Study Of Lattice Dynamics Research Articles

Vibrations of a chain of Xe atoms in a groove in a carbon nanotube bundle

We present a lattice dynamics study of the vibrations of a linear chain of Xe adsorbates in groove positions of a bundle of carbon nanotubes. The characteristic phonon frequencies are calculated and the adsorbate polarization vectors discussed. Comparison of the present results with the ones previously published shows that the adsorbate vibrations cannot be treated as completely decoupled from the vibrations of carbon nanotubes and that a significant hybridization between the adsorbate and the tube modes occurs for phonons of large wavelengths.

Exact study of lattice dynamics of single-walled carbon nanotubes

Based on the model of lattice dynamics with force-constant matrix, we have calculated phonon spectrum and then specific heats of single-walled carbon nanotubes. The results show that with a more complicated phonon spectrum, a single-walled carbon nanotube has analogous good thermal conductivity to the two-dimensional graphite. However, the ratio of thermal conductivity to phonon relaxation time is inversely proportional to the diameter of either zigzag or armchair carbon nanotubes.

Pressure dependent phonon properties of cubic group III‐nitrides

AbstractBy constructing rigid‐ion models (RIMs) at ambient and high pressures we present a comprehensive study of lattice‐dynamics and thermodynamical properties in cubic III‐nitrides. Murnaghan's equation of state is adopted for relating the volume dependence to pressure. The force constants in the RIM scheme are optimized using non‐linear least square fitting procedures with constrained parameters and weighting of the data on critical‐point phonons, lattice and elastic constants. Theoretical results for the phonon dispersions, density of states, mode Grüneisen parameters, specific heat, and thermal expansion coefficients are compared and discussed with the existing experimental and ab initio data.

Dynamical Properties of the Partially Disordered Crystals of Cs 5 H 3 (SO 4 ) 4 · x H 2 O

This paper presents studies of lattice dynamics of a crystal of Cs 5 H 3 (SO 4 ) 4 x H 2 O (PCHS) and its deuterated analog Cs 5 D 3 (SO 4 ) 4 x D 2 O (DPCHS) in wide temperature and frequency ranges by dielectric spectroscopy and modulated temperature differential scanning calorimetry. It is shown that deuteration of PCHS gives rise to an additional structural phase transition at T c3 , 250 K. The temperature of the isostrctural phase transition T c2 (372 K for PCHS and 370 K for DPCHS) has been determined more accurately. It has been found that deuteration does not suppress phase transition at T c2 . The temperature dependence of dielectric response is analyzed.

Ab-initio density-functional lattice-dynamics studies of ice

We present the results of first-principles computational studies of the dynamical properties of hexagonal ice using both the ab-initio pseudopotential method and the full-potential augmented plane-wave method. Properties obtained using both the generalized gradient approximation (GGA) and the meta-GGA in density-functional theory are compared. The lattice-dynamical properties of the structures are obtained using a finite-difference evaluation of the dynamical matrix and force-constant matrix from atomic forces. Phonon dispersion is evaluated by the direct determination of the force-constant matrix in supercells derived from the primitive molecule unit cells with the assumption that force constants are zero beyond the second molecular nearest neighbors. The k-dependent phonon frequencies are then obtained from the force-constant matrix and dispersion relations, and the Brillouin-zone integrated density of states is evaluated. The importance of phonon dispersion in the various regions of the phonon spectra is then assessed and compared to existing neutron-scattering data. Frozen-phonon calculations are used to compare phonon frequencies evaluated in both the GGA and meta-GGA. PACS Nos.: 61.12Ex, 63.20Dj

Inelastic neutron scattering, lattice dynamics, and synchrotron x-ray diffraction study ofFePO4

The quartz structure compounds $M{\mathrm{PO}}_{4}$ $(M=\mathrm{Al},$ Fe, and Ga) are of interest to understand the nature of bonding in the tetrahedral coordinated phosphates. We report detailed lattice dynamical studies involving experimental inelastic neutron scattering measurements and theoretical shell model calculations of vibrational and thermodynamic properties of ${\mathrm{FePO}}_{4}.$ X-ray diffraction measurements are also carried out for ${\mathrm{FePO}}_{4}$ from 100 to 300 K using an Elettra synchrotron radiation source. The measured phonon density of states and thermal expansion for ${\mathrm{FePO}}_{4}$ have been interpreted based on the shell model calculations. The lattice dynamical model is used for calculating various thermodynamic properties like specific heat, thermal expansion, bulk modulus, and thermal amplitudes. The calculations are in good agreement with numerous experimental data including our phonon density of states and thermal expansion measurements. Our calculated pressure variation of phonon frequencies shows that a zone boundary mode at $(\frac{1}{3},\frac{1}{3},0)$ becomes soft at 4 GPa, which may be associated with the mechanical instability of the quartz structure of ${\mathrm{FePO}}_{4}$ at high pressure.

