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Lattices

Description: Because lattice theory is so vast, the primary purpose of this paper will be to present some of the general properties of lattices, exhibit examples of lattices, and discuss the properties of distributive and modular lattices.
Date: August 1966
Creator: Rintala, Richard Arne
Partner: UNT Libraries

The crystal structure of neptunium metal

Description: From abstract: "In this paper the number of displaced atoms in equilibrium in a thin cyclotron-bombarded target is estimated as a function of the bombarding particle energy and target temperature."
Date: January 4, 1952
Creator: Zachariasen, William H.
Partner: UNT Libraries Government Documents Department

Countable Additivity, Exhaustivity, and the Structure of Certain Banach Lattices

Description: The notion of uniform countable additivity or uniform absolute continuity is present implicitly in the Lebesgue Dominated Convergence Theorem and explicitly in the Vitali-Hahn-Saks and Nikodym Theorems, respectively. V. M. Dubrovsky studied the connection between uniform countable additivity and uniform absolute continuity in a series of papers, and Bartle, Dunford, and Schwartz established a close relationship between uniform countable additivity in ca(Σ) and operator theory for the classical continuous function spaces C(K). Numerous authors have worked extensively on extending and generalizing the theorems of the preceding authors. Specifically, we mention Bilyeu and Lewis as well as Brooks and Drewnowski, whose efforts molded the direction and focus of this paper. This paper is a study of the techniques used by Bell, Bilyeu, and Lewis in their paper on uniform exhaustivity and Banach lattices to present a Banach lattice version of two important and powerful results in measure theory by Brooks and Drewnowski. In showing that the notions of exhaustivity and continuity take on familiar forms in certain Banach lattices of measures they show that these important measure theory results follow as corollaries of the generalized Banach lattice versions. This work uses their template to generalize results established by Bator, Bilyeu, and Lewis.
Date: August 1999
Creator: Huff, Cheryl Rae
Partner: UNT Libraries

Dually Semimodular Consistent Lattices

Description: A lattice L is said to be dually semimodular if for all elements a and b in L, a ∨ b covers b implies that a covers a ∧ b. L is consistent if for every join-irreducible j and every element x in L, the element x ∨ j is a join-irreducible in the upper interval [x,l]. In this paper, finite dually semimodular consistent lattices are investigated. Examples of these lattices are the lattices of subnormal subgroups of a finite group. In 1954, R. P. Dilworth proved that in a finite modular lattice, the number of elements covering exactly k elements is equal to the number of elements covered by exactly k elements. Here, it is established that if a finite dually semimodular consistent lattice has the same number of join-irreducibles as meet-irreducibles, then it is modular. Hence, a converse of Dilworth's theorem, in the case when k equals 1, is obtained for finite dually semimodular consistent lattices. Several combinatorial results are shown for finite consistent lattices similar to those already established for finite geometric lattices. The reach of an element x in a lattice L is the difference between the rank of x*, the join of x and all the elements covering x, and the rank of x; the maximum reach of all elements in L is the reach of L. Sharp lower bounds for the total number of elements and the number of elements of a given reach in a semimodular consistent lattice given the rank, the reach, and the number of join-irreducibles are found. Extremal lattices attaining these bounds are described. Similar results are then obtained for finite dually semimodular consistent lattices.
Date: May 1988
Creator: Gragg, Karen E. (Karen Elizabeth)
Partner: UNT Libraries

A PROCEDURE FOR THE EVALUATION OF NEUTRON-SCATTERING CROSS SECTION IN THE INCOHERENT APPROXIMATION

Description: Calculational procedures oriented toward computer application are preserted to evaluate the neutron inelastic scattering cross section in the incoherent approximation for a simple cubic Bravais lattice. The differential scattering cross section, the scattering law, or inelastic scattering matrices and transport cross sections for multigroup calculations are evaluated using the contributions of 25 phonons. The inelastic scattering cross section for graphite is calculated as an example of polycrystalline media where the phonon-frequency distribution is dependent on the direction of polarization. (H.D.R.)
Date: September 1, 1962
Creator: Jankus, V.Z.
Partner: UNT Libraries Government Documents Department

