Crystal growth,structure and crystal field splitting and fitting of Yb:GdScO_(3)

A good quality(5 at.%Yb:GdScO_(3))single crystal of F30 mm37 mm was grown successfully by the Czochralski method.Its structure is studied by the x-ray diffraction(XRD),and its atomic coordinates are obtained by Rietveld refinement.The crystal field energy level splitting of Yb^(3+)in GdScO_(3) is determined by employing the absorption and photoluminescence spectra at 8 K.Only ^(2)F_(7/2)(4)is far from the ground state ^(2)F_(7/2)(1)by 710 cm-1 among the crystal field energy levels split from ^(2)F_(7/2),so it is more easier to realize the laser operation of ^(2)F5/2(1)^(2)F_(7/2)(4)with wavelength 1060 nm.The spin–orbit coupling parameters and intrinsic crystal field parameters(CFPs).The intrinsic crystal field parameters¯B k(k=2,4,6)of the crystal were fitted by the superposition model.The CFPs evaluated with¯Bk and coordination factor are taken as the initial parameters to fit the crystal field energy levels of the crystal,and the crystal field parameters Bk q are obtained finally with the root-mean-square deviation 9 cm-1.It is suggested that the ligand point charge,covalency and overlap interaction are slightly weaker than charge interpenetration and coulomb exchange interaction for Yb^(3+)in GdScO_(3).The obtained Hamiltonian parameters can be used to calculate crystal field energy levels and wave functions of Yb:GdScO_(3) to analyze the mechanism of the luminescence or laser.

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.

Pressure Effects on Spectra of Tunable Laser Crystal GSGG:Cr3+ II: Energy Spectra at Normal Pressure, Low and Room Temperatures

With the strong-field scheme and trigonal bases, the complete d3 energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the normal-pressure energy spectra and wavefunctions of GSGG:Cr3+ at 70 K and 300 K have been calculated without the electron-phonon interaction (EPI), respectively. Further, the contributions to energy spectra from EPI at two temperatures have also been calculated, where temperature-independent terms of EPI are found to be dominant. The sum of aforementioned two parts gives rise to the total energy spectrum. The calculated results are in good agreement with all the optical-spectral experimental data and the experimental results of and . It is found that the contribution from EPI to R1 line of GSGG:Cr3+ with taking into account spin-orbit interaction (Hso) and trigonal field (Vtrig) is much larger than the one with neglecting Hso and Vtrig, and accordingly it is essential for the calculation of the EPI effect to take first into account Hso and Vtrig. The admixture of base-wavefunctions,and , the average energy separation and their variations with temperature have been calculated and discussed.

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,

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.

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.

Theoretical analysis of the anisotropy of the magnetization of the Ho^(3+) ion in holmium iron garnet single crystals

The spontaneous magnetization of the Ho^3＋ ion in holmium iron garnet （HoIG） single crystals in the temperature range of 4.2-294K along the directions [111], [110], and [100] are calculated, taking into account the effects of six magnetically inequivalent sites occupied by the Ho^3＋ ions based on the quantum theory. The calculated results show that the magnetization of the Ho^3＋ ion in HoIG is obviously anisotropic. The theoretical results ave in agreement with those of experiments. A primary interpretation of the anisotropy of magnetization of the Ho^3＋ ion in HoIG is put forward.

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.

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.

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.

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.

Phase field crystal study of the crystallization modes within the two-phase region

Using the phase field crystal approach, the crystallization process within the liquid-solid coexistence region is inves- tigated for a square lattice on an atomic scale. Two competing growth modes, i.e., the diffusion-controlled growth through long-range atomic migration in liquid and the diffusionless growth through local atom rearrangement, which give rise to two completely different crystallization behaviors, are compared. In the diffusion-controlled regime, the interface migrates in a layerwise manner, leading to a gradual change of crystal morphology from truncated square to four-fold symmetric dendrite with the increase of driving force. For the diffusionless growth mode, a single crystal with no significant density change occupies the whole system at a faster rate while exhibiting a small growth anisotropy. The competition between these two modes is also discussed from the key input of the phase field crystal model： the correlation function.

Faceting transitions in crystal growth and heteroepitaxial growth in the anisotropic phase-field crystal model

We modify the anisotropic phase-field crystal model （APFC）, and present a semi-implicit spectral method to numerically solve the dynamic equation of the APFC model. The process results in the acceleration of computations by orders of magnitude relative to the conventional explicit finite-difference scheme, thereby, allowing us to work on a large system and for a long time. The faceting transitions introduced by the increasing anisotropy in crystal growth are then discussed. In particular, we investigate the morphological evolution in heteroepitaxial growth of our model. A new formation mechanism of misfit dislocations caused by vacancy trapping is found. The regular array of misfit dislocations produces a small-angle grain boundary under the right conditions, and it could significantly change the growth orientation of epitaxial layers.

