University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei
Metropolis Monte Carlo: Examples
Adam DiNardo, undergraduate REU
student from Penn State University,
Metropolis Monte Carlo simulations of
the compositional ordering in SiGe
clusters.
30
40
50
60
Z
30
40
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60
X
30
40
50
60
Y
X
30
40
50
60
Z
30
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6
0
X
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6
0
Y
X
Si  blue
,
Ge  red
initial
final
Oscillatory surface segregation of SiGe alloys
Kelires & Tersoff,
Phys. Rev. Lett.
63
, 1164, 1989.
Two types of Monte Carlo moves – small atomic displacements and interchange of atom type are
used to investigate surface segregation vs temperature in SiGe alloys.
surface layer
second layer
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Lattice Monte Carlo.
Ising Model.
∑
∑
−
−
=
)
(
ij
i
i
j
i
S
H
S
S
J
E
Models in which particles belong to the lattice sites and interact locally can be a good
representation of a number of real systems (magnetic materials, binary alloys, etc.).
There are
several modifications of lattice MC:
In the original Ising model
the internal energy of a system (e.g. magnetic material) is calculated
as the sum of pair interaction energies between the atoms or molecules, which are attached to the
nodes of a regular lattice.
In terms of
magnetic material
, we have a discrete set of degrees of
freedom interacting with each other and an external magnetic field.
The spin variable S
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 Fall '11
 Zhigilei
 Magnetism, Statistical Mechanics, Ferromagnetism, Leonid Zhigilei

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