G. Sutton

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.

Correction of NPL-2013 estimate of the Boltzmann constant for argon isotopic composition and thermal conductivity

In 2013, a team from NPL, Cranfield University and SUERC published an estimate of the Boltzmann constant based on precision measurements of the speed of sound in argon. A key component of our results was an estimate of the molar mass of the argon gas used in our measurements. To achieve this we made precision comparison measurements of the isotope ratios found in our experimental argon against the ratios of argon isotopes found in atmospheric air. We then used a previous measurement of the atmospheric argon isotope ratios to calibrate the relative sensitivity of the mass spectrometer to different argon isotopes. The previous measurement of the atmospheric argon isotope ratios was carried out at KRISS using a mass spectrometer calibrated using argon samples of known isotopic composition, which had been prepared gravimetrically.We report here a new measurement made at KRISS in October 2014, which directly compared a sample of our experimental gas against the same gravimetrically-prepared argon samples. We consider that this direct comparison has to take precedence over our previous more indirect comparison. This measurement implies a molar mass which is 2.73(60) parts in 106 lighter than our 2013 estimate, a shift which is seven times our 2013 estimate of the uncertainty in the molar mass.In this paper we review the procedures used in our 2013 estimate of molar mass; describe the 2014 measurement; highlight some questions raised by the large change in our estimate of molar mass; and describe how we intend to address the inconsistencies between them. We also consider the effect of a new estimate of the low pressure thermal conductivity of argon at 273.16 K. Finally we report our new best estimate of the Boltzmann constant with revised uncertainty, taking account of the new estimates for the molar mass and the thermal conductivity of the argon.

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.

Estimates of the difference between thermodynamic temperature and the International Temperature Scale of 1990 in the range 118 K to 303 K

Using exceptionally accurate measurements of the speed of sound in argon, we have made estimates of the difference between thermodynamic temperature, T, and the temperature estimated using the International Temperature Scale of 1990, T90, in the range 118 K to 303 K. Thermodynamic temperature was estimated using the technique of relative primary acoustic thermometry in the NPL-Cranfield combined microwave and acoustic resonator. Our values of (T−T90) agree well with most recent estimates, but because we have taken data at closely spaced temperature intervals, the data reveal previously unseen detail. Most strikingly, we see undulations in (T−T90) below 273.16 K, and the discontinuity in the slope of (T−T90) at 273.16 K appears to have the opposite sign to that previously reported.

Pyknometric volume measurement of a quasispherical resonator

We have measured the internal volume of a 1 litre, diamond-turned copper quasispherical resonator with a fractional uncertainty of approximately 1 part in 106 using two independent techniques. This is in response to the need for a uniquely accurate measurement of resonator volume, for the purpose of measuring the Boltzmann constant in pursuit of the redefinition of the kelvin. The first technique is a pyknometric measurement using water as a liquid of known density. We describe the development of a procedure that results in stable, reproducible volume measurements. We provide a detailed discussion of the factors that affect the water density, such as dissolved gases. The second technique is microwave resonance spectroscopy. Here, we measure the resonant frequencies of the TM1n modes and relate them to the dimensions of the resonator. We evaluate the frequency perturbations that arise from the coupling waveguides and the electrical resistivity of the copper surface. The results of the microwave measurements show evidence of a dielectric coating on the surface. We propose that this is an oxide layer and estimate its thickness from the microwave data. Finally, we compare the volume estimates from the two methods, and find that the difference is within the combined uncertainty.

Outgassing of water vapour, and its significance in experiments to determine the Boltzmann constant

The rate of outgassing of water vapour from metal tubing and spheres is estimated and formulae given for the expected amount fraction of water added to otherwise pure gases. The relevance of these estimates to current efforts to redetermine the Boltzmann constant with relative uncertainty of measurement uR(kB) ≈ 1 × 10−6 is supported with experimental results using trace moisture sensors and combined acoustic and microwave resonators. The outgassing does not represent an insuperable obstacle to accurate determinations of the Boltzmann constant in any of the current experiments. However, all workers in this field need to evaluate the extent of outgassing and devise a strategy for estimating and minimizing its effect.

New temperature references and sensors for the next generation of nuclear power plants

In preparation for the new challenges posed by the higher temperature environments which are likely to be encountered in the next generation of nuclear power plants, to maintain the safety and to ensure the long-term reliability of such plants, it is crucial that new temperature sensors and methods for in-situ measurement are investigated and developed. This is the general objective of the first workpackage of the joint research project, ENG08 MetroFission, funded in the framework of the European metrology research program. This paper will review the results obtained in developing and testing new temperature sensors and references during the course of the project. The possible continuation of these activities in the future is discussed.

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...

Response to Macnaughton’s ‘Comment on “A low-uncertainty measurement of the Boltzmann constant”’

In his comment on our 2013 paper ‘A low-uncertainty measurement of the Boltzmann constant’ [1] Macnaughton claims that his re-analysis “…reveals systematic non-random patterns in residuals of the key fitted model equation”. He claims that “these patterns violate the assumptions underlying the analysis” and “raise questions about the validity of [our] estimate of kB”. He also claims that we deleted “troublesome” data in a “somewhat arbitrary” manner. While we are grateful to Macnaughton for his attention to our freely accessible data, we disagree with his conclusions. The dataset we analysed consists of 263 data points, while the ‘trends’ in the data to which he refers constitute at most 12 points. Concerning the improper removal of data points to which he alludes we note that all 324 data points that we acquired were included in the supplementary data, but some data were excluded from the analysis for the reasons stated in the original text. Macnaughton was able to determine the effect of including or excluding these data but did not do so. In this paper we demonstrate that none of the issues to which Macnaughton draws attention could conceivably have any significant effect on our final estimate for the Boltzmann constant or its uncertainty.

Internal consistency in the determination of the Boltzmann constant using a quasispherical resonator

The use of a combined microwave and acoustic resonator to determine the Boltzmann constant, kB, permits several checks on the internal consistency of the data. Using measurements in argon gas in the NPL-Cranfield quasispherical copper resonator (NPLC-2), we describe four distinct types of internal consistency check. Firstly, we estimate kB using six distinct acoustic resonances varying in frequency from 3.55 kHz to 21.77 kHz. We thus span a wide range of systematic corrections, most notably in the effect of the thermal boundary layer (TBL), which varies strongly with mode. Secondly, the same theory which predicts the TBL corrections to the acoustic resonance frequencies also predicts the widths of the resonances. By comparing the measured and theoretically-expected widths we can place limits on the effect of any un-modeled physics. Thirdly, the equivalent radius of the resonator (∼62.03 mm) is inferred from analysis of 8 TM microwave resonances and the spread of the radius values inferred from each mode i...