REBOUNDS WITH A RESTITUTION COEFFICIENT LARGER THAN UNITY IN
NANOCLUSTER COLLISIONS Hiroto Kuninaka Faculty of Education, Mie
Univ. Physics of Granular Flows (2013/JUN/27) Collaborator: Hisao
Hayakawa (YITP, Kyoto Univ.)
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Outline Background Collision modes of nanoclusters Summary of
previous results Motivation Our model Simulation results Summary
and discussion
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Background Nanoscale collisions are subject to thermal
fluctuation and cohesive interaction. Collisional properties of
nanoscale objects are different from those of macroscopic objects
M. Kalweit and D. Drikakis: Phys. Rev. B 74, 235415 (2006) Binary
collision of Lennard-Jones clusters Collision modes are classified
into two main modes: coalescence and stretching separation which
depends on impact speed and impact parameter. Impact parameter
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Some collision modes in cohesive collisions M. Kalweit and D.
Drikakis: Phys. Rev. B 74, 235415 (2006) Coalescence u=1.58 X=0.0
u=5.38 x=0.36 Stretching separation
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M. Suri and T. Dumitrica, Phys. Rev. B 78, 081405R (2008)
Rebound mode of nanoclusters Nano-scale object can exhibit elastic
rebound mode under special condition Surface-coated clusters are
known to show elastic rebounds. H-passivated Si cluster and
substrate
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Each cluster has 682 atoms. Atoms are bound together by
modified Lennard-Jones potential U(r ij ). : distance between atoms
in one cluster z cohesive parameter : material parameter ( atoms in
each cluster) ( surface atom of C u ) ( surface atom of C l ) HK
and H. Hayakawa: Phys. Rev. E. 79, 031309 (2009) Our model
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T=0.02 (1.2[K]) N. V. Brilliantov et al. (2008) (i)Stick (ii)
multitime collision (iii) e1: super rebound HK and H. Hayakawa:
Phys. Rev. E. 79, 031309 (2009) Summary of our previous
results
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Motivation What is the difference between the ordinary rebound
mode and the super rebound mode? We investigate the thermodynamic
and structural properties of the clusters. We introduce an order
parameter to characterize the crystalline structure of the system.
HK and H. Hayakawa: Phys. Rev. E. 86, 051302 (2012)
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Simulation Setup Model 9 layers(30.6 ) Each cluster has 236
atoms. Atoms are bound together by modified Lennard-Jones potential
U(r ij ). cohesive parameter ( i, j : atoms in each cluster) ( i :
surface atom of C u ) ( j : surface atom of C l )
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Simulation Setup Initial configuration: FCC with the lowest
volume fraction: Initial equilibration to desired temperature by
velocity scaling method We give translational speed by accelerating
the clusters. (g=0.02/(m)) Kinetic temperature T=0.4 0 Simulation
step 2000 0
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Movie of typical rebound
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Histogram of restitution coefficient Restitution
coefficient:
Calculation of Entropy The 1st law of thermodynamics Work by
the atom j on the atom i
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Time Evolution of Entropy
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Calculation of bond order parameters Steinhardts order
parameter Time average i j : number of neighboring atoms
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3D histogram Super rebound (e>1) (after collision) FCC
(perfect crystal) Peak value Before collisionAfter collision
Ordinary0.14400.1228 Super0.11520.1699 3D histogram of Q4 and Q6(C
l )
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Analysis of Bond Order Parameter Steinharts order parameter We
investigate the distribution of
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Quantifying the discrepancy Chi-square number of atoms at j-th
bin (ordinary) number of atoms at j-th bin (super) The discrepancy
is largest at m=4.
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2 value Structural difference between super and ordinary
rebounds abundant in super clusters found in both clusters
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Potential Energy of Local Structure Atoms with the order
Positioned on corners of the cluster We define a local structure
with the atoms and the nearest atoms to calculate its potential
energy Nearest particles:
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Change in averaged potential energy of local structures
accelerationcollision Simulation step acceleration collision
Potential energy after equillibration at the onset of collision and
at the end of colliison Structure abundant in ordinary clusters
Potential energy / Structure abundant in super clusters Potential
energy of a local structure
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Conclusion We investigated the thermodynamic and structural
properties of nanoclusters. The difference can be found in the
distribution of between super clusters and ordinary clusters. The
potential energy of the characteristic local structure in super
cluster has high potential energy after equilibration. Slight
decrease of the potential energy can be found Such a decrease may
cause super rebounds