Method for fitting crystal field parameters and the energy level fitting for Yb^(3+) in crystal Sc_2O_3

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 Yb^3＋ 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.

The mixed-spins 1/2 and 3/2 Blume-Capel model with a random crystal field

The random crystal field （RCF） effects are investigated on the phase diagrams of the mixed-spins 1/2 and 3/2 Blume-Capel （BC） model on the Bethe lattice. The bimodal random crystal field is assumed and the recursion relations are employed for the solution of the model. The system gives only the second-order phase transitions for all values of the crystal fields in the non-random bimodal distribution for given probability. The randomness does not change the order of the phase transitions for higher crystal field values, i.e., it is always second-order, but it may introduce first-order phase transitions at lower negative crystal field values for the probability in the range about 0.20 and 0.45, which is only the second-order for the non-random case in this range. Thus our work claims that randomness may be used to induce first-order phase transitions at lower negative crystal field values at lower probabilities.

Analyses of crystal field and exchange interaction of Dy_3Ga_5O_(12) under extreme conditions

This paper theoretically investigates the effects of crystal field and exchange interaction field on magnetic properties in dysprosium gallium garnet under extreme conditions （low temperatures and high magnetic fields） based on quantum theory. Here, five sets of crystal field parameters are discussed and compared. It demonstrates that, only considering the crystal field effect, the experiments can not be successfully explained. Thus, referring to the molecular field theory, an effective exchange field associated with the Dy-Dy exchange interaction is further taken into account. Under special consideration of crystal field and the exchange interaction field, it obtains an excellent agreement between the theoretical results and experiments, and further confirms that the exchange interaction field between rare-earth ions has great importance to magnetic properties in paramagnetic rare-earth gallium garnets.

Relation between stabilization energy, crystal field coefficient and the magnetic exchange interaction for Tb^(3+) ion

Based on a single ion model, Hamiltonian of the simplest form about magnetocrystalline anisotropy for Tb3+ ion was solved by using the numerical method. The relation between the stabilization energy, crystal field coefficient B20 and the magnetic exchange interaction was studied as temperature approaches to 0 K. The results show that the stabilization energy contributed by Tb3+ is linear with crystal field coefficient B20 approximately, but it is insensitive to the change of magnetic exchange interaction for the strong magnetic substances such as TbCo5, Tb2Co17 and Tb2Fe14B compounds.

Phase diagrams of spin-3/2 Ising model in the presence of random crystal field within the effective field theory based on two approximations

The bimodal random crystal field （A） effects are investigated on the phase diagrams of spin-3/2 Ising model by using the effective-field theory with correlations based on two approximations： the general van der Waerden identity and the approximated van der Waerden identity. In our approach, the crystal field is either turned on or turned off randomly for a given probability p or q = 1 -p, respectively. Then the phase diagrams are constructed on the （A,kT/J） and （p,kT/J） planes for given p and A, respectively, when the coordination number is z = 3. Furthermore, the effect of randomization of the crystal field is illustrated on the （△,kT/J） plane for p = 0.5 when z - 3,4, and 6. All these are carried out for both approximations and then the results are compared to point out the differences. In addition to the lines of second-order phase transitions, the model also exhibits first-order phase transitions and the lines of which terminate at the isolated critical points for high p values.

Phase diagrams of the spin-2 Ising model in the presence of a quenched diluted crystal field distribution

We have investigated the random crystal field effects on the phase diagrams of the spin-2 Blume-Capel model for a honeycomb lattice using the effective-field theory with correlations. To do so, the thermal variations of magnetization are studied via calculating the phase diagrams of the model. We have found that the model displays both second-order and first-order phase transitions in addition to the tricritical and isolated points. Reentrant behavior is also observed for some appropriate values of certain system parameters. Besides the usual ground-state phases of the spin-2 model including ±2, ~1, and 0, we have also observed the phases ±3/2 and ±1/2, which are unusual for the spin-2 case.

Effective-Field Theory on High Spin Systems with Biaxial Crystal Field

Based on the effective-field theory with self-spin correlations and the differential operator technique, physical properties of the spin-2 system with biaxial crystal field on the .simple cubic, body-centered cubic, as well as faced-centered lattice have been studied. The influences of the external longitudinal magnetic field on the magnetization, internal energy, specific heat, and susceptibility have been discussed in detail The phenomenon that the magnetization in the ground state shows quantum effects produced by the biaxial transverse crystal field has been found.

