Theory Of Lattice Dynamics Research Articles

Raman frequency shift in oxygen-functionalized carbon nanotubes

Based on density functional theory, the geometrical and electronic structures ofoxygen-functionalized single-wall carbon nanotubes (O-SWCNs) are obtained, of which thevibrational properties are calculated in terms of lattice dynamics theory. Both bondexpansion and contraction are found to coexist in O-SWCNs. A distinct Raman shift isobserved in the radial breathing mode (RBM) and the G modes, depending not only on thetube diameter and chirality but also on oxygen coverage and adsorption configurations.With the oxygen coverage increasing, interestingly, a nonmonotonic upshift anddownshift is observed in the G modes, which is attributed to the competitionbetween the bond expansion and contraction. In addition, the resonance Ramaneffect at different oxygen coverage, which may be observable in O-SWCNs, isdiscussed.

Phonons and Jahn–Teller distortion in manganites

In this work, we present the calculated results phonon properties of rhombohedral ( R 3 ¯ c ) La 0.7 A 0.3 ′ MnO 3 (A′: Sr, Ba and Pb) manganites by using a lattice dynamical model theory. The effect of internal pressure determined by the average A-site atomic radius 〈 r A〉 is discussed. The computed zone centre phonon frequencies at ambient condition agree fairly well with the experimental results. The Raman active A 1g mode is most sensitive to the change of A-site atomic radius. The internal pressure hardens the A 1g phonon mode and reduces the electron–phonon interactions and hence the Jahn–Teller distortion. Change in the frequency of the Raman active E g modes with 〈 r A〉 is also observed. Different effect is observed for the low and high average A-site atomic radius. Effect of internal pressure modifies the phonon modes, which is observed to be reflected in calculated phonon density of states.

Pressure-dependent phonon properties ofLa0.7Sr0.3MnO3

In this work, we present the calculated results on the pressure dependent phonon properties of rhombohedral $(R\overline{3}c)$ ${\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}\mathrm{Mn}{\mathrm{O}}_{3}$ manganite by using a lattice dynamical model theory. The effect of internal pressure determined by the average $A$-site atomic radius is also investigated and compared with the effect of applied pressure. The computed zone center phonon frequencies at ambient pressure agree fairly well with the experimental results and the modes related to the octahedral distortion exhibit hardening with the increase in pressure. The Raman active ${A}_{1g}$ mode is most sensitive to pressure with a slope of $1.0\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}∕\mathrm{GPa}$ and shows unusual couple of slope change. Both internal and external pressures harden the ${A}_{1g}$ phonon mode and reduce the electron-phonon interactions. Change in the frequency of the Raman active ${E}_{g}$ modes with frequency is also observed. Different effect is observed for the low and high average $A$-site atomic radius. The phonon dispersion curves in high symmetry directions of the Brillouin zone and phonon density of states are also calculated. The pronounced shift of the peak positions in phonon DOS is observed with the increase in pressure. The analysis of the reduction of the high frequency phonon peak width and effective mode-Gr\"uneisen parameter allows us to draw a conclusion for the decrease in lattice distortion and to some extent Jahn-Teller (JT) distortion, a signature of rhombohedral structure for the manganites. The role of pressure on the lattice specific heat is also discussed.

Lattice Dynamics of Carbon Chain Inside a Carbon Nanotube

Based on the density functional theory, we obtain the optimum geometry of carbon chain inside a carbon nanotube. The phonon spectrum and specific heat of such a chain and nanotube hybrid system are calculated in terms of lattice dynamics theory. Some new phonon branches that have been obtained come from the coupling vibrations of the nanotube and the chain. The bending and stretching modes of the chain appear at about 520 cm(-1)and 1935 cm(-1) at Gamma point, respectively. It is found that the softening of G modes results mainly from the chain induced variations in the bond length on nanotube, independent of van der Waals interaction, while the stiffening of radial breathing mode is developed by the competition between the two factors. In the low-frequency region, the vibrational density of states are very different from that of the bare nanotube. Its specific heat implies the underlying quantized phonon structures and much large thermal conductivity in the hybrid system. In addition, the chain-length dependent vibration modes are calculated, from which it is expected that a finite chain of about 14 carbon atoms in the nanotube may produce the experimental Raman peak at about 1850 cm(-1).

