THE ROOT LATTICE D4 AND PLANAR QUASILATTICES WITH OCTAGONAL AND DODECAGONAL SYMMETRY

1991 ◽  
Vol 05 (11) ◽  
pp. 1927-1953 ◽  
Author(s):  
M. BAAKE ◽  
D. JOSEPH ◽  
M. SCHLOTTMANN
Keyword(s):  
Root Lattice ◽  
Dihedral Groups ◽  
Hypercubic Lattice ◽  
Face Centered ◽  
Two Phases ◽  
Minimal Embedding

Quasiperiodic patterns with eight- and twelvefold symmetry are presented which share the root lattice D4, i.e., the 4-D face-centered hypercubic lattice, for their minimal embedding in four-space. We derive the patterns by means of the dualization method and investigate key properties like vertex configurations, local deflation/inflation symmetries and kinematic diffraction. The generalized point symmetries (and thus the Laue group) of these patterns are the dihedral groups d8 and d12, respectively, which share a common subgroup, d4. We introduce a contiunous one-parameter rotation between the two phases which leaves this subgroup invariant. This should prove useful for modelling alloys like V 15 Ni 10 Si where quasicrystalline phases with eight- and twelvefold symmetry coexist.

scholarly journals Multi-Length Scale Characterization of the Gibeon Meteorite using Electron Backscatter Diffraction

2007 ◽  
Vol 15 (5) ◽  
pp. 6-11 ◽  
Author(s):  
Matthew M. Nowell ◽  
John O. Carpenter
Keyword(s):  
Electron Backscatter Diffraction ◽  
Nickel Content ◽  
Iron Core ◽  
Face Centered Cubic ◽  
Iron Nickel ◽  
Scale Characterization ◽  
Face Centered ◽  
Two Phases ◽  
Backscatter Diffraction

The Gibeon meteorite is a differentiated iron meteorite that fell in Nambia, Africa in prehistoric times, with fragments spread over an area 70 miles wide and 230 miles long. The Gibeon fall was initially discovered in 1836, and hundreds of thousands of kilograms of fragments have been recovered. These fragments represent the iron core of a meteorite that cooled and crystallized over thousands of years (Norton 2002).The microstructure of the Gibeon meteorite, which is primarily an iron-nickel alloy, consists of two phases: kamacite, a body-centered cubic material and taenite, a face-centered cubic material that metallurgists would refer to as ferrite and austenite respectively. This material initially crystallizes as taenite, and as the temperature decreases, transforms into kamacite. This meteorite is classified as a Fine Octahedrite (Of) with an average Nickel content of approximately 7.9%

One Pot, Two Phases: Individual Orthorhombic and Face-Centered Cubic ZnSnO3 Obtained Synchronously in One Solution

2014 ◽  
Vol 53 (23) ◽  
pp. 12289-12296 ◽  
Author(s):  
Ying Wang ◽  
Peng Gao ◽  
Di Bao ◽  
Longqiang Wang ◽  
Yujin Chen ◽  
...  
Keyword(s):  
Face Centered Cubic ◽  
One Pot ◽  
Face Centered ◽  
Two Phases

Plasticity and Size Effects in High Purity Cobalt: An Experimental Study

2016 ◽  
Vol 879 ◽  
pp. 560-565
Author(s):  
Gwendoline Fleurier ◽  
Mayerling Martinez ◽  
Pierre Antoine Dubos ◽  
Eric Hug
Keyword(s):  
Size Effects ◽  
Threshold Value ◽  
Cubic Phase ◽  
Face Centered Cubic ◽  
Tem Analysis ◽  
Cubic Metals ◽  
Hexagonal Close Packed ◽  
A Value ◽  
Face Centered ◽  
Two Phases

The occurrence of size effects in cobalt was examined by the analysis of mechanical properties of samples with thickness t, in a large range of grain size d giving a number of grains across the thickness t/d. On Hall-Petch plots, from the very beginning of plastic strain, two linear behaviors are notable: the polycrystalline one for higher t/d and the multicrystalline one for lower t/d in which the flow stress is strongly reduced. (t/d)c is the threshold value between the two behaviors taking a value of around 14. This high value is directly linked to the low stacking fault energy of cobalt. The microstructure of the polycrystalline samples exhibits a strong basal texture and a small proportion of a secondary face-centered cubic phase in a hexagonal close-packed main phase was evidenced. TEM analysis enables to characterize the dislocations and the stacking faults present in the two phases. To complete the analysis, two plasticity stages can be distinguished: stage A corresponding to dislocations gliding and stage B driven by twinning. Size effects in cobalt are found to occur during gliding process and could be related to surface effects as previously shown in face-centered cubic metals.

