메뉴 건너뛰기




Volumn 122, Issue 1-4, 1998, Pages 202-230

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

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0001087994     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00181-X     Document Type: Article
Times cited : (113)

References (61)
  • 1
    • 0027561304 scopus 로고
    • Role of instabilities in determination of the shapes of growing crystals
    • R.F. Sekerka, Role of instabilities in determination of the shapes of growing crystals, J. Cryst. Growth 128 (1993) 1.
    • (1993) J. Cryst. Growth , vol.128 , pp. 1
    • Sekerka, R.F.1
  • 2
    • 49549150988 scopus 로고
    • Stability of faceted shapes
    • A.A. Chernov, Stability of faceted shapes, J. Cryst. Growth 24/25 (1974) 11.
    • (1974) J. Cryst. Growth , vol.24-25 , pp. 11
    • Chernov, A.A.1
  • 3
    • 0003096295 scopus 로고
    • Shape and growth of crystals
    • C. Godreche (Eds.), Cambridge University Press
    • P. Nozieres, Shape and growth of crystals, in: C. Godreche (Eds.), Solids Far from Equilibrium, Cambridge University Press, 1992, pp. 1-154.
    • (1992) Solids Far from Equilibrium , pp. 1-154
    • Nozieres, P.1
  • 5
    • 0001421454 scopus 로고
    • Zur Frage der Geschwindigkeit des Wachsthums und der Auflösung der Krystallflachen
    • G.Wulff, Zur Frage der Geschwindigkeit des Wachsthums und der Auflösung der Krystallflachen, Z. Kryst. Min. 34 (1901) 449.
    • (1901) Z. Kryst. Min. , vol.34 , pp. 449
    • Wulff, G.1
  • 6
    • 36149008975 scopus 로고
    • Some theorems on the free energies of crystal surfaces
    • C. Herring, Some theorems on the free energies of crystal surfaces, Phys. Rev. 82 (1951) 87.
    • (1951) Phys. Rev. , vol.82 , pp. 87
    • Herring, C.1
  • 7
    • 0002378338 scopus 로고
    • On the kinematic theory of crystal growth and dissolution processes
    • R.H. Doremus, B.W. Roberts, D. Turnbull (Eds.), Wiley, New York
    • F.C. Frank, On the kinematic theory of crystal growth and dissolution processes, in: R.H. Doremus, B.W. Roberts, D. Turnbull (Eds.), Growth and Perfection of Crystals, Wiley, New York, 1958, pp. 411-419.
    • (1958) Growth and Perfection of Crystals , pp. 411-419
    • Frank, F.C.1
  • 8
    • 5244239156 scopus 로고
    • Kinematic theory of ferroelectric domain growth
    • T. Nakamura, Kinematic theory of ferroelectric domain growth, J. Phys. Soc. Japan 15 (1960) 1379.
    • (1960) J. Phys. Soc. Japan , vol.15 , pp. 1379
    • Nakamura, T.1
  • 9
    • 0004264669 scopus 로고
    • W.E. Kingston (Ed.), McGraw-Hill, New York
    • C.Herring, in: W.E. Kingston (Ed.), The Physics of Powder Metallurgy, McGraw-Hill, New York, 1951; The use of classical macroscopic concepts in surface energy problems, in: C.S. Smith, R. Gomer (Eds.), Structure and Properties of Solid Surfaces, University of Chicago Press, Chicago, IL, 1953, pp. 5-81.
    • (1951) The Physics of Powder Metallurgy
    • Herring, C.1
  • 10
    • 0002358415 scopus 로고
    • The use of classical macroscopic concepts in surface energy problems
    • University of Chicago Press, Chicago, IL
    • C.Herring, in: W.E. Kingston (Ed.), The Physics of Powder Metallurgy, McGraw-Hill, New York, 1951; The use of classical macroscopic concepts in surface energy problems, in: C.S. Smith, R. Gomer (Eds.), Structure and Properties of Solid Surfaces, University of Chicago Press, Chicago, IL, 1953, pp. 5-81.
    • (1953) Structure and Properties of Solid Surfaces , pp. 5-81
    • Smith, C.S.1    Gomer, R.2
  • 11
    • 0002403126 scopus 로고
    • Solid surface morphologies governed by capillarity
    • Am. Soc. for Metals, Metals Park, OH
    • W.W. Mullins, Solid surface morphologies governed by capillarity, in: Metal Surfaces, Am. Soc. for Metals, Metals Park, OH, 1963, pp. 17-66.
