- Email: [email protected]
Cubic structure models at the junctions in polycrystalline snow crystals
Journal of Crystal Growth 35 (1976) 262--268 © North-Uollancl Publishing Company
CUBIC STRUCTURE MODELS AT THE JUNCTIONS IN POLYCRYSTALLINE SNOW CRYSTALS T. KOBAYASHI, Y. FURUKAWA aiid T. TAKAHASHI Institute of Lu w Temperature Science, Hokkaido Un il’ersitv, Sap poro, Japan
and H. UYFDA Department of Geophysics, Ilokkaido University, Sapporo, Japan Received 2 June 1976
This paper proposes a twinning model for ice crystals which has cubic structure at the junction of two coniponents with an aim to explain the frequently observed angle 700 at which the c-axes of the two components intersect each other, as found in the plane assemblages of the spatial type in nature. The paper further proposes a modified model on the hypothesis that the configuration of the foregoing model repeats itself; this model has been tested by comparing the c-axis angles of the two component crystals between those based on the model and those found in snow crystals in nature; this comparison is likely to offer a qualitative explanation of the shapes of frequency histograms which appear in the plane assemblage of the radiating type and in the combination of the bullet type crystals in nature.
called. Buerger [31stated: if the structure is of such a nature that it permits a continuation of itself in alternative twin junction configuration without involving violation of immediate coordination requirements of its atoms, the junction has low energy and the twin is energetically possible. This will be a leading principle in considering the polycrystalline structures of snow crystals in this paper. If we consider something apart from the GCSL theory fully described in the previous paper [2], it may be possible to propose more continuous structures in alternative twin junction configuration without violating the immediate coordination recluirements.
1. Introduction Measurements of the c-axes angle between each component have been made for the plane assemblages in the radiating and the spatial type of snow crystals by Lee [1], tJyeda and the present authors~it is interesting and suggestive to note that the distribution of the angle is predominantly concentrated at 700 and less predominantly at 550 and 40° (See fig. 3). The models of K( 3034)) and ((3038)) rotation twins may be possible ones to explain the angle of 70°in view of the GCSL theory proposed by Kobayashi et a!. [2], because the bond niisorientation, ~a’ equals zero for the twinning relation of both models and the reciprocal densities of coincidence sites, Xe, equal 3.67 and 5.18 respectively, which are small. The angles of 550 and 40°may be explained by the GCSL theory as well. 13a and Xe However, a judgement on whether values of are small or large is rather ambiguous and cannot be formed by other ways than examining frequencies of such snow crystals appearing in nature. In considering the twinning structures of snow crystals Buerger’s continuation principle should now be re-
2. Structure models The ice crystal is stable in the hexagonal tridymitetype structure at a normal pressure over a wide range of temperatures down to -—80°C.In this structure each oxygeh atom is surrounded near/v tetrahedrally by four other oxygen atorns~that is, the exact nieasurements indicate that at 0°Cthe length of the O—~Obond paral262
T Kobayashi et al.
/ Cubic Structure models at junctions in
Fig. 1. The rn—c—c—-rn type ofjunction giving 1100 as an an angle between c 1- and c11-axis.
lel to the c-axis, which is mirror-symmetric, is about 0.01 A shorter by 0.4% than the length of the oblique bonds, which are centro-symmetric. This may also involve slight distortions of the tetrahedral bond angles. However, the difference of the length between the two kinds of 0—0 bonds at 0°Capparently tends to equalize at 180°C[4]. Neglecting a slight deviation from an exact relationship of the tetrahedral environment, it may be possible that any of the three oblique bonds can behave as a Caxis of a second component of the crystal forming a continuous structure in an alternative twin junction. It may then be considered that the angle of 70°,frequently observed as the c-axes angle between each component, is related to 110°as the supplementary angle, which is very close to the tetrahedral angle 109°28’. Let us now construct a structure model of the ice crystal in which components I and II have such a relation that the c-a~isof component II is parallel to one of the oblique 0—0 bonds of component I, thereby the c-axes angle, between each component being 110°,as illustrated in fig. 1. In doing so, three requirements must hold: (1) a tetrahedral arrangement for the position of each 0 atom, (2) a mirror-symmetric arrangement of every 0—0 bond that is parallel to the c-axis (m-bond). (3) a centro-symmetric arrangement of every 0—0 bond that is parallel to the oblique axis (c-bond). As shown in fig. 1, the bonds 01—02 and 04—05 behave each as a c-axis for each component (c1- and —
~,
snow crystals
263
Fig. 2. A structure model illustrating a combination of two rn—3c—m type twins which gives cs 111201.
