In 2011, a working group of the Consultative Committee for Thermometry published their best estimates of the differences between the thermodynamic temperature T and its approximation (T90), the temperature according to the International Temperature Scale of 1990, ITS-90. These consensus estimates, in combination with measurements made in accordance with ITS-90, are an important alternative to primary thermometry for those requiring accurate measurements of thermodynamic temperature. Since 2011, there has been a change in the definition of the kelvin and significant improvements in primary thermometry. This paper updates the (T − T90) estimates by combining and analyzing the data used for the 2011 estimates and data from more recent primary thermometry. The results of the analysis are presented as a 12th-order polynomial representing the updated consensus values for the differences and a sixth-order polynomial for their uncertainty estimates.

The International Temperature Scale of 1990 (ITS-90) underpins much of modern thermometry, yet efforts to comprehensively characterize and improve its reproducibility have been limited. Here, a low-uncertainty data set drawn from 13 standard platinum resistance thermometers is used to quantify all three main manifestations of scale irreproducibility over the range 13.8033 K to 273.16 K. Four overlapping ITS-90 subranges are investigated, along with three prospective approaches to temperature scale improvement. The current version of the Guide to the Realization of the ITS-90 is found to overestimate scale realization uncertainties, and recommendations are made to revise the guidance provided therein. Replacing the ITS-90 deviation function of subrange 3 with a new version further improves the interpolation quality of this subrange by a factor of two, and calibrating thermometers at the triple point of xenon rather than the triple point of mercury cuts the realization uncertainty of subrange 4 in half. New linear subranges spanning from the triple point of water to the triple points of mercury or xenon could be added to the scale without compromising the performance of the existing subranges. Combining new interpolation equations with calibration at the triple point of xenon provides the basis for a much more reproducible temperature scale than the ITS-90, with magnification of fixed point uncertainties nearly eliminated for all of subranges 1–4 above the triple point of oxygen.

The redefinition of the kelvin has increased focus on thermometry techniques that use the newly fixed value of the Boltzmann constant to realize thermodynamic temperature. One such technique that has advanced considerably in recent years is refractive-index gas thermometry. Generalized as refractive-index gas metrology (RIGM), this also includes a range of applications outside of temperature realizations, such as pressure standards and measurements of the physical properties of gases. Here, the current data situation in the field is reviewed, encompassing the latest developments and remaining challenges, in order to suggest possible approaches for reducing RIGM uncertainties and improving RIGM applications. New analyses of existing experimental literature data are presented for the second density virial coefficient Bρ of helium, neon, argon, and nitrogen; the third density virial coefficient Cρ of nitrogen; and the third dielectric virial coefficient Cε of helium, neon, and argon. A need is identified for more accurate reference-quality datasets to be measured or calculated in several areas, with robust uncertainty budgets, to support future RIGM advancements. The most urgent of these are the bulk modulus of copper; thermodynamic accuracy of the International Temperature Scale of 1990; molar optical refractivity AR of neon, argon, and nitrogen; diamagnetic susceptibility χ0 of neon and argon; second density virial coefficient Bρ of argon; third dielectric virial coefficient Cε of helium, neon, and argon; and third optical refractivity virial coefficient CR of helium and neon.

The thermal metrology community is considering revising the International Temperature Scale of 1990 (ITS-90), motivated by the opportunity to improve the thermodynamic accuracy, reproducibility, and ease of use of the scale, as well as health and safety concerns with the use of mercury in the current scale. This paper considers the mathematical structure of the standard platinum resistance thermometer (SPRT) interpolations of the ITS-90 and identifies (i) mathematical features that are advantageous and should be retained, (ii) opportunities for improvements, and (iii) the research required to maximise the benefits from such improvements. The improvements considered include minor adjustments that leave ITS-90 intact, numerical adjustments to reference resistance ratios that preserve the structure of ITS-90, fixed-point replacements, new subranges, and large-scale changes in the mathematical structure of the interpolations. A significant research effort will be required to implement some of the changes. Overall, an improvement in the thermodynamic accuracy by a factor of about ten is relatively easily realised, but improvements in reproducibility of the scale of even a couple of tens of percent will be hard won. For most users, the costs and inconvenience of a substantial scale revision may outweigh the benefits.

