Abstract: Starting from a model of microscopic interactions between C-70 molecules, we have developed a theory which describes the orientational dynamics and its coupling to lattice displacements in the rhombohedral phase of C-70 fullerite. The Landau free energy is calculated. We obtain a first-order phase transition to a monoclinic structure with the space group P2(1)/m. The transition is driven by the condensation of orientational quadrupoles at the F point of the Brillouin zone of the rhombohedral lattice. We find no evidence that the monoclinic structure is connected with the freezing in of orientations around the fivefold molecular axis. We calculate the lattice strains that are associated with the transition to the monoclinic structure. The theory is compared with a range of experimental data on the phase transition.

Abstract: The orientation of a C(70) fullerene molecule encapsulated in a single-walled carbon nanotube (SWCNT) depends on the tube radius. First we confirm that chirality effects do not affect the orientation as well by comparing discrete atomistic calculations with the results of a continuous tube approximation for a variety of SWCNTs. The molecular and the tube symmetry are exploited by using symmetry-adapted rotator functions. We accurately determine the optimal molecular orientation as a function of the tube radius; for low (less than or similar to 7 A) and high (greater than or similar to 7.2 A) tube radii, lying and standing molecular orientations are recovered, respectively. In between, we observe a transition regime. In addition, we consider off-axis positions. We perform a one-dimensional liquid description of a chain of on-axis C(70) molecules inside a SWCNT. All results agree well with recent x-ray diffraction experiments.

Abstract: A theoretical model is presented for the description of the metal-insulator transition which accompanies the structural phase transition at T approximate to 50 K in polymerized KC60. The model involves orientational charge density waves (along the C-60 polymer chains) which were introduced previously for a description of the structural phase transition. A satisfactory qualitative and quantitative understanding is obtained when the three-dimensionality of the crystal and the presence of the K+ counterions is properly taken into account.

Abstract: The structural phase transitions with electric-quadrupole long-range order in NpO2 (Fm (3) over barm-->Pn (3) over barm) and UO2 (Fm (3) over barm-->Pa (3) over bar) are analyzed from a group theoretical point of view. In both cases, the symmetry lowering involves three quadrupolar components belonging to the irreducible representation T-2g (Gamma(5)) of O-h and condensing in a triple-q structure at the X point of the Brillouin zone. The Pa (3) over bar structure is close to Pn (3) over barm, but allows for oxygen displacements. The Pa (3) over bar ordering leads to an effective electrostatic attraction between electronic quadrupoles while the Pn (3) over barm ordering results in a repulsion between them. It is concluded that the Pn (3) over barm structure can be stabilized only through some additional process such as strengthening of the chemical bonding between Np and O. We also derive the relevant structure-factor amplitudes for Pn (3) over barm and Pa (3) over bar, and the effect of domains on resonant x-ray scattering experiments.

Abstract: Starting from an empirical force constant model of valence interactions and calculating by Ewalds method the ion-ion force constants, we derive the dynamical matrix for a monolayer crystal of hexagonal boron nitride (h-BN). The phonon dispersion relations are calculated. The interplay between valence and Coulomb forces is discussed. It is shown by analytical methods that the longitudinal and the transverse optical (LO and TO) phonon branches for in-plane motion are degenerate at the Γ point of the Brillouin zone. Away from Γ, the LO branch exhibits pronounced overbending. It is found that the nonanalytic Coulomb contribution to the dynamical matrix causes a linear increase of the LO branch with increasing wave vector starting at Γ. This effect is general for two-dimensional (2D) ionic crystals. Performing a long-wavelength expansion of the dynamical matrix, we use Borns perturbation method to calculate the elastic constants (tension coefficients). Since the crystal is noncentrosymmetric, internal displacements due to relative shifts between the two sublattices (B and N) contribute to the elastic constants. These internal displacements are responsible for piezoelectric and dielectric phenomena. The piezoelectric stress constant and the dielectric susceptibility of 2D h-BN are calculated.

Abstract: We present a unified theory of the phonon dispersions and elastic properties of graphene, graphite, and graphene multilayer systems. Starting from a fifth-nearest-neighbor force-constant model derived from full in-plane phonon dispersions of graphite [Mohr et al., Phys. Rev. B 76, 035439 (2007)], we use Born's long-wave method to calculate the tension and bending coefficients of graphene. Extending the model by interplanar interactions, we study the phonon dispersions and the elastic constants of graphite, and the phonon spectra of graphene multilayers. We find that the inner displacement terms due to sublattice shifts between inequivalent C atoms are quantitatively important in determining the elastomechanical properties of graphene and of graphite. The overall agreement between theory and experiment is very satisfactory. We investigate the evolution from graphene to graphite by studying the increase in the rigid plane optical mode as a function of the number of layers N. At N=10 the graphite value B2g1127 cm−1 is attained within a few percent.

