Keith A. Gillis

The revised definition of the kelvin has created new interest in alternative paths of traceability to the SI. In particular, the development of methods for the direct realization of the kelvin is ongoing, establishing traceability without the need to go through the international-consensus temperature scale, the ITS-90. These direct realization methods are in contrast to the ITS-90 and the measurement infrastructure of reference materials and artefact thermometer calibration chains. This infrastructure has been built up over a century or more of industrialization and scientific progress, and while very robust, is not well suited to address the requirements of the most demanding of application environments. We examine how direct traceability to the kelvin can be applied to address those applications and assess the relative practical merits of various direct realization approaches. Primary thermometry methods are surveyed from the standpoint of achievable uncertainties over the range 4 K to 1800 K with examples of practical direct-realization technologies. This assessment points to a narrow application space of long-term missions, or those occurring in remote or hazardous environments, as the most compelling cases for the direct realization approach. We present two special application environments where direct realizations are well suited for point-of-use temperature measurement. This article is part of the Theo Murphy meeting issue ‘The redefined kelvin: progress and prospects’.

We are extending acoustic gas thermometry (AGT) to temperatures up to 809 K with low uncertainties to measure the difference between the thermodynamic temperature T and the temperature T90 on the International Temperature Scale of 1990 (ITS-90). A cylindrical resonator was machined from a Ni-Cr-Fe alloy and acoustic and microwave waveguides welded to the cavity’s endplates transmitted sound and microwaves to and from the cavity. A long-stemmed standard platinum resistance thermometer (LSPRT) measured T90 at the cavity wall. Pure argon gas flows continuously through the cavity to minimize the effects of desorption from the cavity walls. The resonator was hung in a pressure vessel surrounded by a radiation shield, a heat pipe and a furnace. We measured the acoustic resonant frequencies in argon in the range 580 to 809 K with relative standard uncertainty (3–5)×10−6. We applied a second-order boundary-layer correction to these frequencies. Each microwave resonance frequency was measured with a relative standard uncertainty of 3×10−7. The inconsistency between four independent microwave modes was 2.2×10−6 at 809 K, which contributed an uncertainty of 3.6 mK to the determination of T. The inconsistencies were not temperature dependent, which showed the structural stability of the resonator from room temperature to 809 K. This article is part of the Theo Murphy meeting issue ‘The redefined kelvin: progress and prospects’.

We review recent determinations of the Boltzmann constant kB and the differences T − T90 that used cylindrical acoustic gas thermometry (c-AGT). These determinations measured the acoustic resonance frequencies of argon gas enclosed by metal-walled, cylindrical cavities. (Here, T is the thermodynamic temperature and T90 is the temperature measured on the International Temperature Scale of 1990, ITS-90.) In the range 234–303 K, the standard uncertainty of c-AGT ranges from 1.9 × 10−6T to 2.6 × 10−6T. This uncertainty is much smaller than the errors in ITS-90; therefore, c-AGT can help improve ITS-90. Moreover, we are extending c-AGT up to 1358 K. With increasing temperatures, c-AGT becomes advantageous relative to AGT based on quasi-spherical cavities because long cylindrical cavities (1) naturally fit into cylindrical heat pipes or multi-shelled thermostats; (2) provide the immersion required by transfer temperature standards, such as long-stemmed platinum resistance thermometers; and (3) have more useful, low-frequency acoustic resonances. In preparation for high-temperature c-AGT, we identified suitable materials for fabricating cylindrical cavities and we developed techniques for measuring acoustic resonance frequencies using sources and detectors outside the high-temperature thermostat. We also considered alternative test gases and optimal dimensions of cavities.

The National Institute of Standards and Technology measured gas flows exiting large, unthermostated, gas-filled, pressure vessels by tracking the time-dependent pressure P(t) and resonance frequency f_N(t) of an acoustic mode N of the gas remaining in each vessel. This is a proof-of-principle demonstration of a gas flow standard that uses P(t), f_N(t), and known values of the gas's speed of sound w(p,T) to determine a mode-weighted average temperature ⟨T⟩_φ of the gas remaining in a pressure vessel while the vessel acts as a calibrated source of gas flow. To track f_N(t) while flow work rapidly changed the gas’s temperature, we sustained the gas's oscillations using positive feedback. Feedback oscillations tracked ⟨T⟩_φ with a response time of order 1/f_N. In contrast, driving the gas’s oscillations with an external frequency generator yielded much slower response times of order Q/f_N. (For our pressure vessels, Q ∼ 10³–10⁴, where Q is the ratio of the energy stored to the energy lost in one cycle of oscillation.) We tracked f_N(t) of radial modes in a spherical vessel (1.85 m³) and of longitudinal modes of a cylindrical vessel (0.3 m³) during gas flows ranging from 0.24 to 12.4 g/s to determine the mass flows with an uncertainty of 0.51 % (95 % confidence level). We discuss the challenges in tracking f_N(t) and ways to reduce the uncertainties.

