A Small Angle X-Ray Scattering (SAXS) calculator from coordinate files such as XYZ.

This Julia package is built to compute the X-ray scattering response of atomic clusters at small angles (SAXS). To do so, the Debye formula is utilized:

$$ I(q) = \frac{1}{N} \sum_i^N \sum_j^N f_i(q,E) f_j^*(q,E) \frac{\text{sin}(q r_{ij})}{q r_{ij}} $$

where f are atomic form factors, q is the magnitude of transferred momentum and $r_{ij}$ is the distance of atom $i$ to atom $j$.

Functions to parse xyz/extxyz files are provided, yet at its core the code only requires atomic coordinates and the corresponding chemical species - you can use any other code to obtain them and feed those to the desired functions.

The atomic form factors can be written as:

$$ f(q,E) = f(q) + f_1(E) + if_2(E) $$

They contain :

1. A part dependent on transferred momentum q , deriving from Thomson scattering
2. A part dependent on the energy of the incoming X-ray , or resonant part

The momentum dependent contribution is written using the Cromer-Mann parametrization:

$$ f(q) = \sum_{i=1}^{4} a_i \exp\left(-b_i \left( \frac{q}{4\pi} \right)^2 \right) + c $$

Where the a,b and c are empirical parameters.

Units used are : KeV for energies , Angstrom for distances , Angstrom ^-1 for momenta.