How Crystals Form from a Cloud of Atoms

Structure formation, the condensation of a cloud of atoms to a crystal is still not well understood. Disordered sytems (amorphous/liquid) should be in the center of this research, they are the precursors of any crystal. We consider elementary systems, as well as binary, or ternary amorphous alloys, irrespective whether they are metallically, covalently or ionically bonded and describe the process of structure formation in the formal language of thermodynamics but, as far as we know for the first time, by an extended version (general dynamics), based on the complete Gibbs fundamental equation, applied to internal subsystems. Major structural features evolve from global resonances between formerly independent internal subsystems by exchanging momenta and angular momenta, both accompanied by energy. By this they adjust mutually their internal features and create spherical-periodic structural order at medium-range distances. Under the given external constraints the resonances get optimized by self-organization. Global resonances of the type considered have clearly to be distinguished from local resonances between individual ions (described by quantum chemistry) forming local order. The global resonances cause anti-bonding (non-equilibrium) as well as bonding (equilibrium) states of the coupled total system, occupying the latter to form new structurally extended order. The transition to equilibrium creates entropy which itself leaves the system together with energy. At resonance the energetical splitting between the bonding and anti-bonding state is largest, the creation of entropy and the decrease of the total energy therefore, too. The crystal, finally, evolves by additionally optimizing a resonance based on angular momentum, and the additional adjustments of the local resonances to the global ones, theoretically done by applying Bloch's theorem.