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Japanese work on snow crystals
Journal of Crystal Growth 24/25 (1974) 3—5 © North-Holland Publishing Co.
3
JAPANESE WORK ON SNOW CRYSTALS F. C. FRANK
The H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 JTL, England
The outstanding Japanese work on Snow Crystals is of course that of Ukichiro Nakaya, who gathered the results of 20 years observations on Snow Crystals, natural and artificial, into a book of that title published in 1956 6). One important feature of his work was its objectivity, determining the true frequencies of occurrence of various kinds of snow crystal as they occur in Hokkaido (correcting very false impressions one may gather from earlier work). Well known is his achievement in growing artificial snow crystals, supported on rabbit’s hair, in controlled programmes of environment, so as to simulate many varied kinds of snow crystal seen in nature: the results of which were summarized in a diagram showing the dependence of habit on temperature and supersaturation. Though this diagram has received minor amendments from later work, the most up-to-date version being that of Kobayashi4), it is still very rightly known as the Nakaya diagram. Less fully appreciated among the important results of Nakaya’s work is his elucidation of the three-dimensional nature ofsnow crystals, which appear two-dimensional in too many of the earlier representations, including the artistically objective illustrations of Lord Doi, whose book Sekka—Zusetsu (1833) is the first book wholly devoted to illustration of snow crystals2). The three-dimensionality of snow crystals emerges in several ways: (i) In twins: Nakaya never mentions the term (nor, in fact, does he mention a crystallographic index anywhere in his book, which is in part a protest against orthodox crystallography for its neglect of growth habits), but he
shows repeated examples of crystal combinations with recurrent orientation relationships. Higuchi and Yosida, largely using Nakaya’s observations, have tentatively identified the lattice relationships for some of these3). One kind of twinning which they do not investigate occurs in the twelve-rayed crystals which are pairs of six-rayed crystais with a relative rotation on the basal plane [Doi recorded these, as did Descartes1) in 1637, who recognized their double nature: Nakaya separated the pairs]. It seems likely that, apart from the 30° symmetric case, the angles of rotation, some of which Nakaya lists, should form a Kronberg—Wilson series5). (ii) In Tsuzumi crystals: hexagonal prisms with lateral growth from their ends: Descartes knew these, and described them as like wheels joined by an axle: Nakaya’s contribution was to identify the change of environment during growth which would produce them, as also: (iii) The complementary form of tabular crystals from which axial columns spring. Repetitions of these transitions give one way of generating crystals with multiple levels of planar growth; (iv) In hollow prisms and needles; (v) In the hollowness, or two-layer structure, of many varieties of seemingly flat hexagonal snow-crystals, and, when they are single layer crystals, the distinct difference between the two surfaces of the layer; and (vi) In thefact demonstrated by Nakaya that what seems a planar six-rayed crystal may be separated into two layers with one, two, or three principal rays at one level, and the remainder, equally developed, at a second level.