    • (1963) Metal Surfaces , pp. 17-66
    • Mullins, W.W.1
  • 12
    • 33847303953 scopus 로고
    • Multiphase thermomechanics with interfacial structure 2. Evolution of an isothermal interface
    • S. Angenent, M.E. Gurtin, Multiphase thermomechanics with interfacial structure 2. Evolution of an isothermal interface, Arch. Rational Mech. Anal. 108 (1989) 323.
    • (1989) Arch. Rational Mech. Anal. , vol.108 , pp. 323
    • Angenent, S.1    Gurtin, M.E.2
  • 13
    • 0026986959 scopus 로고
    • A numerical study of the combined effect of anisotropic surface tension and interface kinetics on pattern formation during the growth of two-dimensional crystals
    • E. Yokoyama, R.F. Sekerka, 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 (1992) 389.
    • (1992) J. Cryst. Growth. , vol.125 , pp. 389
    • Yokoyama, E.1    Sekerka, R.F.2
  • 14
    • 0026899706 scopus 로고
    • Mean curvature and weighted mean curvature
    • J.E. Taylor, Mean curvature and weighted mean curvature, Acta Metall. Mater. 40 (1992) 1475.
    • (1992) Acta Metall. Mater. , vol.40 , pp. 1475
    • Taylor, J.E.1
  • 15
    • 0002986270 scopus 로고
    • Asymptotic growth shapes developed from two-dimensional nuclei
    • M. Uwaha, Asymptotic growth shapes developed from two-dimensional nuclei, J. Cryst. Growth. 80 (1987) 84.
    • (1987) J. Cryst. Growth. , vol.80 , pp. 84
    • Uwaha, M.1
  • 16
    • 0001490797 scopus 로고
    • The effect of anisotropic crystal-melt surface tension on grain boundary groove morphology
    • P.W. Voorhees, S.R. Coriell, G.B. McFadden, R.F. Sekerka, The effect of anisotropic crystal-melt surface tension on grain boundary groove morphology, J. Cryst. Growth 67 (1984) 425.
    • (1984) J. Cryst. Growth , vol.67 , pp. 425
    • Voorhees, P.W.1    Coriell, S.R.2    McFadden, G.B.3    Sekerka, R.F.4
  • 19
    • 0000755219 scopus 로고
    • Spinodal decomposition of a crystal surface
    • J. Stewart, N. Goldenfeld, Spinodal decomposition of a crystal surface, Phys. Rev. A 46 (1992) 6505.
    • (1992) Phys. Rev. A , vol.46 , pp. 6505
    • Stewart, J.1    Goldenfeld, N.2
  • 20
    • 0024682693 scopus 로고
    • A numerical study of two-dimensional crystal growth forms in the presence of anisotropic growth kinetics
    • L.N. Brush, R.F. Sekerka, A numerical study of two-dimensional crystal growth forms in the presence of anisotropic growth kinetics, J. Cryst. Growth. 96 (1989) 419.
    • (1989) J. Cryst. Growth. , vol.96 , pp. 419
    • Brush, L.N.1    Sekerka, R.F.2
  • 21
    • 0022237918 scopus 로고
    • Motion of a plane front during crystallization
    • A.R. Umantsev, Motion of a plane front during crystallization, Sov. Phys. Crystallogr. 30 (1985) 87.
    • (1985) Sov. Phys. Crystallogr. , vol.30 , pp. 87
    • Umantsev, A.R.1
  • 22
    • 1542561231 scopus 로고
    • Effect of surface tension anisotropy on cellular morphologies
    • G.B. McFadden, S.R. Coriell, R.F. Sekerka, Effect of surface tension anisotropy on cellular morphologies, J. Cryst. Growth 91 (1988) 180.
    • (1988) J. Cryst. Growth , vol.91 , pp. 180
    • McFadden, G.B.1    Coriell, S.R.2    Sekerka, R.F.3
  • 23
    • 0000911220 scopus 로고
    • The effect of the anisotropy of surface tension and interface kinetics on morphological instability
    • S.R. Coriell, R.F. Sekerka, The effect of the anisotropy of surface tension and interface kinetics on morphological instability, J. Cryst. Growth 34 (1976) 157.
