10 (b) parametric plot of ? (red) and the equilibrium shape (green) for the parameters listed above Bibliography, 1986. ,
Science and Engineering of Casting Solidification. Number v. 2, 2009. ,
Solidification and casting, 1973. ,
Pattern formation in diffusion-limited crystal growth, World Scientific, 1996. ,
DOI : 10.1142/2146
Dynamics of low anisotropy morphologies in directional solidification, Physical Review E, vol.66, issue.5, p.51604, 2002. ,
DOI : 10.1103/PhysRevE.66.051604
Low anisotropy growth in directional solidification, 2001. ,
Chapter 8 -solidification, Physical Metallurgy, pp.669-842, 1996. ,
The redistribution of solute atoms during the solidification of metals, Acta Metallurgica, vol.1, issue.4, p.428, 1953. ,
DOI : 10.1016/0001-6160(53)90126-6
Stability of a Planar Interface During Solidification of a Dilute Binary Alloy, Journal of Applied Physics, vol.35, issue.2, p.444, 1964. ,
DOI : 10.1063/1.1713333
Instabilities and pattern formation in crystal growth, Reviews of Modern Physics, vol.52, issue.1, 1980. ,
DOI : 10.1103/RevModPhys.52.1
Phase Transformations in Metals and Alloys, Third Edition (Revised Reprint), 1992. ,
Lamellar and Rod Eutectic Growth, Transactions of the Metallurgical Society of AIME, vol.236, p.1129, 1966. ,
DOI : 10.1016/B978-0-08-092523-3.50040-X
The role of interfacial energy during solid state phase transformations, Jernkontorets Ann, vol.141, p.773, 1957. ,
Eutectic colony formation: A stability analysis, Physical Review E, vol.60, issue.6, p.6865, 1999. ,
DOI : 10.1103/PhysRevE.60.6865
Microstructures of Directionally Solidified Al???Ag???Cu Ternary Eutectics, Transactions of the Indian Institute of Metals, vol.95, issue.6, pp.777-782, 2012. ,
DOI : 10.1007/s12666-012-0172-3
Theoretical and numerical study of lamellar eutectic three-phase growth in ternary alloys, Physical Review E, vol.83, issue.5, p.51608, 2011. ,
DOI : 10.1103/PhysRevE.83.051608
Eutectic Alloy Solidification. Progress in materials science, 1963. ,
DOI : 10.1016/0079-6425(63)90037-9
Spontaneous parity-breaking transition in directional growth of lamellar eutectic structures, Physical Review A, vol.44, issue.10, pp.6533-6543, 1991. ,
DOI : 10.1103/PhysRevA.44.6533
Morphological instabilities of lamellar eutectics, Metallurgical and Materials Transactions A, vol.236, issue.4, p.635, 1996. ,
DOI : 10.1007/BF02648952
Experimental determination of the stability diagram of a lamellar eutectic growth front, Physical Review E, vol.56, issue.1, p.780, 1997. ,
DOI : 10.1103/PhysRevE.56.780
URL : https://hal.archives-ouvertes.fr/hal-00002634
Imperfections in lamellar eutectic crystals, Materials Science and Engineering, vol.11, issue.6, pp.325-335, 1973. ,
DOI : 10.1016/0025-5416(73)90123-7
Growth of lamellar eutectic structures: The axisymmetric state, Physical Review A, vol.44, issue.10, pp.6513-6532, 1991. ,
DOI : 10.1103/PhysRevA.44.6513
Three-dimensional phase-field simulations of directional solidification, Journal of Crystal Growth, vol.303, issue.1, pp.49-57, 2007. ,
DOI : 10.1016/j.jcrysgro.2006.12.064
Stability of Microstructure in Metallic Systems. Cambridge Modular Sciences, 1997. ,
A Vector Thermodynamics for Anisotropic Surfaces I. Fundamentals and Application to Plane Surface Junctions, Surface Science, vol.3, p.368, 1972. ,
DOI : 10.1002/9781118788295.ch28
On phase-field modeling with a highly anisotropic interfacial energy, The European Physical Journal Plus, vol.75, issue.10, p.12695, 2011. ,
DOI : 10.1140/epjp/i2011-11095-7
The influence of solid???liquid interfacial energy anisotropy on equilibrium shapes, nucleation, triple lines and growth morphologies, Scripta Materialia, vol.62, issue.12, pp.904-909, 2010. ,
DOI : 10.1016/j.scriptamat.2010.02.039
Solidification microstructures and solid-state parallels: Recent developments, future directions, Acta Materialia, vol.57, issue.4, pp.941-971, 2009. ,
DOI : 10.1016/j.actamat.2008.10.020
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.460.1125
