Dislocations glide plane

Fig. 13—Normalized o>/b as function of tglb, cta/b is the critical shear stress to move a dislocation from the B layer into the A layer, Q=(G -Gb)/(G +Gg), G and Gg are the shear moduli of A and B, b is the Burgers vector, fg is the thickness of one single B layer, and e is the angle between the A/B interfaces and the dislocation glide plane.

The Burgers vectors, glide plane and ine direction of the dislocations studied in this paper are given in table 1. Included in this table are also the results for the Peierls stresses as calculated here and, for comparison, those determined previously [6] with a different interatomic interaction model [16]. In the following we give for each of the three Burgers vectors under consideration a short description of the results. 

The core structure of the (100) screw dislocation is planar and widely spread w = 2.66) on the 011 plane. In consequence, the screw dislocation only moves on the 011 glide plane and does so at a low Peierls stress of about 60 MPa. 

The edge dislocation on the 011 plane is again widely spread on the glide plane w = 2.9 6) and moves with similar ease. In contrast, the edge dislocation on the 001 plane is more compact w = 1.8 6) and significantly more difficult to move (see table 1). Mixed dislocations on the 011 plane have somewhat higher Peierls stresses than either edge or screw dislocations. 

Table 1 Summary of the calculated properties of the various dislocations in NiAl. Dislocations are grouped together for different glide planes. The dislocation character, edge (E), screw (S) or mixed type (M) is indicated together with Burgers vector and line direction. The Peierls stresses for the (111) dislocations on the 211 plane correspond to the asymmetry in twinning and antitwinning sense respectively.

When the two vectors are parallel, the crystal planes perpendicular to the line form a helix, and the dislocation is said to be of the screw type. In a nearly isotropic crystal structure, the dislocation is no longer associated with a distinct glide plane. It has nearly cylindrical symmetry, so in the case of the figure it can move either vertically or horizontally with equal ease. 

Figure 4.1 Schematic dislocation line a simple cubic crystal structure. The line enters the crystal at the center of the left-front face. It emerges at the center of the right-front face. The shortest translation vector of the structure is the Burgers Vector, b. The line bounds the glided area of the glide plane (100) from the unglided area.

Figure 4.2 Quasi-hexagonal dislocation loop lying on the (111) glide plane of the diamond crystal structure. The <110> Burgers vector is indicated. A segment, displaced by one atomic plane, with a pair of kinks, is shown a the right-hand screw orientation of the loop. As the kinks move apart along the screw dislocation, more of it moves to the right.

When there are no distinct bonds crossing a glide plane, there are no distinct kinks. This is the case for pure simple metals, for pure ionic crystals, and for molecular crystals. However, the local region of a dislocation s core still controls the mobility in a pure material because this is where the deformation rate is greatest (Gilman, 1968). 

The glide planes on which dislocations move in the diamond and zincblende crystals are the octahedral (111) planes. The covalent bonds lie perpendicular to these planes. Therefore, the elastic shear stiffnesses of the covalent bonds... 

Figure 5.7 Schematic edge dislocation after Peierls. Top part of crystal, T and bottom part B, are joined between planes a and P across a glide plane with an extra half-plane of atoms ending at c. The displacement along the glide plane is b, and the glide plane spacing is a.

Dislocation motion in covalent crystals is thermally activated at temperatures above the Einstein (Debye) temperature. The activation energies are well-defined, and the velocities are approximately proportional to the applied stresses (Sumino, 1989). These facts indicate that the rate determining process is localized to atomic dimensions. Dislocation lines do not move concertedly. Instead, sharp kinks form along their lengths, and as these kinks move so do the lines. The kinks are localized at individual chemical bonds that cross the glide plane (Figure 5.8). 

As screw dislocations move, since they are nearly cylindrically symmetric in simple metals, they move readily from one glide plane to another, and back... 

The sigma phases are hard and brittle at below their Debye temperatures, but have some plasticity at higher temperatures. Thus there is some covalent bonding in them, and their glide planes are puckered, making it difficult for dislocations to move in them until they become partially disordered. Their structures are too complex to allow realistic hardness values to be calculated for them. Their shear moduli indicate their relative hardnesses. 

The structure of Ni3Al is the Ll2 (Cu3Au) structure (Figure 8.5). It is fee with the corners occupied by A1 atoms, and the face-centers by Ni atoms. The primary glide planes are (111) and the glide directipns are (110). Therefore, the shears in the cores of dislocations in these crystals are broken into four parts as illustrated in Figures 8.6, 8.7, and 8.8. Each unit dislocation in the structure is split into four partial dislocations. 

The coefficient, p, of the viscosity resisting dislocation motion is the shear stress at the glide plane, x divided by the frequency of momentum transfer, v. The maximum value that x can have is about Coct/47i, and as mentioned above v = 1013/sec for the Al atoms,so p = Coct./47rv = 4x 10 3 Poise.This is comparable to the dislocation viscosity coefficients in other metallic systems. Another view of the viscosity is Andrade s theory in which ... 

Before a dislocation on one of the glide planes passes through the complex, the distance between the two charge centers is d = b = a0/>/2. After it has passed by the distance is d = V2(b) = a0. Therefore, if K is the static dielectric constant, and q = electron s charge, the energy difference between the before and after states is AU = (q2/Ka0)(V2-l). 

Figure 3.8. Explanation of dislocations in relation to glide. The solid arrow, b, corresponds to the Burgers vector of the dislocation. SV is the screw dislocation, WE is the edge dislocation, and VW is a mixed dislocation. The shaded area represents a glide plane.

The edge dislocation moves easily on its glide plane perpendicular to s under the influence of a shearing force. This force is well below the theoretical shear strength of a perfect crystal since not all of the atoms of a glide plane perform their slip at... 

Figure 3-1. a) Edge dislocation model b) Burgers vector h with Burgers circuit and glide plane indicated. Dislocation motion during plastic deformation under the action of force F. Jog and kink. 

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