Towards implementing the new kelvin

The kelvin redefinition and the MeP-K

Dr Bernd Fellmuth, Physikalisch-Technische Bundesanstalt, Germany

Abstract

Historically, the best guide for the realisation of the kelvin has been the text of the International Temperature Scales and accompanying documents. Recent developments and its redefinition have motivated the creation of a more flexible document: the Mise-en-Pratique of the definition of the kelvin (MeP-K). The MeP-K provides the information needed to perform a practical measurement of temperature.

In this contribution, the background and the content of the second version of the MeP-K is presented. This version is based on the planned redefinition of SI base unit kelvin via an explicit-constant definition. The kelvin will be defined in terms of the SI derived unit of energy, the joule, by fixing the value of the Boltzmann constant. The explicit-constant definition is sufficiently wide to encompass any form of thermometry and leaves the MeP-K to spell out the practical details.

The second version of the MeP-K consists of four parts:

• Introduction, stating the redefinition of the kelvin, the rationale for the change, and the effect on its realisation.
• Nomenclature, defining fundamental terms of thermometry to support an unambiguous taxonomy of methods.
• Primary thermometry, describing the realisation based on fundamental laws of statistical thermodynamics. Two primary methods, namely acoustic gas thermometry and radiometric thermometry, are shortly described. Details are given in appendices.
• Defined temperature scales, providing information for the ITS 90 and PLTS 2000. Further important information is given in appendices and guides.

• Audio recording (mp3)

Low uncertainty Boltzmann constant determinations and the kelvin redefinition

Dr Joachim Fischer, Physikalisch-Technische Bundesanstalt, Germany

Abstract

The General Conference on Weights and Measures agreed at its 24th meeting in October 2011 on new definitions for four of the seven base units of the International System of Units (SI). Kilogram, ampere, kelvin, and mole will be defined in terms of fixed numerical values of the Planck constant, elementary charge, Boltzmann constant and Avogadro constant, respectively.

The effect of the new definition of the kelvin referenced to the value of the Boltzmann constant is that the kelvin is equal to the change of thermodynamic temperature that results in a change of thermal energy  kT  by  1.380 650 x 10⁻²³ J. The new definition would be in line with modern science where nature is characterised by statistical thermodynamics, which implies the equivalence of energy E and temperature T as expressed by the Maxwell-Boltzmann equation E = kT.

A refined value of the Boltzmann constant suitable for defining the kelvin is presently determined by fundamentally different primary methods like acoustic gas thermometry, dielectric constant gas thermometry, noise thermometry, and the Doppler broadening technique. Details of the measurements, progress to date, and further perspectives will be reported.

Necessary conditions to be met before proceeding with changing the definition are given. The consequences of the new definition of the kelvin on temperature measurement will be outlined.

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On the meaning of temperature

Professor Peter Hänggi, University of Augsburg, Germany

Abstract

Most importantly, temperature is a derived quantity. It is given as the thermodynamic force of the thermodynamic state function, known as the entropy S. The absolute temperature T then obeys: 1/T = ∂S/∂E, wherein E denotes the internal thermodynamic energy state function. The inverse absolute temperature provides the integrating factor for the Second Law of thermodynamics, dS = δQrev/T, where δQrev refers to the reversible, quasi-static heat exchange.

JW Gibbs introduced two thermodynamic entropy expressions. A first one (i) known as volume entropy, termed here the `Gibbs entropy’ S_G, reading: S_G(E, λ) = k_B ln Ω(E, λ), with λ denoting the set of external control parameters, such as the available volume, magnetic field, etc. Ω(E, λ) is the integrated, non-negative valued density of states. Gibbs also discussed a second entropy expression (ii) that is referred to as surface entropy S_B (nowadays, commonly known also as the Boltzmann entropy), reading S_B(E, λ) = k_B ln [ε ω(E, λ)], with ε being some small energy constant so that the argument of the logarithm becomes dimensionless.

As recently shown with Ref. [1], for the consistency of an entropy function S with thermodynamics, that is to say with S obeying the celebrated 0^th, 1^st and 2^nd thermodynamic laws singles out the Gibbs-entropy [1]. I point out shortcomings for the thermodynamics of systems of finite size and/or with an upper bound in energy if using (Boltzmann) entropy. The two corresponding thermodynamic temperatures T_G and T_B are then not equivalent and can considerably differ.

[1] S. Hilbert, P. Hänggi, and J. Dunkel, Thermodynamic Laws in Isolated Systems, Phys. Rev. E 90, 062116 (2014).