Symmetry-broken double fingers and seaweed patterns in thin-film directional solidification of a nonfaceted cubic crystal, Physical Review E, vol.51, issue.5, pp.4751-4773, 1995. ,
DOI : 10.1103/PhysRevE.51.4751
URL : https://hal.archives-ouvertes.fr/hal-00002632
Crystal anisotropy and growth directions in directional solidification, Europhysics Letters (EPL), vol.76, issue.2, pp.291-297291, 2006. ,
DOI : 10.1209/epl/i2006-10247-9
URL : https://hal.archives-ouvertes.fr/hal-00094347
Growth directions of microstructures in directional solidification of crystalline materials, Physical Review E, vol.78, issue.1, p.11605, 2008. ,
DOI : 10.1103/PhysRevE.78.011605
URL : https://hal.archives-ouvertes.fr/hal-00286355
Maximal curvature and crystal orientation on directionally solidified dendrites, Physical Review E, vol.81, issue.5, p.51608, 2010. ,
DOI : 10.1103/PhysRevE.81.051608
URL : https://hal.archives-ouvertes.fr/hal-01327847
Orientation selection in solidification patterning, Acta Materialia, vol.60, issue.2, pp.657-663, 2012. ,
DOI : 10.1016/j.actamat.2011.10.006
Directional solidification of inclined structures in thin samples, Acta Materialia, vol.74, pp.255-267, 2014. ,
DOI : 10.1016/j.actamat.2014.04.023
URL : https://hal.archives-ouvertes.fr/hal-01181275
Two-dimensional phase-field simulations of dendrite competitive growth during the directional solidification of a binary alloy bicrystal, Acta Materialia, vol.81, issue.0, pp.81272-283, 2014. ,
DOI : 10.1016/j.actamat.2014.08.035
Growth competition of columnar dendritic grains: A phase-field study, Acta Materialia, vol.82, issue.0, pp.64-83, 2015. ,
DOI : 10.1016/j.actamat.2014.08.049
Lamellar eutectic growth with anisotropic interphase boundaries, IOP Conference Series: Materials Science and Engineering, vol.84, pp.3206-3214, 2012. ,
DOI : 10.1088/1757-899X/84/1/012083
URL : https://hal.archives-ouvertes.fr/hal-01469035
The solid???liquid interfacial energy of metals: calculations versus measurements, Materials Letters, vol.53, issue.4-5, pp.364-366, 2002. ,
DOI : 10.1016/S0167-577X(01)00508-0
Experimental measurement of anisotropy in crystal-melt interfacial energy, Interface Science, vol.10, issue.2/3, pp.217-232, 2002. ,
DOI : 10.1023/A:1015884415896
Ginzburg-landau theory of crystalline anisotropy for bcc-liquid interfaces, Phys. Rev. B, vol.73, p.94101, 2006. ,
A theory of thin lamellar eutectic growth with anisotropic interphase boundaries, Acta Materialia, vol.60, issue.6-7, pp.3199-3205, 2012. ,
DOI : 10.1016/j.actamat.2012.02.031
URL : https://hal.archives-ouvertes.fr/hal-01448369
Surface tension anisotropy and the dendritic growth of pivalic acid, Journal of Crystal Growth, vol.110, issue.3, pp.501-508, 1991. ,
DOI : 10.1016/0022-0248(91)90286-E
Phase field method, Materials Science and Technology, vol.1198, issue.7, pp.803-811, 2010. ,
DOI : 10.1179/mst.1997.13.4.308
Phase-Field Methods in Materials Science and Engineering, 2010. ,
DOI : 10.1002/9783527631520
An introduction to phase-field modeling of microstructure evolution, Calphad, vol.32, issue.2, pp.268-294, 2008. ,
DOI : 10.1016/j.calphad.2007.11.003
Phase-Field Models for Microstructure Evolution, Annual Review of Materials Research, vol.32, issue.1, pp.113-140, 2002. ,
DOI : 10.1146/annurev.matsci.32.112001.132041
Unified derivation of phase-field models for alloy solidification from a grand-potential functional, Physical Review E, vol.84, issue.3, p.31601, 2011. ,
DOI : 10.1103/PhysRevE.84.031601
Quantitative phase-field model of alloy solidification, Physical Review E, vol.70, issue.6, p.61604, 2004. ,
DOI : 10.1103/PhysRevE.70.061604
Phase-field models in materials science, Modelling and Simulation in Materials Science and Engineering, vol.17, issue.7, p.73001, 2009. ,
DOI : 10.1088/0965-0393/17/7/073001
Phase-Field Simulation of Solidification, Annual Review of Materials Research, vol.32, issue.1, pp.163-194, 2002. ,
DOI : 10.1146/annurev.matsci.32.101901.155803
