Progress towards the determination of thermodynamic temperature with ultra-low uncertainty

Gavioso, R. M.; Ripa, D. Madonna; Steur, P. P. M.; Gaiser, Christof; Zandt, Thorsten; Fellmuth, B.; Podesta, Michael de; Underwood, Robin; Sutton, Gavin; Pitre, Laurent; Sparasci, F.; Risegari, L.; Gianfrani, L.; Castrillo, A.; Machin, G.

doi:10.1098/rsta.2015.0046

Cited by 28 publications

(29 citation statements)

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“…Since 1990, however, new measurements have indicated that T 90 deviates from T over a broad temperature range [3,4]. The most accurate (T − T 90 ) measurements in which R = N A k B is the molar gas constant, N A is the Avogadro constant, k B is the Boltzmann constant, T is the thermodynamic temperature, and B ρ , C ρ and D ρ are density virial coefficients.…”

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confidence: 99%

“…These measurements indicate differences between the thermodynamic temperature T and ITS-90 temperature T 90 of (T − T 90 ) = −0.60 ± 0.56 mK at T 90 = 24.5561 K, (T − T 90 ) = −2.0 ± 1.3 mK at T 90 = 54.3584 K, and (T − T 90 ) = −4.0 ± 2.9 mK at T 90 = 83.8058 K. The present results at T 90 = 24.5561 K and T 90 = 83.8058 K agree with previously reported measurements from other primary thermometry techniques of acoustic gas thermometry and dielectric constant gas thermometry, and the result at T 90 = 54.3584 K provides new information in a temperature region where there is a gap in other recent data sets.Keywords Primary thermometry · Thermodynamic temperature · T − T 90 · Polarizing gas thermometry · Refractive index gas thermometry · RIGT 1 IntroductionThe International Temperature Scale of 1990 (ITS-90) [1, 2] is a practical temperature scale used worldwide to approximate thermodynamic temperature T by ITS-90 temperature T 90 . The ITS-90 was created based on the best thermodynamic temperature measurements available in 1990, mainly those performed using the constant-volume gas thermometry (CVGT) technique.Since 1990, however, new measurements have indicated that T 90 deviates from T over a broad temperature range [3,4]. The most accurate (T − T 90 ) measurements in which R = N A k B is the molar gas constant, N A is the Avogadro constant, k B is the Boltzmann constant, T is the thermodynamic temperature, and B ρ , C ρ and D ρ are density virial coefficients.…”

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NRC Microwave Refractive Index Gas Thermometry Implementation Between 24.5 K and 84 K

Rourke

2017

Int J Thermophys

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Vous avez des questions?Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n'arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca.Access and use of this website and the material on it are subject to the Terms and Conditions set forth at NRC microwave refractive index gas thermometry implementation between 24.5 K and 84 K Rourke, P. M. C. https://publications-cnrc.canada.ca/fra/droits L'accès à ce site Web et l'utilisation de son contenu sont assujettis aux conditions présentées dans le site Abstract The implementation of microwave refractive index gas thermometry at the National Research Council between 24.5 K and 84 K is reported. A new gas-handling system for accurate control and measurement of experimental gas pressure has been constructed and primary thermometry measurements have been performed using a quasi-spherical copper resonator and helium gas at temperatures corresponding to three defining fixed points of the International Temperature Scale of 1990 (ITS-90). These measurements indicate differences between the thermodynamic temperature T and ITS-90 temperature T 90 of (T − T 90 ) = −0.60 ± 0.56 mK at T 90 = 24.5561 K, (T − T 90 ) = −2.0 ± 1.3 mK at T 90 = 54.3584 K, and (T − T 90 ) = −4.0 ± 2.9 mK at T 90 = 83.8058 K. The present results at T 90 = 24.5561 K and T 90 = 83.8058 K agree with previously reported measurements from other primary thermometry techniques of acoustic gas thermometry and dielectric constant gas thermometry, and the result at T 90 = 54.3584 K provides new information in a temperature region where there is a gap in other recent data sets.Keywords Primary thermometry · Thermodynamic temperature · T − T 90 · Polarizing gas thermometry · Refractive index gas thermometry · RIGT 1 IntroductionThe International Temperature Scale of 1990 (ITS-90) [1, 2] is a practical temperature scale used worldwide to approximate thermodynamic temperature T by ITS-90 temperature T 90 . The ITS-90 was created based on the best thermodynamic temperature measurements available in 1990, mainly those performed using the constant-volume gas thermometry (CVGT) technique.Since 1990, however, new measurements have indicated that T 90 deviates from T over a broad temperature range [3,4]. The most accurate (T − T 90 ) measurements in which R = N A k B is the molar gas constant, N A is the Avogadro constant, k B is the Boltzmann constant, T is the thermodynamic temperature, and B ρ , C ρ and D ρ are density virial coefficients. The presence of T in Eq. 4 is the key to experimentally determining the thermodynamic temperature of the gas.

