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Development of Platinum Dendrite in Lithium Tetraborate Crystal Grown by the Czochralski Method
Materials Research Bulletin, Vol. 33, No. 3, pp. 433– 440, 1998 Copyright © 1998 Elsevier Science Ltd Printed in the USA. All rights reserved 0025-5408/98 $19.00 1 .00
PII S0025-5408(97)00248-1
DEVELOPMENT OF PLATINUM DENDRITE IN LITHIUM TETRABORATE CRYSTAL GROWN BY THE CZOCHRALSKI METHOD
R. Komatsu* and S. Uda Central Research Institute, Mitsubishi Materials Corp., 1–297 Kitabukuro-cho, Omiya, Saitama 330 Japan (Refereed) (Received June 16, 1997; Accepted August 4, 1997)
ABSTRACT Platinum dendrites were found in lithium tetraborate crystals grown by the Czochralski method using a platinum crucible. The mode of occurrence and formation mechanism of platinum dendrite in lithium tetraborate were examined. It is revealed that platinum dendrites developed in the cellular structure that occurred during growth. The formation of platinum dendrite that is discussed is associated with the growth condition leading to cellular growth. The morphology of platinum dendrite is also explained by its specific crystallographic symmetry. © 1998 Elsevier Science Ltd KEYWORDS: A. oxides, B. crystal growth, D. defects INTRODUCTION Lithium tetraborate (Li2B4O7) is a piezoelectric material belonging to the space group I41cd [1]. It has attracted much attention as a surface acoustic wave substrate for high frequency because of its high coupling factor (k2) and low temperature coefficient of frequency. Ever since Whatmore et al. [2] first reported this single crystal, many efforts have been made to apply it to surface acoustic wave substrate devices [3,4]. Recently, we reported that this crystal is a new nonlinear crystal for ultraviolet frequency conversion, including the fourth and fifth harmonics generation of the Nd:YAG laser [5]. Its application to nonlinear devices in the ultraviolet region is also promising.
*To whom correspondence should be addressed. 433
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With respect to the growth of lithium tetraborate single crystals, Li2B4O7 melts congruently and, consequently, crystals can be grown by the Czochralski (CZ) or the Bridgman method. The growth of large crystals has been investigated for commercial use since a report by Garrett et al. [6]. The growth of single crystals with a 3-inch diameter by the CZ method was reported by Matsumura et al. [7], whereas growth by the Bridgman method was reported by Fan et al. [8]. One of the most serious problems to solve is macroscopic “opaque defects” in the grown crystals. The opaque defects are classified into two types. One is a opaque ring perpendicular to the pulling direction, which tends to spread from the central core to the peripheral, and the other is the array of core inclusions (voids) running parallel to the pulling direction. We have found metallic dendrites in opaque defects, which might have been derived from metal dissolved from the platinum crucible [9]. It has been reported [10] that when a platinum or iridium crucible was used for the growth of oxide crystals, metal from the crucible was often observed as inclusions in the grown oxide crystals. These inclusions were made of hexagonal or trigonal plates of micrometer size. However, there were no reports of dendrites of such metals in the crystals. In this paper, we investigate the mode of occurrence of platinum dendrites in Li2B4O7 single crystals grown by the CZ method and discuss the formation mechanism of the dendrites associated with the cellular structure formation of Li2B4O7 single crystal. The growth condition for preventing such dendrite formation is also considered. EXPERIMENTAL Lithium tetraborate (Li2B4O7) single crystals were grown by the CZ method using rf heating combined with an automatic diameter control system as shown in Figure 1 [11]. The starting materials were commercially available Li2B4O7 polycrystals in the molar ratio (B/Li) of 2.00; they were melted in a platinum crucible, either 50 mmf 3 50 mm/h or 130 mmf 3 130 mm/h. The crystal was pulled along the ^110& and ^001& directions. The selected oxygen gas flow rate during growth was 0 to 1000 mL/min. The crystal rotation rate was 0.2 to 10 rpm and the growth rate was 0.6 to 2.0 mm/h. The diameter of the grown crystals was 25 to 80 mm. Thin sections were made perpendicular to the pulling axis in order to investigate the opaque defects in the crystal with an optical microscope. A sample containing opaque