Dislocations critical density

To answer questions regarding dislocation multiplication in Mg-doped LiF single crystals, Vorthman and Duvall [19] describe soft-recovery experiments on <100)-oriented crystals shock loaded above the critical shear stress necessary for rapid precursor decay. Postshock analysis of the samples indicate that the dislocation density in recovered samples is not significantly greater than the preshock value. The predicted dislocation density (using precursor-decay analysis) is not observed. It is found, however, that the critical shear stress, above which the precursor amplitude decays rapidly, corresponds to the shear stress required to disturb grown-in dislocations which make up subgrain boundaries. 

Beside dislocation density, dislocation orientation is the primary factor in determining the critical shear stress required for plastic deformation. Dislocations do not move with the same degree of ease in all crystallographic directions or in all crystallographic planes. There is usually a preferred direction for slip dislocation movement. The combination of slip direction and slip plane is called the slip system, and it depends on the crystal structure of the metal. The slip plane is usually that plane having the most dense atomic packing (cf. Section 1.1.1.2). In face-centered cubic structures, this plane is the (111) plane, and the slip direction is the [110] direction. Each slip plane may contain more than one possible slip direction, so several slip systems may exist for a particular crystal structure. Eor FCC, there are a total of 12 possible slip systems four different (111) planes and three independent [110] directions for each plane. The... 

Experimentally, it has been observed for single crystals of a number of metals that the critical resolved shear stress is a function of the dislocation density, Pd -... 

The synthesis of carbonyls by the reaction of Ni, Fe or Mo with carbon monoxide is possible under low-temperature and low-pressure conditions. The apparent activation energy is reduced under milling conditions. The difference between non-acti-vated solid, pretreated solid and simultaneous reaction and milling is depicted in Fig. 14.15 [10]. At normal temperatures, a distinct decrease in activation energy and frequency factor can be seen this higher reactivity is derived from a high dislocation density. Below a critical temperature, the solid alters the breakage behavior from... 

In Ref. [312], TEM plan views at different depths were observed for an HOD film of 2-pm thickness, and those near the surface were observed for a 25-pm thick HOD film. These results showed that in the HOD film growth, there was a critical thickness that was determined by the growth parameters, the nucleation density, and the density of oriented nuclei. Below the critical thickness, diamond grains contained a high density of dislocations perpendicular to the (100) faces, while above the critical thickness, the dislocation and other defect densities were markedly lower. 

A more elegant (and mathematically tractable) description of the problem of dislocation pile-ups is to exploit the representation of a group of dislocations as a continuous distribution. This type of thinking, which we have already seen in the context of the Peierls-Nabarro model (see section 8.6.2), will see action in our consideration of cracks as well. The critical idea is that the discrete set of dislocations is replaced by a dislocation density pb (x) such that... 

At low temperatures, the energy term in the free energy dominates the entropy term, and the density of dislocations is small, with dislocations occurring in bound pairs. The density of bound dislocations increases with increasing temperature, until, at a critical temperature given by... 

Using Eq. 11, we can compare the effect of dissolution at dislocations to the overall dissolution rate. For instance, one predicts that the critical dislocation density pc at which the dissolution rate due to dislocations and to the dislocation-free surface become equal is pc 2.109, 3.109, and 10locm-2 for quartz, calcite, and rutile, respectively. These values compare well with experimental data and calculations of Blum and Lasage (1987) for quartz. Obviously, the effect of dislocation on the overall rate of dissolution become significant only lor very high dislocation densities. 

Nanocrystalline materials comprising sub-100 / metal particles, when compressed to 50% of their bulk density, show properties (specific heat, thermal conductivity, saturation magnetization and critical temperature for superconductivity) provocatively different from those of their crystalline or glassy counterparts.(48) It is well known that the interfaces of mechanically reduced composites are effective in interacting with dislocations and with flux lines in superconducting composites. Precursor materials for the preparation of ultrafine filamentary composites can also be imagined. Here the combinations of interphasial boundaries and dislocations can... 

The increase in the TD density in the films grown on relatively thick (6-8 pm) PSC is most probably caused by a specific plastic relaxation process, occurring as a reaction to a particular state of strain that appears in these epitaxial films. This can be stated on the basis of strain inversion in the films grown on PSC, as well as on the increase in compressive stress with the thickness of the PSC layer increasing. These effects show that apart from the stress caused by the GaN/SiC lattice mismatches, an additional built-in stress arises in the films. Obviously, the additional stress is caused by the presence of (0001) PDs, because one can expect that a part of GaN film within the faulted region may have altered its mechanical properties as compared with unfaulted material [72]. Then the increase in dislocation density in GaN grown on relatively thick PSC can be explained by a plastic relaxation process, which relieves the built-in stress and occurs because this internal stress/(0001) PD density reaches a certain critical value. 

R. F. W. Bader and associates at Canada s McMaster University have derived a means of describing the electron distribution associated with specific atoms in a molecule, called the atoms in molecules (AIM) method. The foundation of this approach is derived from quantum mechanics and principles of physics. It uses the methods of topology to identify atoms within molecules. The electron density of a molecule is depicted by a series of contours. Bond paths are the paths of maximum electron density between any two atoms. The critical point is a point on the bond path where the electron density is a maximum or a minimum with respect to dislocation in any direction. The bond critical point is defined by the equation... 

---