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.
Atomistic modeling based on the density functional theory combined with the quasi-harmonic approximation is used to investigate the lattice parameters and elastic moduli of the P6 and P6＇ phases of Si3N4. β-Si3N4 is set as a benchmark system since accurate experiments are available. The calculated lattice constants and elastic constants of β-Si3N4 are in good agreement with the experimental data. The crystal anisotropy, mechanical stability, and brittle behavior of P6- and P6＇-Si3N4 are also discussed in the pressure range of 30-55 GPa. The results show that these two polymorphs are metallic compounds. The brittleness and elastic anisotropy increase with applied pressure increasing. Besides, the phase boundaries of the β→P6＇→δ transitions are also analysed. The β phase is predicted to undergo a phase transition to the P6＇ phase at 40.0 GPa and 300 K. Upon further compression, the P6＇→δ transition can be observed at 53.2 GPa. The thermal and pressure effects on the heat capacity, cell volume and bulk modulus are also determined. Some interesting features are found at high temperatures.
This paper describes the results of structural, electronic and elastic properties of silicon nitride （in its high-pressure P61 and P62 phases） through the first-principles calculation combined with an ultra-soft pseudo- potential. The computed equilibrium lattice constants agree well with the experimental data and the theoretical results. The strongest chemical bond （N-Si bond） shows a covalent nature with a little weaker ionic character. P61- Si3N4 is more stable than P62-Si3N4 due mainly to the fact that the shorter N-Si bond in the P61 phase allows stronger electron hybridizations. We have also predicted the phase stability of Si3N4 using the quasi-harmonic approximation, in which the lattice vibration and phonon effect are both considered. The results show that the 13 P61 phase transition is very likely to occur at 42.9 GPa and 300 K. The reason why the β→P61→3 phase transitions had never been observed is also discussed.
Atomistic modeling based on the accurate first-principles method is used to investigate the lattice parameter, elastic constant, elastic modulus including bulk modulus （B） and shear modulus （G）, Poisson＇s ratio, and elastic anisotropy of Al, NiAl and NiaAl under extreme condition. The elastic constants obtained from calculations meet their mechanical stability criteria. Both NiAl and Ni3Al exhibit ductile behavior due to their high bulk mudulus to shear modulus ratios of B/G ratios. Through the full-electronic quasi-harmonic approximation, in which the mobile electrons are considered, we successfully obtain the thermo-physical properties including the thermal expansion coefficient, bulk modulus, heat capacity and entropy at simultaneously high temperatures and high pressures. The calculated quantities agree well with the available results. Some silent results are also interpreted. Several interesting features in the thermodynamic properties can also be observed.
Motivated by the first measurement on B（Bs→ Ф μ^＋ μ^-by the CDF Collaboration, we study the supersymmetric effects in semi-leptonic Bs→ Ф μ^＋ μ^-ecay. In our evaluations, we analyze the dependences of the dimuon invariant mass spectrum and the forward-backward asymmetry on relevant supersymmetric couplings in the MSSM with and without R-parity. The analyses show that the new experimental upper limits of B（Bs→ Ф μ^＋ μ^-from the LHCb Collaboration could further improve the bounds on sneutrino exchange couplings and （δ^u LL）23 as well as （δ^d LL,RR）23 mass insertion couplings. In addition, within the allowed ranges of relevant couplings under the constraints from B（Bs→ Ф μ^＋ μ^- B（B → K^（＊） μ^＋ μ^-and B（Bs → μ^＋ μ^-, the dimuon forward-backward asymmetry and the differential dimuon forward-backward asymmetry of Bs→Ф μ^＋ μ^-re highly sensitive to the squark exchange contribution and the （ LL）23 mass insertion contribution. The results obtained in this work will be very useful in searching for supersymmetric signals at the LHC.
The equilibrium lattice constants, elastic constants and elastic moduli of wll- and post-spinel Si3Na have been investigated in the pressure ranges of 0-40 GPa and 160-240 GPa, respectively. These two phases are found to be dynamically stable. The post-spinel phase is one of the strongest materials yet investigated under extreme compressions. Some fundamental properties and phase transition characters are evaluated from the quasi-harmonic approximation. The transition pressures from the γ phase to the post-spinel phase are 152.5 GPa （at 300 K） and 181.8 GPa （at 1500 K）. The phase transition pressures of theβ→wll and γ→postspinel transitions increase with the rise of temperature; hence, at higher temperature it requires higher pressure to synthesize post-spinel Si3Na. The heat capacity, thermal expansion and bulk modulus of the new phases are computed as functions of pressure and temperature. The heat capacity of post-spinel Si3Na is large at high temperature and only weakly pressure dependent.
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.
