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Growth of near stoichiometric LiNbO3 crystals by a modified zone melting method
Journal of Alloys and Compounds 402 (2005) 224–226
Growth of near stoichiometric LiNbO3 crystals by a modified zone melting method W.Y. Wang ∗ , X.L. Chen, D.Q. Ni, D.F. Zhang, X. Wu Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603-49, Beijing 100080, PR China Received 17 January 2005; accepted 16 February 2005 Available online 6 June 2005
Abstract Near stoichiometric Lithium niobate (LiNbO3 ) bulk crystals have been grown by a modified zone melting method. In this method, a platinum strip immersed in melting zone was used as heater. The Li content in the crystal was achieved to 49.95 mol%, which was determined by the UV absorption edge of the grown crystal. The characteristics of this technique have been discussed. © 2005 Elsevier B.V. All rights reserved. Keywords: Ferroelectrics; Crystal growth; Light absorption and reflection
1. Introduction Lithium niobate (LiNbO3 ) is an outstanding ferroelectric material. It integrates various excellent properties, such as piezoelectrical, electro-optical, acousto-optical, non-linear optical, photorefractive, and crystallographic properties [1]. However, LiNbO3 has a tendency to non-stoichiometry (Li/Nb < 1), which strongly influences many of its properties [2–5]. The commercially available LiNbO3 is congruent (Li/Nb ∼ 0.94), having high concentrations of intrinsic defects due to the Li deficiency [6]. By comparison, nearstoichiometric LiNbO3 (ns-LN) or stoichiometric LiNbO3 (s-LN) (Li/Nb = 1) contain much fewer intrinsic defects, and therefore better performance in a number of cases. Especially, the coercive field of ns-LN or s-LN crystals is 1–2 orders of magnitude lower than that of congruent crystals [5,7]. This is very favorable for the preparation of periodically poled LiNbO3 crystals (i.e. LiNbO3 optical superlattice), which has potential applications in non-linear optical devices, optical communications and optical computers [8–10]. Therefore, preparing high-quality ns-LN or s-LN crystals is of great importance. Up to now, quite a few methods have been ∗
Corresponding author. Tel.: +86 10 82649032; fax: +86 10 82649646. E-mail address: [email protected] (W.Y. Wang).
0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2005.02.067
used to obtain ns-LN or s-LN crystals, which include the conventional CZ technique, double crucible CZ technique, floating zone method, laser heated pedestal growth, the K2 Ocontaining flux growth, the LiVO3 -containing flux growth, and the vapor transport equilibration method [11–21]. Unfortunately, each method more or less has its drawbacks or limits. Moreover, the compositional inhomogeneity in single crystals remains a main problem. So, here reported the ns-LN crystal growth by a modified zone melting method, i.e., the metal strip heated zone melting (MSHZM) technique, which has some advantages and thereby is promising for growing homogeneous s-LN crystals. The so-called MSHZM technique was first presented by Gasson [22]. The resultant Nd: CaWO4 crystals have been reported to show better optical quality than the CZ pulled crystals. Subsequently, this method has been further studied to grow large and high-quality CaCO3 [23], congruent LiNbO3 [24], -BaB2 O4 [25], NaNO3 [26], Sc: LiNbO3 [27], and (Lix Na1−x )NO3 [28] crystals.
2. Experimental Powders of Li2 CO3 (99.99%) and Nb2 O5 (99.99%) were used as the starting materials. The Li/Nb ratio of the materials
W.Y. Wang et al. / Journal of Alloys and Compounds 402 (2005) 224–226
225
tion spectra of these two samples were recorded with a Cary 2390 spectrometer.
3. Results and discussion
Fig. 1. Schematic diagram of the hard core of the apparatus used for the metal strip heated zone melting growth.
