Abstract: Differential cross sections for neutron and x-ray scattering have been derived for the orientationally disordered phase of solid C60. Interaction centres are placed at nuclei and at the centres of interatomic bonds. Bragg and diffuse scattering cross sections, for single crystals and for powders, are formulated using symmetry-adapted rotator functions. Thermal averages are calculated taking account of crystal field effects. Thermally averaged orientational distribution functions have also been calculated.

Abstract: A ''2222'' cuprate with mercury bilayers (Hg1.5Cu0.2Pr0.3)Ba2Pr2Cu2O10-delta, has been synthesized for the first time. It crystallizes in the P4/nmm space group with a = 3.9072(1) Angstrom and c = 17.219(1) Angstrom. The powder XRD and HREM studies of this new cuprate show that its structure consists of an intergrowth of double pyramidal (oxygen-deficient perovskite) copper layers, with double fluorite-type layers and distorted triple rock salt layers (mercury bilayers). The structure of this phase can be deduced from that of the ''2212'' mercury cuprate (Hg1.5Cu0.2Pr0.3)Ba2PrCu2O8-delta by the introduction of one additional [PrO2]infinity fluorite layer. The regular stacking of the metallic layer and the uniform cationic distribution in the mercury bilayers are remarkable features of this cuprate. The stabilization of the mercury bilayers by praseodymium and the absence of superconductivity are discussed. (C) 1995 Academic Press, Inc.

Abstract: Recently discovered series of high Tc superconductors, characterized by the existence of two types of cations within the same layer, are presented. The first family concerns the mercury based cuprates, Hg(1-x)M(x)A(2)Ca(m-1)Cu(m)O(2m+2+delta), with A = Ba and/or Sr, which exhibit structures closely related to that of the thallium cuprates TlBa2Cam-1CumO2m+3. They differ from the thallium cuprates by a high oxygen deficiency at the level of the mercury layer. It is shown that cations such as M = Cu, Pb, Tl, Bi, Ce, Pr, Cr, V, Mo, W, Ti, Sr, Ca,... can partially substitute for mercury ions, stabilizing the structures. The cationic composition of the layer depends indeed on the nature of the M cation but also on that of the alkaline earth A. For given A and M cations, the a: value remains unchanged even when the number of copper layers varies. M and Hg cations are either statistically distributed over the same site or ordered. Different types of ordering have been detected. Another way of generating mixed layers is to shear periodically the structure, leading to the formation of the so called ''collapsed phase''. In the collapsed bismuth cuprates, bismuth and copper segments, a few octahedra long, alternate in strongly waving layers. In the collapsed oxycarbonates, carbonate groups and M cations are ordered within the intermediate layer so that they can be simply described from a partial and ordered substitution of carbon for Hg,TI, Bi and other M cations building the intermediate layer. The oxycarbonitrates (Y1-xCax)(n)Ba2nCu3n-1(C,N)O3O7n-3 can also be described as an ordered substitution of carbon for copper in the 123 matrix. The different families of superconducting materials which are generated by such mechanisms are described as well as the way the different species are distributed within the mixed layers. Their influence on the physical properties are discussed.

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.