Lattice Dynamics Method Research Articles

Dynamical stabilization of cubicZrO2by phonon-phonon interactions:Ab initiocalculations

Cubic zirconia exhibits a soft phonon mode $({X}_{2}^{\ensuremath{-}})$ which becomes dynamically unstable at low temperatures. Previous ab initio investigations into the temperature-induced stabilization of the soft mode treated it as an independent anharmonic oscillator. Calculations presented here, using the self-consistent ab initio lattice-dynamical method to evaluate the phonons at 2570 K, show that the soft mode should not be treated independently of other phonon modes. Phonon-phonon interactions stabilize the ${X}_{2}^{\ensuremath{-}}$ mode. Furthermore, the effective potential experienced by the mode takes on a quadratic form.

Structure dependent phonon properties of LaMnO 3

We have reported the results of our theoretical investigations on the vibrational properties of LaMnO 3 in its cubic structure by using lattice dynamical simulation method based on the rigid ion model to understand the role of phonons in these systems. The calculated zone centre frequencies agree reasonably well with the available data. The phonon dispersion curves, phonon density of states and lattice specific heat are also reported for the cubic LaMnO 3. We also report the phonon properties for LaMnO 3 in its rhombohedral structure and compare them with the cubic phase phonon properties. The phonon properties are different in these two phases of LaMnO 3 compound. The shift in peak position and appearance of new peaks are also observed in phonon density of states. The low temperature specific heat is different due to the difference in the behaviour of lower frequency phonon modes.

Account of three-body interactions in the lattice dynamics method

The lattice dynamics method is extended with the account of three-body interaction potential in the harmonic approximation. Analytic expressions for the force constants and dynamical matrix elements are presented. Dynamical matrix element responsible for indirect interaction of atoms is single out. Modeling calculations of phonon spectra at the center of Brillouin zone for empty silicon clathrate structures Si 34 and Si 46 have been performed.

Thermodynamics and vibrational spectrums for molecular crystals of β-diketonate of metals: Modeling in frameworks of the lattice dynamics method

Computer modeling and low temperature calorimetry investigations of dynamic and thermodynamic properties for a molecular crystal tris-hexafluoroacetylacetonate iron Fe(O 2C 5HF 6) 3 are presented. A heat capacity C p ( T) has been measured by adiabatic calorimeter method in the temperature range 4.8–321 K. An anomaly passing through the maximum at temperature T c = 44.6 K has been discovered. Intermolecular vibrational spectrum was calculated by lattice dynamics method in quasiharmonic approximation. Intramolecular frequencies are found by solving the Schrödinger equation in harmonic approximation. In the frequency interval ≈30–70 cm −1 overlapping the spectrums intra- and intermolecular oscillations has been found. Calculation of intramolecular spectrums has been carried out on a basis of best coincidence calculated and experimental heat capacities. The good agreement for calculated and experimental C p ( T) was found for two sets of the force constants. Obtained results allow us to assume that heat capacity anomaly mark on a change in intra- or intermolecular vibrational modes or possible resonance interaction between these modes near T c.

Configurational lattice dynamics: The phase diagram ofRh−Pd

Free energies of $\mathrm{Rh}\ensuremath{-}\mathrm{Pd}$ alloys as functions of both temperature and composition are calculated using quasiharmonic lattice dynamics. The free energy of the disordered solid is determined from an ensemble of a large number of randomly generated configurations. Both configurational and vibrational contributions to the entropy and enthalpy of mixing are taken into account. We study the convergence with the number of random configurations, and analyze the validity of the zero static internal stress approximation (ZSISA), where only external strains are relaxed fully dynamically while internal stresses are relaxed in the static approximation. It is shown that the use of ZSISA allows an accurate calculation of free energies in a fraction of the time needed to carry out fully dynamic optimizations. From the values of free energies as functions of composition and temperature the phase diagram of $\mathrm{Rh}\ensuremath{-}\mathrm{Pd}$ alloys is calculated, showing a good agreement with Monte Carlo simulations as well as with experiment. It is also shown that although free energies of mixing appear to be linear functions of temperature to a good approximation, the explicit expressions given by the configurational lattice dynamics method show that both enthalpies and entropies of mixing change appreciably with temperature.