    • (1976) J. Cryst. Growth , vol.34 , pp. 157
    • Coriell, S.R.1    Sekerka, R.F.2
  • 24
    • 0002050838 scopus 로고
    • A deterministic continuum mechanical approach to morphological stability of the solid state interface
    • Willcox (Ed.), Dekker, New York
    • D.J. Wollkind, A deterministic continuum mechanical approach to morphological stability of the solid state interface, in: Willcox (Ed.), Preparation and Properties of Solid State Materials, vol. 4, Dekker, New York, 1979, pp. 111-191.
    • (1979) Preparation and Properties of Solid State Materials , vol.4 , pp. 111-191
    • Wollkind, D.J.1
  • 27
    • 0041195846 scopus 로고    scopus 로고
    • Effect of anisotropy on morphological instability in the freezing of a hypercooled melt
    • A.A. Golovin, S.H. Davis, Effect of anisotropy on morphological instability in the freezing of a hypercooled melt, Physica D 116 (1997) 363.
    • (1997) Physica D , vol.116 , pp. 363
    • Golovin, A.A.1    Davis, S.H.2
  • 28
    • 0001183384 scopus 로고
    • On the weakly nonlinear evolution of a perturbed planar solid-liquid interface
    • M.L. Frenkel, On the weakly nonlinear evolution of a perturbed planar solid-liquid interface, Physica D 27 (1987) 260.
    • (1987) Physica D , vol.27 , pp. 260
    • Frenkel, M.L.1
  • 29
    • 0000808009 scopus 로고
    • Growth from a hypercooled melt near absolute stability
    • A.R. Umantsev, S.H. Davis, Growth from a hypercooled melt near absolute stability, Phys. Rev. A 45 (1992) 7195.
    • (1992) Phys. Rev. A , vol.45 , pp. 7195
    • Umantsev, A.R.1    Davis, S.H.2
  • 30
    • 0000999835 scopus 로고
    • An intrinsic equation of interfacial motion for the solidification of a pure hypercooled melt
    • D.C. Saroka, A.J. Bernoff, An intrinsic equation of interfacial motion for the solidification of a pure hypercooled melt, Physica D 85 (1995) 348.
    • (1995) Physica D , vol.85 , pp. 348
    • Saroka, D.C.1    Bernoff, A.J.2
  • 33
    • 0013356201 scopus 로고
    • Free energy of a nonuniform system. III. Nucleation in a two-component incompressible fluid
    • J.W. Cahn, J.E. Hilliard, Free energy of a nonuniform system. III. Nucleation in a two-component incompressible fluid, J. Chem. Phys. 31 (1959) 688.
    • (1959) J. Chem. Phys. , vol.31 , pp. 688
    • Cahn, J.W.1    Hilliard, J.E.2
  • 35
    • 0031097281 scopus 로고    scopus 로고
    • Origin of scale invariance in growth processes
    • J. Krug, Origin of scale invariance in growth processes, Adv. Phys. 46 (1997) 139.
    • (1997) Adv. Phys. , vol.46 , pp. 139
    • Krug, J.1
  • 36
    • 33746012315 scopus 로고
    • Free energy of a nonuniform system. I. Interfacial free energy
    • J.W. Cahn, J.E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28 (1958) 258.
    • (1958) J. Chem. Phys. , vol.28 , pp. 258
    • Cahn, J.W.1    Hilliard, J.E.2
  • 37
    • 0001386608 scopus 로고
    • Nonlinear aspects of the Cahn-Hilliard equation
    • A. Novick-Cohen, L.A. Segel, Nonlinear aspects of the Cahn-Hilliard equation, Physica D 10 (1984) 277.
    • (1984) Physica D , vol.10 , pp. 277
    • Novick-Cohen, A.1    Segel, L.A.2
  • 38
    • 0000910261 scopus 로고
    • The nonlinear Cahn-Hilliard equation: Transition from spinodal decomposition to nucleation behavior
    • A. Novick-Cohen, The nonlinear Cahn-Hilliard equation: transition from spinodal decomposition to nucleation behavior, J. Stat. Phys. 38 (1985) 707.
    • (1985) J. Stat. Phys. , vol.38 , pp. 707
    • Novick-Cohen, A.1
  • 39
    • 0001192116 scopus 로고    scopus 로고
    • The Cahn-Hilliard equation: Mathematical and modeling perspectives
    • to appear
    • A. Novick-Cohen, The Cahn-Hilliard equation: mathematical and modeling perspectives, Adv. Math. Sci. Appl. (1998), to appear.