defects was also dissolved in acetic acid solution [HCl (1 1 1)] to differentiate dendrites and crystals. Isolated dendrites were examined by means of electron probe microanalysis and scanning electron microscopy. Chemical analysis of the impurities in the as-grown crystals was performed using Leco instrumentation. RESULTS AND DISCUSSION Mode of Occurrence of Platinum Dendrite. During the growth of crystals with a diameter over 25 mm, opaque defects (opaque ring and core inclusion) usually appeared when the growth rate exceeded 1 mm/h. An as-grown crystal containing opaque defects is shown in Figure 2. The defects were more remarkable in the ^001& grown crystal than the ^110& crystal. The opaque rings appear periodically along the pulling axis. The microscopic photograph of an opaque ring in Figure 3 shows that the ring is composed of cells with many elongated voids, including spherical materials. The elongated voids do not intersect the cell boundary.
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FIG. 1 Schematic illustration of the furnace for Li2B4O7 crystal growth. The size of each slender void is less than 500 mm in length. A similar structure is observed in the core defect region; this indicates that the entity of the opaque ring is the same as that of the core defect. The solid–liquid interface was found to be rough (Fig. 4) when the as-grown crystal included opaque regions. The morphology of the rough interface was predominated by the crystallographic symmetry. Thus, it is likely that the formation of opaque defects (opaque ring and core inclusion) is associated with the cellular growth of the Li2B4O7 crystal. Metal dendrites and spherical voids were observed along a cell boundary, as shown in Figure 5. Dendrites were observed in the crystal grown under the oxygen flow rate over 200 mL/min; however, the appearance of opaque defects was not related to the oxygen flow rate. The defects were platelets, because they grew in the flat cell boundary. The size of the
FIG. 2 As-grown Li2B4O7 crystal including opaque defects.
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FIG. 3 Microscopic observation of the opaque ring. It has cellular structures with elongated bubbles and many opaque dots. Cell growth direction is ^001&. dendrites was 50 to 500 mm and the diameter of each branch of a dendrite ranged from 10 to 30 mm. Figure 6 shows a scanning electron microscopy photograph of the dendrites found in the residue after the dissolution of the crystal. The angle between primary and secondary branches of these dendrites is either 90° or 120°. The metal dendrites were identified by electron probe microanalysis to be platinum. Platinum belongs to the space group Fm3m, and the 90° or 120° angle between primary and secondary branches of dendrites may come from four- or threefold symmetry, although the growth direction of each branch was not known. Formation of Platinum Dendrites. The cellular growth is caused by constitutional supercooling. In the case of the crystal growth from the congruent melt, the constitutional supercooling is due to impurities in the melt. Because the void formation was due to the supersaturation of volatile impurities at the solid–liquid interface during growth, it might have been the volatile impurities that led to the cellular growth. Results of the chemical analysis of the volatile components are shown in Table 1. H2O content in the opaque-defect bearing crystal was larger than that in the transparent crystal. Thus, the volatile component related to void formation as well as cellular growth was
FIG. 4 Solid-liquid interface showing the rough plane composed of cells. Growth direction is parallel to ^001&.
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FIG. 5 Platinum dendrites formed along the cell boundary of Li2B4O7: (a) dendrites with a 120° angle between primary and secondary branches and (b) dendrites with a 90° angle. presumed to be H2O. The H2O component in the melt came from the starting materials. The platinum was also an impurity consisting of opaque defects. However, the impurity that dominated the cellular growth was the H2O component, because platinum dendrites were not observed in some crystals with the cellular structure. Platinum reacts in the high-temperature Li2B4O7 melt and is dissolved into the melt, probably taking the form of ions. This electron
FIG. 6 Platinum dendrites found in the residue of an acid-dissolved Li2B4O7 crystal including opaque defects. The “A” is a fiber consisting of the filter paper.
