Pressure and temperature effects on the Γ, N and L-phonons in zirconium

Abstract

The effective potentials for the E_2g,-phonon at the T point of the Brillouin zone of hep Zr, the transverse N- and longitudinal L-phonons of bcc Zr are calculated for different pressures by the “frozen phonon” method. The temperature and pressure dependences of the phonon frequencies are studied within the framework of a modified pseudo-harmonic approximation. The results obtained are in good agreement with the experimental ones. The stability of the hep, bec and ω phases of zirconium at different temperatures and pressures is discussed.     

Lattice dynamics of some binary alloys

Summary The phonon dispersion frequencies for Cu₃Au, Cu₃Zn and Ni₃Fe alloys have been calculated using the model potential approach. The contribution of a short-range three-body interaction to the dynamical matrix has also been included in the present study. The theoretically computed phonon dispersion curves of these alloys are found to be in good agreement with the experimental data.     

First-principles study of lattice dynamics of LiFePO4

Lattice dynamics of lithium iron orthophosphate (LiFePO₄) isostructural with olivine have been investigated using the first-principles calculations taking into account the on-site Coulomb interaction within the GGA + U scheme. Born effective charge tensors, phonon frequencies at the Brillouin zone center and phonon dispersion curves are calculated and analyzed. The Born effective charge tensors exhibit anisotropy, which gives a convincing evidence for the one-dimensional Li migration tunnel along the [010] direction in LiFePO₄, which has been proposed by other theoretical calculations and experimental observation. The calculated phonon frequencies at the Γ point of the Brillouin zone show good agreement with the available experimental observations.     

Pressure dependence of zone-boundary phonons in AlSb

Abstract

We have investigated the effect of hydrostatic pressure on zone-boundary and other critical-point phonon frequencies of AlSb by second-order Raman scattering. A softening of the TA(X), TA(L) and (L/T)A([Sgrave]) modes has been observed for pressures up to the first phase transition at 7.7 GPa. The LA(L) as well as the optical TO at X-, L-, and LO at [Sgrave]-, X-points harden with increasing pressure. Mode Griineisen parameters of all the resolved modes were calculated. Reflectivity measurements indicate that the high pressure phase above 7.7 GPa is metallic.     

Phonons and their dispersion in model ferroelastics Hg2Hal2

Dispersion relations of the acoustic and optical phonon frequencies have been calculated and plotted, and the density of states of the phonon spectrum of Hg₂Cl₂ and Hg₂Br₂ crystals has been derived. The effect of hydrostatic pressure on the frequencies of acoustic and optical phonons and their dispersion has been theoretically analyzed. It has been found that an increase in the pressure leads to a strong softening of the slowest acoustic TA branch (the soft mode) at the X point of the Brillouin zone boundary, which is consistent with the phenomenological Landau theory and correlates with experiment.     

Vibrational properties of vacancy in bcc transition metals using embedded atom method potentials

The embedded atom method (EAM) potentials, with the universal form of the embedding function along with the Morse form of pair potential, have been employed to determine the potential parameters for three bcc transition metals: Fe, Mo, and W, by fitting to Cauchy pressure (C ₁₂???C ₄₄)/2, shear constants $G_\textrm{v} =({C_{11} -C_{12} +3C_{44}})/5$ and C ₄₄, cohesive energy and the vacancy formation energy. The obtained potential parameters are used to calculate the phonon dispersion spectra of these metals. Large discrepancies are found between the calculated results of phonon dispersion using the EAM and the experimental phonon dispersion results. Therefore, to overcome this inadequacy of the EAM model, we employ the modified embedded atom method (MEAM) in which a modified term along with the pair potential and embedding function is added in the total energy. The phonon dispersions calculated using potential parameters obtained from the MEAM show good agreement with experimental results compared to those obtained from the EAM. Using the calculated phonons, we evaluate the local density of states of the neighbours of vacancy using the Green’s function method. The local frequency spectrum of first neighbours of vacancy in Mo shows an increase at higher frequencies and a shift towards the lower frequencies whereas in Fe and W, the frequency spectrum shows a small decrease towards higher frequency and small shift towards lower frequency. For the second neighbours of vacancy in all the three metals, the local frequency spectrum is not much different from that of the host atom. The local density of states of the neighbours of the vacancy has been used to calculate the mean square displacements and the formation entropy of vacancy. The calculated mean square displacements of the first neighbours of vacancy are found to be higher than that of the host atom, whereas it is lower for the second neighbours. The calculated results of the formation entropy of the vacancy compared well with other available results.     

