- Email: [email protected]
Growth and perfection of ice crystals
102
Journal of Crystal Growth 24/25 (1974) 102—107 © North-Holland Publishing Co.
GROWTH AND PERFECTION OF ICE CRYSTALS AKIRA HIGASHI Department of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo, Japan Attempts were made to grow perfect, or nearly perfect, ice by single solid state studies. Dislocation 2 were found in crystals grown the crystals modifiedfor Bridgman method whereas using densities as low as 102 cm the Czochralski method the lowest densities found were of the order of 10~cm2. The configurations and structures of dislocations in the crystals grown by the different techniques and under various conditions were examined by X-ray diffraction topographs. Characteristic features of dislocation images in topographs are interpreted as showing that the Peierls trough is shallow for dislocations having a * (1120> Burgers vector on the basal plane. Thus, dislocations in the basal plane extend perpendicular to the growth interface due to the preferential line tension when the crystal was grown in the direction perpendicular to the c-axis. The generation ofdislocation densities ofthe order of 10~cm2 in Czochralski grown crystals is mainly attributed to those inherited from the large area of seed crystals and in addition to the thermal stresses caused by steep temperature gradients in the crystal. Reduction of dislocation densities to the order of 1 02 cm2 in Bridgman grown crystals is achieved by limiting the inheritance of dislocations or by the selection of a single mosaic from the seed crystal through a neck of the growth cell. Dislocation loops of (0001] Burgers vector and stacking faults found both in NH 3-doped ice are described.
1. Introduction Ice is an interesting substance for the study of crystal growth. For many years the growth of snow crystals has attracted many investigators. Its research has recently reached such a level that the molecular mechanisms or growth processes forming crystal habits can be elucidated through many ingenious experiments. The growth of ice from the melt is related to natural phenomena in a cold environment: the freezing of rivers, lakes and sea water. However experimental research has been carried out not only in morphology, nucleation andstudies growthof kinetics ice itself,mechanisms but also in fundamental crystalof growth using ice as a model substance, Recently, we found it necessary to grow artificial single crystals of ice of very good quality for solid-state studies. For many years our laboratory has used large, natural single ice crystals from the Mendenhall Glacier in Alaska in investigations of the mechanical properties of ice’). These crystals have dislocation densities of approximately l0~cm2, which is quite reasonable for the purposes for which they were used but crystals with far fewer dislocations (102 cm2) are required for our present investigations of the dynamic behavior of such dislocations2). For studies on the electrical properties ofice, crystals ofextreme purity or ofcontrolled doping
with substitutional impurities like HF, NH3 or others are required. We thus needed many crystals for solid state studies which were large and of a good homogeneous quality. In this paper, various attempts in growing dislocation-free ice single crystals or those of low dislocation density are described. Structures and other features of dislocations in the crystals were investigated by the method of X-ray diffraction topography. This method is especially good for ice because of its low absorption coefficient for X-rays in comparison to other crystals and it has been developed extensively for ice by us and 3). others the since the first attempt Hayes and From experimental resultsbyobtained withWebb various growth techniques and conditions, mechanisms of generation and multiplication of dislocations in the growing crystals were derived. 2. Growth techniques and examination of perfection 2.1. CZOCHRALSKI S METHOD Large single crystals of ice (approximately 15 cm in diameter and length) were grown from water by a modified Czochralski method4). The water used to grow ice by this method was distilled-deionized water which had electrical conductivity of approximately 10 jiV/cm. It was boiled for 30 mm for degassing before
11—8
~
103
GROWTH AND PERFECTION OF ICE CRYSTALS
(MM4D4AY)
8~4
~ 10~ U)
olO
-
U)
1o6
10’
io~
io~
I iø~
GROWTH RATE (CM/SEC)
Fig. 1. Relationship between the dislocation density and the growth rate in Czochralski-grown ice single crystals.
