# Fluid Mechanics and Acoustics Laboratory - UMR 5509

LMFA - UMR 5509
Laboratoire de Mécanique des Fluides et d’Acoustique
Lyon
France

## Study of crystal growth situations

Séverine Millet, Valéry Botton, Daniel Henry, Hamda Ben Hadid, S. Kaddeche, F. Mokhtari, M. Albaric, D. Pelletier, J.P. Garandet, Y. Fautrelle, K. Zaidat

The solidification situations we study are known as vertical Bridgman (solidification from the bottom, it is the case of Silicon growth at INES) or horizontal Bridgman (solidification from the side, it is the case of metallic alloys solidification in the Afrodite experiment at SIMAP/EPM). These studies have also been developed in the frame of the PHC Maghreb program "Modeling and optimization of the purification of Silicon by directional solidification", which associates our research team with three teams from Algeria, Morocco and Tunisia.
In the case of Silicon growth, the objective is to get a good stirring of the melt for a better uniformity of its composition. Two approaches were studied: a stirring with an impeller or a non-intrusive stirring by acoustic streaming. The stirring by impeller has been studied experimentally (water setup and real melts) and numerically by M. Chatelain during his PhD (CEA funding), in collaboration between INES and our team [B25, A126, B26]. The thematic related with the stirring by acoustic streaming is presented in the rubric "Flows generated by ultrasound waves".
In a more applied direction and in connection with INES, we want to be able to estimate the effect of these flows on the impurities segregation. According to the models developed at INES by J.P. Garandet, these solutal effects, such as the segregation, can be estimated from the shear at the interface. In the frame of the PhD of N. El Ghani, we have developed an electrochemical method allowing the measurement of the shear at a wall in water and were thus able to characterize the solutal boundary layer induced by an acoustic streaming flow impinging a wall. In the frame of the PHC Maghreb program, we have also studied the effect that could be obtained by vibration, effect on the convection in the melt as well as on the impurities segregation (PhD of S. Bouarab).

Variation of the maximal velocity in a convective flow in a differentially heated cavity submitted to vibrations when the vibration angle $\alpha$ is changed (horizontal vibrations for $\alpha=0^\circ$ and vertical vibrations for $\alpha=90^\circ$). The pure convective flow turns in the trigonometric direction, but the vibrations ($90^\circ<\alpha<180^\circ$) can invert this flow.

In the case of metallic alloys solidification in the Afrodite experiment, the ingots are transversally confined and a temperature difference is applied between the endwalls in order to promote convection and the stirring of the compounds in the melt during the solidification. On this problem, the PhD of R. Boussaa on the three-dimensional numerical simulation of solidification allowed us to find the freckles observed experimentally, which are sources of brittleness in the solidified ingots [A120]. A two-dimensional model with a Hele-Shaw approach (2D½ model) has also been developed [A106]. The PhD of I. Hamzaoui allowed us to show that this 2D½ model was able to catch both purely convective situations and solidification configurations [A130].

Flow in the melt and position of the interface at the equilibrium state of solidification for right and left endwalls temperatures below and above the solidification temperature, respectively [A130].

Older work: crystal growth situations.

We studied more realistic crystal growth configurations taking into account a moving solid-liquid interface in the case of the Bridgman configuration. We particularly analyzed the convective flows in the liquid phase and the dopant concentration in the melt and in the crystal (macrosegregation phenomena) (PhD of S. Kaddeche). We later took into account periodic growth conditions and then considered pure solutal convection (PhD of F.Z. Haddad). These numerical studies were performed in collaboration with the Centre d’Etudes Nucléaires de Grenoble. They provided interesting results for the crystal growth community which were published in the Journal of Crystal Growth [A25, A27, A30, A46, A53, A54]. Within the frame of international collaborations, we also considered other crystal growth configurations (Czochralski, zone-melting) for which we particularly analyzed the flow transitions [A57, A78, A69].

Striations in the crystal due to a fluctuating interface velocity during horizontal Bridgman crystal growth [A46].