Large Tetrahedra Research Articles

Hedgehog lattice and field-induced chirality in breathing-pyrochlore Heisenberg antiferromagnets

We theoretically investigate a ${J}_{1}\text{\ensuremath{-}}{J}_{3}$ classical Heisenberg model on the breathing pyrochlore lattice, where the nearest-neighbor (NN) exchange interactions for small and large tetrahedra, ${J}_{1}$ and ${J}_{1}^{\ensuremath{'}}$, take different values due to the breathing bond alternation and ${J}_{3}$ is the third NN antiferromagnetic interaction along the bond direction. It is found by means of Monte Carlo simulations that for large ${J}_{3}$, a hedgehog lattice, a three-dimensional periodic array of magnetic monopoles and antimonopoles, emerges in the form of a quadruple-$\mathbf{Q}$ state characterized by the ordering vector of $\mathbf{Q}=(\ifmmode\pm\else\textpm\fi{}\frac{1}{2},\ifmmode\pm\else\textpm\fi{}\frac{1}{2},\ifmmode\pm\else\textpm\fi{}\frac{1}{2})$, being irrespective of the signs of ${J}_{1}$ and/or ${J}_{1}^{\ensuremath{'}}$ as long as ${J}_{1}\ensuremath{\ne}{J}_{1}^{\ensuremath{'}}$. It is also found that in an applied magnetic field, there appear six quadruple-$\mathbf{Q}$ states depending on the values of ${J}_{1}$ and ${J}_{1}^{\ensuremath{'}}$, among which three phases including the in-field hedgehog-lattice state exhibit nonzero total chirality ${\mathbit{\ensuremath{\chi}}}^{\mathrm{T}}$ associated with the anomalous Hall effect of chirality origin. In the remaining two chiral phases, which are realized in the presence of ferromagnetic ${J}_{1}$ and/or ${J}_{1}^{\ensuremath{'}}$, the spin structure is not topologically nontrivial, in spite of the fact that ${\mathbit{\ensuremath{\chi}}}^{\mathrm{T}}\ensuremath{\ne}0$. The role of the topological objects of the monopoles in ${\mathbit{\ensuremath{\chi}}}^{\mathrm{T}}$ is also discussed.

Effects of spin-lattice coupling and a magnetic field in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice

We theoretically investigate spin-lattice coupling (SLC) effects on the in-field ordering properties of classical Heisenberg antiferromagnets on the breathing pyrochlore lattice. Here, we use the two possible simplified models describing the effect of local lattice distortions on the spin ordering via the SLC, the bond-phonon and site-phonon models. It is found by means of Monte Carlo simulations that in both models, the $\frac{1}{2}$ plateau shows up in the magnetization curve being relatively robust against the breathing bond alternation, although magnetic long-range orders (LRO's) are realized only in the site-phonon model. In the bond-phonon model, additional further neighbor interactions are necessary to induce a magnetic LRO. In the site-phonon model, it is also found that in addition to the low-field, middle-field $\frac{1}{2}$ plateau, and high-field phases appearing on both the uniform and breathing pyrochlore lattices, various types of unconventional phases which can be viewed as LRO's in units of tetrahedron are induced by the breathing bond alternation just below the $\frac{1}{2}$ plateau and the saturation field. The occurrence of these tetrahedron-based orders could be attributed to the nature characteristic of the breathing pyrochlore lattice, i.e., the existence of the nonequivalent small and large tetrahedra. Experimental implications of our result are also discussed.