Interaction of acoustic waves with an interface in highly anisotropic layered crystals

The scattering of acoustic waves on a planar defect in the interior of a crystal is studied by the methods of lattice dynamics. The model chosen consists of two semi-infinite, highly anisotropic crystals, the forces of interaction between which are distinct from the interactions within the crystals themselves. The model is used to study the resonant transmission of waves through an impurity monolayer. This resonant transmission effect is due to the weak coupling of the defect to the host lattice and cannot be described in the framework of the standard theory of elasticity, since the displacements of the defect layer and of the closest-lying layers of the host matrix are substantially different. For nongrazing angles of incidence the resonant transmission effect can be illustrated qualitatively by the example of an infinite linear chain containing a point impurity.

Lattice dynamics and electron‐phonon coupling in pentacene crystal structures

AbstractThe crystal structures and lattice phonons of pentacene are computed by the quasi harmonic lattice dynamics (QHLD) method. From the eigenvectors of the low frequency phonons we calculate the e‐ph coupling constants due to the modulation of the transfer integrals. The transfer integrals are computed by the Hückel method and by the INDO/S Hamiltonian for all the nearest neighbor pentacene pairs in the ab crystal plane.

Organic Semiconductors: Polymorphism, Phonon Dynamics and Carrier-Phonon Coupling in Pentacene

The crystal structure and phonon dynamics of pentacene is computed with the Quasi Harmonic Lattice Dynamics(QHLD)method, based on atom-atom potential. We show that two crystalline phases of pentacene exist, rather similar in thermodynamic stability and in molecular density. The two phases can be easily distinguished by Raman spectroscopy in the 10–100 cm−1spectral region. We have not found any temperature induced phase transition, whereas a sluggish phase change to the denser phase is induced by pressure. The bandwidths of the two phases are slightly different. The charge carrier coupling to low-frequency phonons is calculated.

Scale Effects in Carbon Nanostrutures: Self-Similar Analysis

The present study focuses on the creation of a framework and methodology to span three orders of magnitude in scale with interconnected models that relate performance of single wall carbon nanotubes (SWCN) at the nanometer scale to a nanoarray, nanowire, and microfiber with self-similar geometries. The geometry chosen is the helical array, where on the nanoscale, the properties of nanotube crystals (collimated arrays of continuous SWCN) predicted by the method of lattice dynamics by Popov4 are employed to determine properties of the elements in a helical, discontinuous nanotube array. The properties of the twisted nanoarray of circular cross-section are then predicted through a layered cylinder analysis in anisotropic elasticity. The nano-array properties are then used to describe the properties of elements in a second helical array, the nanowire, consisting of the helical SWCN arrays suspended in a polymeric matrix. Next the nanowires are assembled in a third helical array composite to form the microfiber. The three-step analysis involves models that are identical in geometry, except that they differ in scale and are thereby self-similar. For a single walled nanotube of diameter 1.38 × 10-9 m, the resulting nanoarray diameter is 1.48 × 10-8 m (equilibrium packing fraction of 79%), the nanowire diameter is 1.69 × 10-7 m (packing fraction of 70%), and the microfiber diameter is 1.32 × 10-6 m. Perhaps the most interesting aspect of the study is the focus on translation of properties from the nanoscale to the microscale and the scale transfer efficiencies. The present study presents predictions for the mechanical properties of the helical nanoarray, the nanowire, and the microfiber such as the axial Young's modulus, shearing modulus, and Poisson's ratio.

Absolute Stability Boundaries of Clathrate Hydrates of Cubic Structure II

Stability of argon, krypton and propane clathrate hydrates of cubic structure II (CS-II) and of empty CS-II hydrate lattice has been investigated in a wide range of temperatures and pressures up to boundaries of absolute stability. The boundaries of mechanical stability in the framework of lattice dynamics method are determined in the quasiharmonic approximation from the Born stability conditions of crystal lattice. It has been shown by comparison of chemical potentials for empty hydrate lattices of structures I and II and ice Ih that at positive pressures empty hydrate lattices are thermodynamically metastable regarding to the ice Ih. At negative pressures there exist equilibrium lines between these phases. It has been found that despite weakness of the guest–host interactions, the guest molecules stabilize metastable host framework and the boundaries of stability depend on the type of the guest molecule. Moreover, in the cases of argon and krypton hydrates, the effect of double occupancy of the large cage on stability of CS-II structure has been also examined.