Lattice Dynamical Properties of the Rare Earth Aluminum Garnets (RE3Al5O12)

This paper reports detailed lattice dynamics studies involving experimental Raman scattering measurements and theoretical rigid ion model calculations of the rare earth aluminum garnets (RE3Al5O12). The studies are fairly involved as these garnets have complex crystal structure with 80 atoms/primitive cell. Our calculations have provided a theoretical understanding of the mode eigenvectors, phonon dispersion relations, density of states, and effective charges of these materials. The calculated Raman mode eigenvectors reveal that they correspond to mixtures of molecular modes of the basic polyhedra, implying thus strongly coupled polyhedra. The assignment of the Raman and infrared active modes has been elucidated and the frequencies of some modes, which do not appear in the vibrational spectrum, have been calculated. Our calculations show a differentiation of the effective charges at the various symmetry sites, which leads to a mostly covalent and to an almost ionic character for the tetrahedral Al–O and the dodecahedral RE–O bonds, respectively. Finally, the dispersion curves along the [100] direction of the Brillouin zone as well as the one and two-phonon density of states have been calculated and discussed.

Comparative Lattice‐Dynamical Study of the Raman Spectra of Monoclinic and Tetragonal Phases of Zirconia and Hafnia

An interpretation of the Raman spectra of monoclinic ZrO2and monoclinic HfO2is made by analyzing the results of the zirconia–hafnia substitution jointly with a lattice dynamical treatment of both structures. The Raman spectra of tetragonal ZrO2and tetragonal HfO2are also interpreted. Emphasis is put on their relations to the spectrum of the parent cubic structure and on the position of the soft mode. The band assignment proposed earlier by other researchers is critically reconsidered.

Unified study of lattice dynamics of NiO

A unified study of lattice dynamics of paramagnetic NiO has been studied by correcting the basic equations of the three-body force shell model for the valency of the cations and anions. The shell charge and core charge parameters are also modified. This approach explains the complete lattice dynamics of NiO successfully only when both the ions are taken to be polarizable. There is good scope for fresh determination of positive ion polarizability and Debye temperature variation.

Study of latticedynamics via extended x-ray absorption fine structure

EXAFS (extended x-ray absorption fine structure), besides being apowerful structural probe, can also give original information onlocal dynamics in solids. EXAFS is peculiarly sensitive to thecorrelation of vibrational motion, both parallel and perpendicularto the bond direction, and to anharmonicity. This paper contains anintroduction to the effects of thermal disorder on EXAFS of crystalsand to the data analysis based on the cumulant expansion. Cumulantsare easily connected to average local vibrational properties.Recently obtained experimental results concerning the mean squarerelative displacement and the thermal expansion in crystals confirmthe potentialities of EXAFS as a dynamical probe.

Zone center phonon frequencies in tetragonal zirconia: lattice dynamical study and new assignment proposition

A normal mode calculation of the zone center phonons in the tetragonal structure of ZrO2 compound has been performed with particular emphasis on the low frequency modes. A restricted set of stretching and bending force constants have been introduced and lead to a good agreement between theoretical and experimental Raman and IR phonon frequencies. The Eg symmetry of the two low frequency Raman modes which are involved in the softening process observed with increasing pressure were confirmed and none were left for a low frequency A1g totally symmetric mode as proposed in the literature.

Surface lattice dynamics of Mg(0001)

A study of the surface lattice dynamics of $s\ensuremath{-}p$ bonded Mg(0001) using momentum-resolved inelastic electron scattering and ab initio calculations is reported. Three phonon modes at $\overline{K}$ and four phonon modes at $\overline{M}$ were observed, all in excellent agreement with calculations. In an attempt to understand the origin of changes in the surface force constants compared to the bulk force constants, the theoretical dispersion of the Rayleigh mode using bulk truncated and real surface force constants was compared for the hexagonal surface of three $s\ensuremath{-}p$ bonded metals, Al, Mg, and Be.

Comparative study of quasiharmonic lattice dynamics, molecular dynamics and Debye model applied to MgSiO 3 perovskite

Abstract We consider three independent methodologies for calculating thermal equation of state (EOS) of the major earth-forming mineral, orthorhombic MgSiO3 perovskite: molecular dynamics (MD), lattice dynamics (LD) and Debye model (DM). Using the most recent developments in the GULP code, we derive a new interatomic potential, which is demonstrated to be extremely robust at both high temperatures and high pressures. With this potential we construct a quasiharmonic self-consistent DM based on elastic properties of the crystal, and compare its results with results of more rigorous LD and MD simulations with the same potential model. We show that the DM reproduces quite accurately harmonic constant-volume heat capacity above 500 K, but gives thermal expansion and Gruneisen parameter (γ) that are too small. We conclude that MgSiO3 perovskite is not a Debye-like solid, in contrast to what has often been assumed in geophysical literature. Acoustic γ, often used in geophysical studies, are a very crude approximation to the true γ. To obtain good accuracy, one needs to know the γ(V) function more accurately than the DM can give. However, analytical functions, given by the Debye theory, are useful for fitting thermal expansion and related parameters at elevated temperatures. A common assumption that q= d ln γ/ d ln V is constant is found to be inadequate: in fact, q varies strongly with volume and can reach negative values towards the base of the lower mantle. This can be relevant for discussion of the anomalous properties of the core-mantle boundary (D″) layer. Comparison of results of LD and MD indicates importance of intrinsic anharmonic contributions in the thermal expansion and γ. Therefore, MD is the most suitable technique for simulating minerals at the Earth’s mantle conditions.

