Analysis of the structure of tetragonal oxygen centers associated with Yb<Superscript>3+</Superscript> ions in the KMgF<Subscript>3</Subscript> crystal

The parameters of the crystal field of the tetragonal oxygen center associated with a Yb³⁺ ion in the KMgF₃ crystal found previously in a study of optical and ESR spectra are applied to analyze lattice distortions in the vicinity of the impurity ion and the O^2? ion compensating for the excess positive charge. Within the superposition model, it was ascertained that the Yb³⁺ ion and the neighboring ions of fluorine and oxygen on the axis of the center shift significantly along the direction from the O^2? ion to the Yb³⁺ ion during the formation of the tetragonal oxygen center. As this takes place, the distances of both (fluorine and oxygen) ions from the impurity ion increase. The four F^? ions of the nearest octahedral neighborhood of Yb³⁺ that are arranged symmetrically in the plane perpendicular to the axis of the center slightly recede from the axis.     

EPR,ENDOR and optical spectroscopy of Yb3+ ion in KZnF3 single crystals

The paramagnetic center of tetragonal symmetry formed by the Yb³⁺ ion in the KZnF₃ crystal has been studied using methods of EPR, ENDOR and optical spectroscopy. The location of the impurity ion and the structural model of the complex differing from the model of the Yb³⁺ center in KMgF₃ have been established. The empirical scheme of the energy levels of the Yb³⁺ ion has been found. The parameters of its interaction with the crystal electrostatic field and the hyperfine interaction with ligands of the nearest environment have been determined. The parameters of the crystal field were used for the analysis of the distortions of the crystal lattice in the vicinity of Yb³⁺. The parameters of the transferred hyperfine interaction have been calculated for the distances between Yb³⁺ and F⁻ ions of the nearest environment obtained taking into account the found distortions. They are in good agreement with the experimental values.     

EPR and optical spectroscopy of Yb<Superscript>3+</Superscript> ions in CaF<Subscript>2</Subscript>: an analysis of the structure of tetragonal centers

CaF₂ crystals doped with Yb³⁺ ions have been studied by electron paramagnetic resonance (EPR) and optical spectroscopy. EPR spectra of paramagnetic centers (PCs) for cubic (T_c) and tetragonal (T_tet) symmetries were identified. Empirical energy level diagrams were established and crystal field parameters were determined. Information on the CaF₂∶Yb³⁺ phonon spectra was obtained from the electron-vibrational structure of the optical spectra. The crystal field parameters were used to analyze the crystal lattice distortions in the vicinity of the Yb³⁺ ion. Within the framework of a superposition model, it is established that four F⁻ ions located symmetrically with respect to the fourfold axis from the side of the ion-compensator approach the impurity ion and deviate from the PC axis. The second set of four fluorine ions also approaches the Yb³⁺ ion and the PC axis. The ion-compensator F⁻ also approaches considerably the impurity ion.     

A method for estimating the local lattice distortions near a magnetic ion from ligand hyperfine parameters: Yb3+trigonal centers in SrF2 and BaF2

An empirical relationship describing the radial dependence of the nondipole part of the anisotropic constant for the ligand hyperfine interaction in alkaline-earth fluorides is proposed. This relationship is used for calculating the distances between the magnetic ion and the fluorine ions involved in its nearest environment. The results of the calculations are in good agreement with the values obtained by other methods for both cubic and tetragonal fluorine centers in these crystals. The distances from the magnetic ion to different groups of nonequivalent fluorine ions of the nearest environment in Yb³⁺ trigonal centers of SrF₂ and BaF₂ are determined. It is found that the Yb³⁺ ion is slightly displaced along the trigonal axis away from the compensating fluorine ion.     

Changes in the structure of the Rb2NaYF6: Yb3+ crystal upon transition from the cubic to tetragonal phase

The pattern of lattice distortions occurring in the vicinity of Yb³⁺ ions during the transition of the Rb₂NaYF₆: Yb³⁺ crystal from the cubic to tetragonal phase has been revealed using all the parameters of the empirically found crystal fields for paramagnetic centers of the Yb³⁺ ions with cubic and tetragonal symmetry. It has been shown that the YbF₆ octahedra are rotated about the fourfold axis through an angle approximately equal to 1.2°. Moreover, the octahedra themselves are deformed so that the F^? ions symmetrically located in the plane perpendicular to the axis of rotation come close to the impurity ion at a distance of 0.0004 nm. The fluoride ions located on the axis of rotation, conversely, move away from the Yb³⁺ ion at a distance of 0.0005 nm. Based on the obtained results, it has been concluded that the total condensate of order parameters of the studied phase transition involves not only the critical rotations of octahedral groups but also the noncritical displacements of atoms in the rotated octahedra.     