A TEM study of the microstructures formed during the crystallization of Ni–Zr metallic glasses

1991 ◽  
Vol 6 (4) ◽  
pp. 755-759 ◽  
Author(s):  
R. Allem ◽  
G. L'Espérance ◽  
Z. Altounian ◽  
J.O. Ström-Olsen
Keyword(s):  
Metallic Glasses ◽  
Crystallization Process ◽  
Early Stage ◽  
Face Centered Cubic ◽  
Simple Cubic ◽  
Transmission Electron ◽  
The Face ◽  
Face Centered ◽  
Two Phases ◽  
Average Size

The microstructure of two metastable crystalline phases, which are formed during the first step of the crystallization process in Ni–Zr metallic glasses, was investigated by transmission electron microscopy. For the composition Ni33Zr67, crystallites with average size of 150 nm having the face-centered cubic E93 structure are formed. For the Ni42Zr58 composition, 100 nm size crystallites with a simple cubic unit cell, space group Pa3 are formed. The microstructure of the crystallites in the early stage of crystallization of the two phases is similar to globular morphology and internal striations.

scholarly journals High-pressure Melting Curves of and Phases of Iron

2019 ◽  
Vol 35 (4) ◽  
Author(s):  
Nguyen Thi Hong ◽  
Ho Khac Hieu
Keyword(s):  
Pressure Effects ◽  
Face Centered Cubic ◽  
Melting Temperatures ◽  
Melting Curves ◽  
Pressure Melting ◽  
Cubic Structure ◽  
Face Centered ◽  
Two Phases ◽  
Increasing Functions ◽  
Statistical Moment Method

Statistical moment method (SMM) has been applied in combination with Lindemann melting criterion to investigate pressure effects on melting temperature of iron. Melting curves of  phase with body-centered cubic structure and  phase with face-centered cubic structure of iron have been derived up to pressure 13 GPa and 90 GPa, respectively. This work shows that melting curves of these two phases of iron are increasing functions of pressure, and the higher the pressure is the lower the slopes of melting curves are. Our results are compared with those of available experimental data to verify the developed theory. The efficiency of the SMM on the investigation of melting temperatures of  and  phases of iron allows us to believe that the present SMM scheme can be developed extensively to determine melting temperatures of other phases of iron as well as other materials.

Pressure induced wurtzite-to-zinc blende phase transition in ZnO at finite temperature

2008 ◽  
Vol 23 (12) ◽  
pp. 3347-3352 ◽  
Author(s):  
Yaping Wu ◽  
Junyong Kang ◽  
Feng Liu
Keyword(s):  
Phase Transition ◽  
Energy Barrier ◽  
Energy Difference ◽  
Vibrational Entropy ◽  
Free Energies ◽  
Zinc Blende ◽  
Face Centered ◽  
Two Phases ◽  
Dynamics Simulations ◽  
Increasing Temperature

We predict a possible phase transition of ZnO from wurtzite to zinc blende structure using first-principles molecular-dynamics simulations. By calculating the Gibbs free energies of the two phases as a function of temperature and hydrostatic pressure, we show that their energy difference decreases continuously with increasing temperature and pressure, and the vibrational entropy plays an important role on the location of the phase transition point. At 300 K, the phase transition is expected to occur at a pressure lower than 30 GPa with an activation energy barrier of 0.386 eV/atom. The transition path was also simulated, along which the system goes through a transient face-centered orthorhombic structure to overcome the energy barrier. Our theory results may be valuable for stabilizating the zinc blende ZnO in experiment.

scholarly journals Prototiles and Tilings from Voronoi and Delone Cells of the Root Lattice An

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1082
Author(s):  
Ozdes Koca ◽  
Al-Siyabi ◽  
Koca ◽  
Koc
Keyword(s):  
General Scheme ◽  
Square Lattice ◽  
Face Centered Cubic ◽  
Root Lattice ◽  
Rhombic Dodecahedron ◽  
Orthogonal Projections ◽  
Seitz Cell ◽  
The Face ◽  
Face Centered ◽  
Coxeter Plane

The orthogonal projections of the Voronoi and Delone cells of root lattice An onto the Coxeter plane display various rhombic and triangular prototiles including thick and thin rhombi of Penrose, Amman–Beenker tiles, Robinson triangles, and Danzer triangles to name a few. We point out that the symmetries representing the dihedral subgroup of order 2h involving the Coxeter element of order h=n+1 of the Coxeter–Weyl group an play a crucial role for h-fold symmetric tilings of the Coxeter plane. After setting the general scheme we give samples of patches with 4-, 5-, 6-, 7-, 8-, and 12-fold symmetries. The face centered cubic (f.c.c.) lattice described by the root lattice A3 , whose Wigner–Seitz cell is the rhombic dodecahedron projects, as expected, onto a square lattice with an h=4-fold symmetry.

