Predictions of pressure-induced structural transition, mechanical and thermodynamic properties of α-and β-Si3N4 ceramics: ab initio and quasi-harmonic Debye modeling

The plane-wave pseudo-potential method within the framework of ab initio technique is used to investigate the structural and elastic properties of α-and β-Si3N4.The ground-state parameters accord quite well with the experimental data.Our calculation reveals that α-Si3N4 can retain its stability to at least 40 GPa when compressed at 300 K.The α→β phase transformation would not occur in a pressure range of 0-40 GPa and a temperature range of 0-300 K.Actually,the α→β transition occurs at 1600 K and 7.98 GPa.For α-and β-Si3N4,the c axes are slightly more incompressible than the a axes.We conclude that β-Si3N4 is a hard material and ductile in nature.On the other hand,β-Si3N4 is also found to be an ionic material and can retain its mechanical stability in a pressure range of 0-10 GPa.Besides,the thermodynamic properties such as entropy,heat capacity,and Debye temperature of α-and β-Si3N4 are determined at various temperatures and pressures.Significant features in these properties are observed at high temperature.The calculated results are in good agreement with available experimental data and previous theoretical values.Many fundamental solid-state properties are reported at high pressure and high temperature.Therefore,our results may provide useful information for theoretical and experimental investigations of the Si3N4 polymorphs.     

mechanical and thermodynamic properties of α-and β-Si3N4 ceramics： ab initio and quasi-harmonic Debye modeling

The plane-wave pseudo-potential method within the framework of ab initio technique is used to investigate the structural and elastic properties of α-and β-Si3N4. The ground-state parameters accord quite well with the experimental data. Our calculation reveals that α-Si3N4 can retain its stability to at least 40 GPa when compressed at 300 K. The α → β phase transformation would not occur in a pressure range of 0-40 （3Pa and a temperature range of 0 300 K. Actually, the α → β transition occurs at 1600 K and 7.98 GPa. For α-and β-Si3N4, the c axes are slightly more incompressible than the a axes. We conclude that β-Si3N4 is a hard material and ductile in nature. On the other hand, β-Si3N4 is also found to be an ionic material and can retain its mechanical stability in a pressure range of 0 - 010 GPa. Besides, the thermodynamic properties such as entropy, heat capacity, and Debye temperature of α-and β-Si3N4 are determined at various temperatures and pressures. Significant features in these properties are observed at high temperature. The calculated results are in good agreement with available experimental data and previous theoretical values. Many fundamental solid-state properties are reported at high pressure and high temperature. Therefore, our results may provide useful information for theoretical and experimental investigations of the Si3N4 polymorphs.     

Investigations of high-pressure and high-temperature behaviors of the newly-discovered willemite-Ⅱ and post-phenacite silicon nitrides

Using the first-principles method of the plane-wave pseudo-potential, the structural properties of the newly-discovered willemite-Ⅱ Si3N4 （wⅡ phase） and post-phenacite Si3N4 （δ phase） are investigated. The α phase is predicted to undergo a first-order α→wⅡ phase transition at 18.6 GPa and 300 K. Within the quasi-harmonic approximation （QHA）, the α→wⅡ phase boundary is also obtained. When the well-known β→γ transition is suppressed by some kinetic reasons, the β→δ phase transformation could be observed in the phase diagram. Besides, the temperature dependences of the cell volume,thermal expansion coefficient, bulk modulus, specific heat, entropy and Debye temperature of the involved phases are determined from the non-equilibrium free energies. The thermal expansion coefficients of wⅡ-Si3N4 show no negative values in a pressure range of 0-30 GPa, which implies that the wⅡ-Si3N4 is mechanically stable. More importantly, the δ-Si3N4 is found to be a negative thermal expansion material. Further experimental investigations may be required to determine the physical properties of wⅡ- and δ-Si3N4 with higher reliability.     

First-principles study of mechanical stability and thermal properties of MNNi₃ （M=Zn,Mg,Al） under pressure

The mechanical stability,elastic,and thermodynamic properties of the anti-perovskite superconductors MNNi 3(M=Zn,Mg,Al) are investigated by means of the first-principles calculations.The calculated structural parameters and elastic properties of MNNi 3 are in good agreement with the experimental and the other theoretical results.From the elastic constants under high pressure,we predict that ZnNNi 3,MgNNi 3,and AlNNi 3 are not stable at the pressures above 61.2 GPa,113.3 GPa,and 122.4 GPa,respectively.By employing the Debye model,the thermodynamic properties,such as the heat capacity and the thermal expansion coefficient,under pressures and at finite temperatures are also obtained successfully.     

