Simple Overlap Model Research Articles

Analytical crystal-field models applied to compounds doped with Eu3+

The point charge electrostatic model (PCEM) and the simple overlap model (SOM), both purely analytical crystal field models, are being briefly revisited, in order to show the evolution of their application to Eu doped compounds. Calculations are made through the method of equivalent nearest neighbours (MENN), and applied to the Eu(dipivaloylmethanate)31,10-phenanthroline [Eu(DPM)3o-phen] complex, with the aim of discussing the Eu–O and Eu–N interactions. The charge of the Eu ion is calculated using the Batista-Longo improved model (BLIM) to give gBLIM = 3,64e around the Eu-NN midpoint. The 7F1 crystal-field levels and level splitting were satisfactorily reproduced with two charge factors, namely, g1 = 0.495 and g2 = 0.415, assuming the luminescent site in a tetragonal point symmetry slightly distorted. In particular, it is shown that the Eu3+, itself, is satisfied by attracting an amount of charge, which neutralize/stabilize its own site electrostatically, no matter what the ligating ions are. The Eu-NN overlap (ρ = <4f|2s2p>) is assumed to be 0.1, which is physically plausible both as a limit in respect to β, the SOM correction factor to the PCEM, and describes the covalent contribution to the Ln-NN interaction, the latter is the most important contribution of the SOM to the crystal-field theory of lanthanide containing compounds. An eloquent comparison with crystal-field levels of the Eu:LiYF4 and Eu(btfa)3(4,4-bipy)(EtOH) is made. Finally, this paper is, indeed, a very simple tribute to Professor Oscar L. Malta, as an acknowledgement of his deep contribution to the author's apprenticeship about crystal-field theory of systems containing lanthanides.

Adaptive guided stochastic optimization: A novel approach for fitting the theoretical intensity parameters for lanthanide compounds

In this study, we introduce a state-of-the-art approach to enhance the fitting accuracy of theoretical intensity parameters in lanthanide spectroscopy. Lanthanide-based compounds play a pivotal role in a wide range of applications due to their distinctive photophysical characteristics. Theoretical understanding and computational descriptions are essential for advancing these applications. The Judd-Ofelt theory stands as a fundamental stone, offering insights into the luminescence exhibited by lanthanide compounds. Our methodology addresses the procedure of fitting charge factors (g in the Simple Overlap Model) and ligand effective polarizabilities (α′ in the Bond Overlap Model), quantities used for the determination of the intensity parameters (Ωλ). We propose Adaptive Guided Stochastic Optimization (AGSO), a method that employs randomized initial points within predefined bounds for each variable. By iteratively updating variable bounds based on population statistics, AGSO systematically minimizes the error function with respect to experimental data. Extensive tests were conducted comparing AGSO with the well-established simulated annealing (SA) method. Remarkably, AGSO consistently outperformed SA, demonstrating its efficacy in fitting intensity parameters for various lanthanide compounds. Through AGSO, we offer a robust and efficient tool for the accurate study of lanthanide-based compounds, with broad implications for diverse applications.

Spectroscopic study of the Eu3+ local symmetry in EuF3 crystal

We employed the simple overlap model (SOM) with the method of equivalent nearest neighbours (MENN) to indicate the local symmetry of the Eu3+ in the europium trifluoride (EuF3) compound through two analyses based on the emission spectra. In first situation, three lines were observed at the 5D0 → 7F1 (0-1) transition. Therefore, based on the amount of non-null crystal field parameters, we indicate that the Eu ion occupies a site with distorted inversion centre as a combination of C2 and C2h symmetries, with the following charge factors: g1 = 0.438, g2 = 0.292, g3 = 0.411, g4 = 0.201, g5 = 0.396 and g6 = 0.293. In second situation, with two lines at the 0-1 transition, we suggested the luminescent site as a combination of the D3d and D3h symmetries with g1 = 0.279 and g2 = 0.495. The 7F1 manifold splitting was obtained through Auzel-Malta equation. All theoretical calculations reproduced satisfactorily the 7F1, 7F2 and 5D1 energy sublevels in good agreement with experimentals data.

