Use of polarized optical absorption to obtain structural information for ${\mathrm{Na}}^{+}$/${\mathrm{Nd}}^{3+}$ ${\beta }^{\prime \prime }$-alumina

Part of the optical absorption spectrum is calculated for the ${\mathrm{Nd}}^{3+}$ -doped ${\mathrm{Na}}^{+}$ ${\beta }^{\prime \prime }$-alumina using a molecular-dynamics- (MD) based approach. The Judd/Ofelt (J/O) theory is modified (and several approximations removed) to treat polarized transition intensities for rare-earth ions in a solid host. Stark-level energies and eigenfunctions of the ground state (${}_{}{}^4{}_{}{}^{}I_{\frac{9}{2}}^{}{}_{}{}^{}$) and excited multiplets (${}_{}{}^4{}_{}{}^{}F_{\frac{3}{2}}^{}{}_{}{}^{}, {}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$) are also calculated for the local environments involved. Energies and polarized transition intensities between individual Stark levels are thus calculated simultaneously for several hundreds of MD-generated environments; summation gives the total bandshape. A high proportion of Beevers-Ross-site occupation (>50%) is indicated for low ${\mathrm{Nd}}^{3+}$ concentrations in ${\beta }^{\prime \prime }$-alumina. The contrary is observed experimentally for high ${\mathrm{Nd}}^{3+}$ concentrations, i.e., then midoxygen site occupation dominates. It is demonstrated that ions in different local environments contribute differently to the absorption spectrum and, particularly, how the polarization of the various transitions changes for ions occupying different sites. Temperature dependence aspects are also considered.