Local structure and the electron paramagnetic resonance parameters for the Cr3+ ions at K+-vacancy site in Cr3+:KZnF3 laser crystal

The quantitative relationship between the electron paramagnetic resonance (EPR) parameters D,g_∥,g_⊥ and the local structure parameters of Cr³⁺ ion in KZnF₃ crystals is established. The local structure for Cr³⁺ paramagnetic center in KZnF₃:Cr³⁺ crystal has been determined from EPR parameters of Cr³⁺ ion. This work shows that the trigonal crystal field of Cr³⁺ ion in KZnF₃ crystals comes from following two origins: (1) the nearest-neighbor K⁺ vacancy caused by the charge compensation in the [1 1 1]-axis direction; and (2) the lattice distortions of the nearest-neighbor fluorine coordination caused by the K⁺ vacancy and the differences in mass, charge, and radius between Cr³⁺ ion and Zn²⁺ ion. The unified calculation of the EPR zero-field splitting and g factors, taking into account the K⁺ vacancy and the lattice distortions, has been carried out on the basis of the complete diagonalization procedure and the superposition crystal-field model, all calculation results are in excellent agreement with the experimental data. Although the main source of the trigonal crystal field comes from the K⁺ vacancy caused by the charge compensation, the contribution of the lattice distortion cannot be neglected.     

Energy of migration of monovalent ions in NaCl: An experimental and theoretical study

Experimental diffusion measurements show that migration enthalpies of Cl^?, Br^? and I^? in NaCl are comparable, while that of F^? is considerably lower. Earlier studies had shown that migration enthalpies of Na⁺, K⁺, Rb⁺ and Cs⁺ in NaCl were similar. The polarised point ion model predicts migration energies of ions (by vacancy mechanism) to monotonically increase with ion size, contrary to experiment. Inversely, the shell model calculations rightly predict the variation of migration energies with ionic size. Thus, migration energies by vacancy mechanism do not vary significantly for ions larger than the host ions. However, in the case of the small ions, Li⁺ and F^?, the migration energies by vacancy mechanism are much lower and in good agreement with experiment for F^?.     

Theoretical investigation of the EPR parameters and the crystal lattice defects of the trigonal symmetry in RbCdF3:Cr3+

In this paper, the electron paramagnetic resonance (EPR) parameters in RbCdF₃:Cr³⁺ have been studied by means of energy matrices and the Newman superposition model, the theoretical results are in excellent agreement with the experimental ones. The existence of Rb⁺ vacancy and the lattice distortion have been verified. The EPR parameters arising from the Rb⁺ vacancy itself and the crystal lattice distortion are analyzed and calculated. We obtain that the six ligand F⁻ ions move to the central Cr³⁺ ion by Δ = 0.0013 nm, and the front three F⁻ ions rotate 2.98° away from the [111] axis while the back three F⁻ ions rotate 1.016° toward it.     

Type I FA (Rb, Cs) and II FA (Li, Na) tunable laser activities and donor-acceptor properties of O and O at KCl (001) surface: first principle calculations

Type I F_A (Rb⁺, Cs⁺) and II F_A (Li⁺, Na⁺) tunable laser activities, adsorptivity and donor-acceptor properties of O and O⁻ adsorbates at the flat surface of KCl crystal were investigated using an embedded cluster model and ab initio methods of molecular electronic structure calculations. Ion clusters were embedded in a simulated Coulomb field that closely approximates the Madelung field of the host surface, and the nearest neighbor ions to the defect site were allowed to relax to equilibrium. Based on the calculated Stokes shifted optical transition bands, F_A tunable laser activities were found to be inversely proportional to the size of the dopant cation (Li⁺, Na⁺, Rb⁺, Cs⁺) relative to the host cation (K⁺). This relation was explained in terms of the axial perturbation of the impurity cation. The probability of orientational bleaching attributed to the RES saddle point ion configuration along the 〈110〉 axis was found to be inversely proportional to the size of the dopant cation, with activation energy barriers of ca. 0.44-3.34 eV. Surface relaxation energies of type II F_A centers were more important than those of type I F_A centers. In terms of defect formation energies, the products of type II F_A center imperfection were more stable than those of type I F_A. The difference between F or F_A band energies and exciton bands depended almost exclusively on the size of the positive ion species. As far as the adsorptivity of O and O⁻ is concerned, the results confirm that surface imperfection enhances the adsorption energies by ca. 4.38-16.37 eV. O and O⁻ penetrate through the defect-containing surface. The energy gap between the adsorbate and the defect containing surface and the donor-acceptor property of adsorbate play the dominant role in the course of adsorbate substrate interactions and the results were explained in terms of electrostatic potential curves and Mulliken population analysis.     