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TABLE 1 Chemical Analysis of Impurities in Li2B4O7 Crystal and Starting Materials
Starting materials Transparent crystal Crystal bearing opaque defect
C
N
H (wt%)
trace trace trace
trace trace trace
0.02 ,0.005 0.02
issue from the platinum is a type of oxidation process. The involvement of the oxidation process in dendrite formation was experimentally shown; the amount of platinum dendrites formed was determined by the oxygen partial pressure in the furnace. The dissolved platinum ions were transferred to the interface of the growing Li2B4O7 mainly by thermal convection. They were rejected by the moving interface and piled up in the solute diffusion boundary layer, because the partition coefficient of platinum is less than unity. When the cellular growth of Li2B4O7 starts, this pile-up becomes much larger, especially for the platinum ions migrating into the narrow space partitioned by the cell wall where the small mixing and rather static melt condition is achieved. As a result, the platinum dendrites grow fast along the growth directions in the cell boundary, and this rapid growth reduces the supersaturation. Subsequent growth occurs more slowly, but only the tip of the filament is located in regions of supersaturation high enough for further dendritic growth. However, a periodic development of side branches from the dendrite axis originates from the periodical perturbation of the overall thermal field or the supersaturation of the growing filament, whereas dendrites select a particular crystallographic direction for optimal growth. Figure 7 is a schematic illustration of the formation of opaque defects associated with the cellular growth of Li2B4O7. The supercooled melt that adhered to the rim of a growth interface contained many voids, which probably were derived from the supersaturation of
FIG. 7 Schematic illustration of the inter-relationship in occurrence between cells, voids, and platinum dendrites.
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H2O component in the melt. As voids do not wet the interface well enough, they are repulsed by the growth front and move together with it during growth. However, the entrapment of those in the crystal takes place by the sudden increase in the growth rate due to cellular growth. Because the void diffusion in the cell is much slower than the cellular growth rate, the captured void is elongated perpendicular to the growth interface by interface dragging. Such an elongated texture is possible if the velocity of the cell front is matched to the void flow rate in the melt. This is very similar to the aligned bubbles observed in an ice cube [12]. A void in a cell boundary is spherical because the interaction with the interface does not act in a cell boundary. Platinum dendrites were not observed inside the cell. This indicates that the dendritic growth of platinum needs the high accumulation of dissolved platinum, which is possible only in the cell boundary formed by cellular growth; the melt near the growth front does not provide such a high supersaturation. The onset of constitutional supercooling is given by G L/R , 2 m(1 2 k0)Ci/D
(1)
where R is the growth rate, m is a slope of the liquidus, Ci is the impurity concentration in the melt at the interface, D is the diffusion constant of the impurity, and k0 is the equilibrium partition coefficient. [13]. Eq. 1 shows that cellular growth tends to occur at a larger growth rate, whereas an increase of the rotation rate results in the reduction of the amount of the impurity at the interface, leading to reduced cellular growth. Thus, we conclude that dendrite formation is closely associated with the cellular growth of Li2B4O7 and is probably caused by the high concentration of the H2O component in the melt. In order to prevent platinum dendrite growth during cellular growth, the partial oxygen pressure must be adjusted to prevent the dissolution of platinum into the melt. CONCLUSIONS Platinum dendrites were found to coexist with opaque defects in grown Li2B4O7 crystals and their morphology represented the crystallographic symmetry. The opaque defect formation was associated with the cellular growth due to H2O component supersaturation in the melt at the solid–liquid interface. The dissolved platinum piled up in the cell boundary during cellular growth of Li2B4O7 crystal. Then dendritic crystals of platinum started to grow from the heavily supersaturated melt in the cell boundary. The occurrence of platinum dendrites was dependent on the oxygen partial pressure during growth. This is probably because the content of soluble platinum in the melt was determined by the oxygen partial pressure. Reduction of the H2O component and platinum in the melt is required to suppress the occurrence of platinum dendrites. REFERENCES 1. 2.
