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One-dimensional nanoribbons usually exhibit considerably different properties compared to their monolayer counterparts due to the formation of edge states and limited width. In this study, we systematically investigate the stability, electronic structures and magnetic properties of CrSiTe3 single-layer nanoribbons with different edge configurations and ribbon widths using first-principles calculations. The results show that the edge energies (less than 0.4 eV/A) for all studied CrSiTe3 nanoribbons are much lower than that of graphene and many transition-metal dichalcogenide nanoribbons, indicating their stability and easy formation. Compared to the CrSiTe3 monolayer with ferromagnetic semiconductor characteristics, some of CrSiTe3 nanoribbons (N-SiCr-ZNRs, N-Te-ZNRs, N-TeCr-ANRs and N-Te-ANRs) become half-metal due to the hybridization between the d orbitals of edge Cr atoms and the p orbitals of edge Te atoms. While N-SiTe-ANRs are bipolar magnetic semiconductors, in which the states near Fermi level are localized around the nanoribbons edge. Our results show that CrSiTe3 single-layer nanoribbons are promising candidates suitable for applications in spintronic devices.

We study the domain wall depinning from a triangle-shaped notch in Ni80Fe20/Pt bilayer nanostrips using electrical detection technique. It is found that for the 630 nm wide strip, the depinning fields are distributed in a narrow range. While for the 300 nm wide strip, the depinning fields are distributed in two distinctly separated ranges. Micromagnetic simulations show that for the 630 nm wide strip, the depinning corresponds to vortex domain wall, while for 300 nm wide strip, the depinnings of both the vortex wall and the transverse wall are observed. The chirality of vortex wall and the polarity of transverse wall have strong influence on the depinning field. Electrical current has a clear impact on the depinning, but its influence is different for different wall configuration. It can decrease or slightly increase the depinning field of the vortex domain wall depending on the wall chirality and the current direction. The depinning field of the transverse domain wall exhibits an oscillation variation with the current density. Compared to the depinning process of the domain wall in a control sample Ni80Fe20/Au, it can be inferred the current influence on the domain wall depinning is caused mainly by the current-induced spin-orbit torque.

The Black Phosphorus (BP) nanosheets were prepared by liquid ultrasonic exfoliating the grinded layered BP bulk in organic solutions under protecting atmosphere. The samples were characterized by X-ray diffraction (XRD), Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM), transmission electron microscopy (TEM), as well as selective electron diffraction (SED). The possible magnetic (Fe, Co, Ni) impurities in the BP material were analyzed by an inductively coupled plasma-atomic emission spectrometry (ICP-AES). Magnetization measurements were performed using a vibrating sample magnetometer (VSM, Quantum Design PPMS-9T). The results indicate that the BP nanosheets sample has a weak ferromagnetic ordering with high magnetization 1.83 emu/g at room temperature. Analysis states the ferromagnetism is intrinsic to the BP samples, ruling out extrinsic ferromagnetism arising from magnetic metal impurities. The combination effects of magnetic moments resulting from defects or vacancies, the formation of edge states and the p orbital spin polarization of the oxygen and phosphorus atoms of the surface P O bonds contribute to the observed ferromagnetism in BP nanosheets sample. The conversion of ferromagnetism of 2D material BP at room temperature will be of great implication for spintronics application in the future.

We study the nonlinear gyrotropic motion of a magnetic skyrmion in a nanodisk by means of micromagnetic simulations. The skyrmion is driven by a linearly polarized harmonic field with the frequency of counterclockwise gyrotropic mode. It is found that the motion of the skyrmion displays different patterns with increasing field amplitude. In the linear regime of weak driving field, the skyrmion performs a single counterclockwise gyrotropic motion. The guiding center of the skyrmion moves along a helical line from the centre of the nanodisk to a stable circular orbit. The stable orbital radius increases linearly with the field amplitude. When the driving field is larger than a critical value, the skyrmion exhibits complex nonlinear motion. With the advance of time, the motion trajectory of the skyrmion goes through a series of evolution process, from a single circular motion to a bird nest-like and a flower-like trajectory and finally, to a gear-like steady-state motion. The frequency spectra show that except the counterclockwise gyrotropic mode, the clockwise gyrotropic mode is also nonlinearly excited and its amplitude increases with time. The complex motion trajectory of the skyrmion is the result of superposition of the two gyrotropic motions with changing amplitude. Both the linear and nonlinear gyrotropic motions of the skyrmion can be well described by a generalized Thiele’s equation of motion.

