Structure factors of harmonic and anharmonic Fibonacci chains by molecular dynamics simulations

The dynamics of quasicrystals is characterized by the existence of phason excitations in addition to the usual phonon modes. In order to investigate their interplay on an elementary level we resort to various one-dimensional model systems. The main observables are the static, the incoherent, and the coherent structure factor, which are extracted from molecular dynamics simulations. For the validation of the algorithms, results for the harmonic periodic chain are presented. We then study the Fibonacci chain with harmonic and anharmonic interaction potentials. In the dynamic Fibonacci chain neighboring atoms interact by double-well potentials allowing for phason flips. The difference between the structure factors of the dynamic and the harmonic Fibonacci chain lies in the temperature dependence of the phonon line width. If a bias is introduced in the well depth, dispersionless optic phonon bands split off.Comment: 12 pages, 15 figure

Surface structure of i-Al(68)Pd(23)Mn(9): An analysis based on the T*(2F) tiling decorated by Bergman polytopes

A Fibonacci-like terrace structure along a 5fold axis of i-Al(68)Pd(23)Mn(9) monograins has been observed by T.M. Schaub et al. with scanning tunnelling microscopy (STM). In the planes of the terraces they see patterns of dark pentagonal holes. These holes are well oriented both within and among terraces. In one of 11 planes Schaub et al. obtain the autocorrelation function of the hole pattern. We interpret these experimental findings in terms of the Katz-Gratias-de Boisseu-Elser model. Following the suggestion of Elser that the Bergman clusters are the dominant motive of this model, we decorate the tiling T*(2F) by the Bergman polytopes only. The tiling T*(2F) allows us to use the powerful tools of the projection techniques. The Bergman polytopes can be easily replaced by the Mackay polytopes as the decoration objects. We derive a picture of ``geared'' layers of Bergman polytopes from the projection techniques as well as from a huge patch. Under the assumption that no surface reconstruction takes place, this picture explains the Fibonacci-sequence of the step heights as well as the related structure in the terraces qualitatively and to certain extent even quantitatively. Furthermore, this layer-picture requires that the polytopes are cut in order to allow for the observed step heights. We conclude that Bergman or Mackay clusters have to be considered as geometric building blocks of the i-AlPdMn structure rather than as energetically stable entities

Structure of smectic defect cores: an X-ray study of 8CB liquid crystal ultra-thin films

We study the structure of very thin liquid crystal films frustrated by antagonistic anchorings in the smectic phase. In a cylindrical geometry, the structure is dominated by the defects for film thicknesses smaller than 150 nm and the detailed topology of the defects cores can be revealed by x-ray diffraction. They appear to be split in half tube-shaped Rotating Grain Boundaries (RGB). We determine the RGB spatial extension and evaluate its energy per unit line. Both are significantly larger than the ones usually proposed in the literatureComment: 4 page

Icosahedral multi-component model sets

A quasiperiodic packing Q of interpenetrating copies of C, most of them only partially occupied, can be defined in terms of the strip projection method for any icosahedral cluster C. We show that in the case when the coordinates of the vectors of C belong to the quadratic field Q[\sqrt{5}] the dimension of the superspace can be reduced, namely, Q can be re-defined as a multi-component model set by using a 6-dimensional superspace.Comment: 7 pages, LaTeX2e in IOP styl

Tiling theory applied to the surface structure of icosahedral AlPdMn quasicrystals

Surfaces in i-Al68Pd23Mn9 as observed with STM and LEED experiments show atomic terraces in a Fibonacci spacing. We analyze them in a bulk tiling model due to Elser which incorporates many experimental data. The model has dodecahedral Bergman clusters within an icosahedral tiling T^*(2F) and is projected from the 6D face-centered hypercubic lattice. We derive the occurrence and Fibonacci spacing of atomic planes perpendicular to any 5fold axis, compute the variation of planar atomic densities, and determine the (auto-) correlation functions. Upon interpreting the planes as terraces at the surface we find quantitative agreement with the STM experiments.Comment: 30 pages, see also http://homepages.uni-tuebingen.de/peter.kramer/ to be published in J.Phys.

