Structure factors of random hard disk packing in 2D by explicit modeling

This paper describes a method that can (1) generate random packing of hard disks in 2D using Monte Carlo simulation, (2) extract the corresponding pair distribution function using normalization by disk line picking probability and (3) convert it to the structure factor. The generated structure factor agrees well with the analytical form based on the Percus-Yevick equation at a low area fraction (that is, within 1% at an area fraction below 0.2 and 2% at an area fraction of 0.3) but differs at a higher area fraction with more pronounced peaks and oscillations. Above an area fraction of 0.69, the hexagonal packing feature appears as sharp peaks at low <i>Q</i>, which are absent in the analytical solution. The structure factors up to an area fraction of 0.65 as a function of <i>QR</i> and the area fraction are stored in table form. The structure factor table can be combined with the cylinder form factors to simulate the X-ray/neutron scattering intensity of wood cell wall scattering.