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Recent studies of the structure of antigorite by Capitani and Mellini (2004, 2005) and by us (Dodony et al. 2002; Dodony and Buseck 2004a) produced contradictory results. The main point of contention is whether 4- and 8-membered rings of tetrahedra occur at the positions where the tetrahedra in the tetrahedral sheets reverse their orientation. We analyzed electron diffraction patterns and transmission electron microscopy images in the paper of Capitani and Mellini (2005) and found no evidence for 4- and 8-membered tings of tetrahedra. On the contrary, we show that their TEM data confirm our antigorite model (Dodony et al. 2002) for the m = 16 structure. The significance of this debate goes beyond the subtleties of the structure of antigorite and highlights ambiguities in interpretation of HRTEM images as well as problems that can arise during image processing. Keywords: Serpentine, antigorite, crystal structure, HRTEM, electron diffraction, image processing

The extension of the rational design of M4L4 [M = Al(III), Ga(III), In(IV)] to the formation of much larger M4L4 tetrahedra with increased cavity capacity and the promise for significant host-guest chemistry are described. The charge-, size-, and shape-selective guest encapsulation is observed and studies are underway to further investigate the differences in guest dynamics between the two tetrahedral cluster architecture and to overcome the increased flexibility of the large ligands in order to assemble still larger M4L4 tetrahedra.

Diamond-like carbon (DLC) is an amorphous carbon with a high fraction of [sp.sup.3] bonds (1). Hydrogen-free DLCs with the highest density and [sp.sup.3]content are called tetrahedral amorphous carbons (ta-C) (1). […]

Ab initio QM/MM dynamics simulation is used to examine the stability of tetrahedral intermediate during the deacylation step in elastase-catalyzed hydrolysis of a simple peptide. The calculations indicate that the tetrahedral intermediate of serine proteases is a stable species on the picosecond time scale.

The author describes a way to construct a model of the Pascal Pyramid displayed in space of trinomial coefficients. He demonstrates how to obtain a rhombic dodecahedron and provides a proof for its being a space filler, leading to the Pascal Pyramid as a space lattice.

Several minerals and inorganic compounds contain (X[A.sub.4]) tetrahedra, with anions, X ([O.sup.2-], [N.sup.3-], and [F.sup.-]), as central atoms and cations, A ([Cu.sup.2+], [Zn.sup.2+], [Pb.sup.2+], [Bi.sup.3+], RE[E.sup.3+], etc.), as ligands. These tetrahedra are well defined in these crystal structures because the bond valences between A and X are essentially higher than the bond valences between A and atoms from other structural units. According to their size, anion-centered tetrahedra may be subdivided into large and small tetrahedra, formed from cations with ionic radii near to 1.0 [angstrom] (e.g., [Pb.sup.2+], [Bi.sup.3+], and RE[E.sup.3+]) and 0.5-0.7 [angstrom] (e.g., [Cu.sup.2+] and [Zn.sup.2+]), respectively. The small anion-centered tetrahedra prefer to link through corners, whereas the large tetrahedra prefer to link through edges. When the tetrahedra are built from both 'small' and 'large' cations, 'small' cations prefer to be corners shared between lesser numbers of tetrahedra and not involved in linking tetrahedra via edges. The general crystal-chemical formula of minerals and compounds containing anion-centered tetrahedra may be written as [A[prime].sub.k][[X.sub.n][A.sub.m]][[A.sub.p][X.sub.q]][X[prime].sub.l] where [[X.sub.n] [A.sub.m]] (usually n [less than or equal to] m) is a structural unit based on anion-centered tetrahedra (ACT) and [[A.sub.p][X.sub.q]] (p < q) is a structural unit based on cation-centered polyhedra (CCP). A[prime] is a cation that does not belong to anion- or cation-centered polyhedra; it is usually an interstitial cation such as an alkali metal; X[prime] is an interstitial anion such as halide or [S.sup.2-]. Structures containing both ACT and CCP units may be ordered according to the values of their dimensionality. In structures without CCP units, an important role is played by large interstitial anions that link finite ACT units, chains, or layers into three-dimensional structures or fill cavities in ACT frameworks.