Mode dispersion in the optical-phonon spectra of mixed crystals ZnS1−x Sex

The IR reflection and the Raman spectra of ZnS1−xSex crystals (0≤ x ≤ 1) are measured. The mode dispersion of the solid solutions is found to deviate from that calculated using an isodisplacement model. The reasons behind this deviation are discussed. Two additional modes are found in the frequency range between the ZnS-like TO and LO modes. It is assumed that one of them is a line of the second-order spectrum amplified by the Fermi resonance and the other is linked to the resonance (additional local) mode of Se impurity atoms. The latter conclusion is confirmed by calculating the spectrum of a Se impurity in a ZnS crystal in terms of the microscopic lattice dynamics theory in the low impurity concentration approximation. The oscillator strengths of the main and additional optical phonons in ZnS1−xSex solid solutions are discussed.

Phonon band structure and thermal transport correlation in a layered diatomic crystal

To elucidate the relationship between a crystal's structure, its thermal conductivity, and its phonon dispersion characteristics, an analysis is conducted on layered diatomic Lennard-Jones crystals with various mass ratios. Lattice dynamics theory and molecular dynamics simulations are used to predict the phonon dispersion curves and the thermal conductivity. The layered structure generates directionally dependent thermal conductivities lower than those predicted by density trends alone. The dispersion characteristics are quantified using a set of novel band diagram metrics, which are used to assess the contributions of acoustic phonons and optical phonons to the thermal conductivity. The thermal conductivity increases as the extent of the acoustic modes increases, and decreases as the extent of the stop bands increases. The sensitivity of the thermal conductivity to the band diagram metrics is highest at low temperatures, where there is less anharmonic scattering, indicating that dispersion plays a more prominent role in thermal transport in that regime. We propose that the dispersion metrics (i) provide an indirect measure of the relative contributions of dispersion and anharmonic scattering to the thermal transport, and (ii) uncouple the standard thermal conductivity structure-property relation to that of structure-dispersion and dispersion-property relations, providing opportunities for better understanding of the underlying physical mechanisms and a potential tool for material design.

Finite-temperature quasicontinuum method for multiscale analysis of silicon nanostructures

In this paper, we extend the quasicontinuum approach for a multiscale analysis of silicon nanostructures at finite temperature. The quasicontinuum method uses the classical continuum mechanics framework, but the constitutive response of the system is determined by employing an atomistic description. For finite-temperature solid systems under isothermal conditions, the constitutive response is determined by using the Helmholtz free energy density. The static part of the Helmholtz free energy density is obtained directly from the interatomic potential while the vibrational part is calculated by using the theory of quantum-mechanical lattice dynamics. Specifically, we investigate three quasiharmonic models, namely the real space quasiharmonic model, the local quasiharmonic model, and the reciprocal space quasiharmonic model, to compute the vibrational free energy. Using the finite-temperature quasicontinuum method, we compute the effect of the temperature and strain on the phonon density of states, phonon Gruneisen parameters, and the elastic properties of the Tersoff silicon. We also compute the mechanical response of silicon nanostructures for various external loads and the results are compared to molecular dynamics simulations.

Calculation of phonon spectrum for noble metals by modified analytic embedded atom method (MAEAM)

In the harmonic approximation, the atomic force constants are derived and the phonon dispersion curves along four major symmetry directions [00ζ], [0ζζ], [ζζζ] and [0ζ1] (or Δ, Σ, Λ and Z in group-theory notation) are calculated for four noble metals Cu, Ag, Au and Pt by combining the modified analytic embedded atom method (MAEAM) with the theory of lattice dynamics. A good agreement between calculations and measurements, especially for lower frequencies, shows that the MAEAM provides a reasonable description of lattice dynamics in noble metals.

Nondegenerate hard‐mode Raman studies of phase transition in antiferroelectric lead ytterbium niobate‐based perovskite compound

AbstractBy using Slater's phenomenological theory of atomic lattice dynamics, general results for the nondegenerate hard mode of phase transition are rederived in a simpler form. The change in inverse dielectric susceptibility (χ−1) associated with the phase transition is related to the hard‐mode frequency shift (ωQ) as ${\Delta}(\chi^{-1}) = R\omega_{\rm Q}^{2}$, where the proportionality constant R can be determined from the experimental data. This relation ${\Delta}(\chi^{-1}) = R\omega_{\rm Q}^{2}$ between the changes in χ−1 and $\omega_{\rm Q}^{2}$ was verified for the antiferroelectric phase transition observed in 0.94PYN [Pb(Yb1/2Nb1/2)O3]–0.06PT[PbTiO3], with the proportionality constant R as −1.6 × 10−7 cm2 in the antiferroelectric phase. Copyright © 2006 John Wiley & Sons, Ltd.