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NRC Microwave Refractive Index Gas Thermometry Implementation Between 24.5 K and 84 K

Rourke

2017

Int J Thermophys

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“…Several elements of such standards will be established by ab initio quantum mechanical calculations [3][4][5][6][7]. An important theory input is the helium pair potential.…”

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Pair Potential with Submillikelvin Uncertainties and Nonadiabatic Treatment of the Halo State of the Helium Dimer

et al. 2017

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The pair potential for helium has been computed with accuracy improved by an order of magnitude relative to the best previous determination. For the well region, its uncertainties are now below 1 millikelvin. The main improvement is due to the use of explicitly correlated wave functions at the nonrelativistic Born-Oppenheimer (BO) level of theory. The diagonal BO and the relativistic corrections were obtained from large full configuration interaction calculations. The nonadiabatic perturbation theory was used to predict the properties of the halo state of helium dimer. Its binding energy and the average value of interatomic distance are found to be 138.9(5) neV and 47.13(8)Å. The binding energy agrees with its first experimental determination of 151.9(13.3) neV [Zeller et al., PNAS 113, 14651 (2016)].Helium is expected to become an important medium in determining thermodynamic metrology standards and the future system of SI units [1,2]. Several elements of such standards will be established by ab initio quantum mechanical calculations [3][4][5][6][7]. An important theory input is the helium pair potential. Its knowledge is required to account for the imperfection of helium gas and the necessary extrapolations to zero pressure [2]. The more accurate this potential is, the smaller will be the uncertainties of the resulting standards.There are other reasons of interest in the helium pair potential. The dimer composed of 4 He atoms, 4 He 2 , has a single very weakly bound vibrational state-an example of a quantum halo state-where atoms move mainly in the classically forbidden tunneling region of the configuration space [8]. This state was the subject of several experimental investigations [9][10][11][12][13][14]. We present here the development of a new potential with uncertainties reduced by an order of magnitude compared to the previous most accurate determination [15]. This potential and the nonadiabatic perturbation theory [16], accounting for the coupling of the electronic and nuclear motion, are used to obtain an accurate theoretical prediction of the properties of the halo state.The potential of Ref.[15] contained the BornOppenheimer (BO) component from Ref. [17]. Its uncertainty, amounting to several millikelvin (mK) in the well region, was due to the slow convergence of a part of the wave function expanded in terms of orbital products. Since it is impossible to converge the orbital expansion sufficiently well [18], we now follow Refs. [19,20] and expand the BO wave function using the four-electron explicitly correlated Gaussian (ECG) basis. Several improvements to the approach of Refs. [19,20] In Ref.[15], the BO potential of Ref.[17] was combined with the adiabatic (diagonal BO), relativistic, and quantum electrodynamics (QED) contributions, as well as with an appropriate retardation correction [24]. Its uncertainties were almost entirely determined by the uncertainties of the BO component. With the much improved BO potential computed in the present work, the accuracy of the adiabatic and relativistic co...

