Diffusion at solid-solid interfaces

Finite volume methods implemented in Matlab to model solute diffusion at solid-solid interfaces, accounting for energy barriers and interfac

Diffusion at solid-solid interfaces

Finite volume methods implemented in Matlab to model 1D solute diffusion at solid-solid interfaces, accounting for energy barriers and interfacial segregation. The derivation of the models has been published in: F.D. León-Cázares and E.I. Galindo-Nava. Phys. Rev. Mat., 5 (2021) 123802. Please cite this publication if you benefit from this repository.

Requirements

Coded in Matlab R2021a. There is no need for additional packages.

License

This repository is published under a GNU GPL v3 license (). See LICENSE.txt for full licensing information.

Contents and how to use

The Examples.m file showcases the usage of all the functions in this repository. The user can open the example of their preference and change the input parameters. If the simulation diverges, a smaller convergence criterion ~D*dt/dx^2<0.5 (printed by the functions) should be selected. Relevant plots of the concentrations and fluxes are also added for each diffusion case.

Functions - Diffusion simulations

These functions solve the 1D diffusion equations for a compendium of model bicrystal interfaces. The geometry can be set to cartesian, cylindrical or spherical coordinates. Boundary conditions 'perm' of constant concentrations at both surfaces were implemented for all these cases:

• traps1D_perm.m - Interfacial energy barrier.
• traps1D_perm_t.m - Monolayer interfacial trap.
• traps1D_perm_t_diff.m - Diffuse interfacial trap.
• traps1D_perm_t_inh.m - Monolayer inhomogeneous interfacial trap.

Additionally, the monolayer interfacial trap case is implemented for other two sets of boundary conditions: 'open system' with zero flux (left) and constant concentration (right) surfaces, and 'closed system' with two no flux surfaces.

• traps1D_open_t.m - Monolayer interfacial trap.
• traps1D_closed_t.m - Monolayer interfacial trap.

Functions - Plotting energy landscapes

• energy_landscape_plot.m - Plotting an energy landscape of a monolayer or no trap.
• energy_landscape_plot_diff.m - Plotting the energy landscape of a diffuse trap.