ess.diffraction.pdf

Pair distribution functions and related functions.

Here, we use the following definitions and naming convention:

Name	Definition
Pair correlation function	\(G(r) = \frac{2}{\pi} \int_o^\infty\, Q (S(Q) - 1) \sin(Qr) \text{d}Q\)
Pair distribution function	\(g(r) = 1 + \frac{G(r)}{4 \pi \rho r}\)
Radial distribution function	\(\text{RDF}(r) = 4\pi r^2 \rho g(r)\)
Linearized radial distribution function	\(T(r) = \text{RDF}(r) / r\)
Running coordination number	\(C(r) = \int_0^r\, \text{RDF}(r') \text{d}r'\)

Where \(\rho\) is the atomic density.

The implementations provided here are defined in terms of each other and must be called in the order shown in the table.

Functions

linearized_radial_distribution_function(rdf)	Compute the linearized radial distribution function from a radial distribution function.
pair_correlation_function(s, r, *[, ...])	Compute the pair correlation function from a structure factor.
pair_distribution_function(G, *, atomic_density)	Compute the pair distribution function from a pair correlation function.
radial_distribution_function(g, *, ...)	Compute the radial distribution function from a pair distribution function.
running_coordination_number(rdf)	Compute the running coordination number from a radial distribution function.