heterogenous nucleation in hard spheres...

Some facts about EDMDHomogenous NucleationHeterogenous nucleation

Heterogenous Nucleation in Hard Spheres Systems

Sven Dorosz and Tanja Schilling

University of Luxembourg,Softmatter Theory Group

May, 2012

Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems


Table of contents

1 Some facts about EDMD

2 Homogenous Nucleation

3 Heterogenous nucleation



Motivation Event Driven Molecular Dynamics

Time Driven MD simulation vs. Event Driven MD simulation

V (r) =

{

∞ if r < σ0 if r ≥ σ

⇒ free flight between collisions

NVE ensemble.

τ = σ2

D sets the timescale

B. J. Alder and T. E. Wainwright, J. Chem. Phys., 27, 1208 (1957).



Phasediagram for Hard Spheres

Md. Rintoul and S. Torquato, PRL 77, 20, 4198-4201 (1996).



Definition of the order parameter

Observables for the Local Bond Ordering:

In 3d:

q6m(i) :=1

n(i)

n(i)∑

j=1

Y6m (~rij) , rij < 1.4

where Y6m (~rij) are the spherical harmonics (with l=6).

P. J. Steinhardt, D. R. Nelson, and M. Ronchetti. Phys. Rev. B, 28(2) (1983)



Detecting emerging crystallites

If particle i and nb neighbouring particle j satisfy~q6(i) · ~q6

∗(j) > 0.7

Crystalline particles (colorcoded ”green”), nb > 10.Low symmetry cluster (LSC)(colorcoded ”light brown”), nb > 5.



Nucleation rates

⇒ MD and MC simulations produce rates match the experimental results

T. Schilling, S. Dorosz et al. JPCM, 23, 19, 194120 (2011).



Precursor nucleation

⇒ Effective two step process. Precursor mediated nucleation

T. Schilling, S. Dorosz et al. JPCM, 23, 19, 194120 (2011).



Motivation

Will the substrate induce different nucleation pathways?

Where does the nucleation happen?

What are the consequences of the mismatch betweensubstrate and equilibrium crystal lattice constant?

What is the crystal structure of the nucleus?

How does the substrate change the nucleation rate?



Setup of the system

Super-saturated fluid of hard spheres in contact with a triangularsubstrate.

1 1,1 1,2 1,3 1,4

lattice constant a [σ]

1,005

1,01

1,015

1,02

num

ber

dens

ity ρ

instantaneous growth

nucleation

limit

of s

tabi

lity

N = 220200 (216000 bulk + 4200 substrate) particlesN/V = 1.005 (η = 0.526) − 1.02 (η = 0.534)Corresponding chemical potentials −∆µ ≃ 0.50 − 0.54 kBT



Immediate wetting

a < asp

t = 6τ t = 70τS.D. and T. Schilling, J. Chem. Phys. 136, 044702 (2012).



Vertical density profile

0 5 10 15distance to the substrate z [σ]

0

0.002

0.004

0.006

0.008de

nsity

ρ(z

)

t = 100 τt = 50 τt = 1 τ

S.D. and T. Schilling, J. Chem. Phys. 136, 044702 (2012).



The first layer

at t > 150τ

a = 1.01σ a = 1.1σS.D. and T. Schilling, J. Chem. Phys. 136, 044702 (2012).



Defect density

1 2 3 4 5layer n

0.1

0.2

0.3

0.4

0.5

defe

ct d

ensi

ty η

a=1.01σa=1.05σa=1.10σ

1 2 3 4 5layer n

3400

3600

3800

4000

4200

# of

par

ticle

s in

laye

r N

(n)

⇒ Induced defects are compensated in the first 3 layers




3 layer stacking

⇒ Domains of ABA and ABC structure




5 layer stacking

⇒ Crystal grows in random hexagonal closed packing (RHCP)



Distinguishing fcc/hcp and bcc

more detailed structure analysis with w4 and w6

wl =

∑

m1+m2+m3

(

l l lm1 m2 m3

)

qlm1qlm2

qlm3

(∑m

l=−m |qlm|2)3/2

fcc −0.05 < w6 < 0 w4 < 0hcp −0.05 < w6 < 0 w4 > 0bcc 0 < w6 < 0.05 w4 > 0

⇒ 85% of the crystal has fcc resp. hcp structure

S. Jungblut and C. Dellago, 2011, J. Chem. Phys. 134, 104501.



Setup of the system

1 1,1 1,2 1,3 1,4

lattice constant a [σ]

1,005

1,01

1,015

1,02

num

ber

dens

ity ρ

instantaneous growth

nucleation

limit

of s

tabi

lity



Nucleation at the wall

a > asp

t = 6τ t = 80τ⇒ Droplet formation on the substrate

S.D. and T. Schilling, 2012, J. Chem. Phys. 136, 044702.



Droplet characterization

0 100 τ 200 τ 300 τ 400 τtime after critical nucleus is formed

100

1000

10000

# of

sol

id p

artic

les

in c

lust

er ρ=1.01ρ=1.0175ρ=1.02

100 1000N

1

10

prin

cipa

l mom

ent

R⊥ ez

R⊥ ez

R||e

z

⇒ non-spherical droplets even up to 4000 particles.




Nucleation rates

1.005 1.01 1.015 1.02 1.025density ρ

0

5e-06

1e-05

1.5e-05

2e-05

nucl

eatio

n ra

te *

[σ5 /6

Dl]

a=1.15σa=1.2σa=1.25σa=1.3σa=1.35σa=1.4σ

a

⇒ Decreasing nucleation rate with increasing mismatch to the substrate




Conclusion

precursor mediated nucleation in homogeneous hard spheressystems

two regimes of crystallization :

immediate full wetting of the surface

heterogeneous nucleation at the substrate



Acknowledgements

Tanja Schilling, University of Luxembourg

Martin Ottel, Frederike Schmid, Hamed Maleki, Hajo Schope,and Kurt Binder, University of Mainz

The present project is supported by the National ResearchFund, Luxembourg and cofunded under the Marie CurieActions of the European Commission (FP7-COFUND)


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