use, but it might absorb CO 2 or air again from its exposed surface during a long period of crystal growth. The crystal was grown from a seed ofmoderate size held at the surface of water in a glass container. The flat seed crystal was made to freeze to a buffer of ice which was frozen to the bottom of the cooling tank or heat sink. The cooling liquid at a temperature between —5 °Cand —20 °C circulated in the tank and extracted heat through the ice during its downward growth into the water. Instead of pulling the crystal the water level was lowered at the rate of growth of the crystal by leaking water through a pinch cock attached to the container. The temperature of the water at the bottom of contamer was kept at 4 °C to avoid thermal conveclion, An improvement in our method compared to that 5) was the rotation of the water container by Landauer at a moderate speed (0.3 rpm). This ensured both a thermally and structurally smooth interface between the ice and the water. The crystals thus obtained were optical1y perfect (no strain shadows appeared when the crystal was examined under crossed polaroids), but the dislocation density as measured by etch pits was not less than the order of 1 04 cm 2 It was found that the dislocation density was proportional to the growth rate as shown in fig. 1. Since it is not practical to grow the crystals at such a slow rate as of the order of 10—6 cm ~ (1 mm day 1) in order to reduce the dislocation density to the order of 1 03 cm -2, this method has only been used for obtaining large single crystals of ice of a
g — .
.
.
Fig. 2. X-ray diffraction topograph of a Czochralski ice single crystal grown in the direction parallel to the c-axis. Diffraction plane: (1010); scanning plane: (0001).
quality which is comparable to the Mendenhall Glacier ice. X-ray diffraction topographic observations on Czochralski grown crystals of ice revealed many characteristic features of dislocations which were related to the growth conditions6’ 7) In crystals grown in the direction perpendicular to the c-axis the dislocations ran parallel to the direction of growth. Since the Burgers vector of these dislocations was always * <1120>, they could be pure screw or 60°when the growth direction was <1120> and pure edge or 30°when it was <1OTO>. When the direction of growth was parallel to the c-axis or [00011,dislocation networks appeared as shown in fig. 2. The Burgers vector was determined as ~ <1120>
11—8
104
AKIRA HIGASHI
the water in the cylindrical glass container (7.0 cm diameter) was kept approximately at 4 °Cby the sur-
___________________
V///,~&’/////771?
‘~/~////,t~,(////~
~
rounding heating tape. The ice crystal was grown downward from the seed through the neck into the
I
growing cell (4.0 cm diameter) immersed in the water
p
growing cell was systematically raised. In this case, heat was extracted to the surface of the cell exposed to ambient air in the cold growth chamber whose ternperature was kept at approximately —5 °C.By very carefully keeping the growing interface flat, single crystals having container. As thedislocation crystal grewdensities down into of the the water, order the of 2 can be obtained even at a growth rate of 102 cm lO5cmsec’.
-~
s
1J
1’
• h
o o
)
o o
)
o ° 0
W
°
f//////7~
,.~
/7,
~
Fig. 3. Schematic diagram ofan improved Bridgman apparatus for the growth of ice single crystals. p: pulling rod; c: growing cell; f: freezing chamber; s: seed crystal; h: heater tape; w: water container,
in this case. The thicker dislocation images in the topograph like those on the left hand side of fig. 2 are of small angle boundaries which are composed of vertical rows of edge dislocations. Similar features ofdislocations as in fig. 2 were found by Jones8) in the Czochralski ice crystals grown by Bilgram in Switzerland during studies of the dielectric properties of ice. The same features were also found in 9) although its growth the Mendenhall ice mechanism may Glacier be completely different from the Czochralski grown crystals. 2.2. BRIDGMAN METHOD An apparatus for our improved Bridgman method is schematically illustrated in fig. 3. The temperature of
Dislocations in crystals grown by the modified Bridgman method were propagated from the seed through the neck when the direction of growth was perpendicular to the c-axis (fig. 4). Their features are almost identical with those found in Czochralski grown crystals of the same growth direction, except their density is much less. It was found that the dislocations which propagated were concentrated in a bundle in the center of the grown crystal when the growth interface was kept almost flat or was a facet plane. As can be seen in fig. 4, beyond the dislocation bundles or polygonized small angle boundaries, some dislocation-free regions were obtained which are sufficiently large for cutting specimens for solid-state studies. The modes of propagation of dislocations from the seed crystal and of the generation of dislocations from other sources in the container have been extensively investigated in situ by the use of a special Lang camera. This camera enabled us to take topographs of the progress of growth in a similar but thinner container as in fig. 3 which was mounted on the camera’s goniorneter head. Results of the observations are to be presented in another paper submitted to this conference. 2.3. NH 3-DOPED Bridgman ICE CRYSTALS The modified method was also used to grow ice single crystals doped with NH 3 10), Even with such a very low concentration of NH3 as 0.1 ppm in the crystal, there appeared a very characteristic feature of dislocations: concentric loops of dislocations as shown in fig. 5. Since the loops were present in topographs taken on three different diffracting planes
11—8
GROWTH AND PERFECTION OF ICE CRYSTALS
105
g
Fig. 5. X-ray diffraction topograph of an ice single crystal doped with NH 3. Diffraction plane: (1010); scanning plane:
________________
I -
Fig. 4.
