Plane surface isotropic growth

Figure 9.8. Isotropic growth on a plane surface with inward development...

CVD graphite can have several structural forms columnar, laminar, or isotropic. The columnar form is shown in Fig. 7.2. The crystallites are deposited with the basal planes (ab directions) essentially parallel to the deposition surface. Their structure tends to be columnar (cone-like) as a result of uninterrupted grain growth toward the reactant source. 

A quantitative basis for these ideas has been provided by Beuth (1992) for the case of steady-state advance of a surface crack in an isotropic elastic film bonded to an isotropic elastic substrate. Under circumstances of steady-state crack propagation, the conditions on system parameters that are necessary for growth can be expressed in terms of the states of plane strain deformation which exist far ahead of and far behind the advancing crack segment see Figure 4.37. The four material parameters i f, E, Vs>... 

Contrary to the growth of c-plane GaN on c-plane sapphire, the lattice mismatch between the substrate and the film in the case of a-plane GaN growth on r-plane sapphire is not spatially isotropic but depends on the crystal direction and respective lattice plane distances. Figure 11.3 shows the projected surface of the r-plane sapphire and the surface unit cell associated to it. On top of this, 1.5-unit cells of a-plane GaN are superimposed. This representation visualizes the relatively small lattice mismatch in [1100] direction of about... 

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