Abstract: We study the confinement of a C-60 molecule encapsulated in a cylindrical nanotube as a function of the tube radius. Drawing the Mercator maps of the potential, we find two distinct molecular orientations; for tubes with small radii, R-T less than or similar to 7 angstrom, a fivefold axis of the molecule coincides with the tube long axis, for larger radii, R-T less than or similar to 8 angstrom, a threefold axis of the molecule coincides with the tube long axis. These different orientations are caused by the relative importance of the repulsive and the attractive parts of the van der Waals potentials of the molecule with the tube wall for small and large tubes respectively. Experimental evidence is provided by the apparent splitting of A(g) modes of the C-60 molecule in resonant Raman scattering.

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: We have developed a microscopic theory which describes the orientational dynamics of C60 molecules in the face-centered-cubic phase of C60 fullerite. The molecular interaction potential and the crystal-field potential are formulated in terms of symmetry-adapted rotator functions. The phase transition to the Pa3BAR structure is driven by an active multipolar mode of T2g symmetry belonging to the l = 10 manifold. The Birman criterion is satisfied. The transition is found to be of first order.

Abstract: Using time-differential perturbed angular correlation spectroscopy we have measured the electric field gradient (EFG) at 111Cd probe nuclei in solid Ce in a pressure range up to 8 GPa. Covering various allotropic phases of Ce, we find that the value of the EFG in the cubic α phase is almost four times larger than in the cubic γ phase and close to values in the noncubic phases α′ and α″. These results together with the differences in time modulation of the spectra are interpreted as evidence for quadrupolar electronic charge-density ordering and symmetry lowering at the γ→α transition while the lattice remains face-centered cubic

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 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: The recently discovered structural phase transition in Polymerized KC60 at about 50K leads to a doubling of the unit cell volume and is accompanied by a metal-insulator transition. Here, we show that the ((a) over right arrow + (c) over right arrow, (b) over right arrow, (a) over right arrow – (c) over right arrow) superstructure results from orientational charge density waves along the polymer chains and correlated displacements of the K+ ions. The presented model can also account for the metal-insulator transition. The effect is specific for the space group Pmnn of KC60 and is absent in both Rb- and CsC60 (space group 12/m), in agreement with the present experimental knowledge of these compounds.

Abstract: The lattice dynamics of low-frequency rigid-plane modes in metallic (graphene multilayers, GML) and in insulating (hexagonal boron-nitride multilayers, BNML) layered crystals is investigated. The frequencies of shearing and compression (stretching) modes depend on the layer number N and are presented in the form of fan diagrams. The results for GML and BNML are very similar. In both cases, only the interactions (van der Waals and Coulomb) between nearest-neighbor planes are effective, while the interactions between more distant planes are screened. A comparison with recent Raman scattering results on low-frequency shear modes in GML [Tan et al., Nat. Mater., in press, doi: 10.1038/nmat3245, (2012)] is made. Relations with the low-lying rigid-plane phonon dispersions in the bulk materials are established. Master curves, which connect the fan diagram frequencies for any given N, are derived. Static and dynamic thermal correlation functions for rigid-layer shear and compression modes are calculated. The results might be of use for the interpretation of friction force experiments on multilayer crystals.

Abstract: The giant isotope effect on the ferro- and antiferroelectric transition temperature upon deuteration of hydrogen-bonded systems is well known experimentally since various decades. Yet, theoretically only recently a microscopic understanding of this effect has been achieved which, specifically, took into account the geometry of the O ... H ... O bond. The implications of this modeling are multiple as numerous hydrogen-bonded organic systems show the same effects as ferro- and antiferroelectrics, i.e., cooperative proton tunneling at a well-defined temperature.

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: The crystallographic structure and the distribution of orientations of molecular ions are studied near the surface in an orientationally disordered crystal with the use of a Green-function formalism. The orientational degrees of freedom are treated by means of symmetry-adapted functions of angular coordinates. The structure of the (001) surface of KCN in its cubic fcc phase is then predicted using the existing data on the interaction of the ions K+ and CN-. A local antiferroelectric and antiferroelastic order i shown to exist in the surface region. The magnitude of the order and the spatial extent of the ordered re ion increase as the temperature approaches the point of the phase transition to the ordered phase. The,influence of the external electric field on the structure of the surface is predicted.

Abstract: The confinement of a C-60 molecule encapsulated in a cylindrical nanotube depends on the tube radius. In small tubes with radius R-T less than or similar to 7 A, a fivefold axis of the molecule coincides with the tube axis. The interaction between C-60 molecules in the nanotube is then described by a O-2-rotor model on a 1D liquid chain with coupling between orientational and displacive correlations. This coupling leads to chain contraction. The structure factor of the 1D liquid is derived. In tubes with a larger radius the molecular centers of mass are displaced off the tube axis. The distinction of two groups of peapods with on- and off-axis molecules suggests an explanation of the apparent splitting of A(g) modes of C-60 in nanotubes measured by resonant Raman scattering.

Abstract: Superexchange interactions in alkali fullerides AC(60) are derived for C-60 molecular ions separated by interstitial alkali-metal ions. We use a multiconfiguration approach which comprises the lowest molecular orbital states of the C-60 molecule and the excited s and d states of the alkali-metal atom A. Interactions are described by the valence bond (Heitler-London) method for a complex (C-60 – A – C-60) – with two valence electrons. The electronic charge transfer between the alkali-metal atom and a neighboring C-60 molecule is not complete. The occupation probability of excited d and s states of the alkali atom is not negligible. In correspondence with the relative positions of the C-60 molecules and A atoms in the polymer crystal, we consider 180degrees and 90degrees (angle) superexchange pathways. For the former case the ground state is found to be a spin singlet separated from a triplet at similar to20 K. For T < 20 K there appear strong spin correlations for the 180degrees superexchange pathway. The results are related to spin lattice relaxation experiments on CsC60 in the polymerized and in the quenched cubic phase. (C) 2005 American Institute of Physics.

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: Starting from a model of rigid interacting C-60 polymer chains on an orthorhombic lattice, we study the mutual orientation of the chains and the stability of the crystalline structures Pmnn and I2/m. We take into account (i) van der Waals interactions and electric quadrupole interactions between C-60 monomers on different chains as well as (ii) interactions of the monomers with the surrounding alkali atoms. The direct interactions (i) always lead to an antiferrorotational structure Pmnn with alternate orientation of the C-60 chains in planes (001). The interactions (ii) with the alkalis consist of two parts: translation-rotation (TR) coupling where the orientations of the chains interact with displacements of the alkalis, and quadrupolar electronic polarizability (ep) coupling, where the electric quadrupoles on the C-60 monomers interact with induced quadrupoles due to excited electronic d-states of the alkalis. Both interactions (ii) lead to an effective orientation-orientation interaction between the C-60 chains and always favor the ferrorotational structure I2/m, where C-60 chains have a same orientation. The structures Pmnn for KC60 and I2/m for Rb- and CsC60 are the result of a competition between the direct interaction (i) and the alkali-mediated interactions (ii). In Rb- and CsC60 the latter are found to be dominant, the preponderant role being played by the quadrupolar electronic polarizability of the alkali ions. (C) 2002 American Institute of Physics.