Determining Hubbard U of VO_(2) by the quasi-harmonic approximation

Vanadium dioxide VO_(2) is a strongly correlated material that undergoes a metal-to-insulator transition around 340 K.In order to describe the electron correlation effects in VO_(2), the DFT+U method is commonly employed in calculations.However, the choice of the Hubbard U parameter has been a subject of debate and its value has been reported over a wide range. In this paper, taking focus on the phase transition behavior of VO_(2), the Hubbard U parameter for vanadium oxide is determined by using the quasi-harmonic approximation(QHA). First-principles calculations demonstrate that the phase transition temperature can be modulated by varying the U values. The phase transition temperature can be well reproduced by the calculations using the Perdew–Burke–Ernzerhof functional combined with the U parameter of 1.5eV. Additionally,the calculated band structure, insulating or metallic properties, and phonon dispersion with this U value are in line with experimental observations. By employing the QHA to determine the Hubbard U parameter, this study provides valuable insights into the phase transition behavior of VO_(2). The findings highlight the importance of electron correlation effects in accurately describing the properties of this material. The agreement between the calculated results and experimental observations further validates the chosen U value and supports the use of the DFT+U method in studying VO_(2).

Finite temperature thermophysical properties of MgCu intermetallic compound from quasi-harmonic Debye model

The influence of pressure and temperature on the thermodynamic properties of MgCu intermetallic compound was investigated by quasi-harmonic Debye model approximation.The equation of state(EoS)parameters has performed using plane-wave pseudopotential(PW-PP)approach in the framework of the density functional theory(DFT)and the generalized gradient approximation(GGA)for the exchange-correlation functional.Our results agree well with other data of the literature.The finite temperature thermophysical properties under pressure up to 16 GPa and high temperature up to 800 K,respectively were determined.Our results of the thermophysical properties are also agree very well with other data of the literature,where for example at ambient temperature,the deviation between our obtained value(11.05 Cal mol^(−1)K^(−1))of C V,and the theoretical value(11.21 Cal mol^(−1)K^(−1))reported in the literature is only around 1.44%.The finite temperature thermophysical properties were found varied monotonically with either temperature or pressure.Compared with other materials previously studied,similar behaviors were observed.

Study on Thermodynamic Properties of Lithium by First-principles and Quasi-harmonic Debye Model

In this paper, the lattice parameter and bulk modulus of lithium(Li) at different pressures and temperatures are calculated by using the density functional theory method within the generalized gradient approximation(GGA).Through the quasi-harmonic Debye model, the thermodynamic properties of Li are predicted. The dependences of the normalized primitive cell volume V/V0 on pressure P, the variation of the thermal expansion coefficient α with pressure P and temperature T, as well as the dependences of the heat capacity Cv on pressure P and temperature T are obtained systematically in the ranges of 0~100 GPa and 0~2 000 K.

LIOUVILLE PROPERTY FOR A CLASS OF QUASI-HARMONIC SPHERE

In this paper we obtain a Liouville type result for a class of quasi-harmonic spheres with rotational symmetry.

Nonexistence of the Quasi-harmonic Spheres and Harmonic Spheres into Certain Manifold

We mainly study the nonexistence of quasi-harmonic spheres and harmonic spheres into spheres of any dimension which omits a neighbourhood of totally geodesic submanifold of co-dimension 2.We will show that such target admits no quasi-harmonic spheres and harmonic spheres.

Surface tidal currents in the open sea area to the east of the Zhoushan Islands measured with high frequency surface wave radar

Based on the quasi-harmonic analysis of 11 d vector ocean currents obtained from two high frequency sur- face wave radars located at Zhujiajian Island and Shengshan Island, the spatial distribution characteristics of surface tidal currents in the open sea area to the east of the Zhoushan Islands of Zhejiang Province, China are studied. The following conclusions are drawn from the analysis： the tidal current pattern in the open sea area to the east of Zhoushan Islands is primarily regular semidiurnal, which is significantly affected by the shallow water constituents. The directions of the major axes of tidal current ellipses of M2 lie approx- imately in the NW-SE direction. With the increasing of distance away from the coast, the directions of the tidal current ellipses gradually shift toward the E-W direction. The tidal currents are mainly reversing cur- rents. The spatial distribution of probable maximum current velocities decreases gradually from northeast to southwest which is basically in accordance with the spatial distribution of measured maximum current velocities. The residual currents near the coast are larger than those far away from the coast. The directions of the residual currents are basically north by east, and the angle to the due north increases gradually with the increasing distance away from the coast. The topography shows a certain impact on the spatial distri- bution of shallow water constituents, the rotation of tidal currents, the probable maximum currents and the residual currents.

