This paper offers a heuristic thermodynamic analysis of the selection of solidification microstructures formed during resolidification of micro layers of molten metal driven by surface tension. This study explores empirical evidence obtained by performing a tightly controlled heating-dwell-cooling materials processing cycle that causes melting followed by resolidification of micro layers of an Al + Si alloy in ultra high purity nitrogen. Identification of characteristic process parameters responsible for crystal pattern formation of the α-phase solid solution during associated rapid quench is discussed. The focus of the inquiry is ultimately directed toward solid solution dendrites population morphology. A transition from a scarce (even single or non existent) dendrite formation toward chaotically distributed α - phase dendrites imbedded in two-phase eutectic is identified. A heuristic approach has been established to interpret alpha phase dendrite pattern formation during solidification phenomena driven by entropy generation at the liquid-solid interfaces.