Liquid-liquid phase transition in a system with impurity

Abstract

This study is devoted to the impurity concentration–temperature phase diagram of a substance (A) contain-ing an impurity (B) and featuring a liquid–liquid phasetransition A1 A2, which is manifested by a sharpchange in the short-order structure of the α solutionbased on component A. This transition is caused byvariation of the solution composition or temperatureand results in a phase separation, which is basically dif-ferent from the usual separation of a liquid into the αsolution based on the main component A and a β solu-tion based on impurity B. Intersection of the two-phaseregion of phase separation in a liquid α solution with atwo-phase region of the liquid–solid system leads tonew, previously unknown binary phase diagrams, thetypes of which can be established using thermody-namic analysis.1. INTRODUCTIONThere are many simple substances exhibiting pres-sure-induced first-order phase transitions in the liquidstate at the melting line on the phase diagram. Anexhaustive review of the corresponding experimentaldata can be found in [1]. These transitions are mani-fested by a sharp change in characteristics of the localstructure of the melt, such as the average interatomicdistance and coordination number, and are accompa-nied by anomalous variation of their physical propertiesboth in the pretransition state and immediately on thephase transition line [1–3]. On the temperature–pressure plane of thermody-namic variables, the first-order phase transition linebegins at the triple point on the melting line (featuringthe coexistence of the two types of liquids and the crys-tal) and is usually terminated by the point of the sec-ond-order phase transition, which was predicted as the“structural boiling” point by Katayama et al. [4]. Thisphase transition line can also be terminated at the pointof intersection with the line of liquid–gas phase transi-tion or with the line of another liquid–liquid phase tran-sition that originates either at the melting line (as, e.g.,in bismuth) or at the liquid–gas equilibrium line [5]. Inthe latter case, the phase diagram exhibits a triple pointin the region of liquid states.In order to describe the phase diagrams of pure sub-stances on the pressure–temperature plane, with contin-uation of the phase transition line to the region of liquidstates and termination at the “structural boiling” point,we have developed a model that was described in [6–9].There is a natural question as to how the structuraltransformation in a pure melt will be influenced by anadditional thermodynamic factor—the presence of asecond component (impurity) in the system—that is, bythe passage to the binary system. The aim of this studywas to elucidate this question.2. A TWO-PHASE REGION ON THE CONCENTRATION–TEMPERATURE DIAGRAMLet us consider a phase transition in a liquid solutionrepresenting a melt of the main component A. Consid-ering the concentration of impurity B as a preset exter-nal parameter and assuming that it is not redistributedbetween phases, we would obtain a line on the temper-ature–concentration diagram (similar to that on thepressure–temperature diagram), which terminates atthe “structural boiling” point ( T