Quasiharmonic Lattice Dynamics Research Articles

Polarized Raman Spectra of a Rubrene Single Crystal

We report for the first time lattice phonon Raman spectra of the organic semiconductor 5,6,11,12-tetraphenyl-tetracene (rubrene). Polarized spectra were recorded for symmetry assignments. A comparison of experimental data with quasi harmonic lattice dynamics calculations, performed starting from the experimental X-ray structures, is given. It is shown that the experimental data can only be explained by invoking an efficient coupling between lattice vibrations and low energy intramolecular modes. Calculations also show that the experimental crystal structure corresponds to a stable thermodynamical minimum, whose temperature dependence reproduces well the experimental thermal expansion of the crystal.

Ab initiocalculations of the thermodynamics and phase diagram of zirconium

The finite-temperature density-functional theory and quasiharmonic lattice dynamics are used to calculate the Gibbs free energy and quasiharmonic phonons of the hexagonal-close-packed (hcp) and omega $(\ensuremath{\omega})$ crystal structures for Zr. The hcp phonon dispersions agree with experiment; the $\ensuremath{\omega}$ phonon dispersions have not been measured yet. From the free energy, the volume thermal expansion coefficients of $\ensuremath{\alpha}\text{-Zr}$ are predicted. The calculated volume thermal expansion coefficients for $\ensuremath{\alpha}\text{-Zr}$ are in good agreement with the experiment data at $T>100\text{ }\text{K}$. Our calculated results found that at zero-temperature the lowest-energy phase is not the $\ensuremath{\omega}$ but the hcp phase. This conclusion is in accordance with the result of Schnell and Albers, but in disagreement with those of Ahuja et al. and Jona and Marcus. The predicted phase boundary of $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\omega}$ is in good agreement with the available experiment; however, other theoretical results are far from the experiment at high temperatures.

Direct evidence of overdamped Peierls-coupled modes in the temperature-induced phase transition in tetrathiafulvalene-chloranil

In this paper, we elucidate the optical response resulting from the interplay of charge distribution (ionicity) and Peierls instability (dimerization) in the neutral-ionic ferroelectric phase transition of tetrathiafulvalene-chloranil, a mixed-stack quasi-one-dimensional charge-transfer crystal. We present far-infrared reflectivity measurements down to $5\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$ as a function of temperature above the phase transition (300--82 K). The coupling between electrons and lattice phonons in the pretransitional regime is analyzed on the basis of phonon eigenvectors obtained through quasiharmonic lattice dynamics, combined with the results of exact numerical diagonalization of the one-dimensional Peierls-Hubbard model. The resulting multiphonon Peierls coupling leads upon approaching the phase transition to a progressive shift of spectral weight and of the coupling strength toward the phonons at lower frequencies, ending in a soft-mode behavior only for the lowest-frequency phonon near the transition temperature. Moreover, in the proximity of the phase transition, the lowest-frequency phonon becomes overdamped due to anharmonicity induced by its coupling to electrons. The implications of these findings for the neutral-ionic transition mechanism are discussed.

The four polymorphic modifications of the semiconductor dibenzo-tetrathiafulvalene

The organic semiconductor dibenzotetrathiafulvalene (DB-TTF) presents, at ambient conditions, four polymorphic modifications. In addition to the already known monoclinic structure (α) with Z = 2, we have resolved by single crystal X-ray diffraction (XRD) a second crystal structure (β), also monoclinic but with Z = 4. Two other polymorphic modifications (γ and δ) have been found by means of lattice phonon confocal Raman microscopy and XRD. In this paper we present a series of growth experiments, from vapour or from solution, in films and in the bulk phase, describing the variety of transformations which occur among the different phases and their mixing, also at a micrometric scale. Quasi harmonic lattice dynamics calculations satisfactorily reproduce the structures of the α and the β polymorphs and help the phonon assignment of polarized Raman spectra in single crystals.

First-principles thermoelasticity of bcc iron under pressure

We investigate the elastic and isotropic aggregate properties of ferromagnetic bcc iron as a function of temperature and pressure by computing the Helmholtz free energies for the volume-conserving strained structures using the first-principles linear response linear-muffin-tin-orbital method and the generalized-gradient approximation. We include the electronic excitation contributions to the free energy from the band structures, and phonon contributions from quasiharmonic lattice dynamics. We make detailed comparisons between our calculated elastic moduli and their temperature and pressure dependences with available experimental and theoretical data. The isotropic aggregate sound velocities obtained based on the calculated elastic moduli agree with available ultrasonic and diamond-anvil-cell data. Birch's law, which assumes a linear increase in sound velocity with increasing atomic density, fails for bcc Fe under extreme conditions. First-principles linear-response lattice dynamics is shown to provide a tractable approach to examine the elasticity of transition metals at high pressures and high temperatures.