Molecular-strain engineering of double-walled tetrahedra

<h2>Summary</h2> The synthesis of multi-walled nanostructures represents a formidable challenge owing to the limitations imposed by existing synthetic strategies. Herein, we report a strategy involving molecular-strain engineering (MSE) for constructing double-walled polyhedra from strained bow-shaped macrocycles called molecular bows (MBs). As a proof of concept, four double-walled tetrahedra have been assembled from L-shaped dual-panels subtending ∼70.5° and producing MBs, which incorporate porphyrin and <i>o</i>-xylylene units, forming strained shape-persistent conformations. The head-to-tail closed-loop stacking of these units, driven by complementary non-covalent bonding interactions, leads to a large porphyrin-lined tetrahedron encapsulating a small <i>o</i>-xylylene-lined tetrahedron. The synergistic aromatic shielding effects emanating from the porphyrin tetrahedron result in the largest upfield chemical shifts of −7.7 ppm for protons and −8.8 ppm for carbons from those for the free dual panels. This demonstration, which features the launching of MSE for constructing sophisticated supramolecular nanostructures, could herald a fresh approach to the fabrication of multi-porphyrin photocatalytic systems.

Generating Hexahedral Mesh for Wire-wrapped Fuel Assembly With RBF Mesh Deformation Method

Fuel assemblies with wire spacer are widely used in Generation IV liquid nuclear reactors. With the rapid development of computational power, the Computational Fluid Dynamic (CFD) method is becoming an effective tool to investigate the detailed three-dimensional thermal hydraulic characteristics in wire-wrapped fuel assemblies. Due to the complexity of geometry, most of the published researches are performed with large number tetrahedron or polyhedral cells. The simulation is quite time-consuming and is generally limited to assemblies with small number of fuel pins. In this paper, a hexahedron meshing strategy is developed based on the Radial Basis Function (RBF) theory in present paper. This strategy would be beneficial for the modeling for the wire-wrapped fuel assemblies in real nuclear reactor core with large number of fuel pins. To validate this strategy, two experiments are simulated and detailed flow parameter distributions within the bundle, including the pressure distribution and the temperature distribution, have been compared. Good agreements have been achieved between the simulation results and the experimental results.

Hedgehog-lattice spin texture in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice

The hedgehog lattice, a three-dimensional periodic array of magnetic monopoles and antimonopoles, is known to be realized in the presence of the Dzyaloshinskii-Moriya (DM) interaction. Here, we demonstrate by means of Monte Carlo simulations that the hedgehog lattice is induced by not the DM interaction but frustration in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice. In the model, the breathing bond-alternation is characterized by the ratio of the nearest-neighbor (NN) antiferromagnetic exchange interaction for large tetrahedra to that for small ones, J1'/J1. A quadruple-q state with the ordering vector of q=(\pm 1/2,\pm 1/2,\pm 1/2), which is realized for a large third NN antiferromagnetic interaction along the bond direction J3, turns out to become the hedgehog-lattice state in the breathing case of J1'/J1 <1, while in the uniform case of J1'/J1 =1, it is a collinear state favored by thermal fluctuations. It is also found that in a magnetic field, the structure of the (1/2,1/2,1/2) hedgehog lattice is changed from cubic to tetragonal, resulting in a nonzero net spin chirality which in a metalic system, should yield a characteristic topological Hall effect.

Cluster Frustration in the Breathing Pyrochlore Magnet LiGaCr_{4}S_{8}.

We present a comprehensive neutron scattering study of the breathing pyrochlore magnet LiGaCr_{4}S_{8}. We observe an unconventional magnetic excitation spectrum with a separation of high- and low-energy spin dynamics in the correlated paramagnetic regime above a spin-freezing transition at 12(2)K. By fitting to magnetic diffuse-scattering data, we parametrize the spin Hamiltonian. We find that interactions are ferromagnetic within the large and small tetrahedra of the breathing pyrochlore lattice, but antiferromagnetic further-neighbor interactions are also essential to explain our data, in qualitative agreement with density-functional-theory predictions [Ghosh etal., npj Quantum Mater. 4, 63 (2019)2397-464810.1038/s41535-019-0202-z]. We explain the origin of geometrical frustration in LiGaCr_{4}S_{8} in terms of net antiferromagnetic coupling between emergent tetrahedral spin clusters that occupy a face-centered-cubic lattice. Our results provide insight into the emergence of frustration in the presence of strong further-neighbor couplings, and a blueprint for the determination of magnetic interactions in classical spin liquids.