Development of local shear bands and orientation gradients in fcc polycrystals

Description: A finite element formulation which derives constitutive response from crystal plasticity theory is used to examine localized deformation in fcc polycrystals. The polycrystals are simple, idealized arrangements of grains. Localized deformations within individual grains lead to the development of domains that are separated by boundaries of high misorientation. Shear banding is seen to occur on a microscopic scale of grain dimensions. The important consequences of these simulations are that the predicted local inhomogeneities are meeting various requirements which make them possible nucleation sites for recrystallization.
Date: May 1, 1995
Creator: Beaudoin, A. J., Jr.; Mecking, H. & Kocks, U. F.
Partner: UNT Libraries Government Documents Department

Consistency in Lattices

Description: Let L be a lattice. For x ∈ L, we say x is a consistent join-irreducible if x V y is a join-irreducible of the lattice [y,1] for all y in L. We say L is consistent if every join-irreducible of L is consistent. In this dissertation, we study the notion of consistent elements in semimodular lattices.
Date: May 1986
Creator: Race, David M. (David Michael)
Partner: UNT Libraries

Interdiffusion in the Ni-Cr-Co-Mo system at 1300/sup 0/C

Description: Interdiffusion was investigated with solid-solid diffusion couples in the ..cap alpha.. (fcc) region of the quaternary Ni-Cr-Co-Mo system at 1300/sup 0/C for the determination of diffusion paths and diffusional interactions among the components. The concentration profiles for a given couple exhibited a common cross-over composition, Y/sub c/, which reflected the relative depths of diffusion in the terminal alloys. Interdiffusion fluxes were calculated directly from the concentration profiles and the quaternary interdiffusion coefficients were calculated at selected compositions. Ni and Co exhibited up-hill diffusion against their individual concentration gradients in a direction opposite to the interdiffusion of Cr. Quaternary diffusion paths were presented as a set of partial diffusion paths on the basis of relative concentration variables.
Date: January 1, 1985
Creator: Heaney, J.A. III & Dayananda, M.A.
Partner: UNT Libraries Government Documents Department

Theoretical studies of zirconia and defects in zirconia. Final report

Description: Supported by this grant the author has performed total energy electronic structure calculations for cubic, tetragonal, and monoclinic zirconia. The results of these calculations agree with the observed ordering of structures in the phase diagram. He has developed model potentials based on the total energy results. Molecular dynamics calculations using these model potentials give a good description of the phase transitions in and the thermal properties of zirconia.
Date: November 1, 1995
Creator: Jansen, H.J.F.
Partner: UNT Libraries Government Documents Department

Diffuse scattering studies as a tool for characterizing the local order structure and for obtaining pairwise interaction energies

Description: Diffuse scattering is a mature method for characterizing the local order structure of alloy systems. An extension of such structural investigations, for alloys at equilibrium, allows one to obtain pairwise interaction energies. Having experimental pairwise interaction energies for the various coordination shells offers one the potential for more realistic Monte Carlo modelling of alloy systems as they relax toward equilibrium. The diffuse scattering method and the recovery of the interaction energies are reviewed and some preliminary results are used to demonstrate the kinetic {Iota}sing modeling technique.
Date: January 1, 1992
Creator: Epperson, J.E. (Argonne National Lab., IL (United States)); Chen, H. & Anderson, J.P. (Illinois Univ., Urbana, IL (United States). Dept. of Materials Science and Engineering)
Partner: UNT Libraries Government Documents Department

PHYSICS DIVISION SUMMARY REPORT. June 1960

Description: Informal reports are presented on experimental nuclear physics, mass spectroscopy, and crystallography. Each individual project reports about once in 3 months. Those not reported in a particular issue are listed separately in the table of contents with a reference to the last issue in which each appeared. (For preceding period see ANL6164.) (W.D.M.)
Date: October 31, 1960
Partner: UNT Libraries Government Documents Department

DETERMINATION OF LATTICE PARAMETERS WITH THE AID OF A COMPUTER. Final Report of Metallurgy Program 4.1.8.

