Crystalline Fields in Corundum-Type Lattices

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Abstract
Dipole moments of the deformable O2— ions in the corundum‐type crystals Al2O3, Cr2O3, and Fe2O3 are calculated self‐consistently. The magnitudes and signs of the dipole moments depend sensitively on the crystal parameters and vary widely over the series Al2O3, Cr2O3, and Fe2O3. Using the calculated dipole moments, the dipolar contributions to the crystalline components B10, B20, B30, B33, C33, B40, B43, and C43 have been calculated at the metal ion sites. The dipolar contributions are found to be substantial and in some cases to alter the sign of the crystalline field components obtained from point charges alone. The modified values of B20, B40, and B43 are used to obtain expressions for the optical parameters v, v′, and Dq in terms of the expectation values 〈r2〉 and 〈r4〉 for the d electrons of Cr3+ ions in Cr2O3 and ruby, and Fe3+ ions in Fe2O3 and sapphire. The coefficients of 〈r4〉 in the expressions for v and v′ are substantially altered on including the effect of the dipoles. The effect of the dipoles on the coefficient of 〈r4〉 in the case of Dq is less marked. This difference in behavior of v, v′, and Dq can be explained by the different dependences of these parameters on the trigonal departure from the cubic field. The values of Dq are, however, still seriously underestimated when Hartree—Fock values of 〈r4〉 are used. Reasonable agreement with experiment is obtained using values of 〈r2〉 and 〈r4〉 calculated with the Slater effective charge model. The comparison between theoretical and experimental quadrupole coupling constants and optical parameters is utilized to speculate on the factors which could improve agreement with experiment.