Atomistic simulation and spectroscopic study of the [formula omitted] doped [formula omitted] crystal

The CaSO4:Eu3+ has been prepared by the slow evaporation route with different concentrations of the luminescent ion, characterized by XRD and emission spectra techniques and studied by atomistic simulation and crystal field theory. The lattice parameters were obtained with a new set of potentials which is proving to be more appropriate to simulate the lattice parameters and the local Eu3+ luminescent site than those published elsewhere. The Simple Overlap Model (SOM) was applied in the frame of the Method of Equivalent Nearest Neighbours (MENN) in order to predict the charge factors devoted do the Eu–O bond and the 7F1 energy sub-levels through the crystal field parameters. The central ion charge (gEu) was predicted by the Batista–Longo Improved Model (BLIM). Our calculations indicated that the Eu3+ prefers the Ca2+ site compensated by calcium vacancy or interstitial oxygen. Using the four simulated structures the 7F1 Stark levels were satisfactory reproduced. Thus, based on the simulations and the number of lines exhibited in the emission spectra, one has a strong indication that the Eu ion occupies a distorted local symmetry which is a combination of the D2 and C2v point groups.

Theoretical spectroscopic investigation of the Eu3+ local symmetry in LiF through crystal field models

We employed the simple overlap model (SOM) with the method of equivalent nearest neighbours (MENN) in the Auzel-Malta equation and in the energy sublevels equations to investigate the local symmetry of the Eu3+ in the LiF crystal and predict the 7F1, 7F2 and 5D1 energy sublevels. The Batista-Longo Improved Model (BLIM) was helpful to predict the Eu3+ ion charge and establish the Eu–F interaction charge position considering the covalence on the chemical bonding by the Brik-Avram overlap integrals matching with the octet rule. The LiF:Eu3+ were studied elsewhere in two situations. In the first case, the Eu3+ occupies a site without inversion centre because the 5D0 – 7F2 (0-2) transition is more intense than 5D0 – 7F1 (0-1) transition, which we indicate spectral behaviour of the a α-EuF3 polymorphic phase. Thus, with a combination of non-null crystal field parameters, we obtained the luminescent site as being a distorted C2v symmetry with charge factors g1 = 0.485, g2 = 0.499, g3 = 0.403, g4 = 0.343 and g5 = 0.257. This set of charge factors reproduced the 7F1 manifold in good agreement with experimental data. In the second case, with the 0-1 transition more intense than the 0-2 transition, we have the indication which the Eu3+ occupies a site with distorted inversion centre. Furthermore, due to the asymmetry of the peaks, we performed a deconvolution of these peaks with two lines in both 7F1 and 7F2 manifolds. Assuming the distorted luminescent site have being D4h or D4d symmetries with g = 0.383 and D2d symmetry with g1 = 0.400 and g2 = 0.396, we have reproduced satisfactory the 7F1 level splitting and 7F2 and 5D1 sublevel positions, considering the Eu3+ octacoordinated.

High pressure luminescence of Nd3+ in YAlO3 perovskite nanocrystals: A crystal-field analysis.

Pressure-induced energy blue- and red-shifts of the 4F3/2 → 4I9/2,11/2 near-infrared emission lines of Nd3+ ions in YAlO3 perovskite nano-particles have been measured from ambient conditions up to 29 GPa. Different positive and negative linear pressure coefficients have been calibrated for the emission lines and related to pressure-induced changes in the interactions between those Nd3+ ions and their twelve oxygen ligands at the yttrium site. Potentiality of the simple overlap model, combined with ab initio structural calculations, in the description of the effects of these interactions on the energy levels and luminescence properties of the optically active Nd3+ ion is emphasized. Simulations show how the energies of the 4f3 ground configuration and the barycenters of the multiplets increase with pressure, whereas the Coulomb interaction between f-electrons decreases and the crystal-field strength increases. All these effects combined explain the wavelength blue-shifts of some near-infrared emission lines of Nd3+ ions. Large pressure rates of various emission lines suggest that a YAlO3 perovskite nano-crystal can be a potential candidate for near-infrared optical pressure sensors.

