Geometric selection in two-dimensional crystal aggregates

The simultaneous growth of randomly oriented crystals nucleated at a surface rapidly produces a coarsely crystalline radial or columnar aggregate possessing a strong preferred shape and lattice orientation. Such textures are common in natural crystalline aggregates and are considered to arise because those crystals having their fastest growth direction normal to the initial substrate outdistance and eventually eliminate their less favorably oriented neighbors. In its simplest form the process of elimination is a purely geometric phenomenon. Detailed analysis and computer simulation of textural changes accompanying geometric selection in random two dimensional needlelike crystal aggregates demonstrate that selection initially proceeds exceedingly rapidly but slows drastically once roughly 90 percent of the crystals originally present are eliminated. Subsequent decrease in crystal density is inversely proportional to the square root of the distance from the initial substrate. Increases in crystal size larger than one or two orders of magnitude are thus unlikely to arise in natural crystalline aggregates in which only simple geometric selection is involved.