- Email: [email protected]
Viscosity measurement with an improved torsion pendulum method
Journal of Non-Crystalline Solids 250±252 (1999) 111±115
www.elsevier.com/locate/jnoncrysol
Viscosity measurement with an improved torsion pendulum method Xinguo Hong *, Kunquan Lu Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080, People's Republic of China
Abstract In this paper, we report an improved torsion pendulum method for the viscosity measurement on molten K2 O±Nb2 O5 system and BaB2 O4 melts, with and without ¯ux, at high temperature in air ambient atmosphere. In K2 O±Nb2 O5 molten system, the viscosity shows time-dependence, indicating that the annealing process of the liquid is useful for crystal growth from the liquid. The viscosity of BaB2 O4 melt has a dierent property between the normal and supercooling region. For the purpose of comparison, the viscous property of ¯uid Hg from the reference from the normal to expanded region has been discussed. The improved torsion pendulum method shows high potential to the study of the relationship between the viscosity and composition, atmosphere, temperature and history of a liquid. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction In the ®eld of crystal growth, viscosity is important not only for the proper control of crystal growth from a liquid, but also for better understanding on liquid properties concerning specially the defects and inhomogeneity [1]. It is known that the growth of b-BaB2 O4 single crystal, a new nonlinear optical material, is aected by heat treatments including the melting process [2]. To understand the kinetics of reaction in a liquid and control the level of defects in a crystal, accurate viscosity measurement is necessary. The viscosity of liquids at room temperature is relatively easy to measure with sucient accuracy by choosing a proper technique such as capillary method, rota-
* Corresponding author. Present Address: c/o Prof. K. Tamura, Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima, 739-8521, Japan. Tel.: +81 824 24 6555; fax: +81 824 24 0757.
tion method, oscillating plate method and the oscillating vessel method. A review of these methods has been made recently by Iida and Guthrie [3]. Unfortunately, it is still dicult to measure viscosity at high temperature, for instance of oxide liquids with low viscosity, although much eort has been made in last decades. The purpose of this report is to present an improved method on torsion pendulum and some results on KNbO3 and BaB2 O4 liquids at temperatures >1000°C.
2. Experiment The schematic diagram of the instrument, which is based on the principle of a torsion pendulum [4,5], is illustrated in Fig. 1. The operation of this apparatus is as follows: while the platinum cylinder being immersed into a liquid, an equal but opposite torque oered by a couple of electromagnets turns the torsion pendulum a small angle
0022-3093/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 2 9 1 - 4
112
X. Hong, K. Lu / Journal of Non-Crystalline Solids 250±252 (1999) 111±115
Fig. 1. Schematic diagram of the double-wire torsion pendulum method.
and then is released. Unless the liquid is highly viscous, the torsion pendulum system will oscillate; thus the viscosity of the liquid can be determined from the calculation on this damped oscillating process. We call this method the double-wire torsion pendulum method since there are two torsion wires used in the apparatus [6]. This improvement increases both the anti-disturbance and the repeatability of the experiment, and makes it possible to measure the viscosity of oxide liquids in air ambience. For a more detailed description and some experimental results, please see Refs. [6±8].
