Energy Spectrum of YAG:Cr3+ and Thermal Shifts of Its R Lines

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 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 t₂³⁴A₂ (or t₂³²E) 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.     

Pressure-Induced Shifts of R, R', and B Line-Groups and Ground-State Zero-Field-Splitting of Ruby

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 R₁, R₂, B₁, B₂, B₃, and R'₃ lines and the ground-state zero-field-splitting of ruby have been uniformly calculated. The calculation results are in very good agreement with all the experimental data. At normal pressure, ruby is a crystal with very strong crystal field. Thus, the admixture of |t₂²(³T₁)e⁴T₂〉and |t³₂²E〉bases in the wavefunction of R₁ level of ruby is small at normal pressure, and it gradually decreases with increasing pressure, which causes the R₁-line PS of ruby to monotonously red shift with approximate linearity. The combined effect of the pure electronic PS of R₁ line and the PS of R₁ line due to EPI gives rise to the total PS of R₁ line. The analyses and comparisons among the features of R₁-line PS's of three laser crystals (ruby, GSGG:Cr³⁺ and GGG:Cr³⁺) have been made, and the origin of their difference has been revealed.     

Theoretical Calculations of Thermal Shifts of Ground-StateZero-Field-Splitting for Ruby

By taking into account all the irreducible representations and their components in the electron-phonon interaction (EPI) as well as all the levels and the admixtures of wavefunctions within d³ electronic configuration, the thermal shifts (TS) of the ground-state zero-field-splitting (GSZFS) due to EPI for ruby have microscopic-theoretically been calculated; the contribution to TS of GSZFS from thermal expansion has also been calculated. The results are in very good agreement with experiments. It is found that the contributions from the first-order perturbation of the second-order term in EPI Hamiltonian are dominant in the Raman term and optical-branch term for TS of GSZFS; the different between the TS due to EPI of t₂^{3 4}A₂±(1/2) e₂ (G₂) level and the TS due to EPI of t₂^{3 4}A₂±(3/2) e₂ (G₁) level gives rise to the TS due to EPI of GSZFS, which is very small in comparison with the TS due to EPI of G₂ or G₁ level. Among various terms in TS of GSZFS, Raman term is the largest one and the signs of the Raman term and optical-branch term are opposite to the sign of the thermal-expansion term; the optical-branch term plays an important role in TS of GSZFS and increases rapidly with temperature; all various contributions to TS of GSZFS have to be taken into account, since the subtle balance among them determines the total result. The comparison between the features of TS of GSZFS and those of TS of R₁ and R₂ lines has been made. For TS of GSZFS, the contribution from thermal expansion is especially important; the neighbor-level term is insignificant.     

Energy Spectra of the Tunable Laser Crystal Gd3Ga5O12:Cr3+ and Their Pressure-Induced Shifts

By means of both the theory for pressure-induced shifts (PS) of energy spectra and the theory for shifts of energy spectra due to electron-phonon interaction (EPI), at 300 K, the `pure electronic' contributions and the contributions 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 been explained. It is found that the mixing-degree of |t₂²(³T₁)e ⁴T₂> and |t₂³²E> base-wavefunctions in the wavefunctions of R₁ level of GGG:Cr³⁺ is considerable under normal pressure, and the mixing-degree rapidly decreases with increasing pressure. The change of the mixing-degree with pressure plays a key role for PS of R₁ line or R₂ line. At 300 K, both the temperature-independent contribution to R₁ line (or R₂ line or U band) from EPI and the temperature-dependent one are important. The remarkable difference between pressure-dependent behaviors of PS of R₁ lines of GGG:Cr³⁺ and GSGG:Cr³⁺ results from the differences of their microscopic properties. The features of emission spectra of GGG:Cr³⁺ at various pressures have satisfactorily been explained.     

Theoretical Calculations of Thermal Broadenings and Transition Probabilities of R,R' and B Line-Groups for Ruby

On the basis of the unified calculation of the thermal shifts of R₁ line, R₂ line and ground-state-splitting transition probabilities of direct and Raman processes have theoretically been calculated. The thermal broadenings of R, R'and B line-groups for ruby, by taking into account all the levels and admixtures of wavefunctions within d³ electronic configuration and all the ΓM in electron-phonon interaction,the transition probabilities of direct and Raman processes have theoretically been calculated, The thermal broadenings of R,R' and B line-groups have successfully been interpreted in terms of the direct and Raman processes of acoustic phonons. The theoretically predicted transition probabilities are in good agreement with the experimental ones.     