1
(0001). Circular dislocation 1oops and stacking fault images (shadows on the right) are characteristic.
X-ray diffraction topograph of a Bridgman ice single
fraction plane : (lOTO); scanning plane: (0001).
the c-axis. Dif-
(different g vectors of <1OTO>) and the loops had deficits in the images in the direction perpendicular to the g vector, the Burgers vector was determined as [00011. The number of 1oops increased as the NH3 concentration increased. As can be seen in the right side of fig. 5, the X-ray diffraction topographs revealed images of comparatively wide stacking faults’ 1), The fault vector f was determined from three other topographs taken with three different g vectors of <1120>. Using the condition f g = 0 for disappearance of the images of the dislocation lines surrounding stacking faults, it is ~ <1010>. The dissociation of dislocations should be ~ [1120] = ~ [IOTO]-i4 [0110].
Reduction of the stacking fault energy by a ,large amount which corresponds to the width shown in the topographs could be attributed to the adsorption of segregated NH3. Both the dislocation loops and the stacking faults changed their shapes and sizes when the crystals were annealed. These phenomena may be primarily caused by rapid diffusion of NH3 at or near the surface of specimens thinned for X-ray diffraction topography. However, even in bulk ice single crystals, such features due to the dopants should not be stable, especially at high temperatures when diffusion becomes appreciable. 3. Discussion and conclusions The limited2)success of growing densingle crystals of icelow by dislocation the Czochralski sity (10~cm” method in contrast to the success of growing much
11—8
106
AKIRA HIGASHI
better ones (102 cm2) by the Bridgrnan method suggests a possible mechanism of generation of dislocations in the two methods. The major difference between these two methods is the manner in which the crystal was grown from its seed. In the Czochralski method the crystal was grown from a comparatively large area of the seed crystal whilst in the Bridgman method the growth took place through a neck from a small seed crystal. It has been already known9) that the Mendenhail Glacier ice used for the seed had many small angle tilt boundaries composed of vertical arrays of ~ <1120> edge dislocations lying on the basal plane. The tilt angles did not exceed I mm of arc. Therefore, the basal plane of the seed crystal is composed of small mosaics (approximately 10’ ~ cm in dimension) which are tilted with respect to each other by less than 1 mm, although the interface appeared flat in the experiments. These mosaic planes will propagate with the same tilt as further growth takes place on the interface. This is the reason why the Czochralski grown crystals have a dislocation density in the order of iO~cm2 and also have a dislocation structure, similar to the seed even though the growth mechanism is completely different from that of the glacier ice. The fact that the dislocation density increased with increasing growth rate as illustrated in fig. 1 can be interpreted by the production ofadditional dislocations due to thermal stresses in the growing crystal. It is possible that a much larger, non-uniform temperature gradient in the large Czochralski grown crystals gives rise to thermal stresses which have been demonstrated to be a source of dislocations in many other crystals. Fig. 2 shows many curved dislocation lines which indicate that on the basal plane of ice, the Peierls troughs are very shallow for dislocations with <1120> Burgers vectors; irrespective of the dislocation type. The dislocation may move very easily from one trough to another thus forming many kinks. The characteristic features of the dislocations when the growth direction is perpendicular to the c-axis, their alignment parallel to the growth direction, may be explained if one assumes that the Peierls troughs are so shallow that line tension is the dominant factor for determining the structural features of dislocations when one of their ends is exposed to the interface. The same interpretation can be made for dislocations which propagated from the
