Shear Plane Nucleation

It seems therefore that little or no stability is to be expected for the point defect aggregates which provide the necessary shear-plane precursors in the homogeneous shear-plane formation mechanisms. These homogeneous nucleation mechanisms are therefore unlikely to operate, and we turn our attention now to a heterogeneous mechanism, in which point defects aggregate at pre-existing planar-defect sites. 

The most obvious heterogeneous mechanism follows from our discussion in Section 2 where we showed that shear planes could be related to metal interstitial defects, but that a pre-existing anti-phase boundary (APB) is required. Thus shear-plane formation may occur by metal interstitial capture at pre-exist ng APBs (Bursill et More particularly, it is proposed that metal interstitial ions produced by 

The most obvious feature of this mechanism to test by our theoretical calculations concerns the energetics of APB formation. Thus atomistic calculations of the type discussed in Section 2 for the shear planes, showed that the 011 APB had a considerably lower formation energy than boundaries with other orientations. The result is in line with the proposed mechanism, as interstitial capture at the 011  

APB converts these into 121 shear planes. It would also obviously be desirable to calculate the activation energies for interstitial migration down the APBs. This is at present beyond the scope of our calculations, although developments in the field may soon render such calculations feasible. 

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The difference between the observed and theoretical growth rates has been reconciled by the Frank screw-dislocation theory. Actual space lattices of real crystals are far from perfect and crystals have imperfections called dislocations. Planes of particles on the surfaces and Mtliin the crystals are displaced, and several kinds of dislocations are known. One common dislocation is a screw dislocation (Fig- 27.9), where the individual particles are shown as cubical building blocks. The dislocation is in a shear plane perpendicular to the surface of the crystal, and the slipping of the crystal creates a ramp. The edge of the ramp acts like a portion of a two-dimensional nucleus and provides a kink into which particles can easily fit, A complete face never can form, and no nucleation is necessary, As growth... 

The displacement of the atoms is a shear in the 101 planes of the cubic structure (Figure 8.14). The shearing process nucleates at a number of points within the crystal as it cools, and each... 

In Fig. 2a, from data in Shaw (2004), the test conditions are at room temperature and low strain rate. Conditions are isothermal, and strain softening is due to the nucleation and growth of voids. The different curves result from applying compressive pressure p to the shear plane. The larger the ratio p/k, where k is the peak shear flow stress from the test, the larger is the strain y at which dx/dy = 0. 

At Ms temperature TiNi initiates a uniform (inhomogeneous) distortion of its lattice — through a collective atomic shear movement. The lower the temperature, the greater the magnitude of shear movements. As a result, between Ms and Mr temperature the crystal structure is not definable. In sharp contrast, other known martensitic transformations initiate a nonuniform (heterogeneous) nucleation at Ms and thereafter the growth of martensite is achieved by shifting of a two dimensional plane known as invariant plane [28] at a time. Thus, between Ms and Mr temperature the crystal structure is that of austenite and/or martensite . 

Another manifestation of the strain in the films is the presence of the half-loop dislocations extending out from the open tubes in the GaN films grown on the porous substrates, as discussed in the previous section. Regarding the origin of these half-loops, it is easy to see that open tubes (or voids) in a strained film will act as stress concentrators since the normal component of the stress is necessarily zero at the tube wall, the material near the wall will be displaced relative to its position in the absence of the void, and the tangential in-plane component of the stress is thereby increased. In other words, during growth, the shear stress field of the GaN film will be locally concentrated around these open tubes in the film. The open tubes provide a free surface where these half-loops can nucleate due to the increased stress. 

Glide of an edge dislocation occurs when a half-plane of atoms is moved over the atoms below the glide plane. The movement occurs by the nucleation and movement of kinks. Remember that the reason that dislocations are so important in plasticity is because it is easier to move one block of material over another (shear the crystal) one halfplane of atoms at a time. Similarly, it is easier to move a dislocation by moving a kink along it one atom at a time. In fee metals, the Peierls valleys are not deep, so the energy required to form a kink is small and dislocations bend (create kinks) quite easily. 

In all three modes of nucleation the mean-free-path length is close to A, and the attempt frequency vq = vd/20, where vd, the lattice shear vibration frequency on the (100) plane in the [001] direction, is estimated to be close to 6.0 x 10 s and the factor 1/20 comes from the expected characteristic saddle-point half-loop diameter of 20h. Thus, with these considerations we have... 

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