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: 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: 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.

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 have studied the molecular energy terms of the hole configurations (h(u)(+))(m), m=2,3,4,5 of C-60(m+) cations and the electronic configurations (t(1u))(n) n=2,3,4, as well as (t(1u))(n-1)t(1g) of the C-60(n-) anions. The lowest terms (within an energy span of 0.03 eV) for C-60(2+) are three triplets T-3(1g), (3)G(g), T-3(2g) and for C-60(3+) are three quartets T-4(1u), (4)G(u), T-4(2u), which favor Jahn-Teller distortions. For the ground state of C-60(2-) we find a triplet T-3(1g) in agreement with Hund's rules. Our method takes into account intramolecular direct and exchange multipolar Coulomb interactions.

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: We have developed a microscopic theory which describes the orientational dynamics of C-70 molecules and its coupling to lattice displacements in the face-centered-cubic phase of C-70 fullerite. The single-molecule orientational density distribution in the disordered phase is calculated. The ferroelastic transition to the rhombohedral phase is investigated. The discontinuity of the orientational order parameter at the phase transition is calculated. It is found that the transition leads to a stretching of the primitive unit cell along a [111] cubic direction. A softening of the elastic constant c(44) at the transition is predicted.

Abstract: The recently discovered structural transition in polymerized KC60 at about 50 K results in a doubling of the unit cell volume and accompanies the 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 small orientational charge density waves along the polymer chains and concomitant displacements of the surrounding K+ ions. The effect is specific for the space group Pmnn of KC60 and is absent in RbC60 and CsC60 (space group I2/m). The mechanism is relevant for the metal-insulator 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.