On a geometric model of crystal growth on a flat substrate

This paper is devoted to computer simulation of crystalline aggregates growth from a homogeneous solution. This process is considered from the geometric point of view, when crystals can be represented as a collection of flat faces, growing layer by layer with stable relative growth rates in the directions of their perpendiculars. Simply speaking, we extend Frank's model [H. Muller-Krumbhaar, Yu. Saito, Crystal Growth and Solidification, in: Surfactant Science Series, vol. 89, CRC Press, Boca Raton, FL, 2000, pp. 853–854] to the case of simultaneous growth of several individuals placed on a flat unbounded static substrate. Attention is given not only to finding the outer boundary of an aggregate but to determining the interfacing surfaces between individuals. In other words, our goal is to construct detailed bounding surfaces of all individuals included in an aggregate.