Critical angle channeling

For crystals which have flat faces which extend for a fraction of 1 ym, a new type of phenomenon may be observed. Electrons incident at the edge of the crystal parallel to the surface may be channelled along the surface. The potential field of the crystal extending into the vacuum deflects the electrons so that they tend to enter the surface but they are scattered out of the crystal by the surface atoms or by diffraction from the crystal lattice planes parallel to the surface. If the scattering angle is less than the critical angle for total external reflection, the scattered electrons can not surmount the external potential barrier and are deflected back into the crystal (figure 4 (a)). 

In constructing the helices, the assumption is made that a minimum distance between source atoms in the channel wall can be tolerated. Because of the nature of the repeat units, it is easy to establish a critical angle to ensure appropriate separation. One finds, therefore, that if d is a minimum, or contact, distance, then... 

Fig. 8.4. Schematic representation of ion trajectories for axial channeling. The crystal lattice is depicted as a set of atomic strings, i.e., the shaded rows, (a) Trajectories for various angles of incidence, y/, relative to the lattice row B and C represent trajectories for values less than the critical angle, and A for values greater than the critical angle, (b) Trajectories for parallel incidence as a function of impact position (after Mayer et al. 1970)...

The calculation is for a uniform beam incident on isolated atoms in a channel (Fig. 8.7). Since we are only interested in scattering angles greater than the critical angle (y/c 1°), the impact parameter is relatively small (rt 10 2 A) thus we use the unscreened Coulomb potential. In this calculation the dechanneling is a result of binary scattering by isolated displaced atoms in an otherwise perfect crystal. 

Channeling occurs not only along strings of atoms in axial directions but also between sheets of atoms that make atomic planes. Which would have a greater critical angle for MeV He ... 

On a completely wetting chemical channel ( eq = 0), one can observe axially homogeneous rivulets only if the contact angle 6 of the rivulet (which is pinned at the channel edge by the chemical step if 9 is smaller than the equilibrium contact angle on the surrounding substrate) is smaller than a certain critical angle. Macroscopically... 

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