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F. C. FRANK
Nakaya described all these forms, other than the twins, as developments of skeletal growth. In full agreement, I would develop that theme further, as follows: The elementary form of the ice crystal is a hexagonal prism bounded by six ~1 OTO} and two ~0001 } faces. At low supersaturations, when growth is possibly dislocation-aided, c: a dimensional ratios are not far from equant as Kobayashi shows, 1.4 columnar, or 0.8, tabular. Extreme dimensional ratios occur at higher supersaturation, when growth is led by surface nucleation occurring at the outermost corners. At these, there are two faces of one kind, one of a different kind. If the quasi-critical supersaturation for surface nucleation on {0001} is less than for {10T0}, nearly all the nucleation will occur on the prism faces: because nucleation rate is such a highly sensitive function of supersaturation. When the curves representing quasicritical supersaturation for the two kinds of singular face, as a function of temperature, cross, we have an abrupt transition from axial growth, namely on basal planes, to lateral growth, namely on prism planes (the origin ofTsuzumi crystals), or the reverse. We are still in need of an explanation of why there are three crossings between 0 °Cand 22 °C, but the abruptness of the transitions is no problem, and requires no abrupt change in surface properties. Growth steps spreading from the corners come closer together in regions of reduced supersaturation elsewhere in the growing face. They can only compensate a limited reduction of supersaturation in this way, and where there is a greater decrease there results a lacuna in the growth front, within which no deposition occurs, Skeletal crystals result from this phenomenon, but I prefer the term “lacunary growth” to cover its more general consequences. Among other factors, large absolute (rather than relative) supersaturation, producing fast growth, makes the growth increasingly lacunary. In columnar growth, with increasing lacunary tendency, the lacuna first appears in the centre of the basal faces, making a hollow prism. A larger lacuna reaches the <(0001) (1010)> edges, dividing the further growth of the crystal into separate columns, which now grow unequally, for whichever gets ahead has the highest supersaturation and nucleation rate, and deprives those which fall behind it. Such is needle snow. In tabular growth, lacunae first appear in the centres of the prism faces, producing a tabular prism with six
sectors of hollowness: alternatively described as an upper and a lower hexagonal plate joined by six webs or walls extending from the centre to their corners. Larger lacunae breach the <(0001) (1010)> edges: the resulting crystal has six sectors separated by clefts symmetrical about {1120} planes. These are the sectorplate crystals. Still larger lacunae narrow the sectors, which now acquire subsidiary ~l0T0} facets. With yet further enlargement of the lacunae <(1010) (0110)> edges are breached. This produces a cleft in the walls which previously joined the upper and lower plates of the crystal, so that these are reduced to a pair of ridges on the inner surfaces of these layers, extending radially to the corners. The ratio of nucleation rates on the two kinds of surface is large, not infinite. Nucleation on the corners of {0001 } faces gives a low density of inward-migrating growth steps so that these basal faces, though having no lacuna, are slightly dished. The lacunary nature of growth on the prism faces limits the thickness of the upper and lower plates, so that their inner surfaces follow their outer surfaces, gradually growing apart. Favoured access of material at the corners emphasizes the ridges on the inner surfaces, and produces new, gradually developing ridges leading to the subsidiary corners. The latter have no simple crystallographic direction, and are generally curved. After the <(1010)(0110)> edges have been cut, there is no connection between growth fronts on the upper and lower plates, to cause them to keep pace with each other: if either falls behind it grows much slower, becoming a stunted rudiment. The main growth is now in the form of single-layer sectors, each belonging to one or other of the two levels, with ridges leading to the corners on what was its inner face. {000l } nucleation on this surface occurs on the ridges, tending to emphasize them: between ridges, the growth steps, present in low density, are retarded close to the ridges, which are vapour sinks, so that ridges are flanked by troughs on either side. (A trough on the other {000l } face, opposite a ridge, remains unexplained. However Nakaya’s plate 181, No. 1304 and p. 214, fig. 394 show that it is not necessarily present.) Extreme lacunarity reaches to the corners, so that no {1OTO} face is even vicinally present. Nakaya limits his application of the term “dendritic” to this condition.
