It was recalled that, when a substrate crystal was of higher symmetry than the structure of the overgrown film, a finite number (n) of differently oriented island nuclei developed. This gave rise to a finite number (m) of misorientations across boundaries in the film, where m = C(n, 2). Such degenerate epitaxy was observed in the double positioning of [111] face-centered cubic metal films on MoS2 with (112) twin boundaries, and in the triple positioning of tetragonal Cu3Ba2YO7 on lattice-matched cubic SrTiO3 with 90 boundaries of  = 3. The  in situ  growth of Cu3Ba2YO7 films on (001) MgO was a good example of coincidence epitaxy, where the lattice misfit was large. Differently oriented island nuclei formed in order to minimize the interfacial energy by maximizing the lattice coincidence according to the near coincidence site lattice model and minimizing the misfit and strain energy across the film/substrate interface. The number of possible misorientations (m) from the number of differently oriented island nuclei (n) was given by m = n2/2, when n was even, and by m = (n-1)(n+1)/4 when n was odd. Only 9 misorientations were observed as compared with the calculated value of 64. Extensive grain growth and annihilation were suggested to be responsible for the disappearance of many misorientations. The [001] tilt boundaries which corresponded to  = 5,  = 17,  = 29, off- = 13 and 45 were all observed.

S.W.Chan: Journal of the Physics and Chemistry of Solids, 1994, 55[10], 1137-45