We have utilized a phase-field model to investigate the evolution of eutectic silicon in Al-Si alloy. The interfacial fluctuations are included into a phase-field model of two-phase solidification, as stochastic noise terms and their dominant role in eutectic silicon formation is discussed. We have observed that silicon spherical particles nucleate on the foundation of primary aluminum phase and their nucleation continues on concentric rings, through the Al matrix. The nucleation of silicon particles is attributed to the inclusion of fluctuations into the phase-field equations. The simulation results have shown needle-like, fish-bone like and flakes of silicon phase by adjusting the noise coefficients to larger values. Moreover, the role of primary Al phase on nucleation of silicon particles in Al-Si alloy is elaborated. We have found that the addition of fluctuations plays the role of modifiers in our simulations and is essential for phase-field modeling of eutectic growth in Al-Si system. The simulated finger-like Al phases and spherical Si particles are very similar to those of experimental eutectic growth in modified Al-Si alloy.
 S. Akamatsu, M. Plapp, Current Opinion in Solid State and Mater. Sci. 20, 46-54 (2016).
 S. Ghosh, A. Choudhury, M. Plapp, S. Bottin-Rousseau, G. Faivre, S. Akamatsu, Phys. Rev. E 91, 022407 (2015).
 S.G. Pavlik, R.F. Sekerka, Physica A 277, 415-431 (2000).
 K.R. Elder, F. Drolet, J.M. Kosterlitz, M. Grant, Phys. Rev. E 72, 677 (1993).
 Z. Ebrahimi, J.L. Rezende, J. Kundin, J. Crystal. Growth. 349, 36-42 (2012).
 U. Hechta, L. Granasy, T. Pusztai, B. Bottger, M. Apel, V. Witusiewicz, L. Ratke, J.D. Wilde, L. Froyen, D. Camel, B. Drevet, G. Faivre, S.G. Fries, B. Legendre, S. Rex, Mater. Sci. and Eng. R 46, 1-49 (2004).
 A. Karma, W.J. Rappel, Phys. Rev. E. 57, 4323-4349 (1998).
 P. Fratzl, O. Penrose, J.L. Lebowitz, J. of Stat. Phy. 95 (5), 1429-1503 (1999).
 K. Thornton, J. Agren, P.W. Voorhees, Acta Mater. 51, 5675-5710 (2003).
 B. Echebarria, R. Folch, A. Karma, M. Plapp, Phys. Rev. E. 70, 061604 (2004).
 J. Tiaden, B. Nestler, H.J. Diepers, I. Steinbach, I. Physica D. 115, 73-86 (1998).
 T. Takaki, M. Ohno, T. Shimokawabec, T. Aoki, Acta Mater. 81, 272-283 (2014).
 T. Takaki, M. Ohno, Y. Shibuta, S. Sakane, T. Shimokawabe, T. Aoki, J Crystal Growth 442, 14-24 (2016).
 M. Asle Zaeem, H. Yin, S.D. Felicelli, Appl. Math. Modell. 37, 3495-3503 (2013).