Misorientation angles

The investigation ofboundary mobility was confined to <111> tilt boundaries with misorientation angles in the vicinity of the special misorientation X7 ((p = 38.2°). These... 

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. 

Figure 11.8. Polar (x) and azimuthal (< > misorientation angles as a function of HOD film thickness [264].

Figure 11.12. Thickness dependence of the FWHMs for (11 l)XPF. Ax and A(p are the tilt and azimuthal rotation angles, respectively, and A0,ot is the FWHM of the deduced rotational misorientation angle [275],...

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

Figure 4. Effect of cumulative strain on the distribution of boundaries by misorientation angles in Ti.

Many TEM studies show that the GB films grown by physical vapor deposition (PVD) on bicrystal substrates are wavy and the typical facet size is about 50 nm [4.35-4.37]. Therefore, the dependence of critical current density on misorientation angle is difficult to study with these films. Recently, liquid-phase epitaxy (LPE) was successfully used to obtain large single-facet grain boundaries. Fig. 4.20 shows a plan-view image of the GB of a YBCO film grown on a 24° MgO bicrystal. It clearly shows that the GB is a symmetrical... 

Therefore, these GBs can be used to study the real dependence of the critical current density on GB misorientation angle. Primary measurements on electrical properties for the bicrystal junction grown by LPE indicate that high critical density values and reproducible X products can be obtained from these GBs grown by LPE. Further studies of Jc dependence on misorientation angle are in progress [4.38]. 

Fig. 10.1. Critical current densities Jc for grain boundaries in YBCO films grown by epitaxy on suitably treated single crystal or bicrystal substrates, plotted against the [001] misorientation angle [10.4, 10.7, 10.51, 10.59, 10.60].

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