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.

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.

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.

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.

The symmetry origin of the austenite-cementite orientation relationships in steels

2019 ◽  
Vol 234 (4) ◽  
pp. 237-245 ◽  
Author(s):  
Valentin Kraposhin ◽  
Alexander Talis ◽  
Nenad Simich-Lafitskiy
Keyword(s):  
Crystal Structure ◽  
Orientation Relationship ◽  
Formation Mechanism ◽  
Mutual Orientation ◽  
Crystallographic Group ◽  
Mutual Transformation ◽  
Orientation Relationships ◽  
Nucleus Formation ◽  
Crystallographic Symmetry ◽  
Initial Crystal

Abstract The connection between austenite/cementite orientation relationships and crystal structure of both phases has been established. The nucleus formation mechanism at the mutual transformation of austenite and cementite structures has been proposed. Mechanism is based on the interpretation of the considered structures as crystallographic tiling onto triangulated polyhedra, and the said tiling can be transformed by diagonal flipping in a rhombus consisting of two adjacent triangular faces. The sequence of diagonal flipping in the fragment of the initial crystal determines the orientation of the fragment of the final crystal relative to the initial crystal. In case of the mutual austenite/cementite transformation the mutual orientation of the initial and final fragments is coinciding to the experimentally observed in steels Thomson-Howell orientation relationships: ${\left\{ {\bar 103} \right\}_{\rm{C}}}||{\left\{ {111} \right\}_{\rm{A}}};{\rm{}} < {\kern 1pt} 010{\kern 1pt} { > _{\rm{C}}}{\rm{||}} < {\kern 1pt} 10\bar 1{\kern 1pt} { > _{\rm{A}}};\; < {\kern 1pt} 30\bar 1{\kern 1pt} { > _{\rm{C}}}\;||\,\, < {\kern 1pt} \bar 12\bar 1{\kern 1pt} { > _{\rm{A}}}{\rm{}}$ The observed orientation relationship between FCC austenite and cementite is determined by crystallographic group-subgroup relationship between transformation participants, and non-crystallographic symmetry which is determining the transformation of triangulated clusters of transformation participants.

Highly Oriented Co Soft Magnetic Films on Si Substrates

1999 ◽  
Vol 562 ◽  
Author(s):  
Heng Gong ◽  
Wei Yang ◽  
Maithri Rao ◽  
David E. Laughlin ◽  
David N. Lambeth
Keyword(s):  
Magnetic Properties ◽  
Magnetic Films ◽  
Face Centered Cubic ◽  
X Ray Diffraction ◽  
Orientation Relationships ◽  
Soft Magnetic ◽  
X Ray ◽  
Si Substrates ◽  
The Face ◽  
Face Centered

ABSTRACTThin Co and Co based alloy films with the face centered cubic (FCC) structure have been epitaxially grown on single crystal Si wafers by sputter deposition. Epitaxial orientation relationships have been determined by x-ray diffraction, x-ray pole figure scans and TEM. Magnetic properties have been characterized using vibrating sampling magnetometer (VSM), torque magnetometer and BH loop tracer. Soft magnetic properties have been observed for the pure Co films.

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.

Representation of orientation relationships in Rodrigues–Frank space for any two classes of lattice

2007 ◽  
Vol 40 (3) ◽  
pp. 559-569 ◽  
Author(s):  
Youliang He ◽  
John J. Jonas
Keyword(s):  
Phase Transformation ◽  
Symmetry Group ◽  
Quaternion Algebra ◽  
Symmetry Groups ◽  
Face Centered Cubic ◽  
Body Centered Cubic ◽  
Orientation Relationships ◽  
Hexagonal Close Packed ◽  
Face Centered

The fundamental zones of Rodrigues–Frank (R-F) space applicable to misorientations between crystals of any two Laue groups are constructed by using a unified formulation in terms of quaternion algebra. Some of these regions are fully bounded by planes that are determined solely by the symmetries of the groups, while others have at least one unbounded direction. Each of the bounded fundamental zones falls into one of nine geometrically distinct configurations. The maximum symmetry-reduced angles and the corresponding Rodrigues–Frank vectors for these fundamental zones are evaluated. The use of Rodrigues–Frank space for the representation of orientation relationships between crystals of any two symmetry groups is also addressed. Examples concerning the transition of phases of the same symmetry group,i.e.from face-centered cubic to body-centered cubic, and of different groups,i.e.from body-centered cubic to hexagonal close-packed, are given to illustrate the usefulness of this space for representing orientation relationships during phase transformation or precipitation.

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