In the 19th century mineralogists noticed that two different naturally occurring crystal species sometimes grew together with some definite and unique orientation relationship, as revealed by their external forms [1.1]. These observations led to attempts to reproduce the effect artificially, during crystal growth from solution, and the first recorded successful attempt was reported in 1836 by Frankenheim [1.2], when the now well-known case of parallel oriented growth, or “parallel overgrowth” [1.3], of sodium nitrate on calcite was observed for the first time. Based on the reviews on natural overgrowth phenomena [1.4] and on structural data from X—ray diffraction studies. Royer established in 1928 the conditions for oriented overgrowth, defining the term epitaxy (“arrangement on”), too [1.5]. He formulated the following rule of epitaxy: “epitaxy occurs only when it involves the parallelism of two lattice planes that have networks of identical or quasi-identical form and of closely similar spacings”. Experimental data gained later indicated that epitaxy occurs if the lattice misfit, defined as 100 (af—as)/as, where as and af are the corresponding network spacings (lattice constants) in the substrate and film, respectively, is not larger than 15%. This geometrical approach to the understanding of epitaxy, introduced by Royer, has remained prominent to the present day [1.6–8].