Skip to main content
main-content
Top

Hint

Swipe to navigate through the chapters of this book

Published in:
Cover of the book

2017 | OriginalPaper | Chapter

1. An Overview of the Phase-Field Method and Its Formalisms

Author : S. Bulent Biner

Published in: Programming Phase-Field Modeling

Publisher: Springer International Publishing

share
SHARE

Abstract

A microstructure can be described as the spatial arrangement of the phases and possible defects that have different compositional and/or structural character (for example, the regions composed of different crystal structures and having different chemical compositions, grains of different orientations, domains of different structural variants, and domains of different electric or magnetic polarizations). The size, shape, volume fraction, and spatial arrangement of these microstructural features determine the overall properties of any type of multiphase and/or multicomponent materials.
Literature
1.
go back to reference Cahn JW, Hilliard JE (1958) Free energy of a non-uniform system. I. Interfacial energy. J Chem Phys 28:258 CrossRef Cahn JW, Hilliard JE (1958) Free energy of a non-uniform system. I. Interfacial energy. J Chem Phys 28:258 CrossRef
3.
go back to reference Allen SM, Cahn JW (1972) Ground state structures in ordered binary alloys with second neighbor interactions. Acta Metall 20:423 CrossRef Allen SM, Cahn JW (1972) Ground state structures in ordered binary alloys with second neighbor interactions. Acta Metall 20:423 CrossRef
4.
go back to reference Allen SM, Cahn JW (1973) A correction to the ground state of fcc binary ordered alloys with first and second neighbor pairwise interactions. Scr Metall 7:1261 CrossRef Allen SM, Cahn JW (1973) A correction to the ground state of fcc binary ordered alloys with first and second neighbor pairwise interactions. Scr Metall 7:1261 CrossRef
5.
go back to reference Landau LD, Khalatikow IM (1963) The selected works of L.D. Landau (English translation). Pergamon, Oxford Landau LD, Khalatikow IM (1963) The selected works of L.D. Landau (English translation). Pergamon, Oxford
6.
go back to reference Wheeler AA, Boettinger WJ, McFadden GB (1992) Phase-field model for isothermal transformations in binary alloys. Phys Rev A 45:7424 CrossRef Wheeler AA, Boettinger WJ, McFadden GB (1992) Phase-field model for isothermal transformations in binary alloys. Phys Rev A 45:7424 CrossRef
7.
go back to reference Wheeler AA, Boettinger WJ, McFadden GB (1993) Phase-field model of solute trapping during solidification. Phys Rev E 47:1893 CrossRef Wheeler AA, Boettinger WJ, McFadden GB (1993) Phase-field model of solute trapping during solidification. Phys Rev E 47:1893 CrossRef
8.
go back to reference Wheeler AA, Boettinger WJ, McFadden GB (1996) Phase-field model of a eutectic alloy. Proc R Soc Lond Ser A 452:495 CrossRef Wheeler AA, Boettinger WJ, McFadden GB (1996) Phase-field model of a eutectic alloy. Proc R Soc Lond Ser A 452:495 CrossRef
9.
go back to reference Moelans N (2011) A quantitative and thermodynamically consistent phase-field interpolation function for multi-phase systems. Acta Mater 59:1077 CrossRef Moelans N (2011) A quantitative and thermodynamically consistent phase-field interpolation function for multi-phase systems. Acta Mater 59:1077 CrossRef
10.
go back to reference Langer JS (1986) Models of pattern formation in first-order phase transitions. In: Grinstein G, Mazenko G (eds) Directions in condensed matter physics. World Scientific, Singapore, p 165 CrossRef Langer JS (1986) Models of pattern formation in first-order phase transitions. In: Grinstein G, Mazenko G (eds) Directions in condensed matter physics. World Scientific, Singapore, p 165 CrossRef
11.
go back to reference Fix GJ (1983) Phase field models for free boundary problems. In: Fasano A, Primicerio A (eds) Free boundary problems: theory and applications, vol 2. Pitman, Boston, MA, p 580 Fix GJ (1983) Phase field models for free boundary problems. In: Fasano A, Primicerio A (eds) Free boundary problems: theory and applications, vol 2. Pitman, Boston, MA, p 580
12.
