On the Habit of Snow Crystals Artificially Produced at Low

On the Habit of Snow Crystals Artificially Produced

at Low Pressures*

By T. Kobayashi

Institute of Low Temperature Science, Hokkaido University, Sapporo, Japan

(Manuscript received 8 Aug. 1958)

Abstract

A series of artificial snow-making experiment was carried out in the air at low pres-sures, and the relation between crystal forms and ambient temperature and pressure as represented by the Ta -p diagram (Fig. 9) was established. It was found that solid hex-

, agonal columns are formed at pressures lower than 70 mmHg, which is to be attributed to

the slow rate of growth, that is, very slight supersaturation of the ambient vapour. The

mode of growth at low pressure may probably be considered to have the same characteris-

tics as the growth under quasi-equilibrium condition.

By the aid of the results obtained from the present and previous experiments, we

obtain the following scheme as to the snow crystal habit:

1. Introduction

We carried out a series of experiments on

artificial snow crystals in aerosol-free air and

concluded in the previous paper1 that the

snow crystal habit, in particular, whether a

crystal develops as a prismatic column or a

plate, is primarily determined by the tempera-ture. The manner in which the crystal habit

varies with temperature is represented in the

following scheme :

The direction of preferred growth is de-

finitely determined by the temperature of the

* Contribution No . 459 from the Institute of

Low Temperature Science,

ambient air where the crystals grow. These changes in crystal habit with temperature are

very similar to those observed in the experi-

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194 Journ.Met.Soc.Japan,Vol.36,No.5,1958

ments conducted by Nakaya2), auf m Kampe et a1.3) and Shaw and Mason.4) Recently Mason5) and Hallett carried out a new ex-

periment by the use of a diffusion chamber, and arrived at the same result as ours.

This result is at variance with the sugges-tion made by Marshall and Langleben6) that the crystal habit is principally controlled by the excess of the ambient vapour density over that at equilibrium with the ice crystal at its own temperature. There is consider-able difference between the critical values of the vapour-density excess required by the hypotheses of Marshall and Langleben so as to define each crystal-type domain and the ones which were obtained from our experiments

(cf. Fig. 6 in our previous paper1)). This discrepancy, however, does not mean

that Marshall-Langleben's theory should be wholly discarded : For instance, as is well affirmed, in the temperature range from -12* to -18* , dendritic crystals develop from the corners of a hexagonal plate, pro-vided the ambient vapour density excess is sufficiently large, and such a change in

growth type may well be explained by the mode of the diffusion field of water vapour around the crystal as Marshall and Langleben suggested.

Thus, it becomes desirable to investigate to what extent Marshall-Langleben's theory is applicable. Let it be assumed that the type of growth is closely connected with the rate of growth, or with D*, where D denotes the diffusivity of water vapour in air and * is the excess of the ambient vapour density. Then it may be expected that, in the air at low pressures or in the gases where the dif-fusion velocity of water vapour molecules is different from that in atmospheric air, some different change in growth type will take

place. In fact, Isono et al,7) studied the mode of growth of ice crystals in the atmos-

pheres of hydrogen and carbon dioxide; they attributed the modification of the ice crystal habit in hydrogen to the large diffu-sion coefficient of water vapour in hydrogen.* It has also been found that organic and in-organic vapours modify the ice crystal habit

* Whether their interpretation is correct or not

will be discussed in section 4,

(Schaefer8), Vonnegut9), Nakaya10), Kobaya-shil),11) and Isono and Ono12)). This effect, however, is very probably due to the adsorp-tion of molecules of vapours on particular faces of an ice crystal. Therefore, in order to study the effect of D (as well as of *) on the crystal habit, it is better to perform the experiments in the air at low pressures ex-cluding the effect of foreign molecules.

In this paper, the experiments carried out in the air by varying the pressure from 10-2 mmHg up to 1 atm. are described in detail and the accompanying changes in snow-crystal habit are discussed.