Thermodynamically consistent models of phase-field type for the kinetic of phase transitions, Physica D: Nonlinear Phenomena, vol.43, issue.1, pp.44-62, 1990. ,
DOI : 10.1016/0167-2789(90)90015-H
Phase-field and sharp-interface alloy models, Physical Review E, vol.48, issue.3, pp.1897-1909, 1993. ,
DOI : 10.1103/PhysRevE.48.1897
Phase-field model of eutectic growth, Physical Review E, vol.49, issue.3, pp.2245-2250, 1994. ,
DOI : 10.1103/PhysRevE.49.2245
A phase field concept for multiphase systems, Physica D: Nonlinear Phenomena, vol.94, issue.3, pp.135-147, 1996. ,
DOI : 10.1016/0167-2789(95)00298-7
Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application, Physical Review E, vol.73, issue.6, p.66122, 2006. ,
DOI : 10.1103/PhysRevE.73.066122
A multi-phase-field model of eutectic and peritectic alloys: numerical simulation of growth structures, Physica D: Nonlinear Phenomena, vol.138, issue.1-2, pp.114-133, 2000. ,
DOI : 10.1016/S0167-2789(99)00184-0
Multicomponent alloy solidification: Phase-field modeling and simulations, Physical Review E, vol.71, issue.4, p.41609, 2005. ,
DOI : 10.1103/PhysRevE.71.041609
URL : http://digbib.ubka.uni-karlsruhe.de/volltexte/documents/1367780
Grand-potential formulation for multicomponent phase transformations combined with thin-interface asymptotics of the double-obstacle potential, Physical Review E, vol.85, issue.2, p.21602, 2012. ,
DOI : 10.1103/PhysRevE.85.021602
Phase-field theory of edges in an anisotropic crystal, Proc. R. Soc. A, pp.3363-3384, 2006. ,
DOI : 10.1098/rspa.2006.1721
Phase-field model for binary alloys, Phys. Rev. E, vol.60, pp.7186-7197, 1999. ,
Thermodynamic phase-field model for microstructure with multiple components and phases: The possibility of metastable phases, Physical Review E, vol.83, issue.6, p.61602, 2011. ,
DOI : 10.1103/PhysRevE.83.061602
Multiphase solidification in multicomponent alloys, Materials Science and Engineering: R: Reports, vol.46, issue.1-2, pp.1-49, 2004. ,
DOI : 10.1016/j.mser.2004.07.002
Dynamical polygonization below the cellular-bifurcation threshold in thin-sample directional solidification, Physical Review B, vol.66, issue.5, p.54102, 2002. ,
DOI : 10.1103/PhysRevB.66.054102
URL : https://hal.archives-ouvertes.fr/hal-00002637
Free Energy of a Nonuniform System. I. Interfacial Free Energy, The Journal of Chemical Physics, vol.28, issue.2, pp.258-267, 1958. ,
DOI : 10.1063/1.1744102
Quantitative phase field model for phase transfomations in multi-component alloys, 2012. ,
Interphase anisotropy effects on lamellar eutectics: A numerical study, Physical Review E, vol.91, issue.2, p.22407, 2015. ,
DOI : 10.1103/PhysRevE.91.022407
URL : https://hal.archives-ouvertes.fr/hal-01472474
Quantitative phase-field modeling of two-phase growth, Physical Review E, vol.72, issue.1, p.11602, 2005. ,
DOI : 10.1103/PhysRevE.72.011602
A phase-field model for highly anisotropic interfacial energy, Physica D: Nonlinear Phenomena, vol.150, issue.1-2, pp.91-103, 2001. ,
DOI : 10.1016/S0167-2789(00)00222-0
A new phase-field model for strongly anisotropic systems, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.226, issue.1946, pp.1337-1359, 2009. ,
DOI : 10.1098/rspa.1996.0026
Deviations from cooperative growth mode during eutectoid transformation: Insights from a phase-field approach, Acta Materialia, vol.81, issue.0, pp.81204-210, 2014. ,
DOI : 10.1016/j.actamat.2014.08.015
Eutectic grains, Adv. Mater. Res, vol.5, pp.83-216, 1971. ,
Multiphase solidification in multicomponent alloys, Materials Science and Engineering: R: Reports, vol.46, issue.1-2, pp.1-49, 2004. ,
DOI : 10.1016/j.mser.2004.07.002
Directionally solidified eutectic ceramic oxides, Progress in Materials Science, vol.51, issue.6, p.711, 2006. ,
DOI : 10.1016/j.pmatsci.2005.10.002
Lamellar eutectic growth of CBr 4 ?C 2 Cl 6 : effect of crystal anisotropy on lamellar orientations and wavelength dispersions, J ,
