Qualitative evaluation of the effect of morphology, spatial distribution and coherent interfaces on the coarsening kinetics and size distribution of particles during Ostwald ripening

References

• P.E. Di Nunzio, A discrete model of Ostwald ripening based on multiple pairwise interactions. Phil. Mag. 98 (2018), pp. 1674–1695. doi: 10.1080/14786435.2018.1455994
   Google Scholar
• P.E. Di Nunzio, A theoretical interpretation of self-similar right-skewed particle size distributions in Ostwald ripening of cementite in ferrite. Phil. Mag 98 (2018), pp. 388–407. doi: 10.1080/14786435.2017.1407880
   Google Scholar
• P.W. Voorhees, Ostwald ripening of two-phase mixtures. Ann. Rev. Mater. Sci 22 (1992), pp. 197–215. doi: 10.1146/annurev.ms.22.080192.001213
   Web of Science ®Google Scholar
• I.M. Lifshitz and V.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 Niederschlägen durch Umlösen. Z. Elektrochem 65 (1961), pp. 581–594.
   Google Scholar
• M. Ode, T. Suzuki, S.G. Kim and W.T. Kim, Ostwald ripening analysis using phase-field model. Mater. Trans. 42 (2001), pp. 2410–2414. doi: 10.2320/matertrans.42.2410
   Web of Science ®Google Scholar
• K.G. Wang, X. Ding, K. Chang and L.Q. Chen, Phase-field simulation of phase coarsening at ultrahigh volume fractions. J. Appl. Phys 107 (2010), pp. 061801–8. doi: 10.1063/1.3340517
   Web of Science ®Google Scholar
• M.K. Rajendran, O. Shchyglo and I. Steinbach, Large scale 3-D phase-field simulation of coarsening in Ni-base superalloys. MATEC Web Conf. 14 (2014), pp. 11001. doi: 10.1051/matecconf/20141411001
   Google Scholar
• H. Ravash, E. Specht, J. Vleugels and N. Moelans, 3D phase-field simulation and characterization of microstructure evolution during liquid phase sintering. Adv. Sci. Technol. 87 (2014), pp. 132–138. doi: 10.4028/www.scientific.net/AST.87.132
   Google Scholar
• H. Yan, K.G. Wang and J.E. Jones, Large scale three-dimensional phase-field simulations on high performance architectures. Model. Simul. Mater. Sci. Eng. 24 (2016), pp. 055016–30. doi: 10.1088/0965-0393/24/5/055016
   Web of Science ®Google Scholar
• J. Park, R. Darvishi Kamachali, S.-D. Kim, S.-H. Kim, C.-S. Oh, C. Schwarze and I. Steinbach, First evidence for mechanism of inverse ripening from in-situ TEM and phase-field study of δ′ precipitation in an Al–Li alloy. Sci. Rep. 9 (2019), pp. 3981. doi: 10.1038/s41598-019-40685-5
   PubMed Web of Science ®Google Scholar
• A. Spettl, R. Wimmer, T. Werz, M. Heinze, S. Odenbach, C.E. Krill III and V. Schmidt, Stochastic 3D modeling of Ostwald ripening at ultra-high volume fractions of the coarsening phase. Modelling Simul. Mater. Sci. Eng 23 (2015), pp. 065001. doi: 10.1088/0965-0393/23/6/065001
   Web of Science ®Google Scholar
• I. Sobchenko, J. Pesicka, D. Baither, R. Reichelt and E. Nembach, Superellipsoids: a unified analytical description of the geometry of nanoscale second phase particles of any shape. Appl. Phys. Lett 89 (2006), pp. 133107. doi: 10.1063/1.2357583
   Web of Science ®Google Scholar
• S.P. Marsh and M.E. Glicksman, Ostwald ripening of non-spherical morphologies. Mater. Sci. Eng. A 238 (1997), pp. 140–147. doi: 10.1016/S0921-5093(97)00440-1
   Web of Science ®Google Scholar
• E. Kozeschnik, J. Svoboda and F.D. Fischer, Shape factors in modeling of precipitation. Mater. Sci. Eng. A 441 (2006), pp. 68–72. doi: 10.1016/j.msea.2006.08.088
   Web of Science ®Google Scholar
• K. Kim and P.W. Voorhees, Ostwald ripening of spheroidal particles in multicomponent alloys. Acta Mater. 152 (2018), pp. 327–337. doi: 10.1016/j.actamat.2018.04.041