J. Krough-Moe, Acta Crystallogr. 15, 190 (1962). J.R.W. Whatmore, N.M. Shorrocks, C. O’Hara, F.W. Ainger, and I.W. Young, Electron. Lett. 17, 11 (1981). 3. Y. Ebata, H. Suzuki, S. Matsumura, and K. Fukuda, Jpn. J. Appl. Phys. 22 (Suppl. 22–2), 160 (1983). 4. M. Adachi, T. Shiosaki, H. Kobayasi, O. Ohnishi, and K. Kawabata, Proc. IEEE Ultrasonic Symp., 228 (1987).
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5. 6. 7. 8. 9. 10. 11. 12. 13.
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R. Komatsu, T. Sugawara, K. Sassa, N. Sarukura, Z. Liu, S. Izumida, Y. Segawa, S. Uda, T. Fukuda, and K. Yamanouchi, Appl. Phys. Lett. 70 (26), 30 (1997). J.D. Garrett, M.N. Iyer, and J.E. Greedan, J. Cryst. Growth 41, 225 (1977). S. Matsumura, T. Omi, N. Yamaji, and Y. Ebata, Proc. IEEE Ultrasonic Symp., 247 (1987). S. Fan, S. Shen, and W. Wang, J. Cryst. Growth 99, 811 (1990). R. Komatsu, T. Suetsugu, S. Uda, and M. Ono, Ferroelectrics 95, 103 (1989). C.D. Brandle, D.C. Miller, and J.W. Nielsen, J. Cryst. Growth 12, 195 (1972). R. Komatsu, S. Uda, and K. Hikita, Jpn. J. Appl. Phys. 32, 4364 (1993). Ya.E. Geguin and A.S. Dzuba, J. Cryst. Growth 52, 337 (1981). W.A. Tiller, J. Cryst. Growth 2, 69 (1968).
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DEVELOPMENT OF PLATINUM DENDRITE IN LITHIUM TETRABORATE CRYSTAL GROWN BY THE CZOCHRALSKI METHOD
R. Komatsu* and S. Uda Central Research Institute, Mitsubishi Materials Corp., 1–297 Kitabukuro-cho, Omiya, Saitama 330 Japan (Refereed) (Received June 16, 1997; Accepted August 4, 1997)
ABSTRACT Platinum dendrites were found in lithium tetraborate crystals grown by the Czochralski method using a platinum crucible. The mode of occurrence and formation mechanism of platinum dendrite in lithium tetraborate were examined. It is revealed that platinum dendrites developed in the cellular structure that occurred during growth. The formation of platinum dendrite that is discussed is associated with the growth condition leading to cellular growth. The morphology of platinum dendrite is also explained by its specific crystallographic symmetry. © 1998 Elsevier Science Ltd KEYWORDS: A. oxides, B. crystal growth, D. defects INTRODUCTION Lithium tetraborate (Li2B4O7) is a piezoelectric material belonging to the space group I41cd [1]. It has attracted much attention as a surface acoustic wave substrate for high frequency because of its high coupling factor (k2) and low temperature coefficient of frequency. Ever since Whatmore et al. [2] first reported this single crystal, many efforts have been made to apply it to surface acoustic wave substrate devices [3,4]. Recently, we reported that this crystal is a new nonlinear crystal for ultraviolet frequency conversion, including the fourth and fifth harmonics generation of the Nd:YAG laser [5]. Its application to nonlinear devices in the ultraviolet region is also promising.
