Exact Constructions of a Family of Dense Periodic Packings of Tetrahedra

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 $\phi= 4000/4671 = 0.856347...$. 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

Dense Packings of Superdisks and the Role of Symmetry

We construct the densest known two-dimensional packings of superdisks in the plane whose shapes are defined by |x^(2p) + y^(2p)| <= 1, which contains both convex-shaped particles (p > 0.5, with the circular-disk case p = 1) and concave-shaped particles (0 < p < 0.5). The packings of the convex cases with p 1 generated by a recently developed event-driven molecular dynamics (MD) simulation algorithm [Donev, Torquato and Stillinger, J. Comput. Phys. 202 (2005) 737] suggest exact constructions of the densest known packings. We find that the packing density (covering fraction of the particles) increases dramatically as the particle shape moves away from the "circular-disk" point (p = 1). In particular, we find that the maximal packing densities of superdisks for certain p 6 = 1 are achieved by one of the two families of Bravais lattice packings, which provides additional numerical evidence for Minkowski's conjecture concerning the critical determinant of the region occupied by a superdisk. Moreover, our analysis on the generated packings reveals that the broken rotational symmetry of superdisks influences the packing characteristics in a non-trivial way. We also propose an analytical method to construct dense packings of concave superdisks based on our observations of the structural properties of packings of convex superdisks.Comment: 15 pages, 8 figure

The upper critical field and its anisotropy in LiFeAs

The upper critical field $\mu_0H_{c2}(T_c)$ of LiFeAs single crystals has been determined by measuring the electrical resistivity using the facilities of pulsed magnetic field at Los Alamos. We found that $\mu_0H_{c2}(T_c)$ of LiFeAs shows a moderate anisotropy among the layered iron-based superconductors; its anisotropic parameter $\gamma$ monotonically decreases with decreasing temperature and approaches $\gamma\simeq 1.5$ as $T\rightarrow 0$. The upper critical field reaches 15T ($H\parallel c$) and 24.2T ($H\parallel ab$) at $T=$1.4K, which value is much smaller than other iron-based high $T_c$ superconductors. The temperature dependence of $\mu_0H_{c2}(T_c)$ can be described by the Werthamer-Helfand-Hohenberg (WHH) method, showing orbitally and (likely) spin-paramagnetically limited upper critical field for $H\parallel c$ and $H\parallel ab$, respectively.Comment: 5 pages,5 figure

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

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

Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres

Hyperuniform many-particle distributions possess a local number variance that grows more slowly than the volume of an observation window, implying that the local density is effectively homogeneous beyond a few characteristic length scales. Previous work on maximally random strictly jammed sphere packings in three dimensions has shown that these systems are hyperuniform and possess unusual quasi-long-range pair correlations, resulting in anomalous logarithmic growth in the number variance. However, recent work on maximally random jammed sphere packings with a size distribution has suggested that such quasi-long-range correlations and hyperuniformity are not universal among jammed hard-particle systems. In this paper we show that such systems are indeed hyperuniform with signature quasi-long-range correlations by characterizing the more general local-volume-fraction fluctuations. We argue that the regularity of the void space induced by the constraints of saturation and strict jamming overcomes the local inhomogeneity of the disk centers to induce hyperuniformity in the medium with a linear small-wavenumber nonanalytic behavior in the spectral density, resulting in quasi-long-range spatial correlations. A numerical and analytical analysis of the pore-size distribution for a binary MRJ system in addition to a local characterization of the n-particle loops governing the void space surrounding the inclusions is presented in support of our argument. This paper is the first part of a series of two papers considering the relationships among hyperuniformity, jamming, and regularity of the void space in hard-particle packings.Comment: 40 pages, 15 figure

Progress and challenges in photocatalytic ammonia synthesis

Photocatalytic ammonia (NH_{3}) synthesis from N_{2} and water driven by solar energy is a sustainable and environmentally friendly technology, which has gained considerable attention in recent years. In this review, the recent development in the fundamental understanding of photocatalytic NH_{3} synthesis and the methods of precise NH_{3} detection are summarized. More importantly the strategy for surface engineering and interface engineering of photocatalysts toward photocatalytic NH_{3} production has been thoroughly analyzed with the aim to stimulate critical thinking about the effective methodology for catalyst modification instead of exploring new materials. At the end the challenges and a few concerns are raised from the current reports and future perspectives in this research field are discussed targeting to clarify the reliability and reproducibility of the photochemical process and to direct the future research direction, such as flow reactor design and in-depth understanding of the underlying reaction pathway

CO hydrogenation reaction on sulfided molybdenum catalysts

Adsorption of reaction intermediates appearing during CO hydrogenation at the sulfur covered MoS2(1 0−1 0) surfaces, Mo-termination with 42% S coverage and S-termination with 50% S coverage, are investigated systematically using periodic density functional theory methods. Computed vibrational frequencies of all intermediates are compared with observed data from infrared (IR) spectroscopy allowing a detailed interpretation and assignment of the different features in the experimental spectra. The pathway for CO hydrogenation on both terminations has been studied in detail where the most likely reaction path involves C1 type surface species in the sequence CO→CHO→CH2O→CH2OH→CH2→CH3→CH4 in agreement with the experiment