Thermodynamic property of ternary compound MgCaSi: A study from ab initio Debye-Grüneisen model

The thermodynamic properties of Mg Ca Si and its mother phase Ca2 Si are comparatively investigated from ab initio calculations and quasi-harmonic Debye-Grüneisen model. At 0 K, Mg Ca Si is more thermodynamically stable. Under high temperature, the advantage of higher thermodynamically stability of Mg Ca Si is reduced, originating from the less negative entropy contribution because the thermodynamic entropy of Mg Ca Si increases more slowly with temperature and the entropy values are slightly smaller.With increasing temperature, the anti-softening ability for Mg Ca Si is slightly smaller due to the slightly faster decrease trend of bulk modulus than that of Ca2 Si, although the bulk modulus of Mg Ca Si is higher in the whole temperature range considered. The thermal expansion behaviors of both Mg Ca Si and Ca_(2)Si exhibit similar increase trend, although thermal expansion coefficient of MgCaSi is slightly lower and the increases is slightly slower at lower temperature. The isochoric heat capacity CVand isobaric heat capacity CPof MgCaSi and Ca_(2)Si rise nonlinearly with temperature, and both CVare close to the Dulong–Petit limit at high temperature due to the negligibly small electronic contribution. The Debye temperature of both phases decrease with increasing temperature, and the downtrend for Mg Ca Si is slightly faster.However, MgCaSi possess slightly higher Debye temperature, implying the stronger chemical bonds and higher thermal conductivity than the mother phase Ca_(2)Si. The Grüneisen parameter of MgCaSi and Ca_(2)Si increase slightly with temperature, the values of MgCaSi are slightly larger. The investigation of electronic structures shows that with substitution of partial Ca by Mg in Ca_(2)Si, the stronger MgASi,MgACa and SiASi covalent bonds are formed, and plays a very significant role for the structural stability and mechanical properties.

First-principles calculations on the elastic and thermodynamic properties of NbN

The elastic and thermodynamic properties of NbN at high pressures and high temperatures are investigated by the plane-wave pseudopotential density functional theory （DFT）. The generalized gradient approximation （GGA） with the Perdew-Burke Ernzerhof （PBE） method is used to describe the exchange-correlation energy in the present work. The calculated equilibrium lattice constant a0, bulk modulus B0, and the pressure derivative of bulk modulus B~ of NbN with rocksalt structure are in good agreement with numerous experimental and theoretical data. The elastic properties over a range of pressures from 0 to 80.4 GPa are obtained. Isotropic wave velocities and anisotropic elasticity of NbN are studied in detail. It is indicated that NbN is highly anisotropic in both longitudinal and shear-wave velocities. According to the quasi-harmonic Debye model, in which the phononic effect is considered, the relations of （V - Vo）/Vo to the temperature and the pressure, and the relations of the heat capacity Cv and the thermal expansion coefficient α to temperature are discussed in a pressure range from 0 to 80.4 GPa and a temperature range from 0 to 2500 K. At low temperature, Cv is proportional to T3 and tends to the Dulong Petit limit at higher temperature. We predict that the thermal expansion coefficient α of NbN is about 4.20 × 10-6/K at 300 K and 0 GPa.

First-principles calculations of structural and thermodynamic properties of β-PbO

We employed ab-initio calculations to investigate the structural and thermodynamic properties of Massicot or orthorhombic phase of PbO named β-PbO using the projector augmented-wave（PAW） method within the generalized gradient approximation（GGA）. The temperature and pressure dependence of bulk modulus, heat capacity at constant pressure and constant volume, entropy, thermal expansion coefficient and Grüneisen parameter were discussed. Accuracy of two different models, the Debye and Debye-Grüneisen which are based on the quasi-harmonic approximation（QHA） for producing thermodynamic properties of material were compared. According to calculation results, these two models can be used to designate thermodynamic properties for β-PbO with sensible accuracy over a wide range of temperatures and pressures, and our work on the properties of this structure will be useful for more deeply understanding various properties of this structure.