*To whom correspondence should be addressed. 433
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With respect to the growth of lithium tetraborate single crystals, Li2B4O7 melts congruently and, consequently, crystals can be grown by the Czochralski (CZ) or the Bridgman method. The growth of large crystals has been investigated for commercial use since a report by Garrett et al. [6]. The growth of single crystals with a 3-inch diameter by the CZ method was reported by Matsumura et al. [7], whereas growth by the Bridgman method was reported by Fan et al. [8]. One of the most serious problems to solve is macroscopic “opaque defects” in the grown crystals. The opaque defects are classified into two types. One is a opaque ring perpendicular to the pulling direction, which tends to spread from the central core to the peripheral, and the other is the array of core inclusions (voids) running parallel to the pulling direction. We have found metallic dendrites in opaque defects, which might have been derived from metal dissolved from the platinum crucible [9]. It has been reported [10] that when a platinum or iridium crucible was used for the growth of oxide crystals, metal from the crucible was often observed as inclusions in the grown oxide crystals. These inclusions were made of hexagonal or trigonal plates of micrometer size. However, there were no reports of dendrites of such metals in the crystals. In this paper, we investigate the mode of occurrence of platinum dendrites in Li2B4O7 single crystals grown by the CZ method and discuss the formation mechanism of the dendrites associated with the cellular structure formation of Li2B4O7 single crystal. The growth condition for preventing such dendrite formation is also considered. EXPERIMENTAL Lithium tetraborate (Li2B4O7) single crystals were grown by the CZ method using rf heating combined with an automatic diameter control system as shown in Figure 1 [11]. The starting materials were commercially available Li2B4O7 polycrystals in the molar ratio (B/Li) of 2.00; they were melted in a platinum crucible, either 50 mmf 3 50 mm/h or 130 mmf 3 130 mm/h. The crystal was pulled along the ^110& and ^001& directions. The selected oxygen gas flow rate during growth was 0 to 1000 mL/min. The crystal rotation rate was 0.2 to 10 rpm and the growth rate was 0.6 to 2.0 mm/h. The diameter of the grown crystals was 25 to 80 mm. Thin sections were made perpendicular to the pulling axis in order to investigate the opaque defects in the crystal with an optical microscope. A sample containing opaque defects was also dissolved in acetic acid solution [HCl (1 1 1)] to differentiate dendrites and crystals. Isolated dendrites were examined by means of electron probe microanalysis and scanning electron microscopy. Chemical analysis of the impurities in the as-grown crystals was performed using Leco instrumentation. RESULTS AND DISCUSSION Mode of Occurrence of Platinum Dendrite. During the growth of crystals with a diameter over 25 mm, opaque defects (opaque ring and core inclusion) usually appeared when the growth rate exceeded 1 mm/h. An as-grown crystal containing opaque defects is shown in Figure 2. The defects were more remarkable in the ^001& grown crystal than the ^110& crystal. The opaque rings appear periodically along the pulling axis. The microscopic photograph of an opaque ring in Figure 3 shows that the ring is composed of cells with many elongated voids, including spherical materials. The elongated voids do not intersect the cell boundary.
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FIG. 1 Schematic illustration of the furnace for Li2B4O7 crystal growth. The size of each slender void is less than 500 mm in length. A similar structure is observed in the core defect region; this indicates that the entity of the opaque ring is the same as that of the core defect. The solid–liquid interface was found to be rough (Fig. 4) when the as-grown crystal included opaque regions. The morphology of the rough interface was predominated by the crystallographic symmetry. Thus, it is likely that the formation of opaque defects (opaque ring and core inclusion) is associated with the cellular growth of the Li2B4O7 crystal. Metal dendrites and spherical voids were observed along a cell boundary, as shown in Figure 5. Dendrites were observed in the crystal grown under the oxygen flow rate over 200 mL/min; however, the appearance of opaque defects was not related to the oxygen flow rate. The defects were platelets, because they grew in the flat cell boundary. The size of the
FIG. 2 As-grown Li2B4O7 crystal including opaque defects.
