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Phase-field based simulation of microstructure evolution in technical alloy grades

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Abstract

Scope of the present article is to review the current state of the art with respect to simulation of microstructure evolution based on the multiphase-field approach in technical alloy grades. Starting from a short overview about computational thermodynamics and kinetics and respective databases for technical alloys, an engineering approach to phase-field and multiphase-field models will be depicted in order to allow for a basic explanation of these methods—in general being developed by physicists and mathematicians—for materials scientists and metallurgists. These explanations are followed by examples of applications of the multiphase-field method to solidification and solid state transformations in steels, cast iron, superalloys, Al- and Mg-alloys, solders and other alloys and compounds. The article is concluded by a short description of present and future trends.

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References

  1. FactSage: www.gtt-technologies.de

  2. JMatPro/ThermoTech: http://www.sentesoftware.co.uk

  3. www.computherm.com

  4. Thermo-Calc Software: www.thermocalc.se

  5. Saunders, N., Miodownik, A.: CALPHAD Calculation of Phase Diagrams: A Comprehensive Guide. Elsevier, New York. www.calphad.org (1998)

  6. Diffusion Controlled TRAnsformations: Software Provided by Thermo-Calc. www.thermocalc.se

  7. Kobayashi, R.: Modeling and numerical simulations of dendritic crystal growth. Physica D 63, 410–423 (1993)

    Article  MATH  Google Scholar 

  8. Steinbach, I., Pezzolla, F., Nestler, B., Seeßelberg, M., Prieler, R., Schmitz, G.J., Rezende, J.L.L.: A phase field concept for multiphase systems. Physica D 94, 135–147 (1996)

    Article  MATH  Google Scholar 

  9. Fries, S.G., Böttger, B., Eiken, J., Steinbach, I.: Upgrading CALPHAD to microstructure simulation: the phase-field method. Int. J. Mater. Res. 100, 2 (2009)

    Article  Google Scholar 

  10. Kitashima, T.: Coupling of the phase-field and CALPHAD methods for predicting multicomponent, solid-state phase transformations. Philos. Mag. 88(11), 1615–1637 (2008)

    Article  Google Scholar 

  11. Steinbach, I., Böttger, B., Eiken, J., Warnken, N., Fries, S.G.: CALPHAD and phase-field modeling: a successful liaison. J. Phase Equilib. Diffus. 28(1), 101 (2007)

    Article  Google Scholar 

  12. Steinbach, I.: Phase-field models in materials science—topical review. Model. Simul. Mater. Sci. Eng. 17, 073001 (2009)

    Article  MathSciNet  Google Scholar 

  13. Emmerich, H.: Advances of and by phase-field modelling in condensed-matter physics. Adv. Phys. 57, 1 (2008)

    Article  Google Scholar 

  14. Hecht, U., et al.: Advances of and by phase-field modelling in condensed-matter physics. Adv. Phys. 59(3), 257 (2010)

    Google Scholar 

  15. Beckermann, C., Diepers, H.-J., Steinbach, I., Karma, A., Tong, X.: Modeling melt convection in phase-field simulations of solidification. J. Comput. Phys. 154, 468–496 (1999)

    Article  MATH  Google Scholar 

  16. Diepers, H.J.: Diploma thesis. Access, RWTH Aachen (1997)

  17. Eiken, J.: Phase-field simulation of microstructure formation in technical magnesium alloys. Int. J. Mater. Res. 2010/04, 503–509

    Google Scholar 

  18. Eiken, J.: A phase-field model for technical alloy solidification. PhD thesis, Access RWTH Aachen (2010)

  19. Tiaden, J.: Phase field simulations of the peritectic solidification of Fe-C. J. Cryst. Growth 198/199, 1275–1280 (1999)

    Article  Google Scholar 

  20. Nestler, B., Wheeler, A.A.: Anisotropic multiphase-field model: interfaces and junctions. Phys. Rev. E 57(3), 2602 (1998)

    Article  Google Scholar 

  21. Nestler, B., Wheeler, A.A.: Phase-field modeling of multiphase solidification. Comput. Phys. Commun. 147(1–2), 230 (2002)

    Article  MATH  Google Scholar 

  22. Karma, A.: Phase field formulation for quantitative modelling of alloy solidification. Phys. Rev. Lett. 8711(11), 115701 (2001)