    • (1998) Adv. Math. Sci. Appl.
    • Novick-Cohen, A.1
  • 40
    • 0012658793 scopus 로고    scopus 로고
    • Coarsening dynamics of a one-dimensional driven Cahn-Hilliard system
    • C.L. Emmott, A.J. Bray, Coarsening dynamics of a one-dimensional driven Cahn-Hilliard system, Phys. Rev. E 54 (1996) 4568.
    • (1996) Phys. Rev. E , vol.54 , pp. 4568
    • Emmott, C.L.1    Bray, A.J.2
  • 41
    • 0001015096 scopus 로고
    • Theory of morphological instability in driven systems
    • K. Leung, Theory of morphological instability in driven systems, J. Stat. Phys. 61 (1990) 345.
    • (1990) J. Stat. Phys. , vol.61 , pp. 345
    • Leung, K.1
  • 43
    • 5944238203 scopus 로고
    • Theory of linear facet growth during thermal etching
    • W.W. Mullins, Theory of linear facet growth during thermal etching, Philos. Mag. 6 (1961) 1313.
    • (1961) Philos. Mag. , vol.6 , pp. 1313
    • Mullins, W.W.1
  • 44
    • 0000291359 scopus 로고
    • The spiral growth of crystals
    • A.A. Chernov, The spiral growth of crystals, Sov. Phys. Uspekhi 4 (1961) 116.
    • (1961) Sov. Phys. Uspekhi , vol.4 , pp. 116
    • Chernov, A.A.1
  • 45
    • 0040916533 scopus 로고
    • On stability of structure of crystal surfaces
    • American Society for Testing and Materials, Philadelphia
    • N. Cabrera, On stability of structure of crystal surfaces, in: Symposium on Properties of Surfaces, American Society for Testing and Materials, Philadelphia, 1963, pp. 24-31.
    • (1963) Symposium on Properties of Surfaces , pp. 24-31
    • Cabrera, N.1
  • 46
    • 0016118199 scopus 로고
    • A vector thermodynamics for anisotropic surfaces - II. Curved and facetted surfaces
    • J.W. Cahn, D.W. Hoffman, A vector thermodynamics for anisotropic surfaces - II. Curved and facetted surfaces, Acta Metall. 22 (1974) 1205.
    • (1974) Acta Metall. , vol.22 , pp. 1205
    • Cahn, J.W.1    Hoffman, D.W.2
  • 47
    • 0027647619 scopus 로고
    • The dynamics of nucleation for the Cahn-Hilliard equation
    • P.W. Bates, P.C. Fife, The dynamics of nucleation for the Cahn-Hilliard equation, SIAM J. Appl. Math. 53 (1993) 990.
    • (1993) SIAM J. Appl. Math. , vol.53 , pp. 990
    • Bates, P.W.1    Fife, P.C.2
  • 48
    • 33646109512 scopus 로고
    • The kinetics of precipitation from supersaturated solid solutions
    • I.M. Lifshitz, V.V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids 19 (1961) 35.
    • (1961) J. Phys. Chem. Solids , vol.19 , pp. 35
    • Lifshitz, I.M.1    Slyozov, V.V.2
  • 49
    • 0001333772 scopus 로고
    • Theorie der Alterung von Niederschlägen dürch Umlösen (Ostwald-Reifung)
    • C. Wagner, Theorie der Alterung von Niederschlägen dürch Umlösen (Ostwald-Reifung), Z. Elektrochem. 65 (1961) 581.
    • (1961) Z. Elektrochem. , vol.65 , pp. 581
    • Wagner, C.1
  • 50
    • 0001659604 scopus 로고
    • Dispersion relation around the kink solution of the Cahn-Hilliard equation
    • A. Shinozaki, Y. Oono, Dispersion relation around the kink solution of the Cahn-Hilliard equation, Phys. Rev. E. 47 (1993) 804.
    • (1993) Phys. Rev. E. , vol.47 , pp. 804
    • Shinozaki, A.1    Oono, Y.2
  • 51
    • 0028447762 scopus 로고
    • Simulation of particle growth and Ostwald ripening via the Cahn-Hilliard equation
    • T. Küpper, N. Masbaum, Simulation of particle growth and Ostwald ripening via the Cahn-Hilliard equation, Acta Metall. Mater. 42 (1994) 1847.
