Thermometry below 1 K

Abstract

Temperature measurements below 1 K are relatively easy if they are only made to provide a scaling parameter for some other physical quantity because there is a multitude of practical methods to use. That there is problem of relating these measurements to the thermodynamic basis of temperature, however, becomes obvious when any two methods are applied simultaneously and produce discrepant results. Solving this problem requires identification and correction of systematic errors by analysing their sources for each thermometer in detail. In the very few cases where this procedure is successful, one obtains a primary thermometer. Since no primary thermometer is available that is also easily reproducible, one has to leave the firm thermodynamic basis frequently in favour of the reliability of secondary thermometers.This paper reviews the current status of thermometry from a metrological point of view. It emphasizes the relation to thermodynamic temperature without completely ignoring practical questions. Thus principles and limitations are discussed in detail for primary thermometers as well as for those secondary thermometers that can be employed to extend the temperature range by extrapolation. Practical thermometry is covered in a few instructive examples which illustrate the effects of experimental problems on temperature measurement. A considerable fraction of the paper is devoted to temperature reference standards, and the actual state of their underlying scales, that are used to reproduce accurately temperature values for calibration of secondary thermometers without running primary thermometers.

On the Paramagnetic Impurity Concentration of Silicate Glasses from Low-Temperature Physics

“…Without the RERs, hence no distribution of the type (3), the interference from separate tunneling paths is only likely to give rise to a very weak Aharonov-Bohm effect. Hence, it will be those TSs nesting within the RERs that will give rise to an enhanced A-B effect and these TSs can be minimally described -for example -through Hamiltonian (5) and with distribution (3) thus modified to favour near-degeneracy [11]:…”

“…n AT S being the ATSs' concentration (a parameter always lumped together with P * ) and with H 3LS given by Eq. (5). The angular brackets · · · denote quantum, statistical and disorder averaging.…”

Multilevel Tunnelling Systems and Fractal Clustering in the Low‐Temperature Mixed Alkali‐Silicate Glasses

“…This is not surprising, for materials made up of a good glass-former (e.g., SiO 2 , Al 2 O 3 , etc.) and good crystal-formers (e.g., BaO, K 2 O,…) are known to be multiphased [4] with the good crystal-formers generating their own pockets and channels carved out within the otherwise homogeneously amorphous network of the good glass-former's ions [5]. Within these pockets and channels, incipient nano- or even microcrystals may form, but the point of view will be taken in this work that on general grounds even the purest, single-component (e.g., As, SiO 2 ) glass-former will be rich in RER unless the quench-rate from the melt is so large as to avoid the formation of crystalline regions or RER.…”

“…A typical glass giving such strong response has the composition Al 2 O 3 -BaO-SiO 2 thus, a MAS ceramic-glass, herewith termed AlBaSiO. The measurements were made on thick sol-gel fabricated films, a fabrication procedure favoring microcrystal formation [4], cooled in a 3 He- 4 He dilution refrigerator reaching temperatures as low as 6 mK. Magnetic effects have been reported for both the real and imaginary part of ϵ at low frequency ( ω ~ 1 kHz), for the heat capacity C p (see, e.g., [21]) and for the polarization echo (where changes in the presence of a magnetic field have been the strongest [10–12]) as well.…”

The Roles of the Mise en Pratique for the Definition of the Kelvin

“…The first, based on a noisevoltage measurement using cross correlators, has been used to measure temperatures in the range from a few kelvins to 2500 K. Although it provides useful experimental validation of other methods (e.g., [17,18]), it cannot easily achieve the low relative uncertainties (<0.002 %) obtainable with other direct methods such as acoustic gas thermometry. The second class of noise thermometer is based on noise measurement using superconductive quantum interference devices (SQUID) at temperatures of a few kelvins down to a few millikelvins [19][20][21][22]. At these temperatures where relative uncertainties of 0.1 % are very useful, a well-behaved, primary noise thermometer has considerable appeal.…”