Regular Article

Phase diagram of a pure substance?

Laboratoire d’Ingénierie des Systèmes de Versailles (LISV), EA 4048, CNRS, Université de Versailles Saint Quentin, 45 avenue des Etats-Unis, 78035 Versailles, France

^a e-mail: jamil.nasser@uvsq.fr

Received: 3 February 2020
Received in final form: 7 April 2020
Published online: 1 June 2020

Abstract

We discuss a two-dimensional model that leads to a phase diagram which reproduces at least qualitatively that of a pure substance. It is known that a spring between two atoms is due to a bond created by the interaction between the electrons of both atoms. Consequently a variation of the quantum state of the electrons involved in the bond can modify the elastic force constant of the spring. That is a kind of atom-phonon coupling. We consider a square lattice of N identical atoms linked by springs between atoms first and second nearest neighbors. We assume that the elastic force constants of all the springs can vary. The system is studied by using a variational method. First order phase transitions are obtained. The phase diagram of the system displays the features observed in the phase diagram of a pure substance: three thermodynamic phases, three coexistence curves, one triple point and one critical point. Applied pressure can be introduced in the model.