Ab initio thermodynamics and phase diagram of solid magnesium: A comparison of the LDA and GGA

The finite temperature density functional theory and quasiharmonic lattice dynamics have been used to compute numerous thermodynamic properties of hexagonal close packed magnesium using both the local density approximation (LDA) and the generalized gradient approximation (GGA) for the exchange-correlation potential. Generally, it is found that there exist only minor differences between the LDA and GGA computed properties, with both giving good agreement with experiment. The hcp-bcc phase boundary has also been computed and is found to be in agreement with experimental observation. Again, only slight differences are found between the LDA and GGA.

Crystal structure of oligoacenes under high pressure

We report crystal structures of anthracene, tetracene, and pentacene under pressure. Energy dispersive x-ray diffraction experiments up to $9\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ were performed. Quasiharmonic lattice dynamics calculations are compared to the experimental results and show excellent agreement. The results are discussed with particular emphasis on the pressure dependence of the unit cell dimensions and the rearrangement of the molecules. The high pressure data also allow an analysis of the equation of state of these substances as a function of molecular length. We report the bulk modulus of tetracene and pentacene (${B}_{0}=9.0$ and $9.6\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, respectively) and its pressure derivative (${B}_{0}^{\ensuremath{'}}=7.9$ and 6.4, respectively). We find that the unit-cell volume and bulk modulus at ambient pressure follow a linear relationship with the molecular length.

Polymorphs of α-sexithiophene probed by lattice phonon Raman microscopy

We report for the first time lattice phonon Raman spectra of the organic semiconductor α-sexithiophene (T6) measured with a Raman microprobe technique. We identify spectroscopically two polymorphs, as expected from available structural diffraction studies. Polarized spectra were recorded for symmetry assignment. A comparison of experimental data with Quasi Harmonic Lattice Dynamics calculations, performed starting from the experimental X-ray structures, is given.

Thermal properties ofCaMoO4: Lattice dynamics and synchrotron powder diffraction studies

The structure of calcium molybdate was studied by means of synchrotron based high-resolution powder diffraction methods in the temperature range $12--300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The scheelite structure type was confirmed for $\mathrm{Ca}\mathrm{Mo}{\mathrm{O}}_{4}$ in the temperature region investigated and no structural anomalies were observed. Thermal expansion coefficients extracted from the thermal dependencies of the cell sizes are found to be in good agreement with the predictions from our lattice dynamics calculations that form the background for microscopic interpretation of the experimental data. From the analyses of experimental results and the calculated thermal expansion coefficients, elastic constants, phonon density of states, heat capacities, entropy, and Gr\"uneisen parameters it is concluded that a quasiharmonic lattice dynamics approach provides a good description of these properties for $\mathrm{Ca}\mathrm{Mo}{\mathrm{O}}_{4}$ at temperatures below $800\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.

Lattice dynamics of TTF–CA across the neutral–ionic transition

We present the temperature evolution of polarised Raman and IR reflectivity spectra of Tetrathiafulvalene–Chloranil (TTF–CA) in the lattice phonon region (10–200 cm −1). Quasi Harmonic Lattice Dynamics (QHLD) calculations prove to be essential in discussing the assignment of the phonons and their evolution across the temperature induced neutral–ionic phase transition.

Lattice vibrations in high-pressure phases of LiYF 4

Possible variations in the dynamical behaviour of LiYF 4 due to its several structural changes under pressure are examined by quasi-harmonic lattice dynamics calculations. The phonon spectra in the entire Brillouin zone together with the respective Gibbs free energies are calculated for the three high-pressure polymorphs of LiYF 4 (that are stable at T = 0 ) with a view to better understand their relative stabilities as functions of pressure and temperature. The present work predicts anomalous thermal expansion at low temperatures in phases I and IIa. Molecular dynamics simulations provide qualitative impressions about a temperature-driven second-order transition and also of kinetic effects in the subsequent pressure-driven first-order phase transformation.

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.

Thermal Expansion of the Perovskite‐Type NdGaO3.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Lattice dynamics and thermal properties ofCaWO4

Thermodynamic properties of $\mathrm{Ca}\mathrm{W}{\mathrm{O}}_{4}$ were studied using the GULP code incorporating semiclassical simulations based on quasiharmonic lattice dynamics and static lattice minimisation methods. Free energy minimization along with so called ``relax'' fitting was used to obtain the parameters characterising the interatomic interaction potential. From analyses of the calculated and experimental cell sizes, thermal expansion coefficients, elastic constants, phonon density of states, heat capacity, entropy, and Gr\"uneisen parameters it is concluded that quasiharmonic lattice dynamics give a good description of these properties of $\mathrm{Ca}\mathrm{W}{\mathrm{O}}_{4}$ at temperatures up to $800\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.