Extracting structural information from low symmetry crystal field parameters-case study:Er^(3+) and Nd^(3+) ions in YAlO_3

The experimental monoclinic CF parameter （CFP） sets obtained by Duan et al. （Phys. Rev. B 75 （2007） 195130） for Er3＋ and Nd3＋ ions in YAIO3 were reanalyzed. These CFPs fitted using R-approach, i.e. with the monoclinic second-rank CFP set to zero, and additionally with one six-rank CFP fixed to zero, turned out to be non-standard. In order to understand better the low symmetry aspects involved in the fitted CFPs and extract useful structtral information inherent in monoclinic CFPs, an approach comprising four methods was utilized. First, superposition model （SPM） was applied to calculate CFPs in the crystallographic axis system. Second, the principal values for the SPM determined CFPs and the orientation of the principal axis system w.r.t, the crystallographic axis system were obtained using the procedure 3DD for diagonalization of the 2rid-rank CFPs. Third, analysis of higher symmetry approximations, i.e. orthorhombic and tea＇agonal, was carried out using the pseudosymmetry axes method. Fourth, the closeness factors and norm ratios were employed for quantitative comparisons of various CFP sets. Partial results for Er3＋ ions in YAlO3 were presented here, whereas detailed results would be given in a follow-up paper.

First-principles study of the local structure and crystal field of Yb^(2+) in sodium and potassium halides

The local coordination structures around the doping Yb2＋ ions in sodium and potassium halides were calculated by using the first-principles supercell model. Both the cases with and without the charge compensation vacancy in the local environment of the doping Yb2＋ were calculated to study the effect of the doping on the local coordination structures of Yb2＋. Using the calculated local structures, we obtained the crystal-field parameters for the Yb2＋ ions doped in sodium and potassium halides by a method based on the combination of the quantum-chemical calculations and the effective Hamiltonian method. The calculated crystal-field parameters were analyzed and compared with the fitted results.

Ground-State Phase Diagram of Transverse Spin-2 Ising Model with Longitudinal Crystal-Field

The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram and the tricritical point are obtained in the transverse field Ω/ zJ-longitudinal crystal D / zJ field plane. We find that there are the first order-order phase transitions in a very small range of D /zJ besides the usual first order-disorder phase transitions and the second order-disorder phase transitions,

Spin-1 Blume-Capel model with longitudinal random crystal and transverse magnetic fields:A mean-field approach

The spin-1 Blume–Capel model with transverse and longitudinal external magnetic fields h, in addition to a longitudinal random crystal field D, is studied in the mean-field approximation. It is assumed that the crystal field is either turned on with probability p or turned off with probability 1 p on the sites of a square lattice. Phase diagrams are then calculated on the reduced temperature crystal field planes for given values of γ=Ω/J and p at zero h. Thus, the effect of changing γ and p are illustrated on the phase diagrams in great detail and interesting results are observed.

Crystal field and magnetism with Wannier functions: rare-earth doped aluminum garnets

Using the recently developed method we calculated the crystal field parameters m yttrium anct lutetium aluminum garnets doped with seven trivalent Krarners rare-earth ions. We then inserted calculated parameters into the atomic-like Hamiltonian taking into account the electron-electron, spin-orbit and Zeeman interactions and determined the multiplet splitting by the crystal field as well as magnetic tensors. We compared calculated results with available experimental data. Very good agreement with the spectroscopic data and qualitative agreement with experimental tensors was found.

Effects of crystal field on photoluminescence properties of Ca_2Al_2SiO_7:Eu^(2+) phosphors

A series of single-phased Ca2Al2SiOT：EU2＋phosphors were synthesized by the solid-state reaction. Their structure and photoluminescence properties were investigated by the X-ray powder diffraction （XRD） and excitation and emission spectra in detail. The emission spectra of Ca2Al2SiO7：Eu2＋ phosphors consisted of blue and green band located at 419 and 542 nm, respectively. The relative intensities of the blue and green emission changed with Eu2＋ concentration and were sensitive to the excitation wavelength. The unique photoluminescence property originated from the 4f^7→4f65d transition of Eu2＋ at different energy levels, on which the effect of the crystal field strength was con- sidered to be tailed by adjusting the host composition.