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The new SI: progress and prospects

Professor Marc E. Himbert, LNE-Cnam, France

Abstract

Most national metrology laboratories and some major physics laboratories have been working for decades to improve the determination of several fundamental physical constants. As the uncertainty in the measurements tends to the accuracy of the materialisations of the relevant SI units, time has come for a major change in the SI definitions, where the so-called based units will be scaled relative to fixed values of a set of fundamental constants or constants of nature.

The frame of this new SI was proposed 10 years ago. Major resolutions were adopted by the CIPM and the CGPM to fix which conditions should be fulfilled before a final decision for the change. Such a decision is expected to be taken in 2018. The new SI will highly improve the accuracy and the sustainability of the set of references. It will also open the way to an easier traceability at the nano- and quantum scales.

The new kelvin will be linked to a fixed value of the Boltzmann constant k. Consequently the triple point of water will remain as a practical reference, to be calibrated. A draft of the future SI brochure, with the new definition of the kelvin, is on the way. New techniques, new concepts and new technologies are investigated to link new ways of measurements to the International temperature scale. The aim is to make profit of this new definition for absolute and relative determinations of temperatures.

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Chair

Professor Martin Trusler, Imperial College London, UK

Thermodynamic temperature measurement by absolute radiometry

Dr Klaus Anhalt, Physikalisch-Technische Bundesanstalt, Germany

Abstract

Above the freezing temperature of silver (961.78°C) the International temperature scale of 1990 (ITS-90) defines a temperature t₉₀ in terms of a defining fixed-point and Planck’s law of thermal radiation. Using Planck’s law the thermodynamic temperature t can also be directly determined by applying radiation detectors calibrated in absolute terms for their spectral responsivity. With the advent of high-quality semiconductor photo-diodes and the development of high-accuracy cryogenic radiometers during the last two decades radiometric detector standards with very small uncertainties in the 0.01% range have been developed for direct, absolute radiation thermometry with uncertainties comparable or even smaller than the uncertainties of approximating thermodynamic temperature t by t₉₀. This talk will give an overview of design variants of the applied radiometers and their calibration chain. Furthermore, details and requirements regarding the experimental procedure for obtaining thermodynamic temperatures with these radiometers are presented. Finally, relevant results of these methods obtained, which are also applicable for temperatures significantly below the silver fixed point, are reviewed.

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Realisation and dissemination of thermodynamic temperature above the silver point

Dr Mohamed Sadli, LNE-Cnam, France
Professor Graham Machin, National Physical Laboratory, UK

Abstract

The European Metrology Research Programme (EMRP)-funded joint research project ‘Implementing the new kelvin’ is partly devoted to the evaluation of the high-temperature thermodynamic temperature determination and dissemination. Thermodynamic temperatures determined by various radiometric methods and instruments will be assigned to metal-carbon eutectic transitions materialised by high-temperature fixed points (HTFP). Once these temperatures are assigned, it will be possible to disseminate thermodynamic temperature in the frame of the mise-en-pratique of the definition of the kelvin at high temperature. It is, however, important for users to evaluate these differences in terms of practicality and achievable uncertainty level between dissemination mediated by HTFPs, and dissemination using instruments, such as filter radiometers or absolutely calibrated pyrometers.

To achieve a thorough assessment of these two distinct dissemination methods, respectively source-based and detector-based, two dissemination exercises were organised in the form of comparisons.

The high-temperature fixed point dissemination route is assessed using a set of HTFP cells at the eutectic points of Co-C (~1324°C), Pt-C (~1738°C), Ru-C (~1953°C) and Re-C (~2474°C) supplied by NPL and LNE-Cnam. Four cells were first measured at LNE-Cnam in terms of ITS-90 melting temperatures before being circulated between CEM, PTB, TUBITAK-UME and NPL and back to LNE-Cnam.

In parallel the participants to the dissemination exercise via absolutely calibrated radiometers/pyrometers, namely PTB, MIKES, CEM and LNE-Cnam have characterised and calibrated their instruments before and after a comparison, which was held at PTB. The instruments were put in front of a variable temperature blackbody and determined its thermodynamic temperature between 1000°C and 2500°C in 200°C steps.

This presentation will be devoted to the description of the experimental work performed in this part of the InK project, as well as the expectations in terms of uncertainty. The results of the two dissemination exercises will be presented with a preliminary conclusion about the possibilities offered by these two potential future dissemination techniques in the frame of the mise-en-pratique of the definition of the kelvin at high temperature.

