Note on the Scattering of X-Rays from Fluids Containing Polyatomic Molecules

The intensity of the (unmodified) scattered radiation from a fluid containing one kind of molecules is given by:

S = (\frac{1}{Σ \overset{}{n} Z_{n}}) [{F_{1}}^{2} + {F_{2}}^{2} \int \frac{P_{(R)} d R (sin k R)}{kR}],

where

{F_{1}}^{2} = Σ n^{} Σ m^{} \frac{f_{n} f_{m} (sin k r_{nm})}{k r_{nm}}

, while

{F_{2}}^{2}

depends both upon the molecular structure and upon the relative orientation of the molecules. It is shown that the radial distribution function

P_{R}

may be obtained directly from the observed scattering curve if the molecular structure is known:

P_{(R)} = 4 π R^{2} ρ_{0} + \frac{2 R}{π} \int 0^{\infty} k [\frac{S Σ \overset{}{n} Z_{n}}{{F_{1}}^{2}} - 1] \frac{{F_{1}}^{2}}{{F_{2}}^{2}} sin (kR) d k,

where

ρ_{0}

is the density of the fluid in molecules per unit volume.

This publication has 3 references indexed in Scilit: