A First Order Phase Transition Studied by an Ising-Like Model Solved by Entropic Sampling Monte Carlo Method
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 whic...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/4/587 |
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| author | Jorge Linares Catherine Cazelles Pierre-Richard Dahoo Kamel Boukheddaden |
| author_facet | Jorge Linares Catherine Cazelles Pierre-Richard Dahoo Kamel Boukheddaden |
| author_sort | Jorge Linares |
| collection | DOAJ |
| description | 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 <i>J</i>, and <i>G</i>. Furthermore, an environmental <i>L</i> parameter accounting for surface effects is also introduced. The wealth of SCO transition properties between its bi-stable low spin (<i>LS</i>) and high spin (<i>HS</i>) states are simulated using Monte Carlo Entropic Sampling (MCES) method which favors the scanning of macro states of weak probability occurrences. For given <i>J</i> and <i>G</i>, the focus is on surface effects through parameter <i>L</i>. It is shown that the combined first-order phase transition effects of the parameters of the Hamiltonian can be highlighted through two typical temperatures, <i>T<sub>O.D</sub>.</i>, the critical order-disorder temperature and <i>T<sub>eq</sub></i> the equilibrium temperature that is fixed at zero effective ligand field. The relative positions of <i>T<sub>O.D.</sub></i> and <i>T<sub>eq</sub></i> 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 (<i>L</i> = 0), the equilibrium transition temperature, <i>T<sub>eq</sub></i><sub>.</sub> becomes constant, while the thermal hysteresis’ width increases with size. When surface effects are considered, <i>L</i> ≠ 0, <i>T<sub>eq</sub></i><sub>.</sub> 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. |
| first_indexed | 2024-03-10T12:39:32Z |
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| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T12:39:32Z |
| publishDate | 2021-04-01 |
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| series | Symmetry |
| spelling | doaj.art-524f4b90f0e549cbb1135afc1d3246512023-11-21T13:58:48ZengMDPI AGSymmetry2073-89942021-04-0113458710.3390/sym13040587A First Order Phase Transition Studied by an Ising-Like Model Solved by Entropic Sampling Monte Carlo MethodJorge Linares0Catherine Cazelles1Pierre-Richard Dahoo2Kamel Boukheddaden3Université Paris-Saclay, UVSQ, CNRS, GEMAC, 78000 Versailles, FranceUniversité Paris-Saclay, UVSQ, IUT de Mantes en Yvelines, 78200 Mantes la Jolie, FranceUniversité Paris-Saclay, UVSQ, CNRS, LATMOS, 78290 Guyancourt, FranceUniversité Paris-Saclay, UVSQ, CNRS, GEMAC, 78000 Versailles, FranceTwo-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 <i>J</i>, and <i>G</i>. Furthermore, an environmental <i>L</i> parameter accounting for surface effects is also introduced. The wealth of SCO transition properties between its bi-stable low spin (<i>LS</i>) and high spin (<i>HS</i>) states are simulated using Monte Carlo Entropic Sampling (MCES) method which favors the scanning of macro states of weak probability occurrences. For given <i>J</i> and <i>G</i>, the focus is on surface effects through parameter <i>L</i>. It is shown that the combined first-order phase transition effects of the parameters of the Hamiltonian can be highlighted through two typical temperatures, <i>T<sub>O.D</sub>.</i>, the critical order-disorder temperature and <i>T<sub>eq</sub></i> the equilibrium temperature that is fixed at zero effective ligand field. The relative positions of <i>T<sub>O.D.</sub></i> and <i>T<sub>eq</sub></i> 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 (<i>L</i> = 0), the equilibrium transition temperature, <i>T<sub>eq</sub></i><sub>.</sub> becomes constant, while the thermal hysteresis’ width increases with size. When surface effects are considered, <i>L</i> ≠ 0, <i>T<sub>eq</sub></i><sub>.</sub> 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.https://www.mdpi.com/2073-8994/13/4/587Monte Carlo simulationsentropic-sampling algorithmspin-crossoverfirst-order phase transitionthermal hysteresis |
| spellingShingle | Jorge Linares Catherine Cazelles Pierre-Richard Dahoo Kamel Boukheddaden A First Order Phase Transition Studied by an Ising-Like Model Solved by Entropic Sampling Monte Carlo Method Symmetry Monte Carlo simulations entropic-sampling algorithm spin-crossover first-order phase transition thermal hysteresis |
| title | A First Order Phase Transition Studied by an Ising-Like Model Solved by Entropic Sampling Monte Carlo Method |
| title_full | A First Order Phase Transition Studied by an Ising-Like Model Solved by Entropic Sampling Monte Carlo Method |
| title_fullStr | A First Order Phase Transition Studied by an Ising-Like Model Solved by Entropic Sampling Monte Carlo Method |
| title_full_unstemmed | A First Order Phase Transition Studied by an Ising-Like Model Solved by Entropic Sampling Monte Carlo Method |
| title_short | A First Order Phase Transition Studied by an Ising-Like Model Solved by Entropic Sampling Monte Carlo Method |
| title_sort | first order phase transition studied by an ising like model solved by entropic sampling monte carlo method |
| topic | Monte Carlo simulations entropic-sampling algorithm spin-crossover first-order phase transition thermal hysteresis |
| url | https://www.mdpi.com/2073-8994/13/4/587 |
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