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Microscopic insight into electronic and structural properties of Cr3+ and Fe3+ impurities in Cs2NaAlF6 via DFT and SPM analyses
Abstract
Allowing high transition metal (TM) ions doping concentrations makes the fluoroelpasolite crystals Cs2NaMF6 (M = Al, Ga) quite interesting in various laser applications. In this study, we explored the influence of the dopant ions on the electronic and structural properties of Cs2NaAlF6. Particular attention is paid to the influence of trivalent TM ions (Cr³⁺ and Fe³⁺) on the local structure around the possible substitutional cation sites by investigating the optimized geometry around impurity sites due to Cr³⁺ and Fe³⁺ using density functional theory (DFT). The obtained structural data are utilized for the calculations of zero-field splitting (ZFS) parameters (ZFSPs) and crystal field parameters (CFPs) of both dopant ions independently in the frame of semi empirical superposition model (SPM). It is shown that remarkable change on the ZFSPs comes not from the distortion on metal-ligand distance but from that on the angular positions of the ligands around the impurity centers. It is clearly shown that the substitution of both Cr³⁺ and Fe³⁺ ions take place with significant influence on electronic structure and geometry for the trivalent Al³⁺ sites. The presented results here have significant potential to better understand the low-symmetry effects in especially optical applications of Cs2NaAlF6:Cr³⁺ and Cs2NaYF6:Fe³⁺ systems. Particularly, the calculated CFPs for Cs2NaYF6:Fe³⁺ system may serve as the only record in literature.
The local structure around Cr3+ centers in perovskite KMgF3 crystal have been investigated through the applications of both an ab-initio, density functional theory (DFT), and a semi empirical, superposition model (SPM), analyses. A supercell approach is used for DFT calculations. All the tetragonal (Cr3+–VMg and Cr3+–Li+), trigonal (Cr3+–VK), and CrF5O cluster centers have been considered with various structural models based on the previously suggested experimental inferences. The significant structural changes around the Cr3+ centers induced by Mg2+ or K+ vacancies and the Li substitution at those vacancy sites have been determined and discussed by means of charge distribution. This study provides insight on both the roles of Mg2+ and K+ vacancies and Li+ ion in the local structural properties around Cr3+ centers in KMgF3.
We have studied the influence of the electron-lattice coupling on the luminescence quantum yield for Cr3+ ions in a Cs2NaAlF6 crystal. For this purpose, we analyze the absorption and emission spectra of Cr3+ ions by means of the configurational coordinate model in the harmonic approximation. We have found the energy of the breathing phonon associated to Cr3+ ions in this host. In our findings we explain the high value of luminescence quantum yield reported previously (near to 70%), if we take into account the uncoupling between the breathing phonon and the normal modes associated to the bulk vibration. The Cr3+:Cs2NaAlF6 crystals promise to be a potential efficiency tunable laser device in the near infrared (700–900 nm) spectral range.
. The equilibrium geometry of the C
4ν FeOF5
4− center in KMgF3 has been explored by means of density functional theory calculations. Particular attention has been paid to the changes of
electronic density on passing from the O
h
FeF6
3− center in KMgF3 to FeOF5
4−, as well as to the variations undergone by the isotropic superhyperfine constant of axial A
s(Fax) and equatorial A
s(Feq) fluorine nuclei placed from Fe3+ at distances R
ax and R
eq, respectively. As a salient feature it is found for FeOF5
4− that, even if R
eq = R
ax, A
s(Feq) is significantly higher than A
s(Fax) thus pointing out that such quantities depend not only on the Fe3+–F− distance of the corresponding bond. Accordingly the obtained equilibrium distances R
ax = 0.2178 nm and R
eq = 0.2055 nm are not reproduced by any model based on the bond transferability. A slight off-center 0.018 nm displacement
of Fe3+ towards O2− is derived through the present calculations which reproduce reasonably well the experimental ratio A
s(Feq)/A
s(Fax) = 2.3.
