A First Order Phase Transition Studied by an Ising-Like Model Solved by Entropic Sampling Monte Carlo Method

Jorge Linares,Pierre-Richard Dahoo,Catherine Cazelles,Kamel Boukheddaden

doi:10.3390/sym13040587

Abstract

Two-dimensional (2D) square, rectangular and hexagonal lattices and 3D parallelepipedic lattices of spin crossover (SCO) compounds which represent typical examples of first order phase transitions compounds are studied in terms of their size, shape and model through an Ising-like Hamiltonian in which the fictitious spin states are coupled via the respective short and long-range interaction parameters J, and G. Furthermore, an environmental L parameter accounting for surface effects is also introduced. The wealth of SCO transition properties between its bi-stable low spin (LS) and high spin (HS) states are simulated using Monte Carlo Entropic Sampling (MCES) method which favors the scanning of macro states of weak probability occurrences. For given J and G, the focus is on surface effects through parameter L. It is shown that the combined first-order phase transition effects of the parameters of the Hamiltonian can be highlighted through two typical temperatures, TO.D., the critical order-disorder temperature and Teq the equilibrium temperature that is fixed at zero effective ligand field. The relative positions of TO.D. and Teq control the nature of the transition and mediate the width and position of the thermal hysteresis curves with size and shape. When surface effects are negligible (L = 0), the equilibrium transition temperature, Teq. becomes constant, while the thermal hysteresis’ width increases with size. When surface effects are considered, L ≠ 0, Teq. increases with size and the first order transition vanishes in favor of a gradual transition until reaching a threshold size, below which a reentrance phenomenon occurs and the thermal hysteresis reappears again, as shown for hexagonal configuration.

Highlights

The quest to improve our knowledge on phenomenon and processes driving the properties of complex materials is challenging for researchers involved in experimental and in theoretical research fields
A first order transition with thermal hysteresis occurs with an increase in the width of the hysteresis loop when the size increases
The thermal hysteresis increases when the size of the system decreases and when the shape gradually evolves towards an elongated rectangular 2 × 72. This feature is connected to the relative positions of the equilibrium temperature Teq and the order-disorder transition TO.D. temperature

Summary

Introduction

The quest to improve our knowledge on phenomenon and processes driving the properties of complex materials is challenging for researchers involved in experimental and in theoretical research fields. Concerning SCO materials [1,2,3,4,5,6,7,8,9,10,11,12], a typical example of a first-order phase transition, the Monte Carlo methods are used in combination with certain models such as: Ising-like model, atom-phonon coupling (APC) model or mechanical-elastic model All these models are used to simulate the response of SCO materials when they are subjected to external perturbations such as: thermal or/and pressure variation, light irradiation, applied external magnetic or electrical fields. The interactions between the molecules are at the origin of a thermal hysteresis, that is the fingerprint of a first order phase transition

Methods

Results

Conclusion