Direct Determination of the Boltzmann Constant by an Optical Method

Daussy, Christophe; Guinet, M.; Amy‐Klein, Anne; Djerroud, Khelifa; Hermier, Y.; Briaudeau, S.; Bordé, Christian J.; Chardonnet, Christian

doi:10.1103/physrevlett.98.250801

Cited by 133 publications

(131 citation statements)

References 13 publications

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“…Secondly, it demonstrates our ability to reach a statistical uncertainty below 10 ppm. The mean of the 02005-p.7 [29,31,32,[49][50][51] is illustrated in Figure 3. To our knowledge, 6.4 ppm represents the best statistical uncertainty ever obtained for the measurement of k B using the DBT.…”

Section: Statistical Uncertaintymentioning

confidence: 99%

Accurate determination of the Boltzmann constant by Doppler spectroscopy: Towards a new definition of the kelvin

Darquié

Mejri

Sow

et al. 2013

EPJ Web of Conferences

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Abstract. Accurate molecular spectroscopy in the mid-infrared region allows precision measurements of fundamental constants. For instance, measuring the linewidth of an isolated Doppler-broadened absorption line of ammonia around 10 m enables a determination of the Boltzmann constant k B . We report on our latest measurements. By fitting this lineshape to several models which include Dicke narrowing or speeddependent collisional effects, we find that a determination of k B with an uncertainty of a few ppm is reachable. This is comparable to the best current uncertainty obtained using acoustic methods and would make a significant contribution to any new value of k B determined by the CODATA. Furthermore, having multiple independent measurements at these accuracies opens the possibility of defining the kelvin by fixing k B , an exciting prospect considering the upcoming redefinition of the International System of Units.

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Section: Statistical Uncertaintymentioning

confidence: 99%

Accurate determination of the Boltzmann constant by Doppler spectroscopy: Towards a new definition of the kelvin

Darquié

Mejri

Sow

et al. 2013

EPJ Web of Conferences

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“…This is even the basis for proposals aiming to measure the Boltzmann constant by the Doppler broadening of a thermal gas, in view of a redefinition of the temperature scale [1].…”

Section: ~85°-885° From the Normal To The Surface And No Deviation mentioning

confidence: 99%

Testing the limits of the Maxwell distribution of velocities for atoms flying nearly parallel to the walls of a thin cell

Todorov

Bloch

2017

The Journal of Chemical Physics

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2 For a gas at thermal equilibrium, it is usually assumed that the velocity distribution follows an isotropic 3-dimensional Maxwell-Boltzmann (M-B) law. This assumption classically implies the assumption of a "cos ~85°-88.5° from the normal to the surface and no deviation from the M-B law is found within the limits of our elementary set-up. Finally we suggest tracks to explore more parallel velocities, when surface details -roughness or structureand the atom-surface interaction should play a key role to restrict the applicability of a M-B-type distribution.3 I. The Maxwell-Boltzmann distribution of atomic velocities in a dilute gas and the signature of atoms moving close to a wall container.It is usually unquestioned, in the field of Atomic and Molecular Physics, that the atomic velocity distribution in a gas at thermal equilibrium is governed by a MaxwellBoltzmann (M-B) distribution for kinetic energy, with a 3-dimensional isotropy. This is even the basis for proposals aiming to measure the Boltzmann constant by the Doppler broadening of a thermal gas, in view of a redefinition of the temperature scale [1].However, in the vicinity of a wall, the isotropy is locally lost in a region, often called the Knudsen layer [2], where the atom-wall collisions modify the behavior of the gas. The microscopic description of an atom-surface collision or interaction is a rich field, which has been addressed experimentally for a long time. The possibility of a velocity distribution depending upon the vessel shape, has been sometimes considered, although the proofs for self-consistency seem delicate [3]. Despite the variety of behaviors found microscopically at the frontier of the gas, it remains usually assumed that the overall gas behavior obeys a M-B distribution (see e.g. [4]).As recalled in detail in the review by Comsa and David [5], which includes a significant historical approach, the distribution of atomic velocities established by Maxwell for an isotropic volume of a gas with molecules undergoing numerous collisions (the basis for the ideal gas kinetics) has been founded upon questionable hypotheses concerning the effect of the surface. The Maxwell model assumes that a fraction f of the molecules sticks onto the wall, for further scattering or "desorption" according to the expected "gas law", while the remaining fraction (1-f) just undergoes an ideal (specular) reflection on the wall.Retrospectively, it is clear that specular atomic reflection cannot be considered as a general 4 phenomenon for an unprepared surface and a high atomic density. Rather, quantum reflection on a wall potential is an effect well identified but difficult to observe, and applies to atoms cooled to extremely slow motion [6] (along the normal), while requiring perfectly polished surfaces [7]. For the desorption process, occurring on considerably longer time scale, arguments based upon conservation laws of the flux to and from the surface, combined with the assumed isotropic M-B distribution in the surrounding gas, lead to the cos law (Knudsen l...

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“…Ammonia was the first thermometric substance on which DBT was tested, followed by carbon dioxide. In the former case a narrow CO 2 laser, frequency stabilized on an OsO 4 saturated absorption line, was used to probe a strong 14 NH 3 line at 10.34 μm [2]. In the subsequent implementation an extended-cavity diode laser (ECDL) at 2 μm was used to interrogate a vibration-rotation transition of CO 2 [3].…”

Section: Introductionmentioning

confidence: 99%

Frequency-comb-calibrated Doppler broadening thermometry

Gatti

Mills²,

Vizia³

et al. 2013

Phys. Rev. A

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We describe an implementation of Doppler broadening thermometry based upon a room-temperature continuous-wave quantum cascade laser at 9.07 μm, coherently phase locked to a thulium optical frequency comb centered at 2 μm. The thermodynamic temperature is retrieved from the analysis of multiple-line absorption spectra of the NH 3 ν 2 band, adopting semiclassical line-shape models and taking into full account the speed dependence of collisional broadening. We demonstrate that a precision of approximately five parts over 10 5 can be reached as a result of the analysis of only 90 absorption spectra, as acquired as a function of the gas pressure.

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Direct Determination of the Boltzmann Constant by an Optical Method

Cited by 133 publications

References 13 publications

Accurate determination of the Boltzmann constant by Doppler spectroscopy: Towards a new definition of the kelvin

Accurate determination of the Boltzmann constant by Doppler spectroscopy: Towards a new definition of the kelvin

Testing the limits of the Maxwell distribution of velocities for atoms flying nearly parallel to the walls of a thin cell

Frequency-comb-calibrated Doppler broadening thermometry

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