# hardsphere

Hard sphere structure factor, with Percus-Yevick closure

Parameter Description Units Default value
scale Source intensity None 1
background Source background cm-1 0.001
volfraction volume fraction of hard spheres None 0.2

The returned value is a dimensionless structure factor, $$S(q)$$.

Calculate the interparticle structure factor for monodisperse spherical particles interacting through hard sphere (excluded volume) interactions. May be a reasonable approximation for other shapes of particles that freely rotate, and for moderately polydisperse systems. Though strictly the maths needs to be modified (no Beta(Q) correction yet in sasview).

radius_effective is the effective hard sphere radius. volfraction is the volume fraction occupied by the spheres.

In sasview the effective radius may be calculated from the parameters used in the form factor $$P(q)$$ that this $$S(q)$$ is combined with.

For numerical stability the computation uses a Taylor series expansion at very small $$qR$$, there may be a very minor glitch at the transition point in some circumstances.

The S(Q) uses the Percus-Yevick closure where the interparticle potential is

$\begin{split}U(r) = \begin{cases} \infty & r < 2R \\ 0 & r \geq 2R \end{cases}\end{split}$

where $$r$$ is the distance from the center of the sphere of a radius $$R$$.

For a 2D plot, the wave transfer is defined as

$q = \sqrt{q_x^2 + q_y^2}$

References

J K Percus, J Yevick, J. Phys. Rev., 110, (1958) 1