Anharmonic stabilization of the high-pressure simple cubic phase of calcium

The phonon spectrum of the high-pressure simple cubic phase of calcium, in the harmonic approximation, shows imaginary branches that make it mechanically unstable. In this Letter, the phonon spectrum is recalculated by using density-functional theory ab initio methods fully including anharmonic effects up to fourth order at 50 GPa. Considering that the perturbation theory cannot be employed with imaginary harmonic frequencies, a variational procedure based on the Gibbs-Bogoliubov inequality is used to estimate the renormalized phonon frequencies. The results show that strong quantum anharmonic effects make the imaginary phonons become positive even at zero temperature so that the simple cubic phase becomes mechanically stable, as experiments suggest. Moreover, our calculations find a superconducting T(c) in agreement with experiments and predict an anomalous behavior of the specific heat.     

石墨带的晶格动力学研究

基于晶格动力学理论,采用力常数模型,计算了石墨带的声子色散关系、振动模式密度和比热.计算结果表明,石墨带的声子谱特征介于一维碳纳米管和二维石墨片之间.扶手椅型和锯齿型石墨带的中、高频声子支分别与锯齿型和扶手椅型碳纳米管的类似.由于声子限域效应,低频声子支随着石墨带带宽的改变出现明显的频移现象.振动模式密度在高频区几乎不敏感于带宽,而低频区的峰位随着带宽的增加而逐渐向低频移动.此外,无论是在低温还是高温,比热都随着带宽的增加而逐渐降低,呈现量子尺寸效应.在300K时,比热可以拟合成C_V=C_Vg+A/n,其中C_Vg为石墨片的热容,而A/n项反映了石墨带中边缘效应对比热的影响. 关键词： 石墨带 声子色散关系 比热     

Theoretical analysis of cross-plane lattice thermal conduction in graphite

A theoretical analysis of the cross-plane lattice thermal conduction in graphite is performed by using first-principles calculations and in the single-mode relaxation time approximation. The out-of-plane phonon acoustic mode ZA and optical mode ZO have almost 80% and 20% of contributions to cross-plane heat transfer, respectively. However, these two branches have a small part of total specific heat above 300 K. Phonons in the central 16% of Brillouin zone contribute80% of cross-plane transport. If the group velocity angle with respect to the graphite layer normal is less than 30?, then the contribution is 50% at 300 K. The ZA phonons with long cross-plane mean free path are focused in the cross-plane direction, and the largest mean free path is on the order of several micrometers at room temperature. The average value of cross-plane mean free path at 300 K is 112 nm for ZA phonons with group velocity angle with respect to the layer normal being less than 15?. The average value is dropped to 15 nm when phonons of all branches in the whole Brillouin zone are taken into account, which happens because most phonons have small or even no contributions.     

Phonon dispersion relations in semiconductor superlattices in the adiabatic bond-charge model

The phonon dispersion in semiconductor superlattices is studied in the adiabatic bond-charge model. The complex phonon dispersion relations of the constituent bulk materials are obtained via the eigenvalue method in a zeroth-order calculation, which includes only short range forces and Coulomb interactions between ions and bond charges in the same and neighboring layers. The eigenmode displacements of the superlattice are obtained by matching the eigenvectors associated with complex phonon branches at the interfaces. The effect of the remaining Coulomb interactions are then included in the first-order approximation. The results for the superlattice phonon frequencies compare favorably with the existing experimental data.     

Lattice thermal conductivity of skutterudite compounds

A generalized expression is used on the basis of relaxation time approximation to facilitate calculation of lattice thermal conductivity of dielectric materials as well as skutterudite family consists of compounds of the form AB₃. It is assumed that phonon scattering processes are independent and is represented by frequency dependent relaxation times. The contributions of normal three phonon scattering processes are included explicitly as redistribution of phonon momentum between two oscillation branches is considered. Magnitudes of relaxation times are estimated from the experimental data. The result for CoSb₃ is in reasonably good agreement with the experimental result in the temperature range 1–1000°K. It is observed that redistribution of phonon momentum between two oscillation branches leads to a significant suppression of thermal conductivity maximum and it is observed that for unfilled skutterudite the main dominant mechanism at the thermal conductivity maximum is three phonon normal scattering process.     

多原子半无限晶体中表面极化子的内部激发态

研究多原子半无限晶体中电子与表面光学(SO)声子耦合强,而与体纵光学(LO)声子耦合弱的极化子的激发态性质.采用线性组合算符和幺正变换方法导出与SO声子耦合强而与LO声子耦合弱情形下极化子的基态能量、第一内部激发态能量和激发能量.结果表明,多原子半无限晶体中与SO声子耦合强,而与LO声子耦合弱的极化子的基态能量、第一内部激发态能量不仅包含不同支LO声子和不同支SO声子与电子耦合的能量,而且也包含不同支SO声子之间相互作用贡献的附加能量.激发能量与体纵光学声子无关.     