Catalytic-Hairpin-Assembly-Assisted DNA Tetrahedron Nanoprobe for Intracellular MicroRNA Imaging.

The aberrant expression levels of microRNAs (miRNAs) are tightly linked with the initiation and development of various diseases and genetic disorders. Here, we reported a catalytic-hairpin-assembly-assisted DNA tetrahedron nanoprobe for intracellular miRNA detection. The target miRNA initiated the catalytic-hairpin-assembly reaction between the tetrahedron nanoprobes to generate large tetrahedron clusters with an enhanced fluorescence resonance energy transfer between the Cy3 and Cy5 dyes. The proposed nanoprobes were capable of visualizing the expression levels and spatial distributions of miRNA in living cells, providing a feasible approach in designing versatile nanostructures for reliable bioanalysis and clinical diagnosis.

Spin ordering induced by lattice distortions in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice

We theoretically investigate effects of lattice distortions on the spin ordering of classical Heisenberg antiferromagnets on the breathing pyrochlore lattice. In the model, local lattice distortions originating from the site vibration are taken into account to yield effective spin interactions via the spin-lattice coupling (SLC). The breathing lattice-alternation is characterized by the ratio of the nearest-neighbor interaction for large tetrahedra to that for small ones, J'/J. It is found by Monte Carlo simulations that the system exhibits a first-order transition into four different types of collinear magnetic ordered states. In the uniform case (J'/J=1), the state realized at stronger SLC is cubic-symmetric characterized by the (1/2,1/2,1/2) magnetic Bragg peaks, while the one at weaker SLC is tetragonal-symmetric characterized by the (1,1,0) ones. With increasing the breathing distortion (decreasing J'/J), the ordering pattern of the (1/2,1/2,1/2) state becomes non-cubic with its magnetic Bragg reflections almost unchanged, while the (1,1,0) state is robust. The non-cubic state peculiar to the breathing pyrochlores is further categorized into two types. We demonstrate that these two non-cubic orderings result in the massive degeneracy of the ground state and that the associated residual entropy per spin takes characteristic values of k_B ln(4)/16 and k_B ln(6)/16. Experimental implications of the results are discussed.

Magnetic and Structural Properties of A-Site Ordered Chromium Spinel Sulfides: Alternating Antiferromagnetic and Ferromagnetic Interactions in the Breathing Pyrochlore Lattice

We report a comprehensive study on the magnetic and structural properties of the spinel sulfides LiInCr4S8, LiGaCr4S8, and CuInCr4S8, where Li+/Cu+ and Ga3+/In3+ ions form a zinc-blende-type order. On the basis of synchrotron X-ray diffraction and magnetization data obtained using polycrystalline samples, these three sulfides are suggested to be breathing pyrochlore magnets with alternating antiferromagnetic and ferromagnetic interactions on the small and large tetrahedra, respectively. The measured magnetization processes of the three sulfides up to 72 T are significantly different. The magnetization curves of LiInCr4S8 and CuInCr4S8 have large hysteresis loops with different shapes, while there is no hysteresis in that of LiGaCr4S8. Geometrical frustration of the small tetrahedron is likely to give rise to a wide variety of ground states, indicating the rich physics in these antiferromagnetic-ferromagnetic breathing pyrochlore magnets.