Chromium-doped Cs2NaAlF6 and Cs2NaGaF6 crystals have been investigated by using the techniques of electron paramagnetic resonance (EPR) and electron nuclear double resonance (ENDOR) at X-band (9.5 GHz) and Q-band (34 GHz) frequencies. In both crystals, which have the hexagonal elpasolite structure, two inequivalent Cr3+ centers are detected. From the angular dependence of the ENDOR spectra for the central 53Cr nucleus and the nearest shells of 19F and 23Na nuclei, the crystallographic sites at which the paramagnetic Cr3+ ions are incorporated in these crystals have been unambiguously determined for each type of center. The results of the EPR and ENDOR investigation are discussed in the context of their correlation with optical and crystallographic data for these crystals and give considerable information about local distortions around the paramagnetic impurity ions.
The influence of site-symmetry and electron phonon coupling in Cs 2 NaAlF 6 :Cr 3 is probed by correlation of optical and structural measurements. Based on neutron and x-ray analysis the structure is a distorted R3m, exhibiting a unique stacking interaction. Selection rules have been used to assign the Raman-active zone-center vibrations. Although local and bulk mode frequencies differ slightly, indicating that the guest Cr 3 ion does not significantly perturb the host structure, vibrational analysis indicates the Cr 3 ion is coupled to the first coordination sphere of the Al–F lattice. © 2001 American Institute of Physics.
This article reviews the microscopic origin of properties due to transition-metal (TM) impurities, M, in insulator materials. Particular attention is paid to the influence of pressure upon impurity properties. Basic concepts such as the electronic localization in an MX(N) complex, the electrostatic potential, V(R), arising from the rest of the lattice ions or the elastic coupling of the complex to the host lattice are initially exposed. The dependence of optical and magnetic parameters on the impurity-ligand distance, R, in cubic lattices is discussed in a first step. Emphasis is put on the actual origin of the R dependence of 10Dq. Examples revealing that laws for strict cubic symmetry cannot in general be transferred to lower symmetries are later given. This relevant fact is shown to come from allowed hybridizations like nd-(n+1)s as well as the influence of V(R). As a salient feature the different colour in ruby and emerald is stressed to arise from distinct V(R) potentials in Al(2)O(3) and Be(3)Si(6)Al(2)O(18). The last part of this review deals with electronic instabilities. The phenomena associated with the Jahn-Teller (JT) effect in cubic lattices, the origin of the energy barrier among equivalent minima and the existence of coherent tunnelling in systems like MgO:Cu(2+) are discussed. An increase of elastic coupling is pointed out to favour a transition from an elongated to a compressed equilibrium conformation. Interestingly the equilibrium geometry of JT ions in non-cubic lattices is shown to be controlled by mechanisms different to those in cubic systems, V(R) playing again a key role. The relevance of first principles calculations for clarifying the subtle mechanisms behind off-centre instabilities is also pointed out. Examples concern monovalent and divalent TM impurities in lattices with the CaF(2) structure. The instability due to the transition from the ground to an excited state is finally considered. For complexes with significant elastic coupling vibrational frequencies and the Stokes shift are expected to undergo bigger changes through a chemical rather than a hydrostatic pressure. The reduction of Huang-Rhys factors upon increasing the pressure is discussed as well.
The structural properties of 3d ions (Cr³⁺ and Fe³⁺) centers in Cs2NaGaF6 have been investigated by performing density functional theory (DFT) and semi-empirical superposition model (SPM) calculations. The local geometry (i.e. equilibrium ligand distance and angles between the host cation ion (Cs⁺, Na⁺, or Ga³⁺) and F ligands) for pure, Cr³⁺ doped and Fe³⁺ doped structures have been determined after a fully relaxed geometry optimization at each lattice site. The previous experimental zero-field splitting (ZFS) parameters (ZFSPs) have been analyzed by SPM calculations using the obtained structural properties from DFT. The combination of two methods provide us to confirm the main result of the previous electron magnetic resonance and optical investigations stating that transition metal (TM) ions substitute for octahedral sites instead of being distributed randomly in the lattice of Cs2NaGaF6.
An investigation of the zero-field splitting (ZFS) of Cr3+ ions at the centers with the tetragonal (TE) and orthorhombic (OR) symmetries has been carried out in Cr3+ ion doped into A2CdF4 (A= Cs, K) fluorine compounds in the frame of semi-empirical superposition model (SPM). Various structural formations, namely uncompensated Cr3+ center (TE center I), Cr3+-VM (OR center III) and Cr3+-Li+ (OR center IV), and the relevant distortions have been verified in Cs2CdF4 and K2CdF4 crystals. Three different structural models have been examined for OR Cr3+ centers. The reasonableness of these structural models has been discussed.