   Web of Science ®Google Scholar
• B.A. Pletcher, K.G. Wang and M.E. Glicksman, Experimental, computational and theoretical studies of (’ phase coarsening in Al–Li alloys. Acta Mater. 60 (2012), pp. 5803–5817. doi: 10.1016/j.actamat.2012.07.021
   Web of Science ®Google Scholar
• F.C. Larché and J.W. Cahn, The effect of self-stress on diffusion in solids. Acta Metall. 30 (1982), pp. 1835–1845. doi: 10.1016/0001-6160(82)90023-2
   Google Scholar
• F.C. Larché and J.W. Cahn, The interaction of composition and stress in crystalline solids. Acta Metall. 33 (1985), pp. 331–357. doi: 10.1016/0001-6160(85)90077-X
   Google Scholar
• N. Creton, V. Optasanu, T. Montesin, S. Garruchet and L. Desgranges, A Thermodynamic Approach of the Mechano-Chemical Coupling During the Oxidation of Uranium Dioxide, Defect and Diffusion Forum 289–292, Trans Tech Publications, 2009. pp. 447-454
   Google Scholar
• W.J. Liu and J.J. Jonas, Characterisation of critical nucleus/matrix interface: application to Cu-Co alloys and microalloyed austenite. Mater. Sci. Technol 5 (1989), pp. 8–12. doi: 10.1179/mst.1989.5.1.8
   Web of Science ®Google Scholar
• P.K. Rastogi and A.J. Ardell, The coarsening behavior of the γ′ precipitate in nickel-silicon alloys. Acta Metall. 19 (1971), pp. 321–330. doi: 10.1016/0001-6160(71)90099-X
   Google Scholar
• R. Darvishi Kamachali, E. Borukhovich, O. Schyglo and I. Steinbach, Solutal gradients in strained equilibrium. Phil. Mag. Lett 93 (2013), pp. 680–687. doi: 10.1080/09500839.2013.847288
   Web of Science ®Google Scholar
• W. Tirry and D. Schryvers, Quantitative determination of strain fields around Ni4Ti3 precipitates in NiTi. Acta Mater. 53 (2005), pp. 1041–1049. doi: 10.1016/j.actamat.2004.10.049
   Web of Science ®Google Scholar
• K.G. Wang, M.E. Glicksman and C. Lou, Correlations and fluctuations in phase coarsening, Phys. Rev. E 73 (2006), pp. 061502. doi: 10.1103/PhysRevE.73.061502
   Web of Science ®Google Scholar
• K.G. Wang, M.E. Glicksman and K. Rajan, Modeling and simulation for phase coarsening: a comparison with experiment, Phys. Rev. E 69 (2004), pp. 061507. doi: 10.1103/PhysRevE.69.061507
   Web of Science ®Google Scholar
• K.G. Wang, M.E. Glicksman and K. Rajan, Length scales in phase coarsening: theory, simulation and experiment, Comp. Mater. Sci 34 (2005), pp. 235–253. doi: 10.1016/j.commatsci.2004.11.005
   Web of Science ®Google Scholar
• K.G. Wang, Unified model equations for microstructure evolution. Physica A 387 (2008), pp. 3084–3092. doi: 10.1016/j.physa.2008.02.012
   Web of Science ®Google Scholar
• K.G. Wang and G.Q. Wang, Phase coarsening in multicomponent systems, Phys. Rev. E 95 (2017), pp. 022609. doi: 10.1103/PhysRevE.95.022609
   PubMed Web of Science ®Google Scholar
• P.P. Bansal and A.J. Ardell, Average nearest-neighbor distances between uniformly distributed finite particles. Metallography 5 (1972), pp. 97–111. doi: 10.1016/0026-0800(72)90048-1
   Google Scholar
• J.W. Martin, Precipitation Hardening, 2nd ed. Butterworth-Heinemann, Oxford, 1988, pp. 58-59 and p. 81.
   Google Scholar
• A.V. Nadkarni, in High Conductivity Copper and Aluminium Alloys, E. Ling and P.W. Taubenblat, eds., The Metall. Soc. AIME, Warrendale, PA, 1984. pp. 77-101.
   Google Scholar
• G.E. Dieter, Mechanical Metallurgy, 3rd ed. McGraw-Hill, New York, NY, 1986. p. 215.
   Google Scholar
• J. Gurland, Spectral distribution of discrete particles, in Quantitative Microscopy, R.T. DeHoff, F.N. Rhines, eds., McGraw-Hill, New York, 1968. pp. 283.
   Google Scholar