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: 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: A unified theory of phonon dispersions and piezoelectricity in bulk and multilayers of hexagonal boron nitride (h-BN) is derived. The dynamical matrix is calculated on the basis of an empirical force constant model of intralayer valence and interlayer van der Waals interactions. Coulomb interactions are calculated by Ewalds method, adapted for the three-dimensional (3D) and the multilayer case. The deformation of the ionic charge distribution with long-wave lattice displacements is taken into account. Special attention is devoted to the nonanalytic long-range Coulomb contribution to the dynamical matrix which is different for the 3D crystal and the multilayer case. Consequently there is a splitting of the transverse optical (TO) and longitudinal optical (LO) phonon branches of E1u symmetry and a discontinuity of the A2u branch at the Γ point in 3D h-BN. No such splitting and discontinuity at Γ are present in multilayer crystals with a finite number N of layers. There a diverging bundle of N overbending optical phonon branches emerges from Γ. Borns long-wave theory is applied and extended for the study of piezoelectricity in layered crystals. While 3D h-BN and h-BN multilayers with an even number of layers (symmetry D6h) are not piezoelectric, multilayers with an uneven number of Nu layers (symmetry D3h) are piezoelectric; the piezoelectric coefficient e1,11 is inversely proportional to Nu.

Abstract: Starting from an empirical force constant model of valence interactions and calculating by Ewald's method the electrostatic force constants, we derive the dynamical matrix for a monolayer and for multilayer systems of hexagonal boron nitride (h-BN). Solution of the secular problem leads to the corresponding phonon dispersion relations. The interplay between valence forces and Coulomb forces is discussed. A comparison with previous results on graphene and graphene multilayers is made. Our spectra on the h-BN monolayer are rather similar to previous ab initio theory results. Comparison is also made with Raman and infrared experimental results.

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: Born's long wave method is used to study the elastic properties of graphite and graphene. Starting from an empirical force constant model derived from full inplane phonon dispersions of graphite [Mohr et al., Phys. Rev. B 76, 035439 (2007)] we calculate the tension coefficients of graphene. Extending the model by interplanar interactions, we calculate the elastic constants of graphite. The agreement of our theoretical values with inelastic x-ray scattering results on elastic constants of graphite [Bosak et al., Phys. Rev. B 75, 153408 (2007)] is very satisfactory.

Abstract: Starting from a Hamiltonian with anharmonic coupling between in-plane acoustic displacements and outof-plane (flexural) modes, we derived coupled equations of motion for in-plane displacements correlations and flexural mode density fluctuations. Linear response theory and time-dependent thermal Green's functions techniques are applied in order to obtain different response functions. As external perturbations we allow for stresses and thermal heat sources. The displacement correlations are described by a Dyson equation where the flexural density distribution enters as an additional perturbation. The flexural density distribution satisfies a kinetic equation where the in-plane lattice displacements act as a perturbation. In the hydrodynamic limit this system of coupled equations is at the basis of a unified description of elastic and thermal phenomena, such as isothermal versus adiabatic sound motion and thermal conductivity versus second sound. The general theory is formulated in view of application to graphene, two-dimensional h-BN, and 2H-transition metal dichalcogenides and oxides.

Abstract: Starting from a microscope model of the intermolecular potential, a unified description is presented of the Bragg scattering law in the orientationally disordered and in the ordered phase of solid C-60. The orientational structure factor is expanded in terms of symmetry-adapted surface harmonics. The expansion coefficients are calculated from theory and compared with experiment Their temperature evolution is studied in the disordered phase at the 260 K transitions and in the ordered phase. In the ordered phase, new results from high-resolution neutron powder diffraction are given. In the disordered phase, space group Fm $($) over bar$$ 3m, the reflections have A(1g) symmetry; in the ordered phase, space group Pa $$($) over bar 3, reflections of T-2g symmetry appear and in addition the A(1g) reflections are renormalized. The orientational density distribution is calculated. The effective crystal-field potential is constructed, its temperature evolution in the ordered phase is studied and related to the occurrence of an orientational glass.

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 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: A microscopic theory, which describes the orientational dynamics of C60 molecules in the face-centered cubic phase of C60-fullerite, is formulated or the case of a complex molecular structure. Interaction centers which comprise atoms, double bonds, and single bonds as molecular constituents contribute to the intermolecular potential. Orientation dependent physical properties are described in terms of symmetry-adapted rotator functions. It is found that a same set of rotator functions is sufficient even in the case of a complex molecular structure. Phase transition temperatures are discussed for various models of molecular structure.

Abstract: Neutron and high resolution X-ray diffraction investigations on perfect single crystals of RbH2PO4 (RDP), a hydrogen bonded ferroelectric of KDP type are reported. The results of crystal structure analysis from diffraction data, below and above the paraelectric – ferroelectric phase transition, support a disorder – order character Of [PO4H2](-)-groups. The tetragonal symmetry of the paraelectric phase with the double well potential of the hydrogen atoms obtained by diffraction, results simply from a time-space average of orthorhombic symmetry. According to the group – subgroup relation between the tetragonal space group 142d and the orthorhombic Fdd2 a short range order of ferroelectric clusters in the tetragonal phase is observed. With decreasing temperature the ferroelectric clusters increase and the long range interaction between their local polarisation vectors leads to the formation of lamellar ferroelectric domains with alternating polarisation directions at T-C = 147 K. From the high resolution X-ray data it is concluded that below T-C the ferroelastic strain in the (a,b)-plane leads to micro-angle grain boundaries at the domain walls. The tilt angle is enhanced by an applied electric field parallel to the ferroelectric axis. The resulting dislocations at the domain walls persist in the paraelectric phase leading to a memory effect for the arrangement of twin lamellae. With increased electric field the phase transition temperature T-C is decreased.