Theoretical analysis of the Fe3+ centers observed in Tl2MgF4 fluorine crystals have been carried out by means of semi-empirical approaches. The most appropriate models are proposed by matching the theoretically predicted zero-field splitting parameters (ZFSPs) with the experimental ones obtained by EPR spectroscopy. Compression on the MF6 octahedron of tetragonal (TE) center I is indicated in both Tl2MgF4 and Tl2ZnF4. A structural model for monoclinic (MO) center II and orthorhombic (OR) Fe3+ center IV in Tl2ZnF4 is proposed by assuming that the substitution of Fe3+ induces both ligand length and angular distortions.
The temperature dependent zero-field splitting parameters (ZFSPs) for Mn2+ doped Cs2NaLaCl6 are analyzed theoretically. Assuming two different structural distortions models we have concerned the effect of temperature on ZFSPs for two structurally different Mn2+ centers. Analyses have been carried out based on the thermal expansion part (TE) of ZFSPs. Remarkable structural changes taking place in Mn2+ doped Cs2NaLaCl6 with lowering the temperature have been demonstrated. Good agreement between the theoretical and experimental results of ZFSPs shows that the models revealing the local structural distortions around the Mn2+ centers are reasonable. Some anomalies have been found in the temperature dependence of the ZFSPs and the temperature variation of the structural distortions.
Theoretical analysis is carried out to investigate the characteristics of the local environment around paramagnetic centers formed by Fe3+ ions in fluoroelpasolite crystals. All cation sites in the structure of these crystals are taken into consideration to be substituted by a Fe3+ ion. The modeling of the zero-field splitting parameters for Fe3+ ions located at the substitutional sites is achieved using several modeling approaches through superposition model. The results presented here provide theoretical interpretation of available electron magnetic resonance data.
Structural modeling has been carried out for Cr3+ centers in YAl3(BO3), YAB, single crystal, which is a potential laser host material. Superposition model (SPM) analysis is applied to predict the zero-field splitting parameters (ZFSPs) the as well as the crystal field parameters (CFPs) for Cr3+ ions located at possible cation sites in YAB. Our analysis of the crystal structure data and the available EPR spectra has revealed considerable low symmetry features. These findings indicate an approximated nature of the previous interpretation of EPR spectra and necessitate their reconsideration taking into account low symmetry aspects. The theoretically predicted ZFSPs and CFPs corroborate the significance of low symmetry aspects. Comparison of the theoretical and experimental ZFSP values obtained from EPR measurements enables analysis of the structural distortions at the Y3+ and Al3+ sites. It is shown that the ZFSPs of the six-coordinated Cr3+ centers are well described by a structural model for the Y3+ and Al3+ sites based on the angular distortions of the surrounding oxygens. The results obtained from our SPM analysis support the earlier finding that Cr3+ ions substitute for Al3+ ions in YAl3(BO3). The predicted ZFSPs and CFPs may be useful in future studies aimed at technological applications of the Huntite-type borates with the formula RM3(BO3)4.
Zero-field splitting (ZFS) and local distortion of Cr3+ ions doped into fluoroelpasolite (Cs2NaGaF6 and Cs2NaAlF6) crystals at both room temperature and 20 K have been studied using theoretical analyses. The results are discussed in connection with the experimental results. The agreement between the experimental and the present theoretical results indicates that the substitution of Cr3+ occurs for M3+ sites in Cs2NaMF6 crystals. It is shown that the six nearest-neighbor flour atoms have moved from trigonal [1 1 1]-axis more for all sites except for C site in Cs2NaAlF6 when the temperature is lowered from room temperature to 20 K.
This work is devoted to the study of optical properties of the elpasolite Cs2NaAlF6 with 0.1, 1.0, 3.0, 10.0, 30.0 and 50.0% of Cr3+ ions. The interest in this system lies on the fact that it presents a high quantum yield in the visible and infrared regions and therefore can be considered for laser applications. The photoluminescence and excitation spectra were obtained at 5 and 300 K, while the absorption spectra were measured at 300 K. The spectra at 300 K show broad bands attributed to the Cr3+ ions in two non-equivalent sites, both of them with octahedral coordination, while at 5 K we can observe the vibrational modes of the [CrF6]3− complex. The ensemble of our results lead us to conclude that the material has potential applications as a lasing system.