The paper introduces non-conforming edge elements for tetrahedral, wedge and pyramid geometries and demonstrates the advantage of mixed shaped meshing on TEAM 20 benchmark problem. Index terms - Magnetic analysis, Finite element method, Edge elements, Non-conforming, TEAM 20

A new type of second order edge elements for simplexes (triangles and tetrahedra) is proposed. The element is geometrically symmetric and the shape functions are orthogonal to each other in the integrals of the tangential components on edges. The number of nodes and edges are 14 and 24 in a tetrahedral element. The proposed elements are validated by eigenmode calculations in a cavity using newly developed method to solve eigenvalue problems with large matrices. Highly accurate eigenvalues are calculated using the elements. Index terms - Edge elements, eigenvalue problems

The Delaunay incremental insertion method for tetrahedral grid generation can be used for the automatic generation of unstructured grids made up of tetrahedra and prisms. This method has been shown to be robust for complex geometries, with no user intervention required during the grid generation process. It has been demonstrated that the Delaunay background grid can be efficiently used as the data structure for checking prism intersections and for the automatic termination of prism generation.

An algorithm used for adaptive refinement of three-dimensional finite element tetrahedral meshes is simple and does not produce any nonconforming elements during refinement. The use of this algorithm for mesh refinement does not significantly change the aspect ratio of the element. This procedure provides an efficient solution of three-dimensional models for linear strain or higher order elements.

A new set of scalar and vector tetrahedral finite elements are presented. The elements are hierarchal, allowing mixing of polynomial orders; scalar orders up to 3 and vector orders up to 2 are defined. The vector elements impose tangential continuity on the field but not normal continuity, making them suitable for representing the vector electric or magnetic field. Further, the scalar and vector elements are such that they can easily be used in the same mesh, a requirement of many quasi-static formulations. Results are presented for two 50 Hz problems: the Bath Cube, and TEAM Problem 7.

A study was conducted on the influence of temperature on the bond lengths and volumes of silicate tetrahedra at a temperature range of 15 to 1,250 Kelvin. Results showed that the bond lengths and volumes of the tetrahedra with four bridging O atoms increased rapidly with temperature. Meanwhile, bond lengths and volumes for tetrahedra with two or three nonbridging atoms were observed to increase at an intermediate rate.

The author provides a method to calculate the volume of a tetrahedron when only the length of 3 edges and the measures of the 3 angles between them are known. A theorem is proposed and proven.

Bang's theorem regarding congruence for faces of a tetrahedron has been proven geometrically and with trignometry. The author offers another proof using vectors and the trignometric identity.

The authors have discovered a result relating the areas of the faces of a right tetrahedron with the Pythagorean theorem. They offer two theorems and proofs.

The crystal structures in terms of octahedral and tetrahedral sites in close-packed structures of metals and many other elements are described by using PTOT system. In the PTOT sequence, for two P (packing of atom) layer there is an O (octahedral) layer and two T (tetrahedral) T layer.

The new ternary intermetallic SmPd2Ga2 by metal flux techniques and its crystal structure are determined. It reveals that the crystal structure is composed of layers of isolated Sm atoms and layers of PdGa4 edge-sharing tetrahedra alternating along the c-axis.

A study was conducted, using x-ray photoelectron spectroscopy (XPS), Raman spectroscopy, spectroscopic elipsometry, ultraviolet photoelectron spectroscopy and temperature dependent resistance measurement, to examine the nitrogenated tetrahedral amorphous carbon (N:ta-C) films prepared by the filtered cathodic vacuum arc (FCVA) technique. The result shows that the nitrogen content in the deposited film increases from 0 to 4.6 at. %, as the nitrogen flow rate varies from 0 to 20 sccm.

Nano-clusters not only behave like huge pseudo atoms serving as building blocks for construction of super lattices with properties that are different from individual or bulk clusters but also display size-dependent properties. A different nanocrystal super lattice, UCR 15, that extends the size of super tetrahedral clusters, is reported.

Tn supertetrahedral clusters were used in the synthesis of inorganic frameworks based on TX4 tetrahedra of 20 A dimension in a Cd4In16S3310- cristobalite.

The configuration of chiral fluoromethyl group of the tetrahedral reaction intermediate formed at the active site of UDP-GlcNAc enolpyruvyl transferase (MurZ) in D2O from the pseudosubstrates (E)- and (Z)-3-fluorophosphoenolpyruvate (FPEP) is analyzed. The enzyme-catalyzed addition of D+ to FPEP and the protonation of C-3 of phosphoenolpyruvate in normal enolpyruvyl transfer catalyzed by MurZ is described.

A solution to the problem determining the sections of a triangle that can occur as regular tetrahedrons by planes which separate vertices is yet to be obtained. Since the size of the triangle can be varied arbitrarily, the determination of the solution becomes difficult. However, restrictions on the shape of the triangle enables the derivation of the solution with respect to the inequalities of the angles.