Spatial Distribution Characteristics of Surface Tidal Currents in the Southwest of Taiwan Strait

This study was conducted on the spatial distribution characteristics of surface tidal currents in the southwestern Taiwan Strait based on the quasi-harmonic analysis of current data obtained by two high frequency surface wave radar(HFSWR) systems. The analysis shows that the tidal current pattern in the southwestern Taiwan Strait is primarily semi-diurnal and influenced significantly by shallow water constituents. The spatial distribution of tidal current ellipses of M2 is probably affected by the interaction between two different systems of tide wave, one from the northern mouth of Taiwan Strait and the other from the Bashi Channel. The directions of the major axes of M2 tidal current ellipses coincide roughly with the axis of the Taiwan Strait. The spatial distribution of the magnitudes of the probable maximum current velocity(PMCS) shows gradual increase of the velocity from northeast to southwest, which is in accordance with the spatial distribution of the measured maximum current velocity(MMCS). The directions of the residual currents are in accordance with the direction of the prevailing monsoon wind at the Taiwan Strait and the direction of the Taiwan warm current during summer. The bathymetry also shows a significant effect on the spatial distribution characteristics of tidal currents.

Thermoelasticity of CaO from first principles

The thermoelastic properties of CaO over a wide range of pressure and temperature are studied using density functional theory in the generalized gradient approximation. The transition pressure taken from the enthalpy calculations is 66.7 GPa for CaO, which accords with the experimental result very well. The athermal elastic moduli of the two phases of CaO are calculated as a function of pressure up to 200 GPa. The calculated results are in excellent agreement with existing experimental data at ambient pressure and compared favourably with other pscudopotential predictions over the pressure regime studied. It is also found that the degree of the anisotropy rapidly decreases with pressure increasing in the B1 phase, whereas it strongly increases as the pressure increases in the B2 phase. The thermodynamic properties of the B1 phase of CaO are predicted using the quasi-harmonic Debye model; the heat capacity and entropy arc consistent with other previous results at zero pressure.

First-Principle Calculations for Transition Phase and Elastic Properties of SrS

The transition phase and elastic properties of SrS from NaCl structure （B1） to CsCl structure （B2） are investigated by ab initio plane-wave pseudopotential density functional theory method and by the quasi-harmonic Debye model. The transition pressure varies non-linearly with temperature, and the pressure of the mechanical instability increases linearly with increasing temperature. It is shown that the B1 structure SrS is a most elastically anisotropic minerat any pressure. The Debye temperature, the heat capacity, thermal expansion and Gruneisen parameter over a wide range of pressures and temperatures are also obtained.

First principle calculation of elastic and thermodynamic properties of stishovite

Using ab initio plane-wave pseudo-potential density functional theory method, the elastic constants and band structures of stishovite were calculated. The calculated elastic constants under ambient conditions agree well with previous experimental and theoretical data. C13, C33, C44, and C66 increase nearly linearly with pressure while C11 and C12 show irregularly changes with pressure over 20 GPa. The shear modulus （Cll-C12）/2 was observed to decrease drastically between 40 GPa and 50 GPa, indicating acoustic mode softening in consistency with the phase transition to CaC12-type structure around 50 GPa. The calculated band structures show no obvious difference at 0 and 80 GPa, being consistent with the high incompressibility of stishovite. With a quasi-harmonic Debye model, thermodynamic properties of stishovite were also calculated and the results are in good agreement with available experimental data.

Temperature-induced phase transition of two-dimensional semiconductor GaTe

GaTe is a two-dimensional Ⅲ-Ⅵ semiconductor with suitable direct bandgap of~1.65 eV and high photoresponsivity,which makes it a promising candidate for optoelectronic applications.GaTe exists in two crystalline phases:monoclinic(m-GaTe,with space group C2/m) and hexagonal(h-GaTe,with space group P63/mmc).The phase transition between the two phases was reported under temperature-varying conditions,such as annealing,laser irradiation,etc.The explicit phase transition temperature and energy barrier during the temperature-induced phase transition have not been explored.In this work,we present a comprehensive study of the phase transition process by using first-principles energetic and phonon calculations within the quasi-harmonic approximation framework.We predicted that the phase transition from h-GaTe to m-GaTe occurs at the temperature decreasing to 261 K.This is in qualitative agreement with the experimental observations.It is a two-step transition process with energy barriers 199 meV and 288 meV,respectively.The relatively high energy barriers demonstrate the irreversible nature of the phase transition.The electronic and phonon properties of the two phases were further investigated by comparison with available experimental and theoretical results.Our results provide insightful understanding on the process of temperature-induced phase transition of GaTe.

Structural, Anisotropic and Thermodynamic Properties of Imm2-BCN

Structural, anisotropic, and thermodynamic properties of Imm2-BCN were studied based on density function theory with the ultrasoft psedopotential scheme in the frame of the generalized gradient approximation（GGA）. The elastic constants were confirmed that the predicted Imm2-BCN is mechanically stable. The anisotropy of elastic properties were also studied systematically. The anisotropy studies of Young＇s modulus, shear modulus, linear compressibility, and Poisson＇s ratio show that the Imm2-BCN exhibits a large anisotropy. Through the quasi-harmonic Debye model, the relations between the equilibrium volume V, thermal expansion α, the heat capacity C_V and CP, the Grüneisen parameter γ, and the Debye temperature Θ_D with pressure P and temperature T were also studied systematically.

