Derivation of the phase field equations from the thermodynamic extremal principle

0369694 - ÚFM 2012 RIV GB eng J - Journal Article
Svoboda, Jiří - Fischer, F. D. - McDowell, D.L.
Derivation of the phase field equations from the thermodynamic extremal principle.
Acta Materialia. Roč. 60, č. 1 (2012), s. 396-406. ISSN 1359-6454. E-ISSN 1873-2453
R&D Projects: GA ČR GAP108/10/1781
Institutional research plan: CEZ:AV0Z20410507
Keywords : Phase-field method * Phase transformation * Thermodynamic extremal principle
Subject RIV: BJ - Thermodynamics
Impact factor: 3.941, year: 2012

Thermodynamics employs quantities that characterize the state of the system and provides driving forces for system evolution. These quantities can be applied by means of the thermodynamic extremal principle to obtain models and consequently constitutive equations for the evolution of the thermodynamic systems. The phase field method is a promising tool for simulation of the microstructure evolution in complex systems but introduces several parameters that are not standard in thermodynamics. The purpose of this paper is to show how the phase field method equations can be derived from the thermodynamic extremal principle, allowing the common treatment of the phase field parameters together with standard thermodynamic parameters in future applications. Fixed values of the phase field parameters may, however, not guarantee fixed values of thermodynamic parameters. Conditions are determined, for which relatively stable values of the thermodynamic parameters are guaranteed during phase field method simulations of interface migration. Finally, analytical relations between the thermodynamic and phase field parameters are found and verified for these simulations. A slight dependence of the thermodynamic parameters on the driving force is determined for the cases examined.
Permanent Link: http://hdl.handle.net/11104/0203699