9,466 research outputs found

    Exact Constructions of a Family of Dense Periodic Packings of Tetrahedra

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    The determination of the densest packings of regular tetrahedra (one of the five Platonic solids) is attracting great attention as evidenced by the rapid pace at which packing records are being broken and the fascinating packing structures that have emerged. Here we provide the most general analytical formulation to date to construct dense periodic packings of tetrahedra with four particles per fundamental cell. This analysis results in six-parameter family of dense tetrahedron packings that includes as special cases recently discovered "dimer" packings of tetrahedra, including the densest known packings with density Ï•=4000/4671=0.856347...\phi= 4000/4671 = 0.856347.... This study strongly suggests that the latter set of packings are the densest among all packings with a four-particle basis. Whether they are the densest packings of tetrahedra among all packings is an open question, but we offer remarks about this issue. Moreover, we describe a procedure that provides estimates of upper bounds on the maximal density of tetrahedron packings, which could aid in assessing the packing efficiency of candidate dense packings.Comment: It contains 25 pages, 5 figures

    Magnetic structure of superconducting Eu(Fe0.82Co0.18)2As2 as revealed by single-crystal neutron diffraction

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    The magnetic structure of superconducting Eu(Fe0.82Co0.18)2As2 is unambiguously determined by single-crystal neutron diffraction. A long-range ferromagnetic order of the Eu2+ moments along the c-direction is revealed below the magnetic phase transition temperature Tc = 17 K. In addition, the antiferromagnetism of the Fe2+ moments still survives and the tetragonal-to-orthorhombic structural phase transition is also observed, although the transition temperatures of the Fe-spin density wave (SDW) order and the structural phase transition are significantly suppressed to Tn = 70 K and Ts = 90 K, respectively, compared to the parent compound EuFe2As2.We present the microscopic evidences for the coexistence of the Eu-ferromagnetism (FM) and the Fe-SDW in the superconducting crystal. The superconductivity (SC) competes with the Fe-SDW in Eu(Fe0.82Co0.18)2As2.Moreover, the comparison between Eu(Fe1-xCox)2As2 and Ba(Fe1-xCox)2As2 indicates a considerable influence of the rare-earth element Eu on the magnetism of the Fe sublattice.Comment: 7 pages, 7 figures, accepted for publication in Physical Review

    Upper critical field and thermally activated flux flow in single crystalline Tl0.58_{0.58}Rb0.42_{0.42}Fe1.72_{1.72}Se2_2

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    The upper critical field μ0Hc2(Tc)\mu_0H_{c2}(T_c) of Tl0.58_{0.58}Rb0.42_{0.42}Fe1.72_{1.72}Se2_2 single crystals has been determined by means of measuring the electrical resistivity in both a pulsed magnetic field (∼\sim60T) and a DC magnetic field (∼\sim14T). It is found that Hc2H_{c2} linearly increases with decreasing temperature for H\textbf{H}∥\parallelcc, reaching μ0Hc2H∥c(0K)≃60\mu_0H_{c2}^{\textbf{H}\parallel c}(0\textrm{K})\simeq60 T. On the other hand, a larger μ0Hc2(0K)\mu_0H_{c2}(0\textrm{K}) with a strong convex curvature is observed for H\textbf{H}⊥\perpcc (μ0Hc2H⊥c\mu_0H_{c2}^{\textbf{H}\perp c}(18K)≃\simeq60T). This compound shows a moderate anisotropy of the upper critical field around TcT_c, but decreases with decreasing temperature. Analysis of the upper critical field based on the Werthamer-Helfand-Hohenberg (WHH) method indicates that μ0Hc2(0K)\mu_0H_{c2}(0\textrm{K}) is orbitally limited for H\textbf{H}∥\parallelcc, but the effect of spin paramagnetism may play an important role on the pair breaking for H\textbf{H}⊥\perpcc. All these experimental observations remarkably resemble those of the iron pnictide superconductors, suggesting a unified scenario for the iron-based superconductors. Moreover, the superconducting transition is significantly broadened upon applying a magnetic field, indicating strong thermal fluctuation effects in the superconducting state of Tl0.58_{0.58}Rb0.42_{0.42}Fe1.72_{1.72}Se2_2. The derived thermal activation energy for vortex motion is compatible with those of the 1111-type iron pnictides.Comment: 7 pages, 6 figure

    Modeling Heterogeneous Materials via Two-Point Correlation Functions: II. Algorithmic Details and Applications

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    In the first part of this series of two papers, we proposed a theoretical formalism that enables one to model and categorize heterogeneous materials (media) via two-point correlation functions S2 and introduced an efficient heterogeneous-medium (re)construction algorithm called the "lattice-point" algorithm. Here we discuss the algorithmic details of the lattice-point procedure and an algorithm modification using surface optimization to further speed up the (re)construction process. The importance of the error tolerance, which indicates to what accuracy the media are (re)constructed, is also emphasized and discussed. We apply the algorithm to generate three-dimensional digitized realizations of a Fontainebleau sandstone and a boron carbide/aluminum composite from the two- dimensional tomographic images of their slices through the materials. To ascertain whether the information contained in S2 is sufficient to capture the salient structural features, we compute the two-point cluster functions of the media, which are superior signatures of the micro-structure because they incorporate the connectedness information. We also study the reconstruction of a binary laser-speckle pattern in two dimensions, in which the algorithm fails to reproduce the pattern accurately. We conclude that in general reconstructions using S2 only work well for heterogeneous materials with single-scale structures. However, two-point information via S2 is not sufficient to accurately model multi-scale media. Moreover, we construct realizations of hypothetical materials with desired structural characteristics obtained by manipulating their two-point correlation functions.Comment: 35 pages, 19 figure
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