Atomistic modeling techniques are a class of models that, unlike more commonly used continuum models, incorporate atomic-level information to simulate macroscopic material properties. Atomistic modeling considers the basic building blocks of materials as its smallest entity, i.e., atoms. The most fundamental models, based on so-called ‘first principles,’ take into account both atomic nuclei and electron location. Our group utilizes plane-wave basis-set density functional theory (DFT) as a first principles model. Molecular dynamics (MD), often thought of as a force field model, in essence, models the forces felt/exerted on/by each atom to determine macroscopic material properties. These methods, along with many other models, are useful tools to elucidate fundamental mechanisms which give rise to intrinsic material properties.

**Density Functional Theory**

Density functional theory is just one of the tools our group utilizes to interpret atomic resolution images and spectra obtained using the TEM facilities at ASU. Currently, our group uses the Vienna Ab-initio Software Package (VASP) to study the relationship between grain boundary character and ionic conductivity in solid oxide fuel cells (SOFC). This work is a continuation of the work done by several group members, both experimental and theoretical. The experimental research was performed by a previous graduate student, William Bowman, who worked on correlating nanoscale grain boundary composition with electrical conductivity in ceria. The theoretical work was done by a post-doctoral research assistant, Pratik Dholabhai, who worked with kinetic lattice monte carlo (KLMC) and DFT to optimize ionic conductivity in ceria through doping. Our groups current theorist is a graduate research assistant, Tara Boland, who is working to correlate grain boundary character with ionic conductivity in ceria grain boundaries.

Molecular dynamics (MD) is also used to reduce the number of grain boundary orientations which are studied using DFT because of the large computational resources needed to simulate these materials. Various other methods such as image simulation, and spectral simulation using FEFF, are implemented to correlate the structure with certain functionalities of materials.

The figure to the left is the Σ3(210)/[001] symmetric tilt grain boundary (GB) before relaxing the structure. Each supercell has a volume of 28.80 x 12.09986 x 5.4112 Å^{3}. The supercell has 2 identical GB per supercell. The restricting of the GB core clearly increased in volume. A total of 0.6 Å in the x direction was added to the cell per GB.

The figure below is the DFT relaxed supercell. The restructuring of the GB core resulted in an increase in the core volume of 0.6 Å in the x direction per GB. The accurate location of atoms within a structure in essential for the accuracy of image and spectral simulations.

The image below is a slice of charge density distribution from the above supercell. This plane is the charge density associated with the Ce atomic layer. Blue represents the least amount of charge density, and green depicts an increase in charge density.