go back to reference Collins JB, Levin H (1985) Diffuse interface model of diffusion-limited crystal growth. Phys Rev B 31:6119 CrossRef Collins JB, Levin H (1985) Diffuse interface model of diffusion-limited crystal growth. Phys Rev B 31:6119 CrossRef
13.
go back to reference Caginalp G, Fife P (1986) Phase-field methods for interfacial boundaries. Phys Rev B 33:7792 CrossRef Caginalp G, Fife P (1986) Phase-field methods for interfacial boundaries. Phys Rev B 33:7792 CrossRef
14.
go back to reference Caginalp G, Fife P (1987) Higher order phase-field models and detailed anisotropy. Phys Rev B 34:4940 CrossRef Caginalp G, Fife P (1987) Higher order phase-field models and detailed anisotropy. Phys Rev B 34:4940 CrossRef
15.
go back to reference Caginalp G, Jones J (1995) A derivation and analysis of phase field models of thermal alloys. Ann Phys 237:66 CrossRef Caginalp G, Jones J (1995) A derivation and analysis of phase field models of thermal alloys. Ann Phys 237:66 CrossRef
16.
go back to reference Caginalp G, Socolovsky EA (1991) Computation of sharp phase boundaries by spreading: the planar and spherically symmetric cases. J Comput Phys 95:85 CrossRef Caginalp G, Socolovsky EA (1991) Computation of sharp phase boundaries by spreading: the planar and spherically symmetric cases. J Comput Phys 95:85 CrossRef
17.
go back to reference Penrose O, Fife PC (1990) Thermodynamically consistent models of phase-field type for the kinetics of phase transitions. Physica D 43:44 CrossRef Penrose O, Fife PC (1990) Thermodynamically consistent models of phase-field type for the kinetics of phase transitions. Physica D 43:44 CrossRef
18.
go back to reference Penrose O, Fife PC (1993) On the relation between the standard phase-field model and a ‘thermodynamically consistent’ phase-field model. Physica D 69:107 CrossRef Penrose O, Fife PC (1993) On the relation between the standard phase-field model and a ‘thermodynamically consistent’ phase-field model. Physica D 69:107 CrossRef
19.
go back to reference Kobayashi R (1992) Simulations of three dimensional dendrites. In: Kai S (ed) Pattern formation in complex dissipative system. World Scientific, Singapore, p 121 Kobayashi R (1992) Simulations of three dimensional dendrites. In: Kai S (ed) Pattern formation in complex dissipative system. World Scientific, Singapore, p 121
20.
go back to reference Kobayashi R (1993) Modeling and numerical simulations of dendritic crystal growth. Physica D 63:410 CrossRef Kobayashi R (1993) Modeling and numerical simulations of dendritic crystal growth. Physica D 63:410 CrossRef
21.
go back to reference Kobayashi R (1994) Numerical approach to three-dimensional dendritic solidification. Exp Math 3:59 CrossRef Kobayashi R (1994) Numerical approach to three-dimensional dendritic solidification. Exp Math 3:59 CrossRef
22.
go back to reference Chen LQ, Yang W (1994) Computer simulation of the domain dynamics of quenched system with a large number of non-conserved order parameters: the grain-growth kinetic. Phys Rev B 50:15752 CrossRef Chen LQ, Yang W (1994) Computer simulation of the domain dynamics of quenched system with a large number of non-conserved order parameters: the grain-growth kinetic. Phys Rev B 50:15752 CrossRef
23.
go back to reference Morin B, Elder KR, Sutton M, Grant M (1995) Model of the kinetics of polymorphous crystallization. Phys Rev Lett 75:2156 CrossRef Morin B, Elder KR, Sutton M, Grant M (1995) Model of the kinetics of polymorphous crystallization. Phys Rev Lett 75:2156 CrossRef
24.
go back to reference Kobayashi R, Warren JA, Carter WC (2000) A continuum model of grain boundaries. Phys D: Nonlinear Phenom 140:141 CrossRef Kobayashi R, Warren JA, Carter WC (2000) A continuum model of grain boundaries. Phys D: Nonlinear Phenom 140:141 CrossRef
25.
go back to reference Steinbach I, Pezzolla F, Nestler B, Seeβelberg M, Prieler R, Schmitz GJ, Rezende JLL (1996) A phase-field concept for multiphase systems. Physica D 94:135 CrossRef Steinbach I, Pezzolla F, Nestler B, Seeβelberg M, Prieler R, Schmitz GJ, Rezende JLL (1996) A phase-field concept for multiphase systems. Physica D 94:135 CrossRef
26.
go back to reference Steinbach I, Pezzolla F (1999) A generalized field method for multiple transformations using interface fields. Physica D 134:385 CrossRef Steinbach I, Pezzolla F (1999) A generalized field method for multiple transformations using interface fields. Physica D 134:385 CrossRef