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5
JAPANESE WORKS ON SNOW CRYSTALS
In illustration of the lecture, the following were shown as slides: I: Ref. 4. The Nakaya diagram, Kobayashi’s revised version. II: Ref. 2. 2nd figure plate ofthe Zoku—Sekka— Zusetsu, showing a 12-rayed crystal. III: Ref. 6. P1. 63, No. 336: 12-rayed crystal. IV: Ref. 6. P. 27, fig. 54: 12-rayed crystal. V: Ref. 6. P. 27, figs. 50, 51: 12-rayed crystal separated. VI: Ref. 6. P. 33, figs. 64, 65: 6-rayed crystal separated. VII: Ref. 6. P. 34, fig. 72: 6-rayed, 2-level (1—2—4 type). VIII: Ref. 6. P. 40, fig. 86: 8-rayed crystal. IX: Ref. 1. Descartes’ figures of snow crystals. X: Ref. 6. P1. 117, Nos. 723, 724: two capped columns. XI: Ref. 6. P. 57, fig. 138: the Tsuzumi crystal. XII: Ref. 6. P. 58, fig. 141: plan and side view of unequal-ended Tsuzumi crystal. XIII, XIV: Ref. 5. Pp. 285, 286: laboratory development of Tsuzumi crystal, 6 stages. XV: Ref. 6. P. 56, figs. 137(a), (b): transition from plate to column growth. XVI: Ref. 6. P1. 122, No. 754: multiple transitions make multilayer crystal. XVII: Ref. 6. P. 31, figs. 60, 61: multilayer 12rayed crystal. XVIII: Ref. 6. P1. 27 No. 130: 3-level crystal in plan view. XIX XX Ref 6 P1 98 Nos 567 568 and 47 ~ ~
XXI: XXII:
Ref. Ref.
XXIII:
Ref.
XXIV: XXV:
Ref. Ref.
109: planar crystals, c-axes inclined a 75°. 3. Figs. 1, 2: the same (from Nakaya). 3. Figs. 14, 15: planar twinning examples. 3. Figs. 10, 11 12, 13: needle and planar dendrite turns (from Nakaya). 6. P. 56, fig. 133: needle twins. 3. Fig. 18: some twinning modes.
XXVI:
Ref. 3. Fig. 32: histogram of angles between c-axes. XXVII: Ref. 6. P. 26, fig. 54: Nakaya’s diagram of 2-layer skeletal structure. XXVIII: Ref. 2. Fig. 43: Kobayashi’s diagram of skeletal structure. XXIX: Ref. 6. P. 51, fig. 118: hollow column. XXX: Ref. 6. P1. 114, No. 696: needle. XXXI: Ref. 6. Fig. 167: unequal 2-level development. XXXII: Ref. 6. P1. 46, No. 232: centre hexagon eccentric. XXXIII: Ref. 6. P1. 53, No. 274: the same. XXXIV: Ref. 6. P1. 36, No. 199: pseudo-symmetry— branching at different levels. XXXV: Ref. 6. P1. 181, No. 1304: minor growth steps reveal four surfaces, two smooth, two ridged. XXXVI: Ref. 6. P.213, figs. 389, 390, cross-sections. XXXVII: Ref. 6. P. 214, figs. 393, 394: sections cut by Y. Miyazaki. XXXVIII: Ref. 6. P. 103, fig. 208: highly symmetric crystal double layer within hexagon, single layer extensions. XXXIX: Ref. 3. Figs. 44, 45: crystal top right interpreted as two principal levels of growth, both hollow (Kobayashi and Doi illustrations together). —
References 1) R. Descartes, Les Météores (1637), published with Discours de Ia Méthode; in: Oeuvres de Descartes, Vol. VI Eds. Adam and Tannery (Leopold Cerf, Paris, 1902). 2) T. Doi, Sekka-Zusetsu (1833) and Zoku-Sekka-Zusetsu(1840), reprinted with a commentary by T. Kobayashi (Tsukiji Sho3) K. Higuchi and T. Yosida, in: Physics of Snow and Ice, Vol. I (Proc. Sapporo Conf., August 1966) (Institute of Low TernScience, Sapporo, 1966) p. 79. Sap4) perature T. Kobayashi, in:Hokkaido Physics ofUniv., Snow and Ice, Vol. I (Proc. poro Conf., August 1966) (Institute of Low Temperature Science, Hokkaido Univ., Sapporo, 1966) p. 95. 5) M. Kronberg and P.Crystals, Wilson, Natural Trans. AIME 185 (1949) 50. 6) U. Nakaya, Snow and Artificial (Harvard Univ. Press, Cambridge, Mass., 1954).