Structural and phonon dynamical properties of perovskite manganites: (Tb, Dy, Ho)MnO3

A shell model has been used to study the structure, phonon dynamics and phase coexistence of perovskite manganites RMnO₃ (R=Tb, Dy, Ho). The calculated crystal structure, Raman and IR frequencies and specific heats are found to be in good agreement with the available experimental data. The phonon density of states, elastic constants, elastic stiffness, shear constants and phonon dispersion curves have been computed for these manganites. A zone center imaginary A_u mode is revealed in these phonon dispersion curves, which indicates the occurrence of the metastability of the perovskite phase. The Gibbs free energy values calculated as a function of temperature and pressure for RMnO₃ in the orthorhombic phase, when compared with those of the hexagonal phase, reveal the possibility of coexistence of these two phases in the present multiferroic manganites under ambient conditions.     

Elementary vibrations in rare-gas crystals: Frequencies of phonons in compressed argon, krypton, and xenon crystals

The lattice dynamics of rare-gas crystals is investigated in the framework of the ab initio approach with the inclusion of the nonadiabatic effects over a wide range of pressures. The frequencies of phonons in argon, krypton, and xenon crystals are calculated at pressures p ≠ 0. Analysis of the contributions from different interactions to the lattice dynamics of the crystals demonstrates that the difference between the phonon frequencies calculated within several models is most pronounced at the boundary of the Brillouin zone. Under strong compressions, the phonon spectrum along the Δ direction is distorted and the longitudinal mode is softened as a result of the electron-phonon interaction, with the relative contribution decreasing in the series Ar, Kr, and Xe. The calculated phonon frequencies are in good agreement with the experimental data available in the literature for argon crystals at a pressure p = 3.1 GPa.     

Electronic,elastic and dynamical properties of MgSe under pressure: rocksalt and iron silicide phase

The electronic, elastic and dynamical properties of MgSe in the rocksalt (B1) and iron silicide (B28) phase and the effects of pressure on these properties are investigated using first-principles method. The calculated electronic band structure indicates that the B1 phase of MgSe presents an indirect band-gap feature and the band gaps initially increase with pressure and subsequently decrease upon compression. Remarkably, an indirect-to-direct band-gap transition has been observed at the phase transition pressure. The elastic constants, bulk modulus, shear modulus, Young’s modulus, elastic anisotropy and B/G ratio of MgSe in the B1 and B28 phase at high pressure have also been investigated. The bulk modulus, shear modulus and Young’s modulus all increase monotonously with the increasing of pressure for the B1 and B28 phase of MgSe. The calculated phonon frequencies of the B1 phase at zero pressure agree well with available theoretical results. And the transverse acoustic phonon TA(X) mode of this phase completely softening to zero at 82 GPa. The phonon curves of the B28 phase under pressure have also been successfully investigated.     