    Article  Google Scholar 

  23. Echebarria, B., Folch, R., Karma, A., Plapp, M.: Quantitative phase-field model of alloy solidification. Phys. Rev. E 70(6), 061604 (2004)

    Article  Google Scholar 

  24. Folch, R., Plapp, M.: Quantitative phase-field modeling of two-phase growth. Phys. Rev. E 72(1), 011602 (2005)

    Article  MathSciNet  Google Scholar 

  25. Plapp, M., Karma, A.: Eutectic colony formation: a phase-field study. Phys. Rev. E 66(6), 061608 (2002)

    Article  Google Scholar 

  26. Steinbach, I., Pezzolla, F.: A generalized field method for multiphase transformations using interface fields. Physica D 134, 385 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  27. Ofori-Opoku, N., Provatas, N.: A quantitative multi-phase field model of polycrystalline alloy solidification. Acta Mater. 58(6), 2155 (2010)

    Article  Google Scholar 

  28. Provatas, N., Goldenfeld, N., Dantzig, J.: Efficient computation of dendritic microstructures using adaptive mesh refinement. Phys. Rev. Lett. 80(15), 3308–3311 (1998)

    Article  Google Scholar 

  29. Provatas, N., Goldenfeld, N., Dantzig, J.: Adaptive mesh refinement computation of solidification microstructures using dynamic data structures. J. Comput. Phys. 148(1), 265–290 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  30. Eiken, J., Böttger, B., Steinbach, I.: Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application. Phys. Rev. E 73, 066122 (2006)

    Article  Google Scholar 

  31. Allen, S., Cahn, J.W.: A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall. 27, 1084 (1979)

    Google Scholar 

  32. Diepers, H.J., Beckermann, C., Steinbach, I.: Simulation of convection and ripening in a binary alloy mush using the phase-field-method. Acta Mater. 47(13), 3663–3678 (1999)

    Article  Google Scholar 

  33. Fan, D., Chen, L.Q.: Computer simulation of grain growth using a continuum field model. Acta Mater. 45(2), 611–622 (1997)

    Article  MathSciNet  Google Scholar 

  34. Moelans, N., Blanpain, B., Wollants, P.: Phase field simulations of grain growth in two-dimensional systems containing finely dispersed second-phase particles. Acta Mater. 54(4), 1175–1184 (2006)

    Article  Google Scholar 

  35. Moelans, N., Blanpain, B., Wollants, P.: Quantitative phase-field approach for simulating grain growth in anisotropic systems with arbitrary inclination and misorientation dependence. Phys. Rev. Lett. 101(2), 025502 (2008)

    Article  Google Scholar 

  36. Schaffnit, P., Apel, M., Steinbach, I.: Simulation of ideal grain growth using the multi-phase-field model. Mater. Sci. Forum 558–559, 1177 (2007)

    Article  Google Scholar 

  37. Apel, M., Böttger, B., Rudnizki, J., Schaffnit, P., Steinbach, I.: Grain growth simulations including particle pinning using the multi-phase-field concept. ISIJ Int. 49(7), 1024 (2009)

    Article  Google Scholar 

  38. Wheeler, A.A., Boettinger, W.J., McFadden, G.B.: Phase-field model for isothermal phase transitions in binary alloys. Phys. Rev. A 45(10), 7424 (1992)

    Article  Google Scholar 

  39. Kim, S.G., Kim, W.T., Suzuki, T., Ode, M.: Phase field modelling of eutectic solidification. J. Cryst. Growth 261(1), 135 (2004)

    Article  Google Scholar 

  40. Tiaden, J., Nestler, B., Diepers, H.-J., Steinbach, I.: The multiphase-field model with an integrated concept for modelling solute diffusion. Physica D 115, 73–86 (1998)

    Article  MATH  Google Scholar 

  41. Ramirez, J.C., Beckermann, C., Karma, A., Diepers, H.-J.: Phase-field modeling of binary alloy solidification with coupled heat and solute diffusion. Phys. Rev. E 69, 051607 (2004)

