Crystal orientation dislocation density

Germanium single crystals intended for electronic apphcations are usuaHy specified according to conductivity type, dopant, resistivity, orientation, and maximum dislocation density. They may be specified to be lineage-free unless the specified resistivity is below about 0.05 H-cm. Minority carrier lifetime and majority carrier mobHity are occasionaHy specified. 

Kumar and Clifton [31] have shock loaded <100)-oriented LiF single crystals of high purity. The peak longitudinal stress is approximately 0.3 GPa. Estimates of dislocation velocity are in agreement with those of Flinn et al. [30] when extrapolated to the appropriate shear stress. From measurement of precursor decay, inferred dislocation densities are found to be two to three times larger than the dislocation densities in the recovered samples. 

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. 

Fig. 12. Derivative curves of EPR in a highly dislocated As-doped germanium crystal grown in a H2 atmosphere. The magnetic field is oriented along the [100] direction. T= 2 K, /= 25.16 GHz. Note the sign reversal of the new lines as compared to the As-donor hyperfine structure. Dislocation density 2 x 104 cm 2. (Courtesy Pakulis and Jeffries, reprinted with permission from the American Physical Society, Pakulis, E.J., Jeffries, C D. Phys. Rev. Lett. (1981). 47, 1859.)...

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... 

More recently Mackwell, Kohlstedt, and Paterson (1985) studied the deformation of single crystals of San Carlos (Arizona) olivine deformed under hydrous conditions at 1,300 C, 300 MPa confining pressure, and 10 s strain-rate and found they were a factor of 1.5-2 weaker than those deformed in an anhydrous environment. TEM observations showed that specimens deformed under dry conditions, in an orientation such that the slip systems (001)[100] and (100)[001] would be activated, were characterized by a microstructure of generally curved dislocations and dislocation loops, but no organization into walls. The dislocation density was 10 -10 cm compared with an initial value of < 10 cm . Most of the dislocations and the loops lie approximately in the (010) plane because they are in contrast for g = 004, they probably have b = [001] dislocations with b = [010] and [100] would be out-of-contrast for this reflection. However, the slip system (010) [001] is not expected to be active. It is not clear, therefore, if these dislocations are actually involved in the deformation. The general geometry of the dislocation microstructure is not inconsistent with some climb mobility in fact, on the basis of the observations of Phakey et al. (1972), climb is certainly expected at 1,300°C. 

In FCC materials, there are 12 different slip systems, which can contribute to the deformation process. Dislocation density histories at a peak stress of 4.5 GPa for [001], [111] and [Oil] orientations and isotropic case with [001] orientation are calculated and plotted as shown in Fig. 13. It is clear that the dislocation density is very sensitive to crystal orientation with the highest density exhibited by [111] orientation followed by the isotropic media, [011] and [001] orientations respectively. This may be attributed to the number of slip systems activated and to the way in which these systems interact. The [001] orientation has the highest symmetry among all orientations with four possible slip planes 111 that have identical Schmid factor of 0.4082, which leads to immediate work hardening. The [011] orientation is also exhibits symmetry with 2 possible slip planes that have Schmid factor of 0.4082. 

Fig, 13. The influence of crystal orientation on the dislocation density history in copper single crystal shocked for 1.5 nanoseconds. 

Slip bands and kink bands were first studied in compression of oriented nylon 6,6 and 6,10 by Zaukelies, and subsequently in tensile specimens of oriented high density polyethylene (HOPE) by Kurakawa and Ban and Keller and Rider Zaukelies interpreted the angle between kink bands in oriented nylon and the compression axis in terms of Orowan s theory of crystal kinking, postulating dislocation mechanisms for the process. Keller and Rider ° and Kurakawa and Ban were impressed by the appearance of deformation bands in high density polyethylene in directions close to the IDD. In this polymer system the... 

The diffusion of Ni into Si, and into a transition layer between these elements in a diffusion couple, was studied at 470 to 1070K. The samples used were plates which were oriented in the (111) plane, and had dislocation densities of the order of 1000/cm2. Layers (0.0003mm) of Ni which contained Ni were then deposited onto the Si. The distribution of Ni in the Si single crystals and in the transition layers was determined via the autoradiography of oblique sections. It was found that the results at above 870K could be described by ... 

Despite the high dislocation density, the disturbed portion of the crystal takes up only a small percentage of the total volume. This lets us define a mean crystallographic orientation for each volume element and consequently to use the isoclinic configurations in tlie model. 

Most wurtzite GaN films have been grown on either 6H-SiC(0001) (see Datareview A7.8) or sapphire (A1203) substrates. The orientation of sapphire most frequently used is C-plane (0001) although there have been some structural characterisation studies made for growth on A-plane (1120) [1-4] and R-plane (0112) [1,2,5-7] substrates. Other defects found in the a-phase include inversion domain boundaries, prismatic faults, nanopipes, pits, voids and cracks. The limited structural information available on bulk single crystals of a-GaN shows that they contain a low density of line dislocations and stacking faults near inclusions [12] (see Datareview A7.5). 

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