Two Phases of Simplex Method

1982 ◽  
pp. 62-75
Author(s):  
L. S. Srinath
Keyword(s):  
Simplex Method ◽  
Two Phases

scholarly journals Several modifications of simplex method

Filomat ◽  
2003 ◽  
pp. 169-176
Author(s):  
Nebojsa Stojkovic ◽  
Predrag Stanimirovic ◽  
Marko Petkovic
Keyword(s):  
Simplex Method ◽  
Simplex Algorithm ◽  
Basic Solution ◽  
Computational Results ◽  
Test Set ◽  
Numerical Examples ◽  
Two Phases

We analyze the problem of finding the first basic solution in the two phases simplex algorithm. Also, a modification and several improvements of the simplex method are introduced. We report computational results on numerical examples from Netlib test set.

Precipitation of NiHfsi phase in NiAl single crystals containing Hf

1995 ◽  
Vol 53 ◽  
pp. 532-533
Author(s):  
A. Garg ◽  
R. D. Noebe ◽  
R. Darolia
Keyword(s):  
High Temperature ◽  
Single Crystals ◽  
High Temperature Strength ◽  
Bridgman Technique ◽  
Shell Mold ◽  
Third Phase ◽  
Unknown Phase ◽  
Transmission Electron ◽  
Two Phases ◽  
Nial Matrix

Small additions of Hf to NiAl produce a significant increase in the high-temperature strength of single crystals. Hf has a very limited solubility in NiAl and in the presence of Si, results in a high density of G-phase (Ni16Hf6Si7) cuboidal precipitates and some G-platelets in a NiAl matrix. These precipitates have a F.C.C structure and nucleate on {100}NiAl planes with almost perfect coherency and a cube-on-cube orientation-relationship (O.R.). However, G-phase is metastable and after prolonged aging at high temperature dissolves at the expense of a more stable Heusler (β'-Ni2AlHf) phase. In addition to these two phases, a third phase was shown to be present in a NiAl-0.3at. % Hf alloy, but was not previously identified (Fig. 4 of ref. 2 ). In this work, we report the morphology, crystal-structure, O.R., and stability of this unknown phase, which were determined using conventional and analytical transmission electron microscopy (TEM).Single crystals of NiAl containing 0.5at. % Hf were grown by a Bridgman technique. Chemical analysis indicated that these crystals also contained Si, which was not an intentional alloying addition but was picked up from the shell mold during directional solidification.

Imaging of Al-Li-Cu alloys with a Scanning Ion Microprobe

1990 ◽  
Vol 48 (2) ◽  
pp. 314-315
Author(s):  
K.K. Soni ◽  
D.B. Williams ◽  
J.M. Chabala ◽  
R. Levi-Setti ◽  
D.E. Newbury
Keyword(s):  
Mass Spectrometry ◽  
Secondary Ion Mass Spectrometry ◽  
Equilibrium Phase ◽  
Icosahedral Symmetry ◽  
Ion Microprobe ◽  
X Ray ◽  
Cu Alloys ◽  
Two Phases ◽  
The University ◽  
Secondary Ion

In contrast to the inability of x-ray microanalysis to detect Li, secondary ion mass spectrometry (SIMS) generates a very strong Li+ signal. The latter’s potential was recently exploited by Williams et al. in the study of binary Al-Li alloys. The present study of Al-Li-Cu was done using the high resolution scanning ion microprobe (SIM) at the University of Chicago (UC). The UC SIM employs a 40 keV, ∼70 nm diameter Ga+ probe extracted from a liquid Ga source, which is scanned over areas smaller than 160×160 μm2 using a 512×512 raster. During this experiment, the sample was held at 2 × 10-8 torr.In the Al-Li-Cu system, two phases of major importance are T1 and T2, with nominal compositions of Al2LiCu and Al6Li3Cu respectively. In commercial alloys, T1 develops a plate-like structure with a thickness <∼2 nm and is therefore inaccessible to conventional microanalytical techniques. T2 is the equilibrium phase with apparent icosahedral symmetry and its presence is undesirable in industrial alloys.

