A04_DIFFUSION_Report_Template_2023 (2)

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Material Science

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Apr 3, 2024

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1 Chris Franzese ENGR1600: Materials Science for Engineers Interactive Activity #04 DIFFUSION SIMULATION REPORT TEMPLATE Objective : Run simulations of random walk model of diffusion to, (1) understand diffusion at the atomic level, (2) calculate diffusion coefficient, D, by simulating diffusion distance versus time at four different temperatures, (3) create an Arrhenius plot to determine the activation energy, Q. Procedure : Download CDF App of Diffusion-Simulation from LMS. Follow instructions on the CDF app. Step 1 (Part B: Obtain diffusion coefficient, D, from RMS displacement versus time at four different temperatures) : a) On a single graph, insert a figure with the RMS displacement versus square root of time (obtained in Part B), at four different temperatures, showing the best linear curve fit for each (y = mx + b) and the R^2 value. The slopes of each line is the square root of 6D, or (6D) 1/2 , from which the diffusion coefficient at each temperature can be calculated. b) Insert a table of the Diffusion Coefficient at the 4 different temperatures you selected from part (a). Include correct units Temp(K) Diffusion Coefficient(m^2/s) 1000 418.3 2000 126.8 3000 84.55 4000 73.49 IMPORTANT: Discussion is encouraged, but each student should do their own simulations, calculations, and graph preparation.
2 Step 2 (Obtain activation energy from Arrhenius plot) : Plot the natural log of D versus inverse temperature (K -1 ). From the slope of the curve determine the activation energy, Q. Discussions : 1. What did you notice as you changed the number of particles in the simulation (Part A)? What were the similarities and differences? As I increased the number of particles, the x,y and z displacements became increasingly more constant. This is an advantage when looking for overall displacement. 2. What are advantages of using a large number of particles in a simulation? Disadvantages? You get a more accurate displacement measurement due to more consistent directional measurements. 3. Were your group members’ activation energies the same or different? Explain why. They were slightly different due to human error and calculation but overall they displayed the same findings.
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