Energy Spectrum of La3Lu2Ga3O12：Cr^3＋ and Its Pressure-Induced R-Line-Shift Reversal

By means of both the theory for pressure-induced Shifts （PS） of energy spectra and the theory for shifts of energy spectra due to electron-phonon interaction （EPI）, the normal-pressure energy spectra of α and β centers of Cr^3＋ ions for LLGG：Cr^3＋ and the PS＇s of R1 lines and U band of these centers have been calculated at 10 K, respectively. The total calculated results are in very good agreement with the experimental data. For LLGG：Cr^3＋, the pressureinduced low-high crystal-field transition and the reversal of R1-line PS take place. The pressure-dependent variation of Rmix^ei （2E - 4T2） [mixing-degree of （t2^2 （^3T1）e^4T2） and （t2^3 E） base-wavefunctions in the wavefunction of R1 state without EPI] plays a key role for the reversal of R1-line PS. The behavior of the pure electronic PS of R1 line is quite different from that of the PS of R1 line due to EPI. It is the combined effect of them that gives rise to the total PS of R1 line. The comparison between R1-line PS＇s of GSGG：Cr^3＋ and LLGG：Cr^3＋ has been made. It is found that a peak of R1-line PS appears at Rmix^ei （^2E - ^4T2） ≈ 0.08.     

Energy Spectrum,g Factors,Strain-Induced Level-Splittingsand R-Line Thermal Shift of MgO:V2+

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, the R line, t₂^{3 2}T₁ and t₂^{3 2}T₂ lines, t₂² (³T₁)e⁴T₂, t₂² (³T₁)e⁴T₁ and t₂ e²(⁴A₂)⁴T₁ bands, g factors of t₂^{3 4}A₂ and t₂^{3 2}E, four strain-induced level-splittings and R-line thermal shift of MgO:V₂₊ have been calculated. The results are in very good agreement with the experimental data. It is found that for MgO:V₂₊, the contributions due to electron-phonon interaction (EPI) come from the first-order term; the contributions from the second-order and higher terms are insignificant. In thermal shift of R line of MgO:V₂₊, the temperature-dependent contribution due to EPI is dominant. The results obtained in this work may be used in theoretical calculations of other effects of EPI.     

R-Line Thermal Shift and Thermal Broadenings of R,R',and B Lines for Ruby

The unified theoretical calculation of thermal shifts (TS) of R₁ and R₂ lines and thermal broadenings (TB) of R, R' and B lines for ruby was carried out for the first time.The calculated results are in very good agr&ment with a great number of experimental data. Especially, by using quantum theory and taking into account all the admixtures of wavefunctions within d³ electronic configuration, all the TM in electron-phonon interaction (EPI), the electronic energy spectrum and lattice-vibration Spectrum, the very important contributions to TS and TB from single-phonon direct process were theoretically calculated in detail. The microscopic essentials of various contributions are revealed, and the mistakes in previous work are remedied.     

Pressure-Induced Shift of R-Line of MgO：Cr^3＋ with Electron-Phonon Interaction Effect

By means of improved ligand-field theory, the ＂pure electronic＂ pressure-induced shift （PS） and the PS due to electron-phonon interaction （EPI） of R-line of MgO：Cr^3＋ have been calculated, respectively. The calculated results are in very good agreement with the experimental data. The behaviors of the pure electronic PS of R-line of MgO：Cr^3＋ and the PS of its R-line due to EPI are different. It is the combined effect of them that gives rise to the total PS of R-line, which has satisfactorily explained the experimental results. The comparison between the feature of R-line PS of MgO：Cr^3＋ and that of R1-line PS of ruby has been made.     

Energy Spectrum and Its Pressure-Induced Shift and J-T Effect of ZnTe:Mn2+

By using strong-field scheme, the complete d⁵ energy matrix with symmetry has been constructed. Then, by diagonalization of this matrix at normal and various pressures,the whole energy spectrum [including the ground-state zero-field splitting (GSZFS)] and its pressure-induced shift (PS) of Znlb:Mn²⁺ have uniformly been calculated. The results are in very good agreement with experimental data. According to the eigenfimctions and PS, the assignments of four absorption bands have been given. By taking into account the dect of different deformations of t₂ and e radial wavefunctions on t₂³(⁴A₂)e²(³A₂)⁴ A₁ and t₂³(²E)e²(³A₂)⁴E, the position of the third absorption band at normal pressure has been estimated.The tetragonal field is important for GSZFS of ZnTe:Mn²⁺ and its PS, which supports the existence of tetragonal Jahn-Teller distortion in ZnTe:Mn²⁺ The physical essentials of typical levels, GSZFS and their PS have been revealed.     