Pressure-induced phase transition in silicon nitride material

The equilibrium crystal structures,lattice parameters,elastic constants,and elastic moduli of the polymorphs α-,β-,and γ-Si3N4,have been calculated by first-principles method.β-Si3N4 is ductile in nature and has an ionic bonding.γSi3N4 is found to be a brittle material and has covalent chemical bonds,especially at high pressures.The phase boundary of the β→γ transition is obtained and a positive slope is found.This indicates that at higher temperatures it requires higher pressures to synthesize γ-Si3N4.On the other hand,the α→γ phase boundary can be described as P = 14.37198+ 3.27 × 10?3T-7.83911 × 10?7T2-3.13552 × 10?10T3.The phase transition from α-to γ-Si3N4 occurs at 16.1 GPa and 1700 K.Then,the dependencies of bulk modulus,heat capacity,and thermal expansion on the pressure P are obtained in the ranges of 0 GPa-30 GPa and 0 K-2000 K.Significant features in these properties are observed at high temperatures.It turns out that the thermal expansion of γ-Si3N4 is larger than that of α-Si3N4 over wide pressure and temperature ranges.The evolutions of the heat capacity with temperature for the Si3N4 polymorphs are close to each other,which are important for possible applications of Si3N4.     

Compression behavior and phase transition of β-Si_3N_4 under high pressure

The compressibility and pressure-induced phase transition of β-Si_3N_4 were investigated by using an angle dispersive x-ray diffraction technique in a diamond anvil cell at room temperature. Rietveld refinements of the x-ray powder diffraction data verified that the hexagonal structure(with space group P63/m, Z = 2 formulas per unit cell) β-Si_3N_4 remained stable under high pressure up to 37 GPa. Upon increasing pressure, β-Si3 N4 transformed to δ-Si_3N_4 at about 41 GPa. The initial β-Si_3N_4 was recovered as the pressure was released to ambient pressure, implying that the observed pressureinduced phase transformation was reversible. The pressure–volume data of β-Si_3N_4 was fitted by the third-order Birch–Murnaghan equation of state, which yielded a bulk modulus K_0= 273(2) GPa with its pressure derivative K_0= 4(fixed)and K0= 278(2) GPa with K 0= 5. Furthermore, the compressibility of the unit cell axes(a and c-axes) for the β-Si_3N_4 demonstrated an anisotropic property with increasing pressure.     

High-pressure dynamic,thermodynamic properties,and hardness of CdP_2

Using a pseudopotential plane-waves method,we calculate the phonon dispersion curves,thermodynamic properties,and hardness values of α-CdP_2 and β-CdP_2 under high pressure.From the studies of the phonon property and enthalpy difference curves,we discuss a phase transform from β-CdP_2 to a-CdP_2 in a pressure range between 20 GPa and 25 GPa.Then,the thermodynamic properties,Debye temperatures,and heat capacities are investigated at high pressures.What is more,we employ a semiempirical method to evaluate the pressure effects on the hardness for these two crystals.The results show that the hardness values of both α-CdP_2 and β-CdP_2 increase as pressure is increased.The influence mechanism of the pressure effect on the hardness of CdP_2 is also briefly discussed.     

Influence of Pressure on the Annealing Process of β-Ca_2SiO_4(C_2S) in Portland Cement

Portland cement is the most common type of cement in general use around the world as a basic ingredient of concrete, mortar, stucco, and non-speciality grout. Dicalcium silicate(Ca_2SiO_4) is the primary constituent of a number of different types of cement. The β-Ca_2SiO_4 phase is metastable at room temperature and will transform into γ-Ca_2SiO_4 at 663 K. In this work, Portland cement is annealed at a temperature of 950 K under pressures in the range of 0–5.5 GPa. The high pressure experiments are carried out in an apparatus with six anvil tops. The effect of high pressure on the obtaining nano-size β-Ca_2SiO_4(C_2 S) process is investigated by x-ray diffraction and transmission electron microscopy. Experimental results show that the grain size of the C_2 S decreases with the increase of pressure. The volume fraction of the C_2 S phase increases with the pressure as the pressure is below3 GPa, and then decreases(P 3 GPa). The nano-effect is very important to the stabilization of β-Ca_2SiO_4. The mechanism for the effects of the high pressure on the annealing process of the Portland cement is also discussed.     

