Lattice Dynamical Model Research Articles

Phonon Transmission and Thermal Conductance in FibonacciWire at Low Temperature

We investigate the phonon transmission and thermal conductance in ageneral Fibonacci quasicrystal by the model of lattice dynamics andthe technique of transfer matrix. It is found that quasiperiodicdistribution of masses may greatly destroy the phonon transport atboth low and high frequencies and thus may affect the thermalconductance. The thermal conductance increases with temperature atlow temperatures and displays saturation with further increase of thetemperature. Such saturation behaviour is preserved even when the mass ratioof atoms in the Fibonacci chain is changed.

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.

Theoretical studies of nonradiative 4f–4f multiphonon transitions in dielectric crystals containing rare earth ions

Detailed calculations have been performed of multiphonon relaxation rates of optical excitations in Nd-doped LiYF 4 and Pr-doped CsCdBr 3 crystals in the frameworks of the exchange charge model of the crystal fields and rigid ion harmonic models of lattice dynamics. It is shown that the empirical energy gap low emerges from the exponential diminishing of spectral densities of n-phonon correlation functions with the increase of an order n. Calculated transition probabilities for 2-, 3-phonon processes agree with experimental data. However, for energy gaps exceeding the maximum phonon energy more than twice, the existing theory which neglects the lattice anharmonicity brings about underestimated relaxation rates.

Phonon intrinsic mean free path in zincblende AlN

We have carried out calculations of phonon anharmonic inverse relaxation time in the cubic phase of AlN by using phonon dispersion results from a full lattice dynamical model and applying Fermi's golden rule formula. The cubic anharmonicity in crystal potential has been modelled within the anharmonic elastic continuum model. The relative roles of three-phonon Normal and Umklapp processes have been examined at different temperatures. Increase in the relaxation rate of acoustic phonons due to their interaction with optical phonons has also been quantified. The calculated results for the relaxation times of the acoustic phonon modes show appreciable differences from the results obtained from the application of the isotropic continuum model, both at low and high temperatures. The calculated results for the mean free path over a large temperature range have been compared with available estimates obtained from thermal conductivity measurements.

Lattice dynamics investigations of phonon thermal conductivity of Si∕Ge superlattices with rough interfaces

Phonon thermal conductivities in both growth and in-plane directions of Si∕Ge superlattices (SLs) with perfect and rough interfaces are calculated by using a lattice dynamics model. In addition to the general trend, the results show that there exist fluctuations of thermal conductivity in both directions for SLs with even or odd number of layers when the layer thickness is small. Thermal conductivities in both directions of Si∕Ge SLs with rough interfaces are shown to be much lower than those of SLs with perfect interfaces. To understand the influences of rough interfaces, thermal conductivities of homogeneous alloy are further calculated and compared. The results show that along the in-plane direction, the thermal conductivity of SLs with rough interfaces is about the same as that of random alloy, while in the growth direction it is lower than that of the random alloy.

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.

Inelastic neutron scattering and lattice dynamics studies of AlPO 4 and GaPO 4

The compounds AlPO 4 and GaPO 4 show phase transitions at high pressure depending on the compressibility of the constituent tetrahedra. Semi-empirical interatomic potentials are available for AlPO 4 and GaPO 4. Molecular dynamics simulations have been reported using these potentials to understand the nature of phase transitions in different polymorphs of these compounds. In order to check these potentials we have carried out lattice dynamical studies for AlPO 4 and GaPO 4. The phonon density of states measurements from the polycrystalline samples of low-cristobalite phase of AlPO 4 and GaPO 4 are carried out using High-Resolution Medium-Energy Chopper Spectrometer at ANL in the energy transfer range 0–160 meV. The calculated phonon spectra for both the compounds using the available potentials show fair agreement with the experimental data. However, the agreement between the two is improved by including the polarizibility of the oxygen atoms in the framework of the shell model. The lattice dynamical model is used for the calculation of specific heat and thermal expansion.

Phonon dispersion relation measurements on zircon, ZrSiO 4

Zircon, ZrSiO 4, is a geophysically important mineral for which a knowledge of the phonon spectra and interatomic potentials would be very useful for modeling the thermodynamic properties at high temperatures and high pressures. We have carried out extensive phonon studies in zircon using the triple axis spectrometer 1T1 at LLB, Saclay, which extend previous measurements to several branches not yet studied, in particular at high energy transfer up to 85 meV. The data of the phonon frequencies and the crystal structure have been used to refine an interatomic potential with a lattice dynamical shell model. The model calculations produce a very good description of the available data on the phonon density of states measured on a polycrystalline sample.