2. Apparatus

The whole apparatus used in the experi-ment is shown in Fig. 1 and Photo. 1. Two types of snow-making chamber were used, i.e., a diffusion type (see Fig. 1) and convec-tion type (Fig. 2). They are constructed of a glass jar covered with thermal insulator and a brass box containing a cooling coil (Photo. 2). The brass box is immersed in a cold brine bath, and the brine is circulated through the cooling coil with the aid of a gear pump. The temperature of the brine bath is maintained at any desired tempera-ture down to -40* by the aid of a 1/4 H.P. refrigerating machine charged with Freon 22. The glass jar having a pair of windows with plane-parallel glass plates is placed on the upper brim of the brass box, the sealing being secured by the use of a silicone rubber packing and D. C. silicone high vacuum grease.* Prior to the starting of the experiment,

fine filaments on which snow crystals are to be produced are put into the chamber through the observing window. As the filament serves a rabbit hair or a methacrylic-acid-ester-resin filament spattered with AgI smoke particles which behave as active ice-forming nuclei. The latter filament was made by stretching Methalack lacquer and wound on a thin silver wire frame several turns at a few mm intervals; this was then exposed to

* The vapour pressure of the grease is indicat-

ed to be lower than 10-6 mmHg, and the influence

of the vapour upon the snow crystal growth has

been found to be completely negatives

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On the Habit of Snow Crystals Artificially Produced at Low Pressures 195

Fig. 1. Apparatus involving the chamber of diffusion type.

Photo. 1. The apparatus used in the experiments,

Photo. 2. 'l'he snow-making chamber: glass jar (mid die), the cooling coil for the diffusion chamber

(left), and the cooling coil for the convection chamber (rieht).

Fig. 2. The Chamber of convection type .


AgI smoke generated within a brown-coloured

glass desiccator immediately before the ex-perimental use. The filament was located near the same level as the center of the observing window and 5 cm distant from the inner wall.

The temperature of the ambient air Ta was measured by means of a fine thermistor the tip of which was set up near the filament.

After the chamber was evacuated by the aid of a gas-ballast type vacuum pump, the experiment was started. For observing the

growing process of the crystal, a camera pro-vided with an extra-long extension tube was used (magnification at the surface of film : 6.3*).

3. Experimental

The experiments carried out are divided into two series according to the main fea-tures of the apparatus and experimental pro-cedures as described in the followings :

i) The growth of ice crystals in the air at constant low pressure by means of the

chamber of diffusion type. The chamber used in this series of experi-

ment is shown in Fig. 1. The bottom part of the chamber was chilled down to about -30* by circulating the cold brine through

the cooling tube and the top was warmed up to +30* by electric heating. The vapour

produced by the "boiling" water in the re-servoir was introduced from the top of the chamber and transmitted downward through diffusion. At first the chamber was thorough-ly evacuated to 10-2 mmHg, and the tempera-ture Tw of the water in the reservoir was maintained nearly at 0*.

As soon as water vapour was introduced into the chamber, a number of isolated crys-tals appeared to grow in the form of short hexagonal column on the surface of the cool-ing tube. The crystals on the tube became larger and larger up to several mm in dia-meter in a short time, but none of the crys-tals appeared on the filament suspended in the chamber. Photos. 3 and 4 show the ice crystals grown up on the glass plate which was placed horizontally on the top of the cooling tube. The temperature of the glass surface was -26* and the total pressure,

after the supply of vapour, was 0.65 mmllg.

When the pressure of the air previously introduced into the chamber was increased up to several mmHg (not less than 6 mmHg under the present experimental conditions), the condensation of tiny dew droplets occur-red on the inner wall from the upper part of the chamber downward with a clear-cut horizontal front. When the front of the con-densation zone came down near the level at which the filament had been suspended, crys-tal germs began to manifest themselves on the filament and grew into solid hexagonal columns.

Many experiments were tried, evacuation and supply of water vapour being alternately repeated, while the air pressure in the cham-ber was increased one after another finally up to about 100 mmHg. For this purpose, fresh air was introduced, after thorough evac-uation, from out of doors into the chamber through a cotton-wool filter, a Millipore filter

(pore size of 0.8 ,u), and a cooling coil dipped in the freezing mixture.

