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This article applies to ice initiation in the Earth's atmosphere specifically the Troposhere and lower Stratosphere

Before ice/snow crystals can grow a process called nucleation is required, or alternatively an existing ice particle (produced by splintering or crystal breakup known as "Secondary Ice Production" or "Secondary Ice Nucleation") will also allow growth. Very often clouds contain many more ice crystals than can possibly be explained by primary nucleation indicating that a secondary production process is dominant. An excellent explanation of Primary ice nucleation is provided by Gabor Vali http://www-das.uwyo.edu/~vali/nucl_th.pdf, he also explains just how difficult it is accurately predict ice concentrations, however we do seem to do remarkably well. Further complications arise when we include the fact that a newly created ice crystal interacts with its environment, it will become a great sink for water vapour inhibiting nucleation that is based on vapour supersaturation and can lead to evaporation of liquid water, which generally inhibits nucleation involving droplets or haze. In a very simple modelling comparison case study the models agreed pretty well when just considering homogeneous nucleation, however just the effect of changing one parameter which reduces the rate of ice growth (weaker vapour sink) leads to much higher concentrations of ice nucleation.

Primary Nucleation
Primary nucleation is split into two categories, Homogeneous nucleation and Heterogeneous nucleation

Homogeneous nucleation
This process requires no foreign body (ice nuclei) only water molecules.

Homogeneous deposition
(straight from vapour to ice) does not occur as it is statistically unlikely to occur. The chances of enough water vapour molecules randomly grouping to form a critical-sized ice nucleus of a size such that its rate of growth is equal to its rate of decay is very low.

Homogeneous freezing
(from an existing cloud droplet to ice) This occurs at cold temperatures and usually plays an insignificant role compared with other nucleation until temperatures are well into the -30's degC. Water molecules randomly group within the pre-existing water drop until they form a critical-sized ice nucleus(germ) of a size such that its rate of growth is equal to its rate of decay