Thermal expansion of the perovskite-type NdGaO3

The structure of NdGaO3 was investigated by means of powder diffraction using synchrotron radiation in the temperature range 12–1173K. The NdGaO3 structure can be assigned to the GdFeO3-type (space group Pbnm) in the whole temperature range investigated. The thermal behaviour of the cell parameters was measured and found to be highly anisotropic. NdGaO3 shows practically the same thermal expansion along [100] and [001] directions, whereas the expansion along [010] is about 40% lower. In order to calculate the NdGaO3 thermal expansion three independent simulation techniques were applied: lattice dynamics, molecular dynamics and the Debye model. Using the GULP code and interatomic potentials described in the Buckingham form the Nd–O and Ga–O interactions have been derived. The total phonon DOS, its projections onto atomic species, the heat capacity Cv, the Grüneisen parameter γ and the thermal expansion coefficient α were determined using quasiharmonic lattice dynamics. Molecular dynamic simulations were applied to model the thermal expansion at different pressures and temperatures. The structure, its elastic properties and melting temperature are close to the experimentally observed values, which indicate the correct choice of the interatomic potential form and parameters. Comparison between the total DOS and its projections with the Debye DOS and Grüneisen parameter values calculated for different approaches allows to conclude that NdGaO3 cannot be considered as a good Debye-like solid.

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.

Quasiharmonic free energy and derivatives for many-body interactions: The embedded atom method

We present a method using many-body potentials and lattice statics and quasiharmonic lattice dynamics for the calculation of the free energy of periodic crystals and its analytic derivatives with respect to all external and internal degrees of freedom. Derivatives are calculated by means of first-order perturbation theory and detailed expressions for the lattice sums required are presented. No approximations regarding the coupling of vibrations of different atoms are made. The approach is illustrated using the embedded atom method. As an example we calculate the temperature variation of the entropy and free energy of mixing of disordered RhPd by using configurational lattice dynamics, in which the free energies of a number of configurations is determined directly by means of fully dynamic structural minimizations. The method is particularly useful for quantities such as the vibrational contributions to the entropy of mixing.

Intramolecular and Low-Frequency Intermolecular Vibrations of Pentacene Polymorphs as a Function of Temperature

Single crystals of pentacene with different morphologies (polymorphs C and H) have been studied by Raman spectroscopy as a function of temperature from 79 to 300 K. All Raman active lattice modes and a range of low-frequency intramolecular modes have been identified and assigned. The experiments are compared with quasi harmonic lattice dynamics (QHLD) calculations of the crystallographic structures and vibrational frequencies as a function of temperature. Experiments and calculations both indicate that the two polymorphs are stable over a wide temperature range.

The crystal structure and thermal expansion of the perovskite-typeNd0.75Sm0.25GaO3: powder diffraction and lattice dynamical studies

The structure of Nd0.75Sm0.25GaO3 was studied by high-resolution powder diffraction methods using conventionalx-ray and synchrotron radiation in the temperature range 85–1173 K. TheGdFeO3 structure typewas confirmed for Nd0.75Sm0.25GaO3 in the temperature region investigated and no structural transitions were observed. The cellparameters show a monotonic and anisotropic increase with temperature. The interatomicpotential was fitted using the GULP code. Using this potential, a self-consistentapproximation following the Debye model was constructed from the elastic constants of thecrystals. The total phonon DOS, its projections onto atomic species, heat capacityCv, Grüneisen parameterγ and thermalexpansion coefficient α were considered in the framework of quasiharmonic lattice dynamics and the Debye model.The shape of the phonon DOS calculated from lattice dynamics differs significantly fromthe respected Debye DOS. The rare earth, gallium and oxygen atoms dominate in differentfrequency regions of the phonon spectrum. The heat capacity is well reproduced by theDebye model below 100 K, where acoustic phonons play an important role and above800 K when the classical limit is reached. Predicted values of Grüneisen parameterand thermal expansion coefficients in the frame of the Debye model are too low. Therefore, the thermal properties ofNd0.75Sm0.25GaO3 cannot be explained by acoustic phonons only and hence,Nd0.75Sm0.25GaO3 cannot be described perfectly as a Debye-like solid with respect to its thermodynamicproperties.

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.