Molecular Dynamic Simulation of Collision-Induced Third-Body Formation in Hydrogen-Free Diamond-Like Carbon Asperities.

The collision of two cylindrical hydrogen-free diamond-like carbon (DLC) asperities with approximately 60 % sp3 hybridization has been studied using classical molecular dynamics. The severity of the collision can be controlled by the impact parameter b that measures the width of the projected overlap of the two cylinders. For a cylinder radius of R = 23 nm, three collisions with b = 0.5 nm, b = 1 nm and b = 2.0 nm are compared. While for the two small b a single shear band between the collision partners and a strongly localized sp2/sp1 hybridised third-body zone between the asperities is observed, the b = 2 nm collision is accompanied by pronounced plastic deformation in both asperities that destabilize the metastable sp3-rich phase leading to a drastic increase in the amount of rehybridized tribomaterial. In addition, pronounced roughening of the cylinder surfaces, asymmetric material transfer and the generation of wear debris are found in this case. For the b = 0.5 and 1 nm collision, the evolution of third-body volume can be quantitatively described by a simple geometric overlap model that assumes a sliding-induced phase transformation localized between both asperities. For b = 2 nm, this model underestimates the third-body volume by more than 150 % indicating that plasticity has to be taken into account in simple geometric models of severe DLC/DLC asperity collisions.

Molecular dynamics simulation and crystal field calculations of the Eu2O3-PbO-SiO2 glassy system submitted to long annealing time

The Eu2O3-PbO-SiO2 glassy system submitted to a long annealing time (100ps) has been obtained by molecular dynamics calculations. The average of 87/86 sites of the Eu3+ ion with six/seven nearest neighbours are used to discuss the number of lines and the local symmetry of the luminescent site through the crystal field parameters, using the simple overlap model in the frame of the method of equivalent nearest neighbours. The magnitude of the Bq2(q=0, 1, 2) and the non-negligible B44 and B46(B34, B36 and B66) lead to the indication of distorted C4h and C3i site symmetries of the six and seven nearest neighbours, respectively. We have then compared very satisfactorily our 7F1 sublevels calculations with those observed in the emission spectra of an Eu-borate glass annealed for 30min and 17h. This comparison is justified because the emission behaviour of europium ions in different glassy systems are honestly very similar. Further, the decrease observed in the 5D0→7F2/5D0→7F1 transition intensity ratio is a clear indication that the Eu3+ ion are nucleating a crystalline phase. Such satisfactory comparisons indicate that we have obtained a transparent glass-ceramics.

Determination of the Eu3+ ion local structure in oxide and fluoride crystals

In this work a procedure to determine the local structure of the optically active site was developed. The local structure of the Eu3+ ion in high symmetry sites of the SnO2(D2h) and BaLiF3(D4d) crystals was carried out using the simple overlap model (SOM) and the method of equivalent nearest neighbours (MENN). From equations of the crystal field parameters (CFP), of the maximum splitting of F17 multiplet and of the electrostatic equilibrium of luminescent site it was possible to predict the Eu-NN distances. The overlap between the 4f and 2p orbitals has been 0.05 and the charge factor between 0.45≤gj≤8.0. The Batista–Longo Improved Model (BLIM) was used to show that the Eu3+ ion charge can be greater than its own valence. The F17 level splitting (316cm−1 for the SnO2; and 83cm−1 for the BaLiF3) and the predicted Stark levels are in very good agreement with the experimental data. In all cases the magnitude of the charge factors are quite close to each other. This strongly indicates that the Eu3+ ion treats any chemical species in its immediate neighbourhood as negative charges.

Europium Luminescence: Electronic Densities and Superdelocalizabilities for a Unique Adjustment of Theoretical Intensity Parameters.