First-Principles Calculations of Phase Transition and Stability of Si2CN4 under High Pressure

A pressure-induced phase transition and stability in Si2 CN4 polymorphs under high pressure are studied by firstprinciples calculations. The result shows that the phase transition pressure of α- and β-Si2 CN4 to the cubic spinal phase is 29.9 GPa and 27.5 GPa predicted by thermodynamic method respectively. Under ambient condition, all of the three Si2CN4 polymorphs are metastable with positive formation enthalpy. Unlike the stability of Si3N4 polymorphs, α-Si2 CN4 is more stable than the β phase.     

Compression Behaviour of Bulk Metallic Glasses and Binary Amorphous Alloy

The compression properties of Zr41Ti14Cu12.aNi10Be22.5, Zr44.4Nb7Cu13.5Ni10.8Be24.3 bulk metallic glasses and Ni77P23 binary amorphous alloy are investigated at room temperature up to 24 GPa, 39 GPa and 30.5 GPa, respectively, using in-situ high pressure energy dispersive x-ray diffraction with a synchrotron radiation source. The pressure-volume relationship of Ni77P23 amorphous alloy is consistent well with the second order BirchMurnaghan （B-M） equation within the experimental pressure range. However, under higher pressure, the experimental data of Zr-based specimens deviate from the B-M equation. Compare to the binary amorphous alloy less excess free volume existing in the bulk metallic glass and multi-component atomic configuration results in a two-stage relationship between compressibility and pressure.     

Thermodynamic properties of ZnSe under pressure and with variation in temperature

The thermodynamic properties of Zn Se are obtained by using quasi-harmonic Debye model embedded in Gibbscode for pressure range 0–10 GPa and for temperature range 0–1000 K. Helmholtz free energy, internal energy, entropy,Debye temperature, and specific heat are calculated. The thermal expansion coefficient along with Gruneisen parameter are also calculated at room temperature for the pressure range. It is found that internal energy is pressure dependent at low temperature, whereas entropy and Helmholtz free energy are pressure sensitive at high temperature. At ambient conditions,the obtained results are found to be in close agreement to available theoretical and experimental data.     

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 66.7GPa 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 200GPa. The calculated results are in excellent agreement with existing experimental data at ambient pressure and compared favourably with other pseudopotential 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 are consistent with other previous results at zero pressure.     

Theoretical Study of Thermodynamics Properties and Bulk Modulus of SiC under High Pressure and Temperature

In extended pressure and temperature ranges, a theoretical study of the isothermal bulk modulus of SiC in B3 structure under high pressure and temperature is carried out by means of first-principles density functional theoretical calculations combined with the quasi-harmonic Debye model. Through the quasi-harmonic Debye model, the isothermal bulk modulus and its first and second pressure derivatives are successfully obtained. The thermodynamics properties of 3C-SiC are investigated in the pressure range of 0-100 GPa and the temperature range of 0-2000 K.     

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

<正>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 B₀’ 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-V₀）/V₀ to the temperature and the pressure,and the relations of the heat capacity C_V and the thermal expansion coefficientαto 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,C_V is proportional to T³ and tends to the Dulong-Petit limit at higher temperature.We predict that the thermal expansion coefficientαof NbN is about 4.20×10^-6/K at 300 K and 0 GPa.     

Structural analysis and crystal-field calculations of Nd³⁺ in Gd_x Lu_1-x TaO₄（x = 0.85） polycrytalline

The crystal structural parameters of Nd 3+-doped rare earth orthotantalate Gd x Lu 1 x TaO 4(x = 0.85) are determined by applying the Rietveld refinement to its X-ray diffraction,and its emission and excitation spectra at 77 K are analysed.The relativistic model of ab initio self-consistent DV-Xα method,which is applied to the cluster NdO 8 in Gd x Lu 1 x TaO 4,and the effective Hamiltonian model are used to investigate its spin-orbit and crystal-field parameters.The free-ions and crystal-field parameters are fitted to the experimental energy levels at 77 K with a root-mean-square deviation of 14.92 cm 1.According to the crystal-field calculations,96 levels of Nd 3+ are assigned.Finally,the fitting results of free-ions and crystal-field parameters are compared with those already reported for Nd 3+:YAlO 3.The results indicate that the free-ion parameters are similar to those of the Nd3+ in Gdx Lu1-x TaO4 and YAlO 3 hosts,and the crystal-field interaction of Nd3+ in Gdx Lu1-x TaO4 is stronger than that in YAlO 3.     