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Chair

Rod White, Measurement Standards Laboratory of New Zealand, New Zealand

Low uncertainty thermodynamic temperature assignment to high temperature fixed points

Dr Emma Woolliams, National Physical Laboratory, UK

Abstract

This talk will describe the assignment of low-uncertainty thermodynamic temperatures to the melting transition of Re-C, Pt-C and Co-C metal-carbon eutectics; realising the hope expressed in Yamada’s original 1999 papers on eutectics that these should become assigned high temperature fixed-points. At the simplest level, these fixed-points will provide new temperature references for the calibration of pyrometers at temperatures above the freezing point of silver (1234.93 K) and will thus reduce the uncertainties associated with high temperature measurement compared to those achievable using the International Temperature Scale of 1990 (ITS-90).

The thermodynamic temperatures of these fixed-points have been determined through direct measurement of the radiance of a blackbody cavity surrounded by the fixed-point material from Planck’s law and hence the Boltzmann Constant. The evolving mise-en-pratique for the definition of the kelvin encourages the realisation and dissemination of thermodynamic temperature. This may be directly – and the work described in this talk shows that filter radiometry is sufficiently mature for this, or it may be by providing fixed-points with reference thermodynamic temperatures that have associated uncertainties – and this talk will outline such temperatures.

The work described here is the culmination of an eight-year collaborative international research programme which has developed robust fixed point cells, studied their sensitivity to furnace effects and impurities and finally measured their melting transition temperature. The realisation may be direct, and the work described in this talk shows that filter radiometry is sufficiently mature for this, or the realisation may be via fixed-points with consensus values for the thermodynamic temperatures and associated uncertainties as suggested by this talk.

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High-accuracy primary spectral radiometry from 400 K to 1300 K

Dr Howard Yoon, The National Institute of Standards and Technology, USA

Abstract

The proposal for the redefinition of the kelvin based upon the fixed Boltzmann constant has led to active research in various, different thermodynamic temperature measurements primarily for a more accurate determination of the Boltzmann constant. Additionally work is also underway to re-examine values of both primary and secondary fixed-point temperatures used in the current international temperature scale. In the temperature region from 400 K to 1300 K, the number of thermodynamic temperature measurement techniques which can be used are quite limited. Acoustic thermometry is at present limited to an upper temperature limit of 550 K, primarily due to materials and sensor issues in the experimental setup. Thermodynamic temperature measurements using visible-band spectral radiation thermometry, which is quite successful at higher temperature above about 1000 K, are not possible in this temperature region due to the lack of visible radiation from blackbodies which are at temperatures below 1000 K. However, direct thermodynamic temperature measurements of blackbodies are possible by shifting the wavelengths used for the spectral radiation thermometry to the near-infrared region. We describe the development of a radiation thermometer and a radiometric calibration procedure designed to directly measure fixed-point blackbodies from the Sn-point to the Cu-point temperatures. Preliminary data showing the initial radiometric calibration steps will be discussed.

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A synthetic approach to ultra-low uncertainty determination of T-T90

Dr Roberto M. Gavioiso, Istituto Nazionale di Ricerca Metrologica, Italy

Abstract

The 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, electrical or optical property of a simple macroscopic system at the temperature of the triple point of water.

Presently, these experiments are under test 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 point (1358 K). We discuss how this progress and activities will improve the formal approximation to the thermodynamic temperature currently provided by the International Temperature Scale of 1990 (ITS-90). We also consider the perspectives of these advancements for the dissemination of calibrated temperature standards.

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On the use of Doppler-broadened laser absorption spectroscopy in primary gas thermometry

Professor Livio Gianfrani, Seconda Universita' di Napoli, Italy

Abstract

The expression of the Doppler width of a spectral line, valid for a gaseous sample at the thermodynamic equilibrium, represents a powerful tool to link the thermodynamic temperature to an absolute frequency (in the optical domain) and a frequency interval. This is the basis of a relatively new method of primary gas thermometry, known as Doppler broadening thermometry (DBT). Implemented at the Second University of Naples on H₂¹⁸O molecules at the temperature of the triple point of water, this method recently allowed to determine the Boltzmann constant with a global uncertainty of 24 parts in 10⁶ [1]. In order to contribute to the new definition of unit kelvin, but also for being useful as a tool for TT90 measurements, DBT has to approach the target accuracy of 1 part per million (ppm). This talk will resume recent efforts performed in Naples to further develop and optimize DBT. The molecular targets of interest are H₂¹⁸O and C₂H₂, both showing relatively strong combination vibrational bands at 1.39 μm. Main progresses and current limitations will be highlighted. Furthermore, a revised uncertainty budget will be presented and discussed. It will be shown that the achievement of the ppm-level is a realistic possibility for the DBT method.