In this study, superposition model (SPM) parameters consisting of intrinsic parameters (IPs) b2¯(R0) and t2 and the reference distance R0, have been obtained for Cr3+ ions in flourine ligand systems (Cr–F combination) by combining the EPR data and the crystallographic data of Cr3+ ions in several crystals. It is shown that the obtained SPM parameters are very effective for the investigations of ZFSPs of Cr3+ centers with different trigonal and tetragonal symmetries. The values of the SPM parameters proposed here may serve as resource to the theoretical investigations of other Cr3+–F− systems.
The local environment around Fe3+ and Mn2+ ions doped into anatase TiO2 crystal is investigated and interpretation of EPR data, suggesting remote charge compensation, is provided. Using superposition model, the zero-field splitting (ZFS) parameters are modeled for Fe3+ and Mn2+ at the substitutional Ti4+ and interstitial sites (D2d). Several approaches are used to match the modeled b20 ZFS parameter with experimental values and thus to discriminate between various structural models. Theoretical predictions of the b4q parameters are also provided and tentative matching with experimental data is considered. The feasible values of the structural distortion parameters are predicted. The uniqueness and thus reliability of the predicted ZFS and distortion parameters are discussed.
Superposition model (SPM) calculations are carried out to provide theoretical interpretation of the zero-field splitting (ZFS) parameters and investigate the local environment around the Fe3+ centers in a TlGaSe2 single crystal. Experimental electron magnetic resonance (EMR) data are analyzed and compared with the ZFS parameter values predicted by SPM based on the orthorhombic approximation of structural data. The results provide an adequate interpretation of the ZFS parameters obtained by fitting EMR spectra and indicate that Fe3+ ions substitute for the Ga3+ ions in TlGaSe2 crystal.
Die Ergebnisse vollständiger röntgenographischer Einkristallstrukturbestimmungen an den in der Raumgruppe R3m kristallisierenden isostrukturellen Verbindungen Cs2NaCrF6 und Cs2NaFeF6 mit 12 L-Struktur, sowie an 2 L-Cs2LiGaF6 (Raumgruppe P3m1), werden mitgeteilt. Die flächenverknüpfte Oktaeder enthaltenden Strukturen der Verbindungen werden im Vergleich zu den hexagonalen Fluorperowskiten diskutiert und die gefundenen Mittelwerte der Abstände Cr-F = 1.910 Å, Fe-F = 1.926 Å, Ga-F = 1.93 Å neueren Literaturdaten gegenübergestellt. The results of complete X-ray single-crystal structure determinations of the isostructural compounds Cs2NaCrF6 and Cs2NaFeF6, crystallizing in a 12 L-structure in space group R3m, as well as of 2 L-Cs2LiGaF6 (space group P3m1), are reported. The structures, which contain face sharing octahedra, are discussed in comparison to the hexagonal fluoroperovskites. The mean distances observed, Cr-F = 1.910 Å, Fe-F = 1.926 Å, Ga-F = 1.93 Å, are compared to recently published data.
A new study of the strong axial EPR spectra of Fe3+ in KMgF3 is presented. In addition to the previously reported spin-Hamiltonian parameters g||, g⊥, and b20 for this axial site, values for the crystal-field parameters b40 and b44 are determined for the first time. Forbidden transitions of the type DeltaMs=±2and±3, previously unreported, are observed in the EPR spectra. The applicability of the superposition model to the second- and fourth-order spin-Hamiltonian parameters for the strong axial site of Fe3+ in the fluoroperovskite compounds KMgF3, KZnF3, and RbCdF3 is analyzed. It is established that the experimental reported values for the b20 parameter can be fitted if the intrinsic parameter b¯2F of the fluorine ion is -0.09 ± 0.03 cm-1 and the power-law coefficent t2 of b¯2F is taken to be equal to 12 ± 2. On the other hand, it is found that in order to get a consistent model for the FeOF5 cluster center, responsible for the observed strong axial EPR spectra of Fe3+ in the fluoroperovskite compounds, the sign of both spin-Hamiltonian parameters b40 and b44 must be positive and opposite to that of b20. Values for the intrinsic parameter b¯4F of the fluorine ion and for the power-law coefficient t4 of b¯4F are also determined.
