A numerical model of solute and heat transport in extremely pure materials is described. Its purpose is to characterize the effect of impurities on the freezing curves of metals containing impurities at the level of less than 1 part per million. It is used to simulate experiments performed using a commercially available zinc fixed-point cell for SPRT calibrations. The aim is to determine the effect of different vertical temperature gradients on the freezing curve and to find out whether a range of conditions could be determined where there was a good fit between theory and experiment. For this fixed-point cell, agreement between the model and experiment improves as the distribution coefficient k → 0. It is found that the model only agrees with the measured freezing curves over the entire freeze for a narrow range of furnace settings where the temperature profile is most uniform. We suggest that this is because if the furnace settings are not optimized, the solid does not grow uniformly, and freezing may continue in regions remote from the SPRT after the material in the vicinity of the SPRT has finished freezing, so distorting the freezing curve. This effect is not present in the model and so the method presented here enables optimization of the furnace to ensure the SPRT is surrounded by a liquid–solid interface over the entire freezing range. We find that the optimum thermal environment is extremely sensitive to the furnace settings; the optimum thermal environment is found when the temperature is slightly cooler at the top of the cell, as measured in the re-entrant well of the cell. We note that optimizing the freezing process is a necessary step towards using a thermal analysis to correct for the effects of impurities in the sample.

By using a simple model to relate the electromotive force drift rate of Pt–Rh thermoelements to dS/dc, i.e. the sensitivity of the Seebeck coefficient, S, to rhodium mass fraction, c, the composition of the optimal pair of Pt–Rh wires that minimizes thermoelectric drift can be determined. The model has been applied to four multi-wire thermocouples each comprising 5 or 7 Pt–Rh wires of different composition. Two thermocouples were exposed to a temperature of around 1324 °C, one thermocouple to around 1492 °C, i.e. the melting points of the Co–C and Pd–C high temperature fixed points, respectively, and one thermocouple to a series of temperatures between 1315 °C and 1450 °C. The duration of exposure at each temperature was several thousand hours. By performing repeated calibrations in situ with the appropriate fixed point during the high temperature exposure, the drift performance has been quantified with high accuracy, entirely free from errors associated with thermoelectric homogeneity. By combining these results it is concluded that the Pt-40%Rh versus Pt-6%Rh is the most stable at the temperatures investigated. A preliminary reference function was determined and is presented.

Impurities in pure metal fixed points for the calibration of standard platinum resistance thermometers (SPRTs) causes significant variations in the freezing temperature, of the order of sub-mK to several mK. This often represents the largest contribution to the overall uncertainty of the fixed point temperature, and it is therefore of great interest to explore ways of correcting for this effect. The sum of individual estimates (SIE) method, in which the contributions of all the impurities are summed, is the recommended way of determining the correction if one has an accurate knowledge of the impurities present and their low concentration liquidus slopes. However, due to the difficulty in obtaining reliable in-ingot impurity corrections, it remains useful to investigate the influence of impurities on freezing curves using modeling techniques, and ultimately to parameterize the freezing curve by e.g. least-squares fitting to make corrections to the temperature of the freeze. Some success in analyzing freezing curves has been achieved. When parameterizing experimentally determined freezing curves, it is necessary to reliably determine the freezing end-point, and minimize spurious thermal effects. We outline some methods for meeting these requirements. As the influence of impurities is always convolved with thermal influences it is instructive to construct a model which takes into account both heat and impurity transport. We describe the development of more sophisticated models which take both these effects into account.

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