Effect of N2 Flow on Microstructure, Mechanical Properties and Oxidation Resistance of CrNx Coatings

2013 ◽  
Vol 750-752 ◽  
pp. 2117-2120
Author(s):  
Guo Zheng Nie ◽  
Chun Liang Zhong ◽  
Lan E Luo ◽  
Ren Long Zhou ◽  
Qiang Liu
Keyword(s):  
Mechanical Properties ◽  
Oxidation Resistance ◽  
Single Phase ◽  
High Hardness ◽  
Hexagonal Structure ◽  
Mixed Phase ◽  
Hard Coatings ◽  
Face Centered Cubic ◽  
Face Centered ◽  
Two Phases

A series of CrNx coatings were deposited by direct-current reactive magnetron sputtering. The microstructure, the hardness and oxidation resistance of the thin films were characterized respectively with X-ray diffraction (XRD) and nanoindentor. The effect of N2 flow on the microstructure, the hardness and oxidation resistance was studied. It was found that the CrNx film has two phases, the conformation of hcp-Cr2N (hexagonal structure) and fcc-CrN (face-centered cubic). In CrNx film phase structure, with N2 flow increasing, there is the conformation of CrNx films transition from Cr2N to Cr2N and CrN mixed phase, the final CrN single-phase. A single phase of CrNx films has very high hardness while thin film as mixed phase showed a low hardness. CrN has better oxidation resistance with the oxidation resistance temperature of 500°C to 600°C compared to Cr2N. Comparison of Cr2N and CrN on the mechanical properties and oxidation resistance, CrN has better comprehensive performance for protective hard coatings.

ELASTIC AND VIBRATIONAL PROPERTIES OF ORDERED AND DISORDERED CuMnPt6

2013 ◽  
Vol 27 (27) ◽  
pp. 1350195 ◽  
Author(s):  
SHUO HUANG ◽  
CHUAN-HUI ZHANG ◽  
JING SUN ◽  
JIANG SHEN
Keyword(s):  
Elastic Anisotropy ◽  
Point Of View ◽  
Vibrational Properties ◽  
Face Centered Cubic ◽  
Vibrational Entropy ◽  
Embedded Atom ◽  
Face Centered ◽  
Two Phases ◽  
Fcc Phase ◽  
Experimental Values

In this paper, we have measured the elastic and vibrational properties of CuMnPt 6 with embedded-atom method in three states of chemical order: as a disordered FCC (face-centered cubic) solid solution and as the equilibrium L1 2 and ABC 6 ordered structures. Our results agree quite well with the comparable experimental values. The present calculations indicate that the ABC 6 and L1 2 phases are energetically more stable than FCC phase. Numerical estimates of a set of elastic parameters, including aggregate elastic modulus, Poisson's ratio, and elastic anisotropy are performed, and the results demonstrate that the FCC phase is much softer than other two phases. Further analysis from the point of view of vibrational properties such as phonon density of states and vibrational entropy difference are also presented in this study.

Porous NiO-SDC Carbonates Composite Anode for LT-SOFC Applications Produced by Pressureless Sintering

2011 ◽  
Vol 52-54 ◽  
pp. 488-493 ◽  
Author(s):  
Raharjo Jarot ◽  
Andanastuti Muchtar ◽  
Wan Ramli Wan Daud ◽  
Norhamidi Muhamad ◽  
Edy Herianto Majlan
Keyword(s):  
Average Particle Size ◽  
Average Particle ◽  
Face Centered Cubic ◽  
X Ray Diffraction ◽  
Weight Percentage ◽  
Composite Anodes ◽  
Optimum Porosity ◽  
Face Centered ◽  
Two Phases ◽  
Cold Pressed

Composite anodes made of NiO and SDC-(Li/Na)2CO3 were investigated in relation to their structure, morphology, and porosity. As a first step, the anode powder was prepared by mixing the NiO with SDC-(Li/Na)2CO3 via solid state reaction in weight percentage of 60 : 40 wt% and in various compositions of carbonates (20 and 30wt%), namely NiO-SDC8020 and NiO-SDC7030, respectively. The powder mixtures were then calcined at 680oC. The resultant powder was fine with surface area of about 13.10-13.70 m2/g and an average particle size of 0.32-0.37µm. The powders consist of two phases i.e. the cubic NiO and face-centered cubic structure SDC-(Li/Na)2CO3 as confirmed with x-ray diffraction. The microstructures were observed under scanning electron microscopy (SEM). The anode pellets were later compacted at different pressures (27, 32 and 37 MPa) and sintered at 600oC. The optimum porosity (20.99-24.78%) was achieved for samples of NiO-SDC8020 and NiO-SDC7030 sintered at 600oC and cold pressed at 32 and 37 MPa.

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