    Article  Google Scholar 

  42. Böttger, B., Grafe, U., Ma, D., Fries, S.G.: Simulation of microsegregation and microstructural evolution in directionally solidified superalloys. Mater. Sci. Technol. 16, 1425 (2000)

    Article  Google Scholar 

  43. Steinbach, I.: Pattern formation in constrained dendritic growth with solutal buoyancy. Acta Mater. 57, 2640–2645 (2009)

    Article  Google Scholar 

  44. Diepers, H.J.: Simulation des Primärabstandes gerichtet erstarrter Dendriten mit der Phasenfeldmethode. PhD thesis, Access RWTH Aachen (2002)

  45. Diepers, H.J., Ma, D., Steinbach, I.: History effects during the selection of primary dendrite spacing. Comparison of phase-field simulations with experimental observations. J. Cryst. Growth 237–239, 149–153 (2002)

    Article  Google Scholar 

  46. Diepers, H.J., Steinbach, I.: Interaction of interdendritic convection and dendritic primary spacing: phase-field simulation and analytical modeling, solidification and gravity IV. Mater. Sci. Forum 508, 145 (2006)

    Article  Google Scholar 

  47. Zimmermann, G., Sturz, L., Walterfang, M., Dagner, J.: „Effect of melt flow on dendritic growth in AlSi7-based alloys during directional solidification. Int. J. Cast Met. Res. 22(1–4), 335 (2009)

    Article  Google Scholar 

  48. Grafe, U., Böttger, B., Tiaden, J., Fries, S.G.: Coupling of multicomponent thermodynamic databases to a phase field model: application to solidification and solid state transformations of superalloys. Scr. Mater. 42(12), 1179–1186 (2000)

    Article  Google Scholar 

  49. Grafe, U., Böttger, B., Tiaden, J., Fries, S.G.: Simulations of the initial transient during directional solidification of multicomponent alloys using the phase field method. Model. Simul. Mater. Sci. Eng. 8(6), 871 (2000)

    Article  Google Scholar 

  50. Grafe, U.: Numerische Simulation der Gefügebildung bei der Erstarrung und Wärmebehandlung von EInkristallsuperlegierungen. PhD thesis, Access RWTH Aachen (2000)

  51. MICRESS®—The MICRostructure Evolution Simulation Software. www.micress.de

  52. Qin, R.S., Wallach, E.R., Thomson, R.C.: A phase-field model for the solidification of multicomponent and multiphase alloys. J. Cryst. Growth 279(1–2), 163 (2005)

    Article  Google Scholar 

  53. Granasy, L., Egry, I., Ratke, L., et al.: Diffuse interface model of bulk heterogeneous nucleation. Scr. Metall. Mater. 31(5), 601–606 (1994)

    Article  Google Scholar 

  54. Warren, J.A., Pusztai, T., Kornyei, L., et al.: Phase field approach to heterogeneous crystal nucleation in alloys. Phys. Rev. B 79(1), 014204 (2009)

    Article  Google Scholar 

  55. Böttger, B., Eiken, J., Steinbach, I.: Phase field simulation of equiaxed solidification in technical alloys. Acta Mater. 54(10), 2697 (2006)

    Article  Google Scholar 

  56. Böttger, B., Eiken, J., Apel, M.: Phase-field simulation of microstructure formation in technical castings—a self-consistent homoenthalpic approach to the micro–macro problem. J. Comput. Phys. 228, 6784–6795 (2009)

    Article  MATH  Google Scholar 

  57. Khachaturyan, A.G., Semenovskaya, S., Tsakalakos, T.: Elastic strain energy of inhomogeneous solids. Phys. Rev. B 52(22), 15909 (1999)

    Article  Google Scholar 

  58. Wang, Y.Z., Li, J.: Phase field modeling of defects and deformation. Acta Mater. 58(4), 1212–1235 (2010)

    Article  Google Scholar 

  59. Steinbach, I., Apel, M.: Multi phase field model for solid state transformation with elastic strain. Physica D 217, 153 (2006)

    Article  MATH  Google Scholar 

  60. Steinbach, I., Apel, M.: The influence of lattice strain on pearlite formation in Fe–C. Acta Mater. 55, 4817 (2007)

    Article  Google Scholar 

  61. Laschet, G., Apel, M.: Thermo-elastic homogenization of 3-D steel microstructure simulated by phase-field method. Steel Res. Int. 81(8), 637 (2010)

