Thermodynamical insight on the role of additives in shifting the equilibrium between white and grey tin

TL;DR

This paper uses statistical thermodynamics to analyze how additives with different Debye temperatures influence the equilibrium between white and grey tin, providing a predictive rule consistent with experimental data.

Contribution

It introduces a thermodynamic model linking additive Debye temperatures to tin phase stability, offering a new predictive rule for phase stabilization.

Findings

Additives with Debye temperatures above 214K stabilize grey tin.

Additives with Debye temperatures below 214K stabilize white tin.

The proposed rule aligns with existing experimental observations.

Abstract

In this study methods of statistical thermodynamics were applied to white tin - grey tin equilibrium to find if there is any correlation between Debye temperature of an additive and its effect on the equilibrium. Gibbs free energy of the transition was calculated for a composite system comprised of tin and the additive in assumption of Debye temperature of the composite system being a linear combination of Debye temperatures of the components with their respective molar fractions as weighing coefficients. Calculations showed that additives which Debye temperatures are above 214oK should stabilize grey tin, while the additives with Debye temperatures below 214oK should stabilize the white one. Devised rule corroborates with all previously reported experimental data on the effect of different additives on the transition. Predictions of the rule about non reported additives provide a mean for its experimental verification.