We advance the concept that the charge factors of the simple overlap model and the polarizabilities of Judd-Ofelt theory for the luminescence of europium complexes can be effectively and uniquely modeled by perturbation theory on the semiempirical electronic wave function of the complex. With only three adjustable constants, we introduce expressions that relate: (i) the charge factors to electronic densities, and (ii) the polarizabilities to superdelocalizabilities that we derived specifically for this purpose. The three constants are then adjusted iteratively until the calculated intensity parameters, corresponding to the 5D0→7F2 and 5D0→7F4 transitions, converge to the experimentally determined ones. This adjustment yields a single unique set of only three constants per complex and semiempirical model used. From these constants, we then define a binary outcome acceptance attribute for the adjustment, and show that when the adjustment is acceptable, the predicted geometry is, in average, closer to the experimental one. An important consequence is that the terms of the intensity parameters related to dynamic coupling and electric dipole mechanisms will be unique. Hence, the important energy transfer rates will also be unique, leading to a single predicted intensity parameter for the 5D0→7F6 transition.

Energy transfer upconversion dynamics in YVO4:Yb3+,Er3+

A new approach to calculate the effective Ln–Ln energy transfer rates in a doped crystal matrices was proposed and successfully applied to the YVO4:Yb3+,Er3+ upconversion system. This approach is based on the known set of Ln–Ln distances obtained from the crystal structure of the matrix and the probabilities of their occurrence. The non-radiative energy transfer rates were calculated in the intermediate coupling scheme taking into account the shielding of the 4f electrons. The required partial (that is, forced electric dipole-only, lacking the dynamic coupling contribution) Judd–Ofelt Ωλ parameters were calculated using the Simple Overlap Model (SOM). The spectral overlap factor F was estimated from optical absorption measurements. A simplified “one level-one manifold” energy level scheme was applied. The F7/24,H11/22andS3/24 states of Er3+ were treated as an effective level. The set of rate equations containing radiative, non-radiative and energy transfer processes was solved numerically using fourth-order Runge–Kutta method. Both continuous and pulsed excitation modes were simulated. The dependence of the upconversion intensity upon the pump power was found. The simulations resulted in good agreement with the experimental results and provided new insights into the dynamics of the upconversion process and a connection between the macroscopic properties and the microscopic description.

Anisotropy of the spectroscopic, optical and thermo-mechanical properties of Li_6Eu_1-xGd_x(BO_3)_3 crystals optimized for heat-scintillation cryogenic bolometers

Optical, spectroscopic and thermo-mechanical properties of monoclinic Li6Eu1-xGdx(BO3)3 (x = 0,0.25,0.35) bulk single crystals, grown to be used in the design of heat-scintillation cryogenic bolometers (HSCBs), were investigated. The linear thermal expansion was determined along the a, b, c and c* directions over the temperature range 303–873 K, and its tensor principal coefficients were calculated for both x = 0.25 and x = 0. In addition, the anisotropic thermal conductivity was measured over the temperature range 20-400 K in Li6Eu0.75Gd0.25(BO3)3 (LGEB7, x = 0.25), and the principal components of its tensor at 300 K were established. Spectroscopic properties such as polarized absorption, polarized emission, Raman spectroscopy and optical refractive indices are also reported for the first time. Based on the polarized emission spectra, the line and oscillator strengths, the radiative lifetimes and fluorescent branching ratios were obtained. The intensity parameters Ωλ (λ = 2,4) were obtained and then predicted via the Judd–Ofelt theory. The crystal field parameters and the 7F1 level splitting were discussed using the simple overlap model (SOM) and the method of equivalent nearest neighbours (MENN). The 613 nm emission originates from the 5D0→7F2 transition and the associated stimulated emission peak cross section reaches its maximum value in π-polarization, ≈1.07 × 10−20 cm2 in LGEB7. The thermo-mechanical characterizations and spectroscopic analysis in LGEB7 suggest that this crystal has better optical properties than the Eu3+-doped Li6Y(BO3)3 crystals. However, its potential for solid-state laser applications is still quite speculative, unless a clever thermo-mechanical management of the crystal under laser operation is designed.

An alternative description for the interaction between the Eu3+ ion and its nearest neighbours

The LiYF4:Eu3+ and the Eu (btfa)3(4,4-bipy)(EtOH) compounds are being revisited by the method of equivalent nearest neighbours (MENNs) and the simple overlap model, this time to suggest a comparison between: the europium local symmetry in complexes containing β-diketones and the S4 symmetry in the LiYF4:Eu3+; and the ionic bonding in lanthanide containing compounds as pure electrostatic attraction. The 7F1 level splitting was satisfactorily predicted in both cases by very similar sets of charge factors. This similarity indicates that the lanthanide ion treats the chemical species (N, O and F) in its first neighbourhood merely as negative charges.