Suppression of intervalley scattering and enhanced phonon anharmonic interactions in 2D Bi_(2)TeSe_(2):Crystal-field symmetry and band convergence

The electron-phonon(el-ph)and phonon-phonon interactions play a key role in determining electronic and thermal transport properties,respectively,in promising two-dimensional(2D)semiconductor de-vices.In this study,we investigated el-ph interactions using Wannier-Fourier interpolation method and renormalized phonon scattering considering finite-temperature effects in Bi_(2)TeSe_(2)monolayer.The re-sults show that the optical phonon modes dominate the carrier scattering,where level repulsion induced by crystal field splitting and spin-orbit coupling(SOC)effect effectively suppresses intervalley scattering,leading to high hole mobility.Moreover,the strong anharmonicity in Bi_(2)TeSe_(2)monolayer results in the temperature-dependent softening of its optical phonons,along with a corresponding variation in interatomic force constants(IFCs).As a result,the lattice thermal conductivity is remarkably low and exhibits weak temperature dependence.Finally,the predicted dimensionless thermoelectric figure of merit exceeds unity in the range of 200-800 K,indicating the potential of Bi_(2)TeSe_(2)monolayer for thermoelectric applications.This work provides new insights into the elimination of intervalley scat-tering by crystal field splitting and SOC effects,and paves the way for the evaluation of thermoelectric properties of materials with complex scattering mechanisms and strong anharmonicity.

Energy Spectra,g Factors and Their Pressure—Induced and ／or Thermal Shifts of SrTiO3：Cr^3＋ and SrTiO3：Mn^4＋ I：energy Spectra and g Factors at Normal Pressure

With the strong-field scheme and cubic bases, the complete d3 energy matrix in a tetragonally distorted cubic-field has been constructed. By diagonalizing this matrix, the energy spectra of SrTiO3:Cr3+ and SrTiO3:Mn4+ at normal pressure and various temperatures have been calculated. Correspondingly, the FORTRAN program calculating the g factor of the ground state has been worked out. By using the program and the wavefunction obtained from diagonalizing the complete energy matrix, the g factors of the ground state of SrTiO3:Cr3+ and SrTiO3:Mn4+ at normal pressure and room temperature have been evaluated. The calculated results are in good agreement with the optical-spectral and EPR experimental data. The comparison and analysis of the results of two crystals have been made. It is demonstrated that the covalency of the bonding between Mn4+ and ligands (O2-) in SrTiO3:Mn4+ is stronger than the one of the bonding between Cr3+ and ligands (O2-) in SrTiO3:Cr3+. It is shown that the obtained wavefunctions and values of parameters are reasonable.

Microscopic—Theoretical Calculations of R—Line Thermal Shifts and Broadenings of MgO：V^2＋

A great improvement on a previous work (Phys. Rev. B48 (1993) 14067) has been made. By taking into account all the irreducible representations and their components in the electron-phonon interaction (EPI) as well as all the levels and the admixtures of basic wavefunctions within d3 electronic configuration, the values of all the parameters in the expressions of thermal shift (TS) and thermal broadening (TB) from EPI for the ground level, R level and R line of MgO:V2+ have microscopically been evaluated; and then, both the TS and TB of R line and various contributions to them have uniformly been calculated. The results are in very good agreement with the experimental data. It is found that all the three terms of TS from EPI are red shifts; the term of the contribution to TS from thermal expansion is blue shift. The Raman term is the largest, and the other terms are also important for TS. The R-line TS of MgO:V2+ comes from the first-order term of EPI. The elastic Raman scattering of acoustic phonons plays a dominant role in R-line TB of MgO:V2+. For calculations of both the TS and TB, it is very important to take into account all the admixtures of wavefunctions.

Microscopic Theoretical Calculations of R—Line Thermal Shifts and Broadenings of MgO：Cr^3＋

By taking into account all the irreducible representations and their components in the electron-phonon interaction (EPI) as well as all the levels and the admixtures of basic wavefunctions within d3 electronic configuration, the values of all the parameters in the expressions of thermal shift (TS) and thermal broadening (TB) due to EPI for the ground level, R level and R line of MgO:Cr3+ have microscopically been evaluated; and then, TS and TB of R line and various contributions to them have uniformly been calculated. The results are in very good agreement with the experimental data. It is found that all the three terms of TS due to EPI are red shifts; the Raman term is the largest one, and the optical-branch term and neighbor-level term are important for TS; the contribution to TS from thermal expansion is blue shift, which is also important. The R-line TS of MgO:Cr3+ comes from the first-order term of EPI. The elastic Raman scattering of acoustic phonons plays a dominant role in R-line TB of MgO:Cr3+. For both TS and TB, it is very important to take into account all the admixtures of basic wavefunctions within d3 electronic configuration.