Measurements of the refractive indices of helium and argon using a quasi-spherical microwave resonator and upgraded experimental protocol are reported at the temperatures of the triple points of water and xenon. The results at the triple point of water are used to determine the compressibility of the resonating cavity, which is bounded by the copper shell of the resonator. This experimentally-determined compressibility is consistent with the literature value for copper, but with much smaller measurement uncertainty. The measured compressibility is extrapolated to the triple point of xenon, and combined with the refractive index results at that temperature to determine the thermodynamic accuracy of the International Temperature Scale of 1990 (ITS-90): (T - T90) = (-6.9 +/- 1.7) mK at ITS-90 temperature T-90 = 161.405 96 K, corresponding to a xenon triple point thermodynamic temperature of T = (161.3991 +/- 0.0017) K. The experimental compressibility is further extrapolated to the triple points of argon, oxygen and neon, and used to re-analyze earlier refractive index gas thermometry measurements made using the same resonator, yielding updated values with reduced uncertainties: (T - T-90) = (-4.1 +/- 1.6) mK at T-90 = 83.8058 K, (T - T-90) = (-2.0 +/- 0.8) mK at T-90 = 54.3584 K, and (T - T-90) = (-0.61 +/- 0.49) mK at T-90 = 24.5561 K. The ITS-90 thermodynamic accuracy results of the present refractive index gas thermometry study agree with those previously reported by acoustic gas thermometry and dielectric constant gas thermometry.

All standard platinum resistance thermometer (SPRT) subranges of the International Temperature Scale of 1990 (ITS-90) extending below 0 ◦C include the triple point of mercury as a defining fixed point [1, 2]. Thus, increasingly restrictive global and local regulations that aim to eventually eliminate the mining, trade and use of mercury [3] threaten the ability of laboratories to realize the ITS-90, and work is underway to develop alternatives to mercury triple point cells for thermometer calibration [4]. Of the leading candidates being explored as alternatives to the mercury triple point, the triple point of xenon is by far the best placed from an interpolation perspective [4]. The desirable positioning of the xenon triple point was considered by the creators of the ITS-90 for inclusion in the scale, but it was rejected due to poor reproducibility of contemporary xenon fixed points, with mercury taking its place as a back-up choice [5]. The xenon reproducibility problem was later resolved as being largely due to chemical contamination by krypton impurities, and a specially prepared batch of ultra-high purity Spectra Gases “SG03” xenon containing 0.003 ppm† of krypton impurity yielded very flat melt plateaux with melting range within ± 10 μK [6]. A commercial xenon product from the same supplier (Spectra Gases “Dark Matter” xenon) containing 0.05 ppm of krypton or less was found to give broader but still satisfactory melt plateaux resulting in a triple point realization temperature close to that of SG03 [7]. The chemical impurity profiles of these two xenon gas samples are listed in table 1. On the basis of these experiments, it is recommended that krypton content in xenon triple point cells does not exceed 0.1 ppm, twice the limiting concentration specified in the commercial sample from reference [7]. Since a reliable low-krypton xenon supply is needed to make xenon a viable mercury replacement, efforts were undertaken to search for present day sources of such gas. The gas sources below represent a snapshot based on communication in 2020; the list of suppliers is not exhaustive and the new gas products in table 1 have not yet been tested in fixed points. Even if xenon triple point cells become widely adopted by the thermometry community, the quantities of gas required will likely remain small compared to other xenon applications.

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.

