Crystal Field Model Research Articles

Magnetic interplay of Mn and Yb sites in YbMn2Si2 – Crystal field splitting

The crystal field splitting of YbMn2Si2 has been investigated over the temperature range 5–65 K using inelastic neutron scattering at a wavelength of 2.345 Å (resolution 800 μeV; dynamic range ∼10 meV). The excitation spectra have been analysed using a crystal field model above and below TN2, the temperature at which the collinear antiferromagnetic structure AFil transforms to the low-temperature structure in which the magnetic cell is doubled along the c-axis (TN1 = 526(4) K > T > TN2 = 32(2) K). The calculated excitation spectra show good agreement with the observed spectra for the unique environment of Yb3+ ions in the collinear antiferromagnetic structure AFil above TN2 and for the inequivalent sites of Yb3+ ions below TN2. This agreement has been obtained with a model for the low-temperature region in which a molecular field with optimal components in the x, y and z directions of Bx = 13.5 T, By = 65 T, Bz = 21.3 T is included. The pronounced components in the x and y directions are discussed in relation to the significant contraction of ∼0.1% of the c lattice parameter below the TN2 magnetic transition.

Correction to “Quantifying the σ and π Interactions between U(V) f Orbitals and Halide, Alkyl, Alkoxide, Amide and Ketimide Ligands”

Author(s): Lukens, Wayne W; Edelstein, Norman M; Magnani, Nicola; Hayton, Trevor W; Fortier, Skye; Seaman, Lani A | Abstract: While preparing a follow-up manuscript, we found an error in one of the orbital reduction factors used in our crystal field models, given in Scheme 2. The third equation in that scheme was published as ka2t2 = 1 - 12 N2 2 a'p ; however, the correct formula is k a2t2 = 1 - 12 N'a'p2. (Table Presented).

A coupled crystal plasticity FEM and phase-field model for crack evolution in microstructures of 7000 series aluminum alloys

A coupled crystal plasticity-phase field (CP-PF) model is developed in this paper for analyzing crack nucleation and propagation in polyphase-polycrystalline microstructures of Aluminum 7000 alloys. The model explicitly represents elastic and plastic anisotropies, tension-compression asymmetry, and the crack surface topology in the material. The phase field model incorporates a regularization length-scale lc that controls the sharpness of the phase-field approximation to the discrete crack. A novel adaptive wavelet-enriched hierarchical FE augmentation is developed for the coupled CP-PF model. It has the unique capability of optimally resolving high gradients in the phase field order parameter s near the crack surface. Parametric studies are conducted with one and two precipitate RVEs in an Al matrix to understand the effect of microstructure and loading on crack evolution. Finally, an image-based microstructural model is developed and simulated to predict crack initiation, growth, and propagation in microstructures of the Al alloy Al7075-T651.

Effect of magnetic anisotropy on direct chiral discrimination in paramagnetic NMR spectroscopy.

We present and analyse a complete analytic expression for the generalized shielding polarizability third-rank tensor Φαβγ, whose isotropic average, the pseudoscalar [capital Phi, Greek, macron], is proportional to a chiral macroscopic electric polarization P measurable in a pulsed nuclear magnetic resonance (NMR) experiment probing molecules with an arbitrarily degenerate ground state, in solution. We have recently predicted that [capital Phi, Greek, macron] can be measurable at room temperature in chiral paramagnetic molecules, and identified strong magnetic anistropy (as featured e.g. in lanthanide complexes) as a crucial molecular property to achieve room temperature chiral discrimination using NMR spectroscopy. As previously proposed, the components of Φαβγ are obtained as analytical third derivatives of the electronic free energy. Here we present the explicit calculation of these derivatives, which provide working expressions for the explicit accurate ab initio calculation of Φαβγ. We apply our theory by performing ab initio multiconfigurational calculations of all contributions to Φαβγ, for a set of ten DyIII complexes, characterized by a strongly axial ground Kramers doublet, but also by thermally accessible excited Kramers doublets at room temperature. The results show that the thermally populated excited state contributions, while generally reducing the value of [capital Phi, Greek, macron] calculated on the assumption of a thermally isolated ground state, still confirm the room temperature detectability of this property for all ten studied complexes. Trends on the relative sign of dominant contributions are then discussed on the basis of a crystal field model electrostatic potential splitting a ground spin-orbit multiplet, which provides an insight into the properties of the generalized shielding polarizability tensor for open shell species.