We investigate the electronic structure and magnetic properties of layered compounds SrBO 2 (B = Co, Ni, Mn) based on first principles calculations in the framework of density functional theory with GGA+ U method. We compute the phonon dispersion of these compounds to probe the dynamical stability and find that all the compounds are dynamically stable. SrCoO 2 and SrNiO 2 are G-type antiferromagnetic insulators, and SrMnO 2 is an A-type antiferromagnetic conductor. The electronic configurations of 3d orbitals are (d xz ) 2 (d z 2 ) 2 ( d yz ) 1 (d xy ) 1 (d x 2 - y 2 ) 1 and (d xz ) 2 (dy z ) 2 (d z 2 ) 2 (d xy ) 1 (d x 2 - y 2 ) 1 in SrCoO 2 and SrNiO 2 , respectively. SrCoO 2 shows a Jahn-Teller distortion ( a > b ) because the down-spin Co 3d electron occupies the degenerate (d xz , d yz ) levels. Using Monte Carlo simulations based on the Heisenberg model with exchange parameters obtained from first principles calculations, we obtain the Neel temperatures ( T N ) of SrCoO 2 and SrNiO 2 , which are 249 K and 85 K, respectively.

Advance in the field of two-dimensional (2D) Van der Waals layered magnetic materials have made the atomic-thickness spintronic devices possible in the near future. The application of the 2D layered magnetic materials inevitably involves the magnetization reversal. Here we study the magnetization reversal of the 2D layered material Fe3GeTe2 by means of magnetic and anomalous Hall resistance measurements. We find the reversal process of Fe3GeTe2 flake is temperature and thickness dependent. For thin flakes and at low temperatures, the hysteresis loops have perfect rectangular shapes with large coercivity, indicating the single domain characteristic during the reversal process. With increasing temperature, a cross-over from single domain to multi-domain structure occurs. For bulk and very thick flakes Fe3GeTe2, the nearly zero magnetic remanence and small coercivity demonstrates that the reversal process is accomplished through the formation of multi-domain structure and its gradual evolution with the magnetic field. The change of magnetization reversal with temperature and flake thickness is explained based on the competition between the long-range magnetic dipolar interaction and the perpendicular magnetic anisotropy. The results obtained in this work provide important reference for designing Fe3GeTe2-based spintronic devices.

Different from the extensive progresses on two-dimensional (2D) intrinsic ferromagnets, modulation of magnetism in a 2D antiferromagnet is less explored. In this work, we investigate the impact of strain on magnetism of monolayer and bilayer FePS3 antiferromagnet using first-principles calculations. Our results show that zigzag antiferromagnetic (AFM) state is the ground state of monolayer FePS3 and the AFM order is very robust to strain. The in-plane and out-of-plane magnetic anisotropy energies (MAEs) of monolayer FePS3 are 0.31 and 1.41 meV/cell, and MAE is mainly provided by Fe atoms. Interestingly, compressive strain can enhance monotonically MAE of monolayer FePS3 while the MAE experiences a fall-rise-fall process under tensile strain. In addition, interlayer coupling of bilayer FePS3 is quite sensitive to strain and undergoes an AFM-FM-AFM transition under both tensile and compressive strain. The out-of-plane direction is also energetically favorable for unstrained bilayer FePS3 with in-plane and out-of-plane MAEs of 0.58 and 1.54 meV/cell, respectively. with the decrease of strain from 8% to −8%, the MAE of bilayer FePS3 can be enhanced except a small decrease at the strain of −8%. These findings are essential for applications of FePS3 based low-dimensional antiferromagnetic spintronic devices.

