Feasibility of primary thermometry using refractive index measurements at a single pressure

Abstract

Refractive index gas thermometry (RIGT) uses the dependence of the relative dielectric permittivity on the density of a noble gas (He), typically measured with a temperature-controlled resonator. On an isotherm, to a good approximation, the slope of the dielectric permittivity versus pressure gives the thermodynamic temperature T. To measure T with a low uncertainty, one must measure the absolute value of the pressure with a low uncertainty and know the compressibility of the resonator wall. This article shows how to use RIGT in a novel way between 5 K and 25 K. Instead of changing the pressure on an isotherm (J.W. Schmidt et al., Phys. Rev. Lett., 98, 254504 (2007)), a constant pressure of pure helium gas is maintained at multiple temperatures. After calibration of the resonator under vacuum at different temperatures, all thermometry is performed at a single pressure and referred to a fixed point of the International Temperature Scale of 1990 (ITS-90) (here the neon triple point at 24.5561 K). The quantity that yields the temperature is the ratio of the resonance frequencies of a microwave mode in the resonator measured at the fixed point and at the unknown temperature. This paper describes the theoretical model of Single-Pressure Refractive Index Gas Thermometry (SPRIGT) and analyses the shifts and broadenings due to non-ideal behaviour. The technique should enable a helium-based measurement of thermodynamic temperature with a resolution better than 25 μK and an uncertainty of around 250 µK.

NRC Microwave Refractive Index Gas Thermometry Implementation Between 24.5 K and 84 K

“…Polarizing gas thermometry has been implemented most prominently in the technique of dielectric constant gas thermometry (DCGT), in which the thermodynamic temperature is obtained from electrical capacitance measurements [8,9]. A different implementation of polarizing gas thermometry is refractive index gas thermometry (RIGT), in which the refractive index of the working gas is linked to the thermodynamic temperature [10][11][12][13][14][15].…”

Resonance frequency measurement with accuracy and stability at the 10−12 level in a copper microwave cavity below 26 K by experimental optimization

“…4f. High-stability of 3.7 parts per trillion (ppt, 1 ppt ≡ times better than those in our previous work [4], 0.064 ppb and 0.095 ppb with the same integration time and Popt = −10 dBm [1]. In SPRIGT, the thermodynamic temperature uncertainty has many influence factors, frequency is one of the major factors as shown in our previous work [1] and the RIGT review paper [2].…”

“…For the pressure control system, the detailed content is not emphasized in this work since it has been presented in our previous work [22]. The uncertainty contribution of pressure to measurements of thermodynamic temperature has also been reported in our previous work [1] and Fig. 2 in the review paper of RIGT [2].…”

“…The stability and uncertainty still have room for improvement, provided later using the time reference, FS740 locked to GPS with rubidium atomic clock configured outdoor antenna, and microwave amplifiers. Besides, thermodynamic temperatures calculated from different modes were determined for the isobar p = 60 kPa, based on the SPRIGT principle [1]. Fig.…”

“…A convenient way to perform experiments is to use a servo loop to lock the oscillator frequency to the maximum of a resonance. Then the frequency stability depends on the shape and sharpness of the resonance, the signal-to-noise ratio, and the type of noise that predominates at the time scale under consideration [1,18,19]. For SPRIGT, in reality, it is essential to perform regular scans of the resonance line to check for any change in the width and shape (see Section 3.1), which will take typically two minutes.…”