C. W. Figure, D. J. Kurz, and . Fisher, 10 (b) parametric plot of ? (red) and the equilibrium shape (green) for the parameters listed above Bibliography, 1986.

D. M. Stefanescu, Science and Engineering of Casting Solidification. Number v. 2, 2009.

G. J. Davies, Solidification and casting, 1973.

K. Kassner, Pattern formation in diffusion-limited crystal growth, World Scientific, 1996.
DOI : 10.1142/2146

B. Utter and E. Bodenschatz, Dynamics of low anisotropy morphologies in directional solidification, Physical Review E, vol.66, issue.5, p.51604, 2002.
DOI : 10.1103/PhysRevE.66.051604

B. Utter, Low anisotropy growth in directional solidification, 2001.

H. Biloni and W. J. Boettinger, Chapter 8 -solidification, Physical Metallurgy, pp.669-842, 1996.

W. A. Tiller, K. A. Jackson, J. W. Rutter, and B. Chalmers, 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

W. W. Mullins and R. F. Sekerka, 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

J. S. Langer, Instabilities and pattern formation in crystal growth, Reviews of Modern Physics, vol.52, issue.1, 1980.
DOI : 10.1103/RevModPhys.52.1

D. A. Porter and K. E. Easterling, Phase Transformations in Metals and Alloys, Third Edition (Revised Reprint), 1992.

K. A. Jackson and J. D. Hunt, 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

M. Hillert, The role of interfacial energy during solid state phase transformations, Jernkontorets Ann, vol.141, p.773, 1957.

M. Plapp and A. Karma, Eutectic colony formation: A stability analysis, Physical Review E, vol.60, issue.6, p.6865, 1999.
DOI : 10.1103/PhysRevE.60.6865

A. Dennstedt and L. Ratke, 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

A. Choudhury, M. Plapp, and B. Nestler, 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

G. A. Chadwick, Eutectic Alloy Solidification. Progress in materials science, 1963.
DOI : 10.1016/0079-6425(63)90037-9

K. Kassner and C. Misbah, 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

A. Karma and A. Sarkissian, Morphological instabilities of lamellar eutectics, Metallurgical and Materials Transactions A, vol.236, issue.4, p.635, 1996.
DOI : 10.1007/BF02648952

M. Ginibre, S. Akamatsu, and G. Faivre, 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

D. D. Double, 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

K. Kassner and C. Misbah, 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

M. Plapp, 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

J. W. Martin, J. W. Martin, R. D. Doherty, and B. Cantor, Stability of Microstructure in Metallic Systems. Cambridge Modular Sciences, 1997.

D. Hoffman and J. Cahn, 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

M. Fleck, L. Mushongera, D. Pilipenko, K. Ankit, and H. Emmerich, 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

M. Rappaz, J. Friedli, A. Mariaux, and M. Salgado-ordorica, 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

M. Asta, C. Beckermann, A. Karma, W. Kurz, R. Napolitano et al., 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

S. Akamatsu, G. Faivre, and T. Ihle, 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

J. Deschamps, M. Georgelin, and A. Pocheau, 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

J. Deschamps, M. Georgelin, and A. Pocheau, 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

A. Pocheau, J. Deschamps, and M. Georgelin, 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

M. Amoorezaei, S. Gurevich, and N. Provatas, Orientation selection in solidification patterning, Acta Materialia, vol.60, issue.2, pp.657-663, 2012.
DOI : 10.1016/j.actamat.2011.10.006

J. Ghmadh, J. Debierre, J. Deschamps, M. Georgelin, R. Guérin et al., 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

T. Takaki, M. Ohno, T. Shimokawabe, and T. Aoki, 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

D. Tourret and A. Karma, 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

S. Akamatsu, S. Bottin-rousseau, M. , and G. Faivre, 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

H. Jones, 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

R. E. Napolitano, S. Liu, and R. Trivedi, 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

. Kuo-an, A. Wu, J. J. Karma, M. Hoyt, and . Asta, Ginzburg-landau theory of crystalline anisotropy for bcc-liquid interfaces, Phys. Rev. B, vol.73, p.94101, 2006.

S. Akamatsu, S. Bottin-rousseau, M. , and G. Faivre, 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

A. Dougherty, 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

R. S. Qin and H. K. Bhadesia, Phase field method, Materials Science and Technology, vol.1198, issue.7, pp.803-811, 2010.
DOI : 10.1179/mst.1997.13.4.308

N. Provatas and K. Elder, Phase-Field Methods in Materials Science and Engineering, 2010.
DOI : 10.1002/9783527631520

N. Moelans, B. Blanpain, and P. Wollants, 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

L. Chen, 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

M. Plapp, 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

B. Echebarria, R. Folch, A. Karma, and M. Plapp, Quantitative phase-field model of alloy solidification, Physical Review E, vol.70, issue.6, p.61604, 2004.
DOI : 10.1103/PhysRevE.70.061604

I. Steinbach, 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

W. J. Boettinger, J. A. Warren, C. Beckermann, and A. Karma, 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

O. Penrose and P. C. Fife, 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

G. Caginalp and W. Xie, Phase-field and sharp-interface alloy models, Physical Review E, vol.48, issue.3, pp.1897-1909, 1993.
DOI : 10.1103/PhysRevE.48.1897

A. Karma, Phase-field model of eutectic growth, Physical Review E, vol.49, issue.3, pp.2245-2250, 1994.
DOI : 10.1103/PhysRevE.49.2245

I. Steinbach, F. Pezzolla, B. Nestler, M. Seeßelberg, R. Prieler et al., 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

J. Eiken, B. Böttger, and I. Steinbach, 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

B. Nestler and A. A. Wheeler, 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

B. Nestler, H. Garcke, and B. Stinner, 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

A. Choudhury and B. Nestler, 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

A. A. Wheeler, Phase-field theory of edges in an anisotropic crystal, Proc. R. Soc. A, pp.3363-3384, 2006.
DOI : 10.1098/rspa.2006.1721

W. T. Seong-gyoon-kim, T. Kim, and . Suzuki, Phase-field model for binary alloys, Phys. Rev. E, vol.60, pp.7186-7197, 1999.