Description: The detemnination of precision lattice parameters using a least-squares analytical treatment has been programmed into a computer. Although it was originally coded for the Argonne AVIDAC and GEORGE computers, it is now programmed for the IBM 704. The present program permits the determination of lattice parametsrs and standard errors for the orthorhombic system and for all other crystal systems of higher symmetry. The angular measurements of line positions from a Debye-Scherrer or symmetrical focusing camera or a diffractometer may be given in degrees or radians from several different wavelengths. Provision was made for using aa many as three separate correction terms for eccentricity, absorption, divergence, and others; however, one, two, three, or none at all, may be used. The exact trigonometric function or functions used in these correction terms may be selected from several of those previously suggested. If desired, a weighting factor may also be used for each reflection which may include an observation weight or trigonometric function or both. Examples will be given of lattice parameters obtained for various crystal systems using different correction terms with and without weighting. (auth)
Date: January 1961
Creator: Mueller, M. H. & Heaton, L.
Partner: UNT Libraries Government Documents Department

Yield Functions and Plastic Potentials for BCC Metals and Possibly Other Materials

Description: Yield functions and plastic potentials are expressed in terms of the invariants of the stress tensor for polycrystalline metals and other isotropic materials. The plastic volume change data of Richmond is used to evaluate the embedded materials properties for some bcc metals and one polymer. A general form for the plastic potential is found that is intended to represent and cover a wide range of materials types.
Date: September 29, 2005
Creator: Christensen, R M
Partner: UNT Libraries Government Documents Department

Development of texture during deformation of hexagonal close packed metals.

Description: Goals of this work: 1. Gain understanding of microscopic deformation mechanisms in anisotropic materials. 2. Create model which may be used as a resource for Finite Element Codes.
Date: January 1, 2002
Creator: Brown, D. W. (Donald W.); Agnew, S. R. (Sean R.); Blumenthal, W. R. (William R.); Holden, T. M. (Thomas M.); Tomé, C. N. (Carlos Norberto), & Bourke, M. A. (Mark A.)
Partner: UNT Libraries Government Documents Department

STROBOSCOPIC IMAGE CAPTURE: REDUCING THE DOSE PER FRAME BY AFACTOR OF 30 DOES NOT PREVENT BEAM-INDUCED SPECIMEN MOVEMENT INPARAFFIN

Description: Beam-induced specimen movement may be the major factor that limits the quality of high-resolution images of organic specimens. One of the possible measures to improve the situation that was proposed by Henderson and Glaeser (Henderson and Glaeser, 1985), which we refer to here as 'stroboscopic image capture', is to divide the normal exposure into many successive frames, thus reducing the amount of electron exposure--and possibly the amount of beam-induced movement--per frame. The frames would then be aligned and summed. We have performed preliminary experiments on stroboscopic imaging using a 200-kV electron microscope that was equipped with a high dynamic range CCD camera for image recording and a liquid N{sub 2}-cooled cryoholder. Single-layer paraffin crystals on carbon film were used as a test specimen. The ratio F(g)/F(0) of paraffin reflections, calculated from the images, serves as our criterion for the image quality. In the series that were evaluated, no significant improvement of the F{sub image}(g)/F{sub image}(0) ratio was found, even though the electron exposure per frame was reduced by a factor of 30. A frame-to-frame analysis of image distortions showed that considerable beam-induced movement had still occurred during each frame. In addition, the paraffin crystal lattice was observed to move relative to the supporting carbon film, a fact that cannot be explained as being an electron-optical effect caused by specimen charging. We conclude that a significant further reduction of the dose per frame (than was possible with this CCD detector) will be needed in order to test whether the frame-to-frame changes ultimately become small enough for stroboscopic image capture to show its potential.
Date: August 1, 2006
Creator: Typke, Dieter; Gilpin, Christopher J.; Downing, Kenneth H. & Glaeser, Robert M.
Partner: UNT Libraries Government Documents Department

PREFERRED ORIENTATION IN ROLLED AND IN RECRYSTALLIZED HIGH-PURITY URANIUM ROD. Final Report of Metallurgy Program.4.1.17

Description: The preferred orientation of a relatively small piece of high-purity uranium rod, rolled to an 85% reduction at 300 deg C, has been determined in the as-rolled and in the recrystallized conditions. The 12 different charts obtained indicated that the as-rolled texture could be described as a duplex (041) and (352) with the (041) being the major component and with considerable spread about each component. The recrystallized rod showed approximate (041) and (392) components with considerable spread. These texture components for both the as- rolled and the recrystallized rods are not too different from those previously reported for reactor-grade uranium rod. However, it was noted that the texture appeared to be quite sharp for the reduction used, and the maximum intensity on an inverse pole figure was considerably displaced from the periphery of an (001) standard projection for both the rolled and recrystallized rods. (auth)
Date: April 1, 1959
Creator: Mueller, M.H. & Knott, H.W.
Partner: UNT Libraries Government Documents Department