Quasi-harmonic Lattice Dynamics Calculations Research Articles

Influence of the exchange-correlation functional on the quasi-harmonic lattice dynamics of II-VI semiconductors.

We perform a systematic comparison of the finite-temperature structure and properties of four bulk semiconductors (PbS, PbTe, ZnS, and ZnTe) predicted by eight popular exchange-correlation functionals from quasi-harmonic lattice-dynamics calculations. The performance of the functionals in reproducing the temperature dependence of a number of material properties, including lattice parameters, thermal-expansion coefficients, bulk moduli, heat capacities, and phonon frequencies, is evaluated quantitatively against available experimental data. We find that the phenomenological over- and under-binding characteristics of the local-density approximation and the PW91 and Perdew-Burke-Enzerhof (PBE) generalised-gradient approximation (GGA) functionals, respectively, are exaggerated at finite temperature, whereas the PBEsol GGA shows good general performance across all four systems. The Tao-Perdew-Staroverov-Scuseria (TPSS) and revTPSS meta-GGAs provide relatively small improvements over PBE, with the latter being better suited to calculating structural and dynamical properties, but both are considerably more computationally demanding than the simpler GGAs. The dispersion-corrected PBE-D2 and PBE-D3 functionals perform well in describing the lattice dynamics of the zinc chalcogenides, whereas the lead chalcogenides appear to be challenging for these functionals. These findings show that quasi-harmonic calculations with a suitable functional can predict finite-temperature structure and properties with useful accuracy, and that this technique can serve as a means of evaluating the performance of new functionals in the future.

Predicting phonon properties and thermal conductivity from anharmonic lattice dynamics calculations and molecular dynamics simulations

Two methods for predicting phonon frequencies and relaxation times are presented. The first is based on quasiharmonic and anharmonic lattice dynamics calculations, and the second is based on a combination of quasiharmonic lattice dynamics calculations and molecular dynamics simulations. These phonon properties are then used with the Boltzmann transport equation under the relaxation-time approximation to predict the lattice thermal conductivity. The validity of the low-temperature assumptions made in the lattice dynamics framework are assessed by comparing to thermal conductivities predicted by the Green-Kubo and direct molecular dynamics methods for a test system of Lennard-Jones argon. The predictions of all four methods are in agreement at low temperature (20 K). At temperatures of 40 K (half the Debye temperature of Lennard-Jones argon) and below, the thermal-conductivity predictions from the two methods that use lattice dynamics calculations are within about 30% of those made using the more accurate Green-Kubo and direct molecular dynamics methods. The thermal-conductivity predictions using the lattice dynamics techniques become inaccurate at high temperature (above 40 K) due to the approximations inherent in the lattice dynamics framework. We apply the results to assess the validity of (i) the isotropic approximation in modeling thermal transport and (ii) the common assertion that low-frequency phonons dominate thermal transport. Lastly, we suggest approximations that can be made within the lattice dynamics framework that allow the thermal conductivity of Lennard-Jones argon to be estimated using two orders of magnitude less computing effort than the Green-Kubo or direct molecular dynamics methods.

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.

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.

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.

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.

Raman phonon spectra of pentacene polymorphs

We report for the first time lattice phonon Raman spectra of pentacene measured by means of a Raman microprobe technique. We experimentally prove the existence of two polymorphs, as expected from recent structural studies. A comparison with Quasi Harmonic Lattice Dynamics calculations, previously performed starting from the available X-ray data, help us in identifying the phase to which each crystal belongs.

Coupling between lattice and intramolecular modes in 9,10-dimethylanthracene: Raman spectra under pressure and quasi-harmonic lattice dynamics calculations

Raman phonon spectra of 9,10-dimethylanthracene crystals have been measured as a function of pressure in the range 0–10 GPa for both lattice and intramolecular modes. Quasi-harmonic lattice dynamics calculations have been used to analyze the effects of the vibrational degrees of freedom on the pressure dependence of the crystallographic structure and phonon wave numbers. We find that the coupling between lattice and intramolecular vibrations contributes significantly to the pressure dependence of the phonon spectra, which is accurately reproduced by the calculations. Vibrational effects on the structure, instead, are less significant.

