A fast algorithm of coexisting phases compositions calculation in binary systems

TL;DR

This paper introduces a rapid algorithm for calculating coexisting phase compositions in binary systems by solving for common tangents to approximating parabolas, improving efficiency in phase diagram analysis.

Contribution

The proposed method offers a fast, exact solution for coexisting phases calculation in binary systems using a sequence of parabola approximations and tangent solutions.

Findings

Algorithm converges to equilibrium compositions efficiently.

Method improves computational speed over traditional approaches.

Applicable to phase diagram analysis in binary systems.

Abstract

A simple fast algorithm of the conodes calculation in binary systems is proposed. The method is based on exact solution of the problem on common tangent to pair of approximating parabolas. Sequence of approximating parabolas pairs having second order tangency points on separated concave parts of free energy isotherm is generated. The sequences of the tangency points pairs conodes with approximating parabolas converge to equilibrium compositions of phases in binary systems. PACS: 64.75.-g; 64.10.+h; 05.70.Ce; 82.60.-s Key words: Phase equilibria; Free energy; Binary systems; Conode; Phase diagrams.