Defect structures of Nb1+αS2 sulfidation scales

1992 ◽  
Vol 50 (1) ◽  
pp. 38-39
Author(s):  
Chuxin Zhou ◽  
L. W. Hobbs
Keyword(s):  
Stacking Faults ◽  
Rhombohedral Structure ◽  
Stacking Sequence ◽  
Defect Structures ◽  
X Ray Diffraction ◽  
X Ray ◽  
Plane Normal ◽  
Lower Case ◽  
Sulfur Layer ◽  
Two Phases

One of the major purposes in the present work is to study the high temperature sulfidation properties of Nb in severe sulfidizing environments. Kinetically, the sulfidation rate of Nb is satisfactorily slow, but the microstructures and non-stoichiometry of Nb1+αS2 challenge conventional oxidation/sulfidation theory and defect models of non-stoichiometric compounds. This challenge reflects our limited knowledge of the dependence of kinetics and atomic migration processes in solid state materials on their defect structures.Figure 1 shows a high resolution image of a platelet from the middle portion of the Nb1+αS2 scale. A thin lamellar heterogeneity (about 5nm) is observed. From X-ray diffraction results, we have shown that Nb1+αS2 scale is principally rhombohedral structure, but 2H-NbS2 can result locally due to stacking faults, because the only difference between these 2H and 3R phases is variation in the stacking sequence along the c axis. Following an ABC notation, we use capital letters A, B and C to represent the sulfur layer, and lower case letters a, b and c to refer to Nb layers. For example, the stacking sequence of 2H phase is AbACbCA, which is a ∼12Å period along the c axis; the stacking sequence of 3R phase is AbABcBCaCA to form an ∼18Å period along the c axis. Intergrowth of these two phases can take place at stacking faults or by a shear in the basal plane normal to the c axis.

Convergent-bceam diffraction studies on lead zirconate titanate Ceramics

1986 ◽  
Vol 44 ◽  
pp. 482-483
Author(s):  
M.L.A. Dass ◽  
T.A. Bielicki ◽  
G. Thomas ◽  
T. Yamamoto ◽  
K. Okazaki
Keyword(s):  
Lead Zirconate Titanate ◽  
Direct Proof ◽  
Lead Zirconate ◽  
Subsolidus Phase ◽  
Pzt Ceramics ◽  
Subsolidus Phase Diagram ◽  
Zirconate Titanate ◽  
Two Phases ◽  
Cbd Method ◽  
Titanate Ceramics

Lead zirconate titanate, Pb(Zr,Ti)O3 (PZT), ceramics are ferroelectrics formed as solid solutions between ferroelectric PbTiO3 and ant iferroelectric PbZrO3. The subsolidus phase diagram is shown in figure 1. PZT transforms between the Ti-rich tetragonal (T) and the Zr-rich rhombohedral (R) phases at a composition which is nearly independent of temperature. This phenomenon is called morphotropism, and the boundary between the two phases is known as the morphotropic phase boundary (MPB). The excellent piezoelectric and dielectric properties occurring at this composition are believed to.be due to the coexistence of T and R phases, which results in easy poling (i.e. orientation of individual grain polarizations in the direction of an applied electric field). However, there is little direct proof of the coexistence of the two phases at the MPB, possibly because of the difficulty of distinguishing between them. In this investigation a CBD method was found which would successfully differentiate between the phases, and this was applied to confirm the coexistence of the two phases.

The stabilization of B.C.C. Cu in Cu/Nb nanolayered composites

1996 ◽  
Vol 54 ◽  
pp. 228-229
Author(s):  
H. Kung ◽  
A.J. Griffin ◽  
Y.C. Lu ◽  
K.E. Sickafus ◽  
T.E. Mitchell ◽  
...  
Keyword(s):  
Electrical Resistivity ◽  
Layer Thickness ◽  
Volume Fraction ◽  
Ion Beam ◽  
High Strength ◽  
Cross Sectional ◽  
Metastable Structure ◽  
High Resolution Tem ◽  
Potential Improvement ◽  
Two Phases