    • (1994) Acta Metall. Mater. , vol.42 , pp. 1847
    • Küpper, T.1    Masbaum, N.2
  • 52
    • 0001859866 scopus 로고
    • Kink dynamics in a one-dimensional conserved TDGL system
    • T. Kawakatsu, T. Munakata, Kink dynamics in a one-dimensional conserved TDGL system, Prog. Theor. Phys. 74 (1985) 11.
    • (1985) Prog. Theor. Phys. , vol.74 , pp. 11
    • Kawakatsu, T.1    Munakata, T.2
  • 53
    • 44949275928 scopus 로고
    • Slow motion for the Cahn-Hilliard equation in one space dimension
    • N. Alikakos, P.W. Bates, G. Fusco, Slow motion for the Cahn-Hilliard equation in one space dimension, J. Diff. Eqs. 90 (1990) 81.
    • (1990) J. Diff. Eqs. , vol.90 , pp. 81
    • Alikakos, N.1    Bates, P.W.2    Fusco, G.3
  • 54
    • 43949159714 scopus 로고
    • Metastable patterns for the Cahn-Hilliard equation, Part 1
    • P.W. Bates, J.P. Xun, Metastable patterns for the Cahn-Hilliard equation, Part 1, J. Diff. Eqs. 111 (1994) 421; Part 2: Layer dynamics and slow invariant manifold, J. Diff. Eqs. 117 (1995) 165.
    • (1994) J. Diff. Eqs. , vol.111 , pp. 421
    • Bates, P.W.1    Xun, J.P.2
  • 55
    • 43949159714 scopus 로고
    • Part 2: Layer dynamics and slow invariant manifold
    • P.W. Bates, J.P. Xun, Metastable patterns for the Cahn-Hilliard equation, Part 1, J. Diff. Eqs. 111 (1994) 421; Part 2: Layer dynamics and slow invariant manifold, J. Diff. Eqs. 117 (1995) 165.
    • (1995) J. Diff. Eqs. , vol.117 , pp. 165
  • 56
    • 0001137528 scopus 로고
    • Late stages of spinodal decomposition in binary mixtures
    • E.D. Siggia, Late stages of spinodal decomposition in binary mixtures, Phys. Rev. A 20 (1979) 595.
    • (1979) Phys. Rev. A , vol.20 , pp. 595
    • Siggia, E.D.1
  • 57
    • 0000899924 scopus 로고    scopus 로고
    • New mechanism of droplet coarsening in phase-separating fluid mixtures
    • H. Tanaka, New mechanism of droplet coarsening in phase-separating fluid mixtures, J. Chem. Phys. 107 (1997) 3734.
    • (1997) J. Chem. Phys. , vol.107 , pp. 3734
    • Tanaka, H.1
  • 58
    • 0022145870 scopus 로고
    • The influence of particle motion on Ostwald ripening in liquids
    • L. Ratke, W.K. Thieringer The influence of particle motion on Ostwald ripening in liquids, Acta Metall. 33 (1985) 1793.
    • (1985) Acta Metall. , vol.33 , pp. 1793
    • Ratke, L.1    Thieringer, W.K.2
  • 59
    • 0025441412 scopus 로고
    • Ostwald ripening in the isothermal rheocasting process
    • G. Wan, P.R. Sahm, Ostwald ripening in the isothermal rheocasting process, Acta Metall. Mater. 38 (1990) 967.
    • (1990) Acta Metall. Mater. , vol.38 , pp. 967
    • Wan, G.1    Sahm, P.R.2
  • 60
    • 0026260765 scopus 로고
    • The effect of convection on Ostwald ripening in solid-liquid mixtures
    • N. Akaiwa, S.C. Hardy, P.W. Voorhees, The effect of convection on Ostwald ripening in solid-liquid mixtures, Acta Metall. Mater. 39 (1991) 2931.
    • (1991) Acta Metall. Mater. , vol.39 , pp. 2931
    • Akaiwa, N.1    Hardy, S.C.2    Voorhees, P.W.3
  • 61
    • 49049141478 scopus 로고
    • Kink dynamics in one-dimensional nonlinear systems
    • K. Kawasaki, T. Ohta, Kink dynamics in one-dimensional nonlinear systems, Physica A 116 (1982) 573.
    • (1982) Physica A , vol.116 , pp. 573
    • Kawasaki, K.1    Ohta, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.