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.     

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, R₃', R₂', and R₁' 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.     

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.     

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.     

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.     

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.     

Energy Spectra,g Factors and Their Pressure—induced and ／or Thermal Shifts of SrTiO3：Cr^3＋ and SrTiO3：Mn^4＋ Ⅱ：Pressure Effects on Ground_State g Factor and Splittings of t2^32E and t2^34A2 of Sr

By using the wavefunctions obtained from diagonalizing the complete d^3 energy matrix at normal and various pressures,the g factor of the ground state of SrTiO3:Cr^3 and its pressure-induced shift have been microscopically calculated.Only by taking the local strains around Cr^3 in SrTiO3:Cr^3 (which are about twice the bulk ones)and corresponding P-χ dependence,can we obtain a good agreement etween the calculated result of pressure-induced shift of ground-state g factor and the experimental one.The physical origins of this pressure-induced shift have been explained.It is found that the change of Dq^-1 with pressure makes main contribution to the pressure-induced shift of ground-state g factor of SrTiO3:Cr^3 .By using the wavefunctions obtained from diagonalizing the complete d^3 energy matrix at normal pressure,the relevant matrix elements and accordingly strain-induced splittings of t2^32E and t2^34A2 of SrTiO3:Cr^3 have been calculated.The important results of Yc.Zc,Pc and Qc have also been evaluated.It is the admixtures of basic wavefunctions resulted from the spin-orbit interaction and /or Coulomb interaction and /or Kramers degeneracy that make the strain-induced splittings of the levels nonzero.It is found that there are nonvanishing matrix elements of operators T2ξ between wavefuncgtions with positive Ms and those with negative Ms′ and those with negative ms′,which have important effects on the strain-induced splittings of the levels.     

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.     

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.     

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.     

Energy Spectra and g Factors of α-A1203:Cr3+ and α-A1203:Mn4+

By diagonalizing the complete d³ energy matrix in a trigonally distorted cubicfield and using the wavefunctions from it, unified calculations of the whole energy spectrum as well as the g factors of the ground state and t₂^{3 2} E excited states for α-A1₂0₃:Cr³⁺ and α-A1₂0₃:Mn⁴⁺ have been carried out respectively. A11 the calculated results are in very good agreement with the experimental data. The comparison between the results of the two crystals has been made, which demonstrates that the covalency of α-A1₂0₃:Mn⁴⁺ is stronger than the one of α-A1₂0₃:Cr³⁺. For the zero-field splittings of the ground state and t₂^{3 2} E , their physical origins are revealed; the comparison and analysis of their values of the two crystals have been made.     

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.     

KCdF3晶体中Cr3+-Li+中心局域结构研究

利用零场分裂参量与晶体结构之间的定量关系,研究了双掺杂晶体KCdF₃:Cr³⁺,Li⁺的局域结构。指出,对于KCdF₃:Cr³⁺,Li⁺晶体,四角晶场的形成包含两个方面:(1)由于电荷补偿而产生的等效电荷形成的四角对称晶场;(2)Cr³⁺的局域结构发生晶格畸变而产生的四角对称晶场。事实上,当Cr³⁺和Li⁺掺入KCdF₃晶体时,Cr³⁺代替了Cd²⁺离子;由于Cr³⁺离子与Cd²⁺离子的半径不同、电荷不同、质量不同,导致Cr³⁺的局域结构发生晶格畸变,由此而产生四角对称晶场;由于电荷补偿,Li⁺离子取代了[001]方向与Cr³⁺离子邻近的Cd²⁺离子,由此产生的等效电荷而形成的四角晶场。这样,Cr³⁺的局域结构由O_h对称变为C_4v点对称。文中建立了ZFS参量和晶体结构之间的定量关系。在考虑晶格畸变和等效电荷的基础上,研究了KCdF₃:Cr³⁺,Li⁺晶体的ZFS参量,理论结果和实验符合很好。得到了F^-离子向中心离子分别移动为ΔR₁=0.00268nm,ΔR₂=0.001nm,ΔR₃=0.00165nm。     

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.     

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.     

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.     

YAG粉末材料中Cr3+敏化的Yb3+近红外发光性质

采用高温固相反应法合成了YAG: 0.02Cr³⁺,yYb³⁺系列粉末材料,研究了该系列材料在近红外区域的发光特性,主要包括Cr³⁺,Yb³⁺的发光性质、Cr³⁺: ⁴T₂和Yb³⁺: ²F_5/2能级辐射跃迁寿命以及其布居时间的比较,给出了Yb³⁺最佳掺杂量为10%。实验表明:通过Cr³⁺→Yb³⁺能量传递,实现了Yb³⁺在1 000 nm附近近红外发光的增强,这对进一步提高c-Si太阳能电池转换效率打下了坚实基础。     

Energy Spectrum and g Factors of α-A12O3:Ni2+ and Their Pressure-Induced Shifts

A unified calculation of the whole energy spectrum and g factors of the ground stateat normal pressure and their pressure-induced shifts for α-A1₂O₃:Ni²⁺ has been carried outon the basis of the theory of pressure-induced shifts and the diagonalization of the completed⁸ energy matrix adopting C_3υ symmetry. The calculated results are in very good agreementwith all the experimental data. The rates of change of all the levels with respect to variousparameters and the contributions to typical levels or splittings from various parameters havebeen calculated. The distinct differences of pressure-induced shifts of various levels are immediatelydetermined by their characteristic dependencies on -the parameters of interactions,and the pressure-induced shifts (especially those of t₂⁶e^{2 1}EÊ) have provided important or,crucial criteria for the correctness of the calculation and assignment of the energy spectrum of α-A1₂O₃:Ni²⁺.     

固相法制备Ce,Cr∶YAG透明陶瓷及其荧光性能研究

以高纯Al_2O_3、Y_2O_3、Cr_2O_3和CeO_2为原料,采用固相法制备了Ce,Cr∶YAG透明陶瓷。通过XRD测试和荧光测试,研究了0.5%Ce~(3+),0.1%Cr~(3+)掺杂的YAG透明陶瓷片的晶相结构和光学性能。结果表明:1 750℃烧结获得的该陶瓷片为YAG纯相,在可见光区的透过率达到了70%以上。在430 nm的光激励下,透明陶瓷同时表现出了Ce~(3+)、Cr~(3+)的特征发射峰,在补充白光LED的红光部分方面具有一定的实际应用价值。     

太阳光泵浦固体激光阈值的理论分析

为了选择适合太阳光泵浦的激光材料,本文从四能级速率方程出发,综合考虑了太阳辐射带状光谱特性和激光材料对泵浦光吸收能力,建立了太阳光泵浦固体激光理论模型。利用该模型推导得到了单束光侧面泵浦和椭球腔侧面泵浦方式下的泵浦阈值表达式,并结合Nd~3+∶YAG、Nd~3+∶glass、Nd~3+∶Cr~3+∶GSGG(Nd~3+∶Cr~3+∶Gd_3Sc_2Ga_3O_12)、Cr~3+∶BeAl_2O_4和Cr~3+∶Nd~3+∶YAG等激光材料的光谱参数,计算了这些材料的泵浦阈值光强。结果表明:在单束光侧面泵浦和椭球腔侧面泵浦方式下,Nd~3+∶YAG的泵浦阈值光强分别为448个太阳常数和224个太阳常数,是比较适合用太阳光泵浦的激光材料。由于椭球腔的特殊结构,采用椭球腔侧面泵浦激光介质,阈值光强比较低。分析了泵浦阈值光强与材料直径的关系。该模型可用于从现有的激光材料中筛选出在太阳光泵浦下最易输出激光的工作物质。