seed trough the neck of the growth cell in the Bridgman method as shown in fig. 4. If the Bridgman method is used for growth parallel to the c-axis, it is possible to obtain a real basal plane facet on the interface without any mosaic, because it may happen that the neck selects only one mosaic from the seed. Then the grown crystal should be dislocationfree, if it is not subjected to any other conditions which generate dislocations. We have occasionally found some dislocation-free regions in ice crystals among several dislocations generated from some unavoidable air bubbles adhering to the inner wall of the growth cell. The most successful method of growing nearly perfect crystals of ice of a certain dimension is, therefore, to grow in a direction parallel to the c-axis by the Bridgman method, and the next best method is to select it avoiding the bundle of dislocations propagated from the seed when the crystal is grown in a direction perpendicular to the c-axis by the same method. Either way, it is most important to keep the interface very flat, so that the few dislocations which appear on the basal plane will remain in the basal plane and not propagate in the growth direction for the case of growth parallel to the c-axis, and in order to keep the dislocations which propagate from the seed through the neck in a narrow range in the crystal as was stated in section 2.2 and shown in fig. 4. The dislocation loops with [0001] Burgers vectors which were observed in the doped crystals could be due to impurity segregation, perhaps resulting from constitutional supercooling at the interface. The much rarer occurrence of the same loops in pure ice crystals may be attributed to the same mechanism or to the existence of minute particles which may become nuclei for shear dislocations’ 2), The fact that dislocations generated from the doped impurities or minute nuclei have a [0001] Burgers vector, different from <1120>, that of the dominant dislocations in pure ice, seems to exclude the possibility that trace impurities contained in the water could be a source of dislocations in pure ice. We have accepted tacitly the mechanism of normal growth on a rough interface when discussing the mosaics at the interface in the Czochralski method whilst that of lateral layer growth on a smooth surface has been accepted in the Bridgman method, either for
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II
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GROWTH AND PERFECTION OF ICE CRYSTALS
107
pure or doped ice. Since the parameter ~ = L~/RT References 1) A. Higashi, Physics of Ice (Plenum, New York, 1969) p. 197. defined by Jackson’3) to determine whether the interface is rough or smooth is calculated to be approxim2) A. Fukuda and A. Higashi, Crystal Lattice Defects 4 (1973) ately 2.5 for ice, it is just intermediate between two 203. 3) C. E. Hayes and W. W. Webb, Science 147 (1965) 44. categories. The real interface may be either rough or 4) A. Higashi and M. Oguro, Oyo Butsuri 36 (1967) 988 (text smooth depending on orientation and perhaps on in Japanese with English summary). slight modifications of other parameters such as the 5) Landauer, Report 48 6) J. A.K. Higashi, M. SIPER Oguro Research and A. Fukuda, J. (1958). Crystal Growth addition of impurities or other unknown conditions. 3/4 (1968) 728. 7) A. Higashi, M. Oguro and A. Fukuda, Oyo Butsuri 38
Acknowledgements The author wishes to express sincere gratitude to M. Uguro who carried out extensive experiments in this paper. This research was supported by the Scientific Research Fund from the Ministry of Education, Japanese Government and also by the Grant from the Mitsubishi Foundation.
(1969) 567. 8) S. J. Jones, private communication (1972). 9) A. Fukuda and A. Higashi, Japan. J. Appi. Phys. 8 (1969) 993. 10) M. Oguro and A. Higashi, Phil. Mag. 24 (1971) 713. 11) M. Oguro and A. Higashi, Physics and Chemistry of Ice (Roy. Soc. Canada, 1973). 12) M. F. Ashby and L. Johnson, Phil. Mag. 20 (1969) 1009. 13) K. A. Jackson, D. R. Uhlmann and J. D. Hunt, J. Crystal Growth 1 (1967) 1.