Preparation and luminescence properties of Yb3+ activated Gd2GeO5

Polycrystalline Yb:Gd2GeO5 was prepared by solid state reaction method, and its structure, spectral properties, and energy structure were studied. The Yb:Gd2GeO5 belongs to space group P21/c, and its photoluminescence spectrum includes the range from 975 to 1088nm which is one of the known broader emission of Yb3+. The broad emission spectrum is necessary for ultrashort laser operation and laser tuning. Crystal field parameters Bqk and energy levels of Yb3+ at two symmetry sites in Gd2GeO5 were calculated by the simple overlap model, respectively. The calculated energy levels are consistent with the experimental very well. The energy splitting of Yb3+2F7/2 ground state in Gd2GeO5 is up to 1065cm−1. According to Boltzmann distribution, the thermal population ratio of the highest terminal laser level is about 0.605% and less than 2.32% of YAG by one order, which is very beneficial to population inversion. All results indicate that Yb:Gd2GeO5 may be a promising laser crystal material for ultrashort and tunable all-solid laser.

Method for fitting crystal field parameters and the energy level fitting for Yb3+ in crystal SC2O3

A method to compute the numerical derivative of eigenvalues of parameterized crystal field Hamiltonian matrix is given, based on the numerical derivatives the general iteration methods such as Levenberg–Marquardt, Newton method, and so on, can be used to solve crystal field parameters by fitting to experimental energy levels. With the numerical eigenvalue derivative, a detailed iteration algorithm to compute crystal field parameters by fitting experimental energy levels has also been described. This method is used to compute the crystal parameters of Yb3+ in Sc2O3 crystal, which is prepared by a co-precipitation method and whose structure was refined by Rietveld method. By fitting on the parameters of a simple overlap model of crystal field, the results show that the new method can fit the crystal field energy splitting with fast convergence and good stability.

Comparative analysis of crystal-field parameters for rare-earth ions at monoclinic sites inAB(WO4)2 crystals:I. Tm3+ inKGd(WO4)2 andKLu(WO4)2, andHo3+ andEr3+ ionsin KGd(WO4)2

The crystal-field (CF) parameters determined by various authors for rare-earth ions at monoclinic sitesin AB(WO4)2 crystals are reanalyzed using a methodology incorporating several approaches, namely standardization,multiple-correlated fitting technique and closeness of CFP sets. In Part I recent spectroscopic data forTm3+ ions inKGd(WO4)2 (KGdW) andKLu(WO4)2 (KLuW),and Ho3+ and Er3+ ions in KGdW, which were interpreted using the free-ion (FI) and CF parameter (CFP)sets, are thoroughly revisited. Our reanalysis enables clarification of several doubtfulaspects involved in the previous studies. The initial CFPs for fitting, calculatedusing the simple overlap model (SOM), differ markedly from the fitted CFPs forTm3+ ions in KGdW and KLuW. An inspection of the pertinent CFP sets reveals deeper intrinsicdifferences between the model and fitted CFPs. The model CFPs and the fitted CFPs forRE3+ ions in both KGdW and KLuW crystals turn out to be non-standard. Importantly, themodel and fitted CFP sets for Tm-KLuW belong to disparate regions of the CFP space andthus are intrinsically incompatible, i.e. such sets should not be directly compared. Thus theCFP sets reported in the literature require reconsideration in view of the intrinsicproperties of monoclinic CF Hamiltonians previously not taken into account.Standardization of the originally non-standard CFP sets is carried out to ensure directcomparability of the CFP sets in question with other literature data. The correlatedalternative CFP sets are calculated for each original set to facilitate future applications ofthe multiple correlated fitting technique, which enables improving overall reliabilityof the fitted CFPs. The closeness of the standardized CFP sets is assessed in aquantitative way. Our considerations indicate also the importance of proper definitionsof the axis system used in the CFP model calculations and provide argumentsfor the nominal meaning of the axis systems assigned to the fitted CFPs. Theconsistent methodology proposed here may be considered as a general framework foranalysis of CF levels and CFP modelling for rare-earth and transition-metal ionsat monoclinic symmetry sites in crystals. CFP sets for other rare-earth ions inAB(WO4)2 crystals will be reanalyzed in Part II.