In this series of experiments, the metha-crylic-acid-ester-resin filaments treated with AgI smoke were used, which proved to be more advantageous than the rabbit hair. The ice crystals which grew up on the filament are shown in Photos. 5, 6 and 7. The nucle-us substances on the filament most of which are likely to be AgI particles easily form the ice germs at a slight supersaturation with respect to ice, while it has been ascertained that on the rabbit hair crystal germs are pro-

duced only when the condition of supersatu-ration, which is above or slightly below sat-uration with respect to water, is attained.

Photo. 8 (aid) shows typical examples of the successive stages of crystal growth in dif-fusion chamber at low pressure. The crystal which is formed in the downward diffusion flow of the water vapour grows preferentially in upward direction, while the lower side of the crystal sublimates downward towards the lower-temperature sink (cooling tube) owing " to the temperature dependence of equilibrium vapour pressure. In Photo. 8 (c), the large crystal `looks as if it were raised upward and supported by a fine thread of ice; the ice crystal produced` by the sublimation of water

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On the Habit of Snow Crystals Artificially Produced at Low Pressufes 197

vapour from the mother crystal right above can also be seen in the picture. Since the filament was set up about 2 cm above the cooling tube, there must have existed a consi-derably steep gradient of temperature. Photo. 8 (d) shows that all of the crystals stand on one or more fine legs assuming as a whole a fantastic shape. It may be an in-teresting problem to study the structure of such thread-like legs. It is to be noted that the lower the pressure in the chamber, the more marked is the tendency to formation of such an odd shape of crystal.

At pressures lower than ca. 70 mmHg, the only crystal form that appeared was the solid hexagonal columns; skeleton structure and dendritic growth of ice crystal have never been observed. This proved to be the case for any temperature down to -30*. The skeleton with hollows at both basal planes were usually observed at pressures higher than ca. 70 mmHg (Photo. 9).

From the photomicrographic data of the

growing process of solid columns, the limit-ing habit * defined by Mason4) and the rate of growth was 'calculated. It was found that ['given by

where c and a are respectively the principal and the secondary axes, is scattered around the average value which is nearly equal to unity, but shows no systematic change with varying temperature and pressure. It may

probably be due to a certain fluctuation of supersaturation around the crystal.

Since the crystals produced at pressures below ca. 70 mmHg surely belong to solid hexagonal columns (free of cavity or hollow), their masses can easily be calculated if both the major and minor axes are measured (on the assumption that the density of ice crystal is 0.92). As the major and minor axes of the crystal observed are nearly equal in size, successive stages of a growing crystal may well be represented, in the first order of approximation, by those of a growing sphere of ice with equal mass. In Fig. 3, the square of radius of the equivalent sphere is plotted against time, the pressure being taken as a

parameter. The dashed line in the figure re-

presents the growth of an ice sphere in the air saturated with respect to water at -15* under atmospheric pressure (D=0.199 cm2/sec;

*p*=0.1676 g/m3 (after Marshall and Langle-ben6))). Fig. 3 shows clearly that the rate of growth, dr2/dt, which is proportional to D** p, has a tendency to become smaller with

Fig. 3. The rate of growth of equivalent sphere of ice growing at low pressures.

decreasing total pressure p. This means that the decrease of ** is more rapid than the increase of D, which is inversely propor-

tional to p, hence that a higher degree of supersaturation over ice cannot be attained at low pressure under the experimental condi-tions mentioned above.

It may be considered, therefore, that it is the slow rate of growth (D**), i.e., very slight supersaturation of the ambient vapour**, that plays a principal role in the formation of the solid columns at lower pressure.

* The excess of the ambient vapour density

over that at the surface of growing ice crystal which is assumed to be at equilibrium with ice at slightly higher temperature than the ambient, T+*T; **=*aT-*i(T+ *T).

** In the case of 9 mmHg ( -13 ~9**) in Fig . 3, for example, the degree of supersaturation is estimated to be about 100.06% with respect to ice.

