Theory of the Diffuse Scattering of X-rays by Solids

The classical theory of x-ray scattering has been applied to the scattering of x-rays by the electrons in the atoms of a solid. The case in which the solid consists of atoms of one kind has been considered. The interactions of the waves scattered by each electron with those scattered by every other electron in the solid has been considered. The analysis is simplified by the fact that the orbital periods of the electrons in the atoms are very much shorter than the vibrational periods of the atoms due to thermal agitations. The final formula obtained is $S=1+(Z-1\mathrm{})\mathrm{}\frac{f^{\prime 2}}{Z^2}+\frac{F^2}{\mathrm{ZN}}X$ where $S$ is the scattered intensity per electron relative to the scattered intensity from a single isolated electron, $Z$ is the atomic number, $F$ the atomic structure factor including the effect of thermal agitation, $f^{\prime }$ is related to $f$ the true atomic structure factor (without thermal agitation), $N$ is the total number of atoms, and $X$ is a certain double summation. The value of $X$ has not been obtained for an amorphous substance but it has been evaluated for the case of a simple cubic crystal by Jauncey and Harvey in the following paper in this issue of the Physical Review.