Optimization of SPRT measurements of freezing in a zinc fixed-point cell

Abstract

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.

Impurity and thermal modelling of SPRT fixed-points

“…It was shown in [18] that the departure from the shape predicted by the numerical model towards the end of freezing could be explained by the fact that a significant amount of metal continues freezing elsewhere in the fixed-point cell, after the metal immediately surrounding the SPRT sensing element has completely frozen. This often leads to a slow decline in the freezing curve before the sudden fall in temperature as the last material freezes.…”

“…A series of measurements of the freezing curve of a zinc fixedpoint cell was described in [18] and compared with a numerical model (described in the next section) to elucidate the influence of furnace environment by varying the temperature setpoint of the top heater zone of a three-zone furnace. These curves are shown in Figure 5.…”

“…It is a one-dimensional model based on finite element analysis, and includes a 'control volume' method to explicitly track the material phase as a function of position, and models recalescence. This model was employed in [18] to parameterize zinc freezing curves. As the shape of the freezing curve predicted by the model is dictated primarily by impurity effects, it was used, in conjunction with experimental results, to determine the furnace settings for which spurious thermal effects are absent, that is, to optimize the furnace.…”

“…As the shape of the freezing curve predicted by the model is dictated primarily by impurity effects, it was used, in conjunction with experimental results, to determine the furnace settings for which spurious thermal effects are absent, that is, to optimize the furnace. It was also used to parameterize impurity effects [18].…”

“…It is found that freezing durations significantly shorter than ~15 hours yield freezing curve shapes which vary widely depending on the particular freezing duration. The model also allows visualization of the impurity distribution as a function of time and position, and was parameterized to the same zinc freezing curves as in [18], yielding comparable impurity levels.…”