=
1100; projected along
c11-axis for components I and II, respectively), and therefore they are mirror-symmetric (m-bond). The bonds 02—03 and 03—04 must then be centro-symmetric (c-bond), because they compose an oblique bond in each of components land II, respectively. Thus two components I and II are connected by two successive c-bonds in order that c1 and c11-axes make angle of 110°,which may be called the m—c—c—rn type of junction. This does mean that a stacking fault is introduced vertically to the c1-axis between 03 and 04 positions in the original hexagonal component I, while another stacking fault is introduced vertically to the c11-axis between 02 and 03 positions in the second component II. In general, any number of layers of the stacking fault can be introduced for each c-axis direction and the number of the c-bonds connecting components I and II is 2n, corresponding to the number n of layers of the stacking fault introduced at the junction. (The number n may not always be the same for both the c1- and c11-axis directions.) On the basis of the above consideration, it may be easily understood that the rn—c—rn type of junction composes a single crystalline ice structure and the rn—c—c—c—rn type (rn—3c—m, for short) of junction gives a [1120] rotation twin structure, which has been called “twin prism” [5]. A junction involving any odd number of the c-bond larger than three for connecting the two hexagonal components produces simply a repetition of the [1120] rotation twin relation. Fig. 2 shows one of the simplest models which illu-
264
T. Kohayashi et al.
/ Cubic structure models at junctions in snow crystals
strates the rn—c--c—rn type of structure in making the angle 110°as ~, which is actually composed of a cornhination of two m—3c-—m type twins. Each pair of components 1--I’ and lI--U’ is in the relation of the [1120] rotation twin; the entire crystal composes a kind of penetration twin. There can be no violation of immediate coordination requirements excepting a fault layer in stacking order at the coiilpOSitiOfl plane. A more complicated structure model giving 110°as the angle o has been illustrated in the previous paper [6], which represents a combination of the m—3c—-rn and the rn—-Sc—rn type twins, These structure models suggest a formation of an ice germ in a cubic system which is of the metastable structure in ice [7] and a subsequent growth into a stable hexagonal system. This might be a probable process when ice crystals are nucleated at a high degree of supersaturation (supersaturation twin as suggested by Buerger [3]) and at low temperatures, or when a supercooled cloud droplet freezes in contact with a snow crystal at low temperatures. It may be summarized that an rn—c-—c--ill type of junction gives rise to a change of 70°(=180° — 110°) in the c-axis direction for connecting two hexagonal
80-
components. Then, as the next step of further application of this concept, two successive occurrences of the tn--c—c—rn junction may be considered. Thus au ni-— c_c_m_c*_c~~mtype of junction gives rise to a change of 40° ( 110°+ 110° --- 180°)in the c-axis direction as the result, when the c~ -bond of the second rn~_c*--c--rn junction is oriented on one and the same plane of the first m—c---c---m junction. But the c*.bond in the second junction can be oriented, in an equal probability, in either of two other directions of the three oblique bond orientations. In such case the resultant change in the c-axis direction is equal as to either of the directions and is approximately 56°. As a further step, if three successive rn--c—c -in junctions are supposed to occur, the resultant change in the c-axis direction may he 3 1.5°,88.0°,66.0°and 21.5°. In the growth of an ice crystal, a transitioun from a cubic to a hexagonal system may be probable, but a reverse one from a hexagonal to a cubic system may be less probable. Accordingly, two or more numbers of the successive occurrences of rn-—c--c--rn junction may become less and less probable as the number increases.