    Article  Google Scholar 

  62. Benke, S.: A multi-phase-field model including inelastic deformation for solid state transformations. PAMM 8(1), 10407–10408 (2008)

    Article  Google Scholar 

  63. Böttger, B., Apel, M., Eiken, J., Schaffnit, P., Schmitz, G.J., Steinbach, I.: Phase-field simulation of equiaxed solidification: a homoenthalpic approach to the micro-macro problem. In: Modelling of Casting, Welding and Advanced Solidification Processes MCWASP—XII, Vancouver, pp. 119–127 (2009)

  64. Böttger, B., Apel, M., Eiken, J., Schaffnit, P., Steinbach, I.: Phase-field simulation of solidification and solid-state transformations in multicomponent steels. Steel Res. Int. 79(8), 608 (2008)

    Google Scholar 

  65. Fukumoto, S., Nomoto, S.: Microstructure simulation for solidification of stainless steel by multi-phase-field model. J. Jpn. Inst. Met. 73(7), 502–508 (2009). (in Japanese)

    Article  Google Scholar 

  66. Böttger, B., Stratemeier, S., Subasic, E., Göhler, K., Steinbach, I., Senk, D.: Modeling of hot ductility during solidification of steel grades in continuous casting—part II. Adv. Eng. Mater. 12(4), 101 (2010)

    Article  Google Scholar 

  67. Senk, D., Stratemeier, S., Böttger, B., Göhler, K., Steinbach, I.: Modeling of hot ductility during solidification of steel grades in continuous casting—part I. Adv. Eng. Mater. 12(4), 94 (2010)

    Article  Google Scholar 

  68. Pariser, G., Schaffnit, P., Steinbach, I., Bleck, W.: Simulation of the gamma-alpha-transformation using the phase-field method. Steel Res. 72(9), 354–360 (2001)

    Google Scholar 

  69. Pariser, G.C.: Modeling the austenite to ferrite phase transformation for steel development. PhD thesis, Institute of Ferrous Metallurgy, RWTH Aachen (2006), Shaker, Aachen ISBN: 3-8322-5014-X

  70. Mecozzi, M.G., Sietsma, J., van der Zwaag, S., Apel, M., Schaffnit, P., Steinbach, I.: Analysis of the gamma-alpha transition in C-Mn steels by dilatometry, Laser confocal scanning microscopy and phase-field modelling. In: Proceedings MS&T, p. 353ff (2003)

  71. Mecozzi, M.G., Sietsma, J., van der Zwaag, S., Apel, M., Schaffnit, P., Steinbach, I.: Analysis of the gamma-alpha transformation in C-Mn steel by phase-field modelling. Metall. Mater. Trans. A 36A(9), 2327 (2005)

    Article  Google Scholar 

  72. Mecozzi, M.G.: Phase field modelling of the austenite to ferrite transformation in steels. PhD thesis, TU Delft (2007)

  73. Thiessen, R.G., Richardson, I.M., Sietsma, J.: Physically based modelling of phase transformations during welding of low-carbon steel. Mater. Sci. Eng. A 427, 223 (2006)

    Article  Google Scholar 

  74. Thiessen, R.G., Richardson, I.M.: A physically based model for microstructure development in a macroscopic heat-affected zone: grain growth and recrystallization. Metall. Mater. Trans. B 37B, 655 (2006)

    Article  Google Scholar 

  75. Thiessen, R.G.: Physically-based modelling of material response to welding. PhD thesis, TU Delft (2006)

  76. Militzer, M., Mecozzi, M.G., Sietsma, J., van der Zwaag, S.: Three-dimensional phase field modelling of the austenite-to-ferrite transformation. Acta Mater. 54(15), 3961–3972 (2006)

    Article  Google Scholar 

  77. Apel, M., Benke, S., Steinbach, I.: Virtual dilatometer curves and effective Young’s modulus of a 3D multiphase structure calculated by the phase-field method. Comput. Mater. Sci. 45, 589 (2009)

