Energy Spectrum and g Factor of MgO:Cr3+ and Their Pressure-Induced Shifts

The unified calculation of the whole energy spectrum and g factor of the ground state for MgO:Cr³⁺ at normal pressure and their pressure-induced shifts has been carried out on the basis of the theory of pressure-induced shifts and the diagonalization of the complete d³ energy matrix in a regular octahedral field. All the calculated results are in very good agreement with a lot of experimental data. For the first time, by using the wavefunctions obtained by diagonalization of the complete energy matrix, the pressure-induced shifts of g factor have satisfactorily been calculated and explained by microscopic theory. The rates of change of levels with respect to various parameters and the contributions to levels from various parameters have been calculated. The distinct differences in magnitude and/or sign of pressure-induced shifts of various levels are immediately determined by their characteristic dependencies on the parameters of interactions. The pressure-induced shifts of levels and g factor have provided important criteria for the correctness of the calculations and assignments of the energy spectrum and wavefunctions, and it is quite necessary and important to carry out the unified calculation of the whole energy spectrum and g factor at normal pressure and their pressure-induced shifts.     

Complete Ligand-Field Calculations of Energy Spectrum and g Factor of CaO:Ni2+ and Their Pressure-Induced Shifts

The calculations of the whole energy spectrum and the g factor of the ground state for CaO:Ni²⁺ at ,normal pressure and their pressure-induced shifts have been carried out on the basis of the theory of pressure-induced shifts and the diagonalization of the complete d⁸ energy matrix in a regular octahedral field. The calculated results are in very good agreement with experimental data. The physical essentials of the pressure-induced shifts of typical levels and g factor for the ground state have been revealed by using the wavefunctions and energy spectra at various pressures.     

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.     

The Pressure-Induced Shifts of Energy Spectra of ZnS:Ni2+

The calculations of the whole energy spectrum of Zns:Ni²⁺ at normal pressure and pressure-induced shifts of its levels have been carried out on the basis of the theory of pressure-induced shifts and the diagonalization of the complete d⁸ energy matrix in a regular tetrahedral field. The calculated results are in very good agreement with experimental data at normal and high pressures. The comparison between the results of ZnS:Ni²⁺ and Mg0:Ni²⁺ indicates that the comlency of ZnS:Ni²⁺ is obviously stronger than the one of MgO:Ni²⁺;the expansion of electron wavefunctions of ZnS:Ni²⁺ under pressure is obviously larger than that of MgO:²⁺; and the pressure-induced shifts of levels of znS:NiZf show strong nonlinearity.     

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.     

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

By making use of the diagonalization of the complete d^3 energy matriz in a trigonally distorted cubic-field and the theory of pressure-induced shifts (PS) of energy spectra,the whole energy spectrum of α-Al2O3:Mn^4 and PS of levels have been calculated.All the calculated results are in excdellent agreement with the experimental data.The comparison between the results of α-Al2O3:Mn^4 and ruby has been made.It is found that on one hand,R1-line and R2-line PS of α-Al2O3:Mn^4 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:Mn^4 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 of d-electron wavefunctions of α-Al2O3:Mn^4 with compression is slightly larger than the one of ruby,and the effective charge experienced by d-electrons of α-Al2O3:Mn^4 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:Mn^4 are larger than those of ruby respectively,due to the charge of Mn^4 to be larger than that of Cr^3 .     

晶体NiF2的吸收光谱和电子顺磁共振谱的一种完全对角化计算

采用半自洽场(semi-SCF)自由Ni²⁺的d轨道波函数、点电荷-偶极子模型和Ni²⁺-6X^-(X=F,Cl,Br,I)络合物的μ-κ-α模型,建立结构参数与光谱、电子顺磁共振(EPR)谱(零场分裂D,E和顺磁g因子)之间的定量关系.利用能量矩阵完全对角化方法(CDP)和高阶微扰方法,统一解释NiF₂晶体的局部结构、吸收光谱和电子顺磁共振谱(EPR).比较两种方法计算得到的零场分裂D,E和顺磁g因子.结果表明:①高阶微扰方法算出的D,E值误差大;②能量矩阵完全对角化方法(CDP)算出的D,E值、光谱、顺磁g因子的值都与实验符合很好.     

Theoretical Studies of Energy Spectra and g Factors of Cr3+-Doped YAl3(BO3)4

With the strong-field scheme and trigonal bases, by diagonalizing the complete d³ energy matrix in a trigonally distorted cubic-field, the energy spectra and wavefunctions of YAl₃(BO₃)₄:Cr³⁺ have been calculated. The rates of change of levels with respect to various parameters and the contributions to levels from various parameters are calculated, and the physical origins of various levels or splittings have been clearly and quantitatively shown. By using the wavefunctions obtained from diagonalizing the complete energy matrix, the g factors of the ground state of YAl₃(BO₃)₄:Cr³⁺ have been evaluated. The calculated results are in good agreement with the optical-spectral and EPR experimental data. It is demonstrated that the bonding between Cr³⁺ and ligands (O^2-) is ionic.     