Controllable creation of magnetic skyrmions in nanostructures is a prerequisite for the application of skyrmions in spintronics. Here, we propose a new method for the creation of skyrmions. We show by using micromagnetic simulations that the skyrmions can be nucleated by resonantly exciting one of the skyrmion intrinsic oscillation modes. We first studied the dynamics of skyrmion in a ferromagnetic nanodisk with perpendicular anisotropy. One breathing mode and two non-degenerate gyrotropic modes are identified. Then we applied a circular-polarized microwave field to excite the uniformly magnetized nanodisk. When the frequency of the driving field is equal to the eigenfrequency of the skyrmion gyrotropic mode, stable skyrmions can be created from the initial uniform state. The number of skyrmions can be effectively controlled by appropriately choosing the duration of the driving field or tuning the field amplitude.

We present our first-principles calculations of a new two-dimensional material, arsenic nitrogen monolayer. The structural, electronic, and mechanical properties are investigated in detail by means of density functional theory computations. The calculated binding energy and the phonon spectra demonstrate that the AsN can form stable monolayer in puckered honeycomb structure. It is a semiconductor with indirect band gap of 0.73 eV, and displays highly anisotropic mechanical properties. Strain has obvious influence on the electronic properties of AsN monolayer. It is found that in the armchair direction, a moderate compression strain (−12%) can trigger an indirect to direct band gap transition and a tensile strain of 18% can make the AsN becoming a stable metal. In the zigzag direction, a rather smaller strain than armchair direction (12% for compression and 8% for stretch) can induce the indirect band gap to metal transition.

Most of the two-dimensional layered materials discovered so far are intrinsically nonmagnetic. Introducing ferromagnetism into these materials will expand their application greatly in the field of spintronics. Here we study the introduction of ferromagnetism into the PtTe2 monolayer via doping the 3d transition metal atoms and the group VA and VIIB atoms by means of the first-principles calculations. Results show that the magnetic order can be introduced in the V-, Mn-, Fe-, Cu- and Zn-doped PtTe2 monolayers, among which the V-, Cu- and Zn-doped monolayers have ferromagnetic ground state, and the Mn- and Fe-doped monolayers have antiferromagnetic ordering in ground state. Among the group VA atom doped systems, N-, P- and As-doped monolayers exhibit ferromagnetic, and Sb doped monolayer is a nonmagnetic metal. All the VIIB atom doped PtTe2 monolayers are nonmagnetic, while the doping makes the PtTe2 monolayer transit from an indirect bandgap semiconductor to metal. The findings obtained in this work may initiate new experimental exploration and expand the application of the layered transition-metal ditellurides in spintronics.

Spin-wave propagation in periodic magnetization-modulated cylindrical nanowires is studied by micromagnetic simulation. Spin wave scattering at the interface of two magnetization segments causes a spin-wave band structure, which can be effectively tuned by changing either the magnetization modulation level or the period of the cylindrical nanowire magnonic crystal. The bandgap width is oscillating with either the period or magnetization modulation due to the oscillating variation of the spin wave transmission coefficient through the interface of the two magnetization segments. Analytical calculation based on band theory is used to account for the micromagnetic simulation results.

We systematically study the strain-tuning effect on the electronic and magnetic properties of single-layer MnTe2 using first-principles calculations. The calculations show that the unstrained single-layer MnTe2 is an intrinsic ferromagnetic metal with a perpendicular magnetocrystalline anisotropy. The in-plane biaxial tensile strain greatly enhances the perpendicular magnetocrystalline anisotropy. The orbital-projected spin-orbit coupling energy indicates that the magnetocrystalline anisotropy energy mainly comes from the contribution of the Te atom although its magnetic moment is small. The ferromagnetic interaction between the nearest two Mn atoms is also strengthened significantly by the tensile strain. The Curie temperature increases from 88 K without strain to 440 K at 10% strain. Moreover, the single-layer MnTe2 becomes a half metal when the tensile strain is larger than 6%. If compressive strain is applied, the single-layer MnTe2 undergoes a spin reorientation transition from out-of-plane to in-plane magnetization. The compressive strain also induces the transition of the Mn–Mn exchange coupling from ferromagnetic to antiferromagnetic. The intrinsic ferromagnetic properties and the strong strain-tuning effect make the single-layer MnTe2 a promising candidate for spintronics applications.

