A new interpolation equation in the ITS-90 subrange from the triple point of water to the freezing point of indium

For all the subranges above 0.01 degrees C, other than the interpolation between the triple point of water (TPW) to the melting point of gallium, temperatures on the international temperature scale of 1990 (ITS-90) are specified without the melting point of gallium. This study suggests a new interpolation equation in the subrange from the TPW to the freezing point of indium which is a polynomial of fractional third order with two coefficients to be determined by the measuring values of standard platinum resistance thermometers (SPRTs)' resistance ratios at the melting point of gallium (W Ga) and at the freezing point of indium (W In). A sample set of 30 SPRTs from various countries and laboratories is used to quantify the comparisons between this new interpolation and the ITS-90. Analyses show that the reproducibility is significantly improved compared with the ITS-90 in the same subrange. The peak value of overlapping subrange inconsistencies (SRI) from TPW to the melting point of gallium is reduced from 0.91 mK to 0.21 mK. Both the mean and standard deviation of the SRI peak values for the new equation decrease by approximately a factor of four compared to those of the ITS-90 (mean decreasing form 0.20 mK to 0.05 mK and standard deviation decreasing form 0.32 mK to 0.07 mK). Type 3 non-uniqueness (NU3) determinations of the same subrange have also been looked into with a data set of four SPRTs compared in thermostatic baths using a copper block and the results show that NU3 scales down from a range -0.15 mK-0.25 mK of the ITS-90 to -0.10 mK-0.15 mK of the new interpolation equation. Propagation of Uncertainties investigation shows that the new equation inflates merely 7% the measurement uncertainties of fixed points in a relatively short interval from 30 degrees C to 60 degrees C.