Angle of misorientation

Read has shown 21) that an equation of the form of (16) gives the variation of energy with angle of misorientation for all kinds of small-angle boundaries. 

For all vicinal samples a resistance Rpe perpendicular to the step edges are higher than resistance Rpa parallel to the steps. The anisotropy of resistance ka is increased under cooling. The same dependence of kj was observed earlier in vicinal GaAs s tructures with 5 -doping b y t in [ 4]. T he a nisotropy of r esistance d ecreased when the angle of misorientation increased from a=0.50 to 0=3.00. A reference sample SI had an n-type conductivity and p, 2000 cm2A s. The anisotropy of resistance i n t his s ample was n ot f ound. S ome p arameters f or a 11 s amples a 11 wo temperatures are listed in Table 1. 

The other example is related to fullerene tubular structures [8-30], Such structures have been generated by vapor condensation of carbon on atomically flat graphite surfaces. Due to a misorientation of the top layer relative to the second layer, a Moir pattern is created whose lattice parameter is determined by the angle of misorientation. The structural model of the superpattern produced by two misoriented sheets is illustrated by Figure 8-44. 

According to (7.22), the rate of anodic dissolution at a given potential increases with the density of atomic steps. For slightly misoriented planes with respect to a low index plane, it is therefore expected to vary with the angle of misorientation. 

Figure 4.9 Demonstration of how a tilt boundary having an angle of misorientation 6 results from an alignment of edge dislocations.

The pore growth direction is along the (100) direction and toward the source of holes. For the growth of perfect macropores perpendicular to the electrode surface (100), oriented Si substrates are required. Tilted pore arrays can be etched on substrates with a certain misorientation to the (100) plane. Misorientation, however, enhances the tendency to branching and angles of about 20° appear to be an upper limit for unbranched pores. For more details see Section 9.3. 

Figure 9.8 Composite image of a series of double-crystal topographs recorded at different incidence angles of a SI LEC GaAs sample. The image is a set of contours of equal effective misorientation. (Courtesy S.J.Bamett)...

Figure 1.7 View down the [001] direction of a tilt boundary between two crystals (A, B) with a misorientation angle of 36.9° about [001], The grain boundary is perpendicular to the plane of the page. Every fifth atom in the [010] direction in B is a coincidence point (shaded). The area enclosed by the CSL unit cell (bold lines) is five times that of the crystal unit cell, so 2 = 5. (After Lalena and Cleary, 2005. Copyright John Wiley Sons, Inc. Reproduced with permission.)...

In polycrystals, misorientation angles rarely correspond to exact CSL configurations. There are ways of dealing with this deviation, which set criteria for the proximity to an exact CSL orientation that an interface must have to be classified as belonging to the class E=n. The Brandon criterion (Brandon et al., 1964) asserts that the maximum deviation permitted is voE-1/2. For example, the maximum deviation that a E3 CSL configuration with a misorientation angle of 15° is allowed to have and still be classified as E3 is 15°(3)-1 2 = 8.7°. The coarsest lattice characterizing the deviation from an exact CSL orientation, which contains the lattice points for each of the adjacent crystals, is referred to as the displacement shift complete (DSL) lattice. 

Figure 7.6. Dependence of the surface morphology of diamond films on the off-angle (misorientation angle) of the (100) substrate and the CH4 concentration. Diamond films were grown at Ts = 815 and 1200°C [109].

The control of the tilt and azimuthal angles of (100) faces is important to improve the quality of HOD films. In Ref. [264], the tilt (x) and azimuthal 4>) misorientation angles of the (100) faces were measured by both the X-ray precession method and the X-ray rocking curve measurements for HOD films with thicknesses of 1, 4, 20, and 100 pm, which were made by the three-step process (see Figure 5.3). The results are shown in Figure 11.8. 

In Fig. 2C we illustrate a schematic model of such a superpattern. Two graphite sheets that are rotated relative to each other are superimposed, which results in a giant honeycomb lattice. By choosing an angle of 9° for the misorientation, we obtain a superlattice period of 16 A. 

Fig. 11.9. Energy of tilt grain boundary as a function of misorientation angle (adapted from Sutton andBalluffl (1995)).

The definition of low-angle grain boundaries generally covers the range of misorientations from 0° to 10°. In this regime, the grain boundary plane can be considered to be a linear array of separated dislocation cores. For [001] tilt boundaries in YBCO, the boundary plane will be composed of [100] or [010] dislocations, as shown in Fig. 11.6 (for YBCO the small distortion between the a- and fi-axes needs to be incorporated for quantitative models, but structurally results in no observable differences in the dislocation cores). 

Fig. 11.13. Experimental observations of (T = 4.2 K) as a function of misorientation angle from the results of several groups [11.1-11.3] show an exponential dependence. Where the results were reported at E = 77 K, the values at 4.2 K were extrapolated from the temperature dependence of Jq [11.45]. The grain boundary tunneling current calculated from eq. 11.2 using the grain boundary widths from Fig. 11.12 shows excellent quantitative agreement for a width defined by a copper(I) valence between 1.5 and 1.9. This copper valence corresponds to the copper(I) valence in bulk YBCO when it becomes non-superconducting. The predicted drop in due to the symmetry of the superconducting order parameter is insufficient by two orders of magnitude to account for the observed behavior.

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