Refraction of X-Rays by Small Particles

The broadening of a beam of x-rays passed through a mass of small particles is investigated mathematically. It is shown that if the width of the beam, as given by the rocking curve of the second crystal of a double x-ray spectrometer, is $w_0$ before passing through the refracting material and $w$ afterward, then $w^2-{w_0}^2=8\mathrm{}{\delta }^2{n}_0\left(\frac{log2}{\delta +1\mathrm{}}\right)$, $\delta$ being equal to $1-\mu$, the refractive index of the material and $n_0$ being the average number of particles passed over. The radius of the particles may be found from the expression $R=\frac{3 \mathrm{VD}}{4n_0}$, where $V$ is the volume of refracting material per cm and $D$ the thickness of the material passed through. The above expressions are checked by experiments on graphite as to their dependence on $\delta$, and quantitatively by measurements on graded aluminum powder.