Nucleation and growth of L1_(2)-Al_(3)RE particles in aluminum alloys:A first-principles study

The internal mechanisms of nucleation and growth of L1_(2)-AI_(3)RE(RE=Sc,Y,La-Lu) second phases in Al alloys were investigated by combining first-principles calculations with quasi-harmonic approximation(QHA).The calculated results show that the diffusion rate D_s and chemical potential AG_V increase with the increase of temperature.With the increase of atomic number,the D_s and the strain energy ΔE_(CS)increase firstly from Sc to La,and then decreases,while the calculated interface energy γ_(α/β) and ΔG_V show opposite tendency.Based on above calculated results,the critical nucleation radius R*and coarsening rate K_(LSW) are obtained from the classical nucleation theory(CNT) and LSW model of the Ostwald ripening of particles,respectively.With the increase of atomic number,the R*increases firstly,and then decreases for all planes at finite temperatures.Whereas the K_(LSW) shows opposite variation to the R^(*).From this point of view,it is reasonably speculated that Y and later RE elements can replace the expensive Sc for heat-resistance Al alloys.The solubility c_(∞) of particles is usually very small at low temperature,and there is obvious solubility only when the temperature reaches 600 K.The surface energies E_(sur) of AI_(3)RE compounds and Al solid solution are respectively larger and smaller than that of pure Al,respectively,except for the surface(001) and(110) of Al_(3)La.For all planes,with the increase of atomic number of RE,E_(sur) decreases firstly from Sc to La,and then increases linearly to Lu.These results are helpful for designing high performance heat-resistance Al alloys.

LDA＋U calculation of structural and thermodynamic properties of Ce2O3

We investigated the structure and thermodynmnic properties of the hexagonal Ce2O3 by using LDA＋U scheme in the fi＇ame of density functional theory （DFT）, together with the quasi-harmonic Debye model. The obtained lattice constants, bulk modulus, and the insulating gap agree well with the available experimental data. We successfully yielded the temperature dependence of bulk modulus, volume, thermal expansion coefficient, Debye temperature, specific heat as well as the entropy at different U values. It is found that the introduction of the U value cannot only correct the calculation of the structure but also improve the accurate description of the thermodynamic properties of Ce2Oa. When U = 6 eV the calculated volume （538 Bohra） at 300 K agrees well with the experimental value （536 Bohr3）. The calculated entropy curve becomes more and more close to the experimental curve, with the increasing U value.

Synthesis,formation mechanism,and intrinsic physical properties of several As/P-containing MAX phases

321 phases are an atypical series of MAX phases,in which A=As/P,with superior elastic properties,fea-turing in the MA-triangular-prism bilayers in the crystal structure.Until now,besides Nb 3 As 2 C,the pure phases of the other 321 compounds have not been realized,hampering the study of their intrinsic prop-erties.Here,molten-salt sintering(MSS)and solid-state synthesis(SSS)were applied to synthesize As/P-containing 321 phases and 211 phases.Analyzing the phase composition of the end-product via multiple-phase Rietveld refinement,we found that MSS can effectively improve the purity of P-containing MAX phases,with the phase content up to 99%in Nb_(3)P_(2)C and 75.4(5)%in Nb 2 PC.In contrast,MSS performed poorly on As-containing MAX phases,only 8.9(4)%for Nb 3 As 2 C and 64(2)%for Nb 2 AsC,as opposed to the pure phases obtained by SSS.The experimental analyses combined with first-principles calculations reveal that the dominant formation route of Nb_(3)P_(2)C is through NbP+Nb+C→Nb_(3)P_(2)C.Moreover,we found that the benefits of MSS on P-containing MAX phases are on the facilitation of three consid-ered chemical reaction routes,especially on Nb 2 PC+NbP→Nb_(3)P_(2)C.Furthermore,the intrinsic physical properties and Fermi surface topology of two 321 phases consisting of electron,hole,and open orbits are revealed theoretically and experimentally,in which the electron carriers are dominant in electrical trans-port.The feasible synthesis methods and the formation mechanism are instructive to obtain high-purity As/P-containing MAX phases and explore new MAX phases.Meanwhile,the intrinsic physical properties will give great support for future applications on 321 phases.