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Fig. 4. The conditions under which the ice crystals shown in Photo. 10 grew.

Fig. 5. The conditions under which the crystals shown in

Photo. 11 grew.

Fig. 6. Change in growth

type shown in Photo.

11, as plotted on the

Ta-p diagram.

Fig. 7. The conditions under which the crystals shown in

Photo, 12 grew.

Fig. 8. Change in growth

type shown in Photo. 12, as

plotted on the Ta - p dia-

gram.

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ii) The change in growth type of crystal under varying ambient pressure.

After crystal germs had ap-peared on the filaments at low pressure, the pressure was grad-ually recovered up to 1 atm. by the same procedures as mention-ed above. As long as the diffu-sion chamber was used, however, neither plate nor dendritic growth was observed even at -15*, but only the columns continued to grow until the pressure reached 1 atm. (Photo. 10 (a~d) and Fig. 4). This may be due to insuf-ficient supply of water vapour. For this reason, the chamber was replaced by a chamber of con-vection type which contains the water reservoir at the bottom (Fig. 2). At the beginning, a rabbit hair* was set in the cham-ber at ordinary pressure, and the germs produced on the hair were made to grow into crystal forms characteristically determined by the ambient temperature and

Fig. 9. Ta - p diagram, showing the relation between the crystal

form, the ambient temperature Ta, and the pressure p.

supersaturation. Then the chamber was care-

fully evacuated down to 10~20 mmHg. The crystals which had grown up, e.g., in the

dendritic form, now turned into thick hex-agonal plates having no surface structure, and

continued to grow thicker and thicker. The clean air was then introduced anew into the

chamber and the pressure was gradually re-covered up to 1 atm. When it became near

300 mmHg, the sector or the dendritic branches began to develop again from the corner of

the thick plate passing through the transition state of scroll, provided the temperature of

water in the reservoir was properly regulated.

Photos. 11 and 12 illustrate the successive

stages of change in growth type of crystals , and Figs. 5 and 7 show the change of condi-

* In this series of experiments, the filament

treated with AgI smoke was found not to be ap-

propriate for the object of making a few isolated germs grow up to seizable dimension in proper shape, because of too large a number of AgI nu-clei spattered on the filament.

tions--ambient temperature Ta, temperature of water in the reservoir Tw and ambient

pressure p - during each course of crystal growth. The change of growth type of crys-tals is represented by Ta-p diagram in Figs. 6 and 8. As the result of ten series of experiments, the relation between the crystal form, Ta, and p plotted on the T a - p dia-

gram is given in Fig. 9. Here the results obtained by the experiment carried out at constant pressure by means of the chamber of diffusion type are also included.

As seen from the figure, various crystal types (column, sheath, scroll, sector, dendrit-ic form, and needle) are distributed into four regions in the Ta-p diagram (region III for the sector and region IV for the dendritic

growth overlap each other). a) Column : Columns are formed, as pre-

viously described, at pressures lower than about 100 mmHg, at any temperature down to -30*. They are confined to region I in the Ta-p diagram. At pressures below 70

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200 Journ.Met.Soc,Japan,Vol.36,No.5,1958

mmHg columns generally grow free of cavity or hollow, while above 70 mmHg skeleton structures often make their appearance. If sector or dendritic crystals formed at ordina-ry pressure are brought into region I, they

grow thicker and thicker to turn into thick plates with simple hexagonal branches. In Fig. 9 the thick plates thus formed are to be regarded as columns in consideration of their

growing process. b) Sector and dendritic growth : If Ta is

between -10* and -20*, sector and den-dritic crystals begin to develop when the

pressure exceeds 300 mmHg. Region III for sector and region IV for dendritic growth cannot be separated in the Ta-p diagram. But the condition of supersaturation is consid-erably different, i.e., higher degree of super-saturation is needed for dendritic growth than for sector. In the case of dendritic

growth, there were usually observed a number of water droplets condensed on the hair, which means that the necessary condition for den-dritic development is that a certain degree of supersaturation with respect to water must exist around the growing crystal.

c) Sheath and scroll: As an extreme case of skeleton structure, there is a type shaped like a column but composed only of its side

planes (1010) (Fig. 10). We call it a scroll type and the one whose side is extremely

Fig. 10. Model of scroll (left) and a sheath

(right).

extended in the direction of c-axis a sheath type (Photos. 13 and 14). The scroll develop-ed at the transition stage from the skeleton column to sector or dendritic form assumes a cup-like shape. These types are scattered in Ta-p diagram within region II, which surrounds region III.