was around 0.49–0.51. By the conventional sintering technique, a condensed ceramic rod 28 mm in diameter and 180 mm in length was obtained and used as the feed rod. Fig. 1 shows the hard core of the apparatus for the MSHZM growth. The key part is an electrically heated platinum strip 1 mm thick × 50 mm wide × 160 mm long, mounted horizontally between water-cooled leads. The center part of the Pt strip is perforated by some small holes, which allow the transfer of melt. The maximum AC current of 500 A at 3 V is enough to raise the Pt strip to the operating temperature. A feed rod is suspended over the Pt strip. Under the strip is a commercially available congruent LiNbO3 crystal seed in [0 0 1] direction. When the Pt strip is heated to the desired temperature, the ends of the feed rod and the seed rod are moved into contact with the strip. Then, the melts formed above and below the strip get in touch with each other through the small holes. In the whole growth procedure, the melt zone is stable and only 2–3 mm thick. The feed rod and the seed rod counter-rotated coaxially with a speed of 30 rpm. The crystal growth rate was 2–7 mm/h. In order to study the compositional homogeneity of grown crystals, a crystal grown from a feed rod with the composition of 49.49 mol% Li2 O was divided into several parts along the growth direction [0 0 1]. Then four different parts as listed in Table 1 were chemically analyzed by the inductively coupled plasma-atomic emission spectroscopy (ICP-AES). The experimental error is 0.2%. In addition, two 1 mm thick slices were cut from a commercially available congruent LiNbO3 crystal and another crystal grown from a feed rod with the composition of 50.0 mol% Li2 O, respectively. The absorp-
As-grown crystals are colorless and transparent, without any visible defects. By using the metal strip with the abovementioned size, the size of the crystals varies with the growth conditions, usually 10–19 mm in diameter and 10–50 mm in length. Fig. 2 gives a photo of an as-grown crystal. The white points appeared on the crystal is due to the strong reflection of the glossy crystal surface. As the UV absorption edge is very sensitive to the composition of the LiNbO3 crystal, here adopted the measurement of the UV absorption edge for characterizing the crystal composition [12]. After the reflection correction, the roomtemperature absorption spectra of the samples are shown in Fig. 3. From Fig. 3, it can be seen that the as-grown LiNbO3 sample exhibits a blue shift from 320 to 304 nm at the absorption coefficient α = 20 cm−1 . According to the equation [12], the crystal composition of the as-grown sample is calculated as 49.95 mol% Li2 O.
Fig. 2. Photo of an as-grown LiNbO3 crystal.
Table 1 Li content vs. crystal length along the growth direction of an as-grown LiNbO3 crystal Crystal length along the growth direction (mm)
Li content in the crystal (mol% Li2 O)
0–6 29–33 42–44 45–47
49.24 49.49 49.49 49.49
Fig. 3. The room-temperature UV absorption spectra of samples. (a) Asgrown near-stoichiometric LiNbO3 crystal; (b) congruent LiNbO3 crystal.
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W.Y. Wang et al. / Journal of Alloys and Compounds 402 (2005) 224–226
MSHZM technique has several advantages and is promising for growing compositional homogeneous off-congruent oxide crystals such as stoichiometric LiNbO3 due to the segregation effect.
Acknowledgements This work is supported by National Natural Science Foundation of China under Grant No. 50002013 and by Chinese Academy of Sciences through a Hundred Talents Project. Fig. 4. The plot of Li content vs. crystal length along the growth direction of an as-grown LiNbO3 crystal.
Compared to other preparation methods, the MSHZM technique is expected to have some advantages. Above all, by taking advantage of the solute segregation effect, compositional homogeneous s-LN crystals can be obtained by the MSHZM technique. This can be illustrated by the table and the plot of the Li content versus the crystal length along the growth direction of an as-grown LiNbO3 crystal (Table 1; Fig. 4). From Table 1, the different parts from 29 to 47 mm have the same Li content (49.49 mol% Li2 O), which is equal to the composition of the feed rod. Correspondingly, in Fig. 4, the crystal composition at the BC stage is constant at 49.49 mol% Li2 O. In other words, the as-grown LiNbO3 crystal is compositional homogeneous at the BC stage. This phenomenon is the result caused by the solute segregation effect since the equilibrium segregation coefficient of Li2 O is smaller than 1 when LiNbO3 crystallizes from the nearly stoichiometric melt according to the Li2 O–Nb2 O5 phase diagram [29]. In addition, the MSHZM technique also has the following advantages: (1) Because a metal strip heater is immersed in the melting zone, the thermocapillary and gravity-induced convection in the melting zone can be reduced significantly. Therefore, the melt/crystal interface can be readily kept constant. This is very favorable to obtain large and highquality crystals. (2) Since the melting zone is very thin (usually 2–3 mm), the melt is uniform, stable and not easy to collapse. (3) The direct coupling of the metal strip heater and the material to be melted makes heat losses very low. (4) By choosing a metal strip compatible with the material to be melted, various materials can be prepared by this method.
