Estimating the influence of impurities on the freezing point of tin

Abstract

The sum of individual estimates (SIE) and the overall maximum estimate (OME) are two methods recommended to estimate the influence of impurities on the temperatures of the liquid–solid phase transformations of high-purity substances. The methods are discussed starting with the basic crystallographic facts, and their application is demonstrated in detail by applying them to the freezing point of tin as a first example. The SIE method leads to a temperature correction with a corresponding uncertainty while the OME method yields only an uncertainty that is, perhaps not unexpectedly, larger than that of the SIE approach. The necessary sensitivity coefficients (derivatives of the liquidus lines) are tabulated, together with the equilibrium distribution coefficients. Other than the necessity of obtaining a complete elemental analysis of the fixed-point material using glow discharge mass spectrometry (or other suitable techniques), there remain no technical barriers to adopting the preferred SIE method. While the use of the method, and particularly the application of a temperature correction to account for the impurity influence, requires a paradigm shift within the thermometry community, improved interoperability and harmonization of approach are highly desirable goals. The SIE approach maximizes the application of scientific knowledge and represents the best chance of achieving these common goals.