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3
JAPANESE WORK ON SNOW CRYSTALS F. C. FRANK
The H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 JTL, England
The outstanding Japanese work on Snow Crystals is of course that of Ukichiro Nakaya, who gathered the results of 20 years observations on Snow Crystals, natural and artificial, into a book of that title published in 1956 6). One important feature of his work was its objectivity, determining the true frequencies of occurrence of various kinds of snow crystal as they occur in Hokkaido (correcting very false impressions one may gather from earlier work). Well known is his achievement in growing artificial snow crystals, supported on rabbit’s hair, in controlled programmes of environment, so as to simulate many varied kinds of snow crystal seen in nature: the results of which were summarized in a diagram showing the dependence of habit on temperature and supersaturation. Though this diagram has received minor amendments from later work, the most up-to-date version being that of Kobayashi4), it is still very rightly known as the Nakaya diagram. Less fully appreciated among the important results of Nakaya’s work is his elucidation of the three-dimensional nature ofsnow crystals, which appear two-dimensional in too many of the earlier representations, including the artistically objective illustrations of Lord Doi, whose book Sekka—Zusetsu (1833) is the first book wholly devoted to illustration of snow crystals2). The three-dimensionality of snow crystals emerges in several ways: (i) In twins: Nakaya never mentions the term (nor, in fact, does he mention a crystallographic index anywhere in his book, which is in part a protest against orthodox crystallography for its neglect of growth habits), but he
shows repeated examples of crystal combinations with recurrent orientation relationships. Higuchi and Yosida, largely using Nakaya’s observations, have tentatively identified the lattice relationships for some of these3). One kind of twinning which they do not investigate occurs in the twelve-rayed crystals which are pairs of six-rayed crystais with a relative rotation on the basal plane [Doi recorded these, as did Descartes1) in 1637, who recognized their double nature: Nakaya separated the pairs]. It seems likely that, apart from the 30° symmetric case, the angles of rotation, some of which Nakaya lists, should form a Kronberg—Wilson series5). (ii) In Tsuzumi crystals: hexagonal prisms with lateral growth from their ends: Descartes knew these, and described them as like wheels joined by an axle: Nakaya’s contribution was to identify the change of environment during growth which would produce them, as also: (iii) The complementary form of tabular crystals from which axial columns spring. Repetitions of these transitions give one way of generating crystals with multiple levels of planar growth; (iv) In hollow prisms and needles; (v) In the hollowness, or two-layer structure, of many varieties of seemingly flat hexagonal snow-crystals, and, when they are single layer crystals, the distinct difference between the two surfaces of the layer; and (vi) In thefact demonstrated by Nakaya that what seems a planar six-rayed crystal may be separated into two layers with one, two, or three principal rays at one level, and the remainder, equally developed, at a second level.