Integrated crystal plasticity and phase field model for prediction of recrystallization texture and anisotropic mechanical properties of cold-rolled ultra-low carbon steels

A multi-scale approach integrating a polycrystal plasticity finite element (CPFEM) and a multi-phase field model (PFM) is developed in this study and employed to the prediction of anisotropic mechanical properties of annealed ultra-low carbon steel. The CPFEM simulates inhomogeneous local deformation and orientation distribution of ultra-low carbon steel, while the PFM predicts microstructure evolution originating from nucleation and growth. The present study highlights a systematic modeling process including reduction of the stored energy by the recovery process, nucleation of grains with preferred orientation based on generalized strain energy release maximization theory (GSERM), and grain growth with consideration of the stored energy difference and misorientation between neighboring grains, which are provided from local effects in the CPFEM. The two computational approaches are numerically mapped by the Wigner-Seitz cell method to efficiently transfer state variables between the domains of finite element and finite difference schemes for CPFEM and PFM, respectively. The proposed multiscale model is quantitatively validated through experimentally measured microstructural characteristics of annealed ultra-low carbon steel after the rolling deformation, i.e., its recrystallization texture in the aspect of pole figures and ODF, grain size, and distributions. Finally, the predicted microstructural information after the thermo-mechanical process is used as input for virtual mechanical tests simulating orientation-dependent tensile properties. The comparison of predicted orientation-dependent yield stresses and Lankford coefficients as measures for anisotropic mechanical properties with those of experiments confirm the validity and accuracy of the proposed CPFEM-PFM approach as an efficient tool for understanding the relationship between the thermo-mechanical process, microstructure, and mechanical properties in the material design stage.

Wavelet-enriched adaptive hierarchical FE model for coupled crystal plasticity-phase field modeling of crack propagation in polycrystalline microstructures

This paper develops a novel, wavelet-enriched adaptive finite element model for solving coupled crystal plasticity-phase field models to simulate crack propagation in polycrystalline microstructures. No a-priori assumption of the crack path is needed. Crack propagation under conditions of finite deformation is driven by stored elastic energy that accounts for material anisotropy and tension–compression asymmetry, and defect energy resulting from slip system dislocation glide and hardening. The resulting finite element model is capable of simulating both brittle and ductile crack propagation in material microstructures. A major contribution of this work is the creation of the adaptive, multi-resolution wavelet-based hierarchical enrichment of the FE model. The adapted enrichment follows the path of crack growth and is able to successfully overcome the challenges of high resolution required for the regularized crack in the coupled model. The multi-resolution wavelet basis functions adaptively construct optimal enrichment basis for the high gradients in the phase field order parameter near the crack path. The wavelet-enriched adaptive finite element model is found to be robust with excellent convergence characteristics in multiple validation tests conducted with the polycrystalline Ti–6V–4Al alloy.

Intrinsic electronic excitations and impurity luminescent centres in NaMgF3 and MgF2 doped with Yb2+

The relaxation pathways of states in the energy region of the fundamental absorption of NaMgF3:Yb2+ and MgF2:Yb2+ are investigated using time-resolved vacuum ultraviolet spectroscopy. For NaMgF3:Yb2+, excitation into intrinsic free exciton states or above the band gap results in emission features associated with self-trapped excitons and impurity-trapped excitons. Excitation into host-related states of MgF2:Yb2+ similarly exhibits self-trapped exciton emission as well as emission from Yb2+ 4f135d states. The excitation features related to Yb2+ 4f14→4f135d transitions are interpreted using semi-empirical crystal field models. For both materials, the interplay between intrinsic distortions and Yb impurity centres, as the excitation wavelength and sample temperature are varied, is presented and analysed.