Normal quasiparticle scattering and kinetic effects in degenerate semiconductors

The influence of normal processes of electron-electron and phonon-phonon scattering on quasiparticle momentum relaxation in nonequilibrium electron-phonon systems of degenerate semiconductors is investigated. A system of kinetic equations is solved for the electron and phonon distribution functions, and the kinetic coefficients of a semiconductor are calculated in the linear approximation in the degeneracy parameter. The influence of normal scattering of quasiparticles on the electrical conductivity, thermopower, and heat conductivity of a degenerate semiconductor is analyzed. Redistribution of the phonon momentum in N processes within each branch of the vibrational spectrum, as well as among different branches, is taken into account.     

High-resolution phonon study of the Ag(100) surface

Using high-resolution electron energy loss spectroscopy the phonon dispersion of Ag(100) has been studied at two different sample temperatures of 86 and 300 K. The dominant feature in the spectra corresponds to the Rayleigh wave. Its full dispersion is determined along the ΓX high symmetry direction in the first and second Brillouin zones. The Rayleigh phonon maximum at the X point shows a redshift with increasing temperature. This is explained based on a surface anharmonicity with an anharmonicity constant of 0.014, comparable to the value reported for Cu(100). In the vicinity of the Γ point two additional phonon features have been discovered at about 110 and 160 cm(-1), which are tentatively assigned to high density of states features from the bulk phonon bands. However, the observed steep dispersion is in contrast to theoretical calculations. Along ΓX two surface resonance branches have been observed with maximum frequencies in the range of 90-110 cm(-1) near to the zone boundary. These branches agree with helium atom scattering data where available, but are not predicted by theory.     

TiC lattice dynamics from ab initio calculations

Ab initio calculations and a direct method have been applied to derive the phonon dispersion curves and phonon density of states for the TiC crystal. The results are compared and found to be in a good agreement with the experimental neutron scattering data. The force constants have been determined from the Hellmann-Feynman forces induced by atomic displacements in a supercell. The calculated phonon density of states suggests that vibrations of Ti atoms form acoustic branches, whereas the motion of C atoms is confined to optic branches. The elastic constants have been found using the deformation method and compared with the results obtained from acoustic phonon slopes. Received 23 February 1998     

Relaxation times and mean free paths of phonons in the boundary scattering regime for silicon single crystals

The phonon focusing in cubic dielectric crystals and its influence on the heat transfer in the boundary phonon scattering regime at low temperatures have been investigated. The mean free paths of phonons of different polarizations in samples of infinite and finite lengths with circular and square cross sections have been calculated in the anisotropic continuum model. For samples of infinite length with circular and square cross sections in the case of the equality of the cross-sectional areas, the angular dependences of the mean free paths normalized by the Casimir length almost completely coincide. It has been shown that the anisotropy of the mean free paths decreases significantly upon changing over from infinite samples to samples of finite length. For silicon crystals, the anisotropy of the phonon mean free paths has been analyzed for each of the branches of the phonon spectrum. It has been found that the mean free paths for phonons of each vibrational mode reach maximum values in the directions of focusing, and, in these directions, they exceed the mean free paths for phonons of the other vibrational modes.     

Impact of anisotropy on polar optical vibration in a wurtzite cylindrical nanowire with ring geometry

The quasi-confined (QC) phonon modes, surface optical (SO) phonon modes and corresponding Fröhlich-like Hamiltonian in a wurtzite cylindrical nanowire with ring geometry are investigated in the framework of the dielectric continuum model and Loudon’s uniaxial crystal model. Numerical calculations are focused on the dispersion relations of the SO phonons and the electron–SO phonon coupling strength. Results show that there are only two branches of SO phonon modes. The dispersions of the two branches of SO phonon modes are obvious when the phonon wave-number k_z or the azimuthal quantum number m is small. Typical degenerating behavior of the SO modes is evidenced due to the anisotropic effect of wurtzite crystal. Moreover, when k_z or m are large enough, the frequencies of the two branches of SO modes converge to a definite limiting frequency in single planar heterostructure. The calculations of the electron–SO phonon coupling strength reveal that the high-frequency SO modes (SO₊) play a more important role in the coupling strength than the low-frequency ones (SO₋). Furthermore, the long-wavelength SO phonons with small m are the main factor contributing to the electron–phonon interaction.     

Phonon anomalies due to collective stripe modes in high T(c) cuprates

Phonon anomalies observed in various high T(c) cuprates by neutron experiments are analyzed theoretically in terms of the stripe concept. The phonon self-energy correction is evaluated by taking into account the charge collective modes of stripes, giving rise to dispersion gap, or kink and shadow phonon modes at twice the wave number of spin stripe. These features coincide precisely with observations. The gapped branches of the phonon are found to be in-phase and out-of-phase oscillations relative to the charge collective mode.     