Energy Spectrum and Its Pressure-Induced Shift and g Factor of ZnS:Mn2+

By using strong-field scheme, the complete d⁵ energy matrix with D_2d symmetry has been constructed. Then, by diagonalization of this matrix at normal and various pressures,the whole energy spectrum [including the ground-state zero-field-splitting (GSZFS)], its PS and the g factor of the ground state for zns:Mn²⁺ have uniformly been calculated. According to the eigenfunctions and PS, the new assignments of five absorption bands have been given.The variation of tetragonal field with pressure makes a main contribution to the pressureinduced shift (PS) of GSZFS of zns:Mn²⁺, which supports the existence of tetragonal Jahn-Teller distortion in zns:Mn²⁺. It is found that when P≥62 kbar, t₂⁴(³T₁)e⁴T₁ merges with t₂e^{4 2}T₂, which has to be taken into account in the calculation of PS of the fifth band in the range of 1 bar ~ 95 kbar. It is demonstrated that the Mn²⁺ ions in ZnS:Mn²⁺ have tetrahedral coordination, and the difference between ζ and ζ' caused by the covalency effect is very important for GSZFS. The physical essentials of typical levels, GSZFS and their PS have been revealed. By taking into account the influence of covalency on t₂³(⁴A₂)e²(³A₂)⁴A₁ and t₂³(²E)e²(³A₂)⁴E, the positon of the third absorption band at normal pressure has been estimated.     

The DV-Xα Calculations of Optical Spectra and Their Pressure-Induced Shifts for Ruby

The R line and U band at normal pressure and their pressure-induced shifts of ruby have been calculated by making use of the SCF embedded-cluster discrete variational (DV-X_α) method. The calculated results of the spectral pressure-induced shifts of ruby by making use of the crystal-field theory have also been given. The results of the first-principle calculations are in very good agreement with the experimental data and the calculated results by using crystal-field theory. The results of local lattice relaxations around the Cr³⁺ ion are obtained by the DV-X_α calculations.     

Improved Ligand-Field Calculation of Energy Spectrum and R-Line Thermal Shift of MgO：Cr^3＋

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, the R-line, t^3 2^2 T1 lines, t^2 2（^3 T1）e^4 T2, and t^2 2（^3T1）e^4T1 bands, ground-state g factor, four strain-induced level- splittings, and R-line thermal shift of MgO：Cr^3＋ have been calculated. The results are in very good agreement with the experimental data. It is found that for MgO：Cr^3＋, the contributions due to electron-phonon interaction （EPI） come from the first-order term. In thermal shift of R-line of MgO：Cr^3＋, the temperature-dependent contribution due to EPI is dominant.     

Energy Matrix of the d3 Configuration in Trigonal Field and Analysis of the Entire Energy Spectrum of Ruby

By using the strong-field scheme, we have calculated all the reduced matrix elements and the matrix elements of the trigonal crystal field and all the matrix elements of the spinorbit interaction for the d³ electronic configuration: The complete energy matrix of the d³ configuration in trigonal field has been constructed. This matrix has been diagonalized to fit the experimental optical and microwave spectral data of ruby. The calculated results are in good agreement with the experimental data. In particular, the zero-field splitting δ of the ground state and the splitting between R₁ and R₂ lines agree very well with the experimental results. The assignments of all the energy levels and the rates of change of the levels with respect to various parameters are given. The contributions from various parameters to δ and the splitting between R₁ and R₂ lines are also given.     

Photoluminescence of LLGG:Cr crystals under high pressure

We present photoluminescence spectra of La_2.7Lu_2.29Cr_0.01Ga₃O₁₂ and La_2.32Lu_2.59Cr_0.02Ga_3.07O₁₂ doped with Cr³⁺ obtained at high hydrostatic pressure up to 220 kbar, applied in a diamond anvil cell at 20 K and room temperature. In both materials we have obtained a pressure-induced ⁴T₂–²E electronic cross-over. On the basis of the low-temperature R line luminescence at pressures above 100 kbar we have distinguished two dominant Cr³⁺ sites: and β, existing in both materials, and one minor site δ, that exists only in La_2.32Lu_2.59Cr_0.02Ga_3.07O₁₂. The pressure-induced shifts of the R₁, R_1β and R_1δ lines as well as the pressure shift of the broad band related to the ⁴T₂→⁴A₂ transition in both materials have been estimated.     

