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 ...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.展开更多
By means of improved ligand-field theory, the 'pure electronic'presure-induced shifts (PS's) and the PS's due to electron-phonon interaction (EPI) of the R_1, R_2,B_1, B_2, B_3, and R′_3 lines and the...By means of improved ligand-field theory, the 'pure electronic'presure-induced shifts (PS's) and the PS's due to electron-phonon interaction (EPI) of the R_1, R_2,B_1, B_2, B_3, and R′_3 lines and the ground-state zero-Geld-splitting of ruby have been uniformlycalculated. The calculation results are in very good agreement with all the experimental data. Atnormal pressure, ruby is a crystal with very strong crystal field. Thus, the admixture of ∣t_2~2(~3T_1)e~4T_2 】 and ∣t_2~(32)E＞ bases in the wavefunction of R_1 level of ruby is small at normalpressure, and it gradually decreases with increasing pressure, which causes the R_1-line PS of rubyto monotonously red shift with approximate linearity. The combined effect of the pure electronic PSof R_1 line and the PS of R_1 line due to EPI gives rise to the total PS of R_1 line. The analysesand comparisons among the features of R_1-line PS's of three laser crystals (ruby, GSGG:Cr~(3+) andGGG:Cr~(3+)) have been made, and the origin of their difference has been revealed.展开更多
By means of both a theory for pressure-induced shifts (PS) of energy spectra and a theory for shifts of energy spectra due to electron-phonon interaction (EPI), the 'pure electronic' PS and the PS due to EPI o...By means of both a theory for pressure-induced shifts (PS) of energy spectra and a theory for shifts of energy spectra due to electron-phonon interaction (EPI), the 'pure electronic' PS and the PS due to EPI of R<SUB>1</SUB> line, R<SUB>2</SUB> line, and U band of GSGG:Cr<SUP>3+</SUP> at 300 K have been calculated, respectively. The calculated results are in good agreement with all the experimental data. Their physical origins have also been explained. It is found that the mixing-degree of and base-wavefunctions in the wavefunctions of R<SUB>1</SUB> level of GSGG:Cr<SUP>3+</SUP> at 300 K is remarkable under normal pressure, and the mixing-degree rapidly decreases with increasing pressure. The change of the mixing-degree with pressure plays a key role not only for the 'pure electronic' PS of R<SUB>1</SUB> line and R<SUB>2</SUB> line but also the PS of R<SUB>1</SUB> line and R<SUB>2</SUB> line due to EPI. The pressure-dependent behaviors of the 'pure electronic' PS of R<SUB>1</SUB> line (or R<SUB>2</SUB> line) and the PS of R<SUB>1</SUB> line (or R<SUB>2</SUB> line) due to EPI are quite different. It is the combined effect of them that gives rise to the total PS of R<SUB>1</SUB> line (or R<SUB>2</SUB> line). In the range of about 15 kbar ~ 45 kbar, the mergence and/or order-reversal between levels and levels take place, which cause the fluctuation of the rate of PS for with pressure. At 300 K, both the temperature-dependent contribution to R<SUB>1</SUB> line (or R<SUB>2</SUB> line or U band) from EPI and the temperature-independent one are important.展开更多
By means of both the theory for pressure-induced shifts (PS) of energy spectra and the theory for shiftsof energy spectra due to electron-phonon interaction (EPI), at 300 K, the 'pure electronic' contributions...By means of both the theory for pressure-induced shifts (PS) of energy spectra and the theory for shiftsof energy spectra due to electron-phonon interaction (EPI), at 300 K, the 'pure electronic' contributions and the contri-butions from EPI to R1 line, R2 line, and U band of GGG:Cr3+ as well as their PS have been calculated, respectively.The total calculated results are in good agreement with all the experimental data. Their physical origins have beenexplained. It is found that the mixing-degree of [t2/2(^3T1)e^4T2) and [t3/2^2E) base-wavefunctions in the wavefunctions of R1 level of GGG:Cr^3+ is considerable under normal pressure, and the mixing-degree rapidly decreases with increasingpressure. The change of the mixing-degree with pressure plays a key role for PS of R1 line or R2 line. At 300 K, boththe temperature-independent contribution to R1 line (or R2 line or U band) from EPI and the temperature-dependentone are important. The remarkable difference between pressure-dependent behaviors of PS of R1 lines of GGG:Cr^3+ andGSGG:Cr^3+ results from the differences of their microscopic properties. The features of emission spectra of GGG:Cr^3+at various pressures have satisfactorily been explained.展开更多
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 o...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 Ri lines, U band, ground-state zero-field-splitting (GSZFS) and ground-state g factors as well as thermal shifts of R1 line and R2 line of YAG:Cr3+ have been calculated. The results are in very good agreement with the experimental data. In contrast with ruby, the octahedron of ligand oxygen ions surrounding the central Cr3+ ion in YAG:Cr3+ is compressed along the [111] direction. Thus, for YAG:Cr3+ and ruby, the splitting of t23 4A2 (or t23 2E) has opposite order, and the trigonal-field parameters of the two crystals have opposite signs. In thermal shifts of R1 and R2 lines of YAG:Cr3+, the temperature-dependent contributions due to EPI are dominant.展开更多
文摘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.