Phonon dispersion relations, phase transitions, and thermodynamic properties ofZrSiO4: Inelastic neutron scattering experiments, shell model, and first-principles calculations

Zircon, $\mathrm{Zr}\mathrm{Si}{\mathrm{O}}_{4}$, is a geophysically important mineral for which a knowledge of the phonon spectra and interatomic potentials would be very useful for modeling the thermodynamic properties at high temperatures and high pressures. We have carried out extensive inelastic neutron scattering experiments on zircon which extend previous phonon measurements to several branches not yet studied, in particular at high energy transfer up to $85\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. First principles density functional perturbation theory calculations of the phonon dispersion relations have been completed and found to be in agreement with the measurements. The experimental data of the phonon frequencies and the crystal structure have been used to refine an interatomic potential with a lattice dynamical shell model. The shell model calculations produce a very good description of the available data on the phonon density of states measured on a polycrystalline sample. The model is used further to calculate the structure, dynamics, and the Gibb's free energy as a function of pressure, in the zircon and scheelite phases. The free energy calculation reproduces the stability of the scheelite phases above $10\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ as compared to the zircon phase.

Lattice vibrations inLa(Ce)Fe4Sb12andCoSb3: Inelastic neutron scattering and theory

We present results of time-of-flight inelastic neutron scattering phonon density of states measurements on ${(\mathrm{La},\mathrm{Ce})}_{0.9}{\mathrm{Fe}}_{4}{\mathrm{Sb}}_{12}$ and $\mathrm{Co}{\mathrm{Sb}}_{3}$ as well as of a detailed comparison with lattice dynamical models in the literature. The MARI experimental setup is replicated by a theory for scattering from a polycrystalline material. The model considered for the filled materials is a local density approximation (LDA) based short-range force constant model and those considered for $\mathrm{Co}{\mathrm{Sb}}_{3}$ are the LDA-based model with the La-related parameters removed and a semiempirical model. We show that the presence of La significantly affects the shape of the spectrum. We also conclude that upon filling the Sb intrasquare force constants are weakened and that the transition-metal Sb bonds are almost unchanged.

Adiabatic bond charge model for lattice dynamics of ternary chalcopyrite semiconductors

AbstractThe adiabatic bond charge model of Rustagi and Weber is extended to study lattice dynamical properties of ternary chalcopyrite semiconductors AgGaS2, AgGaSe2, CuInS2, CuInSe2, CuGaS2, CuGaSe2, CuAlS2 and CuAlSe2. The new model calculations agree well with the results of Raman/IR and neutron measurements of Brillouin zone center phonon frequencies for both low and high frequency modes which was difficult for other phenomenological lattice dynamical models. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Physical properties of Ni fcc lattice in terms of the self-consistent phonon theory

The results of studies of physical properties of Ni fcc lattice obtained with the help of thereduced all-neighbour approximation of the self-consistent phonon theory are presented.The interatomic interactions are described by the modified form of the generalized Morsepotential, proposed lately by Akgün and Uğur, with parameters derived from theexperimental data for the lattice constant, cohesive energy, bulk modulus and elasticconstants. As a test of the validity of both the model of interatomic interactions andthe model of lattice dynamics the temperature variations of selected physicalproperties of Ni are given and compared with experimental and other theoretical data.

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.

Lattice vibrations of pure and doped GaSe

The Bridgman method is used to grow especially undoped and doped single crystals of GaSe. Composition and impurity content of the grown crystals were determined using X-ray fluorescence (XRF) method. X-ray diffraction, Raman scattering, photoluminescence (PL), and IR transmission measurements were performed at room temperature. The long wavelength lattice vibrations of four modifications of GaSe were described in the framework of modified one-layer linear-chain model which also takes into consideration the interaction of the selenium (Se) atom with the second nearest neighbor gallium (Ga) atom in the same layer. The existence of an eight-layer modification of GaSe is suggested and the vibrational frequencies of this modification are explained in the framework of a lattice dynamical model considered in the present work. Frequencies and the type of vibrations (gap, local, or resonance) for the impurity atoms were calculated and compared with the experimental results.

Phonon transmission and thermal conductance in quasi-one-dimensional disordered systems

Based on a lattice dynamics model and transfer matrix technique, we investigate the phonon transmission and thermal conductance in a quasi-one-dimensional disordered system. It is found that the existence of disorder may greatly destroy the phonon transport on Van Hove singularity which exhibits excellent transparency in case of pure lattice. At deeply low temperatures, the thermal conductance displays quantized features in a temperature range. Such quantization behavior is preserved even in the presence of disorder due to the robust transmission of phonon branches with zero cutoff frequency.

