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.

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.

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.

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.

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.

A study of interface sliding at F.C.C.-B.C.C. boundaries in a Cu-Zn alloy

1978 ◽  
Vol 36 (1) ◽  
pp. 422-423
Author(s):  
F. Monchoux ◽  
A. Rocher ◽  
J.L. Martin
Keyword(s):  
Face Centered Cubic ◽  
Creep Tests ◽  
High Voltage Electron Microscopy ◽  
Diffusion Treatment ◽  
Voltage Electron ◽  
The Face ◽  
Face Centered ◽  
Interface Sliding ◽  
Zn Alloy ◽  
Made In

Interphase sliding is an important phenomenon of high temperature plasticity. In order to study the microstructural changes associated with it, as well as its influence on the strain rate dependence on stress and temperature, plane boundaries were obtained by welding together two polycrystals of Cu-Zn alloys having the face centered cubic and body centered cubic structures respectively following the procedure described in (1). These specimens were then deformed in shear along the interface on a creep machine (2) at the same temperature as that of the diffusion treatment so as to avoid any precipitation. The present paper reports observations by conventional and high voltage electron microscopy of the microstructure of both phases, in the vicinity of the phase boundary, after different creep tests corresponding to various deformation conditions.Foils were cut by spark machining out of the bulk samples, 0.2 mm thick. They were then electropolished down to 0.1 mm, after which a hole with thin edges was made in an area including the boundary

Sign in / Sign up

Export Citation Format

Share Document