Previously, we demonstrated accurate determinations of the mass of gas in a large collection vessel of known volume from measurements of the pressure and the resonance frequencies of a few acoustic modes. We achieved accurate mass measurements even when linear temperature gradients persisted after adding or removing gas. The change in mass Δm from before and after flow and the collection time Δt may be used to calibrate mass flowmeters. Because the resonance quality factors Q are very high (up to 30000), measuring the complex-valued frequency response using a lock-in amplifier to determine the resonance frequency is slow. This static measurement of mass requires sufficient time to elapse for transient non-linear gradients to dissipate through convection and diffusion. Here, we demonstrate a method to dynamically track the resonance frequency of a large, gas-filled collection vessel while gas is flowing into or out of the vessel. We use positive feedback to excite sustained oscillations at the desired resonance frequency without a lock-in amplifier or frequency synthesizer. As the speed of sound changes, the sustained oscillations track the changing resonance frequency f with response time ~1/f. Preliminary mass flow measurements using this technique agree with a flow standard within their combined uncertainties.

We characterized a 1.8 m³, quasi-spherical resonator, a pressure vessel informally known as the “big blue ball” or “BBB.” The BBB will be the collection volume of a NIST-designed gas-flow standard that will operate at pressures up to 7 MPa. Using microwave resonance frequencies, we determined the volume of the BBB filled with argon as a function of pressure (up to 7 MPa) and temperature (near ambient). The measured pressure- and temperature-dependences of the BBB’s volume are consistent with the published properties of carbon steels. We filled the BBB with 220 kg of argon in weighed increments of approximately 20 kg. We also determined the mass m _acoust of argon in the BBB by measuring the pressure, the acoustic resonance frequencies f _acoust of 3 modes, and using the known thermophysical properties of argon. The values of m _acoust were within ±0.03 % of the gravimetrically determined masses. In a typical application, the BBB will never be isothermal. Nevertheless, the acoustic resonance frequencies quickly and accurately determine the average temperature and mass of the gas in the BBB despite significant, long-lived thermal gradients that are created by pressure changes. A theoretical model for effect of temperature gradients on the acoustic resonance frequencies is presented.

Understanding of today's climate and predictions of future climate require accurate input data to model the energy balance between the sun's irradiance and Earth’s atmosphere, oceans, land, and surface ice. An important driver of climate change is the absorption and scattering of sunlight by carbon-based aerosols (soot, smoke, etc) that have widely-varying, source-dependent, and history-dependent optical properties. We use a resonant photoacoustic spectrometer (PAS) to measure the optical absorption cross-section of various carbonaceous aerosols that we generate and characterize in situ. The photoacoustic signal is directly proportional to the energy absorbed by the particles. When combined with simultaneous measurements of the total extinction using cavity ring-down spectroscopy, we obtain the particles’ wavelength-dependent albedo (fraction of incident light scattered). Another important driver of climate change is atmospheric carbon dioxide, a greenhouse gas. With the remarkable linearity, sensitivity, and resolution of our PAS resonator, we measure the individual concentrations of ¹²CO₂ and ¹³CO₂ in atmospheric samples to determine the isotopic ratio ¹³C/¹²C, which gives a clue to its origin. A temperature-controlled portable PAS system continuously monitors the concentration of atmospheric ¹²CO₂ on a NIST rooftop.

We measured the pressure p and the acoustic resonance frequency fa of argon gas in a 300 L tank. We then used the ratio p/fa2 (proportional to the mass M of gas) to determine the fractional leak rate (dM/dt)/M ≈ −13×10−6/hr of gas from the tank. The tank was filled with argon at 450 kPa and was exposed to sunshine-driven temperature and pressure fluctuations as large as (dT/dt)/T ≈ (dp/dt)/p ≈ 5×10-2 h-1 (i.e., 1000× larger) in a 24-hour record. This leak could not be detected in a 72-hour record of p/T. Theory predicts that the resonance frequencies are insensitive to linear temperature gradients; however, we do not have a detailed understanding of why the acoustic frequencies are insensitive to asymmetric, time-dependent heating of the tank. From auxiliary measurements and information from the literature, we believe that convective currents near the tank's walls carry most of the heat between the hot and cool regions, leaving a linear temperature gradient in the majority of the gas's volume. We plan to report preliminary measurements for a much larger (1800 L) tank. We expect that the results of this investigation will lead to effective acoustic methods for flow calibrations and leak detection in large volumes.