A convective Cahn-Hilliard model for the formation of facets and corners in crystal growth

Sekerka, 1993, Role of instabilities in determination of the shapes of growing crystals, J. Cryst. Growth, 128, 1, 10.1016/0022-0248(93)90288-8 Chernov, 1974, Stability of faceted shapes, J. Cryst. Growth, 24/25, 11, 10.1016/0022-0248(74)90277-2 Nozieres, 1992, Shape and growth of crystals, 1 Bates, 1997, Phase field models for hypercooled solidification, Physica D, 104, 1, 10.1016/S0167-2789(96)00207-2 Wulff, 1901, Zur Frage der Geschwindigkeit des Wachsthums und der Auflösung der Krystallflachen, Z. Kryst. Min., 34, 449 Herring, 1951, Some theorems on the free energies of crystal surfaces, Phys. Rev., 82, 87, 10.1103/PhysRev.82.87 Frank, 1958, On the kinematic theory of crystal growth and dissolution processes, 411 Nakamura, 1960, Kinematic theory of ferroelectric domain growth, J. Phys. Soc. Japan, 15, 1379, 10.1143/JPSJ.15.1379 Herring, 1951 Herring, 1953, The use of classical macroscopic concepts in surface energy problems, 5 Mullins, 1963, Solid surface morphologies governed by capillarity, 17 Angenent, 1989, Multiphase thermomechanics with interfacial structure 2. Evolution of an isothermal interface, Arch. Rational Mech. Anal., 108, 323, 10.1007/BF01041068 Yokoyama, 1992, A numerical study of the combined effect of anisotropic surface tension and interface kinetics on pattern formation during the growth of two-dimensional crystals, J. Cryst. Growth., 125, 389, 10.1016/0022-0248(92)90277-P Taylor, 1992, Mean curvature and weighted mean curvature, Acta Metall. Mater., 40, 1475, 10.1016/0956-7151(92)90091-R Uwaha, 1987, Asymptotic growth shapes developed from two-dimensional nuclei, J. Cryst. Growth., 80, 84, 10.1016/0022-0248(87)90527-6 Voorhees, 1984, The effect of anisotropic crystal-melt surface tension on grain boundary groove morphology, J. Cryst. Growth, 67, 425, 10.1016/0022-0248(84)90035-6 Gurtin, 1993 Carlo, 1992, A regularized equation for anisotropic motion-by-curvature, SIAM J. Appl. Math., 52, 1111, 10.1137/0152065 Stewart, 1992, Spinodal decomposition of a crystal surface, Phys. Rev. A, 46, 6505, 10.1103/PhysRevA.46.6505 Brush, 1989, A numerical study of two-dimensional crystal growth forms in the presence of anisotropic growth kinetics, J. Cryst. Growth., 96, 419, 10.1016/0022-0248(89)90541-1 Umantsev, 1985, Motion of a plane front during crystallization, Sov. Phys. Crystallogr., 30, 87 McFadden, 1988, Effect of surface tension anisotropy on cellular morphologies, J. Cryst. Growth, 91, 180, 10.1016/0022-0248(88)90385-5 Coriell, 1976, The effect of the anisotropy of surface tension and interface kinetics on morphological instability, J. Cryst. Growth, 34, 157, 10.1016/0022-0248(76)90124-X Wollkind, 1979, A deterministic continuum mechanical approach to morphological of the solid state interface, vol. 4, 111 Umantsev, 1988, Non-isothermal relaxation in a non-local medium, Sov. Phys. -Solid State, 30, 651 Umantsev, 1990, Growth from a hypercooled melt near absolute stability Golovin, 1997, Effect of anisotropy on morphological instability in the freezing of a hypercooled melt, Physica D, 116, 363, 10.1016/S0167-2789(97)00297-2 Frenkel, 1987, On the weakly nonlinear evolution of a perturbed planar solid-liquid interface, Physica D, 27, 260, 10.1016/0167-2789(87)90017-0 Umantsev, 1992, Growth from a hypercooled melt near absolute stability, Phys. Rev. A, 45, 7195, 10.1103/PhysRevA.45.7195 Saroka, 1995, An intrinsic equation of interfacial motion for the solidification of a pure hypercooled melt, Physica