We study the electronic structure and magnetism of monolayer 3d transition-metal ditellurides MTe2 (M = Ti, V, Cr, Mn, Fe, Co and Ni) in trigonal prismatic H- and/or octahedral T-phase by means of the first-principles calculations. The results show that H-VTe2, T-VTe2, H-FeTe2 and T-MnTe2 monolayers exhibit intrinsic ferromagnetism, and the others have no ferromagnetism. The exchange splitting of V, Mn and Fe 3d orbitals is responsible for ferromagnetism. The exchange constant and the Curie temperature are estimated by using 2D Ising model and mean field theory. Among the four ferromagnetic monolayers, the H-VTe2 monolayer has the largest exchange constant and the corresponding Curie temperature is near room temperature. Calculations also show that the T-VTe2, H-VTe2 and H-FeTe2 monolayers have in-plane easy magnetization direction, while the easy direction of the T-MnTe2 monolayer is perpendicular to the layer. Moreover, we analyze the relative exchange strength of the four ferromagnetic monolayers based on the competition between the through-bond ferromagnetic interaction and the through-space antiferromagnetic interaction according to the Goodenough–Kanamori rules. The magnetocrystalline anisotropy is explained qualitatively based on the second-order perturbation theory from the spin-orbit coupling between 3d orbitals of M atoms.

Two-dimensional (2D) material of few-layer black phosphorus (BP) has recently attracted extensive interest owing to its tunable band gap and high carrier mobility. We investigate the electronic transport properties of zigzag black phosphorene nanoribbons (ZBPNRs) with asymmetric H, Li, O and Co edge saturations by employing the density functional theory in combination with the non-equilibrium Green's function. The computational results forecast that different types of saturated atoms at both edge of ribbons mainly contribute to the electronic transport properties of molecular junctions. The metal edge saturation of Co atom is used to the one edge of ZBPNR which can induce an identical electronic transport property. Interestingly, the negative differential resistance (NDR) phenomena can be observed in our proposed ZBPNR junctions with an analysis of internal physical mechanism. Our theoretical results could support the possibility of potential applications to design 2D electronic devices based on the material of BP in future.

We study spin wave propagation in a new type of magnonic crystal consisting of a series of periodically distributed magnetic domain walls in a nanostrip by micromagnetic simulation. Spin wave bands and bandgaps are observed in frequency spectra and dispersion curves. Some bandgaps are caused by the Bragg reflection of the spin wave modes at the Brillouin zone boundaries, while others originate from the coupling between different incident and reflected spin wave modes. The control of the spin wave band structure by changing the magnetocrystalline anisotropy or applying an external magnetic field is studied. Increasing the magnetocrystalline anisotropy leads to an increase of the bandgaps. The external field applied perpendicular to the nanostrip gives rise to a doubling of the domain-wall magnonic crystal period. As a result, more bandgaps appear on the frequency spectra of propagating spin waves. The results presented here may find their use in the design of reconfigurable magnonic devices.

We study the dynamic properties of magnetic nanoelements with tapered ends by using micromagnetic simulations. It is found that the spin-wave modes can be effectively manipulated by the element shape. With the increase of the end sharpness (described by tapering parameter h ), the frequency of the spin-wave edge mode increases rapidly and its oscillation areas in the both ends of element gradually increase and move toward to the central area. Finally, the edge mode completely merges into the fundamental mode. During the magnetization reversal processes, the edge mode experiences one or two softening depending on h ≤60 nm or 60 nm h h >100 nm, it is the fundamental mode that goes to zero at the switching field. The evolution of the spin-wave modes reflects the change of the micromagnetic structures of the elements during the reversal. It is the softening of the edge mode that triggers the magnetization reversal in elements with h h >100 nm is induced by the softening of t h e fundamental mode, where the edge mode is completely suppressed. The results presented in this work demonstrate that the dynamic properties and the magnetization reversal can be effectively tuned by changing the shape of the nanoelements and may be useful for designing the nanoscale magnetic devices.