/~
~
TOTAL NUMBER ___
60
iIbI~”
PRESENT AUTHORS 347 LEE 131 UVEDA -
175
-
-.
U
-
z
LU
~20
0
i
10
~
20 30 40 50 60 70 ANGLES BETWEEN C-AXES (DEGREE)
80
.
90
T. Kobayas/ui ci al.
/ Cubic structure models at junctions in snow
crystals
265
b) 100EJ
543 241
80—
189
LU
z >60C-)
z
LU
c~ LU
20
ib
0
2b
~
...-:.
40
60
ANGLES BETWEEN C-AXES (DEGREE)
c) ~B6
~_
6—
~i~~~:-j’ ~
ib ~b
—
3’0~ ~
~
70
80
90
ANGLES BETWEEN C-AXES (DEGREE) Fig. 3. Frequency histograms of angles between the c-axes of each component, obtained by Lee, Uyeda and the present authors: (a) for the plane assemblage crystals in the spatial type; (b) for tile plane assemblage crystals in the radiating type; (c) for the combination of bullets.
T. Kobayashi et a!. / Cubic structure models at junctions in snow crystals
266
3. Discussions: comparison of observational results
with the models It is clearly indicated by the frequency histograms of ~, the angles between the c-axes of each component, obtained by Lee [1] and Uyeda [8] that a high peak appears singly at 70°for the plane assemblage crystals in a spatial type as shown in fig. 3a, while a predominant peak appears at 70°accompanied by less predominant peaks at 55°and 40° for the plane assemblage crystals in the radiating type, as shown in fig. 3b. Lee also confirmed that the a-axes of the secondary branches were always in parallel with those of the substrate crystals, which gives another evidence to support the present structural models as well as the GCSL models. Recently the present authors made the same measurements at Yukomanbetsu in central Hokkaido through a period from January 26 to March 10, 1976, and obtained the same results as Lee’s. These are also shown in fig. 3. Comparing the observational results by Lee, Uyeda and the present authors with the cubic structure models described above, the agreement is remarkably good for the angles s and for the relative frequency of their appearance for the plane assemblages in both the types. A probable explanation may be given as follows: since the secondary branches in the spatial type (fig. 4)
(
~,,)
-
)
.“~
—
ç
,
-
-
a
-
-
-
-
~-
-
_______ -~ --
Fig. 4. A plane assemblage crystal in the spatial type: (a) focused on the hexagonal base, (b) side view (x 32).
of the snow crystals may be initiated by the contacting of’ a cloud droplet onto a dendritic or a plate crystal, it may be considered that freezing of the droplet proceeds at a temperature range between —10°and 20°C which is amenable to the plate growth. The freezing temperature is rather high so that only the m c—c m type of junction may take place, giving a single predominant peak at 70° on the frequency histograms. The radiating type of the plane branches (fig. 5) may be initiated by the freezing of a cloud droplet by itself at temperatures even lower than —20°C as well as the temperature range described above, so that the rn—c—c—rn—c—c- rn type of junction may possibly take place, giving a predominant peak at 70° and less predominant peaks at 55° and 40°on the frequency histograms. As for crystals of the type of combination of bullets (figs. 6 and 3c), Lee. Uyeda and the present authors made the same measurement; the results of which are rather different for those obtained for the
plane assemblages; in their measurements peaks were found around 30°,90°,65°in addition to 70°,55° and 40°;the peaks at these angles appeared with nearly the same frequency. It is considered that this type of the crystals may be nucleated at temperatures much
T. Kobayashi Ct a!.
/ Cubic structure models at junctions in snow
crystals
267
a tig. 6. A combination of bullets (X 115).
