Abstract
We suggest here a possible classification of the thermodynamical potentials for phase transition systems with two state variables. Within each of the single-typed classes, the characters and typical diagrams of the internal energy, enthalpy, Helmholtz and Gibbs free energy are shown. Multivalued potentials appear to be the rules rather than the exceptions. Several known examples of phase transitions, e.g. van der Waals gas, Landau-Devonshire model, are studied within the framework of the present classification.
Sommario
II lavoro suggerisce una possibile classificazione dei potenziali termodinamici per sistemi con due variabili di stato soggetti a transizioni di fase e, per ogni classe individuata, mostra le caratteristiche e i diagrammi tipici dell'energia interna, l'entalpia, le energie libere di Helmholtz e Gibbs. Potenziali termodinamici a più valori appaiono essere la regola più che l'eccezione. Nell'ambito della classificazione trovata sono studiati vari esempi noti, come il gas di van der Waals e il modello di Landau-Devonshire.
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References
Van der Waals, J.D., Ph.D. Thesis, University of Leiden, 1873.
Landau, L.D.,Collected Papers of L.D. Landau (ed. D. ter Haar), Gordon and Breach, New York, 1965.
Devonshire, A.F., ‘Theory of ferroelectrics’,Adv. Phys. 3 (1954) 85.
Falk, F., ‘Ginzburg-Landau theory and solitary waves in shape memory alloys’,Z. Phys. B — Condensed Matter 54 (1984), 159–167.
Ericksen, J.L., ‘Some phase transitions in crystals’,Arch. Rat. Mech. Anal. 73 (1980), 99–124.
Ericksen, J.L., ‘Twinning of crystals (1)’, in: Antman, S.et al. (eds),Metastability and Incompletely Posed Problems, Springer-Verlag, New York, 1987.
Ball, J. and James, R., ‘Fine phase mixtures as minimizers of energy’,Arch. Rational Mech. Analy. 100 (1987), 13–52.
James R. and Kinderlehrer, D., ‘Theory of magnetostriction with applications toTb x Dy 1−x F e2’,Phil. Mag. B. 68 (1993), 237–274.
Müller, I. and Xu, H., ‘On the pseudo-elastic hysteresis’,Acta Metall. 39 (1991), 263–271.
Huo, Y. and Müller, I., ‘Nonequilibrium thermodynamics of pseudoelasticity’,Com. Mech. Thermodyn. 5 (1993), 163–204.
Frémond, M., ‘Shape memory alloys. A thermomechanical model’, in: K.-H. Hoffmann and J. Sprekels (eds),Free Boundary Problems: Theory and Applications, Vol. I, Longman, Harlow, Essex, 1990, pp. 295–306.
Lin, T. and Rogers, R.C.,Computation of phase transition using nonlocal regularization, ICAM Report, 93-09-03.
Müller, I. and Villaggio, P., ‘A model for an elastic-plastic body’,Arch. Rational Mech. Analy. 65 (1976), 25–46.
Müller, L, ‘Pseudoelasticity in shape memory alloys — an extreme case of thermoelasticity’,IMA Preprint No. 168, University of Minnesota, 1985.
Kitsche, W., Müller, I. and Strehlow, P., ‘Simulation of pseudo-elastic behavior in a system of rubber balloons, in: Antman, S.et al. (eds),Metastability and Incompletely Posed Problems, Springer-Verlag, New York, 1987.
Ericksen, J.L., ‘Multi-valued strain energy functions for crystals’,Int. J. Solids Structures 18 (1982), 913–916.
Stanley, E.,Introduction to Phase Transitions and Critical Phenomena., Oxford University Press, New York, 1971.
Ansorg, J.,Thermodynamik Einer Chemo-mechanischen Maschine, Studienarbeit, TU Berlin, 1990.
Funakubo, H. (ed.),Shape Memory Alloys, Gordon and Breach, London, 1987.
Guénin, G., Macqueron, J.L.et al., ‘Calorimetric study of the martensitic transformation of the CuZnAl alloys’,Proc. Int. Conf. Martensitic Transformations, Japan (1986), pp. 794–799.
Huo, Y.,On the thermodynamics of pseudoelasticity, Ph.D. Thesis, TU Berlin, 1992.
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Huo, Y. A Classification of thermodynamical potentials for two-variable transition systems. Meccanica 30, 475–494 (1995). https://doi.org/10.1007/BF01557080
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DOI: https://doi.org/10.1007/BF01557080