Phonon spectra and vibrational mode instability ofMgCNi3

This paper reports a detailed and systematic lattice dynamical calculation of the newly discovered intermetallic superconductor $\mathrm{Mg}\mathrm{C}{\mathrm{Ni}}_{3}$ by using a lattice dynamical model theory based on pairwise interactions under the framework of the rigid ion model. The results bring out the anomalous vibrational mode instability in the phonon dispersion curves and phonon density of states of $\mathrm{Mg}\mathrm{C}{\mathrm{Ni}}_{3}$. The calculated phonon dispersion curves and phonon density of states are in good agreement with the measured and density functional theoretical (DFT) data. The study also illustrates the contradicting results on the magnitude of phonon frequencies due to Mg atoms and the region of the unstable modes in the Brillouin zone of the previously computed two DFT results. The present study on DOS has enabled an atomic level understanding of the phonon density of states. The phonon density of states has been used to compute the specific heat at constant volume. The Debye temperature and temperature-dependent vibrational amplitudes of the different species are also reported. The present calculation suggests that the superconductivity in $\mathrm{Mg}\mathrm{C}{\mathrm{Ni}}_{3}$ is governed by the BCS mechanism.

Phenomenological Theory of Hard-Mode Frequency Shift in Ferroelectric Phase Transition

Useful relations of hard-mode spectroscopy are rederived from Slater's simplified phenomenological theory of lattice dynamics. The phase transition anomaly in inverse dielectric susceptibility (1/χ), related to the hard-mode frequency shift (ωQ) as Δ(χ-1)=RωQ2, can be analyzed to study structural phase transitions associated with a nondegenerate hard mode. This hard-mode frequency shift represents a change in the symmetry-restricted chemical bonding due to the structural phase transition. The effect of phase transition on the respective chemical bonds can be probed to follow the order parameter change by observing frequency shifts of the corresponding vibrational hard mode. The proportionality constant R can be expressed in terms of mode parameters, which may be associated with the reorientational mobility of the dipole clusters in the phase transition system.

LDA or GGA? A combined experimental inelastic neutron scattering and ab initio lattice dynamics study of alkali metal hydrides

In a previous work, we carried out inelastic neutron scattering (INS) spectroscopy experiments and preliminary first principles calculations on alkali metal hydrides. The complete series of alkali metal hydrides, LiH, NaH, KH, RbH and CsH was measured in the high-resolution TOSCA INS spectrometer at ISIS. Here, we present the results of ab initio electronic structure calculations of the properties of the alkali metal hydrides using both the local density approximation (LDA) and the generalized gradient approximation (GGA), using the Perdew–Burke–Ernzerhof (PBE) parameterization. Properties calculated were lattice parameters, bulk moduli, dielectric constants, effective charges, electronic densities and inelastic neutron scattering (INS) spectra. We took advantage of the currently available computer power to use full lattice dynamics theory to calculate thermodynamic properties for these materials. For the alkali metal hydrides (LiH, NaH, KH, RbH and CsH) using lattice dynamics, we found that the INS spectra calculated using LDA agreed better with the experimental data than the spectra calculated using GGA. Both zero-point effects and thermal contributions to free energies had an important effect on INS and several thermodynamic properties.

Interaction of Electrons with Polar Optical Phonons in Semiconductor Superlattices

On the basis of the microscopic theory of lattice dynamics, simulation of the electric potentials created by optical phonons in semiconductor superlattices is performed. It is shown that the spatial distribution of the amplitudes of electric potentials differs from that in a dielectric continuum predicted by the conventional macroscopic model without dispersion. A modified macroscopic continuum theory is proposed that takes into account the dispersion of short-range interatomic forces and allows one to obtain analytical expressions for the potentials of electron-phonon interaction.

Lattice vibration modes and thermal conductivity of potassium dihydrogen phosphate crystal studying by Raman spectroscopy

Potassium dihydrogen phosphate (KDP) crystal was grown from solutions in the presence of doping ethylenediamine tetra acetic acid (EDTA) in the concentration range of 0–100 ppm. Its Raman spectra were measured at room temperature with different geometrical configurations. On the basis of the group theory and lattice dynamics theory, all the Raman peaks were assigned, and a correlation between thermal conductivity and the Raman scattering strength was presented. The calculated thermal conductivity enhancements agree well with experimental enhancement of laser damage threshold, which indicates that the laser damage is a result of local thermal damage of KDP crystals.