[2]. He found two peaks on a frequency histogram, one at 70 again, invariable with the rates of cooling and the other at 20—30°,variable with the rates. It is
-
-
interesting to note that the former angle corresponds to the angle predicted by the rn—c c—rn type of twin junction. It may be considered that two sub-critical
sized ice-nuclei in a supercooled water drop are probably joined together in the rn—c—c m type of twin junction, which has low interfacial energy, and they, -
-
-
obtaining thus twice as large as a single nucleus in volume, may survive to exceed the critical size for a further growth. They grow as a twin when they are able to continue to grow further.
Fig. 5. A plane assemblage crystal in the radiating type; (a) focused on one of the hexagonal plates, (b).side view (X 50).
Acknowledgements
lower than 20°C,which is amenable to the prism growth so that the twinning may be formed in such complicated ways that the two or three successive repetitions of the cubic junction and/or the GCSL type of the configurations might possibly be involved in nearly the same extent as to form this type of the crystals. Uyeda recently measured the number of neighbouring crystals and the angles between the c-axes of neighbouring crystals when a water drop of 1.0—1.7 mm in diameter was frozen under controlled rates of cooling
Y. Mizuno for their cooperation in the period of snow crystal observations at Yukomanbetsu. This work was supported in part by the Scientific Research Fund of the Ministry of Education.
The authors wish to thank Dr. S. Suzuki and Miss
References Ill 121
C.W. Lee, J. Meteor. Soc. Japan 50 (1972) 171. T. Kobayashi, Y. Furukawa, K. Kikuchi and H. Uyeda, J. Crystal Growth 32 (1976) 233.
268
T Kobayazhl neiL
I OthIc structure models at/unction, In snow clystals
131
Mi. Buerget, Am. MIneralogist 30(1945)469. (4J DII. Lonsdale, Proc. Roy. Soc. (London) A247 (1958)
(51
424. T. Kobsyashi and T. Ohtake, J..Atmos. ScL 31(1974)
1377.
(6j T. Kobayashl, in: Proc. Intern. Conf. Cloud Phys., 1976 (In press). N.H. Fletcher, The Chemical Physics of Ice (Cambrklge Univ. Press., 1970) p. 271. t81 II. Uyoda, Master’s thesls(1975).
171
CUBIC STRUCTURE MODELS AT THE JUNCTIONS IN POLYCRYSTALLINE SNOW CRYSTALS T. KOBAYASHI, Y. FURUKAWA aiid T. TAKAHASHI Institute of Lu w Temperature Science, Hokkaido Un il’ersitv, Sap poro, Japan
and H. UYFDA Department of Geophysics, Ilokkaido University, Sapporo, Japan Received 2 June 1976
This paper proposes a twinning model for ice crystals which has cubic structure at the junction of two coniponents with an aim to explain the frequently observed angle 700 at which the c-axes of the two components intersect each other, as found in the plane assemblages of the spatial type in nature. The paper further proposes a modified model on the hypothesis that the configuration of the foregoing model repeats itself; this model has been tested by comparing the c-axis angles of the two component crystals between those based on the model and those found in snow crystals in nature; this comparison is likely to offer a qualitative explanation of the shapes of frequency histograms which appear in the plane assemblage of the radiating type and in the combination of the bullet type crystals in nature.
called. Buerger [31stated: if the structure is of such a nature that it permits a continuation of itself in alternative twin junction configuration without involving violation of immediate coordination requirements of its atoms, the junction has low energy and the twin is energetically possible. This will be a leading principle in considering the polycrystalline structures of snow crystals in this paper. If we consider something apart from the GCSL theory fully described in the previous paper [2], it may be possible to propose more continuous structures in alternative twin junction configuration without violating the immediate coordination recluirements.