KMgF3:Cr3+的EPR参量和K+空位研究

EPR和ENDOR表明:顺磁离子取代KMgF₃中的Mg²⁺离子后,所处的环境具有轴对称。本文研究了KMgF₃:Cr³⁺的Δg=g_∥-g_⊥和零场分裂值D,证实KMgF₃:Cr³⁺中K⁺空位的存在。并且指出:由于K⁺空位,使Cr³⁺的最近邻F^-离子分 关键词：     

Spin Hamiltonian parameters and local structures for tetragonal and orthorhombic Ir2+ centers in AgCl

The perturbation formulae of the spin Hamiltonian parameters (the anisotropic g factors, hyperfine structure constants and superhyperfine parameters) are established for a 5d⁷ ion in an orthorhombically elongated octahedron based on the cluster approach. These formulae are applied to the theoretical studies of the EPR spectra and the local structures for the tetragonal and orthorhombic Ir²⁺ centers in AgCl. For the tetragonal Ir²⁺ center, the uncompensated substitutional [IrCl₆]⁴ cluster is found to experience a relative elongation of about 0.08 Å along the C ₄ axis due to the Jahn–Teller effect. For the orthorhombic center, the ligand octahedron also suffers Jahn–Teller elongation (by about 0.08 Å) along the [001] (or Z) axis. Meanwhile, the ligand Cl intervening in the impurity Ir²⁺ and the next nearest neighbor silver vacancy V_Ag along the [100] (or X) axis may undergo an inward displacement of 0.004 Å towards the center of the octahedron due to electrostatic repulsion of the V_Ag. The calculated spin Hamiltonian parameters based on the above local structures show good agreement with experimental data for both centers.     

Examination on the electron paramagnetic resonance spectra and the photoluminescence spectra of the Cr ions in the KMgF3 crystal

In this paper, the photoluminescence spectra and the electron paramagnetic resonance spectra of the Cr³⁺ ions in the KMgF₃ crystal are explained based on the complete energy matrix diagonalization procedure and a crystal-field like model. The results agree well with the experimental data. It is also shown that the nearest neighbor F⁻ ions deviate 1.3981 and −0.486° from their original position because of the K⁺ vacancy.     

A Fe[Nb]-Li center in stoichiometric LiNbO<Subscript>3</Subscript> crystals: Mechanism of formation

A new iron center in stoichiometric lithium niobate crystals has been studied by the EPR method. The angular dependences of the EPR spectrum of the center have been used to derive the parameters of its spin Hamiltonian. The data amassed on the variation in the concentrations of two iron centers in lithium niobate crystals annealed in a Li₂CO₃ powder have provided an insight into the mechanism of formation of the new center, as well as corroborated its model proposed by us earlier. According to this model, the center represents a complex of two defects aligned with the polar axis in the crystal: the iron ion at the niobium site and an interstitial lithium ion filling the nearest structural vacancy (Fe³⁺[Nb]-Li⁺[V]). The structure of other Fe³⁺ centers revealed earlier in LiNbO₃ crystals, in which the iron ion occupies the niobium site, has been discussed.     

Anion disorder and ionic motion in lead fluoride (β-PbF2)

The anion disorder in β-PbF₂ has been investigated as a function of temperature by single crystal X-ray diffraction. The results show strong anharmonic thermal vibrations of the F⁻ ions along the body diagonals in the direction of the tetrahedral faces of the Pb²⁺ ions. The mobile F⁻ ions move along a path which leads through the unoccupied octahedron at the center of the elementary cell but this path does not pass through the center of this octahedron. The lattice constant shows a rapid increase near 700 K. Above this temperature the F⁻ ions occupy split positions around their regular lattice sites.     