Pressure and temperature effects in lattice dynamics: 1,4-dibromonaphthalene

Raman phonon spectra of the quasi-linear crystal 1,4-dibromonaphthalene (DBrN) have been recorded as a function of temperature (ambient pressure) and in the pressure range 0–12.5 GPa at room temperature. No phase transition has been detected up to the maximum pressure studied. Quasi-harmonic lattice dynamics calculations, based on intermolecular atom–atom potentials, reproduce well the ambient p, T crystal structure and the pressure and temperature dependence of the Raman-active lattice phonons. The high stability to pressure of the quasi-one-dimensional molecular packing of DBrN is semi-empirically rationalized by comparison to similar systems undergoing pressure-induced phase transitions.

Raman phonon spectra and lattice dynamics of 9,10-dinitroanthracene under pressure

Raman phonon spectra of 9, 10-dinitroanthracene have been recorded in the pressure range 0-6GPa. No phase transition is detected up to the maximum pressure studied. Quasi Harmonic Lattice Dynamics calculations, based on an atom-atom potential previously modeled on homologous 9,10-disubstituted anthracenes, have been performed. The optimized potential was used to calculate the equilibrium geometry and the lattice phonon frequencies as a function of pressure. The calculated structure at ambient conditions closely resembles the experimental one. The calculated phonon frequencies show a good agreement with the experimental values at all pressures measured.

The mechanisms for pressure-induced amorphization of ice Ih

There has been considerable interest in the structure of liquid water at low temperatures and high pressure following the discovery of the high-density amorphous (HDA) phase of ice Ih (ref. 1). HDA ice forms at a pressure close to the extrapolated melting curve of ice, leading to the suggestion that it may have structure similar to that of dense water. On annealing, HDA ice transforms into a low-density amorphous (LDA) phase with a distinct phase boundary2,3. Extrapolation of thermodynamic data along the HDA–LDA coexistence line into the liquid region has led to the hypothesis that there might exist a second critical point for water and the speculation that liquid water is mixture of two distinct structures with different densities4,5. Here we critically examine this hypothesis. We use quasi-harmonic lattice-dynamics calculations to show that the amorphization mechanism in ice Ih changes from thermodynamic melting for T > 162 K to mechanical melting at lower temperatures. The vibrational spectra of ice Ih, LDA ice and quenched water also indicate a structure for LDA ice that differs from that of the liquid. These results call into question the validity of there being a thermodynamic connection between the amorphous and liquid phases of water.

High-pressure elastic constants of solid krypton from quasiharmonic lattice-dynamics calculations

High-pressure elastic constants of solid krypton from quasiharmonic lattice-dynamics calculations

Development of an N-body interatomic potential for hcp and bcc zirconium.

An interatomic potential based on the second-moment approximation of the tight-binding scheme is developed for zirconium, by fitting its four adjustable parameters to the cohesive energy, atomic volume, and elastic constants of the hcp phase. In this work we attempt to model realistically two different crystallographic phases of a solid with the same potential. The reliability of our potential is tested in both the hcp and the bcc phases with regard to defect properties, thermal expansion, phonon properties, and mean-square displacements. For this purpose, we perform quenched molecular-dynamics relaxations, quasiharmonic lattice-dynamics calculations, and molecular-dynamics simulations. The low vacancy-formation and migration energies found in the bcc phase are consistent with the fast diffusivity experimentally observed. Unlike some other N-body potentials recently proposed to model bcc transition metals, our potential is not affected by the flaw of unphysical or even negative thermal expansion. We obtain thermal expansions that agree well with experiments in both phases, although they turned out to be slightly too large. The phonon-dispersion curves and, in particular, the anomalies in the bcc phase are well reproduced. We emphasize the stabilization with temperature of the T1 N-point phonon of the bcc phase, which is related to the bcc- to hcp-phase transition. We obtain a temperature dependence of this mode much weaker than in the experimental case. This influences the temperature behavior of the vibrational properties: In particular the mean-square displacement is markedly higher than the one extracted from experiments in the bcc phase at high temperatures. On the other hand, mean-square displacements in the hcp phase are in excellent agreement with experiment. The results are quite satisfactory in view of the small number of fitting parameters and the difficulties commonly encountered in matching the properties of bcc metals.