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Homework4

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

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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.

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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 ±
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