Although a considerable body of data exists on the parametrization of the ground-state splittings of S-state ions in crystals, relatively little progress has been made in obtaining a quantitative understanding of the mechanisms which determine these parameters. In the course of summarizing our present understanding, we emphasize the need for making planned experiments explicitly aimed at testing theoretical models, such as those proposed in this article. The variable frequency E.P.R. technique is described in some detail, as it has proved to be particularly useful in this respect.
Recent progress in understanding the origin of the lanthanide crystal field is summarized. The basic assumption of the crystal field parametrization is shown to be that the crystalline environment can be represented as a one-electron potential, and the consequences of removing this assumption are traced. It is further shown that overlap and covalency make the dominant contributions to the observed field, the electrostatic contributions only being inportant for the potential components with low angular dependence (i.e. the n=2 parameters). In some circumstances it is found that the observed parameters can usefully be analysed into superposed contributions from the neighbouring ions in the crystal. The importance of crystal field concepts in related problems is emphasized as well as the stimulus crystal field theory gives to the development of formalisms for dealing with non-orthogonal basis states.
Superposition model (SPM) is employed to investigate the local environment around the Fe3+ centers located at the two sites 1 and 2 in TlGaS2 single crystal exhibiting nominally triclinic symmetry. Modeling of the local distortions around Fe3+ ions is carried out using triclinic and orthorhombic SPM analysis of the second-rank zero-field splitting (ZFS) parameters (ZFSPs) fitted from electron paramagnetic resonance (EPR) spectra at room temperature. Using SPM expressions for k=2, q=−2 to 2 and k=4,q=−4 to 4 derived by us, and crystallographic data and model parameters taken from the literature, the triclinic ZFSPs bkq are calculated for the two Fe3+ centers in the undistorted TlGaS2 host. The low symmetry aspects involved in SPM analysis of ZFSPs, which have commonly been omitted in previous studies, are considered. Then a reduction of the crystallographic data for the host crystal is carried out to reflect the ascent from triclinic to orthorhombic symmetry observed in the EPR spectra of doped crystal. This approximation enables matching the SPM-calculated ZFSPs with the experimental values of b20 and b22 and thus determination of the local distortions around Fe3+ ions arising due to doping, while preserving the observed orthorhombic site symmetry. The present modeling results support earlier suggestions that Fe3+ ions substitute for Ga3+ ions in TlGaS2. The fourth-rank ZFS parameters b4q, firstly determined theoretically in this study, have not been measured by EPR as yet. More comprehensive modeling of the local distortions and ZFS parameters for Fe3+ ions in TlGaS2 may be carried out when the experimental values of b4q become available.
The zero-field splitting parameters (ZFSPs) for an Fe3+ centre in single-crystal diammonium indium pentachloride monohydrate ((NH4)2InCl5⋅H2O; DIPM) are calculated using perturbation formulae and crystal-field parameters from the superposition model. The calculated second-order axial and rhombic ZFSPs at the In3+ site turn out to be similar to those obtained from experiments. This supports the notion that the Fe3+ impurity substitutes for the In3+ ion in DIPM.
EPR measurements on Fe3+ centres in RbCdF3 and CsCdF3 for crystals co-doped with Li+ ions have been made in the cubic phase of host crystals. In both the crystals spectra from two kinds of Fe3+ tetragonal centres associated with Cd2+ vacancy (VCd) and Li+ ion at the nearest-divalent-cation sites have been observed. From obtained fine structure parameters in the spin Hamiltonian the metal-ligand distances have been determined by the superposition model. The fine structure parameters have been explained well by the obtained metal-ligand distances, which show the contraction or distortion of fluorine octahedra surrounding Fe3+ ions.
