Internal electric fields and color shift in Cr3+-based gemstones

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Seeking to better understand the origin of the different colors of emerald and ruby, both ab initio periodic and cluster calculations have been carried out. The calculations reproduce the interatomic distances measured for pure Be${}_{3}$Si${}_{6}$Al${}_{2}$O${}_{18}$ and Al${}_{2}$O${}_{3}$ as well as the Cr${}^{3+}$$\ensuremath{-}{\mathrm{O}}^{2\ensuremath{-}}$ distances in emerald and ruby. The mean Cr${}^{3+}$$\ensuremath{-}{\mathrm{O}}^{2\ensuremath{-}}$ distance for Be${}_{3}$Si${}_{6}$Al${}_{2}$O${}_{18}$:Cr${}^{3+}$ and Al${}_{2}$O${}_{3}$:Cr${}^{3+}$ is found to be practically equal to 1.97 \AA{}, in agreement with recent experimental values. The present calculations confirm that the variations of optical properties due to Cr${}^{3+}$ impurities along the series of ionic oxides can be understood merely through the CrO${}_{6}{}^{9\ensuremath{-}}$ unit but subject to the electric field due to the rest of the lattice ions. As a salient feature it is proved that changes in electronic density and covalency due to the internal field are not the cause of the color shift. Therefore, the red color of ruby is not due to the polarization of the electronic cloud around chromium as a result of the C${}_{3}$ local symmetry. The present study also demonstrates that the variation of the ligand field splitting parameter, 10Dq, induced by the internal electric field comes mainly from the contributions of first shells of ions around the CrO${}_{6}{}^{9\ensuremath{-}}$ unit. As a consequence, 10Dq in emerald is not influenced by the internal field, as the contribution from Be${}^{2+}$ first neighbors is practically compensated by that of Si${}^{4+}$ second neighbors. In contrast, in ruby the ${t}_{2g}$ levels are shifted by the internal field 0.24 eV more than the ${e}_{g}$ ones, so explaining the color shift in this gemstone in comparison with emerald. This result is shown to arise partially from the asymmetric form of the internal electrostatic potential along the ${C}_{3}$ axis in Al${}_{2}$O${}_{3}$.