A Standardized Interpolation of Temperature Using Rhodium–Iron Resistance Thermometers Over the Interval 4.2 K to 24.5 K

The worldwide history and present state of development of rhodium–iron resistance thermometers (RIRTs) is briefly reviewed. A standardized interpolation method using RIRTs with the nominal composition of 0.5 % Fe (by mole) is presented, with examples using data taken from 60 RIRTs made from a variety of wire batches and sources worldwide over the last 40 years. The parameterization exploits the favorable characteristics of the Cragoe reduced resistance Z(τ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z(\tau )$$\end{document} and a suitably reduced temperature τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}. A reference function Zref(τ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z_\mathrm{ref}(\tau )$$\end{document} which approximates the average characteristics of selected wire is derived for use over the interval 0.65 K to 24.5561 K on the ITS-90. The deviations of real RIRT data from this reference function are examined, and simple four-parameter Fourier-series solutions for the resulting deviation curves are presented. Despite the fact that the wire samples may be of different origins or state-of-anneal, it was found that the interpolations are successful for most of the samples studied over the 4.2 K to 24.5561 K interval, at the level of ≈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx $$\end{document}1 mK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {mK}$$\end{document} standard uncertainty or less. This method would allow for calibrations of most RIRTs over this interval using only six calibration points, permitting an efficiency not achievable using the common least-squares curve-fitting calibration methods. The potential of this formalism for a standardized interpolation scheme using RIRTs is discussed.