Short dashed lines drawn within and near region II represent the lower limit of the pres-sure above which water droplets were observ-ed to form on the hair. This implies that for the growth of sheath or scroll to occur the supersaturation must be above or near water equilibrium and that the condition can barely be attained before the pressure recov-ers up to ca. 200 mmHg.

d) Needle : At ordinary pressure, needles grow in the narrow temperature range between -4* and -6* . When the pressure decreases down to 30 mmHg, needles lose their thin tip structure and turn into column-like shape. In some cases, when the pressure was reduc-ed to ca. 100 mmHg, thick plates happened to develop at the end of the needles. Our ex-periment so far is not yet sufficient to tell positively on this point.

The general aspect of Ta-p diagram (Fig. 9) which represents the crystal forms as a function of Ta and p has a certain resem-blance to that of Ta-s diagram as regards the snow crystal formation in aerosol-free air at ordinary pressure (cf. Fig. 4 in the pre-vious papery1)). Now in view of the fact that the lowering of the pressure p in the present experiment qualitatively means the lowering of the degree of supersaturation s, region I in the Ta-p diagram may probably make up the deficiency in the data for the region of very low supersaturation on the Ta -s dia-gram in the previous paper.

4. Discussion

i) On the ice-crystal formation at low pressure.

With the object of examining the factors which determine the habit of the ice crystal, Isono et al.7) made a series of experiments in the atmosphere of hydrogen and carbon di-oxide containing the water vapour saturated with respect to water. They found that in hydrogen gas the growth velocities in principal and lateral directions are nearly equal at any temperature, but in carbon dioxide the mode of growth is rather similar to that in ordinary air; they attributed the cause of this diversi-ty to the difference in the coefficient of dif-fusion of water vapour in these gases. In hydrogen water vapour diffuses 3.4 times fast-

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er than in air, while in carbon dioxide the diffusion coefficient is 0.7 times that in air. Lately Isonol3) conducted the expet .iment also in oxygen, nitrogen and air at low pressure

(ca. 30 mb.) and reconfirmed the above con-clusion. But grave doubt exists as to whether in their experiment it is reasonable to infer the saturation of the ambient vapour with respect to water only from the existence of water cloud. As described in this paper, it should be noticed that in the air at low pressure such as 20 mmHg, the degree of supersatura-tion may not exceed 100.3% with respect to ice, as is the case with our observation. It must also be taken into consideration that in hydrogen the heat conductivity is much larger than in air though it is independent of

pressure except for extremely low pressure. In our experiments, we confirmed as shown

in Fig. 3, that the rate of growth (D**) con-siderably diminishes with decreasing pressure. It may therefore be apprehended that the

growth of ice crystals in solid short columns at low pressure is to be regarded as the growth in quasi-equilibrium condition. This means that the number of molecules leaving the crystal and the number of molecules fall-ing upon the crystal are large compared with the number of molecules permanently captured by the crystal as its constituents.

Wo1ff14), Krastanov15) and Higuchi16) inves-tigated the equilibrium form of ice crys-tals and arrived at the same conclusion that the ratio of the c-axis to a-axis should be 0.82 for the crystal consisting of the basal

plane (0001) and the prismatic plane (1010), when only the interaction between the first nearest oxygen neighbours are taken into ac-count. This conclusion seems to be in har-mony with our observational result that c/a is nearly equal to 1.