Materials with compositionally modulated structures have gained much attention recently due to potential improvement in electrical, magnetic and mechanical properties. Specifically, Cu-Nb laminate systems have been extensively studied mainly due to the combination of high strength, and superior thermal and electrical conductivity that can be obtained and optimized for the different applications. The effect of layer thickness on the hardness, residual stress and electrical resistivity has been investigated. In general, increases in hardness and electrical resistivity have been observed with decreasing layer thickness. In addition, reduction in structural scale has caused the formation of a metastable structure which exhibits uniquely different properties. In this study, we report the formation of b.c.c. Cu in highly textured Cu/Nb nanolayers. A series of Cu/Nb nanolayered films, with alternating Cu and Nb layers, were prepared by dc magnetron sputtering onto Si {100} wafers. The nominal total thickness of each layered film was 1 μm. The layer thickness was varied between 1 nm and 500 nm with the volume fraction of the two phases kept constant at 50%. The deposition rates and film densities were determined through a combination of profilometry and ion beam analysis techniques. Cross-sectional transmission electron microscopy (XTEM) was used to examine the structure, phase and grain size distribution of the as-sputtered films. A JEOL 3000F high resolution TEM was used to characterize the microstructure.

Direct imaging of order-disorder and antiphase domain structures in Ti3Al intermetallic compound

1990 ◽  
Vol 48 (4) ◽  
pp. 480-481
Author(s):  
H. Q. Ye ◽  
T.S. Xie ◽  
D. Li
Keyword(s):  
Intermetallic Compound ◽  
Volume Fraction ◽  
Fundamental Problem ◽  
Antiphase Domain ◽  
Atomic Scale ◽  
Orientation Relationships ◽  
Domain Structures ◽  
Α Phase ◽  
Diffraction Patterns ◽  
Two Phases

The Ti3Al intermetallic compound has long been recognized as potentially useful structural materials. It offers attractive strength to weight and elastic modulus to weight ratios. Recent work has established that the addition of Nb to Ti3Al ductilized this compound. In this work the fundamental problem of this alloy, i.e. order-disorder and antiphase domain structures was investigated at the atomic scale.The Ti3Al+10at%Nb alloys used in this study were treated at 1060°C and then aged at 700°C for 2 hours. The specimens suitable for TEM were prepared by standard jet electrolytic-polishing technique. A JEM-200CX electron microscope with an interpretable resolution of about 0.25 nm was used for HREM.The [100] and [001] projections of the α2 phase were shown in Fig.l.The alloy obtained consist of at least two phases-α2(Ti3Al) and β0 structures. Moreover, a disorder α phase with small volume fraction was also observed. Fig.2 gives [100] and [001] diffraction patterns of the α2 phase. Since lattice parameters of the ordered α2 (a=0.579, c=0.466 nm) and disorder α phase (a0=0.294≈a/2, c0=0.468 nm) are almost the same, their diffraction patterns are difficult to be distinguished when they are overlapped with epitaxial orientation relationships.

Misfit Dislocations in the Ilmenite (FeTiO3)-Hematite (Fe2O3) System

1980 ◽  
Vol 38 ◽  
pp. 212-213 ◽  
Author(s):  
K.P.D. Lagerlöf ◽  
A.H. Heuer ◽  
T.E. Mitchell
Keyword(s):  
Misfit Dislocation ◽  
Lattice Parameters ◽  
Dislocation Network ◽  
Misfit Dislocations ◽  
Space Group ◽  
Two Phases ◽  
Hematite Fe2o3

It has been reported by Lally et. al. [1] that precipitates of hematite (Fe2O3, space group R3c) in a matrix of ilmenite (FeTiO3, space group R3) are lens shaped and flattened along the [0001]-direction. The coherency across the interface is lost by the introduction of a misfit dislocation network, which minimizes the strain due to the deviation in lattice parameters between the two phases [2]. The purpose of this paper is to present a new analysis of this network.

Leptin declines in two phases during weight loss: Longitudinal analysis in children

2005 ◽  
Vol 94 (0) ◽  
pp. 53a-53
Author(s):  
J Holm ◽  
M Gamborg ◽  
S Gammeltoft ◽  
L Ward ◽  
B Heitmann ◽  
...  
Keyword(s):  
Weight Loss ◽  
Longitudinal Analysis ◽  
Two Phases
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