The nature of hydrogen in gamma-alumina
  Gibbs free energy models are derived from the calculated electronic and phonon structure of two possible models of $\gamma$-alumina, a defective spinel phase and a hydrogenated spinel phase. The intrinsic vacancies and hydrogen in the two structural models give rise to a considerable configurational (residual) entropy and significantly contribute to thermodynamic stability and physical-chemical properties of $\gamma$-alumina, which was neglected in previous studies but considered in this work. The electronic densities of states, calculated using a hybrid functional for the two structural models of $\gamma$-alumina, are presented. The dynamic stability of the two phases is confirmed by full-spectrum phonon calculations. The two phases share many similarities in their electronic structure, but can be distinguished by their vibrational spectra and specific heat. The defective spinel is found to be the ground state of $\gamma$-alumina, while the hydrogenated spinel to be a metastable phase. However, dehydration of the metastable phase into the ground state is expected to be slow due to the low diffusion rate of H, which leaves hydrogen as a locked-in impurity in $\gamma$-alumina. 
Yunguo Li, Cl\'audio M. Lousada, and Pavel A. Korzhavyic
cond-mat.mtrl-sci