Poisson's Ratio for Central-Force Polycrystals

1976 ◽  
Vol 31 (12) ◽  
pp. 1539-1542 ◽  
Author(s):  
H. M. Ledbetter
Keyword(s):  
Electron Energy ◽  
Poisson Ratio ◽  
The Body ◽  
Central Force ◽  
Face Centered Cubic ◽  
Polycrystalline Aggregate ◽  
Body Centered Cubic ◽  
The Face ◽  
Predicted Values ◽  
Face Centered

Abstract The Poisson ratio υ of a polycrystalline aggregate was calculated for both the face-centered cubic and the body-centered cubic cases. A general two-body central-force interatomatic potential was used. Deviations of υ from 0.25 were verified. A lower value of υ is predicted for the f.c.c. case than for the b.c.c. case. Observed values of υ for twenty-three cubic elements are discussed in terms of the predicted values. Effects of including volume-dependent electron-energy terms in the inter-atomic potential are discussed.

MINIMAL KNOTTING NUMBERS

2009 ◽  
Vol 18 (08) ◽  
pp. 1159-1173 ◽  
Author(s):  
CASEY MANN ◽  
JENNIFER MCLOUD-MANN ◽  
RAMONA RANALLI ◽  
NATHAN SMITH ◽  
BENJAMIN MCCARTY
Keyword(s):  
The Body ◽  
Computer Algorithm ◽  
Face Centered Cubic ◽  
Body Centered Cubic ◽  
Cubic Lattice ◽  
The Face ◽  
Face Centered ◽  
Body Centered Cubic Lattice

This article concerns the minimal knotting number for several types of lattices, including the face-centered cubic lattice (fcc), two variations of the body-centered cubic lattice (bcc-14 and bcc-8), and simple-hexagonal lattices (sh). We find, through the use of a computer algorithm, that the minimal knotting number in sh is 20, in fcc is 15, in bcc-14 is 13, and bcc-8 is 18.

SOLID HARMONICS AS BASIS FUNCTIONS FOR CUBIC CRYSTALS

1959 ◽  
Vol 37 (3) ◽  
pp. 350-361 ◽  
Author(s):  
D. D. Betts
Keyword(s):  
Basis Functions ◽  
The Body ◽  
New Method ◽  
Face Centered Cubic ◽  
Body Centered Cubic ◽  
Cubic Crystals ◽  
Cubic Lattice ◽  
The Face ◽  
Face Centered ◽  
Body Centered Cubic Lattice

The various sets of basis functions useful in discussing cubic crystals must include sets of symmetrized combinations of powers of the co-ordinates ortho-gonalized over the cellular polyhedron. Such polynomials are here called solid harmonics. A study of the actual solid harmonics reveals the limitations of the spherical cell approximation. The solid harmonics can be used to develop a new method over the cellular polyhedron of the body-centered cubic lattice or of the face-centered cubic lattice.

Voids in Irradiated Tungsten and Molybdenum

1969 ◽  
Vol 27 ◽  
pp. 190-191
Author(s):  
Robert C. Rau ◽  
Robert L. Ladd
Keyword(s):  
Melting Point ◽  
Fast Neutron ◽  
Neutron Irradiation ◽  
Elevated Temperatures ◽  
Irradiation Temperature ◽  
The Body ◽  
Face Centered Cubic ◽  
Body Centered Cubic ◽  
Cubic Metals ◽  
Face Centered

Recent studies have shown the presence of voids in several face-centered cubic metals after neutron irradiation at elevated temperatures. These voids were found when the irradiation temperature was above 0.3 Tm where Tm is the absolute melting point, and were ascribed to the agglomeration of lattice vacancies resulting from fast neutron generated displacement cascades. The present paper reports the existence of similar voids in the body-centered cubic metals tungsten and molybdenum.

Formation of the cementite crystal in austenite by transformation of triangulated polyhedra

2019 ◽  
Vol 75 (3) ◽  
pp. 325-332
Author(s):  
V. S. Kraposhin ◽  
N. D. Simich-Lafitskiy ◽  
A. L. Talis ◽  
A. A. Everstov ◽  
M. Yu. Semenov
Keyword(s):  
Interatomic Potential ◽  
Mutual Orientation ◽  
Crystallographic Group ◽  
Mutual Transformation ◽  
Face Centered Cubic ◽  
Body Centered Cubic ◽  
Orientation Relationships ◽  
The Face ◽  
Infinite Crystal ◽  
Face Centered

A mechanism is proposed for the nucleus formation at the mutual transformation of austenite and cementite crystals. The mechanism is founded on the interpretation of the considered structures as crystallographic tiling onto non-intersecting rods of triangulated polyhedra. A 15-vertex fragment of this linear substructure of austenite (cementite) can be transformed by diagonal flipping in a rhombus consisting of two adjacent triangular faces into a 15-vertex fragment of cementite (austenite). In the case of the mutual austenite–cementite transformation, the mutual orientation of the initial and final fragments coincides with the Thomson–Howell orientation relationships which are experimentally observed [Thompson & Howell (1988). Scr. Metall. 22, 229–233] in steels. The observed orientation relationship between f.c.c. austenite and cementite is determined by a crystallographic group–subgroup relationship between transformation participants and noncrystallographic symmetry which determines the transformation of triangulated clusters of transformation participants. Sequential fulfillment of diagonal flipping in the 15-vertex fragments of linear substructure (these fragments are equivalent by translation) ensures the austenite–cementite transformation in the whole infinite crystal. The energy barrier for diagonal flipping in the rhombus with iron atoms in its vertices has been calculated using the Morse interatomic potential and is found to be equal to 162 kJ mol−1 at the face-centered cubic–body-centered cubic transformation temperature in iron.

scholarly journals Calculation of Percolation Thresholds in High Dimensions for FCC, BCC and Diamond Lattices

1998 ◽  
Vol 09 (04) ◽  
pp. 529-540 ◽  
Author(s):  
Steven C. van der Marck
Keyword(s):  
Bond Percolation ◽  
Face Centered Cubic ◽  
Body Centered Cubic ◽  
High Dimensions ◽  
The Face ◽  
Percolation Thresholds ◽  
Six Dimensions ◽  
Face Centered

Site and bond percolation thresholds are calculated for the face centered cubic, body centered cubic and diamond lattices in four, five and six dimensions. The results are used to study the behavior of percolation thresholds as a functions of dimension. It is shown that the predictions from a recently proposed invariant for percolation thresholds are not satisfactory for these lattices.

