Snowflakes mostly form in two different types - plate-like and column-like - but there are many others, including needle-like, prism-like and star-like etc.. Although the many types have been extensively documented, and have been found to be temperature dependent (e.g. large stellar types only grow in a narrow temperature range around -15C) the molecular physics driving the different shape formations at different temperatures is poorly understood.

Understanding the ice/vapor attachment kinetics from molecular first principles is far beyond the state-of-the-art in many-body molecular physics, including modern molecular-dynamics simulations, so we must rely on experimental measurements of snow-crystal growth rates to guide the discussion.

Source : A Quantitative Physical Model of the Snowflake Morphology Diagram Kenneth G.Libbrecht

For extensive technical details, see the work of snowflake investigator Professor Kenneth G. Libbrecht, of the Department of Physics, Caltech, who has published an open-access monograph book on the subject : Snow Crystals Princeton University Press, (544 pages).

Even now, well into the 21st century, our fundamental understanding of why snow crystals grow into the rich variety of structures we see falling from the clouds is remarkably primitive."

Also see : Crystallizationplugin-autotooltip__plain plugin-autotooltip_bigCrystallization

Crystallization is the process by which a solid forms from solution, where the atoms or molecules become highly organized and form a structure.

Some aspects of the process, particularly nucleation is still not completely understood, despite intensive research going back more than a century. and Cloud ice formationplugin-autotooltip__plain plugin-autotooltip_bigCloud ice formation

The formation of ice crystals have important implications for stratospheric ozone chemistry, cloud dynamics, rock weathering, and hydrate formation etc., however the exact mechanisms by which microscopic particulate matter 'seeds' ice-crystals are unknown.

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