II— 8
Journal of Crystal Growth 24/25 (1974) 102—107 © North-Holland Publishing Co.
GROWTH AND PERFECTION OF ICE CRYSTALS AKIRA HIGASHI Department of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo, Japan Attempts were made to grow perfect, or nearly perfect, ice by single solid state studies. Dislocation 2 were found in crystals grown the crystals modifiedfor Bridgman method whereas using densities as low as 102 cm the Czochralski method the lowest densities found were of the order of 10~cm2. The configurations and structures of dislocations in the crystals grown by the different techniques and under various conditions were examined by X-ray diffraction topographs. Characteristic features of dislocation images in topographs are interpreted as showing that the Peierls trough is shallow for dislocations having a * (1120> Burgers vector on the basal plane. Thus, dislocations in the basal plane extend perpendicular to the growth interface due to the preferential line tension when the crystal was grown in the direction perpendicular to the c-axis. The generation ofdislocation densities ofthe order of 10~cm2 in Czochralski grown crystals is mainly attributed to those inherited from the large area of seed crystals and in addition to the thermal stresses caused by steep temperature gradients in the crystal. Reduction of dislocation densities to the order of 1 02 cm2 in Bridgman grown crystals is achieved by limiting the inheritance of dislocations or by the selection of a single mosaic from the seed crystal through a neck of the growth cell. Dislocation loops of (0001] Burgers vector and stacking faults found both in NH 3-doped ice are described.
1. Introduction Ice is an interesting substance for the study of crystal growth. For many years the growth of snow crystals has attracted many investigators. Its research has recently reached such a level that the molecular mechanisms or growth processes forming crystal habits can be elucidated through many ingenious experiments. The growth of ice from the melt is related to natural phenomena in a cold environment: the freezing of rivers, lakes and sea water. However experimental research has been carried out not only in morphology, nucleation andstudies growthof kinetics ice itself,mechanisms but also in fundamental crystalof growth using ice as a model substance, Recently, we found it necessary to grow artificial single crystals of ice of very good quality for solid-state studies. For many years our laboratory has used large, natural single ice crystals from the Mendenhall Glacier in Alaska in investigations of the mechanical properties of ice’). These crystals have dislocation densities of approximately l0~cm2, which is quite reasonable for the purposes for which they were used but crystals with far fewer dislocations (102 cm2) are required for our present investigations of the dynamic behavior of such dislocations2). For studies on the electrical properties ofice, crystals ofextreme purity or ofcontrolled doping
with substitutional impurities like HF, NH3 or others are required. We thus needed many crystals for solid state studies which were large and of a good homogeneous quality. In this paper, various attempts in growing dislocation-free ice single crystals or those of low dislocation density are described. Structures and other features of dislocations in the crystals were investigated by the method of X-ray diffraction topography. This method is especially good for ice because of its low absorption coefficient for X-rays in comparison to other crystals and it has been developed extensively for ice by us and 3). others the since the first attempt Hayes and From experimental resultsbyobtained withWebb various growth techniques and conditions, mechanisms of generation and multiplication of dislocations in the growing crystals were derived. 2. Growth techniques and examination of perfection 2.1. CZOCHRALSKI S METHOD Large single crystals of ice (approximately 15 cm in diameter and length) were grown from water by a modified Czochralski method4). The water used to grow ice by this method was distilled-deionized water which had electrical conductivity of approximately 10 jiV/cm. It was boiled for 30 mm for degassing before
11—8
~
103
GROWTH AND PERFECTION OF ICE CRYSTALS
(MM4D4AY)
8~4
~ 10~ U)
olO
-
U)
1o6
10’
io~
io~
I iø~
GROWTH RATE (CM/SEC)
Fig. 1. Relationship between the dislocation density and the growth rate in Czochralski-grown ice single crystals.
