Patterns encountered in nature, such as those exhibited by snow flakes and many crystallized mineral forms, and those found in the microstructures of cast alloys and fusion weldments, remain subjects of long-standing scientific interest and practical engineering importance [1, 2]. Alan Turing’s paper, “The Chemical Basis of Morphogenesis” , is credited as explaining that diffusion-limited processes can drive thermodynamically “open” systems to instability. Patterns then evolve spontaneously in response to Poincaré’s “very small cause(s).” But what, in fact, are the nature and function of such very small causes?“A very small cause that escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance.”—Henri Poincaré, Science et méthode, 1908.
Experimental observations: capillary-induced shape change
Prior microgravity studies
Interface energy balances
Omnimetric energy balances
Stationary isotropic interfaces
Grain boundary grooves
Wang et al.’s observation and conclusion, quoted above, indicates that GBGs provide the “trigger” mechanism for actually inducing morphological instabilities on polycrystalline solid–liquid interfaces.“\(\dots \) the interface instability occurring first at the grain boundary groove probably becomes the origin of the entire planar interface instability.”