It is widely recognized that the Mercury triple point (MTP) being situated very close to the Water triple point (WTP) constitutes a weakness in the International Temperature Scale of 1990 (ITS-90), in addition to safety concerns related to the use and transportation of Mercury. As such, a substitution for a safer, high-quality fixed point about half way between the Argon and Water triple points would be highly desirable. Now, a direct comparison is described of a Xenon cell filled in 2005 by the National Research Council Canada (NRC) and a more recently produced cell of the Istituto Nazionale di Ricerca Metrologica (INRIM). The present paper discusses the INRiM 2017 measurements on both the INRiM and NRC cells, with a follow-up measurement at NRC, and presents the difference between the two cells, (0.17 +/- 0.08) mK with the uncertainties of each cell's realization of the Xenon triple point (XeTP), 0.11 mK for the INRiM cell and 0.07 mK for the NRC cell (k = 1). In addition, the effect of substituting Mercury with Xenon on Type 1 non-uniqueness ('SRI', subrange inconsistency), Type 3 non-uniqueness ('NU3', cSPRT variability) and propagation of fixed point realization uncertainty is shown and discussed.

The implementation of microwave refractive index gas thermometry at the National Research Council between 24.5 K and 84 K is reported. A new gas-handling system for accurate control and measurement of experimental gas pressure has been constructed, and primary thermometry measurements have been taken using a quasi-spherical copper resonator and helium gas at temperatures corresponding to three defining fixed points of the International Temperature Scale of 1990 (ITS-90). These measurements indicate differences between the thermodynamic temperature T and ITS-90 temperature \(T_{90}\) of \(\left( T - T_{90} \right) = -0.60 \pm 0.56\) mK at \(T_{90} = 24.5561\) K, \(\left( T - T_{90} \right) = -2.0 \pm 1.3\) mK at \(T_{90} = 54.3584\) K, and \(\left( T - T_{90} \right) = -4.0 \pm 2.9\) mK at \(T_{90} = 83.8058\) K. The present results at \(T_{90} = 24.5561\) K and \(T_{90} = 83.8058\) K agree with previously reported measurements from other primary thermometry techniques of acoustic gas thermometry and dielectric constant gas thermometry, and the result at \(T_{90} = 54.3584\) K provides new information in a temperature region where there is a gap in other recent data sets.

A cryogenic fixed point cell has been filled with high purity (99.999%) sulfur hexafluoride (SF6) and measured in an adiabatic closed-cycle cryostat system. Temperature measurements of the SF6 melting curve were performed using a capsule-type standard platinum resistance thermometer (CSPRT) calibrated over the International Temperature Scale of 1990 (ITS-90) subrange from the triple point of equilibrium hydrogen to the triple point of water. The measured temperatures were corrected by 0.37 mK for the effects of thermometer self-heating, and the liquidus-point temperature estimated by extrapolation to melted fraction F = 1 of a simple linear regression versus melted fraction F in the range F = 0.53 to 0.84. Based on this measurement, the temperature of the triple point of sulfur hexafluoride is shown to be 223.555 23(49) K (k = 1) on the ITS-90. This value is in excellent agreement with the best prior measurements reported in the literature, but with considerably smaller uncertainty. An analysis of the detailed uncertainty budget of this measurement suggests that if the triple point of sulfur hexafluoride were to be included as a defining fixed point of the next revision of the International Temperature Scale, it could do so with a total realization uncertainty of approximately 0.43 mK, slightly larger than the realization uncertainties of the defining fixed points of the ITS-90. Since the combined standard uncertainty of this SF6 triple point temperature determination is dominated by chemical impurity effects, further research exploring gas purification techniques and the influence of specific impurity species on the SF6 triple point temperature may bring the realization uncertainty of SF6 as a fixed point material into the range of the defining fixed points of the ITS-90.

The magnetic field-induced changes in the conductivity of metals are the subject of intense interest, both for revealing new phenomena and as a valuable tool for determining their Fermi surface. Here we report a hitherto unobserved magnetoresistive effect in ultra-clean layered metals, namely a negative longitudinal magnetoresistance that is capable of overcoming their very pronounced orbital one. This effect is correlated with the interlayer coupling disappearing for fields applied along the so-called Yamaji angles where the interlayer coupling vanishes. Therefore, it is intrinsically associated with the Fermi points in the field-induced quasi-one-dimensional electronic dispersion, implying that it results from the axial anomaly among these Fermi points. In its original formulation, the anomaly is predicted to violate separate number conservation laws for left- and right-handed chiral (for example, Weyl) fermions. Its observation in PdCoO 2 , PtCoO 2 and Sr 2 RuO 4 suggests that the anomaly affects the transport of clean conductors, in particular near the quantum limit.