Wolff and Krastanov also concluded that if account is taken of the second nearest oxygen

neighbours, the additional (1011), (1120) and

(1012) planes should appear at low supersa-turation (Fig. 11). In the course of our ex-

periments at low pressures, there were some-times observed crystals with the faces which

might belong to the pyramidal (1011) faces or the higher indec faces, Photo. 15 shows an

Fig. 11. Model of a solid column (left) and a hexagonal column with pyramidal faces (right).

example of the hexagonal column with pyra-midal faces which grew at -24*, while the

pressure was being increased from 20 to 200 mmHg. At the initial stages of growing pro-cess we came across the crystals apparently belonging to the rhombohedral system as shown in Photos. 16 and 17. Nakaya also obtained such kind of crystals in his ex-

periment17~ but the detail has been left un-known. It is generally supposed that, when the

surface diffusion of the molecules in the

growing crystal plane becomes insufficient on account of too great a number of condensing molecules at higher supersaturation or of a certain poisoning of the crystal plane through adsorption of foreign molecules, the skeleton or the dendritic structure of the crystal is likely to appear. The surface diffusion be-comes then incapable of distributing the mole-cules to their proper positions in the lattice of the crystal face, so that the molecules stick where they arrive, that is, preferably at edges or corners. Our observational re-sults are in good accord with this supposi-tion. Thus it may be concluded that the for-mation of the solid short columns at low pres-sure is caused not by the augmented diffusion coefficient D but by the slow rate of growth owing to very small supersaturation s.

ii) On the snow crystal habit.

As already reported in our previous paper, we examined the relation between the snow crystal form, Ta., and s by means of a diffu-sion chamber from which the cloud droplets had been removed. The ambient vapour density was calculated from the rate of change in diameter of a supercooled drop-let18),19). The result is reproduced in Fig. 12, where the dashed curves indicate the bound-

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aries which were experimentally determined by Nakaya. If allowances are made for the circumstances that the degree of supersatura-tion obtained by Nakaya and Hanajima20) might have been underestimated owing to the error inherent to their method of measure-ment and that our data obtained from the experiment at low pressure may make up the deficiency in the region of low supersatura-tion, a modified set of boundaries (solid curves), which satisfactorily explains , the change of snow crystal habit, are obtained as shown in Fig. 12. As pointed out in the

previous paper, the supersaturation s can easily be transformed into the excess of the ambient vapour density * in the cloud-free

atmosphere. We can thus obtain Fig. 13, where the ordinate represents ** in place of s in Fig. 12.

From the result in Fig. 13, we may probab-ly draw the following conclusions as to the snow crystal habit in the diffusion field of water vapour.

1. At very low supersaturation crystals

grow in solid hexagonal column at any tem-perature down to -30** (may be, still lower). This type of growth may be considered to be of the same nature as that in quasi-equili-brium condition.

2. The principal factor controlling the basic crystal habit is the temperature of the air where the crystal grows. The tendency to the preferred growth along the principal axis as prismatic crystal or to the preferred devel-opment of the prism faces as plate is a function of Ta, and a remarkable sequence of transforma-

Fig. 12. A revised Ta-s diagram, showing the snow crystal habit in relation to the ambient

temperature Ta and supersaturation s. Nakaya's boundaries (dashed . curves) are also plotted in

the figure,

Fig. 13. The Ta - ** diagram, which clearly il- lustrates the temperature dependency of the

direction of preferred growth and the transition into the edge and corner growth with

increasing excess of ambient vapour density 4p in each temperature domain.

tion, plates-prisms-plates-prisms, occurs as

the temperature is lowered from 0* to -30*

or more. This means that the growth rate of each prism and basal plane, which depends

upon crystallization velocity, diffusion coeffi-

cient of water vapour, and thickness of dif-fusion layer, are likely to be primarily repre-

sented as a function of Ta. 3. The changes in the excess of ambient

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On the Habit of Snow Crystals Aartificially Produced at Low Pressures 203

vapour density do not cause the change in basic crystal habit as between prism and

plate, but govern the development of various secondary features such as sheath or dendri-tic growth as well as the rate of growth.