[1] L. Moretti, A. Castrillo, E. Fasci, M. D. De Vizia, G. Casa, G. Galzerano, A. Merlone, P. Laporta, and L. Gianfrani, Physical Review Letters 111, 060803 (2013).

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Chair

Dr Mike Moldover, The National Institute of Standards and Technology, USA

Acoustic approaches to T-T90

Dr Michael de Podesta, National Physical Laboratory, UK

Abstract

It is now 25 years since the establishment of the International Temperature Scale of 1990, and the scale has been extremely successful in enabling accurate and consistent temperature measurement around the world. However, it has become clear that the thermodynamic temperature estimates on which ITS-90 is based were in error, even at temperatures close to the triple point of water. The discovery and elucidation of this error is largely due to the development of acoustic thermometry.

Over the last decade, the development of combined microwave and acoustic resonators for the measurement of the Boltzmann constant has improved the state-of-the-art significantly and resulted in advances in theory, fabrication, and experimental techniques. The intrinsic redundancy of resonator-based techniques and the agreement between work done in different laboratories using different gases and resonators increases the confidence that the measurement uncertainties are now genuinely at the millikelvin level.

After reviewing some of these advances, we present new data on T – T90 at twenty temperatures in the range from 118 K to 303 K. The differences agree well with recent estimates, but our low type-A uncertainty reveals previously unseen detail. Most strikingly, we see undulations in T - T90 below T_TPW and the discontinuity of the slope of T - T90 at T_TPW has the opposite sign to that previously reported.

Finally we briefly consider the possibilities for extending acoustic thermometry to both higher and lower temperatures.

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Cylindrical acoustic gas thermometers and Johnson noise thermometers for measuring the thermodynamic temperature

Dr Jintao Zhang, National Institute of Metrology, China

Abstract

In previous work, we measured the Boltzmann constant kB using fixed-path, cylindrical, acoustic gas thermometers (c-AGT) and we also measured kB using quantised-voltage-noise-source-calibrated (QVNS) Johnson noise thermometers (JNT). While conducting that research, we have made progress towards disseminating the kelvin using c-AGT and QVNS-JNT. For c-AGT, we measured the performance of three differently-shaped microwave antennas and concluded that a straight wire (probe) antenna is appropriate for our cylindrical cavities. The electromagnetic field of the transverse magnetic modes TM(l01) inside a conducting, cylindrical cavity have nodes of zero magnetic field at the rims of both ends of cylindrical cavity and radially distributed maximums on both end surfaces. We used these modes with 4≤l ≤7 to measure the length of a cavity; the results at 300 K had a scatter of approximately one part in 10⁶ about their mean value. Using a cavity made of HR120 (Haynes alloy), we successfully measured microwave resonance frequencies using home-made microwave antennas up to 1000 K. We successfully used acoustic waveguides to conduct sound to and from a cylindrical cavity at temperatures up to 600 K. The QVNS-JNT relies only on electrical measurements; we used this great advantage to confirm the c-AGT measurements of the Boltzmann constant and we will use this advantage to check the dissemination of the kelvin at other temperatures. Our JNT compares the thermal noise power generated by a temperature-sensing resistor (200 ohm at the triple point of water) with the pseudo-random-noise power synthesised by an array of Josephson junctions. We integrated the noise power over a bandwidth of 550 kHz for 33 days to obtain the value kB = 1.3806514(57)x10^-23 J/K with the relative standard uncertainty of 4.1x10^-6. This value is consistent with the CODATA-2010 recommendation: (kB/kB,_CODATA -1) = (1.9 ± 4.1) x10^-6.

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Low-temperature scales and primary thermometers

Dr Jost Engert, Physikalisch-Technische Bundesanstalt, Germany

Abstract

Practical temperature measurements in accordance with the international system of units (SI) require traceability to the actual international temperature scales ITS-90 and PLTS-2000. A short overview will be given of the history of international low-temperature scales adopted by the International Committee for Weights and Measures (CIPM - Comité international des poids et mesures) since 1887. The construction of the PLTS-2000 is reviewed in detail to present the current status of the temperature scales in the region below 1K.