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FIG. 3 Microscopic observation of the opaque ring. It has cellular structures with elongated bubbles and many opaque dots. Cell growth direction is ^001&. dendrites was 50 to 500 mm and the diameter of each branch of a dendrite ranged from 10 to 30 mm. Figure 6 shows a scanning electron microscopy photograph of the dendrites found in the residue after the dissolution of the crystal. The angle between primary and secondary branches of these dendrites is either 90° or 120°. The metal dendrites were identified by electron probe microanalysis to be platinum. Platinum belongs to the space group Fm3m, and the 90° or 120° angle between primary and secondary branches of dendrites may come from four- or threefold symmetry, although the growth direction of each branch was not known. Formation of Platinum Dendrites. The cellular growth is caused by constitutional supercooling. In the case of the crystal growth from the congruent melt, the constitutional supercooling is due to impurities in the melt. Because the void formation was due to the supersaturation of volatile impurities at the solid–liquid interface during growth, it might have been the volatile impurities that led to the cellular growth. Results of the chemical analysis of the volatile components are shown in Table 1. H2O content in the opaque-defect bearing crystal was larger than that in the transparent crystal. Thus, the volatile component related to void formation as well as cellular growth was
FIG. 4 Solid-liquid interface showing the rough plane composed of cells. Growth direction is parallel to ^001&.
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FIG. 5 Platinum dendrites formed along the cell boundary of Li2B4O7: (a) dendrites with a 120° angle between primary and secondary branches and (b) dendrites with a 90° angle. presumed to be H2O. The H2O component in the melt came from the starting materials. The platinum was also an impurity consisting of opaque defects. However, the impurity that dominated the cellular growth was the H2O component, because platinum dendrites were not observed in some crystals with the cellular structure. Platinum reacts in the high-temperature Li2B4O7 melt and is dissolved into the melt, probably taking the form of ions. This electron
FIG. 6 Platinum dendrites found in the residue of an acid-dissolved Li2B4O7 crystal including opaque defects. The “A” is a fiber consisting of the filter paper.
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TABLE 1 Chemical Analysis of Impurities in Li2B4O7 Crystal and Starting Materials
Starting materials Transparent crystal Crystal bearing opaque defect
C
N
H (wt%)
trace trace trace
trace trace trace
0.02 ,0.005 0.02
issue from the platinum is a type of oxidation process. The involvement of the oxidation process in dendrite formation was experimentally shown; the amount of platinum dendrites formed was determined by the oxygen partial pressure in the furnace. The dissolved platinum ions were transferred to the interface of the growing Li2B4O7 mainly by thermal convection. They were rejected by the moving interface and piled up in the solute diffusion boundary layer, because the partition coefficient of platinum is less than unity. When the cellular growth of Li2B4O7 starts, this pile-up becomes much larger, especially for the platinum ions migrating into the narrow space partitioned by the cell wall where the small mixing and rather static melt condition is achieved. As a result, the platinum dendrites grow fast along the growth directions in the cell boundary, and this rapid growth reduces the supersaturation. Subsequent growth occurs more slowly, but only the tip of the filament is located in regions of supersaturation high enough for further dendritic growth. However, a periodic development of side branches from the dendrite axis originates from the periodical perturbation of the overall thermal field or the supersaturation of the growing filament, whereas dendrites select a particular crystallographic direction for optimal growth. Figure 7 is a schematic illustration of the formation of opaque defects associated with the cellular growth of Li2B4O7. The supercooled melt that adhered to the rim of a growth interface contained many voids, which probably were derived from the supersaturation of
FIG. 7 Schematic illustration of the inter-relationship in occurrence between cells, voids, and platinum dendrites.
