Pressure—Induced Shifts of Energy Spectra of α—Al2O3：Mn^4＋

By making use of the diagonalization of the complete d3 energy matrix in a trigonally distorted cubic-field and the theory of pressure-induced shifts (PS) of energy spectra, the whole energy spectrum of α-Al2 O3 :Mn4+ and PS of levels have been calculated. All the calculated results are in excellent agreement with the experimental data. The comparison between the results ofα-AlO3:Mn4+ and ruby has been made. It is found that on one hand, R1-line and R2line PS of α-Al2O3:Mn4+ and ruby are linear in pressure over 0 ～ 100 kbar, and their values of the principal parameter for PS are very close to each other. On the other hand, the sensitivities of R1-line and R2-line PS of α-Al2O3:Mn4+are higher than those of ruby respectively, which comes mainly from the difference between the values of parameters at normal pressure of two crystals; moreover, the expansion ofd-electron wavefunctions of α-Al2 O3 :Mn4+ with compression is slightly larger than the one of ruby, and the effective charge experienced by d-electrons of α-Al2O3:Mn4+ decreases with compression more rapidly than the one of ruby. In the final analysis, all these can be explained in terms of the facts that the two crystals are doped α-Al2O3 with two isoelectronic ions; the strengths of the crystal field and covalency of α-Al2O3 :Mn4+ are larger than those of ruby respectively, due to the charge of Mn4+ to be larger than that of Cr3+.

Theoretical Calculation of Energy Spectrum of YGG:Cr^(3+)and Thermal Shifts of Its R-Lines

With the strong-field scheme and trigonal bases, the complete d3 energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the energy spectrum of YGG：Cr^3＋ at normal pressure and low temperature has been calculated. The g factor of the ground-state has been evaluated in terms of the energy spectrum. At the same time, by using the wavefunctions obtained from diagonalizing the complete d^3 energy matrix and Thermal Shifts theory, we calculate the thermal shifts of the sharp lines of YGG：Cr^3＋ and determine the relevant parameters. The calculated results are all in good agreement with the optical-spectrum and EPR experimental data. It is demonstrated that the obtained wavefunctions and the values of parameters are reasonable.

Improved Ligand-Field Theory with Effect of Electron-Phonon Interaction

Traditional ligand-field theory has to be improved by taking into account both 'pure electronic' contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy). By means of improved ligand-field theory, R1, R2, R'3, R'2, and R'1 lines, U band, ground-state zero-field-splitting (GSZFS), and ground-state g factors of ruby and/or GSGG: Cr3+ as well as thermal shifts of GSZFS, R1 line and R2 line of ruby have been calculated.The results are in very good agreement with the experimental data. Moreover, it is found that the value of cubic-field parameter given by traditional ligand-field theory is inappropriately large. For thermal shifts of GSZFS, R1 line and R2 line of ruby, several conclusions have also been obtained.