Molecular Dynamics Study of

Solidification in the Aluminum-

Silicon System

Supervisor: Dr. Jeffrey J Hoyt

Peyman Saidi

Winter 2013

Aluminum – Mineral Commodity Summary 2011

0.10

1.60

2.00

3.30

8.65

13.76

13.80

22.00

32.50

33.00

23.0 17.9 2.0

43.45

54.50

98.50

0 20 40 60 80 100

Wheels

Heads

Suspension Arms and Links

Transmissin Cases

Brake Calipers

Steering Knuckles

Blocks

Bumper Beams

Closures

Subframes

Transfer Cases

IP Beams

Front Structures

Complete BIW

2

Motivation (Importance of Aluminum Alloys)

T. Hosch, et al. Material science and engineering A 528 (2010) 226–232.

Al-Si Eutectic 250μm/s

Al-Si Eutectic 20μm/s Al-Si Eutectic 950μm/s

3

Motivation (Quench Modified Aluminum Silicon Alloy)

4

Melting Point

Temperature

Step

Advacancy

Kink

Growth of Silicon crystals

5

Twin Planes Twin Planes

Twin PlanesTwin 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 distanc

e

Newton’s equations of motion:

Stability of System

G=H-TS

H: Heat Content

S: 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

Aluminum Silicon Al-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, 184106, 2009.

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-EAM

Aluminum Potential Silicon Potential Al-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.

U1 U2-U1

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

Thank You