two-body and three-body potentials to calculate the fourth virial coefficients D(T) of 4He and 3He as functions of temperature from 2.6 K to 2000 K. We derive expressions for the contributions of exchange effects due to the bosonic or fermionic nature of the helium isotope; these effects have been omitted from previous calculations. The exchange effects are relatively insignificant for 4He at the temperatures considered, but for 3He, they are necessary for quantitative accuracy below about 4 K. Our results are consistent with previous theoretical work (also with some of the limited and scattered experimental data) for 4He; for 3He, there are no experimental values, and this work provides the first values of D(T) calculated at this level. The uncertainty of the results depends on the statistical uncertainty of the PIMC calculation, the estimated effect of omitting four-body terms in the potential energy, and the uncertainty contribution propagated from the uncertainty of the potentials. At low temperatures, the uncertainty is dominated by the statistical uncertainty of the PIMC calculations, while at high temperatures, the uncertainties related to the three-body potential and omitted higher-order contributions become dominant.
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Affiliation(s)
- Giovanni Garberoglio
- European Centre for Theoretical Studies in Nuclear Physics and Related Areas (FBK-ECT*), Trento, I-38123, Italy
- Trento Institute for Fundamental Physics and Applications (TIFPA-INFN), Trento, I-38123, Italy
| | - Allan H. Harvey
- Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, CO 80305, USA
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Ricker J, Douglass KO, Syssoev S, Stone J, Avdiaj S, Hendricks JH. Transient heating in fixed length optical cavities for use as temperature and pressure standards. METROLOGIA 2021; 58:10.1088/1681-7575/abe8e0. [PMID: 34446973 PMCID: PMC8384112 DOI: 10.1088/1681-7575/abe8e0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Optical refractometry techniques enable realization of both pressure and temperature directly from properties of the gas. The NIST refractometer, a fixed length optical cavity (FLOC) has previously been evaluated for operation as pressure standard, and now in this paper, is evaluated for the feasibility of operation as a primary temperature standard as well. The challenge is that during operation, one cavity is filled with gas. Gas dynamics predicts that this will result in heating which in turn will affect the cavity temperature uniformity, impeding the ability to measure the gas temperature with sufficient accuracy to make the standard useful as a primary standard for temperature or pressure. Temperature uniformity across the refractometer must be less than 0.5 mK for measurements of the refractivity to be sufficiently accurate for the FLOC. This paper compares computer modeling to laboratory measurements, enabling us to validate the model to predict thermal behavior and to accurately determine the measurement uncertainty of the technique. The results presented in this paper show that temperature of the glass elements of the refractometer and 'thermal-shell' copper chamber are equivalent to within 0.5 mK after an equilibration time of 3000 s (when going from 1 kPa to 100 kPa). This finding enables measurements of the copper chamber to determine the gas temperature to within an uncertainty (k = 1) of 0.5 mK. Additionally, the NIST refractometer is evaluated for feasibility of operation as temperature standard.
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Affiliation(s)
- J Ricker
- Thermodynamic Metrology Group, National Institute of Standards and Technology (NIST), Gaithersburg, MD, United States of America
| | - K O Douglass
- Thermodynamic Metrology Group, National Institute of Standards and Technology (NIST), Gaithersburg, MD, United States of America
| | - S Syssoev
- MKS Instruments, Inc, Andover, MA, United States of America
| | - J Stone
- Dimensional Metrology Group, NIST, Gaithersburg, MD, United States of America
- Retired
| | - S Avdiaj
- Department of Physics, University of Prishtina, Prishtina, Kosovo
- Guest researcher (Fulbright Scholar) at Thermodynamic Metrology Group, NIST, Gaithersburg, MD, USA
| | - J H Hendricks
- Thermodynamic Metrology Group, National Institute of Standards and Technology (NIST), Gaithersburg, MD, United States of America
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Harvey AH. What the Thermophysical Property Community Should Know about Temperature Scales. INTERNATIONAL JOURNAL OF THERMOPHYSICS 2021; 42:10.1007/s10765-021-02915-9. [PMID: 36578310 PMCID: PMC9793690 DOI: 10.1007/s10765-021-02915-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2021] [Accepted: 08/24/2021] [Indexed: 06/17/2023]
Abstract
Temperature scales have evolved through many decades in order to more accurately represent the thermodynamic temperature. This creates challenges for those who study thermophysical properties, because the temperatures given for literature data may not correspond to the latest international scale. The resulting differences are small, but not necessarily negligible, especially for reference-quality work. Here, we describe the temperature scales that might be encountered in the literature and give guidance for converting them to the International Temperature Scale of 1990 (ITS-90). We pay special attention to the liquid-helium scales used for cryogenic work, where a potentially confusing number of different scales has been used. Advice is given for avoiding common mistakes in dealing with temperature scales in the context of thermophysical property data, including the responsibility of experimentalists to fully document their reported temperatures and the responsibility of modelers to document their handling of any temperature-scale issues.
