Beyond modified mean field: a case for a stochastic grain growth model

References

• H. Atkinson, Overview no. 65: Theories of normal grain growth in pure single phase systems, Acta Metall. 36 (1988), pp. 469–491. doi: 10.1016/0001-6160(88)90079-X
   Google Scholar
• C. Pande and K. Cooper, Nanomechanics of Hall–Petch relationship in nanocrystalline materials, Prog. Mat. Sci. 54 (2009), pp. 689–706. doi: 10.1016/j.pmatsci.2009.03.008
   Web of Science ®Google Scholar
• I. Lifshitz and V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids 19 (1961), pp. 35–50. doi: 10.1016/0022-3697(61)90054-3
   Web of Science ®Google Scholar
• C. Wagner, Theorie der Alterung von Niederschlaägen durch Umlösen (Ostwald-Reifung), Z. Elektrochem 65 (1961), p. 581.
   Google Scholar
• W. Ostwald, Studien über die Bildung und Umwandlung fester Körper, Z. Physik. Chem. 22 (1897), pp. 289.
   Google Scholar
• M. Hillert, On the theory of normal and abnormal grain growth, Acta Metall. 13 (1965), pp. 227–238. doi: 10.1016/0001-6160(65)90200-2
   Google Scholar
• J. von Neumann, Written discussion of grain shapes and other metallurgical applications of topology, in Metal interfaces, American Society for Metals, Cleveland, 1952. pp. 108–110.
   Google Scholar
• P. Rios and M. Glicksman, Polyhedral model for self-similar grain growth, Acta Mater. 56 (2008), pp. 1165–1171. doi: 10.1016/j.actamat.2007.11.010
   Web of Science ®Google Scholar
• L. Brown, A new examination of classical coarsening theory, Acta Metall. 37 (1989), pp. 71–77. doi: 10.1016/0001-6160(89)90267-8
   Google Scholar
• S. Coughlan and M. Fortes, Self similar size distributions in particle coarsening, Scripta Metall. et Mater. 28 (1993), p. 1471–1476. doi: 10.1016/0956-716X(93)90577-F
   Google Scholar
• P. Rios, Comparison between a computer simulated and an analytical grain size distribution, Scripta Mater. 40 (1999), p. 665–668. doi: 10.1016/S1359-6462(98)00495-3
   Web of Science ®Google Scholar
• R. Kamachali, A. Abbondandolo, K. Siburg and I. Steinbach, Geometrical grounds of mean field solutions for normal grain growth, Acta Mater. 90 (2015), pp. 252–258. doi: 10.1016/j.actamat.2015.02.025
   Web of Science ®Google Scholar
• C. Pande, On a stochastic theory of grain growth, Acta Metall. 35 (1987), pp. 2671–2678. doi: 10.1016/0001-6160(87)90266-5
   Google Scholar
• C. Pande and E. Dantsker, On a stochastic theory of grain growth—II, Acta Metall. 38 (1990), pp. 945–951. doi: 10.1016/0956-7151(90)90166-E
   Google Scholar
• C. Pande and E. Dantsker, On a stochastic theory of grain growth—III, Acta Metall. 39 (1991), pp. 1359–1365. doi: 10.1016/0956-7151(91)90223-N
   Google Scholar
• C. Pande and E. Dantsker, On a stochastic theory of grain growth—IV, Acta Metall. 42 (1994), pp. 2899–2903. doi: 10.1016/0956-7151(94)90231-3
   Google Scholar
• C. Pande, R. Masumura, and S.P. Marsh, Stochastic analysis of two-dimensional grain growth, Phil Mag A. 81 (2001), p. 1229–1239. doi: 10.1080/01418610108214438
   Google Scholar
• C. Pande and A. Rajagopal, Uniqueness and self similarity of size distributions in grain growth and coarsening, Acta Mater. 49 (2001), pp. 1805–1811. doi: 10.1016/S1359-6454(01)00080-5
   Web of Science ®Google Scholar
• C. Pande and K. Cooper, Self-similar grain size distribution in two dimensions: Analytical solution, Acta Mater. 56 (2008), pp. 4200–4205. doi: 10.1016/j.actamat.2008.04.054
   Web of Science ®Google Scholar
• R. MacPherson and D. Srolovitz, The von Neumann relation generalized to coarsening of three-dimensional microstructures, Nature 446 (2007), pp. 1053–1055. doi: 10.1038/nature05745
   PubMed Web of Science ®Google Scholar
• C. Pande and G. McFadden, Self-similar grain size distribution in three dimensions: A stochastic treatment, Acta Mater. 58 (2010), pp. 1037–1044. doi: 10.1016/j.actamat.2009.10.020
   Web of Science ®Google Scholar
• N. Van Kampen, Stochastic Processes in Physics and Chemistry, North Holland, Amsterdam, 1981.
   Google Scholar
• N. Louat, On the theory of normal grain growth, Acta Metall. 22 (1974), pp. 721–724. doi: 10.1016/0001-6160(74)90081-9
   Google Scholar
• S. Marsh, M. Imam, B. Rath and C. Pande, On the kinetics of shrinking grains, Acta Metall. Mat 41 (1993), pp. 297–304. doi: 10.1016/0956-7151(93)90360-5
   Google Scholar
• O. Hunderi and N. Ryum, The kinetics of normal grain growth, J. Mat. Sci. 15 (1980), pp. 1104–1108. doi: 10.1007/BF00551798
   Google Scholar
• W. Mullins, Grain growth of uniform boundaries with scaling, Acta Mater. 46 (1998), pp. 6219–6226. doi: 10.1016/S1359-6454(98)00259-6
   Web of Science ®Google Scholar
• A. Wehrl, General properties of entropy, Rev. Mod. Phys. 50 (1978), pp. 221–260. doi: 10.1103/RevModPhys.50.221
   Web of Science ®Google Scholar
• C. Gardiner, Stochastic Methods, Springer-Verlag, Berlin, 1985.
