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 cryst...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.展开更多
With the strong-field scheme and trigonal bases, the complete d<SUP>3</SUP> energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the normal-pressure energ...With the strong-field scheme and trigonal bases, the complete d<SUP>3</SUP> energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the normal-pressure energy spectra and wavefunctions of GSGG:Cr<SUP>3+</SUP> 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 R<SUB>1</SUB> line of GSGG:Cr<SUP>3+</SUP> with taking into account spin-orbit interaction (H<SUB>so</SUB>) and trigonal field (V<SUB>trig</SUB>) is much larger than the one with neglecting H<SUB>so</SUB> and V<SUB>trig</SUB>, and accordingly it is essential for the calculation of the EPI effect to take first into account H<SUB>so</SUB> and V<SUB>trig</SUB>. The admixture of base-wavefunctions,and , the average energy separation and their variations with temperature have been calculated and discussed.展开更多
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 th...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,展开更多
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 ...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.展开更多
The f-d transition of Ce3+ and Tb3+ in BaBPO5 was studied theoretically using the parametric Hamiltonian model. In order to overcome the difficulty in determining many of the parameter values, we adopted the model-spa...The f-d transition of Ce3+ and Tb3+ in BaBPO5 was studied theoretically using the parametric Hamiltonian model. In order to overcome the difficulty in determining many of the parameter values, we adopted the model-space effective Hamiltonian method to determine the crystal-field parameters and spin-orbit parameters values. The method made use of the energies and eigenvectors, which were obtained from an ab initio calculation using the relativistic self-consistent discrete variational Slater software package (DV-Xα). Other parameters, which were less dependent on host crystals, were taken from published data. The calculated values of parameters were reasonable, and the energy-levels and f-d transition spectra agreed reasonably well with the measured excitation spectra of 5d-4f emission.展开更多
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 ...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.展开更多
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 Rietve...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)F_(5/2)(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 B_(q)^(k) 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.展开更多
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 excitat...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.展开更多
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, New...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.展开更多
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 recursi...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.展开更多
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...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.展开更多
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 field...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.展开更多
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, a...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.展开更多
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 coe...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.展开更多
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 Wae...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.展开更多
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 ...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.展开更多
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 tran...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.展开更多
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...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.展开更多
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 computa...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.展开更多
The influence of temperature on the inverse Hall-Petch effect in nanocrystalline （NC） materials is investigated using phase field crystal simulation method. Simulated results indicate that the inverse Hall-Petch eff...The influence of temperature on the inverse Hall-Petch effect in nanocrystalline （NC） materials is investigated using phase field crystal simulation method. Simulated results indicate that the inverse Hall-Petch effect in NC materials becomes weakened at low temperature. The results also show that the change in microscopic deformation mechanism with temperature variation is the main reason for the weakening of the inverse Hall-Petch effect. At elevated temperature, grain rotation and grain boundary （GB） migration seriously reduce the yield stress so that the NC materials exhibit the inverse Hall-Petch effect. However, at low temperature, both grain rotation and GB migration occur with great difficulty, instead, the dislocations nucleated from the cusp of serrated GBs become active. The lack of grain rotation and GB migration during deformation is mainly responsible for the weakening of the inverse Hall-Petch effect. Furthermore, it is found that since small grain size is favorable for GB migration, the degree of weakening decreases with decreasing average grain size at low temperature.展开更多
文摘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.
文摘With the strong-field scheme and trigonal bases, the complete d<SUP>3</SUP> energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the normal-pressure energy spectra and wavefunctions of GSGG:Cr<SUP>3+</SUP> 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 R<SUB>1</SUB> line of GSGG:Cr<SUP>3+</SUP> with taking into account spin-orbit interaction (H<SUB>so</SUB>) and trigonal field (V<SUB>trig</SUB>) is much larger than the one with neglecting H<SUB>so</SUB> and V<SUB>trig</SUB>, and accordingly it is essential for the calculation of the EPI effect to take first into account H<SUB>so</SUB> and V<SUB>trig</SUB>. The admixture of base-wavefunctions,and , the average energy separation and their variations with temperature have been calculated and discussed.
