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Diffusion and Kinetics
See also Mesoscale simulation tools and RASPA tools
Scaffolding Simulations in a Rate Processes of Materials Course
This learning resource describes a set of programming assignments that are used in a Rate Processes of Materials course. The assignments are designed around the pedagogical principle of scaffolding, in which students are given initial support structures that are gradually removed. The incremental skill-building helps students become independent learners.
Skill Module 1: The introductory activity provides a review of MATLAB syntax and programming skills.
Skill Module 2: In this module, students are introduced to the Finite Difference Method (FDM), which is a computational method used to estimate the solutions to partial differential equations.
Scenario 1: This assignment requires the FDM (from Skill 2) to be used to solve a materials science problem. In this scenario, students take on the role of engineers at a chemical company. They are provided with the concentration of a chemical over time and need to use this information to calculate the reaction order and reaction constant. Finally, students simulate the reaction kinetics assuming a different starting reaction concentration.
- Scenario 2A: In this assignment, students extend their knowledge of the FDM to simulate one-dimensional diffusion based on Fick's laws of diffusion. Students must compare their results from data provided in a paper.
- Scenario 2B: This task is based on analyzing a three-dimensional microstructure. Students are provided with the data, but must develop a MATLAB script to analyze the large data set. Similar to Scenario 2A, students must read and summarize the key points of a paper.
Transport Phenomena Archive
Browse the 40 instructional materials published in nanoHUB from the Transport Phenomena Archive.
From Adam Powell:
I'm pleased to be working with Joe Cychosz to resurrect the Transport Phenomena Archive here on nanoHUB! Matt Krane and I built this in the early- to mid-00s as a resource for materials transport educators. It used to be at teaching.matdl.org until that resource closed down a few years back.
The other day a colleague mentioned that she had been "stealing" my problems and resources from the Archive for her classes years ago. My reply was, and remains, please, "steal" away! There is no higher compliment, as using them indicates their utility and quality. These are meant to be open educational resources for the public at large, their purpose is to facilitate the work of educators and students in formal and informal settings.
But do note that they are (almost all) copyrighted, and their licenses place some limitations on what you can do with them. You may freely read them, print and copy them, share them with friends, and use them in classes as you like. If you distribute them, be sure to include copyright information, and make sure you're abiding by license limitations – or contact the authors regarding separate licensing.
Big thanks to the WPI Morgan Teaching and Learning Center for promoting open educational resources, for the inspiration to seek out a host such as nanoHUB (IIRC that was Laura Robinson), and for a Faculty Learning Community Teaching Innovation Grant to support work on enhancing the impact of these and related resources. Thanks also to Edwin Garcia and Tanya Faltens for facilitating the move to the new host.
Share and enjoy!
2-D Diffusion Game
The Diffusion Game package introduces students to computational materials modeling by simulating the 2D diffusion of metal atoms. See the Supporting Docs tab for more information, and a paper game board.
Grain Boundary Diffusion Calculator
This tool calculates the effective diffusivity in a grain boundary network represented by a three-dimensional Voronoi diagram. Two types of grain boundaries with different diffusivities are randomly distributed in the domain. The effective diffusivity is calculated using the mean squared displacement method, where periodic boundary conditions are applied in all directions. Users are free to choose the fraction of each grain boundary type as well as the activation energy and pre-factor for each grain boundary diffusivity.
Diffusion Calculator: HCP Dilute Solutes
The diffusivity of a dilute solute in an HCP lattice is calculated with Ghate's 8-frequency model. Each of the eight frequencies (w_i) are specified by a transition energy barrier (E_i) and transition attempt frequency (v_i). The vacancy formation energy, vacancy-solute binding energy, and the HCP lattice constants are also required. The output temperature range can also be specified in terms of 1000/T.
Diffusion Calculator: FCC Dilute Solutes
The diffusivity of a dilute solute in an FCC lattice is calculated using LeClaire and Lidiard's 5-frequency model. Each of the five frequencies (w_i) are specified by a transition energy barrier (E_i) and transition attempt frequency (v_i). The vacancy formation energy and the FCC lattice constant are also required. The output temperature range can also be specified in terms of 1000/T.
Particle Trajectory Diffusion Analysis
This tool takes as input particle position data from methods such as molecular dynamics or kinetic Monte Carlo and computes the mean squared displacement for all particles as a function of time. For a system with multiple types of particles, the mean squared displacement is computed for each particle type. The tracer diffusion coefficient is then calculated from the slope of the mean squared displacement vs time curve.
Process Lab: Concentration-Dependent Diffusion
This simulation tool simulates the dopant diffusion process by solving the partial differential equations. The tool gives users the freedom to adjust critical parameters and conditions in the process, such as the initial doping profile, time, temperature, length, and so on. It also gives users opportunities to choose between the delta or box-shaped dopant source, concentration dependency, as well as the type of dopants among 6 commonly used dopant species.
Thermo-Calc
The academic version of Thermo-Calc is now available in nanoHUB. Visit the Thermo-Calc group to get more information and instructions for accessing this software in nanoHUB. A hands-on tutorial is also available.