Weston L. Tew

Acoustic thermometry: new results from 273 K to 77 K and progress towards 4 K

We used a quasi-spherical cavity as an acoustic and microwave resonator to measure the thermodynamic temperatures, T, of the triple points of equilibrium hydrogen, neon, argon and mercury and to measure the difference T − T90, in the range 7 K to 273 K. (T90 is the temperature on the International Temperature Scale of 1990 (ITS-90).) In the range 7 K to 24.5 K, our preliminary values of T − T90 agree with recent results from dielectric-constant gas thermometry and achieve uncertainties that are comparable to or smaller than those achievable using the interpolating constant volume gas thermometer as currently defined on the ITS-90. In the range 90 K to 273 K, the present results for T − T90 obtained using a helium-filled, copper-walled, quasi-spherical cavity agree with earlier results obtained using argon-filled, steel-walled or aluminium-walled, spherical cavities. The agreement confirms our understanding of both acoustic and microwave cavity resonators and demonstrates that resonators function as primary thermometers spanning wide temperature ranges. The mutually consistent acoustic thermometry data from several laboratories imply that the values of (T − T90)/T90 are 5 times larger than the uncertainty of T/T90 near 150 K and near 400 K. They also imply that the derivative dT/dT90 is too large by approximately 10−4 near 273.16 K and that dT/dT90 has a discontinuity of 4 × 10−5 at 273.16 K.

An electronic measurement of the Boltzmann constant

The Boltzmann constant k was measured by comparing the Johnson noise of a resistor at the triple point of water with a quantum-based voltage reference signal generated with a superconducting Josephson-junction waveform synthesizer. The measured value of k = 1.380 651(17) × 10−23 J K−1 is consistent with the current CODATA value and the combined uncertainties. This is our first measurement of k with this electronic technique, and the first noise-thermometry measurement to achieve a relative combined uncertainty of 12 parts in 106. We describe the most recent improvements to our Johnson-noise thermometer that enabled the statistical uncertainty contribution to be reduced to seven parts in 106, as well as the further reduction of spurious systematic errors and electromagnetic interference effects. The uncertainty budget for this measurement is discussed in detail.

Improved electronic measurement of the Boltzmann constant by Johnson noise thermometry

The unit of thermodynamic temperature, the kelvin, will be redefined in 2018 by fixing the value of the Boltzmann constant, k. The present CODATA recommended value of k is determined predominantly by acoustic gas-thermometry results. To provide a value of k based on different physical principles, purely electronic measurements of k were performed by using a Johnson noise thermometer to compare the thermal noise power of a 200 Ohm sensing resistor immersed in a triple-point-of-water cell to the noise power of a quantum-accurate pseudo-random noise waveform of nominally equal noise power. Measurements integrated over a bandwidth of 550 kHz and a total integration time of 33 days gave a measured value of k = 1.3806514(48)x10^-23 J/K, for which the relative standard uncertainty is 3.5x10^-6 and the relative offset from the CODATA 2010 value is +1.9x10^-6.

Johnson noise thermometry measurements using a quantized voltage noise source for calibration

We describe a new approach to Johnson noise thermometry (JNT) that exploits recent advances in Josephson voltage standards and digital signal processing techniques. Currently, high-precision thermometry using Johnson noise is limited by the nonideal performance of electronic measurement systems. By using the perfectly quantized voltage pulses from a series array of Josephson junctions, any arbitrary broadband waveform can be synthesized and used as a calculable noise source for calibrating the cross-correlation electronics used in JNT systems. With our prototype JNT system, we have found agreement to two parts in 10/sup 3/ with a 1/spl sigma/ uncertainty of 1/spl times/10/sup -3/ between the voltage noise of a 100-/spl Omega/ resistor in a triple-point Ga cell (T/sub 90/= 302.916 K) and a pseudo-noise waveform with the same average power that is synthesized by a quantized voltage noise source. We estimate the temperature of the resistor to be 302.5 K/spl plusmn/0.3 K (1/spl sigma/ uncertainty based on the uncertainty from the cross-correlation). With better characterization of our JNT system, we expect to achieve relative accuracies of parts in 10/sup 5/ for arbitrary temperatures in the range between 270 and 1000 K.

Measurement Time and Statistics for a Noise Thermometer With a Synthetic-Noise Reference

This paper describes methods for reducing the statistical uncertainty in measurements made by noise thermometers using digital cross-correlators and, in particular, for thermometers using pseudo-random noise for the reference signal. First, a discrete-frequency expression for the correlation bandwidth for conventional noise thermometers is derived. It is shown how an alternative frequency-domain computation can be used to eliminate the spectral response of the correlator and increase the correlation bandwidth. The corresponding expressions for the uncertainty in the measurement of pseudo-random noise in the presence of uncorrelated thermal noise are then derived. The measurement uncertainty in this case is less than that for true thermal-noise measurements. For pseudo-random sources generating a frequency comb, an additional small reduction in uncertainty is possible, but at the cost of increasing the thermometers sensitivity to non-linearity errors. A procedure is described for allocating integration times to further reduce the total uncertainty in temperature measurements. Finally, an important systematic error arising from the calculation of ratios of statistical variables is described.