Phonons and the electronic gap in FeSi

The partial phonon densities of states of iron atoms in the intermetallic compound FeSi have been measured in the temperature range 46–297 K using nuclear resonant inelastic scattering of synchrotron radiation. A significant phonon softening with increasing temperature has been established. The greatest phonon softening for iron atoms is shown to occur in the region of long-wavelength acoustic phonons, for the acoustic branches near the boundary of the Brillouin zone, and for the low-lying weakly dispersive optical branches. The results obtained are analyzed in terms of the views that relate the change in the phonon density of states of iron atoms to the temperature evolution of the electronic density of state for the compound.     

Lattice dynamics investigations of SiGe core-shell nanowires

We present results from lattice dynamics calculations on the phonon modes and specific heat of SiGe core-shell nanowires. The results show that phonon dispersion relation of SiGe nanowires consists of four acoustic branches. The frequency of the first optical mode at Γ point shifts to low frequency as the Ge concentration is increasing. There are three strong peaks in the spectra of density of states. The peaks at 9.0 THz and 15.0 THz can be attributed to the high frequency Ge-Ge and Si-Si bond vibration. The broad peak around 3.0 THz of pure silicon nanowire corresponds to the transverse acoustic branch of bulk silicon. Moreover, specific heat of SiGe nanowires increases (decreases) with the increase of the concentration x at low (high) temperature. The specific heat at 300 K can be fitted by C _V = x ² C _Ge + (1 − x)C _Si, where C _Ge and C _Si are specific heat of pure germanium and silicon nanowires respectively.     

Effect of normal processes on thermal conductivity of germanium,silicon and diamond

The effect of normal scattering processes is considered to redistribute the phonon momentum in (a) the same phonon branch — KK-S model and (b) between different phonon branches — KK-H model. Simplified thermal conductivity relations are used to estimate the thermal conductivity of germanium, silicon and diamond with natural isotopes and highly enriched isotopes. It is observed that the consideration of the normal scattering processes involving different phonon branches gives better results for the temperature dependence of the thermal conductivity of germanium, silicon and diamond with natural and highly enriched isotopes. Also, the estimation of the lattice thermal conductivity of germanium and silicon for these models with the consideration of quadratic form of frequency dependences of phonon wave vector leads to the conclusion that the splitting of longitudinal and transverse phonon modes, as suggested by Holland, is not an essential requirement to explain the entire temperature dependence of lattice thermal conductivity whereas KK-H model gives a better estimation of the thermal conductivity without the splitting of the acoustic phonon modes due to the dispersive nature of the phonon dispersion curves.      

Phonon softening,chaotic motion,and order-disorder transition in Sn/Ge(111)

The phonon dynamics of the Sn/Ge(111) interface is studied using high-resolution helium atom scattering and first-principles calculations. At room temperature we observe a phonon softening at the Kmacr; point in the (sqrt[3]xsqrt[3])R30 degrees phase, associated with the stabilization of a (3x3) phase at low temperature. That phonon band is split into three branches in the (3x3) phase. We analyze the character of these phonons and find out that the low- and room-temperature modes are connected via a chaotic motion of the Sn atoms. The system is shown to present an order-disorder transition.     

Exciton recombination in silver bromide

The recombination luminescence of the free indirect exciton is studied in pure AgBr single crystals at low temperature. The participation of two phonons with wavenumbers of 96 and 64 cm^?1, respectively, is discussed in view of the unusual behaviour of the transverse phonon branches near L. Weak coupling of the exciton to the LO (Γ) phonon and recombination via a shallow trap are observed.     

三氨基三硝基苯基高聚物粘结炸药热力学性质的理论计算研究

高聚物粘结炸药(PBX)的热力学性质是用于炸药结构响应、安全性评估、数值模拟分析等的重要参数.由于PBX结构的多尺度特性,完全采取实验方法精细表征这些参数存在巨大的挑战.本文运用第一性原理和分子动力学计算的方法,系统研究了三氨基三硝基苯(TATB)基高聚物粘结炸药的热力学参数和界面热传导性质.利用散射失配模型研究了TATB与聚偏二氟乙烯(PVDF)界面的热传导过程,发现热导率随温度升高而上升,并且在高温情况下接近于定值.基于分子动力学获得的TATB热导率并结合界面热导率,分析了PBX炸药的热导与颗粒尺寸的关系,当颗粒尺寸大于100 nm时,界面热阻对于PBX热导率的影响有限.     

The scattering of phonons of arbitrary wavelength at a solid-solid interface: Model calculation and applications

A one-dimensional lattice model of a solid-solid interface is presented within which it is possible to characterize the scattering of phonons at the interface as a function of wavelength. The probability for a phonon to be transmitted across the interface is found generally to decrease with decreasing wavelength, although phenomena such as total reflexion and resonant transmission may occur. Conditions for the existence of a localized interface mode are given. The thermal boundary resistance for heat flow across the interface is expressed in terms of an average temperature-dependent phonon transmission coefficient which generally increases with decreasing temperature and approaches the continuum value at very low temperature. Applications of these results to three-dimensional interfaces in general, and particularly to heat dissipation in catalysts, high-frequency phonon radiators, and Kapitza resistance, are discussed.