Electron atomic scattering factors, Debye–Waller factors and the optical potential for high-energy electron diffraction

High-energy electrons may be elastically and inelastically scattered by a solid. To a good approximation the effect of inelastic scattering on the elastically scattered electrons may be taken into account using the concept of the complex optical potential. The optical potential may be calculated using electron atomic scattering factors and Debye-Waller factors, which in turn can be evaluated numerically using Hartree Fock atomic wave functions and shell models of lattice dynamics. The numerical electron atomic scattering factors have been parameterized using five Gaussian functions for all the neutral atoms of the periodic table and for 106 important ions, and the temperature-dependent Debye-Waller B-factors have been fitted by using fourth degree polynomial regression fitting for 19 compounds with the sodium chloride structure, 5 compounds with the cesium chloride structure, 17 compounds with the zinc-blend structure and 68 elemental crystals.

Raman scattering inHfxZr1−xO2nanoparticles

Raman spectroscopy demonstrates that $\ensuremath{\sim}5\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ dimension ${\mathrm{Hf}}_{x}{\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ nanocrystals prepared by a nonhydrolytic sol-gel synthesis method are solid solutions of hafnia and zirconia, with no discernable segregation within the individual nanoparticles. Zirconia-rich particles are tetragonal and ensembles of hafnia-rich particles show mixed tetragonal/monoclinic phases. Sintering at 1200 \ifmmode^\circ\else\textdegree\fi{}C produces larger particles (20--30 nm) that are monoclinic. A simple lattice dynamics model with composition-averaged cation mass and scaled force constants is used to understand how the Raman mode frequencies vary with composition in the tetragonal ${\mathrm{Hf}}_{x}{\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ nanoparticles. Background luminescence from these particles is minimized after oxygen treatment, suggesting possible oxygen defects in the as-prepared particles. Raman scattering is also used to estimate composition and the relative fractions of tetragonal and monoclinic phases. In some regimes there are mixed phases, and Raman analysis suggests that in these regimes the tetragonal phase particles are relatively rich in zirconium and the monoclinic phase particles are relatively rich in hafnium.

Low-frequency excitations ofC60chains inserted inside single-walled carbon nanotubes

The low frequency excitations of C60 chains inserted inside single-walled carbon nanotubes (SWNTs) have been studied by inelastic neutron scattering (INS) on a high quality sample of peapods. The comparison of the neutron-derived generalized phonon density of states (GDOS) of the peapods sample with that of a raw SWNTs allows the vibrational properties of the C60 chains encapsulated in the hollow core of the SWNTs to be probed. Lattice dynamical models are used to calculate the GDOS of chains of monomers, dimers and polymers inserted into SWNTs, which are compared to the experimental data. The presence of strong interactions between C60 cages inside the nanotube is clearly demonstrated by an excess of mode density in the frequency range around 10 meV. However, the presence of a quasi-elastic signal indicates that some of the C60\'s undergo rotational motion. This suggests that peapods are made from a mixture of C60 monomers and C60 n-mer (dimer, trimer ... polymer) structures.

Vibrational Spectrum and Elastic Properties of KPb[sub 2]Cl[sub 5] Crystals

The Raman spectra and elastic moduli of KPb2Cl5 crystals were studied experimentally. The results are interpreted using a parameter-free model of the crystal lattice dynamics with inclusion of the multipole moments of the electron shells of ions. The calculated and experimental results are in good agreement. It is shown that not only the halogen ions but also the heavy cations make a significant contribution to the eigenvectors of high-frequency lattice vibration modes, which accounts for the relatively low frequencies of these modes.

Lattice-dynamical calculation of phonon scattering at ideal Si–Ge interfaces

Detailed phonon scattering at an ideal Si–Ge interface is studied with a linear lattice dynamics model. Frequency dependent transmission coefficients indicate the significance of acoustic-optical phonon mode conversion at the interface. Applied to multiple interfaces, the method shows how the overall thermal resistance approaches a finite (Bloch mode) limit with the increasing number of interfaces in absence of other scattering mechanisms. The dependence of thermal resistance on the superlattice layer thickness is not significant even in the interface-scattering-only limit we study. We also assess errors incurred by the finite domain size and classical statistics in molecular dynamics simulations of interface thermal resistance. Results suggest that using 6×6 unit cells in the transverse directions, a tractable size for such simulations, will incur only a 5% error in the predicted thermal resistance. Similarly, the error due to the classical (Boltzmann) phonon distribution in molecular dynamics simulations is predicted to be less than 10% for temperatures above 300 K.