    Article  Google Scholar 

  78. Savran, V.I.: Austenite formation in C-Mn steel. PhD thesis, TU Delft (2009)

  79. Azizi-Alizamini, H., Militzer, M.: Phase field modelling of austenite formation from ultrafine ferrite–carbide aggregates in Fe–C. Int. J. Mater. Res. 2010/04, 534–541

    Google Scholar 

  80. Rudnizki, J., Böttger, B., Prahl U., Bleck, W.: Phase-field modelling of austenite formation from a ferrite plus pearlite microstructure during annealing of cold-rolled dual-phase steel. Metall. Mater. Trans. A (in press)

  81. Nakajima, K., Apel, M., Steinbach, I.: The role of carbon diffusion in ferrite on the kinetics of cooperative growth of pearlite: a multi-phase-field study. Acta Mater. 54, 3665–3672 (2006)

    Article  Google Scholar 

  82. Hillert, M.: The role of interfacial energy during solid state phase transformations. Jerekont Ann. 147, 757 (1957)

    Google Scholar 

  83. Zener, C.: Kinetics of the Decomposition of Austenite. Wiley, New York (1947)

    Google Scholar 

  84. Thiessen, R.G., Sietsma, J., Palmer, T.A., Elmer, J.W., Richardson, I.M.: Phase-field modelling and synchrotron validation of phase transformations in martensitic dual-phase steel. Acta Mater. 55, 601–614 (2007)

    Article  Google Scholar 

  85. Rudnizki, J., Zeislmair, B., Prahl, U., Bleck, W.: Prediction of abnormal grain growth during high temperature treatment. Comput. Mater. Sci. 49(2), 209 (2010)

    Article  Google Scholar 

  86. Rudnizki, J., Zeislmair, B., Prahl, U., Bleck, W.: Thermodynamical simulation of carbon profiles and precipitation evolution during high temperature case hardening. Steel Res. Int. 81(6), 472 (2010)

    Article  Google Scholar 

  87. Rudnizki, J., Konovalov, S., Prahl, U., Bleck, W.: Integrative microstructure simulation during high temperature case hardening. Steel Res. Int. (submitted)

  88. Fayek, P., Prahl, U., Bleck, W.: Phase field simulations of the austenite grain growth of a microalloyed line pipe steel including particle pinning during the reheating process. Steel Res. Int. (2010) (submitted)

  89. Schaffnit, P., Stallybrass, C., Bez, S., Schneider, A., Konrad, J., Liessem, A.: Quantitative phase-field simulation of the austenite grain growth between 900°C and 1400°C of a micro-alloyed line-pipe steel. In: 9th International Seminar Numerical Analysis of Weldability Graz-Seggau (2009) (pre-print)

  90. Schaffnit, P., Stallybrass, C., Konrad, J., Kulgemeyer, A., Meuser, H.: Dual-scale phase-field simulation of grain growth upon reheating of a microalloyed line pipe steel. Int. J. Mater. Res. 2010/04, 549–554

    Google Scholar 

  91. Toloui, M., Militzer, M.: Phase field simulation of austenite grain growth in the HAZ of microalloyed linepipe steel. Int. J. Mater. Res. 2010/04, 542–548

    Google Scholar 

  92. Sommerfeld, A., Böttger, B., Tonn, B.: Graphite nucleation in cast iron melts based on solidification experiments and microstructure simulation. J. Mater. Sci. Technol. 24(3), 321–324 (2008)

    Google Scholar 

  93. Herzog, R., Warnken, N., Steinbach, I., Hallstedt, B., Walter, C., Müller, J., Hajas, D., Münstermann, E., Schneider, J.M., Nickel, R., Parkot, D., Bobzin, K., Lugscheider, E., Bednarz, P., Trunova, O., Singheiser, L.: Integrated approach for the development of advanced, coated gas turbine blades. Adv. Eng. Mater. 8(6), 535 (2006)

    Article  Google Scholar 

  94. Rösler, J., Götting, M., Del Genovese, D., Böttger, B., Kopp, R., Wolske, M., Schubert, F., Penkalla, H.J., Seliga, T., Thoma, A., Scholz, A., Berger, C.: Wrought Ni-base superalloys for steam turbine applications beyond 700°C. Adv. Eng. Mater. 5(7), 469–483 (2003)