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.

Magnetic properties of Ho0.9Er0.1Fe3(BO3)4

The magnetic properties of Ho0.9Er0.1Fe3(BO3)4 ferroborate with the competing Ho–Fe and Er–Fe exchange couplings have been experimentally and theoretically investigated. The measured magnetic characteristics (Ma,c(B), χa,c(T)) and observed features are interpreted using a single theoretical approach based on the molecular-field approximation and calculations within the crystal-field model of the rare-earth ion. Interpretation of the experimental data includes determination of the crystal-field parameters for Ho3+ and Er3+ ions in Ho0.9Er0.1Fe3(BO3)4 and parameters of the Ho–Fe and Er–Fe exchange couplings.

Dependence of the Mn4+ spectroscopic properties on the host composition: Case study of stannate pyrochlores A2Sn2O7 (A = La, Gd, Y, Lu)

In this paper we have studied the spectroscopic properties of Mn4+ in four stannate pyrochlores A2Sn2O7 (A = La, Gd, Y, Lu). Photoluminescence and photoluminescence excitation spectra were recorded at low temperature. The Mn4+ energy levels in all four hosts were calculated using the exchange charge model of crystal field. Consistent variation of the main spectroscopic features with the lattice constant and Mn–O distance are revealed. The findings of this combined experimental and theoretical study may be used to predict the Mn4+ spectroscopic characteristics in other similar materials.

Magnetic order and single-ion anisotropy inTb3Ga5O12

Terbium gallium garnet (TGG), Tb$_3$Ga$_5$O$_{12}$, is well known for its applications in laser optics, but also exhibits complex low-temperature magnetism that is not yet fully understood. Its low-temperature magnetic order is determined by means of time-of-flight neutron powder diffraction. It is found to be a multiaxial antiferromagnet with magnetic Tb$^{3+}$ ions forming six sublattices of magnetic moments aligned parallel and anti-parallel to the $\langle100\rangle$ crystallographic directions of the cubic unit cell. The structure displays strong easy-axis anisotropy with respect to a two-fold axis of symmetry in the local orthorhombic environment of the Tb$^{3+}$ sites. The crystal-field splitting within the single-ion ground-state manifold is investigated by inelastic neutron scattering on powder samples. A strong temperature dependence of the quasidoublet ground-state is observed and revised parameters of the crystal-field Hamiltonian are given. The results of bulk magnetic susceptibility and magnetisation measurements are in good agreement with values based on the crystal-field model down to 20~K, where the onset of magnetic correlations is observed.

Modeling length scale effects on strain induced grain boundary migration via bridging phase field and crystal plasticity methods

A coupled crystal plasticity and phase field modeling framework is employed to simulate polycrystalline grain growth via static strain induced grain boundary migration. Specifically, the effect of the average grain size as a microstructural length scale on the development of microstructure and texture in columnar–grained aluminum polycrystal is examined. During annealing, subsequent to plastic tensile straining, a nearly normal grain growth regime is observed for comparatively small microstructural length scales. However, for comparatively large microstructural length scales, abnormal grain growth and development of a specific texture emerge. Hence, grain growth is found to transition from normal to abnormal by enlarging the microstructural length scale. These observations are attributed to the fact that the competing driving forces for grain boundary migration scale differently with the microstructural length scale. In addition, for the case of large microstructural length scale, a transition from abnormal to normal grain growth at later annealing times is observed. This observation is attributed to the weakening of the strain induced boundary migration effects due to the initial rapid reduction of dislocation content.

