The Diffraction of X-Rays in Glass

X-ray diffraction patterns of vitreous Si${\mathrm{O}}_2$ and Ge${\mathrm{O}}_2$ have been made in an evacuated camera using Cu $K\alpha$ radiation monochromatized by crystal reflection. Intensity curves are obtained from the microphotometer records in the usual way. A method is developed for calculating the scattering of x-rays in an amorphous solid and is applied to the diffraction patterns of glass. In vitreous Si${\mathrm{O}}_2$ each Si is tetrahedrally surrounded by 4 oxygens at a distance Si—O=1.60A, and each oxygen is shared between two such tetrahedral groups. The resulting network which is built up is a random network, it does not repeat at regular intervals, and is accordingly non-crystalline. From this picture of the glassy state, scattering curves are calculated for vitreous Si${\mathrm{O}}_2$ and Ge${\mathrm{O}}_2$ which are in good agreement with the experimental curves.