   Google Scholar
• C. Pande and A. Rajagopal, Modeling of grain growth in two dimensions, Acta Mater. 50 (2002), pp. 3013–3021. doi: 10.1016/S1359-6454(02)00130-1
   Web of Science ®Google Scholar
• A. Spanos, Probability Theory and Statistical Inference, Cambridge University Press, New York, 1999.
   Google Scholar
• P. Rios, T. Dalpain, V. Brandao, J. Castro, and A. Oliveira, Comparison of analytical grain size distributions with three-dimensional computer simulations and experimental data, Scripta Mater. 54 (2006), p. 1633–1637. doi: 10.1016/j.scriptamat.2006.01.007
   Web of Science ®Google Scholar
• E. Miyoshi, T. Takaki, M. Ohno, Y. Shibuta, S. Sakane, T. Shimokawabe, and T. Aoki, Ultra-large-scale phase-field simulation study of ideal grain growth, Comput. Mater. 3 (2017), p. 25. doi: 10.1038/s41524-017-0029-8
   Google Scholar
• D. Rowenhorst, A. Lewis and G. Spanos, Three-dimensional analysis of grain topology and interface curvature in a β-titanium alloy, Acta Mater. 58 (2010), pp. 5511–5519. doi: 10.1016/j.actamat.2010.06.030
   Web of Science ®Google Scholar
• K. Wang, M. Glicksman and K. Rajan, Length scales in phase coarsening: Theory, simulation, and experiment, Comput. Mat. Sci 34 (2005), pp. 235–253. doi: 10.1016/j.commatsci.2004.11.005
   Web of Science ®Google Scholar
• M. Tokuyama and Y. Enomoto, Theory of phase-separation dynamics in quenched binary mixtures, Phys. Rev. E 47 (1993), pp. 1156–1179. doi: 10.1103/PhysRevE.47.1156
   PubMed Web of Science ®Google Scholar
• P. Voorhees and M. Glicksman, Solution to the multi-particle diffusion problem with applications to Ostwald ripening—I. Theory, Acta Metall. 32 (1984), pp. 2001–2011. doi: 10.1016/0001-6160(84)90180-9
   Google Scholar
• M. Tokuyama, Dynamics of Ordering Processes in Condensed Matter, Plenum, New York, 1988.
   Google Scholar
• D. Srolovitz, M. Anderson, G. Grest and P. Sahni, Computer simulation of grain growth—I. Kinetics, Acta Metall. 32 (1984), pp. 791.
   Google Scholar
• M. Palmer, M. Glicksman, and K. Rajan, Solidification, TMS, Warrendale, PA, 1998, p. 51.
   Google Scholar
• X. Zhao, About the Stochastic Behaviour in Grain Growth, Scripta Metall. et Mater. 33 (1995), p. 1081–1086.
   Google Scholar
• D. Zollner and P. Streitenberger, Growth history of individual grains in polycrystals: theoretical model and simulation studies, Mat. Sci. Forum 715-716 (2012), pp. 877–882. doi: 10.4028/www.scientific.net/MSF.715-716.877
   Google Scholar
• I. Fielden, Results from in-situ, real-time SEM observations of grain growth in polycrystalline metal, Material Sci. Forum 467-470 (2004), pp. 875–880. doi: 10.4028/www.scientific.net/MSF.467-470.875
   Web of Science ®Google Scholar
• F. Wakai, N. Enomoto and H. Ogawa, Three-dimensional microstructural evolution in ideal grain growth - general statistics, Acta Mater. 48 (2000), pp. 1297–1311. doi: 10.1016/S1359-6454(99)00405-X
   Web of Science ®Google Scholar
• P. Streitenberger and D. Zöllner, Three-dimensional normal grain growth: Monte Carlo Potts model simulation and analytical mean field theory, Scripta Mater. 25 (2006), p. 461–464. doi: 10.1016/j.scriptamat.2006.05.009
   Google Scholar
• P. Streitenberger and D. Zöllner, Effective growth law from three-dimensional grain growth simulations and new analytical grain size distribution, Acta Mater. 55 (2006), pp. 461.
   Google Scholar
• R. Kamachali and I. Steinbach, 3-D phase-field simulation of grain growth: Topological analysis versus mean-field approximations, Acta Mater. 60 (2012), pp. 2719–2728. doi: 10.1016/j.actamat.2012.01.037
   Web of Science ®Google Scholar
• P. Rios and D. Zöllner, Critical assessment 30: Grain growth – unresolved issues, Mat. Sci. Technol. 34 (2018), pp. 629–638. doi: 10.1080/02670836.2018.1434863
   Web of Science ®Google Scholar
• W. Mullins, Estimation of the geometrical rate constant in idealized three dimensional grain growth, Acta Metall. 37 (1989), pp. 2979–2984. doi: 10.1016/0001-6160(89)90333-7
   Google Scholar