Using a classical ensemble model, we investigate the correlation behaviour of electrons originating from nonsequential double ionization （NSDI） of argon atoms by the elliptically polarized laser pulses. Because of the ellipticity, not only the first electron to return but also the later return of tunneled electrons contribute significantly to NSDI. We mainly discuss two kinds of events of NSDI originating from the first and the second return separately. For the NSDI resulting from the recollision of the first return, the correlated electron momentum spectrum along the long axis of the laser polarization plane reveals an obvious V-like shape, located at the first and third quadrant. However, for the NSDI resulting from the recollision of the second return, the momenta of two electrons are distributed in the four quadrants uniformly. By analysing the trajectories of these two kinds, we find that the recollision energy and the laser phase at recollision are different for the first and second returning trajectories, which are responsible for the difference in the correlated behavior of the final electron momentum.
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.
The structural and thermoelasticity of antifluorite magnesium silicide at high temper- atures were studied by using the plane-wave pseudo-potential method in the frame- work of density functional theory. The bulk ground-state quantities such as lattice constants, cell volumes, band structures and elastic constants were calculated. It showed that the elastic constants of Mg2Si were well consistent with the experimen- tal data under ambient conditions. The crystal cell volume and bulk modulus of Mg2Si as functions of applied temperature were also presented. The lattice dynamics was applied to determine the phonon dispersion curves. To complete the fundamental characterisation of this crystal, the coefficients of thermal expansion （CTE）, isochoric heat capacities and Debye temperature of Mg2Si in the whole temperature range from 0 K to 1300 K and pressure range from 0 GPa to 7.48 GPa were investigated. The results were in favourable agreement with the previous theoretical calculations and the existing experimental data.
The optical nonlinearities of an Ag nanoparticle array are investigated by performing Z-scan measurements at the selected wavelengths （400, 600, 650, and 800 nm）. The nonlinear refraction index in the resonant region （around 400 nm） exhibits a significant enhancement by two orders compared with that in the off-resonant region （around 800 nm））, and exhibits an sign alternation of the resonant nonlinear absorption, which results in a negligible nonlinear absorption at a certain excitation intensity. Moreover, a low degree of nonlinear absorption was measured at the edges of the resonant region （600 and 650 nm）, which is attributed to the competition of the saturated absorption and the two-photon absorption processes.
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.
The plane-wave pseudo-potential method within the framework of first principles is used to investigate the structural and elastic properties of Mg2Si in its intermediate pressure （Pnma） and high pressure phases （P63/mrnc）. The lattice constants, the band structures. The bulk moduli of the Mg2Si polymorphs are presented and discussed. The phase transition from anti-cotunnite to Ni2In-type Mg2Si is successfully reproduced using a vibrational Debye-like model. The phase boundary can be described as P = 24.02994 ＋ 3.93 × 10^-3T -- 4.66816 × 10^-5T2 -- 2.2501 × 10^-9T3＋ 2.33786 × 10^-11T4. To complete the fundamental characteristics of these polymorphs we have analysed thermodynamic properties, such as thermal expansion and heat capacity, in a pressure range of 1-40 GPa and a temperature range of 0-1300 K. The obtained results tend to support the available experimental data and other theoretical results. Therefore, the present results indicate that the combination of first principles and a vibrational Debye-like model is an efficient scheme to simulate the high temperature behaviours of Mg2Si.