4. Conclusion Near stoichiometric (49.95 mol% Li2 O) LiNbO3 crystals have been grown by the metal strip heated zone melting technique and characterized by the UV absorption edge. The
References [1] R.S. Weis, T.K. Gaylord, Appl. Phys. A 37 (1985) 191. [2] J.R. Carruthers, G.E. Peterson, M. Grasso, P.M. Bridenbaugh, J. Appl. Phys. 42 (1971) 1846. [3] R.L. Byer, Y.K. Park, R.S. Feigelson, W.L. Kway, Appl. Phys. Lett. 39 (1981) 17. [4] B.C. Grabmaier, W. Wersing, W. Koestler, J. Cryst. Growth 110 (1991) 339. [5] V. Gopalan, T.E. Mitchell, Y. Furukawa, K. Kitamura, Appl. Phys. Lett. 72 (1998) 1981. [6] O.F. Schirmer, O. Thiemann, M. W¨ohlecke, J. Phys. Chem. Solids 52 (1991) 185. ´ P´eeter, Electron. Lett. 36 (2000) [7] A. Grisard, E. Lallier, K. Polg´ar, A. 1043. [8] Y.L. Lu, Y.Q. Lu, X.F. Cheng, C.C. Xue, N.B. Ming, Appl. Phys. Lett. 68 (1996) 2781. [9] R. Byer, J. Nonlinear Opt. Phys. Mater. 6 (1997) 549. [10] K. Sanaka, K. Kawahara, T. Kuga, Phys. Rev. Lett. 86 (2001) 5621. ´ P´eter, L. Kov´acs, G. Corradi, Zs. Szaller, J. Cryst. [11] K. Polg´ar, A. Growth 177 (1997) 211. [12] M. W¨ohlecke, G. Corradi, K. Betzler, Appl. Phys. B 63 (1996) 323. [13] K. Kitamura, J.K. Yamamoto, N. Iyi, S. Kimura, T. Hayashi, J. Cryst. Growth 116 (1992) 327. [14] S. Kan, M. Sakamoto, Y. Okana, K. Hoshikawa, T. Fukuda, J. Cryst. Growth 119 (1992) 215. [15] N. Iyi, K. Kitamura, F. Izumi, J.K. Yamamoto, T. Hayashi, H. Asano, S. Kimura, J. Solid State Chem. 101 (1992) 340. [16] Y.S. Luh, M.M. Fejer, R.L. Byer, R.S. Feigelson, J. Cryst. Growth 85 (1987) 264. [17] G. Malovichko, V.G. Grachev, L.P. Yurchenko, V.Ya. Proshko, E.P. Kokanyan, V.T. Gabrielyan, Phys. Status Solidi (a) 133 (1992) K29. ´ P´eter, L. Kov´acs, G. Corradi, Zs. Szaller, J. Cryst. [18] K. Polg´ar, A. Growth 177 (1997) 211. ´ P´eter, I. F¨oldv´ari, Zs. Szaller, J. Cryst. Growth 218 [19] K. Polg´ar, A. (2000) 327. [20] S. Erdei, R.G. Schlecht, Proc. IEEE 87 (1999) 2121. [21] P.F. Bordui, R.G. Norwood, D.H. Jundt, M.M. Fejer, J. Appl. Phys. 71 (1992) 875. [22] D.B. Gasson, J. Sci. Instrum. 42 (1965) 114. [23] C. Belin, J. Cryst. Growth 34 (1976) 341. [24] J. Aubert, B. Bechevert, J. Daval, US Patent 4 752 451 (1988). [25] R.O. Hengel, F. Fischer, J. Cryst. Growth 114 (1991) 656. [26] C.W. Lan, S. Kou, J. Cryst. Growth 108 (1991) 541. [27] J.K. Yamamoto, K. Kitamura, N. Iyi, S. Kimura, J. Cryst. Growth 121 (1992) 522. [28] H.J. Koh, Y. Furukawa, P. Rudolph, T. Fukuda, J. Cryst. Growth 149 (1995) 236. [29] W.A. Tiller, S. Uda, J. Cryst. Growth 129 (1993) 328.