In the temperature range from -10** to -20** , where the crystals have the tendency to the preferred growth along the lateral direc-tion, i.e., the rate of growth of prism faces is larger than that of basal faces, the change in the growth type, column-plate-dendritic growth, occurs with increasing ambient vapour ex-cess. In the regions from -4** to -10** and below -20**, where the crystal has the tendency to the preferred growth along the c-axis, i.e., the growth rate of basal faces is larger than that of prism faces, the change, column-sheath (hollow column)-needle, oc-curs with increasing ambient vapour excess. As was fully argued by Marshall and Langle-ben6) it is suggested that the variety in the mode of crystal development can be ad-equately explained by means of the vapour density excess provided a non-uniform vapour density at the crystal surface is assumed. According to their argument, changes in crystal type occur first in the growth from edges and secondarily in the growth from corners, when the excess of va-

pour density is large enough to overcome the inhibition which must exist inasmuch as the saturation vapour density is highest at the corners and greater at the edges than at the flat faces of the crystal.

If the ambient vapour-density excess is small, both edge and corner growths are in-hibited, and the crystal grows outward from its faces as a column. If the excess is suf-ficient to overcome the inhibition of edge

growth, but not of corner growth, the crys-tal grows into a plate (sector), its thickness increasing only slowly, in the temperature range favourable for the lateral growth , and into a sheath (scroll or cup) in the temperature range favourable for c-axis growth (see Fig. 14 and Photo. 18). If the excess is still

greater, and sufficient to overcome the inhibi-tion of corner growth, the crystal grows out-ward from its corner into a dendritic form or into a needle according as the temperature is favourable for the growth of lateral (a-axis) or principal direction.

Fig. 14. Lines of constant vapour density and flow favourable for the formation of a sheath

crystal, i.e., for the edge growth in the direction of c-axis.

As far as Nakaya's T a-s diagram is con-cerned, it seems that the frequency of ap-

pearance of scroll or cup is rather small (sheath is omitted in his diagram). In our snow-making experiment, however, sheath is the very common shape observed. Hollow

prisms observed in Mason and Hallett's ex-periment5~ may probably belong to this type of crystal. As described in our previous

paper, this may be explained by supposing that the presence of cloud droplets (as in the case of Nakaya's experiment) prevents such a large excess of true vapour density as to overcome the inhibition at the edge.

As for the dendritic crystal, almost all the crystals produced in our present and previous experiments belong to the "sector" but not the true dendrite according to Nakaya's classification. The growth of this type of crystal in cloud-free air may well be explain-ed by assuming the corner growth through diffusion of vapour alone (Photos. 19 and 20).

In the temperature region above -4*, we usually observed irregular assemblages of columnar crystals. There were a few cases, however, where thin plates were observed to develop at the end of the columnar crystals. In the region close to 0* dendritic crystals were also observed. We shall not be able to say anything definite about the crystal formation in this region, until more detailed data come out available.

Acknowledgement

The author wishes to express his hearty thanks to Prof. Nakaya for his kind advices and encouragements throughout the course of this investigation. This research was aided

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204 J0urn.Met.Soc.Japan,Vol.36,No.3,1958

by grant from the Hokkaido Electric Power Co., for which the author also wishes to express his gratitude. A part of the expense of the research was defrayed from the Fund for Scientific Research of Educational Ministry of

Japan.

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phare, Met. Zs., 60, 15-26. 16. Higuchi, K., 1958: Presented at the Meeting

of Met. Soc. Japan. May, 1958. 17. Nakaya, U., 1954: Reference (2), 229-231. 18. Marshall, J. S. and K. L. S. Gunn, 1957: A

first experiment on snow-crystal growth. Artificial Stimulation of Rain. 340-346.

19. Kobayashi, T., 1957: Experimental researches on the snow crystal habit and growth. Teion-

Kagaku (Low Temp. Sci.), A, 16, 1-26 (in

Japanese). 20. Hanajima, M., 1949: Supplementary remarks

on the conditions of formation of artificial snow crystals. Teion-Kagaku (Low Temp.

