Modelling the freezing behaviour of ITS-90 metal fixed points for better understanding of the influence of impurities and thermal effects

• Main Author: Malik, Zohaib
• Other Authors: McPhail, David ; Lee, Peter D. ; Lowe, Dave H.
• Published: Imperial College London 2012
• Subjects: 669.92
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.560710

The methods currently used by metrologists for estimating the influence of impurities in metal fixed points require accurate knowledge of the concentrations of impurities present and of liquidus slopes of binary systems. In this thesis, two alternative methods are presented that can estimate the influence of impurities without requiring any knowledge of the impurities. Both methods are based on Scheil’s solidification model. By using a numerical solidification model it is shown that the freezing behaviour of a fixed point cell can approximate to Scheil’s model when the freezing time is greater than x2 / D, where x is the thickness of the ingot and D is the diffusion coefficient of impurities in the liquid. The first method uses the gradient of a freezing curve at about 0.5 fraction solid, and is able to predict the influence of impurities with a maximum uncertainty of around 25%. This is assuming that all the important impurities have distribution coefficients much lower than 1, which is often the case in practice. By applying some modifications to this method, it is possible to determine whether or not the distribution coefficients of the dominant impurities lie below or above 1. The second method involves numerically best fitting Scheil’s equation to a freezing curve. This method works for materials with multiple impurities, but problems arise when it is applied to an experimental freezing curve due to distortion in the freeze plateau. This is thought to be caused by the thermal effects arising from the non-uniform thermal conditions under which the fixed point is realised. It is experimentally and numerically demonstrated that the thermal uniformity of the three-zone furnace is improved by separating (thermally isolating) the heating zones. By modelling the freezing behaviour of a silver cell in the three-zone furnace it is shown that (a) increasing the freeze undercooling increases the influence of the thermal effects and adversely affects the shape of the freeze plateau, and (b) making the temperature at the base of the cell higher than that at the top reduces the influence of the thermal effects and improves the shape of the freeze plateau.