Phase-field modelling of ITS-90 fixed-point cells

Calibrations of Standard Platinum Resistance Thermometers (SPRTs), the defined interpolating instrument of the International Temperature Scale of 1990 (ITS-90), are performed using fixed-point cells containing nearly pure materials (of the order of 99.9999%). The effect of impurities at the parts per million levels on the measured temperature during fixed point realisations is often the most significant contribution to the calibration uncertainty budget. The recommended method for evaluating this impurity effect relies on chemical analyses whose uncertainties and detection limits are often too large at the small quantities of impurities present, and as such cannot inform a meaningful correction; rather, this result informs the impurity contribution to the uncertainty budget. In order to elucidate the effects of the myriad experimental parameters which may affect the cell conditions, and hence the measured freezing curve, a 2D-axisymmetric coupled heat and impurity transport model utilising the Phase-field Method is developed. A broad qualitative study of tin point realisations illustrates a range of phenomena—including thermal gradient interface instabilities and solid-state de-wetting—which have effects on the measured temperature of the order of 100-200 μK. The interfacial instability has not, to our best knowledge, been predicted elsewhere with respect to the realisation scheme studied. The instability wavelength observed in the model is λ=3.1±0.7 mm, which compares favourably with the growing Fourier mode of shortest wavelength predicted by Mullins-Sekerka instability theory (λ≈4 mm). The solid-state de-wetting phenomenon offers a potential mechanism which agrees well with several experimental trends noted in the literature; the existence of a ‘critical’ film thickness during freeze initiation and the presence of a variable temperature depression over the freeze duration. This work provides a basis for tailoring of experimental techniques so that reliable corrections for the effect of impurities can be determined, thus leveraging a step decrease in potential calibration uncertainties. Since this exercise is performed with the UK national temperature standards, this work directly benefits all fields that rely on the precise measurement of temperature. Also, there is significant potential for further development of the model; some avenues for research are suggested