$K$-x-ray spectra and electronic band structures of Mg${\mathrm{Cl}}_2$, Ca${\mathrm{Cl}}_2$, Sr${\mathrm{Cl}}_2$, and Ba${\mathrm{Cl}}_2$

The $K\beta$-emission and $K$-absorption spectra of chlorine in Mg${\mathrm{Cl}}_2$, Ca${\mathrm{Cl}}_2$, Sr${\mathrm{Cl}}_2$, and Ba${\mathrm{Cl}}_2$ have been obtained with a 50-cm bent-quartz-crystal vacuum spectrograph. The $K\beta$-emission spectra consist of a prominent band $K{\beta }_1$ and its subbands $K{\beta }_x$ and $K{\beta }_5$ although the subbands are ambiguous in Mg${\mathrm{Cl}}_2$. Going to the higher-atomic-number-metal chlorides, the half-width of the $K{\beta }_1$ band decreases and the subband $K{\beta }_x$ is clearly separated from the $K{\beta }_1$ band. The $K{\beta }_1$ band is discussed in relation to the amounts of ionic character of the bond of these chlorides. The subbands $K{\beta }_x$ and $K{\beta }_5$ are accounted for in terms of a double-ionization model given by Deslattes. The $K$-absorption spectra are compared with the $\mathrm{Cl}{L}_{2.3}$-absorption spectra of these chlorides reported previously. A tentative interpretation for the Cl $K$-absorption and $L_{2.3}$-absorption spectra is made in terms of the core-level-to-band transition. The band gap of these chlorides is estimated.