Uncertainty estimation for the effect of impurities on fixed points requires an accurate assay of the fixed-point material. To apply a correction also needs a knowledge of the liquidus slope of the solute binary system. Two methods are presented here for giving a realistic uncertainty and potential for correction without detailed knowledge of the impurities present. Both methods are based on the Scheil equation. The first method uses the gradient at about 50 % solid; and where some limited knowledge of impurities is available, this method can, in cases where the bulk of impurities segregate preferentially into the liquid phase, be used to apply a correction. To apply an uncertainty simply knowing typical impurities for a particular metal may be considered sufficient. The second method involves a best fit for the four variables in the Scheil equation. It is shown that this second method can work even where multiple impurities are present, but that when applied to real data, problems arise due to deviations from Scheil behavior. This deviation is thought to be due to difficulties in maintaining a uniform solid/liquid interface at the end of a freeze.

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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.

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