Powder samples of hydrothermally grown Cr3+ -doped Cs-2 NaGaF6 crystals have been investigated with electron paramagnetic resonance spectroscopy at X - (9.5 GHz) and Q -band (34 GHz). Analysis of the spectra clearly demonstrates that there are two distinct Cr3+ centres in the Cs2NaGaF6 crystal, having nearly identical g factors, but differing largely from the viewpoint of their zero field splitting. By using the Cr-53 hyperfine spectra observed with electron nuclear double resonance spectroscopy, it is deduced that these centres have opposite signs for the zero field splitting. The spectroscopic properties of the Cr3+ centres in the isostructural Cs2NaGaF6 and Cs2NaAlF6 crystals are compared and discussed.
In this study, using the superposition model (SPM) and crystallographic data, the second- and fourth-rank zero-field splitting (ZFS) parameters (ZFSPs) have been calculated for Fe3+ ions at two In sites in TlInS2 single crystal. Since crystallographic data indicate C1 site symmetry, a full triclinic ZFS Hamiltonian has been employed. Model parameters were adjusted so to obtain best agreement between the SPM calculated ZFSPs and the second-rank ZFSPs measured by electron magnetic resonance (EMR). The effects of site symmetry on the theoretically predicted ZFSPs and interpretation of the available experimental ZFSPs have been considered. The experimental second-rank ZFSPs were obtained using approximated orthorhombic spin Hamiltonian. Hence, to facilitate comparison with the SPM calculated ZFSPs, the ascent in symmetry method has been applied to the crystallographic data to quantify the structural approximation from triclinic to orthorhombic and to tetragonal site symmetry. Our considerations provide additional structural information, especially concerning the low site symmetry aspects, pertinent for Fe3+ impurity centers in TlInS2 and related crystals. Our SPM analysis of ZFSPs indicates that satisfactory so tentative agreement can be achieved between the theoretical predictions and the experimentally measured values of the second-rank ZFSPs. The procedure proposed here may serve as a general framework for modelling of ZFSPs for other ion-host systems. More accurate modelling for Fe3+ ions in TlInS2 may be carried out when better quality EMR results taking into account the low symmetry effects in EMR spectra and the values of the fourth-rank ZFSPs become available. The results of SPM calculations support earlier suggestions that Fe3+ ions substitute for In3+ ions in TlInS2.
Spherical (S) and tesseral (T) tensor operators (TOs) have been extensively used in, for example, EMR and optical spectroscopy of transition ions. To enable a systematic review of the published tables of the operators and their matrix elements (MEs) we have generated the relevant tables by computer, using Mathematica programs. Our review reveals several misprints/errors in the major sources of TTOs—the conventional Stevens operators (CSOs—components ) and the extended ones (ESOs—all q) for rank k = 2,4, and 6—as well as of some STOs with . The implications of using incorrect operators and/or MEs for the reliability of EMR-related programs and interpretation of experimental data are discussed. Studies of high-spin complexes like Mn12 (S = 10) and Fe19 (S = 33/2) require operator and ME listings up to k = 2S, which are not presently available. Using the algorithms developed recently by Ryabov, the generalized ESOs and their MEs for arbitrary rank k and spin S are generated by computer, using Mathematica. The extended tables enable simulation of the energy levels for arbitrary spin systems and symmetry cases. Tables are provided for the ESOs not available in the literature, with odd k = 3,5, and 7 for completeness; however, for the newly generalized ESOs with the most useful even rank k = 8,10, and 12 only, in view of the large listings sizes. General source codes for the generation of the ESO listings and their ME tables are available from the authors.
The superposition model was originally developed to separate the geometrical and physical information in crystal field parameters. Its success in the analysis of lanthanide spectra has been paralleled by the success of the related angular overlap model in the analysis of d-electron spectra. The basic ideas, method of application and reliability of the superposition model are discussed and its relationship with the angular overlap model is clarified. Developments described are the application of the superposition model to the ground (L=0) multiplet splittings of d5 and f7 ions, orbit-lattice interactions, transition intensities and correlation crystal fields. Special attention is paid to work which has been claimed to support or disprove the postulates of the model.