Growth of near stoichiometric LiNbO3 crystals by a modified zone melting method W.Y. Wang ∗ , X.L. Chen, D.Q. Ni, D.F. Zhang, X. Wu Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603-49, Beijing 100080, PR China Received 17 January 2005; accepted 16 February 2005 Available online 6 June 2005
Abstract Near stoichiometric Lithium niobate (LiNbO3 ) bulk crystals have been grown by a modified zone melting method. In this method, a platinum strip immersed in melting zone was used as heater. The Li content in the crystal was achieved to 49.95 mol%, which was determined by the UV absorption edge of the grown crystal. The characteristics of this technique have been discussed. © 2005 Elsevier B.V. All rights reserved. Keywords: Ferroelectrics; Crystal growth; Light absorption and reflection
1. Introduction Lithium niobate (LiNbO3 ) is an outstanding ferroelectric material. It integrates various excellent properties, such as piezoelectrical, electro-optical, acousto-optical, non-linear optical, photorefractive, and crystallographic properties [1]. However, LiNbO3 has a tendency to non-stoichiometry (Li/Nb < 1), which strongly influences many of its properties [2–5]. The commercially available LiNbO3 is congruent (Li/Nb ∼ 0.94), having high concentrations of intrinsic defects due to the Li deficiency [6]. By comparison, nearstoichiometric LiNbO3 (ns-LN) or stoichiometric LiNbO3 (s-LN) (Li/Nb = 1) contain much fewer intrinsic defects, and therefore better performance in a number of cases. Especially, the coercive field of ns-LN or s-LN crystals is 1–2 orders of magnitude lower than that of congruent crystals [5,7]. This is very favorable for the preparation of periodically poled LiNbO3 crystals (i.e. LiNbO3 optical superlattice), which has potential applications in non-linear optical devices, optical communications and optical computers [8–10]. Therefore, preparing high-quality ns-LN or s-LN crystals is of great importance. Up to now, quite a few methods have been ∗
Corresponding author. Tel.: +86 10 82649032; fax: +86 10 82649646. E-mail address: [email protected] (W.Y. Wang).
0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2005.02.067
used to obtain ns-LN or s-LN crystals, which include the conventional CZ technique, double crucible CZ technique, floating zone method, laser heated pedestal growth, the K2 Ocontaining flux growth, the LiVO3 -containing flux growth, and the vapor transport equilibration method [11–21]. Unfortunately, each method more or less has its drawbacks or limits. Moreover, the compositional inhomogeneity in single crystals remains a main problem. So, here reported the ns-LN crystal growth by a modified zone melting method, i.e., the metal strip heated zone melting (MSHZM) technique, which has some advantages and thereby is promising for growing homogeneous s-LN crystals. The so-called MSHZM technique was first presented by Gasson [22]. The resultant Nd: CaWO4 crystals have been reported to show better optical quality than the CZ pulled crystals. Subsequently, this method has been further studied to grow large and high-quality CaCO3 [23], congruent LiNbO3 [24], -BaB2 O4 [25], NaNO3 [26], Sc: LiNbO3 [27], and (Lix Na1−x )NO3 [28] crystals.
2. Experimental Powders of Li2 CO3 (99.99%) and Nb2 O5 (99.99%) were used as the starting materials. The Li/Nb ratio of the materials
W.Y. Wang et al. / Journal of Alloys and Compounds 402 (2005) 224–226
225
tion spectra of these two samples were recorded with a Cary 2390 spectrometer.
3. Results and discussion
Fig. 1. Schematic diagram of the hard core of the apparatus used for the metal strip heated zone melting growth.