27.
go back to reference Tiaden J, Nestler B, Diepers HJ, Steinbch I (1998) The multiphase-field model with an integrated concept for modeling solute diffusion. Physica D 115:73 CrossRef Tiaden J, Nestler B, Diepers HJ, Steinbch I (1998) The multiphase-field model with an integrated concept for modeling solute diffusion. Physica D 115:73 CrossRef
28.
go back to reference Kim SG, Kim WT, Suzuki T (1999) Phase-field model for binary alloys. Phys Rev E 60:7186 CrossRef Kim SG, Kim WT, Suzuki T (1999) Phase-field model for binary alloys. Phys Rev E 60:7186 CrossRef
29.
go back to reference Kim SG (2007) A phase-field model with antitrapping current for multicomponent alloys with arbitrary thermodynamic properties. Acta Mater 55:4391 CrossRef Kim SG (2007) A phase-field model with antitrapping current for multicomponent alloys with arbitrary thermodynamic properties. Acta Mater 55:4391 CrossRef
30.
go back to reference Grafe U, Bottger B, Tiaden J, Fries SG (2000) Coupling of multicomponent thermodynamic databases to a phase-field model: application to solidification and solid state transformations of super alloys. Scr Mater 42:1179 CrossRef Grafe U, Bottger B, Tiaden J, Fries SG (2000) Coupling of multicomponent thermodynamic databases to a phase-field model: application to solidification and solid state transformations of super alloys. Scr Mater 42:1179 CrossRef
31.
go back to reference Nestler B, Wheeler AA (2000) A multiphase-field model of eutectic and peritectic alloys: numerical simulations of growth structures. Physica D 138:114 CrossRef Nestler B, Wheeler AA (2000) A multiphase-field model of eutectic and peritectic alloys: numerical simulations of growth structures. Physica D 138:114 CrossRef
32.
go back to reference Nestler B, Garcke H, Stinner B (2005) Multicomponent alloy solidification: phase-field modeling and simulations. Phys Rev E 71:041609 CrossRef Nestler B, Garcke H, Stinner B (2005) Multicomponent alloy solidification: phase-field modeling and simulations. Phys Rev E 71:041609 CrossRef
33.
go back to reference Garcke H, Nestler B, Stinner B (2004) A diffuse interface model for alloys with multiple components and phases. J SIAM Appl Math 64:775 CrossRef Garcke H, Nestler B, Stinner B (2004) A diffuse interface model for alloys with multiple components and phases. J SIAM Appl Math 64:775 CrossRef
34.
go back to reference Eiken J, Boettger B, Steinbach I (2006) Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application. Phys Rev E 73:0066122 CrossRef Eiken J, Boettger B, Steinbach I (2006) Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application. Phys Rev E 73:0066122 CrossRef
35.
go back to reference Qin RS, Wallach ER (2003) A phase-field model coupled with thermodynamic database. Acta Mater 51:6199 CrossRef Qin RS, Wallach ER (2003) A phase-field model coupled with thermodynamic database. Acta Mater 51:6199 CrossRef
36.
go back to reference Qin RS, Wallach ER, Thomson RC (2005) A phase-field model for the solidification of multicomponent and multiphase alloys. J Crystal Growth 279:163 CrossRef Qin RS, Wallach ER, Thomson RC (2005) A phase-field model for the solidification of multicomponent and multiphase alloys. J Crystal Growth 279:163 CrossRef
37.
go back to reference Steinbach I, Boettger B, Eiken J, Warnken N, Fries SG (2007) Calphad and phase-field modeling: a successful liaison. J Phase Equilib Diffus 28:101 CrossRef Steinbach I, Boettger B, Eiken J, Warnken N, Fries SG (2007) Calphad and phase-field modeling: a successful liaison. J Phase Equilib Diffus 28:101 CrossRef
38.
go back to reference Cogswell DA, Carter WC (2011) Thermodynamic phase-field model for microstructure with multiple components and phases: the possibility of metastable phases. Phys Rev E 83:061602 CrossRef Cogswell DA, Carter WC (2011) Thermodynamic phase-field model for microstructure with multiple components and phases: the possibility of metastable phases. Phys Rev E 83:061602 CrossRef
39.
