# What is "Site Analysis"?

## The Problem

The diffusion of ions through solid materials is a fundamental physical process that underpins applications such as lithium-ion batteries, fuel cells, and chemical sensors. One common technique for studying atomic scale diffusion processes in solids is [molecular dynamics](https://en.wikipedia.org/wiki/Molecular_dynamics) simulation, which can be used to directly calculate macroscopic transport coefficients, i.e. diffusion coefficients and ionic conductivities, and also to examine the detailed atomic scale mechanisms of ionic transport. While molecular dynamics simulations, in principle, provides a description of all atomic scale dynamical processes that occur on a simulation timescale, analysing the resulting raw data to extract quantitative data about diffusion mechanisms can be challenging.

## The Approach

One approach to obtain mechanistic information from a molecular dynamics simulation is to spatially discretise the atomic trajectories by projecting from a set of three dimensional continuous coordinates onto a set of discrete "sites". This approach is founded on the idea that in many solids, diffusion proceeds by ions undergoing a sequence of "jumps" between local potential energy minima. These minima typically correspond to a particular arrangement of the mobile ions within some set of crystallographic sites.

In a site-projection analysis, we first define a set of bounded volumes within the simulation cell, which represent our "sites", and then project the coordinates of the mobile ions onto these volumes. This gives two spatially discretised representations of each configuration in a simulation trajectory:

- From the perspective of the **atoms**, each atom is assigned to zero, one, or multiple sites (depending on whether our sites are defined to be mutually space-filling and / or non-overlapping).
- From the perspective of the **sites**, each site is occupied by zero, one, or more mobile ions.

## What You Can Do With It

This site occupation data can be used to build quantitative descriptions of diffusion mechanisms:

- **Site-occupation probabilities**: Time-averaged site-occupation probabilities, which can be compared to experimental results such as diffraction data.
- **Trajectory analysis**: Because the site-occupation data is time-resolved, specific sequences of sites that an ion moves through can be statistically analysed.
- **Correlation analysis**: Temporal and spatial correlations between the movements of groups of mobile atoms can be quantified.