The awaited redefinition of the unit of temperature and the development of the mise-en-pratique of the definition of the kelvin (MeP-K) will change the practice of temperature measurement by permitting the dissemination of the kelvin also by primary thermometry. To support this process new primary low-temperature thermometers are being developed by the partners of the EMRP InK project within work package 4 led by PTB. Specifically, current sensing and magnetic field fluctuation noise thermometers and Coulomb blockade thermometers will be used to investigate the relation between PLTS-2000 and thermodynamic temperature. PTB contributes a new low-temperature noise thermometer to this project. The thermometer is based on standard dc SQUID technology and exploits a correlation technique with an in-situ flux calibration and an integrated conductivity measurement of the metallic noise sensor. First measurements demonstrating the performance of the thermometer will be presented.

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Noise thermometry at ultra low temperatures

Professor Christian Enss, Heidelberg University, Germany

Abstract

The options for primary thermometry at ultralow temperatures are rather limited. In practice most laboratories are using ¹⁹⁵Pt NMR thermometers in the microkelvin range. In recent years current sensing DC-SQUIDs have enabled the use of noise thermometry in this temperature range. Such devices have also demonstrated the potential for primary thermometry. One major advantage of noise thermometry is the fact that no driving current is needed to operate the device and thus the heat dissipation within the thermometer can be reduced to a minimum. Ultimately, the intrinsic power dissipation is given by the negligible back action of the readout SQUID. For thermometry in low temperature experiments current noise thermometers and magnetic flux fluctuation thermometers have proven to be most suitable. To make use of such thermometers at ultralow temperatures we have developed a cross-correlation technique that reduces the amplifier noise contribution to a negligible value. For this the magnetic flux fluctuations caused by the Brownian motion of the electrons in our noise source are measured inductively by two dc-SQUID magnetometers simultaneously and the signals from these two channels are cross-correlated. Experimentally we have characterised a thermometer made of a cold-worked high purity copper cylinder with a diameter of 5mm and a length of 20mm for temperatures between 43µK and 0.8K. For a given temperature a measuring time below one minute is sufficient to reach an accuracy of better than one percent. The extremely low power dissipation in the thermometer allows continuous operation without heating effects.

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Nanoscale thermometry at sub-kelvin temperatures

Professor Jukka Pekola, Aalto University, Finland

Abstract

Nanostructures provide ways to probe temperature locally. I will discuss a few thermometers probing the distribution of electrons in metallic conductors. I will begin by describing the relevant thermal models with associated paths of heat relaxation. As an example I will present the Coulomb blockade thermometer (CBT), normal-superconductor junctions (NIS) and proximity Josephson junctions (SNS). I will describe the factors limiting the applicability of these thermometers, on one hand, at the very lowest, and on the other, at ever higher temperatures. Nanoscale thermometers naturally probe temperature on small objects as well, and their thermal time constants are short. Therefore they are ideal probes in studies of non-equilibrium thermodynamics and in single-photon calorimetry: I will describe our recent efforts in these directions.

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Chair

Professor John Saunders, Royal Holloway University of London, UK

Precision current sensing noise thermometry in the millikelvin regime

Dr Aya Shibahara, Royal Holloway University of London, UK

Abstract

The use of low temperature platforms with base temperatures below 1 K is rapidly expanding, for fundamental science, sensitive instrumentation and new technologies of potentially significant commercial impact. Precise measurement of the thermodynamic temperature of these low temperature platforms is crucial for their operation. We describe the development of a series of precise current sensing noise thermometers (CSNTs) as practical thermometers for implementing the new kelvin on such platforms. The thermometers have been fabricated with a range of resistances from 1.29 Ω down to 0.2 mΩ. This results in either a thermometer that has been optimised for speed, taking advantage of the improvements in superconducting quantum interference device (SQUID) noise and bandwidth, or a thermometer optimised for ultra-low temperature measurement, minimising the system noise temperature. A cost-effective and user-friendly data acquisition and analysis system has been developed for the CSNT, as a measurement procedure that can be implemented in any laboratory with standard instrumentation. Progress in the use of an in-built superconducting transition fixed point device for self-calibration of the CSNT will be described. The procedure to make the thermometer primary and contributions to the uncertainty budget will be discussed. Initial comparison measurements between a primary CSNT with a superconducting reference device (SRD) traceable to the PLTS-2000 will be presented. Progress in a direct comparison of the CSNT and a ³He melting curve thermometer down to sub mK temperatures, using a new ultralow temperature platform will be discussed.

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