use, but it might absorb CO 2 or air again from its exposed surface during a long period of crystal growth. The crystal was grown from a seed ofmoderate size held at the surface of water in a glass container. The flat seed crystal was made to freeze to a buffer of ice which was frozen to the bottom of the cooling tank or heat sink. The cooling liquid at a temperature between —5 °Cand —20 °C circulated in the tank and extracted heat through the ice during its downward growth into the water. Instead of pulling the crystal the water level was lowered at the rate of growth of the crystal by leaking water through a pinch cock attached to the container. The temperature of the water at the bottom of contamer was kept at 4 °C to avoid thermal conveclion, An improvement in our method compared to that 5) was the rotation of the water container by Landauer at a moderate speed (0.3 rpm). This ensured both a thermally and structurally smooth interface between the ice and the water. The crystals thus obtained were optical1y perfect (no strain shadows appeared when the crystal was examined under crossed polaroids), but the dislocation density as measured by etch pits was not less than the order of 1 04 cm 2 It was found that the dislocation density was proportional to the growth rate as shown in fig. 1. Since it is not practical to grow the crystals at such a slow rate as of the order of 10—6 cm ~ (1 mm day 1) in order to reduce the dislocation density to the order of 1 03 cm -2, this method has only been used for obtaining large single crystals of ice of a
g — .
.
.
Fig. 2. X-ray diffraction topograph of a Czochralski ice single crystal grown in the direction parallel to the c-axis. Diffraction plane: (1010); scanning plane: (0001).
quality which is comparable to the Mendenhall Glacier ice. X-ray diffraction topographic observations on Czochralski grown crystals of ice revealed many characteristic features of dislocations which were related to the growth conditions6’ 7) In crystals grown in the direction perpendicular to the c-axis the dislocations ran parallel to the direction of growth. Since the Burgers vector of these dislocations was always * <1120>, they could be pure screw or 60°when the growth direction was <1120> and pure edge or 30°when it was <1OTO>. When the direction of growth was parallel to the c-axis or [00011,dislocation networks appeared as shown in fig. 2. The Burgers vector was determined as ~ <1120>
11—8
104
AKIRA HIGASHI
the water in the cylindrical glass container (7.0 cm diameter) was kept approximately at 4 °Cby the sur-
___________________
V///,~&’/////771?
‘~/~////,t~,(////~
~
rounding heating tape. The ice crystal was grown downward from the seed through the neck into the
I
growing cell (4.0 cm diameter) immersed in the water
p
growing cell was systematically raised. In this case, heat was extracted to the surface of the cell exposed to ambient air in the cold growth chamber whose ternperature was kept at approximately —5 °C.By very carefully keeping the growing interface flat, single crystals having container. As thedislocation crystal grewdensities down into of the the water, order the of 2 can be obtained even at a growth rate of 102 cm lO5cmsec’.
-~
s
1J
1’
• h
o o
)
o o
)
o ° 0
W
°
f//////7~
,.~
/7,
~
Fig. 3. Schematic diagram ofan improved Bridgman apparatus for the growth of ice single crystals. p: pulling rod; c: growing cell; f: freezing chamber; s: seed crystal; h: heater tape; w: water container,
in this case. The thicker dislocation images in the topograph like those on the left hand side of fig. 2 are of small angle boundaries which are composed of vertical rows of edge dislocations. Similar features ofdislocations as in fig. 2 were found by Jones8) in the Czochralski ice crystals grown by Bilgram in Switzerland during studies of the dielectric properties of ice. The same features were also found in 9) although its growth the Mendenhall ice mechanism may Glacier be completely different from the Czochralski grown crystals. 2.2. BRIDGMAN METHOD An apparatus for our improved Bridgman method is schematically illustrated in fig. 3. The temperature of
Dislocations in crystals grown by the modified Bridgman method were propagated from the seed through the neck when the direction of growth was perpendicular to the c-axis (fig. 4). Their features are almost identical with those found in Czochralski grown crystals of the same growth direction, except their density is much less. It was found that the dislocations which propagated were concentrated in a bundle in the center of the grown crystal when the growth interface was kept almost flat or was a facet plane. As can be seen in fig. 4, beyond the dislocation bundles or polygonized small angle boundaries, some dislocation-free regions were obtained which are sufficiently large for cutting specimens for solid-state studies. The modes of propagation of dislocations from the seed crystal and of the generation of dislocations from other sources in the container have been extensively investigated in situ by the use of a special Lang camera. This camera enabled us to take topographs of the progress of growth in a similar but thinner container as in fig. 3 which was mounted on the camera’s goniorneter head. Results of the observations are to be presented in another paper submitted to this conference. 2.3. NH 3-DOPED Bridgman ICE CRYSTALS The modified method was also used to grow ice single crystals doped with NH 3 10), Even with such a very low concentration of NH3 as 0.1 ppm in the crystal, there appeared a very characteristic feature of dislocations: concentric loops of dislocations as shown in fig. 5. Since the loops were present in topographs taken on three different diffracting planes
11—8
GROWTH AND PERFECTION OF ICE CRYSTALS
105
g
Fig. 5. X-ray diffraction topograph of an ice single crystal doped with NH 3. Diffraction plane: (1010); scanning plane:
________________
I -
Fig. 4.