We study the electronic structures and magnetism of SrFe 0.5 Ru 0.5 O 2 by first-principles calculations in the framework of density functional theory (DFT) with generalized gradient approximation plus on site repulsion (GGA+ U ). The DFT calculations were carried out with ten kinds of Fe-site doping form. Calculations show that the d-orbital electronic configurations of Fe 2+ and Ru 2+ ions are ( d z 2 ) 2 ( d yz d xz ) 2 ( d xy ) 2 ( d x 2 − y 2 ) 1 and ( d z 2 ) 2 ( d yz d xz ) 3 ( d xy ) 1 ( d x 2 − y 2 ) , respectively, which are independent of the doping form. The degenerated ( d xz d yz ) orbitals of Ru 2+ ions are occupied by three electrons, so it gives rise to the Jahn–Teller distortion. The calculated magnetic moments of Fe 2+ and Ru 2+ ions are 3.7 μ B and 1.6 μ B , respectively. The exchange parameters including nearest neighbor (NN) ions and next nearest neighbor (NNN) ions are calculated by using Heisenberg model and the magnetic frustration in the ordered structure is explained by the competition of the exchange parameters. We also study the external pressure effect on the compound. A pressure-induced orthorhombic to tetragonal structure transition accompanied by an insulator to half-metal transition and an antiferromagnetic (or spin glass) to ferromagnetic state transition is observed.

We investigate the electronic structure and magnetic properties of SrFe 1− x Mn x O 2 system using first-principles calculations and the site-random Heisenberg model. Calculations show that the ground state of SrFe 1− x Mn x O 2 with x ≤0.3 is a Mott insulator. The ground state of SrFe 0.875 Mn 0.125 O 2 has the same (πππ) ordered antiferromagnetic state as in the undoped compound. For SrFe 0.75 Mn 0.25 O 2 , the (πππ) as well as the (ππ0) ordered antiferromagnetic state may exist depending on the atomic configuration. The magnetic structure and its change by doping can be explained based on the estimated interlayer exchange interactions. The effects due to random distributions of Fe and Mn ions are investigated by Monte Carlo simulations based on the site-random Heisenberg model with exchange parameters obtained from first principles calculations. The results show that the Neel temperature T N corresponding to the phase transition from the paramagnetic phase to the (πππ) ordered phase decreases with increasing x , and a second transition from the (πππ) ordered phase to a mixed phase with coexistence of both the (πππ) and (ππ0) orderings develops at T N ′ below T N .

Taking Au–Cu system as an example, three discoveries and two methods were presented. First, a new way for boosting sustainable progress of systematic metal materials science (SMMS) and alloy gene engineering (AGE) is to establish holographic alloy positioning design (HAPD) system, of which the base consists of measurement and calculation center, SMMS center, AGE center, HAPD information center and HAPD cybernation center; Second, the resonance activating-sychro alternating mechanism of atom movement may be divided into the located and oriented diffuse modes; Third, the equilibrium and subequilibrium holographic network phase diagrams are blueprints and operable platform for researchers to discover, design, manufacture and deploy advanced alloys, which are obtained respectively by the equilibrium lever numerical method and cross point numerical method of isothermal Gibbs energy curves. As clicking each network point, the holographic information of three structure levels for the designed alloy may be readily obtained: the phase constitution and fraction, phase arranging structure and properties of organization; the composition, alloy gene arranging structure and properties of each phase and the electronic structures and properties of alloy genes. It will create a new era for network designing advanced alloys.