Investigations of phase transition, elastic and thermodynamic properties of GaP by using the density functional theory

The phase transition of gallium phosphide (GaP) from zinc-blende (ZB) to a rocksalt (RS) structure is investigated by the plane-wave pseudopotential density functional theory (DFT). Lattice constant a₀, elastic constants c_ij, bulk modulus B₀ and the pressure derivative of bulk modulus B₀' are calculated. The results are in good agreement with numerous experimental and theoretical data. From the usual condition of equal enthalpies, the phase transition from the ZB to the RS structure occurs at 21.9 GPa, which is close to the experimental value of 22.0 GPa. The elastic properties of GaP with the ZB structure in a pressure range from 0 GPa to 21.9 GPa and those of the RS structure in a pressure range of pressures from 21.9 GPa to 40 GPa are obtained. According to the quasi-harmonic Debye model, in which the phononic effects are considered, the normalized volume V/V₀, the Debye temperature θ, the heat capacity C_v and the thermal expansion coefficient α are also discussed in a pressure range from 0 GPa to 40 GPa and a temperature range from 0 K to 1500 K.     

Influence of pressure on the solid state phase transformation of Cu-Al-Bi alloy

The solid state phase transformation of Cu-Al-Bi alloy under high pressure was investigated by x-ray diffraction, energy dispersive spectroscopy and transmission electron microscopy. Experimental results show that the initial crystalline phase in the Cu-Al-Bi alloy annealed at 750℃ under the pressures in the range of 0-6 GPa is α-Cu solid solution (named as α-Cu phase below), and high pressure has a great influence on the crystallisation process of the Cu-Al-Bi alloy. The grain size of the α-Cu phase decreases with increasing pressure as the pressure is below about 3 GPa, and then increases (P 3 GPa). The mechanism for the effects of high pressure on the crystallisation process of the alloy has been discussed.     

Temperature—Dependent Raman Spectra and Microstructure of Barium Metaborate Crystals and Its Melts

We have measured the Raman spectra of β-and α－barium metaborate in crystal and liquid states from room temperature to 1873K,with a semiconductor laser as the laser source,coupled with a time-resolved detection system to eliminate the dense thermal emission background when temperature was considerably high.Temperature-dependent Raman spectra can clearly indicate that the phase transformation from β-to α-barium metaborate has been completed during 1273-1300K.Variations of different kinds of microstructure units with temperature are identified and discussed.     

Synthesis and characterization of NaAlSi_2O_6 jadeite under 3.5 GPa

The high pressure and high temperature(HPHT) method is successfully used to synthesize jadeite in a temperature range of 1000℃–1400℃ under a pressure of 3.5 GPa. The initial raw materials are Na_2SiO_3·9H_2O and Al_2(SiO_3)_3.Through the HPHT method, the amorphous glass material is entirely converted into crystalline jadeite. We can obtain the good-quality jadeite by optimizing the reaction pressure and temperature. The measurements of x-ray diffraction(XRD),scanning electron microscopy(SEM), Fourier-transform infrared(FTIR) and Raman scattering indicate that the properties of synthesized jadeite at 1260℃ under 3.5 GPa are extremely similar to those of the natural jadeite. What is more, the results will be valuable for understanding the formation process of natural jadeite. This work also reveals the mechanism for metamorphism of magma in the earth.     

Mechanical and thermodynamic properties of cubic YH_2 under high pressure:Prediction from first-principles study

First-principles calculations are used to investigate the mechanical and thermodynamic properties of cubic YH2 at different pressures and temperatures. The generalized gradient approximation （GGA） with Perdew-Burke-Ernzerhof （PBE） method is used to describe the exchange-correlation energy in the present work. The calculated equilibrium lattice constant a and bulk modulus B are in good accordance with the available experimental values. According to the Born-Huang criteria for mechanical stability, elastic constants are calculated from the strain-induced stress method in a pressure range from 0 to 67.1 GPa. Isotropic wave velocities and sound velocities are discussed in detail. It is found that the Debye temperature decreases monotonically with the increase of pressure and that YH2 has low anisotropy in both longitudinal and shear-wave velocities. The calculated elastic anisotropic factors indicate that YH2 has low anisotropy at zero pressure and that its elastic anisotropy increases as pressure increases. Through the quasi-harmonic Debye model, in which phononic effects are considered, the thermodynamic properties of YH2, such as the relations of （V-Vo）/Vo to the temperature and the pressure, the dependences of heat capacity Cv and thermal expansion coefficient a on temperature and pressure ranging from 0 to 2400 K and from 0 to 65 GPa, respectively, are also discussed.