1
(0001). Circular dislocation 1oops and stacking fault images (shadows on the right) are characteristic.
X-ray diffraction topograph of a Bridgman ice single
fraction plane : (lOTO); scanning plane: (0001).
the c-axis. Dif-
(different g vectors of <1OTO>) and the loops had deficits in the images in the direction perpendicular to the g vector, the Burgers vector was determined as [00011. The number of 1oops increased as the NH3 concentration increased. As can be seen in the right side of fig. 5, the X-ray diffraction topographs revealed images of comparatively wide stacking faults’ 1), The fault vector f was determined from three other topographs taken with three different g vectors of <1120>. Using the condition f g = 0 for disappearance of the images of the dislocation lines surrounding stacking faults, it is ~ <1010>. The dissociation of dislocations should be ~ [1120] = ~ [IOTO]-i4 [0110].
Reduction of the stacking fault energy by a ,large amount which corresponds to the width shown in the topographs could be attributed to the adsorption of segregated NH3. Both the dislocation loops and the stacking faults changed their shapes and sizes when the crystals were annealed. These phenomena may be primarily caused by rapid diffusion of NH3 at or near the surface of specimens thinned for X-ray diffraction topography. However, even in bulk ice single crystals, such features due to the dopants should not be stable, especially at high temperatures when diffusion becomes appreciable. 3. Discussion and conclusions The limited2)success of growing densingle crystals of icelow by dislocation the Czochralski sity (10~cm” method in contrast to the success of growing much
11—8
106
AKIRA HIGASHI
better ones (102 cm2) by the Bridgrnan method suggests a possible mechanism of generation of dislocations in the two methods. The major difference between these two methods is the manner in which the crystal was grown from its seed. In the Czochralski method the crystal was grown from a comparatively large area of the seed crystal whilst in the Bridgman method the growth took place through a neck from a small seed crystal. It has been already known9) that the Mendenhail Glacier ice used for the seed had many small angle tilt boundaries composed of vertical arrays of ~ <1120> edge dislocations lying on the basal plane. The tilt angles did not exceed I mm of arc. Therefore, the basal plane of the seed crystal is composed of small mosaics (approximately 10’ ~ cm in dimension) which are tilted with respect to each other by less than 1 mm, although the interface appeared flat in the experiments. These mosaic planes will propagate with the same tilt as further growth takes place on the interface. This is the reason why the Czochralski grown crystals have a dislocation density in the order of iO~cm2 and also have a dislocation structure, similar to the seed even though the growth mechanism is completely different from that of the glacier ice. The fact that the dislocation density increased with increasing growth rate as illustrated in fig. 1 can be interpreted by the production ofadditional dislocations due to thermal stresses in the growing crystal. It is possible that a much larger, non-uniform temperature gradient in the large Czochralski grown crystals gives rise to thermal stresses which have been demonstrated to be a source of dislocations in many other crystals. Fig. 2 shows many curved dislocation lines which indicate that on the basal plane of ice, the Peierls troughs are very shallow for dislocations with <1120> Burgers vectors; irrespective of the dislocation type. The dislocation may move very easily from one trough to another thus forming many kinks. The characteristic features of the dislocations when the growth direction is perpendicular to the c-axis, their alignment parallel to the growth direction, may be explained if one assumes that the Peierls troughs are so shallow that line tension is the dominant factor for determining the structural features of dislocations when one of their ends is exposed to the interface. The same interpretation can be made for dislocations which propagated from the