Abstract: The elastic constant C-11 and piezoelectric stress constant e(1),(11) of two-dimensional (2D) dielectric materials comprising h-BN, 2H-MoS2, and other transition-metal dichalcogenides and dioxides are calculated using lattice dynamical theory. The results are compared with corresponding quantities obtained with ab initio calculations. We identify the difference between clamped-ion and relaxed-ion contributions with the dependence on inner strains which are due to the relative displacements of the ions in the unit cell. Lattice dynamics allows us to express the inner-strain contributions in terms of microscopic quantities such as effective ionic charges and optoacoustical couplings, which allows us to clarify differences in the piezoelectric behavior between h-BN and MoS2. Trends in the different microscopic quantities as functions of atomic composition are discussed.

Abstract: Starting from our previous work in which we obtained a system of coupled integrodifferential equations for acoustic sound waves and phonon density fluctuations in two-dimensional (2D) crystals, we derive here the corresponding hydrodynamic equations, and we study their consequences as a function of temperature and frequency. These phenomena encompass propagation and damping of acoustic sound waves, diffusive heat conduction, second sound, and Poiseuille heat flow, all of which are characterized by specific transport coefficients. We calculate these coefficients by means of correlation functions without using the concept of relaxation time. Numerical calculations are performed as well in order to show the temperature dependence of the transport coefficients and of the thermal conductivity. As a consequence of thermal tension, mechanical and thermal phenomena are coupled. We calculate the dynamic susceptibilities for displacement and temperature fluctuations and study their resonances. Due to the thermomechanical coupling, the thermal resonances such as the Landau-Placzek peak and the second-sound doublet appear in the displacement susceptibility, and conversely the acoustic sound wave doublet appears in the temperature susceptibility, Our analytical results not only apply to graphene, but they are also valid for arbitrary 2D crystals with hexagonal symmetry, such as 2D hexagonal boron nitride, 2H-transition-metal dichalcogenides, and oxides.

Abstract: The determination of the layer number ${\cal N}$ in nanoscale thin layered crystals is a challenging problem of technological relevance. In addition to innovative experimental techniques, a thorough knowledge of the underlying lattice dynamics is required. Starting from phenomenological atomic interaction potentials we have carried out an analytical study of the low-frequency optical phonon dispersions in layered crystals. At the gamma point of the two-dimensional Brillouin zone the optical phonon frequencies correspond to rigid-plane shearing and compression modes. We have investigated graphene multilayers (GML) and hexagonal boron-nitride multilayers (BNML). The frequencies show a characteristic dependence on ${\cal N}$. The results which are represented in the form of fan diagrams are very similar for both materials. Due to charge neutrality within layers Coulomb forces play no role, only van der Waals forces between nearest neighbor layers are relevant. The theoretical results agree with recent low-frequency Raman results on rigid-layer modes [Tan et al., Nature Mater. 11, 294 (2012)] in GML and double-resonant Raman scattering data on rigid-layer compression modes [Herziger et al., Phys. Rev. B 85, 235447 (2012)] in GML. (C) 2012 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim

Abstract: Taking into account covalent, Coulomb and van der Waals interactions, we construct the dynamical matrix and calculate the phonon dispersion relations for multilayer crystals of hexagonal boron-nitride. Coulomb interactions account for a strong overbending of optical phonons. Applying and extending Born's long-wave theory to the case of multilayer crystals, we calculate the piezoelectric stress constant equation image as a function of the number of layers equation image. In agreement with group theory, we find that equation image for equation image even; for an uneven number equation image of layers we obtain equation image, i.e. the piezoelectric constant decreases as equation image.

Abstract: The thermal expansion alpha(T) in layered crystals is of fundamental and technological interest. As suggested by I. M. Lifshitz in 1952, in thin solid films (crystalline membranes) a negative contribution to alpha(T) is due to anharmonic couplings between in-plane stretching modes and out-of-plane bending (flexural modes). Genuine in-plane anharmonicities give a positive contribution to alpha(T). The competition between these two effects can lead to a change of sign (crossover) from a negative value of alpha(T) in a temperature (T) range T <= T-alpha to a positive value of alpha(T) for T > T-alpha in layered crystals. Here, we present an analytical lattice dynamical theory of these phenomena for a two-dimensional (2D) hexagonal crystal. We start from a Hamiltonian that comprises anharmonic terms of third and fourth order in the lattice displacements. The in-plane and out-of-plane contributions to the thermal expansion are studied as functions of T for crystals of different sizes. Besides, renormalization of the flexural mode frequencies plays a crucial role in determining the crossover temperature T-alpha. Numerical examples are given for graphene where the anharmonic couplings are determined from experiments. The theory is applicable to other layer crystals wherever the anharmonic couplings are known. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Abstract: The transition Fm (3) over bar m -->Pa (3) over bar in solid C-60 is driven by the condensation of orientational modes belonging to X-5(+) irreducible representations (irreps) of Fm (3) over bar m. Taking into account irreps up to the manifold l = 12, we have studied the primary and secondary orientational order parameters loops). We have numerically solved the coupled molecular field equations for these oops and calculated the temperature dependence of Bragg reflection intensities. (C) 1998 Elsevier Science B.V. All rights reserved.