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H2O component in the melt. As voids do not wet the interface well enough, they are repulsed by the growth front and move together with it during growth. However, the entrapment of those in the crystal takes place by the sudden increase in the growth rate due to cellular growth. Because the void diffusion in the cell is much slower than the cellular growth rate, the captured void is elongated perpendicular to the growth interface by interface dragging. Such an elongated texture is possible if the velocity of the cell front is matched to the void flow rate in the melt. This is very similar to the aligned bubbles observed in an ice cube [12]. A void in a cell boundary is spherical because the interaction with the interface does not act in a cell boundary. Platinum dendrites were not observed inside the cell. This indicates that the dendritic growth of platinum needs the high accumulation of dissolved platinum, which is possible only in the cell boundary formed by cellular growth; the melt near the growth front does not provide such a high supersaturation. The onset of constitutional supercooling is given by G L/R , 2 m(1 2 k0)Ci/D
(1)
where R is the growth rate, m is a slope of the liquidus, Ci is the impurity concentration in the melt at the interface, D is the diffusion constant of the impurity, and k0 is the equilibrium partition coefficient. [13]. Eq. 1 shows that cellular growth tends to occur at a larger growth rate, whereas an increase of the rotation rate results in the reduction of the amount of the impurity at the interface, leading to reduced cellular growth. Thus, we conclude that dendrite formation is closely associated with the cellular growth of Li2B4O7 and is probably caused by the high concentration of the H2O component in the melt. In order to prevent platinum dendrite growth during cellular growth, the partial oxygen pressure must be adjusted to prevent the dissolution of platinum into the melt. CONCLUSIONS Platinum dendrites were found to coexist with opaque defects in grown Li2B4O7 crystals and their morphology represented the crystallographic symmetry. The opaque defect formation was associated with the cellular growth due to H2O component supersaturation in the melt at the solid–liquid interface. The dissolved platinum piled up in the cell boundary during cellular growth of Li2B4O7 crystal. Then dendritic crystals of platinum started to grow from the heavily supersaturated melt in the cell boundary. The occurrence of platinum dendrites was dependent on the oxygen partial pressure during growth. This is probably because the content of soluble platinum in the melt was determined by the oxygen partial pressure. Reduction of the H2O component and platinum in the melt is required to suppress the occurrence of platinum dendrites. REFERENCES 1. 2.
J. Krough-Moe, Acta Crystallogr. 15, 190 (1962). J.R.W. Whatmore, N.M. Shorrocks, C. O’Hara, F.W. Ainger, and I.W. Young, Electron. Lett. 17, 11 (1981). 3. Y. Ebata, H. Suzuki, S. Matsumura, and K. Fukuda, Jpn. J. Appl. Phys. 22 (Suppl. 22–2), 160 (1983). 4. M. Adachi, T. Shiosaki, H. Kobayasi, O. Ohnishi, and K. Kawabata, Proc. IEEE Ultrasonic Symp., 228 (1987).
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5. 6. 7. 8. 9. 10. 11. 12. 13.
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R. Komatsu, T. Sugawara, K. Sassa, N. Sarukura, Z. Liu, S. Izumida, Y. Segawa, S. Uda, T. Fukuda, and K. Yamanouchi, Appl. Phys. Lett. 70 (26), 30 (1997). J.D. Garrett, M.N. Iyer, and J.E. Greedan, J. Cryst. Growth 41, 225 (1977). S. Matsumura, T. Omi, N. Yamaji, and Y. Ebata, Proc. IEEE Ultrasonic Symp., 247 (1987). S. Fan, S. Shen, and W. Wang, J. Cryst. Growth 99, 811 (1990). R. Komatsu, T. Suetsugu, S. Uda, and M. Ono, Ferroelectrics 95, 103 (1989). C.D. Brandle, D.C. Miller, and J.W. Nielsen, J. Cryst. Growth 12, 195 (1972). R. Komatsu, S. Uda, and K. Hikita, Jpn. J. Appl. Phys. 32, 4364 (1993). Ya.E. Geguin and A.S. Dzuba, J. Cryst. Growth 52, 337 (1981). W.A. Tiller, J. Cryst. Growth 2, 69 (1968).