Progress toward the development of a low-temperature microwave refractive index gas thermometry implementation for primary thermometry at NRC is reported. A prototype quasi-spherical copper resonator has been integrated into a cryogenic system with a 5 K base temperature, and preliminary microwave measurements in vacuum have been completed to characterize the resonator between 5 K and 297 K. The dependence of experimental results on spectral fitting background terms, 1st- and 2nd-order shape corrections, and waveguide corrections has also been explored. The current NRC results agree with previous room-temperature measurements on the same resonator at NIST, and indicate no significant change in resonator shape between room temperature and low temperature. The temperature dependences of the resonator electrical conductivity and linear thermal expansion coefficient, as obtained from the microwave resonances, agree with published literature values for oxygen-free high-conductivity copper measured using other techniques.

The axial anomaly leads to the violation of separate number conservation laws for left- and right-handed massless chiral (or Weyl-) fermions. For a certain class of gapless semiconductors, for which the low-energy band structure is described in terms of Weyl-fermions, the application of a magnetic field parallel to the electrical current is predicted to induce a large suppression of the electrical resistivity. To date, there is no concrete experimental realization of a Weyl semi-metal or unambiguous evidence for this field-induced phenomenon. Here, we report the observation of a very large negative magnetoresistance in the extremely clean quasi-two-dimensional metal PdCoO$_2$. Our experimental study provides strong support for a scenario where this unconventional response results from the axial anomaly of field-induced quasi-one-dimensional conduction channels. The observation of this effect in PdCoO$_2$ demonstrates that the axial anomaly is a general feature of the longitudinal magnetotransport of clean and weakly correlated three-dimensional metals.

The magnetic field-induced changes in the conductivity of metals are the subject of intense interest, both for revealing new phenomena and as a valuable tool for determining their Fermi surface. Here, we report a hitherto unobserved magnetoresistive effect in ultra-clean layered metals, namely a negative longitudinal magnetoresistance that is capable of overcoming their very pronounced orbital one. This effect is correlated with the inter-layer coupling disappearing for fields applied along the so-called Yamaji angles where the inter-layer coupling vanishes. Therefore, it is intrinsically associated with the Fermi points in the field-induced quasi-one-dimensional electronic dispersion, implying that it results from the axial anomaly among these Fermi points. In its original formulation, the anomaly is predicted to violate separate number conservation laws for left- and right-handed chiral- (e.g. Weyl) fermions. Its observation in PdCoO$_2$, PtCoO$_2$ and Sr$_2$RuO$_4$ suggests that the anomaly affects the transport of clean conductors, particularly near the quantum limit.

In the iron pnictides, superconductivity occurs at the border of an antiferromagnetic (AF) order. A natural question, then, is whether quantum criticality plays a role in the phase diagram. At the beginning stage of this six-year-old field, it was proposed that a quantum critical point (QCP) can be realized upon an isoelectronic Pfor As substitution of the AF parent iron arsenides. This has turned out to be a fruitful direction, and the latest work of James Analytis and co-workers has provided the strongest evidence yet that a QCP does exist.

Quantum critical behaviour has been observed in many metallic systems that do not behave conventionally as Fermi liquids. High-magnetic-field experiments now reveal clear evidence for quantum criticality in an iron-based high-temperature superconductor. The physics of quantum critical phase transitions connects to some of the most difficult problems in condensed matter physics, including metal–insulator transitions, frustrated magnetism and high-temperature superconductivity. Near a quantum critical point, a new kind of metal emerges, the thermodynamic and transport properties of which do not fit into the unified phenomenology for conventional metals—the Landau Fermi-liquid theory—characterized by a low-temperature limiting T-linear specific heat and a T2 resistivity1. Studying the evolution of the temperature dependence of these observables as a function of a control parameter leads to the identification of both the presence and the nature of the quantum phase transition in candidate systems. In this study we measure the transport properties of BaFe2(As1−xPx)2 below the critical temperature Tc by suppressing superconductivity with high magnetic fields. At sufficiently low temperatures, the resistivity of all compositions ( ) crosses over from a linear to a quadratic temperature dependence, consistent with a low-temperature Fermi-liquid ground state. As compositions with optimal Tc are approached from the overdoped side, this crossover becomes steeper, consistent with models of quantum criticality where the effective Fermi temperature TF goes to zero.