文摘By means of improved ligand-field theory, the 'pure electronic'presure-induced shifts (PS's) and the PS's due to electron-phonon interaction (EPI) of the R_1, R_2,B_1, B_2, B_3, and R′_3 lines and the ground-state zero-Geld-splitting of ruby have been uniformlycalculated. The calculation results are in very good agreement with all the experimental data. Atnormal pressure, ruby is a crystal with very strong crystal field. Thus, the admixture of ∣t_2~2(~3T_1)e~4T_2 】 and ∣t_2~(32)E＞ bases in the wavefunction of R_1 level of ruby is small at normalpressure, and it gradually decreases with increasing pressure, which causes the R_1-line PS of rubyto monotonously red shift with approximate linearity. The combined effect of the pure electronic PSof R_1 line and the PS of R_1 line due to EPI gives rise to the total PS of R_1 line. The analysesand comparisons among the features of R_1-line PS's of three laser crystals (ruby, GSGG:Cr~(3+) andGGG:Cr~(3+)) have been made, and the origin of their difference has been revealed.
文摘By means of both a theory for pressure-induced shifts (PS) of energy spectra and a theory for shifts of energy spectra due to electron-phonon interaction (EPI), the 'pure electronic' PS and the PS due to EPI of R<SUB>1</SUB> line, R<SUB>2</SUB> line, and U band of GSGG:Cr<SUP>3+</SUP> at 300 K have been calculated, respectively. The calculated results are in good agreement with all the experimental data. Their physical origins have also been explained. It is found that the mixing-degree of and base-wavefunctions in the wavefunctions of R<SUB>1</SUB> level of GSGG:Cr<SUP>3+</SUP> at 300 K is remarkable under normal pressure, and the mixing-degree rapidly decreases with increasing pressure. The change of the mixing-degree with pressure plays a key role not only for the 'pure electronic' PS of R<SUB>1</SUB> line and R<SUB>2</SUB> line but also the PS of R<SUB>1</SUB> line and R<SUB>2</SUB> line due to EPI. The pressure-dependent behaviors of the 'pure electronic' PS of R<SUB>1</SUB> line (or R<SUB>2</SUB> line) and the PS of R<SUB>1</SUB> line (or R<SUB>2</SUB> line) due to EPI are quite different. It is the combined effect of them that gives rise to the total PS of R<SUB>1</SUB> line (or R<SUB>2</SUB> line). In the range of about 15 kbar ~ 45 kbar, the mergence and/or order-reversal between levels and levels take place, which cause the fluctuation of the rate of PS for with pressure. At 300 K, both the temperature-dependent contribution to R<SUB>1</SUB> line (or R<SUB>2</SUB> line or U band) from EPI and the temperature-independent one are important.
文摘By means of both the theory for pressure-induced shifts (PS) of energy spectra and the theory for shiftsof energy spectra due to electron-phonon interaction (EPI), at 300 K, the 'pure electronic' contributions and the contri-butions from EPI to R1 line, R2 line, and U band of GGG:Cr3+ as well as their PS have been calculated, respectively.The total calculated results are in good agreement with all the experimental data. Their physical origins have beenexplained. It is found that the mixing-degree of [t2/2(^3T1)e^4T2) and [t3/2^2E) base-wavefunctions in the wavefunctions of R1 level of GGG:Cr^3+ is considerable under normal pressure, and the mixing-degree rapidly decreases with increasingpressure. The change of the mixing-degree with pressure plays a key role for PS of R1 line or R2 line. At 300 K, boththe temperature-independent contribution to R1 line (or R2 line or U band) from EPI and the temperature-dependentone are important. The remarkable difference between pressure-dependent behaviors of PS of R1 lines of GGG:Cr^3+ andGSGG:Cr^3+ results from the differences of their microscopic properties. The features of emission spectra of GGG:Cr^3+at various pressures have satisfactorily been explained.
文摘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 Ri lines, U band, ground-state zero-field-splitting (GSZFS) and ground-state g factors as well as thermal shifts of R1 line and R2 line of YAG:Cr3+ have been calculated. The results are in very good agreement with the experimental data. In contrast with ruby, the octahedron of ligand oxygen ions surrounding the central Cr3+ ion in YAG:Cr3+ is compressed along the [111] direction. Thus, for YAG:Cr3+ and ruby, the splitting of t23 4A2 (or t23 2E) has opposite order, and the trigonal-field parameters of the two crystals have opposite signs. In thermal shifts of R1 and R2 lines of YAG:Cr3+, the temperature-dependent contributions due to EPI are dominant.