Sci.) 2, 23-29 (in Japanese).

減圧大気中における雪の結晶習性について

､小林禎作

雪の結晶習性が,主として結晶の成長する時の温度によつて支配されることは,前報1)に述べた通りである。一

方,扇形から樹枝への変**にみられるように,成長型の変化に対する結晶周囲の過飽和度,或いは水蒸気の拡散場

の影響も見逃せない。水蒸気の拡散係数は大気の全圧に逆比例するので,減圧大気中で人工雪実験を行い,温度,

気圧と結晶形及び結晶成長速度との関係を調べた。気圧70mmHg以下では-30*までのあらゆる温度範囲で無

垢の六角柱が,それ以上の気圧では骸晶,更に300mmHgを超える圧力の下では-10～-20*の間で,扇形或

いは樹枝状成長がみられた(Fig.9)。

無垢の六角柱状結晶についてその成長速度を調べてみると,我々の行つた実験条件では低圧になる程,成長速度

つまりD**(D:水蒸気の拡散係数, **:結晶周囲と結晶表面との間の水蒸気密度差)が小さくなる傾向にあり

(Fig.3),極:く低い気圧の下での角柱状結晶の成長は準平衡状態での成長とみなされよう。

この実験と前報の実験結果とを併せ考えると,所謂"Ta-sダイヤグラムは"Fig.12のように修正され,雪の

結晶習性としては次のように結論される。結晶が主軸方向に角柱状に伸びるか,主軸に垂直な面に角板状に成長す

るかは温度によって決定される。次に結晶は周囲の水蒸気過飽和度によって二次的な成長の型を示し,-10～

-20*の間では,過飽和度が大きくなるにつれて角柱-骸晶-扇形-樹枝という変化を,-4～-10**及び

-20*以の温度範囲では角柱-サヤ-針の成長型の変化を表わす。

-38-


Photo.3. *52 Photo.4. *34

Photos.3and4.Ice crystals grown up on a glass plate;Ta=-26**,p=0.65mmHg.

Photo.5.Ta=-8.8**,p=31mmHg,*21 Photo.6.Ta=-18.7**,p=511mmHg.*21

Photo. 7. Ta= -13.8**, p=41 mmHg, *33

Photos. 5, 6 and 7. Solid hexagonal columns formed

on the methacrylic-acid-ester-resin filament spat-

tered with AgI smoke particles.

* 33

Photo. 9. Skeleton crystals observed at the

pressure of ca. 72 mmHg.

-39-

206 Journ.Met.Soc.Japan,Vol.36,No,5,1958

photo.8.a) *26 b)

C) d)

Photo.8.Successive stages of crystal formation of odd shape at low pressure;T=-15**-12**,

p=38mmHg.

Photo.10.a) *33 b) Photo.13. *33

c) d)

Photo. 10. Successive stages of crystal formation under varying conditions as shown in Fig. 4 (observed in the chamber of

diffusion type).Photo. 14, * 10 Photos. 13 and 14. Sheath crystal.

-40 -


Photo.11.a) b) c)

d) e) f )

Photo. 11. Successive stages of crystal formation under varying conditions as shown in Fig. 5 (observed in the chamber of convection type).

Photo. 12. a) b) c)

d) e) f)

Photo. 12. Successive stages of crystal formation under varying conditions as shown in Fig . 7 (observed in the chamber of convection type).

- 41-


*51

Photo.15.Columnwithpyramidal

faces.

Photo.16.T=-15.2**,*38

p=38mmHgPhoto.17.T=-16.O**,*38p=72mmHg.

Photos. 16 and 17. The ice crystal apparently belonging to the

rhombohedral system.

Photo. 18. Multi-layer structure of sheath crystal.

Photo.19. a) *23 b) p=214 mmHg･ c) p=285 mmHg.

p=178mmHg.

d) T=-16**, P=310 mmHg. *23Photo 19. Successive stages of dendritic growth from the corners of a sector｡

Photo.20. Dendritic crystals. *27

Ta=-14.7**, p=1atm.

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