Laurent Pitre

Acoustic gas thermometry

We review the principles, techniques and results from primary acoustic gas thermometry (AGT). Since the establishment of ITS-90, the International Temperature Scale of 1990, spherical and quasi-spherical cavity resonators have been used to realize primary AGT in the temperature range 7 K to 552 K. Throughout the sub-range 90 K < T < 384 K, at least two laboratories measured (T − T90). (Here T is the thermodynamic temperature and T90 is the temperature on ITS-90.) With a minor exception, the resulting values of (T − T90) are mutually consistent within 3 × 10−6 T. These consistent measurements were obtained using helium and argon as thermometric gases inside cavities that had radii ranging from 40 mm to 90 mm and that had walls made of copper or aluminium or stainless steel. The AGT values of (T − T90) fall on a smooth curve that is outside ±u(T90), the estimated uncertainty of T90. Thus, the AGT results imply that ITS-90 has errors that could be reduced in a future temperature scale. Recently developed techniques imply that low-uncertainty AGT can be realized at temperatures up to 1350 K or higher and also at temperatures in the liquid-helium range.

Waveguide effects on quasispherical microwave cavity resonators

The perturbing effect of a waveguide on the boundary of a quasispherical cavity resonator is investigated both theoretically and experimentally. Expressions for the frequency perturbation to the triply degenerate TM1mn and TE1mn modes are derived using cavity perturbation theory. The fields in and around the waveguide are calculated in the static limit using finite-element software. Experiments performed using quasispherical and cylindrical cavity resonators confirm the accuracy and generality of the approach. The impact of this study on attempts to re-determine the Boltzmann constant (kB) by an acoustic resonance technique is briefly considered.

Improving acoustic determinations of the Boltzmann constant with mass spectrometer measurements of the molar mass of argon

We determined accurate values of ratios among the average molar masses MAr of 9 argon samples using two completely-independent techniques: (1) mass spectrometry and (2) measured ratios of acoustic resonance frequencies. The two techniques yielded mutually consistent ratios (RMS deviation of 0.16 × 10−6 MAr from the expected correlation) for the 9 samples of highly-purified, commercially-purchased argon with values of MAr spanning a range of 2 × 10−6 MAr. Among the 9 argon samples, two were traceable to recent, accurate, argon-based measurements of the Boltzmann constant kB using primary acoustic gas thermometers (AGT). Additionally we determined our absolute values of MAr traceable to two, completely-independent, isotopic-reference standards; one standard was prepared gravimetrically at KRISS in 2006; the other standard was isotopically-enriched 40Ar that was used during NISTs 1988 measurement of kB and was sent to NIM for this research. The absolute values of MAr determined using the KRISS standard have the relative standard uncertainty ur(MAr) = 0.70 × 10−6 (Uncertainties here are one standard uncertainty.); they agree with values of MAr determined at NIM using an AGT within the uncertainty of the comparison ur(MAr) = 0.93 × 10−6. If our measurements of MAr are accepted, the difference between two, recent, argon-based, AGT measurements of kB decreases from (2.77 ± 1.43) × 10−6 kB to (0.16 ± 1.28) × 10−6 kB. This decrease enables the calculation of a meaningful, weighted average value of kB with a uncertainty ur(kB) ≈ 0.6 × 10−6.

Determination of the Boltzmann constant k from the speed of sound in helium gas at the triple point of water

The Boltzmann constant k has been determined from a measurement of the speed of sound in helium gas in a quasi-spherical resonator (volume 0.5 l) maintained at a temperature close to the triple point of water (273.16 K). The acoustic velocity c is deduced from measured acoustic resonance frequencies and the dimensions of the quasi-sphere, the latter being obtained via simultaneous microwave resonance. Values of c are extrapolated to the zero pressure limit of ideal gas behaviour. We find J⋅K−1, a result consistent with previous measurements in our group and elsewhere. The value for k, which has a relative standard uncertainty of 1.02 ppm, lies 0.02 ppm below that of the CODATA 2010 adjustment.

Determination of the Boltzmann constant using a quasi-spherical acoustic resonator.

The paper reports a new experiment to determine the value of the Boltzmann constant, , with a relative standard uncertainty of 1.2 parts in 106. kB was deduced from measurements of the velocity of sound in argon, inside a closed quasi-spherical cavity at a temperature of the triple point of water. The shape of the cavity was achieved using an extremely accurate diamond turning process. The traceability of temperature measurements was ensured at the highest level of accuracy. The volume of the resonator was calculated from measurements of the resonance frequencies of microwave modes. The molar mass of the gas was determined by chemical and isotopic composition measurements with a mass spectrometer. Within combined uncertainties, our new value of kB is consistent with the 2006 Committee on Data for Science and Technology (CODATA) value: (knewB/kB_CODATA−1)=−1.96×10−6, where the relative uncertainties are and ur(kB_CODATA)=1.7×10−6. The new relative uncertainty approaches the target value of 1×10−6 set by the Consultative Committee on Thermometry as a precondition for redefining the unit of the thermodynamic temperature, the kelvin.