Progress on Johnson noise thermometry using a quantum voltage noise source for calibration

We describe our progress toward a high-precision measurement of temperature using Johnson noise. Using a quantized voltage noise source (QVNS) based on the Josephson effect as a calculable noise source, we have been able to measure the ratio of the gallium and water triple-point temperatures to within an accuracy better than 100 /spl mu/K/K. We also describe the operation of our Johnson noise thermometry system that could be used as a primary thermometer and possible sources of error that limit our absolute temperature measurements to /spl sim/150 /spl mu/K/K.

Isotopic and other influences on the realization of the triple point of hydrogen

Within an international collaboration of the eight metrological institutes represented by the authors, the dependence of the triple-point temperature of equilibrium hydrogen on the deuterium content at low concentrations has been precisely determined so that the uncertainty in realizing the triple point as a temperature fixed point might be reduced by nearly one order of magnitude. To investigate the thermodynamic properties of the hydrogen–deuterium mixtures and to elucidate the factors that influence the melting temperature, 28 sealed fixed-point cells have been filled and measured, and some of these have been compared with an open-cell system. Hydrogen gas with a deuterium content ranging from 27.2 µmol D/mol H to 154.9 µmol D/mol H was studied using cells containing five different types of spin-conversion catalyst, with different catalyst-to-liquid volume ratios (a few per cent to more than 100%) and of different designs. The latter consideration is especially influential in determining the thermal behaviour of the cells and, thus, the temperature-measurement errors. The cells were measured at the eight participating institutes in accordance with a detailed protocol that facilitates a direct comparison of the results. Through analysis of the measurements, significant inter-institute deviations due to different measurement facilities and methods have been ruled out with respect to the determination of both the melting temperatures and the thermal parameters of the cells. The uncertainty estimates for the determination of the deuterium content have been verified by including isotopic analysis results from four different sources. The slope of the dependence of the triple-point temperature of equilibrium hydrogen isotopic mixtures on the deuterium content has been deduced from the melting temperatures of those sample portions not in direct contact with the catalysts. Evaluation of the data using different mathematical methods has yielded an average value of 5.42 µK per µmol D/mol H, with an upper bound of the standard uncertainty of 0.31 µK per µmol D/mol H. This is close to the literature value of 5.6 µK per µmol D/mol H that was obtained at higher deuterium concentrations. (Some figures in this article are in colour only in the electronic version)

Monitoring the mass standard via the comparison of mechanical to electrical power

An ongoing absolute watt experiment that shows the promise of being able to monitor the stability of the kilogram standard to better than 0.05 p.p.m. is discussed. The theory is presented, and the latest improvements to the experimental apparatus are briefly described. >

CCT-K2: key comparison of capsule-type standard platinum resistance thermometers from 13.8 K to 273.16 K

Calibrated capsule-type standard platinum resistance thermometers were used to compare national realizations of the International Temperature Scale of 1990 (ITS-90) from 13.8033 K, the triple point of equilibrium hydrogen, to 273.16 K, the triple point of water, for seven countries in CIPM Key Comparison CCT-K2. Measurements were made at temperatures close to the eight low-temperature defining fixed points of the ITS-90, using a copper comparison block capable of simultaneously holding nine thermometers. Two separate measurement runs were performed, allowing two different groups of capsules from each laboratory to be examined. The results are used to determine the degree of equivalence of the independent national realizations of the scale for use in the Mutual Recognition Arrangement Appendix B database. In addition, measurements were made with the first group of thermometers at approximately eighty temperatures throughout the cryogenic range, which provide information to evaluate some of the so-called scale non-uniqueness issues inherent in the ITS-90 interpolation scheme.

ITS-90 non-uniqueness from PRT subrange inconsistencies over the range 24.56 K to 273.16 K

We have performed calculations to study ITS-90 non-uniqueness from subrange inconsistencies over the range 24.5561 K to 273.16 K, where the scale is defined by an interpolating platinum resistance thermometer (PRT) that is calibrated via sets of defined fixed points. For this work, subrange inconsistency calculations have been performed on eighteen PRTs; fourteen are standard PRTs and four are miniature PRTs. The inconsistency uncertainties, which result from propagation of fixed-point uncertainties, have also been calculated. The calculations show that PRT subrange inconsistencies in the temperature region studied can be as large as 1 mK. We have also studied possible correlations between PRT subrange inconsistencies and other PRT properties/parameters that are simpler to determine; these studies show that there is a correlation between the average magnitude of the inconsistencies and the value of a certain calibration coefficient. Finally, for the range studied we have used a statistical analysis on the inconsistencies of the PRT ensemble to calculate a standard uncertainty to the ITS-90 temperature T90 due to the inconsistencies. Over the temperature intervals 25 K ≤ T90 ≤ 50 K and 100 K ≤ T90 ≤ 200 K, this uncertainty dominates those propagated from fixed-point uncertainties.