Raman scattering study of anomalous spin, charge, and lattice dynamics in the charge-ordered phase of Bi1-xCaxMnO3 (x > 0.5).

We report an inelastic light scattering study of the effects of charge ordering on the spin, charge, and lattice dynamics of Bi1-xCaxMnO3 (x>0.5). We find that charge ordering results in anomalous phonon behavior, such as the appearance of "activated" modes. More significantly, however, the transition to the charge-ordered phase results in the appearance of a quasielastic scattering response with the symmetry of the spin-chirality operator ( T(1g)); this scattering response is thus indicative of magnetic or chiral spin fluctuations in the antiferromagnetic charge-ordered phase.

Electronic structure and ferroelectricity inSrBi2Ta2O9

The electronic structure of SrBi2Ta2O9 is investigated from first-principles, within the local density approximation, using the full-potential linearized augmented plane wave (LAPW) method. The results show that, besides the large Ta(5d)-O(2p) hybridization which is a common feature of the ferroelectric perovskites, there is an important hybridization between bismuth and oxygen states. The underlying static potential for the ferroelectric distortion and the primary source for ferroelectricity is investigated by a lattice-dynamics study using the Frozen Phonon approach.

Free energy and relative stability of the enstatite Mg2Si2O6 polymorphs

Abstract Detailed lattice dynamical studies of the equations of state and the phase diagram of the geophysically important mineral enstatite have been undertaken. There are several enstatite polymorphs: ortho, proto and clinoenstatite, whose structures are characterized by double MgO6 octahedral ribbons and single silicate chains. The computed equations of state are found to be in good agreement with available experimental data and ab initio results. The calculations reveal that the stable phase at ambient conditions is orthoenstatite, which transforms to the protoenstatite phase at high temperatures. The monoclinic C2/c clinoenstatite phase is found to be stable at high pressures. The computed phase diagram is in overall qualitative agreement with the experimental data. These studies have enabled a microscopic understanding of the factors contributing to the relative stability and indicate that while the orthoenstatite to protoenstatite transition is temperature driven, the orthoenstatite to clinoenstatite transition is pressure driven.

Inelastic neutron scattering and lattice-dynamics studies of almandineFe3Al2Si3O12

This paper reports detailed lattice dynamical studies involving experimental inelastic neutron-scattering measurements and theoretical shell model calculations of the vibrational and thermodynamic properties of the garnet mineral almandine ${\mathrm{Fe}}_{3}{\mathrm{Al}}_{2}{\mathrm{Si}}_{3}{\mathrm{O}}_{12}.$ Inelastic neutron-scattering studies using the time-of-flight technique provide the measurement of the phonon density of states (DOS) of almandine, which have been interpreted based on the model calculations. The calculated DOS is in good agreement with the inelastic neutron-scattering data and has been used to compute various macroscopic properties like the specific heat, thermal expansion, equation of state, and mean-square atomic displacements.

A new interpretation of incommensurate phase of quartz

Optical and lattice dynamical studies were performed on the incommensurate(IC) phase in quartz. There are two different regions (fog- and m- zone) near the boundary between α and IC phase. The birefringence in the fog-zone was found to be much larger than that expected from the currently accepted model. The lattice dynamical calculation using the Tsuneyuki potential (Phys. Rev. Lett., 61, 869(1988)), revealed that a stable modulated structure with a short period exists between α and β phases. Both results qualitatively agree with the new model recently proposed by Aslanyan et al. (J. Phys. Condens. Matter, 10, 4575(1998)) which assumes that the softening would occur near b/3 rather than close to γ point.

Vibrational spectra of solid hydrogen sulfide: a lattice dynamics study

A simple force constant model is described and applied to the vibrations of crystalline H2S and D2S in their low-temperature ordered phase III, the structure of which has recently been determined. The model uses 14 adjustable parameters (three intramolecular and 11 intermolecular) to calculate the wavenumbers of 69 optical modes for each crystal, and good agreement with Raman and infrared data is obtained. The most important intermolecular interactions are confirmed to be hydrogen bonds, the formation of which results in a slight weakening of the molecular H — S bonds. In order to model the unusually wide range of lattice wavenumbers for these crystals, it is found necessary to introduce intermolecular bending force constants involving the hydrogen bonds. Copyright © 2000 John Wiley & Sons, Ltd.

Lattice dynamics of BCCD

The paper summarizes the recent studies of lattice dynamics in Betaine Calcium Chloride Dihydrate (BCCD), which are not included in the review by G. Schaack and M. Le Maire (1988). The hard harmonic mode method used previously for determination of amplitudon and pseudo-phason modes in BCCD is formulated in a general manner. It is shown why and how the well-known coupled damped harmonic oscillator model can be systematically used for determination of the bare soft mode parameters directly from a single experimental spectrum. Transmission maximum in IR spectra used previously for monitoring the modulation vector is assigned to the anti-resonance effect caused by coupling between the soft and the transverse acoustic mode.