The determination of solute atom displacements in mixed dumbbell interstitials for the face-centered-cubic lattice

1978 ◽  
Vol 56 (8) ◽  
pp. 1057-1070 ◽  
Author(s):  
N. Matsunami ◽  
M. L. Swanson ◽  
L. M. Howe
Keyword(s):  
Solute Atom ◽  
The Body ◽  
Continuum Approximation ◽  
Face Centered Cubic ◽  
Cubic Lattice ◽  
The Face ◽  
Solute Atoms ◽  
Face Centered ◽  
Small Solute

Interactions between irradiation-produced defects and solute atoms in metals have been investigated using the channeling technique. The interaction of interest in this investigation is the trapping of self interstitials by small solute atoms thus creating a [Formula: see text] mixed dumbbell, consisting of a host atom and a solute atom straddling a lattice site in the face-centered-cubic lattice. The displacement of solute atoms from lattice sites in the mixed dumbbell configuration was determined by comparing the experimentally observed normalized yields from solute atoms and from host atoms with the yields calculated analytically using the continuum approximation. The solute atoms in Al–Mn, Al–Cu, and Cu–Be mixed dumbbells were situated at 0.5 Å from the body-centered position, whereas the Ag atoms in Al–Ag dumbbells were 0.7 Å from this position. This result is consistent with the theoretical expectation that the smallest solute atoms are displaced the greatest amount in mixed dumbbells. In addition, experimentally obtained solute atom yields for [Formula: see text] and [Formula: see text] angular scans were compared with calculated scans. It was concluded that for large displacements of solute atoms into the flux peaking region, the analytical (continuum) calculation is a reliable method of determining solute atom displacements, either from the aligned yields or from the angular scans.

Some Characteristics of Al12Mo in Aluminum Annealed After Implantation with Molybdenum

1985 ◽  
Vol 51 ◽  
Author(s):  
L. D. Stephenson ◽  
J. Bentley ◽  
R. B. Benson ◽  
G. K. Hubler ◽  
P. A. Parrish
Keyword(s):  
Analytical Electron Microscopy ◽  
The Body ◽  
Face Centered Cubic ◽  
Granular Film ◽  
The Face ◽  
Face Centered ◽  
Surface Modified ◽  
Microscopy Techniques ◽  
Annealing Experiments ◽  
Precipitate Structure

ABSTRACTThe characteristics of A112Mo formed in aluminum annealed after implantation with selected maximum molybdenum concentrations were examined by analytical electron microscopy techniques. The A112MO was isolated as the only precipitate in the microstructure for maximum as-implanted molybdenum concentrations up to 11 atomic percent. The morphology of the A112MO can be selected by choosing the maximum as-implanted molybdenum level over the same concentration range. A predominantly lamellar A112MO precipitate structure formed when aluminum was annealed at 550°C after implantation with maximum molybdenum concentrations in the range of 3.3 - 4.4 at.%. The orientation of the body centered cubic (bcc) A112Mo precipitate with respect to the face centered cubic (fcc) matrix can be expressed as (123)p || (002)m and [301]p || [310]m. An explanation for the experimentally observed orientation relationship was developed based on the characteristic relationships between the bcc A112MO precipitate and the fcc matrix. A continuous film of A112MO formed in the surface modified region when aluminum was annealed after implantation with maximum molybdenum concentrations in the approximate range of 8-11 at.%. The microstructure of the A112Mo film was found to depend on the annealing temperature. A granular film formed after annealing at 550°C whereas a mottled film formed after annealing at 400°C. Sequential annealing experiments revealed that the mottled film transforms to a granular film which indicates the mottled film is metastable.

Prediction of metastable phase formation in an immiscible Cu–Cr system from interatomic potential and ab initio calculation

2003 ◽  
Vol 18 (10) ◽  
pp. 2300-2303 ◽  
Author(s):  
H. R. Gong ◽  
L. T. Kong ◽  
B. X. Liu
Keyword(s):  
Ab Initio ◽  
Interatomic Potential ◽  
Metastable Phase ◽  
The Body ◽  
Face Centered Cubic ◽  
The Face ◽  
Bcc Structure ◽  
Face Centered ◽  
Dynamics Simulations ◽  
Cr System

Ab initio calculation was performed to predict the structures, lattice constants, and cohesive energies of metastable Cu75Cr25 and Cu50Cr50 phases. An n-body Cu–Cr potential was derived through fitting to some ab initio calculated results and was capable of reproducing some intrinsic properties of the Cu–Cr system. Based on the derived potential, molecular dynamics simulations predicted that for a Cu100−xCrx alloy, the face-centered-cubic structure is more stable than the body-centered-cubic (bcc) one when 0 ≤ x ≤ 25, while the bcc structure becomes energetically favored when 25 < x ≤ 100. Interestingly, the predictions match well with the experimental observations.

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