1. Introduction Measurements of the c-axes angle between each component have been made for the plane assemblages in the radiating and the spatial type of snow crystals by Lee [1], tJyeda and the present authors~it is interesting and suggestive to note that the distribution of the angle is predominantly concentrated at 700 and less predominantly at 550 and 40° (See fig. 3). The models of K( 3034)) and ((3038)) rotation twins may be possible ones to explain the angle of 70°in view of the GCSL theory proposed by Kobayashi et a!. [2], because the bond niisorientation, ~a’ equals zero for the twinning relation of both models and the reciprocal densities of coincidence sites, Xe, equal 3.67 and 5.18 respectively, which are small. The angles of 550 and 40°may be explained by the GCSL theory as well. 13a and Xe However, a judgement on whether values of are small or large is rather ambiguous and cannot be formed by other ways than examining frequencies of such snow crystals appearing in nature. In considering the twinning structures of snow crystals Buerger’s continuation principle should now be re-
2. Structure models The ice crystal is stable in the hexagonal tridymitetype structure at a normal pressure over a wide range of temperatures down to -—80°C.In this structure each oxygeh atom is surrounded near/v tetrahedrally by four other oxygen atorns~that is, the exact nieasurements indicate that at 0°Cthe length of the O—~Obond paral262
T Kobayashi et al.
/ Cubic Structure models at junctions in
Fig. 1. The rn—c—c—-rn type ofjunction giving 1100 as an an angle between c 1- and c11-axis.
lel to the c-axis, which is mirror-symmetric, is about 0.01 A shorter by 0.4% than the length of the oblique bonds, which are centro-symmetric. This may also involve slight distortions of the tetrahedral bond angles. However, the difference of the length between the two kinds of 0—0 bonds at 0°Capparently tends to equalize at 180°C[4]. Neglecting a slight deviation from an exact relationship of the tetrahedral environment, it may be possible that any of the three oblique bonds can behave as a Caxis of a second component of the crystal forming a continuous structure in an alternative twin junction. It may then be considered that the angle of 70°,frequently observed as the c-axes angle between each component, is related to 110°as the supplementary angle, which is very close to the tetrahedral angle 109°28’. Let us now construct a structure model of the ice crystal in which components I and II have such a relation that the c-a~isof component II is parallel to one of the oblique 0—0 bonds of component I, thereby the c-axes angle, between each component being 110°,as illustrated in fig. 1. In doing so, three requirements must hold: (1) a tetrahedral arrangement for the position of each 0 atom, (2) a mirror-symmetric arrangement of every 0—0 bond that is parallel to the c-axis (m-bond). (3) a centro-symmetric arrangement of every 0—0 bond that is parallel to the oblique axis (c-bond). As shown in fig. 1, the bonds 01—02 and 04—05 behave each as a c-axis for each component (c1- and —
~,
snow crystals
263
Fig. 2. A structure model illustrating a combination of two rn—3c—m type twins which gives cs 111201.
=
1100; projected along
c11-axis for components I and II, respectively), and therefore they are mirror-symmetric (m-bond). The bonds 02—03 and 03—04 must then be centro-symmetric (c-bond), because they compose an oblique bond in each of components land II, respectively. Thus two components I and II are connected by two successive c-bonds in order that c1 and c11-axes make angle of 110°,which may be called the m—c—c—rn type of junction. This does mean that a stacking fault is introduced vertically to the c1-axis between 03 and 04 positions in the original hexagonal component I, while another stacking fault is introduced vertically to the c11-axis between 02 and 03 positions in the second component II. In general, any number of layers of the stacking fault can be introduced for each c-axis direction and the number of the c-bonds connecting components I and II is 2n, corresponding to the number n of layers of the stacking fault introduced at the junction. (The number n may not always be the same for both the c1- and c11-axis directions.) On the basis of the above consideration, it may be easily understood that the rn—c—rn type of junction composes a single crystalline ice structure and the rn—c—c—c—rn type (rn—3c—m, for short) of junction gives a [1120] rotation twin structure, which has been called “twin prism” [5]. A junction involving any odd number of the c-bond larger than three for connecting the two hexagonal components produces simply a repetition of the [1120] rotation twin relation. Fig. 2 shows one of the simplest models which illu-