D, 85, 348, 10.1016/0167-2789(95)00078-I Rowlinson, 1989 Tiller, 1991 Cahn, 1959, Free energy of a nonuniform system. III. Nucleation in a two-component incompressible fluid, J. Chem. Phys., 31, 688, 10.1063/1.1730447 Whitham, 1974 Krug, 1997, Origin of scale invariance in growth processes, Adv. Phys., 46, 139, 10.1080/00018739700101498 Cahn, 1958, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys., 28, 258, 10.1063/1.1744102 Novick-Cohen, 1984, Nonlinear aspects of the Cahn-Hilliard equation, Physica D, 10, 277, 10.1016/0167-2789(84)90180-5 Novick-Cohen, 1985, The nonlinear Cahn-Hilliard equation: transition from spinodal decomposition to nucleation behavior, J. Stat. Phys., 38, 707, 10.1007/BF01010486 Novick-Cohen, 1998, The Cahn-Hilliard equation: mathematical and modeling perspectives, Adv. Math. Sci. Appl. Emmott, 1996, Coarsening dynamics of a one-dimensional driven Cahn-Hilliard system, Phys. Rev. E, 54, 4568, 10.1103/PhysRevE.54.4568 Leung, 1990, Theory of morphological instability in driven systems, J. Stat. Phys., 61, 345, 10.1007/BF01013969 Yeung, 1992, Phase-separation dynamics in driven diffusive systems, J. Stat. Phys., 66, 1071, 10.1007/BF01055717 Mullins, 1961, Theory of linear facet growth during thermal etching, Philos. Mag., 6, 1313, 10.1080/14786436108241227 Chernov, 1961, The spiral growth of crystals, Sov. Phys. Uspekhi, 4, 116, 10.1070/PU1961v004n01ABEH003328 Cabrera, 1963, On stability of structure of crystal surfaces, 24 Cahn, 1974, A vector thermodynamics for anisotropic surface — II. Curved and facetted surfaces, Acta Metall., 22, 1205, 10.1016/0001-6160(74)90134-5 Bates, 1993, The dynamics of nucleation for the Cahn-Hilliard equation, SIAM J. Appl. Math., 53, 990, 10.1137/0153049 Lifshitz, 1961, The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids, 19, 35, 10.1016/0022-3697(61)90054-3 Wagner, 1961, Theorie der Alterung von Niederschlägen dürch Umlösen (Ostwald-Reifung), Z. Elektrochem., 65, 581 Shinozaki, 1993, Dispersion relation around the kink solution of the Cahn-Hilliard equation, Phys. Rev. E, 47, 804, 10.1103/PhysRevE.47.804 Küpper, 1994, Simulation of particle growth and Ostwald ripening via the Cahn-Hilliard equation, Acta Metall. Mater., 42, 1847, 10.1016/0956-7151(94)90010-8 Kawakatsu, 1985, Kink dynamics in a one-dimensional conserved TDGL system, Prog. Theor. Phys., 74, 11, 10.1143/PTP.74.11 Alikakos, 1990, Slow motion for the Cahn-Hilliard equation in one space dimension, J. Diff. Eqs., 90, 81, 10.1016/0022-0396(91)90163-4 Bates, 1994, Metastable patterns for the Cahn-Hilliard equation, Part 1, J. Diff. Eqs., 111, 421, 10.1006/jdeq.1994.1089 Bates, 1995, Metastable patterns for the Cahn-Hilliard equation, Part 2: Layer dynamics and slow invariant manifold, J. Diff. Eqs., 117, 165, 10.1006/jdeq.1995.1052 Siggia, 1979, Late stages of spinodal decomposition in binary mixtures, Phys. Rev. A, 20, 595, 10.1103/PhysRevA.20.595 Tanaka, 1997, New mechanism of droplet coarsening in phase-separating fluid mixtures, J. Chem. Phys., 107, 3734, 10.1063/1.474730 Ratke, 1985, The influence of particle motion on Ostwald ripening in liquids, Acta Metall., 33, 1793, 10.1016/0001-6160(85)90003-3 Wan, 1990, Ostwald ripening in the isothermal rheocasting process, Acta Metall. Mater., 38, 967, 10.1016/0956-7151(90)90168-G Akaiwa, 1991, The effect of convection on Ostwald ripening in solid-liquid mixtures, Acta Metall. Mater., 39, 2931, 10.1016/0956-7151(91)90109-E Kawasaki, 1982, Kink dynamics in one-dimensional nonlinear systems, Physica A, 116, 573, 10.1016/0378-4371(82)90178-9