X-Ray Spectroscopy of the Solid State: Potassium Chloride

Abstract

The experimental $K$ spectral regions of potassium and chlorine in crystalline KCl have a much more complex array of structure, both in emission and in absorption, than can be explained by the conventional energy level diagram for the solid state. The pertinent spectral region is that which involves the valence and conduction bands of the solid. The difficulties seem to arise from a theoretical preoccupation with one-electron transitions.Consideration of the various probable electron configurations of the many-electron solid system shows several additional initial ($1s$ vacancy) and final (outer vacancy) states. The charge density in the outer electron bands, suddenly confronted with the problem of screening the excess positive charge attending a $1s$ vacancy (or any inner vacancy), redistributes itself, distorting the bands and establishing one or more local discrete levels below each band. With the most probable filled discrete level below the $3p$ band, the narrow intense $K{\ensuremath{\beta}}_{1}$ line is explained but it is necessary to account somehow for the very narrow final state ($3p$ vacancy).An obvious conclusion is that the $3p$ valence band itself is therefore very narrow in energy, only 0.33 ev wide. However, if it is indeed wider than this, as is commonly believed in the lore of solid state physics, the $K{\ensuremath{\beta}}_{1}$ emission must be restricted by some (unknown) mechanism to a small energy region within the band. In this event, x-ray emission involving the entire broad $3p$ band may be part of the observed faint emission on the high-energy side of the $K{\ensuremath{\beta}}_{1}$ line, and, if so, the restricted energy position just mentioned must be at the bottom of the band.Also a consequence of the $1s$ vacancy are several normally empty discrete levels below and in the conduction band of KCl. With these levels, the narrow intense $K$ absorption lines are explained.The discussion given is primarily experimental and phenomenological. The qualitative agreements are perhaps compatible with either a narrow or a wide $3p$ band for both potassium and chlorine in KCl, but show a preference for the wide $3p$ band. Either conclusion dictates the need of a new quantitative theoretical treatment.