264
T. Kohayashi et al.
/ Cubic structure models at junctions in snow crystals
strates the rn—c--c—rn type of structure in making the angle 110°as ~, which is actually composed of a cornhination of two m—3c-—m type twins. Each pair of components 1--I’ and lI--U’ is in the relation of the [1120] rotation twin; the entire crystal composes a kind of penetration twin. There can be no violation of immediate coordination requirements excepting a fault layer in stacking order at the coiilpOSitiOfl plane. A more complicated structure model giving 110°as the angle o has been illustrated in the previous paper [6], which represents a combination of the m—3c—-rn and the rn—-Sc—rn type twins, These structure models suggest a formation of an ice germ in a cubic system which is of the metastable structure in ice [7] and a subsequent growth into a stable hexagonal system. This might be a probable process when ice crystals are nucleated at a high degree of supersaturation (supersaturation twin as suggested by Buerger [3]) and at low temperatures, or when a supercooled cloud droplet freezes in contact with a snow crystal at low temperatures. It may be summarized that an rn—c-—c--ill type of junction gives rise to a change of 70°(=180° — 110°) in the c-axis direction for connecting two hexagonal
80-
components. Then, as the next step of further application of this concept, two successive occurrences of the tn--c—c—rn junction may be considered. Thus au ni-— c_c_m_c*_c~~mtype of junction gives rise to a change of 40° ( 110°+ 110° --- 180°)in the c-axis direction as the result, when the c~ -bond of the second rn~_c*--c--rn junction is oriented on one and the same plane of the first m—c---c---m junction. But the c*.bond in the second junction can be oriented, in an equal probability, in either of two other directions of the three oblique bond orientations. In such case the resultant change in the c-axis direction is equal as to either of the directions and is approximately 56°. As a further step, if three successive rn--c—c -in junctions are supposed to occur, the resultant change in the c-axis direction may he 3 1.5°,88.0°,66.0°and 21.5°. In the growth of an ice crystal, a transitioun from a cubic to a hexagonal system may be probable, but a reverse one from a hexagonal to a cubic system may be less probable. Accordingly, two or more numbers of the successive occurrences of rn-—c--c--rn junction may become less and less probable as the number increases.
/~
~
TOTAL NUMBER ___
60
iIbI~”
PRESENT AUTHORS 347 LEE 131 UVEDA -
175
-
-.
U
-
z
LU
~20
0
i
10
~
20 30 40 50 60 70 ANGLES BETWEEN C-AXES (DEGREE)
80
.
90
T. Kobayas/ui ci al.
/ Cubic structure models at junctions in snow
crystals
265
b) 100EJ
543 241
80—
189
LU
z >60C-)
z
LU
c~ LU
20
ib
0
2b
~
...-:.
40
60
ANGLES BETWEEN C-AXES (DEGREE)
c) ~B6
~_
6—
~i~~~:-j’ ~
ib ~b
—
3’0~ ~
~
70
80
90
ANGLES BETWEEN C-AXES (DEGREE) Fig. 3. Frequency histograms of angles between the c-axes of each component, obtained by Lee, Uyeda and the present authors: (a) for the plane assemblage crystals in the spatial type; (b) for tile plane assemblage crystals in the radiating type; (c) for the combination of bullets.
T. Kobayashi et a!. / Cubic structure models at junctions in snow crystals
266
3. Discussions: comparison of observational results
with the models It is clearly indicated by the frequency histograms of ~, the angles between the c-axes of each component, obtained by Lee [1] and Uyeda [8] that a high peak appears singly at 70°for the plane assemblage crystals in a spatial type as shown in fig. 3a, while a predominant peak appears at 70°accompanied by less predominant peaks at 55°and 40° for the plane assemblage crystals in the radiating type, as shown in fig. 3b. Lee also confirmed that the a-axes of the secondary branches were always in parallel with those of the substrate crystals, which gives another evidence to support the present structural models as well as the GCSL models. Recently the present authors made the same measurements at Yukomanbetsu in central Hokkaido through a period from January 26 to March 10, 1976, and obtained the same results as Lee’s. These are also shown in fig. 3. Comparing the observational results by Lee, Uyeda and the present authors with the cubic structure models described above, the agreement is remarkably good for the angles s and for the relative frequency of their appearance for the plane assemblages in both the types. A probable explanation may be given as follows: since the secondary branches in the spatial type (fig. 4)
(
~,,)
-
)
.“~
—
ç
,
-
-
a
-
-
-
-
~-
-
_______ -~ --
Fig. 4. A plane assemblage crystal in the spatial type: (a) focused on the hexagonal base, (b) side view (x 32).
