THE FORMATION OF ICE CRYSTALS 
By UKICHIRO NAKAYA 
Hokkaido University, Sapporo, Japan 
When pure liquid water suspended in the air is 
cooled, it keeps the liquid state till about —385C. 
Liquid water at temperatures below the freezing point 
is called supercooled water. The supercooled water is 
transformed spontaneously into ice at about —35C. 
The rate of freezing is determined by the rate at which 
the latent heat liberated by freezing is removed. In the 
case of freezing of the water supercooled to s degrees 
centigrade, s/80 parts of the volume are transformed 
instantaneously into ice at the moment when freezing 
starts, because the latent heat liberated is 80 cal gt. 
The whole system, s/80 parts of ice plus (1—s/80) parts 
of water, is warmed up to OC, and the speed of later 
freezing is a function of the rate of removal of the 
latent heat liberated by the subsequent freezing. 
Altberg [1] studied the freezing of the rapids in Siberia, 
and found that most of them are supercooled to the 
order of —0.05C just before freezing commences. 
The freezing of still water in nature starts from the 
surface, as the maximum density of water is at 4C. 
X-ray studies show that the thin ice plate obtained at 
the surface of still water is a single crystal, the orienta- 
tion being such that the principal axis is perpendicular 
to the water surface. Under favorable conditions very 
large single crystals are obtained in lake ice. McConnel 
[10] observed single crystals as large as about one foot 
in diameter at Lake Davos. 
In the case of water in turbulent flow or in a re- 
frigerated vessel, crystallization starts at numerous 
points in the water and the crystals develop in random 
directions. The bulk ice thus obtained is composed of a 
mosaic of ice crystals oriented at random. Thus ordi- 
nary ice has a microcrystalline structure and is not a 
crystal in the usual meaning of the word. 
Single crystals of ice are obtained in the most beauti- 
ful and complicated manner by the sublimation of 
water vapor. In nature they are observed as crystalline 
frost, window hoar, and snow crystals. In this article 
the descriptions are confined to the ice crystals obtained 
by the sublimation of water vapor, with special empha- 
sis on the snow crystal. 
THE FORMATION OF ICE CRYSTALS BY 
SUBLIMATION 
Crystalline Frost. It is well known that frost has 
two structural forms: amorphous and crystalline. 
Amorphous frost is produced when the temperature is 
only slightly below OC, or by the deposition of super- 
cooled water droplets. Crystalline frost is formed at 
lower temperatures by the condensation of water vapor 
by sublimation on a solid body. The solid body may be 
a particle of ground snow or other substance. The 
erystalline frost produced on a new snow surface usually 
develops in a fern-like shape and is called surface hoar. 
207 
It is often observed on cold winter mornings after a 
calm, clear night. Crystalline frosts are frequently ob- 
served also on the walls of snow cavities. Cup crystals 
and feather-like forms are typical of these crystals. 
They are called depth hoar. Detailed descriptions of 
these surface and depth hoars have been given by 
Seligman [13, pp. 46-77]. 
The crystalline frosts can be classified into five forms: 
(1) needle, (2) feather-like, (8) plate, (4) cup, and (5) 
dendritic. From the crystallographic point of view, 
each of these frost crystals has its corresponding type 
in the crystals of snow. 
1. Needle form. This crystal often grows out from a 
wall of snow in the form of needles 0.2-0.5 mm in 
diameter and about 1 cm in length. Microscopic ex- 
amination shows that it is an assemblage of parallel 
hexagonal columns. It corresponds to the columnar 
erystal of snow. 
2. Feather-like form. This type is frequently ob- 
served. Sometimes it develops to 5-6 cm in length. 
Under a microscope it is seen to be composed of small 
hexagonal columns, some columns being attached at 
right angles to the sides of others. The corresponding 
snow crystal is also known. 
3. Plate crystal. This type is sometimes observed 
hanging down from the snow ceiling of a cavity and 
also growing out in the air from an exposed object such 
as the wall of a wooden box. The form and structure 
are quite similar to those of one branch of the snow 
crystal called sector form. 
4. Cup crystal. When completely developed this type 
takes the shape of a whisky glass of hexagonal form. 
But usually one side is not completed and appears to 
be rolled up. This is the most common type of depth 
hoar. The corresponding snow crystal is very rarely 
observed. 
5. Dendritic crystal. Dendritic crystals are often ob- 
served, in addition to the surface hoar, among the 
crystalline frosts developed on the branches of trees 
when the weather is calm and the temperature is low. 
This type corresponds to the fern-like crystal of snow, 
the only difference being that snow lacks the minute 
internal structure resulting from sublimation. When 
the temperature is very low, it is sometimes possible 
to observe a remarkable frost crystal that is very 
similar both in form and in structure to one branch of 
a hexagonal crystal of snow. 
The correspondence of the habits of snow and frost 
crystals makes it possible to infer the conditions for the 
formation of various types of snow crystals. Before the 
artificial production of snow crystals, this was the only 
way to study the mechanism of snow-crystal formation. 
Window Frost. On crisp winter mornings, in northern 
countries, various crystals of ice are observed on the 
