Homework4 - Homework#4 Objective Getting experience with...

University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei
Homework #4
1. Review computer code that implements a simple Ising model, mse627-mc.f90,
(the code was written recently and not thoroughly tested, if you find any bugs
or get ideas for improvement please send them to the class mailing list).
2. Perform Metropolis Monte Carlo simulation (MC moves = switch particle
types) to find equilibrium structure (and compositional ordering) for binary
alloys with two sets of parameters (E
AA
= E
BB
= -0.05 eV, E
AB
= -0.01 eV)
and (E
AA
= E
BB
= -0.05 eV, E
AB
= -0.25 eV) and several temperatures.
Choose values of temperature that would allow you to discuss the temperature
dependence of the results of the simulations.
3. Plot snapshots from your simulations to illustrate the structural changes during
the simulations and the final equilibrium structures observed for different
input parameters used (task #2). ( Snapshots can be made using the files
written to sub-directory “data” – you should create this directory before
running the code ). Make plots showing changes of energy, number of AA,
AB, and BB bonds during the simulations. ( Plots can be made using the data
written to file EnBnd.out ). Discuss your results based on thermodynamics of
binary solid solutions briefly outlined in the next two pages.
4. Adapt the code to model a crystal with vacancies. Perform simulations for a
system with energy of vacancy formation of 1 eV. Calculate the equilibrium
vacancy concentrations for several (2-3) values of temperature. Compare your
results to the theoretical equation derived/discussed below. Discuss
agreement/disagreement between the numerical results and the theoretical
equation.
Objective: Getting experience with Metropolis Monte Carlo simulations, using
Ising model to study compositional ordering and segregation in binary alloys.

University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei
Let s consider mixing of two components A and B:
mix mix mix
S T ǻ ǻ H ǻ G ±