Molecular Dynamics Study of Solidification in the Aluminum-Silicon System Supervisor: Dr. Jeffrey J Hoyt Peyman Saidi Winter 2013

Aluminum – Mineral Commodity Summary Motivation (Importance of Aluminum Alloys)

T. Hosch, et al. Material science and engineering A 528 (2010) 226–232. Al-Si Eutectic 250 μ m/sAl-Si Eutectic 20 μ m/sAl-Si Eutectic 950 μ m/s 3 Motivation (Quench Modified Aluminum Silicon Alloy)

4 Melting Point Temperature Ste p Advacancy Kink Growth of Silicon crystals

5 Twin Planes Propagation mechanism in Silicon dendrites is based on interaction of twinning. Quench modified fibrous silicon is twin free. What is the growth mechanism of quench modified silicon in Aluminum-Silicon alloy? What is the critical condition for the transition from anisotropic to isotropic growth for Silicon dendrites? What is the magnitude and anisotropy of step kinetic coefficient, free energy and the stiffness of the interface? What is the effect of twins on kinetic parameters at different undercooling and compositions? D. R. Hamilton and R. G. Seidensticker J. Appl. Phys. 31, 1165 (1960) Twin Plane Reentrant Edge Mechanism (TPRE)

6 Molecular Dynamics Method: A model describing all interactions in the system Cutoff distance Newton’s equations of motion: Stability of System G=H-TS H: Heat ContentS: Randomness H=U+PV U: Internal Energy U=K+E K: Kinetic Energy Vibration Rotation Translation E: Potential Energy Interaction of atoms Where are we? Implementing model in MD code Potential energies for all interactions AluminumSiliconAl-Si What do we need to run a MD simulation?

7 Molecular Dynamics models: Aluminum (Embedding Atom Method) M. S. Daw and M. I. Baskes PHYSICAL REVIEW B 29, 6443 (1984) Aluminum FCC Crystal structure, metallic bond

8 Molecular Dynamics models: Silicon (Stillinger-Weber) F. H. Stillinger and T. A. Weber PHYSICAL REVIEW B 31, 5262 (1985) Silicon Diamond crystal structure, covalent bonds

9 Molecular Dynamics models: Aluminum Silicon Interactions (AEAM) A. M. Dongare et al. PHYSICAL REVIEW B 80, , Idea: Reformulation of Embedding Atom Method by extracting a three body term from the Embedding functional in order to make these two methods (EAM and SW) compatible with each other. Implementing A-EAMAluminum PotentialSilicon PotentialAl-Si Potential

10 Silicon Potential (Stillinger Weber)

11 Silicon Potential (Modified Stillinger-Weber)  The difference between cohesive energy of diamond and wurtzite structures should be the same as the value calculated with DFT.  Modification should not affect the characteristics of the Stillinger-Weber potential which accurately predicts silicon properties. Diamond structure was stabilized by taking into account interaction with the third neighbor.

12 Silicon Potential (Modified Stillinger-Weber)

13 Pure Components: Gibbs-Helmholtz relation Alloy: The alloy’s free energy as a function of composition Semi Grand Canonical Monte Carlo (SGCMC) simulation: Aluminum-Silicon Potential Target: Aluminum-Silicon Potential should predict phase diagram accurately. U1U1 U 2 -U 1 Atom Switches back T, C, P=0 random Si atom is switched to Al P. Sindzingre, D. Frenkel. Chem. Phys. Lett. (1987) 35–41.

14  So far Angular Embedding atom method was implemented on Molecular Dynamics code A modified potential for Silicon was proposed  Current work Making an accurate potential for Al-Si interactions  Studying and modeling nucleation and solidification growth Studying the crystalline anisotropies of the interfacial free energy. Characterizing the magnitude and anisotropy of the step kinetic coefficient. Examining a faceted to non-faceted transition of the interface by changing undercooling. Developing a model for the nucleation and growth phenomena.  Studying the effect of twinning on crystal growth Studying growth rate as a function of undercooling on twinned Si crystals in contact with liquid. Studying growth rate as a function of composition on twinned Si crystals in contact with liquid. Results and Future Work

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