International Journal of Thermophysics

, Volume 35, Issue 6–7, pp 1109–1126 | Cite as

A Phase-Field Solidification Model of Almost Pure ITS-90 Fixed Points

Article

Abstract

A two-dimensional axisymmetric phase-field model of thermo-solutal solidification in freezing-point cells used for calibrating standard platinum resistance thermometers for realization and dissemination of the International Temperature Scale of 1990 is presented. The cell is essentially a graphite crucible containing an ingot of very pure metal (of order 99.9999 %). A graphite tube is inserted along the axis of the ingot to enable immersion of the thermometer in the metal. In this study, the metal is tin (freezing temperature of \(231.928\,^{\circ }\hbox {C}\)). During the freezing of these cells, a steady, reproducible temperature is realized, with a defined temperature that can be used to calibrate thermometers with uncertainties \({<}1\) mK. The model is applied to understand the effect of experimental parameters, such as initiation technique and furnace homogeneity, on the measured freezing curve. Results show that freezing curves whose behavior is consistent with the Scheil theory of solidification can be obtained with a specific furnace temperature profile, and provided that the freeze is of a long duration, the results are consistent with previous one-dimensional models and experiments. Morphological instability is observed with the inner interface initiation technique, causing the interface to adopt a cellular structure. This elevates the measured temperature, in accordance with the Gibbs–Thomson effect. In addition, the influence of initiation techniques on the solidification behavior is examined. The model indicates that an initially smooth inner mantle can ‘de-wet’ from the thermometer well-forming agglomerated solid droplets, following recalescence, under certain conditions. This manifests as a measured temperature depression due to the Gibbs–Thomson effect, with a magnitude of \(100\, {\upmu }\hbox {K}\) to \(200\,{\upmu }\hbox {K}\) in simulations. The temperature rises to that of the stable outer mantle as freezing progresses and the droplets re-melt. It is demonstrated that the effect occurs below a critical mantle thickness. A physical explanation for the origin of the effect is offered showing that it is consistent with solid-state de-wetting phenomena. Consideration is also given to the limitations of the current model configuration.

Keywords

De-wetting Fixed point Freezing point Impurities Modeling Phase-field Thermal effects 

Notes

Acknowledgments

This work was funded by the UK National Measurement Office and the EMRP. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union. Valuable conversations with Richard Rusby (NPL) and John Hunt FRS (Oxford University) are gratefully acknowledged. \({\copyright }\) Crown copyright 2014. Reproduced by permission of the Controller of HMSO and the Queen’s printer for Scotland.

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Copyright information

© Crown Copyright 2014

Authors and Affiliations

  1. 1.National Physical LaboratoryTeddington UK

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