Phase Transition for a Mixed Spin-1／2 and Spin-sB System with a Transverse CrystalField

The critical behaviors of a mixed spin-1/2 and spin-sB Ising system with a transverse crystal field are studiedby use of the effective-field theory with correlations. The effect of the transverse crystal field on transition temperaturesis investigated numerically for the honeycomb (z = 3) and square (z = 4) lattices. The results show that there is notricritical point for the system.

Effect of high magnetic field on the crystallization of Nd_2Fe_(14)B/α-Fe nanocomposite magnets

Nd8.1Dy0.9Fe76.95Co8.55B5.5 nanocomposite magnets annealed with and without a 10 T magnetic field were investigated in this article. The ribbons with coexisting amorphous and crystalline phases were selected to do this study. The resuits of Moessbauer spectroscopy revealed that the content of α--Fe increased when annealed in high strength magnetic field. The size of the grains also increased considerably after the application of magnetic annealing. All these led to the decrease of the magnetic properties, especially the coercivity of the ribbons.

Morphological evolution and growth kinetics of Kirkendall voids in binary alloy system during deformation process-Phase field crystal simulation study

The formation and growth of Kirkendall voids in a binary alloy system during deformation process were investigated byphase field crystal model.The simulation results show that Kirkendall voids nucleate preferentially at the interface,and the averagesize of the voids increases with both the time and strain rate.There is an obvious coalescence of the voids at a large strain rate whenthe deformation is applied along the interface under both constant and cyclic strain rate conditions.For the cyclic strain rate appliedalong the interface,the growth exponent of Kirkendall voids increases with increasing the strain rate when the strain rate is largerthan1.0×10-6,while it increases initially and then decreases when the strain rate is smaller than9.0×10?7.The growth exponent ofKirkendall voids increases initially and then decreases gradually with increasing the length of cyclic period under a square-waveform constant strain rate.

Optical high-resolution spectroscopic study of Tm^(3+) crystal-field levels in LiLuF_4

We report on the fast high-resohition study of LiLuF4：Tm3＋. The accurate energy level scheme of Tm3＋ in the LiLuF4 matrix was obtained for the 3H6.5.4, 3F4.3.2, and ^1G4 multiplets. It was shown that electric-dipole transitions dominate for all the studied multiplets except the 3H5 one.

A phase-field model for simulating various spherulite morphologies of semi-crystalline polymers

A modified phase-field model is proposed for simulating the isothermal crystallization of polymer melts. The model consists of a second-order phase-field equation and a heat conduction equation. It obtains its model parameters from the real material parameters and is easy to use with tolerable computational cost. Due to the use of a new free energy functional form, the model can reproduce various single crystal morphologies of polymer melts under quiescent conditions, including dendritic, lamellar branching, ring-banded, breakup of ring-banded, faceted hexagonal, and spherulitic structures. Simulation results of isotactic polystyrene crystals demonstrate that the present phase-field model has the ability to give qualitative predictions of polymer crystallization under isothermal and quiescent conditions.

SOLIDIFICATION OF NICKEL-BASED SINGLE CRYSTAL SUPERALLOY BY ELECTRIC FIELD

The crystal growth of a nickel-based single crystal superalloy DD3 was researched via controlled directional solidification under the action of a DC electric field. The cellular or dendrite spacing of the single crystal superalloy is refined and microsegregation of alloying elements Al, Ti, Mo and W, is reduced by the electric field. The electric field decreases the interface stability and reduces the critical growth rate of the ceUular-dendritic translation because of Thomson effect and Joule heating. The precipitation of the γ＇ phase is more uniform and the size of the γ＇ phase is smaller with the electric field than that without the electric field.

A numerical study on pattern selection in crystal growth by using anisotropic lattice Boltzmann-phase field method

Pattern selection during crystal growth is studied by using the anisotropic lattice Boltzmann-phase field model.In the model,the phase transition,melt flows,and heat transfer are coupled and mathematically described by using the lattice Boltzmann(LB)scheme.The anisotropic streaming-relaxation operation fitting into the LB framework is implemented to model interface advancing with various preferred orientations.Crystal pattern evolutions are then numerically investigated in the conditions of with and without melt flows.It is found that melt flows can significantly influence heat transfer,crystal growth behavior,and phase distributions.The crystal morphological transition from dendrite,seaweed to cauliflower-like patterns occurs with the increase of undercoolings.The interface normal angles and curvature distributions are proposed to quantitatively characterize crystal patterns.The results demonstrate that the distributions are corresponding to crystal morphological features,and they can be therefore used to describe the evolution of crystal patterns in a quantitative way.