Coupled Crystal Plasticity-Phase Field Modeling of Multi-Phase Metals

A code has been developed based on image based crystal plasticity modeling of multiphase metals. This model coupled with equilibrium equation and compatibility constraint is solved at each material point of representative volume element. A phenomenological equation for dislocation slip is used. Crystal kinematics couples the boundary conditions to constitutive behavior by integrating evolution equation for elastic deformation gradient obtained using the multiplicative decomposition of deformation. The code is tested for linear homogeneous isotropic elastic material with embedded inclusions. We analyze two types of inclusions namely an elastic inclusion and a void. These two baseline studies have been compared against solutions from currently available commercial and open source packages. In the second example we study the time evolution of residual stresses due to a growing phase. Such models are especially useful for understanding the role of interactions and co-deformation of multiple phases on the overall mechanical response of a multiphase metal. Experimental data set found in the literature is used for calibration of the developed crystal plasticity model.

Spin-Hamiltonian parameters and tetragonal distortion for the (WO6)7− octahedral centers in the WO3-doped Zn(PO4)2 ZnO nanopowders

The spin-Hamiltonian parameters (g factors g//, g⊥ and hyperfine structure constants A//, A⊥) of the tetragonal (WO6)7− octahedral center in the WO3-doped Zn(PO4)2ZnO nanopowders are investigated from the high-order perturbation formulas resting on the two-mechanism (crystal-field and charge-transfer mechanisms) model with a suitable assignment of the absorption band at about 14,370 cm−1. The calculated results are in keeping with the experimental values. The tetragonal distortion of the (WO6)7− octahedral center is also achieved on the basis of the calculation. The outcomes are discussed.

Research on the defect structure and g factors for the tetragonal (CrO4)3− impurity center in ZrSiO4: Cr5+ crystal

ABSTRACTThe EPR g factors g// and g⊥ for the tetragonal (CrO4)3− impurity center in ZrSiO4: Cr5+ crystal are studied from the high-order perturbation formulas based on the two-mechanism (the crystal field and charge-transfer mechanisms) model. The studies indicate that differing from the tetragonally-elongated host (SiO4)4- tetrahedron, the dominant defect structure of the substitutional (CrO4)3− tetrahedron is tetragonally- compressed with the ground state |dz2 due to the Jahn-Teller distortion. Furthermore, the agreement of g factors between calculation and experiment requires a small admixture of the first excited state |dx2−y2 to the ground state |dz2 due to the vibrational motion of ligands, which leads a compressed (CrO4)3− tetrahedron to become a twinkling elongated one, These results are discussed.

Determination of the g-factors measured by EPR based on theoretical crystal field and superposition model analyses for lanthanide-based magnetically concentrated crystals – case study: double tungstates and molybdates

ABSTRACTThe methods developed for theoretical determination of g-factors measured by electron paramagnetic resonance (EPR) for single transition ions are extended to lanthanide-based magnetically concentrated crystals. The crystal field (CF) and superposition model (SPM) analyses are employed for optoelectronic materials: double tungstates and molybdates. Using the crystallographic data for Nd3+ ions in RbNd(WO4)2 and Yb3+ ions in KYb(MoO4)2 as input for SPM modelling, the CF parameters (CFPs) are predicted for the respective ions. The matrix for g tensor is calculated by the complete diagonalisation method. By matching three principal g values (gxx, gyy, gzz) to those measured by EPR, three adjustable SPM intrinsic parameters:, and are obtained. The reliability of the related CFPs is verified by comparative analysis of available data. The results demonstrate that the methods suitable for single lanthanide ions in crystal can be successfully applied to magnetically concentrated systems. The predicted g tensor anisotropy enables consideration of EPR linewidths arising from dipolar broadening in ALn(MO4)2 (A = alkali ions, Ln = lanthanide ions, M = W or Mo) systems based on the moment method, which requires accurate g-factors. The model parameters determined here may be utilised for SPM/CFP calculations for Nd3+ and Yb3+ ions in single-molecule magnets and single-ion magnets.