We present band structure calculations and quantum oscillation measurements on LuRh2Si2, which is an ideal reference to the intensively studied quantum critical heavy-fermion system YbRh2Si2. Our band structure calculations show a strong sensitivity of the Fermi surface on the position of the silicon atoms z(Si) within the unit cell. Single crystal structure refinement and comparison of predicted and observed quantum oscillation frequencies and masses yield z(Si) = 0.379 c in good agreement with numerical lattice relaxation.This value of z(Si) is suggested for future band structure calculations on LuRh2Si2 and YbRh2Si2. LuRh2Si2 with a full f electron shell represents the 'small' Fermi surface configuration of YbRh2Si2. Our experimentally and ab intio derived quantum oscillation frequencies of LuRh2Si2 differ significantly from the results of earlier measurements on YbRh2Si2. Consequently, our results confirm the contribution of the f electrons to the Fermi surface of YbRh2Si2 at high magnetic fields. Yet, the limited agreement with refined fully itinerant local density approximation calculations highlights the need for more elaborate models to describe the Fermi surface of YbRh2Si2.

[en] The intermetallic compound LuRh 2 Si 2 is of interest as a non-magnetic reference compound to the heavy fermion material YbRh 2 Si 2. YbRh 2 Si 2 features an intensively studied quantum critical point (QCP) when small magnetic fields suppress the Neel temperature to zero. Signatures in transport and thermodynamic properties suggest a reconstruction of the Fermi Surface from a small configuration with localised f-electrons in the antiferromagnetic phase to a large configuration with itinerant f-electrons in the paramagnetic phase. Hence isostructural LuRh 2 Si 2 with its completely filled f-shell and identical lattice parameters is a perfect reference compound for the small Fermi surface configuration. Here we present band structure calculations of LuRh 2 Si 2 and compare predicted and observed Shubnikov-de Haas frequencies under different angles in dependence of the relative z/c position of the Si atoms.

We present band structure calculations of the non-magnetic compound LuRh2Si2 which serves as a reference for YbRh2Si2, a prototypical material for the investigation of quantum critical points. The relative z position of the Si atoms is found to have a strong impact on the band structure and the Fermi surface topology. We find the total energy to be minimized for z=0.381c whereas a comparison of predicted extremal orbits with Shubnikovde Haas frequencies shows best agreement at the experimental value z=0.379c. We therefore recommend usage of z=0.379c for future electronic structure calculations of LuRh2Si2 and YbRh2Si2. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

We present band structure calculations and quantum oscillation measurements on LuRh {sub 2} Si {sub 2}, which is an ideal reference to the intensively studied quantum critical heavy-fermion system YbRh {sub 2} Si {sub 2}. Our band structure calculations show a strong sensitivity of the Fermi surface on the position of the silicon atoms z {sub Si} within the unit cell. Single crystal structure refinement and comparison of predicted and observed quantum oscillation frequencies and masses yield z {sub Si}= 0.379 c in good agreement with numerical lattice relaxation. This value of z {sub Si} is suggested for future band structure calculations on LuRh {sub 2} Si {sub 2} and YbRh {sub 2} Si {sub 2}. LuRh {sub 2} Si {sub 2} with a full f electron shell represents the'small'Fermi surface configuration of YbRh {sub 2} Si {sub 2}. Our experimentally and ab intio derived quantum oscillation frequencies of LuRh {sub 2} Si {sub 2} differ significantly from the results of earlier measurements on YbRh {sub 2} Si {sub 2}. Consequently, our results confirm the contribution of the f electrons to the Fermi surface of YbRh {sub 2} Si {sub 2} at high magnetic fields. Yet, the limited agreement with refined fully itinerant local density approximation calculations highlights the need for more elaborate models to describe the Fermi surface of YbRh {sub 2} Si {sub 2}.(paper)