was around 0.49–0.51. By the conventional sintering technique, a condensed ceramic rod 28 mm in diameter and 180 mm in length was obtained and used as the feed rod. Fig. 1 shows the hard core of the apparatus for the MSHZM growth. The key part is an electrically heated platinum strip 1 mm thick × 50 mm wide × 160 mm long, mounted horizontally between water-cooled leads. The center part of the Pt strip is perforated by some small holes, which allow the transfer of melt. The maximum AC current of 500 A at 3 V is enough to raise the Pt strip to the operating temperature. A feed rod is suspended over the Pt strip. Under the strip is a commercially available congruent LiNbO3 crystal seed in [0 0 1] direction. When the Pt strip is heated to the desired temperature, the ends of the feed rod and the seed rod are moved into contact with the strip. Then, the melts formed above and below the strip get in touch with each other through the small holes. In the whole growth procedure, the melt zone is stable and only 2–3 mm thick. The feed rod and the seed rod counter-rotated coaxially with a speed of 30 rpm. The crystal growth rate was 2–7 mm/h. In order to study the compositional homogeneity of grown crystals, a crystal grown from a feed rod with the composition of 49.49 mol% Li2 O was divided into several parts along the growth direction [0 0 1]. Then four different parts as listed in Table 1 were chemically analyzed by the inductively coupled plasma-atomic emission spectroscopy (ICP-AES). The experimental error is 0.2%. In addition, two 1 mm thick slices were cut from a commercially available congruent LiNbO3 crystal and another crystal grown from a feed rod with the composition of 50.0 mol% Li2 O, respectively. The absorp-
As-grown crystals are colorless and transparent, without any visible defects. By using the metal strip with the abovementioned size, the size of the crystals varies with the growth conditions, usually 10–19 mm in diameter and 10–50 mm in length. Fig. 2 gives a photo of an as-grown crystal. The white points appeared on the crystal is due to the strong reflection of the glossy crystal surface. As the UV absorption edge is very sensitive to the composition of the LiNbO3 crystal, here adopted the measurement of the UV absorption edge for characterizing the crystal composition [12]. After the reflection correction, the roomtemperature absorption spectra of the samples are shown in Fig. 3. From Fig. 3, it can be seen that the as-grown LiNbO3 sample exhibits a blue shift from 320 to 304 nm at the absorption coefficient α = 20 cm−1 . According to the equation [12], the crystal composition of the as-grown sample is calculated as 49.95 mol% Li2 O.
Fig. 2. Photo of an as-grown LiNbO3 crystal.
Table 1 Li content vs. crystal length along the growth direction of an as-grown LiNbO3 crystal Crystal length along the growth direction (mm)
Li content in the crystal (mol% Li2 O)
0–6 29–33 42–44 45–47
49.24 49.49 49.49 49.49
Fig. 3. The room-temperature UV absorption spectra of samples. (a) Asgrown near-stoichiometric LiNbO3 crystal; (b) congruent LiNbO3 crystal.
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W.Y. Wang et al. / Journal of Alloys and Compounds 402 (2005) 224–226
MSHZM technique has several advantages and is promising for growing compositional homogeneous off-congruent oxide crystals such as stoichiometric LiNbO3 due to the segregation effect.
Acknowledgements This work is supported by National Natural Science Foundation of China under Grant No. 50002013 and by Chinese Academy of Sciences through a Hundred Talents Project. Fig. 4. The plot of Li content vs. crystal length along the growth direction of an as-grown LiNbO3 crystal.
Compared to other preparation methods, the MSHZM technique is expected to have some advantages. Above all, by taking advantage of the solute segregation effect, compositional homogeneous s-LN crystals can be obtained by the MSHZM technique. This can be illustrated by the table and the plot of the Li content versus the crystal length along the growth direction of an as-grown LiNbO3 crystal (Table 1; Fig. 4). From Table 1, the different parts from 29 to 47 mm have the same Li content (49.49 mol% Li2 O), which is equal to the composition of the feed rod. Correspondingly, in Fig. 4, the crystal composition at the BC stage is constant at 49.49 mol% Li2 O. In other words, the as-grown LiNbO3 crystal is compositional homogeneous at the BC stage. This phenomenon is the result caused by the solute segregation effect since the equilibrium segregation coefficient of Li2 O is smaller than 1 when LiNbO3 crystallizes from the nearly stoichiometric melt according to the Li2 O–Nb2 O5 phase diagram [29]. In addition, the MSHZM technique also has the following advantages: (1) Because a metal strip heater is immersed in the melting zone, the thermocapillary and gravity-induced convection in the melting zone can be reduced significantly. Therefore, the melt/crystal interface can be readily kept constant. This is very favorable to obtain large and highquality crystals. (2) Since the melting zone is very thin (usually 2–3 mm), the melt is uniform, stable and not easy to collapse. (3) The direct coupling of the metal strip heater and the material to be melted makes heat losses very low. (4) By choosing a metal strip compatible with the material to be melted, various materials can be prepared by this method.