Characterization of condenser microphones under different environmental conditions for accurate speed of sound measurements with acoustic resonators

Condenser microphones are more commonly used and have been extensively modeled and characterized in air at ambient temperature and static pressure. However, several applications of interest for metrology and physical acoustics require to use these transducers in significantly different environmental conditions. Particularly, the extremely accurate determination of the speed of sound in monoatomic gases, which is pursued for a determination of the Boltzmann constant k by an acoustic method, entails the use of condenser microphones mounted within a spherical cavity, over a wide range of static pressures, at the temperature of the triple point of water (273.16 K). To further increase the accuracy achievable in this application, the microphone frequency response and its acoustic input impedance need to be precisely determined over the same static pressure and temperature range. Few previous works examined the influence of static pressure, temperature, and gas composition on the microphones sensitivity. In this work, the results of relative calibrations of 1/4 in. condenser microphones obtained using an electrostatic actuator technique are presented. The calibrations are performed in pure helium and argon gas at temperatures near 273 K and in the pressure range between 10 and 600 kPa. These experimental results are compared with the predictions of a realistic model available in the literature, finding a remarkable good agreement. The model provides an estimate of the acoustic impedance of 1/4 in. condenser microphones as a function of frequency and static pressure and is used to calculate the corresponding frequency perturbations induced on the normal modes of a spherical cavity when this is filled with helium or argon gas.

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

Previous research effort towards the determination of the Boltzmann constant has significantly improved the supporting theory and the experimental practice of several primary thermometry methods based on the measurement of a thermodynamic property of a macroscopic system at the temperature of the triple point of water. Presently, experiments are under way to demonstrate their accuracy in the determination of the thermodynamic temperature T over an extended range spanning the interval between a few kelvin and the copper freezing point (1358 K). We discuss how these activities will improve the link between thermodynamic temperature and the temperature as measured using the International Temperature Scale of 1990 (ITS-90) and report some preliminary results obtained by dielectric constant gas thermometry and acoustic gas thermometry. We also provide information on the status of other primary methods, such as Doppler broadening thermometry, Johnson noise thermometry and refractive index gas thermometry. Finally, we briefly consider the implications of these advancements for the dissemination of calibrated temperature standards.

A New Generation of Multicells for Cryogenic Fixed Points at BNM/INM

In January 2000 a European Project called “MULTICELLS” started, in the field of the realisation of low‐temperature standards [1]. In the range from 14 K to 234 K, two competing designs of modular multi‐compartment cells (multicells) for the realisation of low‐temperature fixed points of the ITS‐90 were developed and fabricated by two different partners: BNM‐INM and IMGC [2]. The multicells device allows the calibration, in the same run, of up to three thermometers at all the ITS‐90 triple points in the low‐temperature range, including the mercury point. Several secondary reference points could be optionally added to the system. The limitation of the number of elements is mainly due to thermal effects (thermal homogeneity and response time) and to the dimension of the experimental space of the calorimeter used for measuring the melting curves. In order to reduce the response time, the phase‐transition interface of each element of the multicell containing the substance must be in close thermal contact with ...

The IMERAPlus joint research project for determinations of the Boltzmann constant

To provide new determinations of the Boltzmann constant, k, which has been asked for by the International Committee for Weights and Measures concerning preparative steps towards new definitions of the kilogram, the ampere, the kelvin and the mole, an iMERAPlus joint research project has coordinated the European activities in this field. In this major European research project the Boltzmann constant has been determined by various methods to support the new definition of the kelvin. The final results of the project are reviewed in this paper. Determinations of the Boltzmann constant k were achieved within the project by all three envisaged methods: acoustic gas thermometry, Doppler broadening technique, and dielectric constant gas thermometry. The results were exploited by the interdisciplinary Committee on Data for Science and Technology (CODATA) in their 2010 adjustment of recommended values for fundamental constants. As a result, the CODATA group recommended a value for k with a relative standard uncertainty about a factor of two smaller than the previous u(k)/k of 1.7×10−6.To provide new determinations of the Boltzmann constant, k, which has been asked for by the International Committee for Weights and Measures concerning preparative steps towards new definitions of the kilogram, the ampere, the kelvin and the mole, an iMERAPlus joint research project has coordinated the European activities in this field. In this major European research project the Boltzmann constant has been determined by various methods to support the new definition of the kelvin. The final results of the project are reviewed in this paper. Determinations of the Boltzmann constant k were achieved within the project by all three envisaged methods: acoustic gas thermometry, Doppler broadening technique, and dielectric constant gas thermometry. The results were exploited by the interdisciplinary Committee on Data for Science and Technology (CODATA) in their 2010 adjustment of recommended values for fundamental constants. As a result, the CODATA group recommended a value for k with a relative standard uncerta...

The Comparison between a Second‐Sound Thermometer and a Melting‐Curve Thermometer from 0.8 K Down to 20 mK

BNM‐INM has realised the Provisional Low Temperature Scale of 2000 (PLTS‐2000). Additionally, for several years, the low temperature team of BNM‐INM has studied the possibility of using the properties of dilute mixtures of 3He in 4He in order to develop a local temperature scale. The team made the choice to develop a new type of thermometer based on the propagation of sound in dilute solutions of 3He in superfluid 4He, a second‐sound thermometer. For low temperatures, the properties of low concentrations of 3He in superfluid 4He are those of a nearly ideal Fermi gas. The experiments of Greywall and Owers‐Bradley et al. have shown that the velocity of second sound in 3He‐4He mixtures is very sensitive to temperature, especially below 0.6 K. In the second‐sound thermometer developed by BNM‐INM, the speed of sound is determined from the resonance spectra of an acoustic cavity. The temperature is deduced from the measurement of the resonance frequencies, by using a physical model describing the relation betwe...