Ag Raman modes of RBCO (R = Gd, Pr) by density functional theory approach

Ab initio total energy calculations have been performed for superconducting GdBa₂Cu₃O₇ and insulating PrBa₂Cu₃O₇ using the full-potential linear augmented plane-wave method in the local density approximation (LDA) and generalized gradient approximation (GGA). The comparison of the calculated unit cell volume and lattice parameters with the experimental data indicates the improvement of these parameters in the GGA relative to LDA. LDA and GGA give the equilibrium unit cell volume about 6% smaller and 1.25% larger than the experimental data, respectively for both systems. Thus frozen phonon calculations have been performed to determine the eigenvalues and eigenvectors of the k=0 A_g modes of the two systems in equilibrium structure have been obtained in GGA. The calculated frequencies in the GGA are in good agreement with the other LDA calculations for similar systems. Comparison of computational data with experimental data indicates that calculations determine the frequencies about ten percent below the experimental data. Even by improving LDA to GGA in these calculations, the calculated phonon frequencies have remained almost ten percent below the experimental data, even though the calculated unit cell volumes are nearly equal to the experimental data. So, applying GGA has not considerably decreased the difference between the computational and experimental data. The effect of Pr doping on the eigenvalues and eigenvectors have also been investigated.     

Computation of collective excitations and elastic constants of expanded trigonal tellurium

The potential function derived from experimental structure factor data gives a repulsive minimum and also an attractive minimum. These two minima correspond to the first and second nearest-neighbour distances. Similar results have been obtained through the use of Percus-Yevick (PY) and hyper-netted chain (HNC) equations. The Hafner molecular dynamics results also show a similar trend. The first, second and third derivatives of the potential function have been obtained from the expression of the potential function. The first and second derivatives have been used to compute the phonon frequencies using Bhatia and Singh's (BS) method. The phonon frequencies obtained from Hubbard and Beeby's (HB) method show similar results. The elastic constants have also been calculated and the values obtained for C₁₁ by different methods are in good agreement. The Grüneisen constant has been calculated by two different methods which are in very good agreement with each other. From the Grüneisen constant the pressure derivative of the diffusion coefficient has been obtained and has been compared with that of Swalin's equation. The results are in excellent agreement with each other.     

Lattice Dynamics of Some Fcc F-Shell Metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is used to study the binding energy, equation of state, ion-ion interaction, phonon dispersion curves (q-space and r-space analysis), phonon density of states, Debye temperature, mode Grüneisen parameters, dynamical elastic constants, Debye-Waller factor, mean-square displacement, Debye-Waller temperature parameter and propagation velocities of elastic waves of some fcc f-shell metals La, Yb, Ce, and Th. The contribution of the s-like electrons is calculated in the second-order perturbation theory for the model potential while d- and f-like electron is taken into account by introduction of repulsive short-range Born-Mayer term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The parameter of the potential is evaluated by zero pressure condition. Which is independent of any fitting procedure. An excellent agreement between theoretical investigations and experimental findings prove the ability of the potential for d- and f-shell metals exclusively.     

Intervalley Γ- X Deformation Potentials in Ⅲ-V Zincblende and Si Semiconductors by Ab Initio Pseudopotential Calculations

Intervalley Γ- X deformation potential constants (IVDP's) have been calculated by first principle pseudopotential method for the Ⅲ-V zincblende semiconductors Alp, AlAs, AlSb, Gap, GaAs, GaSb, InP, ZnAs and ZnSb. As a pro to type crystal we have also carried out calculations on Si. When comparing the calculated IVDP's of LA phonon for Gap, InP and InAs and LO phonon for AlAs, AlSb, GaAs, GaSb and InSb with a previous calculation by EPM in rigid approximation, good agreements are found. However, our ab initio pseudopotential results of LA phonon for AlAs, AlSb, GaAs, GaSb and InSb and LO phonon for Gap, InP and ZnAs are about one order of magnitude smaller than those obtained by EPM calculations, which indicate that the electron redistributions upon the phonon deformations may be important in affecting Γ- X intervalley shatteri'ngs for these phonon modes when the anions are being displaced. In our calculations the phonon modes of LA and LO at X point have been evaluated in frozen phonon approximation. We have obtained, at the same time, the LAX and LOX phonon frequencies for these materials from total energy calculations. The calculated phonon frequencies agree very well with experimental values for these semiconductors.     