D. A. Cogswell and W. C. Carter, 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

U. Hecht, 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

S. Bottin-rousseau, S. Akamatsu, and G. Faivre, 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

J. W. Cahn and J. E. Hilliard, 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

A. Choudhury, Quantitative phase field model for phase transfomations in multi-component alloys, 2012.

S. Ghosh, S. Akamatsu, S. Bottin-rousseau, G. Faivre, A. Choudhury et al., 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

R. Folch and M. Plapp, Quantitative phase-field modeling of two-phase growth, Physical Review E, vol.72, issue.1, p.11602, 2005.
DOI : 10.1103/PhysRevE.72.011602

J. J. Eggleston, G. B. Mcfadden, and P. W. Voorhees, 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

S. Torabi, J. Lowengrub, A. Voigt, and S. Wise, 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

K. Ankit, R. Mukherjee, T. Mittnacht, and B. Nestler, 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

L. Hogan, F. Kraft, and . Lemkey, Eutectic grains, Adv. Mater. Res, vol.5, pp.83-216, 1971.

U. Hecht, 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

J. Llorca and V. M. Orera, Directionally solidified eutectic ceramic oxides, Progress in Materials Science, vol.51, issue.6, p.711, 2006.
DOI : 10.1016/j.pmatsci.2005.10.002

B. Caroli, C. Caroli, J. Faivre, and . Mergy, Lamellar eutectic growth of CBr 4 ?C 2 Cl 6 : effect of crystal anisotropy on lamellar orientations and wavelength dispersions, J

S. Akamatsu, S. Faivre, and . Moulinet, 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

S. Akamatsu, M. Plapp, G. Faivre, and A. Karma, Pattern stability and trijunction motion in eutectic solidification, Physical Review E, vol.66, issue.3, p.30501, 2002.
DOI : 10.1103/PhysRevE.66.030501

S. Akamatsu, M. Plapp, G. Faivre, and A. Karma, 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

P. Manneville, Dissipative structures and weak turbulence, 1990.
DOI : 10.1007/3-540-60188-0_59

U. Hecht, . Vt-witusiewicz, S. Drevermann, and . Rex, Orientation relationship in univariant Al-Cu-Ag eutectics, Trans. Indian Inst. Met, vol.58, pp.545-551, 2005.

C. Herring, 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

N. Cabrera, The equilibrium of crystal surfaces, Surface Science, vol.2, pp.320-345, 1964.
DOI : 10.1016/0039-6028(64)90073-1

J. Debierre, . Karma, R. Celestini, and . Guerin, 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

V. Kokotin and U. Hecht, 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

S. Akamatsu, S. Bottin-rousseau, and G. Faivre, 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

A. Parisi and M. Plapp, Stability of lamellar eutectic growth, Acta Materialia, vol.56, issue.6, p.1348, 2008.
DOI : 10.1016/j.actamat.2007.11.037

A. Parisi and M. Plapp, Defects and multistability in eutectic solidification patterns, EPL (Europhysics Letters), vol.90, issue.2, p.26010, 2010.
DOI : 10.1209/0295-5075/90/26010

M. Perrut, A. Parisi, S. Akamatsu, S. Bottin-rousseau, G. Faivre et al., 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

A. Hellawell and P. M. Herbert, The developement of preferred orientations during the freezing of metals and alloys, Proc. R. Soc. A, pp.560-574, 1962.

D. Hull and D. J. Bacon, Introduction to Dislocations Materials science and technology, 2011.

K. Kassner and C. Misbah, Similarity laws in eutectic growth, Physical Review Letters, vol.66, issue.4, pp.445-448, 1991.
DOI : 10.1103/PhysRevLett.66.445

U. Hecht, V. Witisiewicz, and S. Rex, Solidification of bulk lamellar eutetcics, Materials Science Forum, pp.790-791343, 2014.

S. Y. Yeh, C. C. Chen, and C. W. Lan, 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

S. R. Coriell and R. F. Sekerka, 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

L. H. Ungar and R. A. Brown, 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

L. H. Ungar and R. A. Brown, 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

W. T. Read and W. Shockley, Dislocation Models of Crystal Grain Boundaries, Physical Review, vol.78, issue.3, pp.275-289, 1950.
DOI : 10.1103/PhysRev.78.275

G. Faivre, S. Bottin-rousseau, and S. Akamatsu, 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

P. Lejcek, Grain Boundary Segregation in Metals, Series in Materials Science, 2010.
DOI : 10.1007/978-3-642-12505-8

A. Karma and W. , 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

E. Kreyszig, Advanced Engineering Mathematics, 2010.