Structure factor

The structure factor, $S (k)$ , for a monatomic system is defined by:

$S(k) = 1 + \frac{4 \pi \rho}{k} \int_0^{\infty} ( g_2(r) -1 ) r \sin (kr) ~dr$

where $k$ is the scattering wave-vector modulus

$k= \frac{4 \pi }{\lambda \sin \left( \frac{\theta}{2}\right)}$

The structure factor is basically a Fourier transform of the pair distribution function $g(r)$ .

At zero wavenumber, i.e. $| k | = 0$ ,

$S(0) = k_BT \left. \frac{\partial \rho}{\partial p}\right\vert_T$

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