of the snow crystals may be initiated by the contacting of’ a cloud droplet onto a dendritic or a plate crystal, it may be considered that freezing of the droplet proceeds at a temperature range between —10°and 20°C which is amenable to the plate growth. The freezing temperature is rather high so that only the m c—c m type of junction may take place, giving a single predominant peak at 70° on the frequency histograms. The radiating type of the plane branches (fig. 5) may be initiated by the freezing of a cloud droplet by itself at temperatures even lower than —20°C as well as the temperature range described above, so that the rn—c—c—rn—c—c- rn type of junction may possibly take place, giving a predominant peak at 70° and less predominant peaks at 55° and 40°on the frequency histograms. As for crystals of the type of combination of bullets (figs. 6 and 3c), Lee. Uyeda and the present authors made the same measurement; the results of which are rather different for those obtained for the
plane assemblages; in their measurements peaks were found around 30°,90°,65°in addition to 70°,55° and 40°;the peaks at these angles appeared with nearly the same frequency. It is considered that this type of the crystals may be nucleated at temperatures much
T. Kobayashi Ct a!.
/ Cubic structure models at junctions in snow
crystals
267
a tig. 6. A combination of bullets (X 115).
[2]. He found two peaks on a frequency histogram, one at 70 again, invariable with the rates of cooling and the other at 20—30°,variable with the rates. It is
-
-
interesting to note that the former angle corresponds to the angle predicted by the rn—c c—rn type of twin junction. It may be considered that two sub-critical
sized ice-nuclei in a supercooled water drop are probably joined together in the rn—c—c m type of twin junction, which has low interfacial energy, and they, -
-
-
obtaining thus twice as large as a single nucleus in volume, may survive to exceed the critical size for a further growth. They grow as a twin when they are able to continue to grow further.
Fig. 5. A plane assemblage crystal in the radiating type; (a) focused on one of the hexagonal plates, (b).side view (X 50).
Acknowledgements
lower than 20°C,which is amenable to the prism growth so that the twinning may be formed in such complicated ways that the two or three successive repetitions of the cubic junction and/or the GCSL type of the configurations might possibly be involved in nearly the same extent as to form this type of the crystals. Uyeda recently measured the number of neighbouring crystals and the angles between the c-axes of neighbouring crystals when a water drop of 1.0—1.7 mm in diameter was frozen under controlled rates of cooling
Y. Mizuno for their cooperation in the period of snow crystal observations at Yukomanbetsu. This work was supported in part by the Scientific Research Fund of the Ministry of Education.
The authors wish to thank Dr. S. Suzuki and Miss
References Ill 121
C.W. Lee, J. Meteor. Soc. Japan 50 (1972) 171. T. Kobayashi, Y. Furukawa, K. Kikuchi and H. Uyeda, J. Crystal Growth 32 (1976) 233.
268
T Kobayazhl neiL
I OthIc structure models at/unction, In snow clystals
131
Mi. Buerget, Am. MIneralogist 30(1945)469. (4J DII. Lonsdale, Proc. Roy. Soc. (London) A247 (1958)
(51
424. T. Kobsyashi and T. Ohtake, J..Atmos. ScL 31(1974)
1377.
(6j T. Kobayashl, in: Proc. Intern. Conf. Cloud Phys., 1976 (In press). N.H. Fletcher, The Chemical Physics of Ice (Cambrklge Univ. Press., 1970) p. 271. t81 II. Uyoda, Master’s thesls(1975).
171