Mass-action law for additive coloration of BaO

Abstract

Crystals of BaO were additively colored at 100°K intervals between 1423 and 1723°K in Ba vapor at pressures from 7 × ${10}^{-4\mathrm{}}$ to 1.7 Torr. A development of the mass-action law for the additive coloration process including complete first ionization and partial second ionization of the anion vacancies is presented. A good fit of the experimental data for the density of induced color centers, $N_{ F}$, as a function of the number of Ba atoms in the vapor, $N_{ \mathrm{Ba}}$, was obtained using the expression $\frac{N_F^2}{N_{ \mathrm{Ba}}}=1.98\mathrm{}\times {10}^{22}{e}^{\frac{-0.42\mathrm{} \mathrm{eV}}{\mathrm{kT}}}$, which assumes first ionization alone. However, a slightly better fit was obtained using a more complex expression which allows for partial second ionization of the anion vacancies. From the parameters of this fit, it was tentatively concluded that the second ionization energy $E_{ 2}$ plus a contribution due to changes in the thermal entropy was $E_{ 2}^{ \prime }=E_{ 2}+(\Delta S_1-\Delta S_2)T=1.07\mathrm{}$ eV. Using Rose and Hensley's value for the first ionization energy of $E_1=0.1\mathrm{}$ eV, the formation energy for neutral-anion vacancies was found to be $E_{ F}=0.05\mathrm{}$ eV. These last results should be regarded as tentative pending verification of the reliability of the barium vapor-pressure curve used.