An analysis of the energy level structure of Cr3+ ions in Cs2NaAlF6 crystal is performed using the exchange charge model (ECM) together with the crystal field analysis/microscopic spin Hamiltonian (CFA/MSH) computer package. Utilizing the crystal structure data, our approach enables modelling of the crystal field parameters (CFPs) and thus the energy level structure for Cr3+ ions at the two crystallographically inequivalent sites in Cs2NaAlF6. Using the ECM initial adjustment procedure, the CFPs are calculated in the crystallographic axis system centred at the Cr3+ ion at each site. Additionally the CFPs are also calculated using the superposition model (SPM). The ECM and SPM predicted CFP values match very well. Consideration of the symmetry aspects for the so-obtained CFP datasets reveals that the latter axis system matches the symmetry-adapted axis system related directly to the six Cr–F bonds well. Using the ECM predicted CFPs as an input for the CFA/MSH package, the complete energy level schemes are calculated for Cr3+ ions at the two sites. Comparison of the theoretical results with the experimental spectroscopic data yields satisfactory agreement. Our results confirm that the actual symmetry at both impurity sites I and II in the Cs2NaAlF6:Cr3+ system is trigonal D3d. The ECM predicted CFPs may be used as the initial (starting) parameters for simulations and fittings of the energy levels for Cr3+ ions in structurally similar hosts.
The quantificational relationship between the EPR zero-field splitting parameter D and the structure parameters of the tetragonal Cr3+ centre in RbCdF3:Cr3+ crystals has been established according to the superposition model and third-order perturbation theory. The existence of the Cd2+ vacancy and the lattice distortion have been verified. Meanwhile, we obtain that the F- ion moves toward the central Cr3+ ion by X1 = 0.0031 nm, X2 = 0.001 01 nm, X3 = 0.002 81 nm. Good agreement between the theoretical results and the experimental values shows that the assumption of the Cd2+ vacancy and the lattice distortion is reasonable. Although the main source of the tetragonal crystal field comes from the Cd2+ vacancy caused by the charge compensation, the contribution of the lattice distortion cannot be neglected.
The luminescent quantum efficiency of Cr3+ ions in single fluoride crystal Cs2NaAlF6 was determined by using the simultaneous multiple-wavelength photoacoustic and luminescent experiments method, based on the generation of photoacoustic and luminescence signals after pulsed laser excitation. The luminescent quantum yield for the most important transition between the vibronic levels was found to be 68±3%. This value agrees with that obtained from the ratio of the lifetimes of the corresponding transition at different temperatures.
The results of high-pressure spectroscopy of Cr3+ and Mn4+ ions in solids are revised. We discuss the influence of external pressure on compression of ion–ligands systems, pressure-induced 4T2–2E level crossover, R-lines pressure shift and influence of pressure on the R-lines emission lifetime. The model of energetic structure of the octahedrally coordinated 3d3 ion that includes electron–phonon and spin–orbit interaction is considered and used for interpretation of the results of high-pressure spectroscopy, especially for quantitative analysis of lattice disorder and crystal field distribution in crystal.
Powder and crystal ESR spectra on the 12R hexagonal perovskite Cs2NaAlF6 doped with Cr3+ have been studied. The positions of the lines in the crystal spectrum versus the direction of the magnetic field and a weighed powder spectrum have been obtained by computer simulation. They indicate the distributions of this cation in the two sites attributed to the tervalent ion. If in Cs2NaAlF6 the (AlF6) site is of Oh symmetry, the introduction of chromium induces an axial distortion.
Emission and excitation spectra for Cs2NaAlF6:Cr3+ are presented. The near-infrared fluorescence observed at 77 and 4.2 K are attributed to the zero-phonon spin-forbidden transition E-2((2)G) --> (4)A(2)(F-4) while at room-temperature the emission is assigned to the T-2(2)(F-2) --> (4)A(2)(F-4) transition. Two non-equivalent octahedral sites are identified through time-resolved measurements and lifetime fluorescence bands are measured. The Racah and crystal-field parameters are calculated for both sites.