    Article  Google Scholar 

  95. Warnken, N.: Simulation of microstructure formation during solidification and solution heat treatment of a novel single crystal superalloy. PhD thesis, Access RWTH Aachen (2007)

  96. Ma, D., Grafe, U.: Microsegregation in directionally solidified dendritic-cellular structure of superalloy CMSX-4. Mater. Sci. Eng. A 270, 339–342 (1999)

    Article  Google Scholar 

  97. Warnken, N., Ma, D., Mathes, M., Steinbach, I.: Investigation of eutectic island formation in SX superalloys. Mater. Sci. Eng. A 413(12), 267–271 (2005)

    Google Scholar 

  98. Warnken, N., Drevermann, A., Ma, D., Fries, S.G., Steinbach, I.: Development of a simulation approach to microstructure evolution during solidification and homogenization using the phase-field method. In: Reed, R.C., et al. (eds.) Superalloys. TMS, Warrendale (2008)

  99. Warnken, N., Ma, D., Drevermann, A., Reed, R.C., Fries, S.G., Steinbach, I.: Phase-field modelling of as-cast microstructure evolution in nickel-based superalloys. Acta Mater. 57, 5862 (2009)

    Article  Google Scholar 

  100. Kovacevic, I.: Simulation of spheroidisation of elongated Si-particle in Al-Si alloys by the phase-field model. Mater. Sci. Eng. A 496(1–2), 345 (2008)

    Google Scholar 

  101. Wang, J.S., Lee, P.D.: Quantitative simulation of Fe-rich intermetallics in Al-Si-Cu-Fe alloys during solidification. In: Proceedings of 138th TMS Annual Meeting and Exhibition, San Francisco, vol. 1: Materials Processing and Properties (2009)

  102. Böttger, B., Carré, A., Schmitz, G.J., Eiken, J., Apel, M.: Simulation of the microstructure formation in technical aluminum alloys using the multi-phase-field method. Trans. Indian Inst. Met. 62(4–5), 299 (2009)

    Article  Google Scholar 

  103. Nomoto, S., Minamoto, S., Nakajima, K.: Numerical simulation for grain refinement of aluminum alloy by multi-phase-field model coupled with CALPHAD. ISIJ Int. 49(7), 1019 (2009)

    Article  Google Scholar 

  104. Bünck, M., Warnken, N., Bührig-Polaczek, A.: Microstructure evolution of rheo-cast A356 aluminium alloy in consideration of different cooling conditions by means of the cooling channel process. J. Mater. Process. Technol. 210(4), 624 (2010)

    Article  Google Scholar 

  105. Carré, A., Böttger, B., Apel, M.: Phase-field modelling of gas porosity formation during the solidification of aluminium. Int. J. Mater. Res. 2010/04, 510–514

    Google Scholar 

  106. Böttger, B., Eiken, J., Ohno, M., Klaus, G., Fehlbier, M., Schmid-Fetzer, R., Steinbach, I., Bührig-Polaczek, A.: Controlling microstructure in magnesium alloys: a combined thermodynamic, experimental and simulation approach. Adv. Eng. Mater. 8(4), 241 (2006)

    Article  Google Scholar 

  107. Eiken, J., Böttger, B., Steinbach, I.: Simulation of microstructure evolution during solidification of magnesium-based alloys. Trans. Indian Inst. Met. 60(2–3), 179–184 (2007)

    Google Scholar 

  108. Eiken, J.: Dendritic growth texture evolution in Mg-based alloys investigated by phase-field simulation. Int. J. Cast Met. Res. 22(1–4), 86–89 (2009)

    Article  Google Scholar 

  109. Eiken, J.: Phase-field simulations of dendritic orientation selection in Mg-alloys with hexagonal anisotropy. Mater. Sci. Forum 649, 199–204 (2010)

    Article  Google Scholar 

  110. Khan, S.S., Hort, N., Eiken, J., Steinbach, I., Schmauder, S.: Numerical determination of heat distribution and castability simulations of as cast Mg-Al alloys. Adv. Eng. Mater. 11(3), 162 (2009)

    Article  Google Scholar 

  111. Schmitz, G.J., Zhou, B., Böttger, B., Villain, J., Klima, S.: Phase-field modeling and experimental observations of microstructures in solidifying Sn-Ag-Cu solders. Paper presented at the COST531 meeting in Bochum, to be submitted to Journal of Electronic Materials (2009)

