Dislocation instability

It is worth taking note that Hsat for a modest Wa is significantly smaller than the thresholds of the well-laiown Helfrich (1970) undulation instability and Parodi s (1972) dislocation instability. These two instabilities are defined by the balance of the field energy... 

A difiiculty with this mechanism is the small nucleation rate predicted (1). Surfaces of a crystal with low vapor pressure have very few clusters and two-dimensional nucleation is almost impossible. Indeed, dislocation-free crystals can often remain in a metastable equilibrium with a supersaturated vapor for long periods of time. Nucleation can be induced by resorting to a vapor with a very large supersaturation, but this often has undesirable side effects. Instabilities in the interface shape result in a degradation of the quality and uniformity of crystalline material. 

Plastic deformation is mediated at the atomic level by the motion of dislocations. These are not particles. They are lines. As they move, they lengthen (i.e., they are not conserved). Therefore their total length increases exponentially. This leads to heterogeneous shear bands and shear instability. 

The author believes that dipoles cause deformation hardening because this is consistent with direct observations of the behavior of dislocations in LiF crystals (Gilman and Johnston, 1960). However, most authors associate deformation hardening with checkerboard arrays of dislocations originally proposed by G. I. Taylor (1934), and which leads the flow stress being proportional to the square root of the dislocation density instead of the linear proportionality expected for the dipole theory and observed for LiF crystals. The experimental discrepancy may well derive from the relative instability of a deformed metal crystal compared with LiF. For example, the structure in Cu is not stable at room temperature. Since the measurements of dislocation densities for copper are not in situ measurements, they may not be representative of the state of a metal during deformation (Livingston, 1962). 

Little is known about the interactions between the transport properties in the melt and the production of defects at the melt-crystal interface. An exception is the swirl microdefect seen during processing of dislocation-free silicon wafers (118). The origins of this defect (119) are related to temperature oscillations and remelting of the interface. Kuroda and Kozuka (120) have studied the dependence of temperature oscillations on operating parameters in a CZ system but have not linked the oscillations to convective instabilities in the melt. 

The textures in homeotropic lamellar phases of lecithin are studied in lecithin-water phases by polarizing microscopy and in dried phases by electron microscopy. In the former, we observe the La phase (the chains are liquid, the polar heads disordered)—the texture displays classical FriedeVs oily streaks, which we interpret as clusters of parallel dislocations whose core is split in two disclinations of opposite sign, with a transversal instability of the confocal domain type. In the latter case, the nature of the lamellar phase is less understood. However, the elementary defects (negative staining) are quenched from the La phase they are dislocations or Grandjean terraces, where the same transversal instability can occur. We also observed dislocations with an extended core these defects seem typical of the phase in the electron microscope. 

It has been shown that several polymers exhibit instabilities in their plastic deformation process. It should finally be mentioned that instabilities may also occur during the plastic deformation of metals This phenomenon which is called the Portevin-Le Chatelier effect, is generally interpreted in terms of different modes of dislocation movement depending on whether or not dislocations move by dragging along their atmosphere of impurities behind them. 

What we have learned is that dislocation nucleation will occur once 4>i np) reaches its maximum allowable value. This idea is depicted graphically in fig. 11.19 where it is seen that instability to dislocation nucleation occurs when (Siip) = Yus, where yus is a material parameter that Rice has christened the unstable stacking energy. This idea is intriguing since it posits that the competition between cleavage and dislocation nucleation has been reduced to consideration of the relative values of two simple material parameters, both of which admit of first-principles determination, and relevant geometrical factors. 

The full KTHNY theory improves upon the simple instability theory presented above in several respects. Kosterlitz and Thouless recognized that the elastic constants of a solid containing thermally excited dislocation pairs are renormalized by the presence of such excitations, so that the coupling constant that appears in the above formula for the transition... 

The present of discontinuities (sudden jump-in or jump-out at some value of the separation D) is due to the mechanical instability of the AFM cantilever at the points where the derivative of the force dF/dD is larger than the elastic constant k of the cantilever [35]. The periodic oscillations are due to the layered structure of the sample and are described by (3.8). For a given number of layers n, the force has a minimum when the separation D is equal to nd, the thickness of the unstressed n layers. Because of the instability of the tip, this is observable only in the run-out force-plot. Starting from the minimum, the force increases more and more, as the separation between the confining surfaces decreases, and it presents a local maximum at d = do when a dislocation loop appears. The tip instabihty makes this point observable only during the run-in. 

Fig. 3.18. The force F, scaled by the local curvature radius iE, as a function of the mica/mica separation D. A complete compression/decompression cycle is shown (filled/open circles). The void regions are caused by the mechanical instability dF/dD > k). Inset the array of dislocation loops.

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