Bulk crystal growth and efficient diode-pumped laser performance of Yb3+:Sc2SiO5

A bulk crystal of Yb:Sc2SiO5 (Yb:SSO) with favorable thermal properties was successfully obtained by the Czochralski method. The energy level diagrams for Yb:SSO crystal were determined by optical spectroscopic analysis and semi-empirical crystal-field calculations using the simple overlap model. The full width at half maximum of the absorption band centering at 976 nm was calculated to be 24 nm with a peak absorption cross-section of 9.2×10-21 cm2. The largest ground-state splitting of Yb3+ ions is up to 1027 cm-1 in a SSO crystal host. Efficient diode-pumped laser performance of Yb:SSO was primarily demonstrated with a slope efficiency of 45% and output power of 3.55 W.

(3+1)-dimensional hydrodynamic expansion with a critical point from realistic initial conditions

We investigate a (3+1)-dimensional hydrodynamic expansion of the hot and dense system created in head-on collisions of Pb+Pb/Au+Au at beam energies from 5 to 200 GeV/nucleon. An equation of state is used that incorporates a critical end point (CEP) in line with the lattice data. The necessary initial conditions for the hydrodynamic evolution are taken from a microscopic transport approach, the ultrarelativistic quantum molecular dynamics (UrQMD) model. We compare the properties of the initial state and the full hydrodynamic calculation with an isentropic expansion employing an initial state from a simple overlap model. We find that the specific entropies ($S/A$) from both initial conditions are very similar and only depend on the underlying equation of state. Using the chiral (hadronic) equation of state, we investigate the expansion paths for both initial conditions. Defining a critical area around the critical point, we show at what beam energies one can expect to have a sizable fraction of the system close to the critical point. Finally, we emphasize the importance of the equation of state of strongly interacting matter in the (experimental) search for the CEP.

Electrostatic equilibrium and charge factors in lanthanide complexes

Based on electrostatics and symmetry, a method to define equivalent nearest neighbours (NN) of the lanthanide ion in complexes is described. Equivalent NN have the same charge factor. The sum of the NN charge factor is required to equal the central ion valence. The high coordination number in lanthanide complexes is explained and the effective charge of the Simple Overlap Model is interpreted as a quantitative demonstration of the weak crystal-field perturbation on the luminescent site. The discussion on the central ion charge is made using the Batista–Longo Improved Model.

Theoretical investigation of the 7F1 level splitting in a series of Eu3+ doped oxides matrixes

The point charge electrostatic model (PCEM) and the simple overlap model (SOM) are applied to a series of oxide crystals (Gd2O3, Y2O3, Lu2O3, In2O3 and Sc2O3) and a silicate glass (Al2O3–SiO2) doped with the Eu3+ ion. The SOM factor ρ(2β)k+1 is input as the shielding factor for all Bqk expressions, which enters in the calculations of the crystal-field strength parameter, NV. The maximum splitting ΔE of the 7F1 manifold of the Eu3+ ion is then obtained as a function of NV. It has been developed another way to calculate alpha, which is an expansion factor in the ΔE expression. For the glass, as the mean metal-ligating ions distances are larger than for the crystals, NV and ΔE are smaller, as expected. The prediction of the PCEM shows a linear dependence between ΔE and NV, even though the known mismatch in respect to the experimental splitting is kept. In the case of the SOM, two situations have been analyzed: firstly the charge factor varies in order to reproduce the experimental splitting (a phenomenological procedure); secondly the charge factor is the valence of the oxygen ions. The agreement between the experimental results and theoretical predictions for all investigated systems is very satisfactory in respect to both the linearity between ΔE and NV and the ΔE splitting.