Crystal electric field excitations in the quasicrystal approximant TbCd6 studied by inelastic neutron scattering

We have performed inelastic neutron scattering measurements on powder samples of the quasicrystal approximant, TbCd6, grown using isotopically enriched 112Cd. Both quasielastic scattering and distinct inelastic excitations were observed below 3 meV. The intensity of the quasielastic scattering measured in the paramagnetic phase diverges as TN∼22 K is approached from above. The inelastic excitations, and their evolution with temperature, are well characterized by the leading term, B02O02, of the crystal electric field (CEF) level scheme for local pentagonal symmetry for the rare-earth ions [S. Jazbec et al., Phys. Rev. B 93, 054208 (2016)] indicating that the Tb moment is directed primarily along the unique local pseudofivefold axis of the Tsai-type clusters. We also find good agreement between the inverse susceptibility determined from magnetization measurements using a magnetically diluted Tb0.05Y0.95Cd6 sample and that calculated using the CEF level scheme determined from the neutron measurements

Phason elasticity of a three-dimensional quasicrystal: transfer-matrix method

We introduce a new transfer matrix method for calculating the thermodynamic properties of random-tiling models of quasicrystals in any number of dimensions, and describe how it may be used to calculate the phason elastic properties of these models, which are related to experimental measurables such as phason Debye-Waller factors, and diffuse scattering wings near Bragg peaks. We apply our method to the canonical-cell model of the icosahedral phase, making use of results from a previously-presented calculation in which the possible structures for this model under specific periodic boundary conditions were cataloged using a computational technique. We give results for the configurational entropy density and the two fundamental elastic constants for a range of system sizes. The method is general enough allow a similar calculation to be performed for any other random tiling model.Comment: 38 pages, 3 PostScript figures, self-expanding uuencoded compressed tar file, LaTeX using RevTeX macros and epsfig.st

Impact of temperature and mode polarization on the acoustic phonon range in complex crystalline phases: A case study on intermetallic clathrates

The low and weakly temperature-varying lattice thermal conductivity, κL (T), in crystals with a complex unit cell such as type-I clathrates is assumed to originate from a reduced momentum and energy space available for propagative lattice vibrations, which is caused by the occurrence of low-energy optical phonon modes. In the context of ab initio self-consistent phonon (SCP) theory, it has been shown that the cubic and quartic anharmonic interactions result in a temperature-induced energy renormalization of these low-lying optical branches which contributes to the anomalous behavior of κL (T) in structurally ordered type-I clathrates [T. Tadano and S. Tsuneyuki, Phys. Rev. Lett. 120, 105901 (2018)]. By means of inelastic neutron scattering, we provide evidence for this energy renormalization in temperature, which has been resolved for transversely and longitudinally polarized phonons in the single crystal type-I clathrate Ba7.81Ge40.67Au5.33. By mapping the neutron intensity in the momentum space, we demonstrate the coherent character of the low-lying optical phonons. The overall phonon spectrum and dynamical structure factors are satisfactorily reproduced by ab initio harmonic calculations using density functional theory with the meta-GGA SCAN functional and a fully ordered structure. However, a polarization-dependent cutoff energy with opposing temperature shifts for longitudinal and transverse acoustic dispersions is experimentally observed which is not reproduced by the simulations. Anharmonicity affects the energies of the low-lying optical phonons in the transverse polarization, which compares quantitatively well with available results from SCP theory, whereas differences are observed for the longitudinal polarizatio

Random Tilings: Concepts and Examples

We introduce a concept for random tilings which, comprising the conventional one, is also applicable to tiling ensembles without height representation. In particular, we focus on the random tiling entropy as a function of the tile densities. In this context, and under rather mild assumptions, we prove a generalization of the first random tiling hypothesis which connects the maximum of the entropy with the symmetry of the ensemble. Explicit examples are obtained through the re-interpretation of several exactly solvable models. This also leads to a counterexample to the analogue of the second random tiling hypothesis about the form of the entropy function near its maximum.Comment: 32 pages, 42 eps-figures, Latex2e updated version, minor grammatical change