Diffusion of proton in alumina-rich nonstoichiometric magnesium aluminate spinel

The phenomenon of the diffusion of proton and deuteron in a single crystal of magnesium aluminate spinel was studied by infrared absorption. The chemical diffusion coefficient of proton was determined by the relaxation time of the absorption intensity upon the substitution of deuteron with proton. The temperature dependence of the chemical diffusion coefficient of proton for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Mg}}_{{\text{1}} - x} {\text{Al}}_{\text{2}} {\text{O}}_{{\text{4}} - {\text{ $ \delta $ }}} \left( {x = 0.34} \right)$$\end{document} was expressed as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde D = 0.16\exp \left( {{{ - 210 \times 10^3 \left( {{\text{J mol}}^{ - {\text{1}}} {\text{K}}^{ - {\text{1}}} } \right)} \mathord{\left/ {\vphantom {{ - 210 \times 10^3 \left( {{\text{J mol}}^{ - {\text{1}}} {\text{K}}^{ - {\text{1}}} } \right)} {{\text{RT}}}}} \right. \kern-\nulldelimiterspace} {{\text{RT}}}}} \right){{{\text{cm}}^2 } \mathord{\left/ {\vphantom {{{\text{cm}}^2 } {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}$$\end{document}. The chemical diffusion coefficient of proton was found to be independent of the composition of spinel and of the atmosphere.