RDF (Module)

Overview

The RDF module calculates a full set of partial radial distribution functions, $g_{ij}(r)$ for each unique pair of atom types $i$ and $j$ present in the target configuration(s).

The RDF module is designed to calculate the necessary input for other modules such as SQ - there is no facility for calculating other types of radial distribution function, e.g. those between the centres-of-mass of molecules. To calculate such quantities see the analysis modules.

Description

For a configuration containing $N$ distinct atom types there are $\frac{1}{2}N(N+1)$ unique partial radial distribution functions $g_{ij}(r)$, where $i$ and $j$ are the $i^{th}$ and $j^{th}$ atom type respectively. The standard formalism for a radial distribution function between atom types $i$ and $j$ is

$$ g_{ij}(r, \Delta r) = \frac{n_j(r,\Delta r)}{\frac{4 \pi}{3}[(r+\Delta_r)^3 - r^3]\rho_j} $$

where $g_{ij}(r, \Delta r)$ is calculated for a spherical shell with inner radius $r$ and thickness $\Delta r$, $n_j(r, \Delta r)$ is the number of particles of type $j$ within the shell, and $rho_j$ is the bulk number density of $j$ over the whole configuration. $g_{ij}(r)$ therefore represents the discretised probability of finding an atom of type $j$ at a distance $r$ from the central atom type $i$, relative to the probability of finding one assuming a uniform distribution of $j$ throughout the simulation box.

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