Multivariate shift invariant operators

AbstractAn unexpected connection between a certain class of exponential approximation operators and polynomial sequences of binomial type was discovered by Ismail (J. Approx. Theory (3) 23 (1978), 117–186). In this paper we present a multivariate analogue of shift invariant operators connected with Sheffer type polynomials

Charge density studies of energetic material: RDX

Experimental charge density study has been carried out for Cyclotrimethylene-trinitramine (space group Pbca), an explosive material from a low temperature X-ray diffraction experiment. The electron density was modeled using the Hansen-Coppens multipole model and refined to R=0.032 for 6226 unique observed reflections. The electron density, laplacian and electrostatic potential distributions are reported and discussed, especially, the properties of the bond (3,-1) critical points, which are thought to play a key role in the decomposition of the molecule. From the bond topological analysis of all the bonds, it is observed that the N–N bond is the weakest. The dominating nature of the oxygen atoms was clearly well understood from isosurface electrostatic potential of isolated and symmetrically sitting molecules in the crystal

Influence of Cr and W alloying on the fiber-matrix interfacial shear strength in cast and directionally solidified sapphire NiAl composites

Sapphire-reinforced NiAl matrix composites with chromium or tungsten as alloying additions were synthesized using casting and zone directional solidification (DS) techniques and characterized by a fiber pushout test as well as by microhardness measurements. The sapphire-NiAl(Cr) specimens exhibited an interlayer of Cr rich eutectic at the fiber-matrix interface and a higher interfacial shear strength compared to unalloyed sapphire-NiAl specimens processed under identical conditions. In contrast, the sapphire-NiAl(W) specimens did not show interfacial excess of tungsten rich phases, although the interfacial shear strength was high and comparable to that of sapphire-NiAl(Cr). The postdebond sliding stress was higher in sapphire-NiAl(Cr) than in sapphire-NiAl(W) due to interface enrichment with chromium particles. The matrix microhardness progressively decreased with increasing distance from the interface in both DS NiAl and NiAl(Cr) specimens. The study highlights the potential of casting and DS techniques to improve the toughness and strength of NiAl by designing dual-phase microstructures in NiAl alloys reinforced with sapphire fibers

Influence of Fabrication Technique on the Fiber Pushout Behavior in a Sapphire-Reinforced Nial Matrix Composite

Directional solidification (DS) of \u27\u27powder-cloth\u27\u27 (PC) processed sapphire-NiAl composites was carried out to examine the influence of fabrication technique on the fiber-matrix interfacial shear strength, measured using a fiber-pushout technique. The DS process replaced the fine, equiaxed NiAl grain structure of the PC composites with an oriented grain structure comprised of large columnar NiAl grains aligned parallel to the fiber axis, with fibers either completely engulfed within the NiAl grains or anchored at one to three grain boundaries. The load-displacement behavior during the pushout test exhibited an initial \u27\u27pseudoelastic\u27\u27 response, followed by an \u27\u27inelastic\u27\u27 response, and finally a \u27\u27frictional\u27\u27 sliding response. The fiber-matrix interfacial shear strength and the fracture behavior during fiber pushout were investigated using an interrupted pushout test and fractography, as functions of specimen thickness (240 to 730 mu m) and fabrication technique. The composites fabricated using the PC and the DS techniques had different matrix and interface structures and appreciably different interfacial shear strengths. In the DS composites, where the fiber-matrix interfaces were identical for all the fibers, the interfacial debond shear stresses were larger for the fibers embedded completely within the NiAl grains and smaller for the fibers anchored at a few grain boundaries. The matrix grain boundaries coincident on sapphire fibers were observed to be the preferred sites for crack formation and propagation. While the frictional sliding stress appeared to be independent of the fabrication technique, the interfacial debond shear stresses were larger for the DS composites compared to the PC composites. The study highlights the potential of the DS technique to grow single-crystal NiAl matrix composites reinforced with sapphire fibers, with fiber-matrix interfacial shear strength appreciably greater than that attainable by the current solid-state fabrication techniques