Taking Au 3 Cu-type sublattice system as an example, three discoveries have been presented. First, the fourth barrier to hinder the progress of metal materials science is that today's researchers do not understand that the Gibbs energy function of an alloy phase should be derived from Gibbs energy partition function constructed of alloy gene sequence and their Gibbs energy sequence. Second, the six rules for establishing alloy gene Gibbs energy partition function have been discovered, and it has been specially proved that the probabilities of structure units occupied at the Gibbs energy levels in the degeneracy factor for calculating configuration entropy should be degenerated as ones of component atoms occupied at the lattice points. Third, the main characteristics unexpected by today's researchers are as follows. There exists a single-phase boundary curve without two-phase region coexisting by the ordered and disordered phases. The composition and temperature of the top point on the phase-boundary curve are far away from those of the critical point of the Au 3 Cu compound; At 0 K, the composition of the lowest point on the composition-dependent Gibbs energy curve is notably deviated from that of the Au 3 Cu compounds. The theoretical limit composition range of long range ordered Au 3 Cu-type alloys is determined by the first jumping order degree.

Taking experimental path on disordering AuCuI A 8 Au A 4 Cu composed of A 8 Au and A 4 Cu stem alloy genes as an example, three discoveries and a method were presented. The ability of AuCuI ( A 8 Au A 4 Cu ) to keep structure stabilization against changing temperature is attributed to the fact that the A 8 Au and A 4 Cu potential well depths greatly surpass their vibration energies, which leads to the subequilibrium of experimental path. A new atom movement mechanism of AuCuI( A 8 Au A 4 Cu ) to change structure for suiting variation in temperature is the resonance activating-synchro alternating of alloy genes, which leads to heterogeneous and successive subequilibrium transitions. There exists jumping order degree, which leads to the existence of jumping T j -temperature and an unexpected so-called “retro-effect” about jumping temperature retrograde shift to lower temperatures upon the increasing heating rate. A set of subequilibrium holographic network path charts were obtained by the experimental mixed enthalpy path method.

Ferromagnetism of two-dimensional layered materials is of considerable interest in spintronics. In the present work, we report the ferromagnetism of the layered material SnSe2 induced by Bi doping. The pure SnSe2 and Bi-doped SnSe2 film samples are prepared by chemical vapor transport method. X-ray diffractions show that both the SnSe2 and Bi-doped SnSe2 have CdI2-type layered structure grown perfectly along the c-axis. Magnetic measurements indicate that the pure SnSe2 is a diamagnet. The doping of nonmagnetic Bi introduces ferromagnetism in SnSe2 with Curie temperature of 65 K. A coercivity as high as 4.4 kOe is observed at T = 10 K. Such high coercivity has never been reported in d0 two-dimensional layered materials. First-principles calculations indicate that the Bi-doping leads to the spin splitting of degenerate px and py orbital states and gives rise to a spin order aligned in ab plane. Calculations also show that the Bi-doped SnSe2 is a half metal. All these features make Bi-doped SnSe2 a potential candidate for spintronic material.

The potential energies, volumes and electronic structures of characteristic atoms coordinated by neighboring configurations were obtained from the experimental heats of formation and lattice parameters of disordered Au1-xCux alloys. From characteristic atom occupation (CAO) patterns of L12-Au3Cu, L12-AuCu3 and L10-AuCu compounds, their electronic structures, volumetric and energetic properties were calculated. The CAO pattern of Johasson-Linde(J-L) model shows that the transition AuCuI→AuCuII is an exothermic and volume contraction reaction, which is opposite from experimental phenomena. According to CAO pattern of Guymont-Feutelais-Legendre(G-F-L) model, the AuCuII cell consists of two periodic antidirection (PAD) AuCuI regions and two PAD boundary regions. The equations derived from CAO pattern of G-F-L model can be used to calculate energetic properties, volumetric properties and ordering degrees of the PAD AuCuI region and PAD boundary region, as well as corresponding average properties of the AuCuII phase. The results are consistent with experimental phenomena.