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Affiliation(s)
- Allan H Harvey
- Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, Colorado, 80305, U.S.A
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Garberoglio G, Harvey AH. Path-Integral Calculation of the Second Dielectric and Refractivity Virial Coefficients of Helium, Neon, and Argon. JOURNAL OF RESEARCH OF THE NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY 2020; 125:125022. [PMID: 39081565 PMCID: PMC11239192 DOI: 10.6028/jres.125.022] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 07/02/2020] [Indexed: 08/02/2024]
Abstract
We present a method to calculate dielectric and refractivity virial coefficients using the path-integral Monte Carlo formulation of quantum statistical mechanics and validate it by comparing our results with equivalent calculations in the literature and with more traditional quantum calculations based on wavefunctions. We use state-of-the-art pair potentials and polarizabilities to calculate the second dielectric and refractivity virial coefficients of helium (both 3He and 4He), neon (both 20Ne and 22Ne), and argon. Our calculations extend to temperatures as low as 1 K for helium, 4 K for neon, and 50 K for argon. We estimate the contributions to the uncertainty of the calculated dielectric virial coefficients for helium and argon, finding that the uncertainty of the pair polarizability is by far the greatest contribution. Agreement with the limited experimental data available is generally good, but our results have smaller uncertainties, especially for helium. Our approach can be generalized in a straightforward manner to higher-order coefficients.
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Affiliation(s)
- Giovanni Garberoglio
- European Centre for Theoretical Studies in Nuclear
Physics and Related Areas (FBK-ECT*) and Trento Institute for Fundamental Physics and
Applications (TIFPA-INFN), Trento, I-38123, Italy
| | - Allan H. Harvey
- European Centre for Theoretical Studies in Nuclear
Physics and Related Areas (FBK-ECT*) and Trento Institute for Fundamental Physics and
Applications (TIFPA-INFN), Trento, I-38123, Italy
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Harvey AH. Influence of Isotopologue Dipole Moments on Precision Dielectric-Constant Measurements. JOURNAL OF RESEARCH OF THE NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY 2019; 124:1-4. [PMID: 34877162 PMCID: PMC7339741 DOI: 10.6028/jres.124.031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 10/30/2019] [Indexed: 06/13/2023]
Abstract
Measurements of the relative permittivity (static dielectric constant) of fluids such as methane have been interpreted with the assumption of zero dipole moment. This assumption is not strictly true, due to the presence of isotopologues with small, nonzero dipole moments. We investigate the significance of this effect by analyzing the effect of the dipole of CH3D on the static dielectric constant of methane. It is found that the isotopologue effect is more than two orders of magnitude smaller than the uncertainty of the best existing measurements. Similar estimates for other compounds such as H2 and CO2 produce even smaller effects. Therefore, the interpretation of these measurements with a dipole moment of zero remains valid.
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Affiliation(s)
- Allan H Harvey
- National Institute of Standards and Technology, Boulder, CO 80305, USA
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Egan PF, Stone JA, Scherschligt JK, Harvey AH. Measured relationship between thermodynamic pressure and refractivity for six candidate gases in laser barometry. JOURNAL OF VACUUM SCIENCE & TECHNOLOGY. A, VACUUM, SURFACES, AND FILMS : AN OFFICIAL JOURNAL OF THE AMERICAN VACUUM SOCIETY 2019; 37:https://doi.org/10.1116/1.5092185. [PMID: 31555023 PMCID: PMC6760043] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Laser refractometers are approaching accuracy levels where gas pressures in the range 1 Pa < p < 1 MPa inferred by measurements of gas refractivity at a known temperature will be competitive with the best existing pressure standards and sensors. Here, the authors develop the relationship between pressure and refractivity p = c 1 ⋅ ( n - 1 ) + c 2 ⋅ ( n - 1 ) 2 + c 3 ⋅ ( n - 1 ) 3 + ⋯ , via measurement at T = 293.1529(13) K and λ = 632.9908(2) nm for p ≤ 500 kPa. The authors give values of the coefficients c 1, c 2, c 3 for six gases: Ne, Ar, Xe, N2, CO2, and N2O. For each gas, the resulting molar polarizabilityA R ≡ 2 R T 3 c 1 has a standard uncertainty within 16 × 10-6·A R . In these experiments, pressure was realized via measurements of helium refractivity at a known temperature: for He, the relationship between pressure and refractivity is known through calculation much more accurately than it can presently be measured. This feature allowed them to calibrate a pressure transducer in situ with helium and subsequently use the transducer to accurately gage the relationship between pressure and refractivity on an isotherm for other gases of interest.
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Affiliation(s)
- Patrick F. Egan
- Sensor Science Division, National Institute of Standards and Technology, 100 Bureau Dr, Gaithersburg, Maryland 20899
| | - Jack A. Stone
- Sensor Science Division, National Institute of Standards and Technology, 100 Bureau Dr, Gaithersburg, Maryland 20899
| | - Julia K. Scherschligt
- Sensor Science Division, National Institute of Standards and Technology, 100 Bureau Dr, Gaithersburg, Maryland 20899
| | - Allan H. Harvey
- Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305
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