Theoretical studies of the Spin Hamiltonian parameters and local structures for Cu2+ centers in MNB ternary glasses

ABSTRACTThe spin Hamiltonian parameters (g factors g|| and g⊥ and the hyperfine structure constants A|| and A⊥) for the doped Cu2+ ion (in the form of CuO) in ternary glasses (i.e. xMgO·(30-x)Na2O·69B2O3·CuO, with 5 < x < 17 mol%) are theoretically investigated based on the high-order perturbation formulas for a tetragonally elongated octahedral 3d9 complex. In these formulas, the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the spin Hamiltonian parameters with the tetragonal distortion (characterized by relative tetragonal elongation δ along the C4 axis due to the Jahn–Teller effect) of [CuO6]10− cluster. The concentration dependences of the spin Hamiltonian parameters are illustrated by the approximately linear increases of the cubic field parameter Dq and the covalency factor N as well as the relative elongation δ with increasing the MgO concentration x. Based on the calculation, the [CuO6]10− clusters in the MNB glasses are found to suffer the relative elongations of about δ (≈ 0.125 Å) along the tetragonal axis due to the Jahn–Teller effect. The theoretical results show good agreement with the experimental data. And the improvement is also achieved in present work with respect to the previous theoretical analysis based on the conventional crystal-field model formulas by including the ligand orbital and spin–orbit coupling contributions.

Magnetic and Magnetodielectric Properties of Ho0.5Nd0.5Fe3(BO3)4

The magnetic and magnetodielectric properties of Ho0.5Nd0.5Fe3(BO3)4 ferroborate with the competing Ho–Fe and Nd–Fe exchange couplings have been experimentally and theoretically investigated. Step anomalies in the magnetization curves at the spin-reorientation transition induced by the magnetic field B ║ c have been found. The spontaneous spin-reorientation transition temperature TSR ≈ 8 K has been refined. The measured magnetic properties and observed features are interpreted using a single theoretical approach based on the molecular field approximation and calculations within the crystal field model of the rare-earth ion. Interpretation of the experimental data includes determination of the crystal field parameters for Ho3+ and Nd3+ ions in Ho0.5Nd0.5Fe3(BO3)4 and parameters of the Ho–Fe and Nd–Fe exchange couplings.

Origin of near-infrared luminescence in Bismuth-doped silica and germanosilicate glass fibers: Crystal field modeling

Bismuth-doped silica-based glasses have already been proved to be promising materials for the fiber lasers and amplifiers operating in the near-infrared (NIR) spectral region. However, the development of such devices, which would have eligible efficiency, is impossible without a solid understanding of the NIR emitting center's nature. In the present work, based on the crystal field calculations we demonstrate that in silica and germanosilicate glasses this center is a univalent Bi ion affected by a rather strong local crystal field. According to our results, a transition from the first excited state to the ground state in Bi+ causes the famous NIR photoluminescence. The relatively high degree of reduction of the spin-orbit coupling constant indicates, most probably, the formation of weak covalent bonding of Bi+ with ions of the environment.

Crystal field in NdPd5Al2 investigated by inelastic neutron scattering

We report on inelastic neutron scattering measurements of the antiferromagnetic NdPd5Al2 compound. NdPd5Al2 crystallizes in the tetragonal I4/mmm space group and exhibits a distinct uniaxial anisotropy due to crystal field effects. In this study, we have revealed the crystal field energy levels of NdPd5Al2 composed of five Kramers doublets. The corresponding four inelastic excitations are located at energies 3.0 meV, 7.4 meV, 8.6 meV and 17.1 meV. We additionally interpreted the neutron spectra within a crystal field model. It has been established that the crystal field parameters found by a Monte Carlo technique and the derived ground-state wavefunctions consisting primarily of the states reproduce correctly magnetic susceptibility data.