Theoretical Calculations of Strain—Induced Splittings and／or Shifts of t2^32E and t2^34A2 Levels for MgO：Cr^3＋

Under various uniaxial stresses, both strains with low symmetry and isotropic strains of crystals take place. The former gives the strain-induced low-symmetry crystal fields and accordingly splittings of levels; the latter gives the isotropic parts of strain-induced crystal fields and accordingly shifts of levels. By using the wavefunctions obtained from the diagonalization of the complete d^3$ energy matrix in a regular octahedral field, the relevant matrix elements and accordingly strain-induced splittings and/or shifts of t₂³²E and t₂³⁴A₂ for MgO:Cr³⁺ have been calculated. Their physical origins have been thoroughly analyzed and revealed. It is the admixtures of basic wavefunctions resulted from the spin-orbit interaction and/or Coulomb interaction and/or Kramers degeneracy that make strain-induced splittings of levels nonzero. In contrast with this, strain-induced shifts come mainly from the zero-order approximate wavefunctions. It is found that there are nonvanishing matrix elements of operators T₂ξ, T₂η and T₂ζ between wavefunctions with positive M_s and those with negative M_s', which have important effects on strain-induced splittings of levels. The shifts of t₂³²E under both hydrostatic pressure and uniaxial pressure have been uniformly calculated. The important results of Y_c, Z_c, P_c, Q_c and 〈t₂|| C(A₁)|| t₂〉have been evaluated.     

N-(2-苯基-1,2,3-连三唑-4-甲酰基)-N′-芳基硫脲的13C NMR谱的研究

研究了最近合成的6种N-(2-苯基-1,2,3-连三唑-4-甲酰基)-N′-芳基硫脲新化合物. 通过测定6种新化合物的¹³C NMR和DEPT谱等,对其结构进行了确定,并对其 全部谱峰做出归属;并给出了这类新化合物中苯的两个新取代基(R₁ 和R₂ )的取代参数;同时,讨论了化学位移与分子结构间的一些关系.     

Improved Ligand-Field Theoretical Calculation of R-Line Pressure-Induced Shift of MgO:V2+

By means of an improved ligand-field theory, the “pure electronic” PS and the PS due to EPI of R line of MgO:V²⁺ have been calculated, respectively. The calculated results are in very good agreement with the experimental data. The behaviors of the pure electronic PS of R line of MgO:V²⁺ and the PS of its R line due to EPI are different. It is the combined effect of them that gives rise to the total PS of R line, which has satisfactorily explained the experimental results. The mixing-degree of |t₂²(³T₁)e⁴T₂〉and |t₂^{3 2}E〉 in the wavefunction of R level and its variation with pressure have been calculated and analyzed. The comparison between the feature of R-line PS of MgO:V²⁺ and that of MgO:Cr³⁺ has been made.     

环二硅氨烷的29Si和13C NMR研究

本文报道了十种环二硅氨烷衍生物(R₁=Me、ф;R₂=Me、ф1 R₃=Me;X=Me、ф、OH、OSiMe₃、H和cl)及与此有关的九种聚合物m+n(m=2,3,4,7,10)的²⁹Si和¹³C化学位移,讨论了取代基X、R₁、R₂及硅氧链节数m对化学位移的影响。通过考察化学位移随R₁、R₂的变化,推断环二硅氨烷中N与其周围的三个Si之间存在(p→d)π相互作用。     

Pressure-Dependent Base-Wavefunction Admixture and Lifetime of R1 State of La3Lu2Ga3O12:Cr3+

As a key factor leading to the pressure-dependent R₁-line-shift reversal and R₁-state lifetime, at 10 K, the pressure-dependent variation of mixing-degree of |t₂²(³T₁)e⁴T₂〉 and |t₂³² E〉base-wavefunctions in the wavefunction of R₁ state of LLGG:Cr³⁺ has been calculated and analyzed. From this, the physical origin of the pressure-dependent R₁-line-shift reversal has been revealed. Furthermore, by using the pressure-dependent values of the sum of all square mixing-coefficients of |t₂²(³T₁)e⁴T₂〉in the wavefunction of R₁ state, the lifetimes of R₁ state of LLGG:Cr³⁺ at various pressures have been calculated, which are in good agreement with observed results. The quantum anticrossing effect between t₂³²E and t₂²(³T₁)e⁴T₂ levels due to both spin-orbital interaction and electron-phonon interaction is remarkable, which is related to the admixture of |t₂²(³T₁)e⁴T₂〉and |t₂³² E〉as well as the low-high crystal-field transition.