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### Mesoscale

## Mesoscale Materials Simulation Tools

This page contains the following Mesoscale simulation tools

### 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.

### GUI for Surface Evolver

This tool is a GUI for the Surface Evolver program which was written by Ken Bracke. The Surface Evolver allows users to describe an object, then simulate the objects evolution based on physical constraints. The GUI is used to simulate the growth of polycrystalline grains in two-dimensions using the Surface Evolver. The tool makes it easier and more efficient to simulate grain growth as well as offering users a way to view/export data on the grains taken throughout the simulation.

Grains Before Grains After

Grains Before Grains After

### Micro-Mechanics Simulation Tool: Thin film

Crystalline films grown epitaxially on substrates consisting of a different crystalline material are of considerable interest in optoelectronic devices and the semiconductor industry. The film and substrate have in general different lattice parameters. This lattice mismatch affects the quality of interfaces and can lead to very high densities of misfit dislocations. Here we study the strengthening of a thin film on a substrate. In particular we consider the motion of a dislocations gliding on its slip plane within the film and their interaction with the substrate.

### Nano Plasticity Lab

The tools uses a phase field approach to simulate plastic deformation in nano-crystalline materials. It captures the competing grain-boundary and dislocation-mediated deformation mechanisms that govern plastic deformation and these materials. The model is based on a multi phase field model in which dislocation and grain boundary sliding are represented by means of scalar phase fields described in “The role of grain boundary energetics on the maximum strength of nanocrystalline Ni”, Koslowski, Lee and Lei, Journal of the Mechanics and Physics of Solids, 59 1427-1436, 2011. The tool enables users to quantify how uncertainties in the input parameters (materials properties such as elastic constants, Peierls energy barrier for dislocation glide and activation barrier for grain boundary sliding) affect the prediction of the yield stress. In addition is provides a sensitivity analysis that quantifies the relative importance of each input variable. In order to achieve this, the phase field simulation code is orchestrated by the PRISM Uncertainty Quantification (PUQ) tool that enables users to select various state-of-the-art methods for uncertainty propagation.

**Virtual Kinetics of Materials Laboratory**

By Alex Bartol, R. Edwin García, David R. Ely

The Virtual Kinetics of Materials Laboratory (VKML) is a web environment to develop microstructural evolution models by using FiPy, a powerful set of python-based libraries to write Partial Differential Equations. A basic set of examples is provided to simulate:

a) Electrochemical transport kinetics of rechargeable lithium-ion batteries;

b) Simple diffusion and spinodal decomposition problems;

c) Symbolic Thermodynamics using the Gibbs infrastructure; and

d) Basic examples to learn how to write a program with a simple GUI.

Each example can be readily edited, debugged, and run online. The developed interface also provides a TKInter-based GUI, which enables the user to rapidly prototype flexible interfaces with sliders, menus, and buttons.

**VKML— Dendritic Growth**

The Virtual Kinetics of Materials Laboratory— Dendritic Growth simulates the anisotropic solidification of a single seed with an N-fold axis of crystallographic symmetry.

**VKML— Polycrystalline Growth and Coarsening**

Virtual Kinetics of Materials Laboratory: Polycrystalline Growth and Coarsening simulates the growth, impingement, and then coarsening of a random distribution of crystallographically oriented nuclei. The user can control every aspect of the model such as the nuclei radius, the size of the simulation cell, and whether the grains are homogeneously dispersed or only on one wall of the simulation.

**VKML—Spinodal Decomposition**

Virtual Kinetics of Materials Laboratory: Spinodal Decomposition simulates the time-dependent segregation of two chemical components and its subsequent coarsening. The resultant microstructure obeys the well-known lever rule.

**VKML—Spinodal Decomposition 3D**

Virtual Kinetics of Materials Laboratory: Spinodal Decomposition 3D applies the classic Cahn-Hilliard equation to simulate the time-dependent segregation of two chemical components in three dimensions. Default values are physical but arbitrary. The presented model is based on the phase field method. NOTE: The present release does not display results in real time. GIF animation is not enabled.

### Linearized Boltzmann transport calculator for thermoelectric materials

Simulation tool to calculate thermoelectric transport properties of bulk materials based on their multiple nonparabolic band structure information using the linearized Boltzmann transport equation.

This simulation tool allows users to calculate various thermoelectric properties such as Seebeck coefficient, electrical conductivity, and electronic thermal conductivity for any semiconductor materials with band structures modeled using the nonparabolic dispersion relation. The linearized Boltzmann transport equation under the relaxation time approximation is used for the calculations. Maximum two conduction bands and two valence bands can be included in the band structure, and temperature- and composition- dependent band parameters can be taken into account. Various scattering mechanism such as the acoustic phonon deformation scattering, ionized impurity scattering, polar optical phonon scatterings and others can be included for the calculation of realistic energy-dependent scattering time. Simpler scattering models with constant scattering time or constant mean free path are also possible as a scattering option. We offer users to plot the differential conductivity and the density of states as a function of electron energy for a given band structure, Fermi level, and temperature. Using this differential conductivity analysis, users would be able to study why there is a trade-off between the Seebeck coefficient and the electrical conductivity, and how these properties can be modified or enhanced using different band structures and parameters.

### 1-D Phonon BTE Solver

Simulate heat transport by solving one dimensional Boltzmann transport equation.

### Powder Compaction

This tool calculates the microstructure evolution of compressible granular systems at high levels of confinement. The microstructure evolution is determined from three-dimensional particle mechanics static calculations of noncohesive frictionless monodispersed granular systems comprised by weightless spherical particles with radius d=0.440mm. Two different elastic materials are considered and the die-compaction of mixtures of different volume fraction can be simulated. The walls of the cylindrical container and of the punches are assumed rigid.