文摘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,
基金Projects(51275178,51405162,51205135) supported by the National Natural Science Foundation of ChinaProjects(20110172110003,20130172120055) supported by the Doctoral Program of Higher Education of China
文摘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.
基金Project supported by National Natural Science Foundation of China (10774140, 10874173, 11074245, 11011120083)Foundation of the Education Committee of Chongqing (KJ090523)+1 种基金the Knowledge Innovation Project of the Chinese Academy of Sciences (KJCX2-YW-M11)the Special Foundation for Talents of Anhui Province, China (2007Z021)
文摘The f-d transition of Ce3+ and Tb3+ in BaBPO5 was studied theoretically using the parametric Hamiltonian model. In order to overcome the difficulty in determining many of the parameter values, we adopted the model-space effective Hamiltonian method to determine the crystal-field parameters and spin-orbit parameters values. The method made use of the energies and eigenvectors, which were obtained from an ab initio calculation using the relativistic self-consistent discrete variational Slater software package (DV-Xα). Other parameters, which were less dependent on host crystals, were taken from published data. The calculated values of parameters were reasonable, and the energy-levels and f-d transition spectra agreed reasonably well with the measured excitation spectra of 5d-4f emission.
基金supported by the Czech Science Foundation(13-09876S)
文摘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.
基金supported by the National Key Research and Development Program of China(Grant Nos.2022YFB3605700 and 2023YFB3507403)the National Natural Science Foundation of China(Grant No.52272011)+2 种基金the Youth Innovation Promotion Association of CAS(Grant No.2023463)Plan for Anhui Major Provincial Science&Technology Project(Grant No.202203a05020002)Open Project of Advanced Laser Technology Laboratory of Anhui Province(Grant No.AHL20220ZR04).
文摘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)F_(5/2)(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 B_(q)^(k) 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.
基金Project supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (20115314120001) the Special Program for National Program on Key Basic Research Project of China (973 Program) (2011CB211708) the Foundation of Natural Science of Yunnan Province (2011FB022)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.50772112 and 50872135)the Natural Science Foundation of Anhui Province of China(Grant No.08040106820)the Knowledge Innovation Program of the Chinese Academy of Sciences(Grant No.YYYJ-1002)
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No 0611054000)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11004005 and 60971019)the Young Scholars Fund of Beijing University of Chemical Technology,China(Grant No.QN0724)
文摘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.
基金The project supported by the Natural Science Foundation of Liaoning Province under Grant＇ No. 20041021, the Scientific Research Foundation of the Educational Department of Liaoning Province under Grant No. 2004C006, and National Natural Science Foundation of China under Grant No. 50477049.
文摘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.
文摘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.
文摘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.
文摘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.
基金The project supported by Science Foundation of the Ministry of Education of China under Grant No.99026
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51174168 and 51274167)the Foundation for Fundamental Research of Northwestern Polytechnical University,China(Grant No.JC20120222)
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.51075335,51174168,10902086,and 51274167)the NPU Foundation for Fundamental Research,China (Grant Nos. 201109 and NPU-FFR-JC201005)
文摘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.
基金financially supported by the National Natural Science Foundation of China(Nos.51174168 and 51274167)Northwestern Polytechnical University Foundation for Fundamental Research(No.NPU-FFR-JC20120222)
文摘The influence of temperature on the inverse Hall-Petch effect in nanocrystalline （NC） materials is investigated using phase field crystal simulation method. Simulated results indicate that the inverse Hall-Petch effect in NC materials becomes weakened at low temperature. The results also show that the change in microscopic deformation mechanism with temperature variation is the main reason for the weakening of the inverse Hall-Petch effect. At elevated temperature, grain rotation and grain boundary （GB） migration seriously reduce the yield stress so that the NC materials exhibit the inverse Hall-Petch effect. However, at low temperature, both grain rotation and GB migration occur with great difficulty, instead, the dislocations nucleated from the cusp of serrated GBs become active. The lack of grain rotation and GB migration during deformation is mainly responsible for the weakening of the inverse Hall-Petch effect. Furthermore, it is found that since small grain size is favorable for GB migration, the degree of weakening decreases with decreasing average grain size at low temperature.