The systematic science of alloys (SSA) is a framework of the total energy and total volume able to be separated. The potential energy sequences of characteristic atoms at the central sites of the basic clusters in the fcc-based lattice Au-Cu system are separated out from smaller experimental heats of formation of L10-AuCu and Ll2-AuCu3 compounds only, by nine potential energy E-functions and through the use of structural unit inversion method. From these potential energy sequences, the potential energies and heats of formation of the disordered Au(subscript 1-x)Cu(subscript x) alloys at 0 K are calculated. The potential energies, heats of formation and T(subscript c)-temperatures of order-disorder transitions of the L10-AuCu, L12-Au3Cu and L12-AuCu3 compounds, as well as the Au3Cu-, AuCu-and AuCu3-type ordered alloys with maximal ordering degrees are calculated too. The results show that the 5th E-function may be chosen for developing it into the free energy-, enthalpy-, vibrational energy-and vibrational entropy-functions for describing thermodynamic properties of the compounds, ordered and disordered phases and for establishing the phase diagram of the Au-Cu system in the future.

Isometric heat capacity c v and isobaric heat capacity c p of Pt with stable and metastable phases were calculated by using pure element systematic theory. These results are in excellent agreement with of SGTE (Scientific Group Thermodata Europe) database and JANAF (Joint Army-Navy-Air Force) experimental values. The calculation results of c v and c p of Pt metal in natural state are in good agreement with those calculated by FP(first-principles) method. It is found that the electron devotion to heat capacity is important to adjust in OA(one-atom) method while calculating heat capacity. The full information about thermodynamic properties of Pt metal with stable and metastable phases, such as entropy( S ), enthalpy( H ) and Gibbs energy( G ) were calculated from 0 K to random temperature. The results are in good agreement with JANAF experimental value. In contrast to SGTE database, the thermodynamic properties from 0 K to 298.15 K are implemented.

The low temperature thermodynamics of the stable phase of vanadium has been assessed by the polynomial and Debye models from the experimental data available in literature. By means of the constrained nonlinear least squares curve fitting arithmetic, two sets of parameter values have been determined. Expressions of the thermodynamic functions Cp(T) and G(T)-H (298.15 K) at 0–298.15 K are presented. The low temperature thermodynamics of the metastable phase of vanadium can only be extrapolated by the Debye model. The expression of the thermodynamic function Cp(T) at 0–298.15 K is presented.

The valence bond structure of tungsten is redetermined at ambient pressure and calculated for pressures up to 300 GPa using the energy and shape method. The outer shell valence electronic distribution of tungsten at ambient pressure is e c 3.7408 ( d c 2.9268 + S c 0.2040 p c 0.6100 ) e f 2.2592 . The value of the single-bond radius is 1.2532 A. Under pressure, the covalent electrons e c ( d c , s c and p c ) increase while near free electrons e f decreases with increasing pressure. The number of covalent electrons e c is 3.7408 under ambient conditions and 5.0321 at 300 GPa and the number of near free electrons e f changes from 2.2592 at ambient pressure to 0.9679 at 300 GPa. The bond length and single-bond radius decrease while bond valence increases with increasing pressure. These results indicate that the electron distributions are more localized and the bonding character of metal becomes more covalent bonding with increasing pressure.

Based on Xie's the one-atom self-consistency method for determining the valence and bond (VB) structures of crystal, the energy and shape (ES) method has been brought forward. New progress has been made in the theory. The VB structures are determined with the unity of lattice constant and energy minimization. To take Mg as an example, the ES method is introduced in detail. The VB structures of Na, Mg, Al, Ti, Zr and Hf are determined. The results are more refined and reliable.

On the basis of energy and shape method for the determination of the valence bond (VB) structures of crystal, the valence bond structure of titanium is redetermined at room temperature and calculated in the whole temperature range of 0–1943K. The outer shell electronic distribution of Ti is ec2.9907. (Sc0.4980 + dc2.4927) ef1.0093 in crystal. The temperature dependences of the VB structures of hcp and bcc phases are the same. The VB structures of hcp and bcc phases monotonically increase or decrease with the increase in temperature, but show discontinuous changes at the phase-transformation temperature 1155K.