Investigations of the local lattice distortions and the EPR parameters for the orthorhombic Pt3+ center in YAG

The local lattice distortions and the EPR parameters (anisotropic g factors and the hyperfine structure constants) for the orthorhombic Pt³⁺ center in YAG are theoretically investigated from the perturbation formulas of these parameters for a 5d⁷ ion in an orthorhombically elongated octahedron. The [ PtO₆] ^9- cluster on Al³⁺ site is found to experience the axial elongation of about 0.01 Å along Z axis, and the planar impurity-ligand bond lengths suffer the relative variation of about 0.11 Å? along X and Y axes due to the Jahn-Teller effect. As a result, the above local lattice distortions produce significant orthorhombic deformation, whereas the original slight trigonal distortion of the host [ AlO₆] ^9- octahedron is entirely depressed by the Jahn-Teller effect. The calculated EPR parameters based on the above lattice distortions show good agreement with the experimental data, and the local structure of the impurity center is also discussed.     

Optical absorption spectra of the Bi<Superscript>+</Superscript> impurity center in CsCdBr<Subscript>3</Subscript> ternary bromide

Optical absorption spectra of the Bi⁺ impurity center isomorphically substituting Cs⁺ in CsCdBr3 are recorded over a wide temperature range (from 3.2 to 300 K). An analysis of the vibrational degrees of freedom of the impurity center within the framework of the model of a single effective phonon mode yields various spectroscopic parameters of the optical transition in the Bi⁺ ion, such as the zero-phonon transition energy, Huang–Rhys parameter, and effective phonon energy. The results are used to compare the properties of the Bi⁺ center in various crystalline matrices.     

Optical spectroscopy of Yb in the Cs2NaYF6 single crystal

Results of the optical spectroscopy investigation of the cubic paramagnetic center Yb³⁺ ion in the Cs₂NaYF₆ single crystal are presented. The Stark level energies of the Yb³⁺ multiplets are established from absorption, luminescence and excitation luminescence spectra and the crystal field parameters are calculated. Information about the phonon spectra of Cs₂NaYF₆ crystals is obtained from the electron-vibrational structure of the optical absorption and luminescence spectra.     

Theoretical evaluation of the electron paramagnetic resonance spin Hamiltonian parameters for the impurity displacements for Fe3+ and Ru3+ in corundum

The impurity displacements for Fe³⁺ and Ru³⁺ in corundum (Al₂O₃) are theoretically studied using the perturbation formulas of the spin Hamiltonian parameters (zero-field splitting and anisotropic g factors) for a 3d⁵ (with high spin S = 5/2) and a 4d⁵ (with low spin S = 1/2) ion in trigonal symmetry, respectively. According to the investigations, the nd⁵ (n = 3 and 4) impurity ions may not locate at the ideal Al³⁺ site but undergo axial displacements by about 0.132 Å and 0.170 Å for Fe³⁺ and Ru³⁺, respectively, away from the center of the ligand octahedron along the C₃ axis. The calculated spin Hamiltonian parameters based on the above axial displacements show good agreement with the observed values. The validity of the results is discussed.     

Local structure of Tm<Superscript>2+</Superscript> and Yb<Superscript>3+</Superscript> impurity centers in <Emphasis Type="Italic">Me</Emphasis>F<Subscript>2</Subscript> (<Emphasis Type="Italic">Me</Emphasis> = Ca,Sr, Ba) fluoride crystals

The local structure of Tm²⁺ and Yb³⁺ cubic impurity centers in MeF₂: Tm²⁺ and MeF₂: Yb³⁺ (Me = Ca, Sr, Ba) fluoride crystals, as well as Yb³⁺ trigonal and tetragonal impurity centers in MeF₂: Yb ³⁺ crystals, is calculated within the shell model in the pair potential approximation.     

Laser-cooling effects in few-ion clouds of Yb+

We report some laser-cooling effects in a few¹⁷²Yb⁺ ions held in a Paul trap. Pronounced cloud-to-crystal phase transitions have been observed as discontinuities in the Yb⁺ fluorescence spectrum of the 369 nm cooling transition. The first reported two-dimensional images of Yb⁺ clouds with evidence of crystal structure have been recorded using a photon-counting position-sensitive detector. An ion temperature of 100 mK has been estimated from the size of a single ion image. Step-wise cooling of a re-heated, few-ion Yb⁺ cloud was also observed.