4. Conclusion Near stoichiometric (49.95 mol% Li2 O) LiNbO3 crystals have been grown by the metal strip heated zone melting technique and characterized by the UV absorption edge. The
References [1] R.S. Weis, T.K. Gaylord, Appl. Phys. A 37 (1985) 191. [2] J.R. Carruthers, G.E. Peterson, M. Grasso, P.M. Bridenbaugh, J. Appl. Phys. 42 (1971) 1846. [3] R.L. Byer, Y.K. Park, R.S. Feigelson, W.L. Kway, Appl. Phys. Lett. 39 (1981) 17. [4] B.C. Grabmaier, W. Wersing, W. Koestler, J. Cryst. Growth 110 (1991) 339. [5] V. Gopalan, T.E. Mitchell, Y. Furukawa, K. Kitamura, Appl. Phys. Lett. 72 (1998) 1981. [6] O.F. Schirmer, O. Thiemann, M. W¨ohlecke, J. Phys. Chem. Solids 52 (1991) 185. ´ P´eeter, Electron. Lett. 36 (2000) [7] A. Grisard, E. Lallier, K. Polg´ar, A. 1043. [8] Y.L. Lu, Y.Q. Lu, X.F. Cheng, C.C. Xue, N.B. Ming, Appl. Phys. Lett. 68 (1996) 2781. [9] R. Byer, J. Nonlinear Opt. Phys. Mater. 6 (1997) 549. [10] K. Sanaka, K. Kawahara, T. Kuga, Phys. Rev. Lett. 86 (2001) 5621. ´ P´eter, L. Kov´acs, G. Corradi, Zs. Szaller, J. Cryst. [11] K. Polg´ar, A. Growth 177 (1997) 211. [12] M. W¨ohlecke, G. Corradi, K. Betzler, Appl. Phys. B 63 (1996) 323. [13] K. Kitamura, J.K. Yamamoto, N. Iyi, S. Kimura, T. Hayashi, J. Cryst. Growth 116 (1992) 327. [14] S. Kan, M. Sakamoto, Y. Okana, K. Hoshikawa, T. Fukuda, J. Cryst. Growth 119 (1992) 215. [15] N. Iyi, K. Kitamura, F. Izumi, J.K. Yamamoto, T. Hayashi, H. Asano, S. Kimura, J. Solid State Chem. 101 (1992) 340. [16] Y.S. Luh, M.M. Fejer, R.L. Byer, R.S. Feigelson, J. Cryst. Growth 85 (1987) 264. [17] G. Malovichko, V.G. Grachev, L.P. Yurchenko, V.Ya. Proshko, E.P. Kokanyan, V.T. Gabrielyan, Phys. Status Solidi (a) 133 (1992) K29. ´ P´eter, L. Kov´acs, G. Corradi, Zs. Szaller, J. Cryst. [18] K. Polg´ar, A. Growth 177 (1997) 211. ´ P´eter, I. F¨oldv´ari, Zs. Szaller, J. Cryst. Growth 218 [19] K. Polg´ar, A. (2000) 327. [20] S. Erdei, R.G. Schlecht, Proc. IEEE 87 (1999) 2121. [21] P.F. Bordui, R.G. Norwood, D.H. Jundt, M.M. Fejer, J. Appl. Phys. 71 (1992) 875. [22] D.B. Gasson, J. Sci. Instrum. 42 (1965) 114. [23] C. Belin, J. Cryst. Growth 34 (1976) 341. [24] J. Aubert, B. Bechevert, J. Daval, US Patent 4 752 451 (1988). [25] R.O. Hengel, F. Fischer, J. Cryst. Growth 114 (1991) 656. [26] C.W. Lan, S. Kou, J. Cryst. Growth 108 (1991) 541. [27] J.K. Yamamoto, K. Kitamura, N. Iyi, S. Kimura, J. Cryst. Growth 121 (1992) 522. [28] H.J. Koh, Y. Furukawa, P. Rudolph, T. Fukuda, J. Cryst. Growth 149 (1995) 236. [29] W.A. Tiller, S. Uda, J. Cryst. Growth 129 (1993) 328.