Relationship between the Dynamic Properties of 1h Ice and Xenon Hydrate and the Interplay of Intramolecular and Intermolecular Vibrations

A new approach was used to simulate vibration spectra of 1h ice and xenon hydrate in the range 0–4000 cm-1, which encompasses both intramolecular and intermolecular vibrations. This approach, based on the lattice dynamics method, enables full spectra to be obtained for molecular crystals with allowance for the coupling of intramolecular and lattice vibrations. It is shown that consideration of this coupling leads to splitting of the peaks of intramolecular vibrations and to a significant change in the spectrum in the range of translation and libration molecular vibrations, which agrees qualitatively with experimental results.

Temperature evolution of pentacene crystal structure and phonon dynamics

AbstractWe investigate the relationships among all currently known X-ray structures of crystalline pentacene by calculating their “inherent” structures of minimum potential energy. We are thus able to show that two distinct bulk crystalline phases of pentacene exist, with very subtle but clear di.erences. We then assess the effects of temperature on the crystal structures, by including both inter- molecular and low-frequency intra-molecular phonons in the framework of quasi harmonic lattice dynamics methods. In this way we properly reproduce the experimental thermal expansion, and obtain a reliable description of the phonon dynamics and of its temperature dependence. The calculated phonon frequencies compare well with the experimental Raman spectrum.

Lattice dynamics and electron-phonon coupling in theβ−(BEDT−TTF)2I3organic superconductor

The crystal structure and lattice phonons of the $(\mathrm{BEDT}\ensuremath{-}\mathrm{TTF}{)}_{2}{\mathrm{I}}_{3}$ superconducting $\ensuremath{\beta}$ phase (where BEDT-TTF is bis-ethylen-dithio-tetrathiafulvalene) are computed and analyzed by the quasiharmonic lattice dynamics (QHLD) method. The empirical atom-atom potential is that successfully employed for neutral BEDT-TTF and for nonsuperconducting $\ensuremath{\alpha}\ensuremath{-}(\mathrm{BEDT}\ensuremath{-}\mathrm{TTF}{)}_{2}{\mathrm{I}}_{3}.$ The rigid molecule approximation has to be relaxed by allowing mixing between lattice and low-frequency intramolecular vibrations. Such a mixing is found to be essential to account for the specific heat measurements, and also yields good agreement with the observed Raman and infrared frequencies. The crystal structure and its temperature and pressure dependence are also properly reproduced, though the effect of the mixing is less important in this case. From the eigenvectors of the low-frequency phonons we calculate the electron-phonon coupling constants due to the modulation of charge transfer (hopping) integrals. The charge transfer integrals are evaluated by the extended H\"uckel method applied to all nearest-neighbor BEDT-TTF pairs in the ab crystal plane. From the averaged electron-phonon coupling constants and the QHLD phonon density of states we derive the Eliashberg coupling function ${\ensuremath{\alpha}}^{2}(\ensuremath{\omega})F(\ensuremath{\omega}),$ which compares well with that experimentally obtained from point contact spectroscopy. The corresponding dimensionless coupling constant $\ensuremath{\lambda}$ is found to be $\ensuremath{\sim}0.4.$

Coupling between intramolecular and lattice vibrations in solid para-diiodobenzene

Optical spectra, phonon density of states and constant volume specific heat of the α-phase of para-diiodobenzene are computed by the harmonic lattice dynamics method. The results provide a detailed assignment of the spectra. The role of intramolecular vibrations is found to be essential to reach agreement with the experimental data.

Conformational properties and dynamics of molecular bottle-brushes: A cellular-automaton-based simulation

Full Paper: Extensive computer simulation was performed using the bond-fluctuation model and cellular-automaton (CA)-based simulation technique to probe the equilibrium structure and dynamical behavior of combbranched polymers in which the flexible side chains of a given length are placed regularly along the backbone and the number of branches increases linearly with total molecular weight. By applying very efficient CA algorithm -the lattice molecular dynamics (LMD) method - we have been able to study the properties of sufficiently large structures (up to 5880 monomeric units). Depending on the length of main and side chains as well as on interbranch spacing, we have calculated mean chain dimensions, local fractal dimensionalities, particle scattering functions, time autocorrelation functions, etc. The following main conclusions may be drawn from the results presented in our study: (i) The critical exponent, governing the mean size of the main chain, remains unchanged from its value known for a 3d self-avoiding walk (SAW). On the other hand, two-dimensional branched macromolecules with one-sided branches are effectively in a collapsed state even under conditions of a good solvent, forming specific helical superstructures. (ii) Comparison of the simulated data with the predictions of the scaling model indicates that the latter is valid in describing the mean dimensions of the backbone as a function of side-chain length and interbranch spacing. (iii) The excluded volume interaction between side chains dramatically slows down the relaxation of the backbone chain.