Magnetic transitions under ultrahigh magnetic fields of up to 130 T in the breathing pyrochlore antiferromagnet LiInCr4O8

The magnetization processes of the spin-3/2 antiferromagnet LiInCr4O8 comprising a "breathing" pyrochlore lattice, which is an alternating array of small and large tetrahedra, are studied under ultrahigh magnetic fields of up to 130 T using state-of-the-art pulsed magnets. A half magnetization plateau is observed above 90 T to 130 T, suggesting that LiInCr4O8 has a strong spin-lattice coupling, similar to conventional chromium spinel oxides. The magnetization of LiGa0.125In0.875Cr4O8, in which the structural and magnetic transitions at low temperatures have been completely suppressed, shows a sudden increase above 13 T, indicating that a spin gap of 2.2 meV exists between a tetramer singlet ground state and an excited state with total spin 1, with the latter being stabilized by the application of a magnetic field. The breathing pyrochlore antiferromagnet is found to be a unique frustrated system with strong spin-lattice coupling and bond alternation.

Formation and Stepwise Self-Assembly of Cadmium Chalcogenide Nanocrystals to Colloidal Supra-Quantum Dots and the Superlattices

Nearly monodisperse colloidal superstructures of cadmium chalcogenide quantum dots (QDs) are reported. The superstructures, which we named as supra quantum dot (SQD), are typically composed of hundreds of a-few-nanometer-sized QDs three-dimensionally (3D) assembled by oriented attachment. The synthesis route for SQD is quite universal and can be extended to CdS, CdSe, CdTe, and CdSeTe alloy. The size of SQD can be tuned from tens of nanometers to over a hundred nanometers. In the case of CdSe SQD, zinc-blende seeds (primary QDs) act as the building block for the formation of the 3D assembled structures, SQDs, with discrete intermediates nanostructures. Primary seeds, 4 nm tetrahedral shaped QDs, assembled into a large tetrahedron of 20 nm. The 20 nm tetrahedrons, in turn, self-assembled into a larger tetrahedron of 40 nm. The discrete-in-size and sequential assemblies were followed by conventional growth from the remaining precursors and ripening within the particles to result in spheroidal SQDs. SQDs all...

Structure of yeast Ape1 and its role in autophagic vesicle formation

In Saccharomyces cerevisiae, a constitutive biosynthetic transport pathway, termed the cytoplasm-to-vacuole targeting (Cvt) pathway, sequesters precursor aminopeptidase I (prApe1) dodecamers in the form of a large complex into a Cvt vesicle using autophagic machinery, targeting it into the vacuole (the yeast lysosome) where it is proteolytically processed into its mature form, Ape1, by removal of an amino-terminal 45-amino acid propeptide. prApe1 is thought to serve as a scaffolding cargo critical for the assembly of the Cvt vesicle by presenting the propeptide to mediate higher-ordered complex formation and autophagic receptor recognition. Here we report the X-ray crystal structure of Ape1 at 2.5 Å resolution and reveal its dodecameric architecture consisting of dimeric and trimeric units, which associate to form a large tetrahedron. The propeptide of prApe1 exhibits concentration-dependent oligomerization and forms a stable tetramer. Structure-based mutagenesis demonstrates that disruption of the inter-subunit interface prevents dodecameric assembly and vacuolar targeting in vivo despite the presence of the propeptide. Furthermore, by examining the vacuolar import of propeptide-fused exogenous protein assemblies with different quaternary structures, we found that 3-dimensional spatial distribution of propeptides presented by a scaffolding cargo is essential for the assembly of the Cvt vesicle for vacuolar delivery. This study describes a molecular framework for understanding the mechanism of Cvt or autophagosomal biogenesis in selective macroautophagy.

Ground State Selection and Spin-Liquid Behaviour in the Classical Heisenberg Model on the Breathing Pyrochlore Lattice