Lattice Dynamics of Potassium-Doped Single-Walled Carbon Nanotubes

We calculate the vibrational properties of potassium-doped single-walledcarbon nanotubes within lattice dynamical theory. The results show that thefrequency of high-frequency Raman mode E2g for K5C40 downshiftsto 1553 cm−1, which is in agreement with the value for highly dopedsamples with effective composition KC8. Moreover, the specific heatcurves have a turnover at 22 K, originating from the saturation of K atomsvibrational modes at low energy.

Raman investigation of lattice vibration modes and thermal conductivity of Nd-doped zircon-type laser crystals

The Raman spectra of neodymium-doped yttrium orthovanadate Nd:YVO 4 (NYV) and neodymium-doped gadolinium orthovanadate Nd:GdVO 4 (NGV) have been measured at room temperature with different geometrical configurations. On the basis of the group theory and lattice dynamics theory, all the Raman peaks are assigned, and a correlation between the thermal conductivity and the Raman scattering strength is presented. The thermal conductivity of Nd:GdVO 4 and Nd:YVO 4 crystals along [1 1 0] and [1 0 1] directions are calculated and a good agreement with experimental results is obtained. The higher thermal conductivity of NGV crystal is mainly attributed to the fact that the effective radius of Gd 3+ ion in NGV crystal is close to that of Nd 3+ ion, which in return, enhances the crystal field strength of the laser crystal.

Application of high pressure–high temperature equation of state for elastic properties of solids

The theory of high pressure–high temperature equation of state recently developed is used to investigate the elastic properties of solids under the effect of temperature as well as pressure. The calculated values of temperature dependence of bulk modulus of NaCl are found to present a better agreement with the experimental data as compared with earlier relation. The results obtained for second-order elastic constants are found to present a good agreement with experimental data. It is concluded that the present approach is very simple and far better compared with the theory of lattice dynamics and two-body central potential. It makes the situation very simple and straightforward as compared with earlier investigations. The results are reported for NaCl, KCl, CaF 2, MgO, CaO, Mg 2SiO 4 and Al 2O 3.

Old and new aspects in lattice-dynamical theory

An overview of the basics of theoretical lattice dynamics is presented.Starting from the classical formulation, a tutorial description of theevolution of the lattice-dynamical theories is reported. After a briefsummary of the mostly used phenomenological models, the modern conceptsof first-principles lattice dynamics are introduced, paying specialattention to the methods based on the density-functional theory. Amongthese methods, the perturbative ab initio approach is highlighted.Furthermore, the application of this formalism to some cases of generalinterest is shown. In particular, we report on the controversy aboutthe origin of a peak in the second-order Raman spectrum of diamond, on thephonon spectrum of the wurtzite nitrides and on the temperature-inducedphase transitions in tin.

Independent anharmonic oscillator approximation in the theory of structural phase transitions in crystals

A new method in the microscopic theory of anharmonic crystal lattice dynamics—the independent anharmonic oscillator (IAO) approximation—is discussed. The method is compared with traditional approaches (such as the mean-field and renormalized self-consistent phonon methods) from the standpoint of the analysis of the main approximations. Different methods are applied to the description of the structural phase transition in a monoatomic anharmonic crystal, the results obtained are analyzed, and the numerical accuracy of different approximations is estimated. It is demonstrated that, for this model in the displacement-type instability range, the new method, unlike the self-consistent phonon method, adequately describes the phase transition as a second-order transition. The phase transition temperature calculated in the displacement limit monotonically tends to the exact value in contrast with the temperature obtained within the mean field approximation.

Effect of pressure on the phonon properties of europium chalcogenides

Lattice vibrational properties of europium chalcogenides have been investigated at high pressure by using a simple lattice dynamical model theory viz. the three-body force rigid ion model (TRIM) which includes long range three-body interaction arising due to charge transfer effects. The dispersion curves for the four Eu-chalcogenides agree reasonably well with the available experimental data. Variation of LO, TO, LA and TA phonons with pressure have also been studied at the symmetry points of the brillouin zone (BZ) for Euchalcogenides for the first time by using a lattice dynamical model theory. We have also calculated the one phonon density of states and compared them with the first order Raman scattering results. The calculation of one phonon density of states for Eu-chalcogenides has also been extended up to the phase transition pressure. We observed a pronounced shift in phonon spectrum as pressure is increased.