We propose a simple analytic representation of the correlation energy εc for a uniform electron gas, as a function of density parameter rs and relative spin polarization zeta. Within the random-phase approximation (RPA), this representation allows for the r-3/4s behavior as rs-->∞. Close agreement with numerical RPA values for εc(rs,0), εc(rs,1), and the spin stiffness alphac(rs)=∂2εc(rs, zeta=0)/deltazeta2, and recovery of the correct rslnrs term for rs-->0, indicate the appropriateness of the chosen analytic form. Beyond RPA, different parameters for the same analytic form are found by fitting to the Green's-function Monte Carlo data of Ceperley and Alder [Phys. Rev. Lett. 45, 566 (1980)], taking into account data uncertainties that have been ignored in earlier fits by Vosko, Wilk, and Nusair (VWN) [Can. J. Phys. 58, 1200 (1980)] or by Perdew and Zunger (PZ) [Phys. Rev. B 23, 5048 (1981)]. While we confirm the practical accuracy of the VWN and PZ representations, we eliminate some minor problems with these forms. We study the zeta-dependent coefficients in the high- and low-density expansions, and the rs-dependent spin susceptibility. We also present a conjecture for the exact low-density limit. The correlation potential musigmac(rs,zeta) is evaluated for use in self-consistent density-functional calculations.
The zero-field splitting of S6-state ions is studied in the intermediate-field coupling scheme by taking the crystal-field and the electrostatic interactions as the unperturbed Hamiltonian and the spin-orbit interaction as a perturbation. This perturbation process shows a very good convergence and provides a comprehensive approach to the derivation of both the rank-2 bq2 and the rank-4 bq4 zero-field splitting parameters, which are shown to come predominantly from the first nonzero peturbation terms. Cubic and tetragonal symmetries are considered and the zero-field splitting parameters D (~b02), a (~b44), and F (~b04) are investigated in detail as functions of the cubic Dq and the tetragonal crystal-field (CF) parameters B20 and B'40. It is found that the tetragonal CF components B20 and B'40 contribute, to the cubic zero-field splitting parameter a, a value at, which is non-negligible. The ratio at/F is found to be insensitive to CF parameters and to lie in the range -0.2 to -0.5. Both parameters at and F depend mainly on B20, whereas D depends mainly on B'40. The results of earlier perturbation procedures are also calculated and compared with the present ones. The present theory deals with the zero-field splitting parameters bq4 (k=2 and 4) by regarding the crystal-field parameters Bkq (k=2 and 4) as freely adjustable phenomenological parameters, thus avoiding problems arising from the application of a specific crystal-model to the evaluation of Bbq. Following this idea, numerical calculations are carried out for the parameters a, D, and F for Mn2+ and Fe3+ ions in cubic and tetragonal fluoroperovskites. The results are in good agreement with experimental data. This work presents examples where the crystal-field theory allows a successful interpretation of the zero-field splitting of S6-state ions.
Fe(3+) ions in hexagonal and cubic fluoroelpasolite crystals (A(1)(2)B(I)M(III)F(6)) have been investigated in a combined Electron Paramagnetic Resonance (EPR) and Electron Nuclear Double Resonance (ENDOR) study. A detailed analysis of the ENDOR spectra for the nearest (19)F and (23)Na shells in X (9.5 GHz) and Q band (34 GHz) allowed the complex EPR spectra to be disentangled and to determine the spin Hamiltonian parameters for the various S = 5/2 Fe(3+) centres. W-band (95 GHz) EPR measurements as a function of temperature were performed to provide unambiguous evidence about the absolute signs of the Zero Field Splitting (ZFS) and SuperHyperFine (SHF) parameters for Fe(3+) in Cs(2)NaAlF(6) as already determined from the ENDOR work. It could be concluded that all principal (19)F hyperfine values were positive, in agreement with earlier assignments in the literature for related systems. A comparative analysis of the (19)F SHF data for Fe(3+) at a perfectly octahedral site in the cubic crystal, and at two slightly trigonally distorted environments in the hexagonal crystals, indicates that the metal-to-ligand distance changes upon doping. The obtained set of parameters concerning one defect in various analogous environments can furthermore be used to test different methods of theoretical calculations for ZFS and SHF values.
We generalize the concept of separable dual-space Gaussian pseudopotentials to the relativistic case. This allows us to construct this type of pseudopotential for the whole periodic table and we present a complete table of pseudopotential parameters for all the elements from H to Rn. The relativistic version of this pseudopotential retains all the advantages of its nonrelativistic version. It is separable by construction, it is optimal for integration on a real space grid, it is highly accurate and due to its analytic form it can be specified by a very small number of parameters. The accuracy of the pseudopotential is illustrated by an extensive series of molecular calculations.