Magnetic pyrochlore oxides, including the spin ice materials, have proved to be a rich field for the study of geometrical frustration in 3 dimensions. Recently, a new family of magnetic oxides has been synthesised in which the half of the tetrahedra in the pyrochlore lattice are inflated relative to the other half, making an alternating array of small and large tetrahedra. These "breathing pyrochlore" materials such as LiGaCr4O8, LiInCr4O8 and Ba3Yb2Zn5O11 provide new opportunities in the study of frustrated magnetism. Here we provide an analytic theory for the ground state phase diagram and spin correlations for the minimal model of magnetism in breathing pyrochlores: a classical nearest neighbour Heisenberg model with different exchange coefficients for the two species of tetrahedra. We find that the phase diagram comprises a Coulombic spin liquid phase, a conventional ferromagnetic phase and an unusual antiferromagnetic phase with lines of soft modes in reciprocal space, stabilised by an order-by-disorder mechanism. We obtain a theory of the spin correlations in this model using the Self Consistent Gaussian Approximation (SCGA) which enables us to discuss the development of correlations in breathing pyrochlores as a function of temperature, and we quantitatively characterise the thermal crossover from the limit of isolated tetrahedra to the strongly correlated limit of the problem. We compare the results of our analysis with the results of recent neutron scattering experiments on LiInCr4O8.

Experimental realization of a quantum breathing pyrochlore antiferromagnet

The synthesis and characterization of a new Yb-based material Ba3Yb2Zn5O11 are reported. This material is identified as the first model system of a pseudospin-1/2 quantum antiferromagnet on "breathing" pyrochlore lattice characterized by an alternating array of small and large Yb tetrahedra. Despite dominant antiferromagnetic interactions J ~ 7 K, a large amount of magnetic entropy (25%) remains at 0.38 K, indicating that each small Yb tetrahedron forms a unique doubly degenerate singlet state. These results are well described by the Heisenberg pseudospin-1/2 single tetrahedron model.

Breathing Pyrochlore Lattice Realized inA-Site Ordered Spinel OxidesLiGaCr4O8andLiInCr4O8

A unique type of frustrated lattice is found in two A-site ordered spinel oxides, LiGaCr(4)O(8) and LiInCr(4)O(8). Because of the large size mismatch between Li(+) and Ga(3+)/In(3+) ions at the A site, the pyrochlore lattice, made up of Cr(3+) ions carrying spin 3/2, becomes an alternating array of small and large tetrahedra, i.e., a "breathing" pyrochlore lattice. We introduce a parameter, the breathing factor B(f), which quantifies the degree of frustration in the pyrochlore lattice: B(f) is defined as J'/J, where J' and J are nearest-neighbor magnetic interactions in the large and small tetrahedra, respectively. LiGaCr(4)O(8) with B(f)~0.6 shows magnetic susceptibility similar to that of conventional Cr spinel oxides such as ZnCr(2)O(4). In contrast, LiInCr(4)O(8) with a small B(f)~0.1 exhibits a spin-gap behavior in its magnetic susceptibility, suggesting a proximity to an exotic singlet ground state. Magnetic long-range order occurs at 13.8 and 15.9 K for LiGaCr(4)O(8) and LiInCr(4)O(8), respectively, in both cases likely owing to the coupling to structural distortions.

Dynamics of dislocation interactions with stacking-fault tetrahedra at high temperature

The interaction process between dislocations and large stacking-fault tetrahedra was observed in real time at high temperature during deformation experiments in situ in the transmission electron microscope. Dislocation interactions with tetrahedra resulted in them being annihilated and converted to another defect type. Dislocation bypass of the tetrahedra occurred by cross-slip. The latter interaction occurred slowly and halted the progress of the dislocation. Annihilation versus bypass by dislocation cross-slip was dictated by the location at which the slip plane intersected the tetrahedron – on the face or along the edges with the stair-rod dislocations. In general, the interactions, at best, were weakly temperature dependent.

