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.     

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,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.     

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 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-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.     

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.     

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 Spectra,g Factors and Their Pressure-Induced and/or Thermal Shifts of SrTiO3:Cr3+ and SrTiO3:Mn4+ III: R-Line Thermal Shifts of SrTiO3:Mn4+

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 basic wavefunctions within d³ electronic configuration, the values of the parameters in the expressions of thermal shift (TS) from EPI for the ground level, R level and R line of SrTiO₃:Mn⁴⁺ have been evaluated; the R-line TS and various contributions to it have been calculated in the low-temperature region. It is found that all the three terms of R-line TS from EPI relevant to the lattice vibration are red shifts. The Raman term is the largest, the neighbor-level term is the second, and the optical-branch term is very small over the range of T≤80 K. The contribution to R-line TS from thermal expansion has been approximately neglected in this work. The very strong EPI relevant to its lattice vibration for SrTiO₃:Mn⁴⁺ causes its R-line TS to be an unusually large red-shift. Only by taking into account the strong softening of the low-frequency acoustic modes of the lattice vibration at low temperatures, can we successfully explain the variation of R-line TS of SrTiO₃$:Mn⁴⁺ with temperature.     

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.     

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.     

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.     

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.     

Microscopic Theoretical Calculations of R—Line Thermal Shifts and Broadenings of MgO：Cr^3＋

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 basic wavefunctions within d^3 electronic configuration,the values of all the parameters in the expressions of thermal shift (TS) and thermal broadening (TB) due to EPI for the ground level,R level and R line of MgO:Cr^3 have microscopically been evaluated;and then,TS and TB of R line and various contributions to them have uniformly been calculated.The results are in very good agreement with the experimental data.It is found that all the three terms of TS due to EPI are red shifts;the Raman term is the largest one,and the optical-branch term and neighbor-level term are important for TS;the contribution to TS from thermal expansion is blue shift,which is also important.The R-line TS of MgO:Cr^3 comes from the first-order term of EPI.The elastic Raman scattering of acoustic phonons plays a dominant role in R-line TB of MgO:Cr^3 .For both TS and TB,it is very important to take into account all the admixtures of basic wavefunctions within d^3 electronic configuration.     

A Phenomenological Expression for Deuteron Electromagnetic Form Factors Based on Perturbative QCD Predict ions

For deuteron's electromagnetic form factors, perturbative QCD (pQCD) predicts that G₀₀⁺ becomes the dominate helicity amplitude and G₊₀⁺ and G_{+ -}⁺ are suppressed by factors A_QCD/Q and A_QCD²/Q² at large Q² respectively. We try to discuss the higher-order corrections beyond the pQCD asymptotic predictions by interpolating an analytical form to the intermediate energy region. From fitting the data, our results show that the helicity-zero to zero matrix element G₀₀⁺ dominates the gross structure function A(Q²) in both the large and intermediate energy regions. It is a good approximation for G_{+ -}⁺ to ignore the higher-order contributions and the higher-order corrections to G₊₀⁺ should be taken into account due to sizeable contributions in the intermediate energy region.     

SrZn2(PO4)2:Sn2+,Mn2+荧光粉的发光性质及其能量传递机理

采用高温固相法制备了SrZn₂(PO₄)₂:Sn²⁺(SZ₂P:Sn²⁺), SrZn₂(PO₄)₂:Mn²⁺(SZ₂P:Mn²⁺), SrZn₂ (PO₄)₂:Sn²⁺, Mn²⁺(SZ₂P:Sn²⁺, Mn²⁺) 荧光粉. 通过X射线衍射、激发和发射光谱详细研究了荧光粉的物相和发光性质. 在SrZn₂(PO₄)₂ 基质中, Sn²⁺离子发射光谱是峰值位于461 nm宽带谱, 归属于Sn²⁺离子的³P₁→¹S₀能级跃迁, SZ₂P:Mn²⁺激发光谱由基质吸收带(200–300 nm)和位于352, 373, 419, 431和466 nm的一系列激发峰组成, 分别对应Mn²⁺离子的⁶A₁(⁶S)→⁴E(⁴D), ⁶A₁(⁶S)→⁴T₂(⁴D), ⁶A₁(⁶S)→[⁴A₁(⁴G), ⁴E(⁴G)], ⁶A₁(⁶S)→⁴T₂(⁴G)和⁶A₁(⁶S)→⁴T₁(⁴G)能级跃迁, 因此, SZ₂P:Sn²⁺ 的发射光谱与SZ₂P:Mn²⁺的激发光谱有较大范围的重叠. 结果表明Sn²⁺对Mn²⁺发光有明显的敏化作用. 基于Dexter电多极相互作用能量传递公式和Reisfeld近似原理分析, 荧光粉SZ₂P:Sn²⁺, Mn²⁺中Sn²⁺-Mn²⁺离子之间的能量传递机理属于电四极-电四极相互作用引起的共振能量传递, 并计算出Sn²⁺-Mn²⁺离子之间能量传递临界距离R_c ≈ 1.78 nm. 通过改变Sn²⁺, Mn²⁺离子掺杂浓度, 实现了荧光粉发光颜色的调节, 在254 nm短波紫外激发下荧光粉发出较强的蓝白光. 研究结果表明SZ₂P:Sn²⁺, Mn²⁺荧光粉有望应用于紧凑型节能灯照明领域, 随着半导体紫外芯片技术的发展, 有潜力应用于未来的白光发光二极管照明领域.     

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.     

CuTe,Cu2和Cu2Te的结构与势能函数

在Cu和Te的RECP(Relativistic Effective Core Potential)近似下,运用B3LYP方法,在LANL2DZ基组水平上对CuTe,Cu₂和Cu₂Te分子体系的结构进行优化计算.结果表明,CuTe和Cu₂分子的基电子状态分别为²Π和¹∑_g⁺,Cu₂Te分子的基态为单重态的C_2V构型,其电子状态为¹A₁.同时还计算了Cu₂Te分子基态的离解能、力常数和振动频率.采用最小二乘法拟合出CuTe和Cu₂分子Murrell-Sorbie势能函数参数.在此基础上,运用多体展式理论方法导出Cu₂Te分子基态势能函数的解析表达式,其势能面准确复现了平衡态的结构特征.     

红色长余辉材料Mg2SiO4：Dy3+,Mn2+的制备及发光特性

用高温固相法制备了长余辉发光材料Mg₂SiO₄:Dy³⁺,Mn²⁺,对这种材料的红色长余辉性质进行了研究.对以不同掺杂浓度单掺杂Mn²⁺、单掺杂Dy³⁺以及双掺杂Dy³⁺,Mn²⁺的Mg₂SiO₄体系,通过在紫外激发下的发射光谱及其激发光谱的研究,确认了在双掺杂体系中,峰值为660nm的发光带对应着Mn²⁺的⁴T₁(⁴G)→⁶A₁(⁶S)跃迁,Mn²⁺为主要发光中心.Mn²⁺的660nm发射的激发谱分布很宽,样品在近紫外和可见光区都有良好的吸收,长波边可达600nm,是这种材料的一个显著优点.还研究了双掺杂体系中Dy³⁺对Mn²⁺的660nm发光带的敏化作用.另外,通过对单掺杂、双掺杂体系热释光曲线的比较,揭示了双掺杂体系中Dy³⁺的陷阱作用.     

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.