The formation of lamellar-eutectic grains in thin samples, Metallurgical and Materials Transactions A, vol.51, issue.8, p.2039, 2001. ,
DOI : 10.1007/s11661-001-0016-y
URL : https://hal.archives-ouvertes.fr/hal-00002636
Pattern stability and trijunction motion in eutectic solidification, Physical Review E, vol.66, issue.3, p.30501, 2002. ,
DOI : 10.1103/PhysRevE.66.030501
Overstability of lamellar eutectic growth below the minimum-undercooling spacing, Metallurgical and Materials Transactions A, vol.45, issue.6, pp.1815-1528, 2004. ,
DOI : 10.1007/s11661-004-0090-z
Dissipative structures and weak turbulence, 1990. ,
DOI : 10.1007/3-540-60188-0_59
Orientation relationship in univariant Al-Cu-Ag eutectics, Trans. Indian Inst. Met, vol.58, pp.545-551, 2005. ,
Some Theorems on the Free Energies of Crystal Surfaces, Physical Review, vol.82, issue.1, pp.87-93, 1951. ,
DOI : 10.1103/PhysRev.82.87
The equilibrium of crystal surfaces, Surface Science, vol.2, pp.320-345, 1964. ,
DOI : 10.1016/0039-6028(64)90073-1
Phase-field approach for faceted solidification, Physical Review E, vol.68, issue.4, p.68, 2003. ,
DOI : 10.1103/PhysRevE.68.041604
URL : https://hal.archives-ouvertes.fr/hal-00737470
Molecular dynamics simulations of Al???Al2Cu phase boundaries, Computational Materials Science, vol.86, pp.30-37, 2014. ,
DOI : 10.1016/j.commatsci.2014.01.014
Experimental Evidence for a Zigzag Bifurcation in Bulk Lamellar Eutectic Growth, Physical Review Letters, vol.93, issue.17, p.175701, 2004. ,
DOI : 10.1103/PhysRevLett.93.175701
Stability of lamellar eutectic growth, Acta Materialia, vol.56, issue.6, p.1348, 2008. ,
DOI : 10.1016/j.actamat.2007.11.037
Defects and multistability in eutectic solidification patterns, EPL (Europhysics Letters), vol.90, issue.2, p.26010, 2010. ,
DOI : 10.1209/0295-5075/90/26010
Role of transverse temperature gradients in the generation of lamellar eutectic solidification patterns, Acta Materialia, vol.58, issue.5, pp.1761-1769, 2010. ,
DOI : 10.1016/j.actamat.2009.11.018
URL : https://hal.archives-ouvertes.fr/hal-01239033
The developement of preferred orientations during the freezing of metals and alloys, Proc. R. Soc. A, pp.560-574, 1962. ,
Introduction to Dislocations Materials science and technology, 2011. ,
Similarity laws in eutectic growth, Physical Review Letters, vol.66, issue.4, pp.445-448, 1991. ,
DOI : 10.1103/PhysRevLett.66.445
Solidification of bulk lamellar eutetcics, Materials Science Forum, pp.790-791343, 2014. ,
Phase field modeling of morphological instability near grain boundary during directional solidification of a binary alloy: The hump formation, Journal of Crystal Growth, vol.324, issue.1, pp.296-303, 2011. ,
DOI : 10.1016/j.jcrysgro.2011.04.008
Morphological stability near a grain boundary groove in a solid-liquid interface during solidification of a binary alloy, Journal of Crystal Growth, vol.19, issue.4, pp.285-293, 1973. ,
DOI : 10.1016/0022-0248(73)90052-3
Cellular interface morphologies in directional solidification. II. The effect of grain boundaries, Physical Review B, vol.30, issue.7, p.3993, 1984. ,
DOI : 10.1103/PhysRevB.30.3993
Cellular interface morphologies in directional solidification. IV. The formation of deep cells, Physical Review B, vol.31, issue.9, p.5931, 1985. ,
DOI : 10.1103/PhysRevB.31.5931
Dislocation Models of Crystal Grain Boundaries, Physical Review, vol.78, issue.3, pp.275-289, 1950. ,
DOI : 10.1103/PhysRev.78.275
The trajectory of subboundary grooves during directional solidification of dilute alloys, Comptes Rendus Physique, vol.14, issue.2-3, pp.149-155, 2013. ,
DOI : 10.1016/j.crhy.2013.01.003
URL : https://hal.archives-ouvertes.fr/hal-01448374
Grain Boundary Segregation in Metals, Series in Materials Science, 2010. ,
DOI : 10.1007/978-3-642-12505-8
Quantitative phase-field modeling of dendritic growth in two and three dimensions, Physical Review E, vol.57, issue.4, pp.4323-4349, 1998. ,
DOI : 10.1103/PhysRevE.57.4323
Advanced Engineering Mathematics, 2010. ,