X-ray Crystal Structure and Specificity of the Plasmodium falciparum Malaria Aminopeptidase PfM18AAP

The malarial aminopeptidases have emerged as promising new drug targets for the development of novel antimalarial drugs. The M18AAP of Plasmodium falciparum malaria is a metallo-aminopeptidase that we show demonstrates a highly restricted specificity for peptides with an N-terminal Glu or Asp residue. Thus, the enzyme may function alongside other aminopeptidases in effecting the complete degradation or turnover of proteins, such as host hemoglobin, which provides a free amino acid pool for the growing parasite. Inhibition of PfM18AAP's function using antisense RNA is detrimental to the intra-erythrocytic malaria parasite and, hence, it has been proposed as a potential novel drug target. We report the X-ray crystal structure of the PfM18AAP aminopeptidase and reveal its complex dodecameric assembly arranged via dimer and trimer units that interact to form a large tetrahedron shape that completely encloses the 12 active sites within a central cavity. The four entry points to the catalytic lumen are each guarded by 12 large flexible loops that could control substrate entry into the catalytic sites. PfM18AAP thus resembles a proteasomal-like machine with multiple active sites able to degrade peptide substrates that enter the central lumen. The Plasmodium enzyme shows significant structural differences around the active site when compared to recently determined structures of its mammalian and human homologs, which provides a platform from which a rational approach to inhibitor design of new malaria-specific drugs can begin.

Crystal Structure of [Al4(OH)6(H2O)12][Al(H2O)6]2Br12: A New Polyaluminum Compound

A vertex-shared tetrahedral [Al(4)(OH)(6)(H(2)O)(12)](6+) (Al(4)) and a disordered [Al(H(2)O)(6)](3+) (Al(1)) that coexist in a 1:2 ratio within each unit cell were observed in the structure of [Al(4)(OH)(6)(H(2)O)(12)][Al(H(2)O)(6)](2)Br(12), which crystallized in a cubic Fd3m space group from a spontaneously hydrolyzed solution of AlBr(3). The former is composed of four AlO(6) octahedra that are connected to each other by sharing three vertexes of each octahedron and form a large regular tetrahedron with ideal T(d) symmetry. The central Al(3+) ion of the latter is coordinated by 6 disordered OH(2) molecules, that form a core-shell structure with ideal D(3d) symmetry.

New family of tilings of three-dimensional Euclidean space by tetrahedra and octahedra

It is well known that two regular tetrahedra can be combined with a single regular octahedron to tile (complete fill) three-dimensional Euclidean space . This structure was called the "octet truss" by Buckminster Fuller. It was believed that such a tiling, which is the Delaunay tessellation of the face-centered cubic (fcc) lattice, and its closely related stacking variants, are the only tessellations of that involve two different regular polyhedra. Here we identify and analyze a unique family comprised of a noncountably infinite number of periodic tilings of whose smallest repeat tiling unit consists of one regular octahedron and six smaller regular tetrahedra. We first derive an extreme member of this unique tiling family by showing that the "holes" in the optimal lattice packing of octahedra, obtained by Minkowski over a century ago, are congruent tetrahedra. This tiling has 694 distinct concave (i.e., nonconvex) repeat units, 24 of which possess central symmetry, and hence is distinctly different and combinatorically richer than the fcc tetrahedra-octahedra tiling, which only has two distinct tiling units. Then we construct a one-parameter family of octahedron packings that continuously spans from the fcc to the optimal lattice packing of octahedra. We show that the "holes" in these packings, except for the two extreme cases, are tetrahedra of two sizes, leading to a family of periodic tilings with units composed four small tetrahedra and two large tetrahedra that contact an octahedron. These tilings generally possess 2,068 distinct concave tiling units, 62 of which are centrally symmetric.

SLIVER REMOVAL BY LATTICE REFINEMENT

I present an algorithm that can create a mesh that is free of slivers away from the boundary, or that can eliminate such slivers from a pre-existing mesh by refining it. The resulting tetrahedra have dihedral angles between 30 and 135 degrees and radius-edge ratios of at most 1.368, except near the boundary. In comparison, previous bounds on dihedral angles were microscopic. The final mesh can respect specified input vertices and a user-defined sizing function. The algorithm comes with a bound on the sizes of the features it creates, and can provably grade from small to large tetrahedra.