heterogenous nucleation in hard spheres facts aboutedmd homogenous nucleation heterogenous...

Download Heterogenous Nucleation in Hard Spheres facts aboutEDMD Homogenous Nucleation Heterogenous nucleation Heterogenous Nucleation in Hard Spheres Systems Sven Dorosz and Tanja Schilling

Post on 11-Apr-2018

217 views

Category:

Documents

1 download

Embed Size (px)

TRANSCRIPT

  • 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 < 0 if r

    free flight between collisions

    NVE ensemble.

    = 2

    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 []

    1,005

    1,01

    1,015

    1,02

    num

    ber

    dens

    ity

    instantaneous growth

    nucleation

    limit

    of s

    tabi

    lity

    N = 220200 (216000 bulk + 4200 substrate) particlesN/V = 1.005 ( = 0.526) 1.02 ( = 0.534)Corresponding chemical potentials 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 = 6 t = 70S.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 []

    0

    0.002

    0.004

    0.006

    0.008de

    nsity

    (z

    )

    t = 100 t = 50 t = 1

    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 > 150

    a = 1.01 a = 1.1S.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

    a=1.01a=1.05a=1.10

    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

    )

    qlm1qlm2qlm3

    (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 []

    1,005

    1,01

    1,015

    1,02

    num

    ber

    dens

    ity

    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 = 6 t = 80 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

    0 100 200 300 400 time after critical nucleus is formed

    100

    1000

    10000

    # of

    sol

    id p

    artic

    les

    in c

    lust

    er =1.01=1.0175=1.02

    100 1000N

    1

    10

    prin

    cipa

    l mom

    ent

    Rez

    Rez

    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

    0

    5e-06

    1e-05

    1.5e-05

    2e-05

    nucl

    eatio

    n ra

    te *

    [5

    /6D

    l]a=1.15a=1.2a=1.25a=1.3a=1.35a=1.4

    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

    Some facts about EDMDHomogenous NucleationHeterogenous nucleation

Recommended

View more >