  112. Eiken, J., Apel, M., Witusiewicz, V.T., Zollinger, J., Hecht, U.: Interplay between α(Ti) nucleation and growth during peritectic solidification investigated by phase-field simulations. J. Phys. Condens. Matter 21, 464104 (2009)

    Article  Google Scholar 

  113. Schmitz, G.J., Nestler, B.: Simulation of phase transitions in multiphase systems: peritectic solidification of (RE)Ba2Cu3O7-x superconductors. Mater. Sci. Eng. B53, 23–27 (1998)

    Article  Google Scholar 

  114. Apel, M., Böttger, B., Diepers, H.-J., Steinbach, I.: 2D and 3D phase-field simulations of lamellar and fibrous eutectic growth. J. Cryst. Growth 237–239, 154–158 (2002)

    Article  Google Scholar 

  115. Apel, M., Franke, D., Steinbach, I.: Simulation of the crystallisation of silicon ribbons on substrate. Crystalline silicon for solar cells. Sol. Energy Mater. Sol. Cells 72, 201–208 (2002)

    Article  Google Scholar 

  116. Steinbach, I.: Ein Multi-Phasen-Feld Modell für facettiertes Kristallwachstum. PhD thesis, Access RWTH Aachen (2000)

  117. Steinbach, I., Apel, M.: Phase-field simulation of rapid crystallization of silicon on substrate. Mater. Sci. Eng. A 449–451, 95 (2007)

    Google Scholar 

  118. de Bruycker, E., De Cooman, B.C., De Meyer, M.: Experimental study and microstructure simulations of Zn-Al-Mg coatings. In: Proceedings Galvatech, p. 723ff (2004)

  119. Phelan, D.: Phase-field modeling of 55 wt% Al-Zn-Si alloy system. In: Proceedings Galvatech, p. 961ff (2004)

  120. Galenko, P.K., Reutzel, S., Herlach, D.M., Fries, S.G., Steinbach, I., Apel, M.: Dendritic solidification in undercooled Ni–Zr–Al melts: experiments and modeling. Acta Mater. 57, 6166–6175 (2009)

    Article  Google Scholar 

  121. Kauzlaric, D., Lienemann, J., Pastewka, L., Greiner, A., Korvink, J.G.: Integrated process simulation of primary shaping: multi scale approaches. Microsyst. Technol. 14, 1789–1796 (2008)

    Article  Google Scholar 

  122. Amancherla, S., Kar, S., Bewlay, B., Ying, Y., Chang, A.: Thermodynamic and microstructural modelling of Nb-Si based alloys. J. Phase Equilib. Diffus. 28(1), 2 (2007)

    Article  Google Scholar 

  123. Schmitz, G.J., Prahl, U.: Toward a virtual platform for materials processing. JOM 61(5), 26 (2009)

    Article  Google Scholar 

  124. Guerdane, M., Wendler, F., Danilov, D., Teichler, H., Nestler, B.: Crystal growth and melting in NiZr alloy: linking phase-field modeling to molecular dynamics simulations. Phys. Rev. B 81(22), 224108 (2010)

    Article  Google Scholar 

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Acknowledgments

Funding of the depicted research by the German Research Foundation (DFG) in the frame of the projects AP196/1 and AP196/3 and within the Cluster of Excellence “Integrative Production in High Wage Countries” is gratefully acknowledged.

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  1. Access e.V., Intzestr 5, 52072, Aachen, Germany

    G. J. Schmitz, B. Böttger, J. Eiken, M. Apel, A. Viardin, A. Carré & G. Laschet

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  1. G. J. Schmitz
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  2. B. Böttger
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  3. J. Eiken
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  4. M. Apel
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  5. A. Viardin
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  6. A. Carré
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  7. G. Laschet
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Correspondence to G. J. Schmitz.

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Schmitz, G.J., Böttger, B., Eiken, J. et al. Phase-field based simulation of microstructure evolution in technical alloy grades. Int J Adv Eng Sci Appl Math 2, 126–139 (2010). https://doi.org/10.1007/s12572-011-0026-y

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  • DOI: https://doi.org/10.1007/s12572-011-0026-y

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