A discrete model of Ostwald ripening based on multiple pairwise interactions

References

• 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. 388–407.10.1080/14786435.2017.1407880
   Google Scholar
• I.M. Lifshitz and V.V. Slyozov , The kinetics of precipitation from supersaturated solid solutions , J. Phys. Chem. Solids 19 (1961), pp. 35–50.10.1016/0022-3697(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
• O. Hunderi and N. Ryum , The effect of volume fraction on the coarsening of second phase particles , Scand. J. Metall. 10 (1963), pp. 238–240.
   Google Scholar
• A.J. Ardell , The effect of volume fraction on particle coarsening: Theoretical considerations , Acta Metall. 20 (1972), pp. 61–71.10.1016/0001-6160(72)90114-9
   Google Scholar
• A.D. Brailsford and P. Wynblatt , The dependence of ostwald ripening kinetics on particle volume fraction , Acta Metall. 27 (1979), pp. 489–497.
   Google Scholar
• C.K.L. Davies , P. Nash , and R.N. Stevens , The effect of volume fraction of precipitate on ostwald ripening , Acta Metall. 28 (1980), pp. 179–189.
   Google Scholar
• K. Tsumuraya and Y. Miyata , Coarsening models incorporating both diffusion geometry and volume fraction of particles , Acta Metall. 31 (1983), pp. 437–452.10.1016/0001-6160(83)90221-3
   Google Scholar
• J.A. Marqusee and J. Ross , Theory of Ostwald ripening: Competitive growth and its dependence on volume fraction , J. Chem. Phys. 80 (1984), pp. 536–543.
   Web of Science ®Google Scholar
• P.W. Voorhees and M.E. Glicksman , Solution to the multi-particle diffusion problem with applications to Ostwald ripening – I. Theory , Acta Metall. 32 (1984), pp. 2001–2011.10.1016/0001-6160(84)90180-9
   Google Scholar
• P.W. Voorhees and M.E. Glicksman , Solution to the multi-particle diffusion problem with applications to Ostwald ripening – II. Computer simulations , Acta Metall. 32 (1984), pp. 2013–2030.10.1016/0001-6160(84)90181-0
   Google Scholar
• L.C. Brown , A new examination of classical coarsening theory , Acta Metall. 37 (1989), pp. 71–77.10.1016/0001-6160(89)90267-8
   Google Scholar
• Y. Enomoto , M. Tokuyama , and K. Kawasaki , Finite volume fraction effects on Ostwald ripening , Acta Metall. 34 (1986), pp. 2119–2128.10.1016/0001-6160(86)90157-4
   Google Scholar
• Y. Enomoto , K. Kawasaki , and M. Tokuyama , Computer modelling of Ostwald ripening , Acta Metall. 35 (1987), pp. 907–913.10.1016/0001-6160(87)90169-6
   Google Scholar
• Y. Enomoto , K. Kawasaki , and M. Tokuyama , The time dependent behavior of the ostwald ripening for the finite volume fraction , Acta Metall. 35 (1987), pp. 915–922.
   Google Scholar
• A.J. Ardell , Precipitate coarsening in solids: Modern theories, chronic disagreement with experiments , Proc. Int. Conf. ‘Phase transformations ‘87’, G.W. Lorimer , ed., The Institute of Metals, London, 1988.
   Google Scholar
• C.S. Jayanth and P. Nash , Factors affecting particle-coarsening kinetics and size distribution , J. Mater. Sci. 24 (1989), pp. 3041–3052.10.1007/BF01139016
   Web of Science ®Google Scholar
• L.C. Brown , A new examination of volume fraction effects during particle coarsening , Acta Metall. 40 (1992), pp. 1293–1303.10.1016/0956-7151(92)90430-M
   Google Scholar
• J. Alkemper , V.A. Snyder , N. Akaiwa , and P.W. Voorhees , Dynamics of late-stage phase separation: A test of theory , Phys. Rev. Lett. 82 (1999), pp. 2725–2728.
   Web of Science ®Google Scholar
• K.G. Wang , Unified model equations for microstructure evolution , Phys. A 387 (2008), pp. 3084–3092.10.1016/j.physa.2008.02.012
   Web of Science ®Google Scholar
• P. Streitenberger , Analytical description of phase coarsening at high volume fractions , Acta Mater. 61 (2013), pp. 5026–5035.10.1016/j.actamat.2013.04.042
   Web of Science ®Google Scholar
• K.G. Wang and G.Q. Wang , Phase coarsening in multicomponent systems , Phys. Rev. E 95 (2017), p. 022609.