Vibrational spectrum, elastic moduli and mechanical stability in ice VIII

The elastic moduli of ice VIII at different temperatures and pressures have been calculated from the quasiharmonic lattice dynamics method employing the TIP4P potential for water. It was found that under decompression, one of the Born’s stability conditions for solids was violated and ice VIII became mechanically unstable which led to a phase transformation. The transition pressure was found to decrease with temperature. This phenomenon is a symmetric equivalent of the pressure-induced crystal→amorphous transformation in ice Ih. Based on the theoretical results, it is proposed that the observed transformation of ice VIII to high density amorphous ice at low temperature is probably due to a mechanical instability in the crystal.

Lattice dynamics and e-ph coupling in BEDT-TTF superconductors

The crystal structures and phonon frequencies of α- and β- phases of (BEDT-TTF) 2I 3 salts are computed by the Quasi Harmonic Lattice Dynamics (QHLD) method. Experimental specific heat data of the β- phase can be reproduced only by introducing also low frequency intra-molecular vibrations. The strength of the electron-phonon ( e-ph) coupling is evaluated.

原子間力第１及び第２微係数と弾性定数

Using the first-and second-derivatives of the effective interatomic potential in the microscopic electronic theory, the interatomic force constants are calculated for practical material Al with low density and for alkali metal K with high density. The interatomic force constants so obtained are in good agreement with those derived from fitting the experimental phonon spectra and give a set of important data for the binding forces of solids. Dynamical elastic constants are also calculated using the long-wave phonon method and are also compared with observed data from ultrasonic pulse method. The compressibility problem, proposed by Brovman and Kagan, is that the lattice dynamical method in terms of second-order perturbation based on the pseudopotential does not give the self-consistent results for calculation of the elastic constants accompanied by a volume change. This problem is studied quantitatively and is shown to be important for Al and K. Consecluently, the obtained data of the elastic constants C11, C12 and bulk modulus B related to volume change are in good agreement with the observed data in spite of introducing no adjustable parameter. Then, in quasi-harmonic approximation considering temperatureand pressure-dependence of the lattice constant, the temperature and pressure effect on the elastic constants are calculated. The obtained data are consistent with the qualitative tendency of observed data and are useful in studying the mechanical and thermal properties of theses materials.

Lattice Dynamics Study of Microstructures of Electrorheological Fluids**The project supported by National Natural Science Foundation of China

The lattice dynamics method is used to study the stability of the chain structures formed in electrorheological (ER) fluids. The appearance of the soft modes in the phonon dispersion of the structures indicates that the chains tend to distort and aggregate into thicker columns due to the electrostatic attractive forces and thermal generated forces between them. The results show that the stability of the chains relies on their width and the separation between them. The complete chain structures are more stable than the chains with defects. The results can be used to elucidate the densification phenomenon of the chains in the structuring process of ER fluids in the quiescent state.

The lattice dynamics of β-hydroquinone clathrate

Dynamic properties of β-hydroquinone (Qβ) clathrate with various guest molecules have been calculated by the method of lattice dynamics within the atom–atom potential approximation; van der Waals interactions, H-bond interactions, and electrostatic interactions for charges localized on the atoms are included. External vibration spectra have been calculated for the empty framework of Qβ and with different guest molecules (HCN, CO2, SO2, C2N2, C2H6, CH3OH, O2CO). Vibrational frequencies of the guest molecules in cavities are determined. The phonon density of states for these compounds has been calculated. The influence of the encaged guest molecules on the vibrational spectrum of the host lattice has been investigated. The most visible changes are observed upon the insertion of guest molecules with large dipole moment or those positioned asymmetrically inside the Qβ clathrate cages. Peculiarities of different interactions have been revealed. Analysis of the calculated and experimental results have been carried out.