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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
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
Table of contents
1 Some facts about EDMD
2 Homogenous Nucleation
3 Heterogenous nucleation
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous 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).
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
Phasediagram for Hard Spheres
Md. Rintoul and S. Torquato, PRL 77, 20, 4198-4201 (1996).
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
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)
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
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.
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
Nucleation rates
⇒ MD and MC simulations produce rates match the experimental results
T. Schilling, S. Dorosz et al. JPCM, 23, 19, 194120 (2011).
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
Precursor nucleation
⇒ Effective two step process. Precursor mediated nucleation
T. Schilling, S. Dorosz et al. JPCM, 23, 19, 194120 (2011).
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
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?
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
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
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
Immediate wetting
a < asp
t = 6τ t = 70τS.D. and T. Schilling, J. Chem. Phys. 136, 044702 (2012).
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
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).
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
The first layer
at t > 150τ
a = 1.01σ a = 1.1σS.D. and T. Schilling, J. Chem. Phys. 136, 044702 (2012).
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
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
S.D. and T. Schilling, J. Chem. Phys. 136, 044702 (2012).
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
3 layer stacking
⇒ Domains of ABA and ABC structure
S.D. and T. Schilling, J. Chem. Phys. 136, 044702 (2012).
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
5 layer stacking
⇒ Crystal grows in random hexagonal closed packing (RHCP)
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
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.
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
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
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
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.
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
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.
S.D. and T. Schilling, 2012, J. Chem. Phys. 136, 044702.
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
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
S.D. and T. Schilling, 2012, J. Chem. Phys. 136, 044702.
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
Conclusion
precursor mediated nucleation in homogeneous hard spheressystems
two regimes of crystallization :
immediate full wetting of the surface
heterogeneous nucleation at the substrate
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems
Some facts about EDMDHomogenous NucleationHeterogenous nucleation
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)
Sven Dorosz and Tanja Schilling Heterogenous Nucleation in Hard Spheres Systems