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“…[9] and [27]. This prompts even more the identification of adequate absorption models and of reliable collisional parameters for interesting DBT candidates such as CO 2 , even in the low-pressure regime here explored. L.G.…”

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“…Among primary methods, important advancements [2] have been obtained over the past decade on dielectric constant gas thermometry and Johnson noise thermometry [3,4]. After a first successful experiment of Doppler-broadening thermometry (DBT) [5], followed by significant improvements [6,7], the international community of fundamental metrology recognized the importance of an optical method that links the thermodynamic temperature to an optical frequency, as an independent confirmation of other primary approaches.…”

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Cavity-ring-down Doppler-broadening primary thermometry

et al. 2018

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A step forward in Doppler-broadening thermometry is demonstrated using a comb-assisted cavity-ring-down spectroscopic approach applied to an isolated near-infrared line of carbon dioxide at thermodynamic equilibrium. Specifically, the line-shape of the P e (12) line of the (30012) ← (00001) band of CO 2 at 1.578 µm is accurately measured and its Doppler width extracted from a refined multispectrum fitting procedure accounting for the speed dependence of the relaxation rates, which were found to play a role even at the very low pressures explored, from 1 to 7 Pa. The thermodynamic gas temperature is retrieved with relative uncertainties of 8 × 10 −6 (type A) and 11 × 10 −6 (type B), which ranks the system at the first place among optical methods. Thanks to a measurement time of only ≈5 h, the technique represents a promising pathway toward the optical determination of the thermodynamic temperature with a global uncertainty at the 10 −6 level.DOI: 10.1103/PhysRevA.97.012512The forthcoming redefinition of the unit kelvin [1], in 2018, in terms of a fixed value of the Boltzmann constant, prompts the interest for primary thermometers that are capable to operate over a relatively large part of the temperature scale with very high accuracy. Among primary methods, important advancements [2] have been obtained over the past decade on dielectric constant gas thermometry and Johnson noise thermometry [3,4]. After a first successful experiment of Doppler-broadening thermometry (DBT) [5], followed by significant improvements [6,7], the international community of fundamental metrology recognized the importance of an optical method that links the thermodynamic temperature to an optical frequency, as an independent confirmation of other primary approaches.DBT consists of retrieving the Doppler width ν D from the highly accurate observation of the shape of a given atomic or molecular line, in a laser-based absorption-spectroscopy experiment under a linear regime of radiation-matter interaction [8]. Once ν D is measured, if the central frequency (ν 0 ) and the atomic or molecular mass (M) are known, the inversion of the well-known equationallows one to determine the thermal energy and, consequently, either the gas temperature (T ) or the Boltzmann constant (k B ). So far, the most accurate implementation of DBT has been performed on a rovibrational transition of a water isotopologue at 1.39 µm. Using a dual-laser spectrometer and adopting a very sophisticated spectral analysis procedure, the Boltzmann constant could be determined with a combined uncertainty of 24 parts per million (ppm) [6,9,10].The history of DBT [11] shows that the major hurdle for a low-uncertainty determination of the Doppler width and hence of the thermal energy is the choice of the line-shape model adopted for the spectral analysis. Since a fully ab initio lineshape calculation is prohibitively complex for self-colliding molecules, a model suitable for being implemented into a fitting routine requires approximations and simplifications. At the same time, th...

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Progress towards the determination of thermodynamic temperature with ultra-low uncertainty

Cited by 28 publications

References 52 publications

NRC Microwave Refractive Index Gas Thermometry Implementation Between 24.5 K and 84 K

NRC Microwave Refractive Index Gas Thermometry Implementation Between 24.5 K and 84 K

Pair Potential with Submillikelvin Uncertainties and Nonadiabatic Treatment of the Halo State of the Helium Dimer

Cavity-ring-down Doppler-broadening primary thermometry

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