I—i
4
F. C. FRANK
Nakaya described all these forms, other than the twins, as developments of skeletal growth. In full agreement, I would develop that theme further, as follows: The elementary form of the ice crystal is a hexagonal prism bounded by six ~1 OTO} and two ~0001 } faces. At low supersaturations, when growth is possibly dislocation-aided, c: a dimensional ratios are not far from equant as Kobayashi shows, 1.4 columnar, or 0.8, tabular. Extreme dimensional ratios occur at higher supersaturation, when growth is led by surface nucleation occurring at the outermost corners. At these, there are two faces of one kind, one of a different kind. If the quasi-critical supersaturation for surface nucleation on {0001} is less than for {10T0}, nearly all the nucleation will occur on the prism faces: because nucleation rate is such a highly sensitive function of supersaturation. When the curves representing quasicritical supersaturation for the two kinds of singular face, as a function of temperature, cross, we have an abrupt transition from axial growth, namely on basal planes, to lateral growth, namely on prism planes (the origin ofTsuzumi crystals), or the reverse. We are still in need of an explanation of why there are three crossings between 0 °Cand 22 °C, but the abruptness of the transitions is no problem, and requires no abrupt change in surface properties. Growth steps spreading from the corners come closer together in regions of reduced supersaturation elsewhere in the growing face. They can only compensate a limited reduction of supersaturation in this way, and where there is a greater decrease there results a lacuna in the growth front, within which no deposition occurs, Skeletal crystals result from this phenomenon, but I prefer the term “lacunary growth” to cover its more general consequences. Among other factors, large absolute (rather than relative) supersaturation, producing fast growth, makes the growth increasingly lacunary. In columnar growth, with increasing lacunary tendency, the lacuna first appears in the centre of the basal faces, making a hollow prism. A larger lacuna reaches the <(0001) (1010)> edges, dividing the further growth of the crystal into separate columns, which now grow unequally, for whichever gets ahead has the highest supersaturation and nucleation rate, and deprives those which fall behind it. Such is needle snow. In tabular growth, lacunae first appear in the centres of the prism faces, producing a tabular prism with six
sectors of hollowness: alternatively described as an upper and a lower hexagonal plate joined by six webs or walls extending from the centre to their corners. Larger lacunae breach the <(0001) (1010)> edges: the resulting crystal has six sectors separated by clefts symmetrical about {1120} planes. These are the sectorplate crystals. Still larger lacunae narrow the sectors, which now acquire subsidiary ~l0T0} facets. With yet further enlargement of the lacunae <(1010) (0110)> edges are breached. This produces a cleft in the walls which previously joined the upper and lower plates of the crystal, so that these are reduced to a pair of ridges on the inner surfaces of these layers, extending radially to the corners. The ratio of nucleation rates on the two kinds of surface is large, not infinite. Nucleation on the corners of {0001 } faces gives a low density of inward-migrating growth steps so that these basal faces, though having no lacuna, are slightly dished. The lacunary nature of growth on the prism faces limits the thickness of the upper and lower plates, so that their inner surfaces follow their outer surfaces, gradually growing apart. Favoured access of material at the corners emphasizes the ridges on the inner surfaces, and produces new, gradually developing ridges leading to the subsidiary corners. The latter have no simple crystallographic direction, and are generally curved. After the <(1010)(0110)> edges have been cut, there is no connection between growth fronts on the upper and lower plates, to cause them to keep pace with each other: if either falls behind it grows much slower, becoming a stunted rudiment. The main growth is now in the form of single-layer sectors, each belonging to one or other of the two levels, with ridges leading to the corners on what was its inner face. {000l } nucleation on this surface occurs on the ridges, tending to emphasize them: between ridges, the growth steps, present in low density, are retarded close to the ridges, which are vapour sinks, so that ridges are flanked by troughs on either side. (A trough on the other {000l } face, opposite a ridge, remains unexplained. However Nakaya’s plate 181, No. 1304 and p. 214, fig. 394 show that it is not necessarily present.) Extreme lacunarity reaches to the corners, so that no {1OTO} face is even vicinally present. Nakaya limits his application of the term “dendritic” to this condition.
