Non-equilibrium Thermodynamic Extension of the Phenomenological Theories of First-order Phase Transitions

Year 2014, , 53 - 59, 31.03.2014

Shutao Ai , Yuanzhen Cai

https://doi.org/10.5541/ijot.77019

Abstract

Because the phenomenological theories of phase transitions which are based on the equilibrium thermodynamics cannot describe the first-order phase transition processes accurately, the non-equilibrium thermodynamics was applied to extending the existing phenomenological theories of first-order phase transitions. First, the internal interactions of system at a first-order phase transition were considered. The nominal stress, the nominal volume force, the internal electric field and the internal magnetic field were introduced to characterize them. Then, the most general Gibbs equation except the factor of chemical reactions was established. Based on the conservation of energy and the transformation between internal energy and kinetic energy, the rate of local entropy production was deduced. Then based on the principle of minimum entropy production and the generalized Onsager reciprocal relations, the local, evolving characteristics of a first-order phase transition (e.g. a first-order ferroelectric phase transition) were described well. It makes up the inadequateness of the older phenomenological theories.

Keywords

First-order phase transition; phenomenological theory; non-equilibrium thermodynamics ; internal field.

References

• Y. A. Izyumov, V. N. Syromyatnikov, Phase Transitions and Crystal Symmetry. Amsterdam: Kluwer Academic Publisher, 1990.
• R. M. White, T. H. Geballe, Long Range Order in Solids. New York: Academic Press, 1979.
• A. Onuki, Phase Transition Dynamics. Cambridge: Cambridge University Press, 2002.
• J. I. Linares, B. Y. Moratilla, F. Ramirez, An equivalent mechanical model for representing the entropy generation in heat exchanger-application to power cycles, Int. J. Thermo., 14, 147-151, 2011.
• A. Sciacovelli, V. Verda, Entropy generation minimization for the optimal design of the fluid distribution system in a circular MCFC, Int. J. Thermo., 14, 167-177, 2011.
• M. E. Lines, A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials. New York: Oxford University Press, 1977.
• B. Cowan, Topics in Statistical Mechanics. London: Imperical College Press, 2005.
• S. T. Ai, C. T. Xu, Y. L. Wang, S. Y. Zhang, X. F. Ning, E. Noll, Comparison of and comments on two thermodynamic approaches (reversible and irreversible) to ferroelectric phase transitions, Phase Transitions, doi: 1080/01411590701877913.
• D. C. Mattis, The Theory of Magnetism Made Simple: An Introduction to Physical Concepts and to Some Useful Mathematical Methods. Singapore: World Scientific, 2006.
• J. R. Waldram, The Theory of Thermodynamics. Cambridge: Cambridge University Press, 1985.
• U. Lucia, Stationary open systems: a brief review on contemporary theories on irreversibility, Physica A, doi: 1016/j.physa.2012.11.027.
• U. Lucia, Physical model for the engineering analysis of the thermoelasticity of solid bodies, Chinese Journal of Mechanical Engineering, 13, 165-170+177, 2000.
• U. Lucia, G. Gervino, Hydrodynamic cavitation: from theory towards a new experimental approach, Central European Journal of Physics, doi: 10.2478/s11534-0090092-y.
• A. R. Allnatt, A. B. Lidiard, Atomic Transport in Solids. Cambridge: Cambridge University Press, 1993.
• A. Gordon, Propagation of solitary stress waves at first-order ferroelectric phase transitions, Physics Letters A, 154, 79-80, 1991.
• G. A. Maugin, W. Muschik, Thermodynamics with internal variables: part I. general concepts; part II. applications, Journal of Non-equilibrium Thermodynamics, 19, 217-289, 1994.
• D. Jou, J. Casas-Vazquez, G. Lebon, Extended Irreversible Thermodynamics, 3 rd Ed. Berlin: Springer, 200