seed trough the neck of the growth cell in the Bridgman method as shown in fig. 4. If the Bridgman method is used for growth parallel to the c-axis, it is possible to obtain a real basal plane facet on the interface without any mosaic, because it may happen that the neck selects only one mosaic from the seed. Then the grown crystal should be dislocationfree, if it is not subjected to any other conditions which generate dislocations. We have occasionally found some dislocation-free regions in ice crystals among several dislocations generated from some unavoidable air bubbles adhering to the inner wall of the growth cell. The most successful method of growing nearly perfect crystals of ice of a certain dimension is, therefore, to grow in a direction parallel to the c-axis by the Bridgman method, and the next best method is to select it avoiding the bundle of dislocations propagated from the seed when the crystal is grown in a direction perpendicular to the c-axis by the same method. Either way, it is most important to keep the interface very flat, so that the few dislocations which appear on the basal plane will remain in the basal plane and not propagate in the growth direction for the case of growth parallel to the c-axis, and in order to keep the dislocations which propagate from the seed through the neck in a narrow range in the crystal as was stated in section 2.2 and shown in fig. 4. The dislocation loops with [0001] Burgers vectors which were observed in the doped crystals could be due to impurity segregation, perhaps resulting from constitutional supercooling at the interface. The much rarer occurrence of the same loops in pure ice crystals may be attributed to the same mechanism or to the existence of minute particles which may become nuclei for shear dislocations’ 2), The fact that dislocations generated from the doped impurities or minute nuclei have a [0001] Burgers vector, different from <1120>, that of the dominant dislocations in pure ice, seems to exclude the possibility that trace impurities contained in the water could be a source of dislocations in pure ice. We have accepted tacitly the mechanism of normal growth on a rough interface when discussing the mosaics at the interface in the Czochralski method whilst that of lateral layer growth on a smooth surface has been accepted in the Bridgman method, either for
~-
II
‘~-
—
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GROWTH AND PERFECTION OF ICE CRYSTALS
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pure or doped ice. Since the parameter ~ = L~/RT References 1) A. Higashi, Physics of Ice (Plenum, New York, 1969) p. 197. defined by Jackson’3) to determine whether the interface is rough or smooth is calculated to be approxim2) A. Fukuda and A. Higashi, Crystal Lattice Defects 4 (1973) ately 2.5 for ice, it is just intermediate between two 203. 3) C. E. Hayes and W. W. Webb, Science 147 (1965) 44. categories. The real interface may be either rough or 4) A. Higashi and M. Oguro, Oyo Butsuri 36 (1967) 988 (text smooth depending on orientation and perhaps on in Japanese with English summary). slight modifications of other parameters such as the 5) Landauer, Report 48 6) J. A.K. Higashi, M. SIPER Oguro Research and A. Fukuda, J. (1958). Crystal Growth addition of impurities or other unknown conditions. 3/4 (1968) 728. 7) A. Higashi, M. Oguro and A. Fukuda, Oyo Butsuri 38
Acknowledgements The author wishes to express sincere gratitude to M. Uguro who carried out extensive experiments in this paper. This research was supported by the Scientific Research Fund from the Ministry of Education, Japanese Government and also by the Grant from the Mitsubishi Foundation.
(1969) 567. 8) S. J. Jones, private communication (1972). 9) A. Fukuda and A. Higashi, Japan. J. Appi. Phys. 8 (1969) 993. 10) M. Oguro and A. Higashi, Phil. Mag. 24 (1971) 713. 11) M. Oguro and A. Higashi, Physics and Chemistry of Ice (Roy. Soc. Canada, 1973). 12) M. F. Ashby and L. Johnson, Phil. Mag. 20 (1969) 1009. 13) K. A. Jackson, D. R. Uhlmann and J. D. Hunt, J. Crystal Growth 1 (1967) 1.
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