1—1
5
JAPANESE WORKS ON SNOW CRYSTALS
In illustration of the lecture, the following were shown as slides: I: Ref. 4. The Nakaya diagram, Kobayashi’s revised version. II: Ref. 2. 2nd figure plate ofthe Zoku—Sekka— Zusetsu, showing a 12-rayed crystal. III: Ref. 6. P1. 63, No. 336: 12-rayed crystal. IV: Ref. 6. P. 27, fig. 54: 12-rayed crystal. V: Ref. 6. P. 27, figs. 50, 51: 12-rayed crystal separated. VI: Ref. 6. P. 33, figs. 64, 65: 6-rayed crystal separated. VII: Ref. 6. P. 34, fig. 72: 6-rayed, 2-level (1—2—4 type). VIII: Ref. 6. P. 40, fig. 86: 8-rayed crystal. IX: Ref. 1. Descartes’ figures of snow crystals. X: Ref. 6. P1. 117, Nos. 723, 724: two capped columns. XI: Ref. 6. P. 57, fig. 138: the Tsuzumi crystal. XII: Ref. 6. P. 58, fig. 141: plan and side view of unequal-ended Tsuzumi crystal. XIII, XIV: Ref. 5. Pp. 285, 286: laboratory development of Tsuzumi crystal, 6 stages. XV: Ref. 6. P. 56, figs. 137(a), (b): transition from plate to column growth. XVI: Ref. 6. P1. 122, No. 754: multiple transitions make multilayer crystal. XVII: Ref. 6. P. 31, figs. 60, 61: multilayer 12rayed crystal. XVIII: Ref. 6. P1. 27 No. 130: 3-level crystal in plan view. XIX XX Ref 6 P1 98 Nos 567 568 and 47 ~ ~
XXI: XXII:
Ref. Ref.
XXIII:
Ref.
XXIV: XXV:
Ref. Ref.
109: planar crystals, c-axes inclined a 75°. 3. Figs. 1, 2: the same (from Nakaya). 3. Figs. 14, 15: planar twinning examples. 3. Figs. 10, 11 12, 13: needle and planar dendrite turns (from Nakaya). 6. P. 56, fig. 133: needle twins. 3. Fig. 18: some twinning modes.
XXVI:
Ref. 3. Fig. 32: histogram of angles between c-axes. XXVII: Ref. 6. P. 26, fig. 54: Nakaya’s diagram of 2-layer skeletal structure. XXVIII: Ref. 2. Fig. 43: Kobayashi’s diagram of skeletal structure. XXIX: Ref. 6. P. 51, fig. 118: hollow column. XXX: Ref. 6. P1. 114, No. 696: needle. XXXI: Ref. 6. Fig. 167: unequal 2-level development. XXXII: Ref. 6. P1. 46, No. 232: centre hexagon eccentric. XXXIII: Ref. 6. P1. 53, No. 274: the same. XXXIV: Ref. 6. P1. 36, No. 199: pseudo-symmetry— branching at different levels. XXXV: Ref. 6. P1. 181, No. 1304: minor growth steps reveal four surfaces, two smooth, two ridged. XXXVI: Ref. 6. P.213, figs. 389, 390, cross-sections. XXXVII: Ref. 6. P. 214, figs. 393, 394: sections cut by Y. Miyazaki. XXXVIII: Ref. 6. P. 103, fig. 208: highly symmetric crystal double layer within hexagon, single layer extensions. XXXIX: Ref. 3. Figs. 44, 45: crystal top right interpreted as two principal levels of growth, both hollow (Kobayashi and Doi illustrations together). —
References 1) R. Descartes, Les Météores (1637), published with Discours de Ia Méthode; in: Oeuvres de Descartes, Vol. VI Eds. Adam and Tannery (Leopold Cerf, Paris, 1902). 2) T. Doi, Sekka-Zusetsu (1833) and Zoku-Sekka-Zusetsu(1840), reprinted with a commentary by T. Kobayashi (Tsukiji Sho3) K. Higuchi and T. Yosida, in: Physics of Snow and Ice, Vol. I (Proc. Sapporo Conf., August 1966) (Institute of Low TernScience, Sapporo, 1966) p. 79. Sap4) perature T. Kobayashi, in:Hokkaido Physics ofUniv., Snow and Ice, Vol. I (Proc. poro Conf., August 1966) (Institute of Low Temperature Science, Hokkaido Univ., Sapporo, 1966) p. 95. 5) M. Kronberg and P.Crystals, Wilson, Natural Trans. AIME 185 (1949) 50. 6) U. Nakaya, Snow and Artificial (Harvard Univ. Press, Cambridge, Mass., 1954).
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