This preview shows pages 1–3. Sign up to view the full content.
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
50
60
X
30
40
50
60
Y
X
30
40
50
60
Z
30
40
50
6
0
X
30
40
50
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
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentUniversity of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei
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
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '11
 Zhigilei

Click to edit the document details