go back to reference Chen LQ, Hu SY (2004) Phase-field method applied to strain-dominated microstructure evolution during solid-state phase transformations. In: Raabe D, Roters F, Barlat F, Chen LQ (eds) Continuum scale simulation of engineering materials. Fundamentals-microstructures-process applications, Wiley Chen LQ, Hu SY (2004) Phase-field method applied to strain-dominated microstructure evolution during solid-state phase transformations. In: Raabe D, Roters F, Barlat F, Chen LQ (eds) Continuum scale simulation of engineering materials. Fundamentals-microstructures-process applications, Wiley
40.
go back to reference Hu SY, Chen LQ (2001) A phase-field model for evolving microstructures with strong elastic inhomogeneity. Acta Mater 49:1879 CrossRef Hu SY, Chen LQ (2001) A phase-field model for evolving microstructures with strong elastic inhomogeneity. Acta Mater 49:1879 CrossRef
41.
go back to reference Biner SB, Hu SY (2009) Simulation of damage evolution in composites: A phase-field model. Acta Mater 57:2088 CrossRef Biner SB, Hu SY (2009) Simulation of damage evolution in composites: A phase-field model. Acta Mater 57:2088 CrossRef
42.
go back to reference Gururajan MP, Abinandanan TA (2007) Phase-field study of precipitation rafting under uniaxial stress. Acta Mater 55:5015 CrossRef Gururajan MP, Abinandanan TA (2007) Phase-field study of precipitation rafting under uniaxial stress. Acta Mater 55:5015 CrossRef
43.
go back to reference Lifshitz EM, Pitaevskii LP (1980) Statistical physics. Part I, Landau and Lifshitz course of theoretical physics. Pergamon Press, Oxford Lifshitz EM, Pitaevskii LP (1980) Statistical physics. Part I, Landau and Lifshitz course of theoretical physics. Pergamon Press, Oxford
44.
go back to reference Aaronson HI, Lee JK (1975) Lectures on the theory of phase transformations. TMS, New York Aaronson HI, Lee JK (1975) Lectures on the theory of phase transformations. TMS, New York
45.
go back to reference Simmons JP, Shen C, Wang Y (2000) Phase-field modeling of simultaneous nucleation and growth by explicitly incorporating nucleation events. Scr Mater 43:935 CrossRef Simmons JP, Shen C, Wang Y (2000) Phase-field modeling of simultaneous nucleation and growth by explicitly incorporating nucleation events. Scr Mater 43:935 CrossRef
46.
go back to reference Simmons JP, Wen Y, Shen C, Wang Y (2004) Microstructural development involving nucleation and growth phenomena with the phase-field method. Mater Sci Eng, A 365:136 CrossRef Simmons JP, Wen Y, Shen C, Wang Y (2004) Microstructural development involving nucleation and growth phenomena with the phase-field method. Mater Sci Eng, A 365:136 CrossRef
47.
go back to reference Heo TW, Zhang L, Du Q, Chen LQ (2010) Incorporating diffuse interface nuclei phase-field simulation. Scr Mater 63:8 CrossRef Heo TW, Zhang L, Du Q, Chen LQ (2010) Incorporating diffuse interface nuclei phase-field simulation. Scr Mater 63:8 CrossRef
48.
go back to reference Chen LQ (2002) Phase-field models for microstructure evolution. Annu Rev Mater Res 32:113 CrossRef Chen LQ (2002) Phase-field models for microstructure evolution. Annu Rev Mater Res 32:113 CrossRef
49.
go back to reference Loginova IS, Singer HM (2008) The phase-field technique for modeling multi materials. Rep Prog Phys 71:106501 CrossRef Loginova IS, Singer HM (2008) The phase-field technique for modeling multi materials. Rep Prog Phys 71:106501 CrossRef
50.
go back to reference Stainbach I (2009) Topical review: phase-field models in material science. Model Simul Mater Sci Eng 17:073001 CrossRef Stainbach I (2009) Topical review: phase-field models in material science. Model Simul Mater Sci Eng 17:073001 CrossRef
51.
go back to reference Wang Y, Li J (2010) Overview: 150, phase-field modeling of defects and deformation. Acta Mater 58:1212 CrossRef Wang Y, Li J (2010) Overview: 150, phase-field modeling of defects and deformation. Acta Mater 58:1212 CrossRef
52.
go back to reference Provates N, Elder K (2010) Phase-Field methods in materials science and engineering. Wiley Provates N, Elder K (2010) Phase-Field methods in materials science and engineering. Wiley
Metadata
Title
An Overview of the Phase-Field Method and Its Formalisms
Author
S. Bulent Biner
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-41196-5_1

Premium Partners