Structure of the 〈100〉 Edge Dislocation in Iron

Abstract

The positions of atoms around the core of a 〈100〉 edge dislocation in iron have been calculated using atomic potentials developed by Johnson, boundary conditions based on anisotropic or isotropic elasticity and the GRAPE computer program. The dislocation is quite narrow and the atoms below the extra half-plane relax into a microcrack. It is shown that particular care must be taken in introducing the dislocation and choosing the potential. The configuration of this particular dislocation is only slightly sensitive to the choice of boundary conditions and the size of the model.

Dislocations and Disclinations in Gradient Elasticity

“…Considering u y for a dislocation dipole with arm d 100 c p [70], we have the estimate u y 0Y 0 % 2X3 b x a4p1 À n which gives % 0X26 a for b x a and n 0X3. This value is in good agreement with the results of direct observation of edge dislocations near an Nb/Al 2 O 3 interface [72], as well as with the results of computer simulations for the core of an edge dislocation in a-Fe [73]. It is worth noting that this estimate cannot be obtained within a Peierls-Nabarro dislocation model [23] because the latter imposes that the u y displacement is identically zero.…”

“…The substitution of the gradient solution (68) to (73) into the governing equations (1) or (2) (with c 1 c 2 c 3 c) gives the same stress fields as the classical theory of elasticity [4 to 6]. where the index``º refers to the solution for the region y b 0,``Àº refers to the solution for y`0, and the functions P ij sY y are given by…”

Effect of Nucleation on the Stability of BCC Metals

“…instability in compression for the bcc lattice results from the violation of the condition defined by Eq. (8). The violation of this condition corresponds to the mode of failure by which the crystal can lower its total energy by undergoing spontaneously the following lattice deformation.…”

“…(i) the nature of a material whether brittle or ductile [4,7]; (ii) the definition of dislocation core radii [8,9]; (iii) the loss of coherency occurring at particle matrix interfaces [10,11] are the problems which involve the ideal strength of solids. Many workers [12][13][14][15][16] have studied this problem of theoretical strength both for undeformed and deformed crystal lattices with various modes of deformations and with various forms of interactions between the atoms.…”

Multiscale Modeling of Point and Line Defects in Cubic Lattices

“…Early models used to study atomistic processes in the vicinity of crack tips or dislocation cores relied heavily on continuum elasticity theory, without including atoms in the far-field. Early work featured one-way [9][10][11][12][13][14] or two-way [15][16][17][18][19] coupled methods, in which displacement fields established at the interface between continuum and atomistic regions were computed either from sophisticated interfacial conditions or from initial conditions derived from continuum elasticity theory. Increases in computing power permitted more realistic two-way couplings, whereby atomistic fields were permitted to affect the far-field elastic continua through the latter's discretization with finite elements [20][21][22][23].…”