"RIV/68081723:_____/11:00435716" . "220159" . "2"^^ . "Advances in Heterogeneous Material Mechanics 2011" . . "Phase field method equations derived from thermodynamic extremal principle" . "Z(AV0Z20410507)" . "Fischer, F. D." . . . . "2"^^ . . "000297713100076" . . "Shanghai" . . . . "1"^^ . . "Svoboda, Ji\u0159\u00ED" . "978-1-60595-054-9" . "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." . . . "thermodynamic extremal principle; phase field method; interface migration; solute segregation and drag"@en . . "2011-05-22+02:00"^^ . "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."@en . "Phase field method equations derived from thermodynamic extremal principle"@en . "RIV/68081723:_____/11:00435716!RIV15-AV0-68081723" . "Lancaster" . "Phase field method equations derived from thermodynamic extremal principle"@en . . "Phase field method equations derived from thermodynamic extremal principle" . . . "[E31701CB4E04]" . . "DEStech Publications, Inc" .