   PubMed Web of Science ®Google Scholar
• S.P. Marsh and M.E. Glicksman , Kinetics of phase coarsening in dense systems , Acta Mater. 44 (1996), pp. 3761–3771.10.1016/1359-6454(95)00451-3
   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. 235–253.10.1016/j.commatsci.2004.11.005
   Web of Science ®Google Scholar
• B.A. Pletcher , K.G. Wang , and M.E. Glicksman , Experimental, computational and theoretical studies of δ’ phase coarsening in Al–Li alloys , Acta Mater. 60 (2012), pp. 5803–5817.10.1016/j.actamat.2012.07.021
   Web of Science ®Google Scholar
• P.E. Di Nunzio , A discrete approach to grain growth based on pair interactions , Acta Mater. 49 (2001), pp. 3635–3643.10.1016/S1359-6454(01)00085-4
   Web of Science ®Google Scholar
• P.E. Di Nunzio , A discrete approach to grain growth based on pair interactions: Effect of local grain-boundary curvature , Metall. Mater. Trans. A 33 (2002), pp. 3329–3337.
   Web of Science ®Google Scholar
• P.W. Voorhees , Ostwald ripening of two-phase mixtures , Ann. Rev. Mater. Sci. 22 (1992), pp. 197–215.
   Web of Science ®Google Scholar
• T. Werz , M. Baumann , U. Wolfram , and C.E. Krill III , Particle tracking during Ostwald ripening using time-resolved laboratory X-ray microtomography , Mater. Characterization 90 (2014), pp. 185–195.10.1016/j.matchar.2014.01.022
   Web of Science ®Google Scholar
• P.W. Voorhees , The theory of Ostwald ripening , J. Stat. Phys. 38 (1985), pp. 231–252.10.1007/BF01017860
   Web of Science ®Google Scholar
• K.G. Wang , M.E. Glicksman , and K. Rajan , Modeling and simulation for phase coarsening: A comparison with experiments , Phys. Rev. E 69 (2004), p. 061507.10.1103/PhysRevE.69.061507
   Web of Science ®Google Scholar
• H. Hougardy and Y. Lan , Modelling of particle growth and application to the carbide evolution in special steels for high temperature service , Final Report EUR 18633 EN, Luxembourg, 1999.
   Google Scholar
• W. Bender and L. Ratke , Ostwald ripening of cobalt particles in liquid copper , Scripta Metall. Mater. 28 (1993), pp. 737–742.10.1016/0956-716X(93)90045-T
   Web of Science ®Google Scholar
• X. Zhao and K. Lücke , Geometric model and applied method for calculation of grain size distributions , Acta Metall. Sin. 28 (1992), pp. 17–24.
   Google Scholar
• D.J. Rowenhorst , J.P. Kuang , K. Thornton , and P.W. Voorhees , Three-dimensional analysis of particle coarsening in high volume fraction solid–liquid mixtures , Acta Mater. 54 (2006), pp. 2027–2039.10.1016/j.actamat.2005.12.038
   Web of Science ®Google Scholar
• B. Meerson , L.M. Sander , and P. Smereka , The role of discrete-particle noise in the Ostwald ripening , Europhys. Lett. 72 (2005), pp. 604–610.10.1209/epl/i2005-10287-7
   Google Scholar
• K.G. Wang , M.E. Glicksman , and C. Lou , Correlations and fluctuations in phase coarsening , Phys. Rev. E 73 (2006), p. 061502.10.1103/PhysRevE.73.061502
   Web of Science ®Google Scholar
• A.M. Gusak and G.V. Lutsenko , Ripening with noise , Phil. Mag. 85 (2005), pp. 1323–1331.10.1080/14786430412331333347
   Google Scholar
• Handbook of Mathematical Functions , M. Abramowitz and I.A. Stegun , 9th ed., Dover, New York, NY, 1970, p. 953.
   Google Scholar
• P.R. Wallace , Mathematical Analysis of Physical Problems , Dover Publ. Inc. New York, 1984, p. 429.
   Google Scholar
• C. Zener , Theory of growth of spherical precipitates from solid solution , J. Appl. Phys. 20 (1949), pp. 950–953.
   Web of Science ®Google Scholar
• C. Wert and C. Zener , Interference of growing spherical precipitate particles , J. Appl. Phys. 21 (1950), pp. 5–8.
   Web of Science ®Google Scholar
• D.E. Kile , D.D. Eberl , A.R. Hoch , and M.M. Reddy , An assessment of calcite crystal growth mechanism based on crystal size distributions , Geochim. Cosmochim. Acta 64 (2000), pp. 2937–2950.10.1016/S0016-7037(00)00394-X
   Web of Science ®Google Scholar
• C. Galli , Experimental determination of the diffusion boundary layer of micron and submicron particles , Int. J. Pharm. 313 (2006), pp. 114–122.10.1016/j.ijpharm.2006.01.030
   PubMed Web of Science ®Google Scholar
• J.J. Sheng , P.J. Sirois , J.B. Dressman , and G.L. Amidon , Particle diffusional layer thickness in a USP dissolution apparatus II: A combined function of particle size and paddle speed , J. Pharm. Sci. 97 (2008), pp. 4815–4829.
   PubMed Web of Science ®Google Scholar