The Radial Distribution Function, R.D.F. , g(r), also called pair distribution function or pair correlation function, is an important structural characteristic, therefore computed by Atomes.
Figure 5.2: Space discretization for the evaluation of the radial distribution function.
Considering a homogeneous distribution of the atoms/molecules in space, the represents the probability to find an atom in a shell at the distance of another atom chosen as a reference point [Fig. 5.2]. By dividing the physical space/model volume into shells dr [Fig. 5.2] it is possible to compute the number of atoms at a distance between and from a given atom: where represents the total number of atoms, the model volume and where is the radial distribution function. In this notation the volume of the shell of thickness is approximated: When more than one chemical species are present the so-called partial radial distribution functions may be computed : where represents the concentration of atomic species . These functions give the density probability for an atom of the species to have a neighbor of the species at a given distance . The example features GeS glass.
Figure 5.3: Partial radial distribution functions of glassy GeS at 300 K.
Figure 5.3 shows the partial radial distribution functions for GeS glass at 300 K. The total RDF of a system is a weighted sum of the respective partial RDFs, with the weights depend on the relative concentration and x-ray/neutron scattering amplitudes of the chemical species involved. It is also possible to use the reduced partial distribution functions defined as: Atomes gives access to:
The partial and distribution functions, and more see [Eq.[s2q_9]].
The corresponding integrated number of neighbors.
Also two methods are available to compute the radial distribution functions:
The standard real space calculation typical to analyze 3-dimensional models
The experiment-like calculation using the Fourier transform of the structure factor obtained using the Debye equation (see section 5.3 for details).