Reclassification of thermal equilibrium phase-transitions in thermodynamic limit systems
Abstract For relaxor-ferroelectrics and relaxor-ferromagnets, the initial Ehrenfest-classification gives no phase-transition that contradicts the measured order-parameter, while the classification according to order-parameter and its derivatives raises the question about the relationships between th...
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Nature Portfolio
2024-11-01
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| author | Lai Wei Li-Li Zhang Yi-Neng Huang |
| author_facet | Lai Wei Li-Li Zhang Yi-Neng Huang |
| author_sort | Lai Wei |
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| description | Abstract For relaxor-ferroelectrics and relaxor-ferromagnets, the initial Ehrenfest-classification gives no phase-transition that contradicts the measured order-parameter, while the classification according to order-parameter and its derivatives raises the question about the relationships between the phase-transition and the specific-heat peak above and near the transition temperature. Here, based on the free-energy (F) of the thermodynamic limit systems when the external-field (h) tends 0, thermal equilibrium phase-transitions of thermodynamic limit systems with temperature (T) are reclassified into: (1) Discontinuous phase-transition. $$\partial F/\partial h|_{h \to 0}$$ and $$\partial F/\partial T|_{h \to 0}$$ have discontinuities in a T range; (2) Continuous phase-transition. $$\partial F/\partial h|_{h \to 0}$$ and $$\partial F/\partial T|_{h \to 0}$$ are continuous with T, while $$\partial^{2} F/\partial h\partial T|_{h \to 0}$$ and $$\partial^{2} F/\partial T^{2} |_{h \to 0}$$ have discontinuities at a T point; and (3) Diffuse phase-transition. $$\partial^{3} F/\partial h\partial^{2} T|_{h \to 0}$$ and $$\partial^{3} F/\partial T^{3} |_{h \to 0}$$ are continuous with T, while they are respectively equal to 0 at the transition-temperature (T d ) and diffuse-temperature (T s ). The diffuse-region of the phase-transition is $$T_{s} - T_{d}$$ and the diffuse-degree $$\left( {T_{s} - T_{d} } \right)/T_{d} \times {1}00\%$$ , naturally giving the relation of the phase-transition to the specific-heat peak. |
| format | Article |
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| spelling | doaj-art-b2245a3486a94d2aa663ecb171fee0372025-08-20T02:22:26ZengNature PortfolioScientific Reports2045-23222024-11-011411710.1038/s41598-024-80454-7Reclassification of thermal equilibrium phase-transitions in thermodynamic limit systemsLai Wei0Li-Li Zhang1Yi-Neng Huang2Xinjiang Laboratory of Phase Transitions and Microstructures in Condensed Matters, College of Physical Science and Technology, Yili Normal UniversityXinjiang Laboratory of Phase Transitions and Microstructures in Condensed Matters, College of Physical Science and Technology, Yili Normal UniversityXinjiang Laboratory of Phase Transitions and Microstructures in Condensed Matters, College of Physical Science and Technology, Yili Normal UniversityAbstract For relaxor-ferroelectrics and relaxor-ferromagnets, the initial Ehrenfest-classification gives no phase-transition that contradicts the measured order-parameter, while the classification according to order-parameter and its derivatives raises the question about the relationships between the phase-transition and the specific-heat peak above and near the transition temperature. Here, based on the free-energy (F) of the thermodynamic limit systems when the external-field (h) tends 0, thermal equilibrium phase-transitions of thermodynamic limit systems with temperature (T) are reclassified into: (1) Discontinuous phase-transition. $$\partial F/\partial h|_{h \to 0}$$ and $$\partial F/\partial T|_{h \to 0}$$ have discontinuities in a T range; (2) Continuous phase-transition. $$\partial F/\partial h|_{h \to 0}$$ and $$\partial F/\partial T|_{h \to 0}$$ are continuous with T, while $$\partial^{2} F/\partial h\partial T|_{h \to 0}$$ and $$\partial^{2} F/\partial T^{2} |_{h \to 0}$$ have discontinuities at a T point; and (3) Diffuse phase-transition. $$\partial^{3} F/\partial h\partial^{2} T|_{h \to 0}$$ and $$\partial^{3} F/\partial T^{3} |_{h \to 0}$$ are continuous with T, while they are respectively equal to 0 at the transition-temperature (T d ) and diffuse-temperature (T s ). The diffuse-region of the phase-transition is $$T_{s} - T_{d}$$ and the diffuse-degree $$\left( {T_{s} - T_{d} } \right)/T_{d} \times {1}00\%$$ , naturally giving the relation of the phase-transition to the specific-heat peak.https://doi.org/10.1038/s41598-024-80454-7 |
| spellingShingle | Lai Wei Li-Li Zhang Yi-Neng Huang Reclassification of thermal equilibrium phase-transitions in thermodynamic limit systems Scientific Reports |
| title | Reclassification of thermal equilibrium phase-transitions in thermodynamic limit systems |
| title_full | Reclassification of thermal equilibrium phase-transitions in thermodynamic limit systems |
| title_fullStr | Reclassification of thermal equilibrium phase-transitions in thermodynamic limit systems |
| title_full_unstemmed | Reclassification of thermal equilibrium phase-transitions in thermodynamic limit systems |
| title_short | Reclassification of thermal equilibrium phase-transitions in thermodynamic limit systems |
| title_sort | reclassification of thermal equilibrium phase transitions in thermodynamic limit systems |
| url | https://doi.org/10.1038/s41598-024-80454-7 |
| work_keys_str_mv | AT laiwei reclassificationofthermalequilibriumphasetransitionsinthermodynamiclimitsystems AT lilizhang reclassificationofthermalequilibriumphasetransitionsinthermodynamiclimitsystems AT yinenghuang reclassificationofthermalequilibriumphasetransitionsinthermodynamiclimitsystems |