ZnO:V3+晶体光谱和电子顺磁共振谱的理论研究

采用强场耦合图像,建立了3d2电子组态在三角对称中的45×45能量矩阵,通过对角化完全能量矩阵的方法,计算出了ZnO:V3 晶体的45条光谱能级和5个电子顺磁共振谱参量(零场分裂D,g因子g//,g⊥和超精细结构常数A//,A⊥),计算结果与实验数值能很好地符合.计算中还发现V3 杂质中心的局部结构与基质晶体的结构不一致,即V3 在ZnO中并不占据准确的Zn2 位置,而是沿c3轴方向位移一段距离△Z≈0.003 nm.作者对上述这些结果的合理性进行了讨论.     

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.     

Energy Spectra,g Factors and Their Pressure—Induced and ／or Thermal Shifts of SrTiO3：Cr^3＋ and SrTiO3：Mn^4＋ I：energy Spectra and g Factors at Normal Pressure

With the strong-field scheme and cubic bases,the complete d^3 energy matrix in a tetragonally distorted cubic-field has been constructed.By diagonalizing this matrix,the energy spectra of SrTiO3:Cr^3 and SrTiO3:Mn^4 at normal pressure and various temperatures have been calculated.Correspondingly,the FORTRAN program calculating the g factor of the ground state has been worked out.By using the program and the wavefunction obtained from diagonalizing the complete energy matrix,the g factors of the ground state of SrTiO3:Cr^3 and SrTiO3:Mn^4 at normal pressure and room temperature have been evaluated.The calculated results are in good agreement with the optical-spectral and EPR experimental data.The comparison and analysis of the results of two crystals have been made.It is demonstrated that the covalency of the bonding between Mn^4 and ligands(O^2-) in SrTiO3:Mn^4 is stronger than the one of the bonding between Cr^3 and ligands(O^2-)in SrTiO3:Cr^3 .It is shown that the obtained wavefunctions and values of parameters are reasonable.     

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⁺.     

EPR谱图模拟软件EasySpin的图形用户界面设计

EasySpin是一款较为流行的电子顺磁共振（EPR）谱图模拟和拟合软件,LabVIEW是一种图形化编程语言开发环境．本文介绍了一款使用LabVIEW为EasySpin设计的图形用户界面LV-EasySpin．LV-EasySpin提供了一种直观的操作方法来实现连续波EPR多组分波谱的可视化模拟和拟合．本文辅以各种模式下的实例进行说明,阐述了LV-EasySpin的设计思路与实现方案,最终希望具有简洁、易操作界面的LV-EasySpin可以降低用户使用EasySpin分析EPR谱图的难度．     

计算晶体CdCl2:Ni2+的电子顺磁共振谱的完全对角化和高阶微扰方法

采用半自洽场自由Ni²⁺的d轨道波函数和点电荷-偶极子模型,建立局部结构、光谱与电子顺磁共振(EPR)谱(零场分裂D和顺磁g因子)之间的定量关系.利用完全对角化方法(CDP)和高阶微扰方法,统一解释CdCl₂:Ni²⁺晶体的局部结构、光谱和电子顺磁共振谱(EPR),并比较两种计算方法得到的结果.     

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.     

Calculations of the Spin-Lattice Coupling Coefficients Fij and Zij for MgO:Co2 Crystal

According to a uniform and simple method of calculating spin-lattice coupling coefficients and the pert1rbation formulas of gi factors and hyperfine structure constants Ai based on the cluster approach for 3d7 ions in cubic,tetragonal and trigonal octahedral crystal fields, the spin-lattice coupling coefficients Fij (F11, Fl2, F44), Zij (Z11, Z12,Z44) and also g factor and hyperfine constant A for MgO:Co2 are calculated by using the parameters obtained from the optical spectra without adjustable parameters. The calculated results show good agreement with the observed values.The difiiculty in explaining the coeficients Fij and Zij is therefore removed.``     

KAl(MoO4)2晶体中掺杂Cr3+的能谱和g因子的理论计算*

采用强场方案和三角基，通过对角化三角畸变的立方晶场下的d3 完全能量矩阵，计算出了KAl(MoO4)2:Cr3+ 的能谱和波函数。使用对角化完全能量矩阵所获得的波函数，进一步计算了KAl(MoO4)2:Cr3+ 的基态g 因子。计算结果与光谱，EPR谱实验数据很好地符合。研究表明,利用对角化完全能量矩阵获得的波函数对 g 因子所作的计算为整个理论计算及波函数的归属提供了重要判据,充分体现了将能谱和g 因子作统一计算的重要性和必要性.     

Ni~(2+):LiNbO_3的光学吸收谱和EPR的研究

应用三角晶场中d2 (d8)电子组态的包括静电相互作用和自旋 轨道耦合相互作用的强场能量矩阵 ,采用完全对角化方法 ,精确地计算了具有C3V 对称的Ni2 +:LiNbO3 的光学吸收谱和EPR谱。理论结果与实验值符合得很好