Coherence and spike death induced by bounded noise and delayed feedback in an excitable system

The first-principles total energy calculations with the generalised gradient approximation and the plane-wave pseudopotential method have been employed to investigate the structural, electronic and dynamical properties of Li₂TiO₃ (lithium titanate). The atomic structure is fully relaxed, and the structural parameters are found to differ by less than 1% from the experimental data. The indirect band-gap with 3.49 eV is predicted from the band structure calculations of this compound. The calculated phonon frequencies at the ??-point for the Raman-active and the infrared-active modes are presented and assigned. The phonon dispersion curves are also calculated along high symmetry lines in the Brillouin zone (BZ). Furthermore, the thermodynamic functions have been worked out using the corresponding phonon density of states, and the results indicate that they are in good agreement with available experimental values.     

The Tersoff potential for phonons in GaAs

We report on the use of the Tersoff empirical potential applied to GaAs. Cohesive and elastic properties, as well as phonon frequencies and Grüneisen parameters at the Γ and X points, are calculated and compared to experimental data. The limitations of the potential and its existing parametrisations are discussed.     

Computation of collective modes and acoustic investigations at different temperatures of vitrous silica

This paper is mainly concerned with elastic and acoustic properties of vitrous silica besides the computation of phonon frequencies. Thus the phonon frequencies of vitrous silica have been calculated assuming the electronic bulk modulus,K _e, as equal to zero. New equations have been derived to relate the pressure derivatives of second order elastic constants to the acoustic Gruneisen’s parameters using both Bhatia-Singh’s parameters and Schofield’s equations. The calculated longitudinal and transverse Gruneisen’s parameters and the predicted absorption band spectra from Nagendranath’s equation and Bhatia Singh’s parameters are in good agreement with experiment. The calculated mean acoustic mode Gruneisen’s parameter evaluated from the pressure derivative of Nagendranath’s equation is also in good agreement with experiment. An erratum to this article is available at .     

Pressure Response of the Higher Fullerene C 84 Studied by Raman and X-ray Scattering

The pressure behavior of the intramolecular phonon modes of the fullerene C 84 and its structural stability have been studied for the first time by means of Raman spectroscopy and synchrotron X-ray diffraction at high pressure up to ～10 GPa. The volume of the cubic unit cell has been measured as a function of pressure. The experimental data fitted by the Murnaghan equation-of-state (EOS) gave K_{0}=19.5\pm 0.9\,\hbox{GPa} and K_{0}^{\prime}=16.4\pm 0.6 . The pressure coefficients and Grüneisen parameters of the intramolecular phonon modes of C 84 have been determined and compared with those of other fullerenes. The data obtained do not show any phase transition and the pressure behavior of the material is entirely reversible in the pressure region investigated.     

High pressure study of the 2D polymeric phase of C60 by means of raman spectroscopy

Abstract

The effect of high hydrostatic pressure, up to 12GPa, on the intramolecular phonon frequencies and the material stability of the two-dimensional tetragonal Cm polymer has been studied by means of Raman spectroscopy in the spectral range of the radial intramolecular modes (200-800cm^?1). A number of new Raman modes appear in the spectrum for pressures ～ 1.4 and ～ 5.0 GPa. The pressure coefficients for the majority of the phonon modes exhibit changes to lower values at P=4.0 GPa, which may be related to a structural modification of the 2D polymer to a more isotropic phase. The peculiarities observed in the Raman spectra are reversible and the material is stable in the pressure region investigated.     

A model for lattice dynamics of hexagonal close packed metals

The point ion axially symmetric model of Lehman et al. has been modified for h.c.p. metals to include the electron-ion interaction on the formalism of Krebs. The calculated phonon frequencies of magnesium have almost reproduced the experimental ones within the limit of experimental error.