Refractive-index gas thermometry.

The principles and techniques of primary refractive-index gas thermometry (RIGT) are reviewed. Absolute primary RIGT using microwave measurements of helium-filled quasispherical resonators has been implemented at the temperatures of the triple points of neon, oxygen, argon and water, with relative standard uncertainties ranging from 9.1 × 10-6 to 3.5 × 10-5. Researchers are now also using argon-filled cylindrical microwave resonators for RIGT near ambient temperature, with relative standard uncertainties between 3.8 × 10-5 and 4.6 × 10-5, and conducting relative RIGT measurements on isobars at low temperatures. RIGT at optical frequencies is progressing, and has been used to perform a Boltzmann constant measurement at room temperature with a relative standard uncertainty of 1.2 × 10-5. Uncertainty budgets from implementations of absolute primary microwave RIGT, relative primary microwave RIGT and absolute primary optical RIGT are provided.

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.

Acoustic field in a quasi-spherical resonator: unified perturbation model.

Gas-filled quasi-spherical resonators are excellent tools for the measurement of thermophysical properties of gas and have also been retained for the determination of the Boltzmann constant with a low uncertainty, which can be derived from measurements of both the speed of sound in a noble gas and the volume of the resonator. To achieve this, a detailed modeling of the acoustic field in quasi-spherical resonators is of importance. Several phenomena and perturbations must be taken into account, including, among inertia and compressibility, heat conduction, viscosity, the shape of the resonator, small irregularities on the wall, and so on. The aim of this paper is to provide improvements to the current models of the acoustic field in such resonator. Namely, the model given here takes into account all the different perturbing elements together in a unique formalism, including the coupling between the different perturbing elements and the resulting modal coupling in a consistent manner. The first results obtained from this analytical model on a simple configuration show that the effect of modal coupling is small but should not be neglected regarding the accuracy required here, even if several improvements could still be provided to this new unified model.

Realization of an ultra-high precision temperature control in a cryogen-free cryostat.

Single-pressure refractive-index gas thermometry (SPRIGT) is a new type primary thermometry jointly developed by TIPC of CAS in China and LNE-Cnam in France. To realize a competitive uncertainty of 0.25 mK for the thermodynamic temperature measurement, a cryogen-free cryostat with high-stability better than 0.2 mK should be designed. This paper presented the first experimental results of temperature control for this cryostat. To realize this objective, multi-layer radiation shields combined with a thermal-resistance method were used to isolate the thermal-noise from surroundings. Besides, a new temperature control method based on a gas-type heat switch and proportional-integral-derivative control method was proposed, which was applicable to different temperature ranges by changing the working modes of the heat switch. After optimizing, the ultra-high precision temperature control in the range of 5-25 K has been fully realized, which was the temperature instability (with standard deviation) of 0.021 mK at 5.0 K, 0.05 mK at 5.7 K, 0.042 mK at 7.4 K, 0.029 mK at 14.3 K, and 0.022 mK at 25 K with the sampling time of 0.8 s. This was almost the best reporting result in the world and showed its great potential in SPRIGT.

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, k(B)=1.3806477(17)×10(-23) J K(-1), with a relative standard uncertainty of 1.2 parts in 10(6). k(B) 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 k(B) is consistent with the 2006 Committee on Data for Science and Technology (CODATA) value: (k(B)(new)/k(B_CODATA)-1)=-1.96×10(-6), where the relative uncertainties are u(r)(k(B)(new))=1.2×10(-6) and u(r)(k(B_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 microphone's 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.