3. Results Fig. 2 shows the results of molten KNbO3 measured by the double-wire torsion pendulum and the conventional torsion pendulum method, respectively. There is only one torsion-wire in the conventional torsion pendulum including the oscillation vessel method. It can be seen that the experimental points, measured with the doublewire torsion pendulum, are in good agreement
with the exponential functions ®tted to the data even at high temperature and in air. In contrast, with the conventional torsion pendulum, which is similar to the apparatus of Morrisson and coworkers [9], except for water at room temperature, the situation at high temperature is much dierent. Modulation of the amplitudes produces the data of molten KNbO3 with bad reproducibility (Fig. 2). No matter what precaution against the convection from melt and air is employed in the experiment, the background noise aects amplitudes and is so serious that no reproducible results can be drawn from the experimental data. This scatter in data is why the kind of apparatus based on conventional torsion pendulum method cannot be used for the viscosity measurement at high temperatures in air. It is then reasonable to place the apparatus based on torsion pendulum in a thermostat [9]. In this case, the torsion pendulum was successfully used to measure the viscosity of liquid helium. We can conclude that the conventional torsion pendulum method is no longer adequate in the case of high temperature and in air, and the lower torsion wire shown in Fig. 1 is important and makes it possible to measure the viscosity of a liquid in air. The logarithmic attenuation factor (damping factor), a, is obtained by ®tting the equation, a ÿ ln AN =A0 =N to the data. From our previous work on the double-wire torsion pendulum method, the following relation was suggested [6,8] g Cakl ;
1
where g is the viscosity of liquid, C is an apparatus constant, al represents the damping factor due to the viscous damping of liquid and k a function of the shape of immersing head, is a constant near unity. From the experiment on a series of standard oils, the C and k are 4.276 ´ 103 and 1.076, respectively. We then calculate the molten viscosity from al by Eq. (1). The still open problem is why a liquid with excess K2 O must be annealed at temperatures > the melting point before KNbO3 single crystal begins to grow. To ®nd the experimental clue about this open problem, we carried out the viscosity measurement for the ®rst time with the double-wire torsion pendulum [8]. Fig. 3 shows
X. Hong, K. Lu / Journal of Non-Crystalline Solids 250±252 (1999) 111±115
113
Fig. 2. The amplitude AN versus the number of oscillation periods N for molten KNbO3 at 1150°C with the improved method and conventional torsion pendulum method, respectively. Diamond with the improved method. Square, circle, up and down triangles, and star with the conventional method.
Fig. 3. Annealing eects on the damping factor and viscosity of molten K2 O±Nb2 O5 system. Down triangle, circle, open circle and open square are the melts with 50, 51, 52 and 56 mol% K2 O, respectively. Lines are drawn as guide for the eye.
the annealing eect on the damping factors of the double-wire torsion pendulum. The right y-axis of Fig. 3 are the viscosities calculated with Eq. (1). It
can be seen that the viscosities of the melts with 50 and 51 mol% K2 O increase markedly with annealing time, but continuously decrease for the melts with 52 and 56 mol%. BaB2 O4 (BBO) exists in two crystalline phases, a-phase (high temperature phase) and b-phase (low temperature phase). b-BaB2 O4 has nonlinear optical properties [7]. Since BaB2 O4 melts congruently at 1095°C whereas the phase transition occurs at 925°C, the investigation, considering the dierence between properties of the normal melt and those of the supercooled liquid, will be essential to understanding the growth of b-BaB2 O4 single crystal. Nevertheless, the viscosity of bBaB2 O4 has only partly been investigated so far [11], without covering the range of the reported growth temperature (1050°C) and the supercooling region below 1050°C. The ¯ux method has been adopted widely by using a ¯ux to grow the low temperature phase of b-BaB2 O4 single crystals at a temperature below the phase transition. There is no reliable data of the fundamental
114
X. Hong, K. Lu / Journal of Non-Crystalline Solids 250±252 (1999) 111±115
Fig. 4. The temperature dependence of viscosity in Arrhenius plot of 1/T versus logarithmic viscosity g (mPa s). (a) For the melts of BaB2 O4 (circle, open circle, S. Imoto et al.), BaB2 O4 ±NaF (square) and BaB2 O4 ±Na2 O (up triangle). (b) For ¯uid Hg (from Ref. [11].)
physical properties such as viscosity of the melt containing ¯ux. Fig. 4(a) shows the viscosity of BBO melts.
4. Discussion In terms of Stokes±Einstein equation D
kT ; 6pga
2
where D is the diusion constant and a is a molecular length. In the compositions of 52 and 56 mol% K2 O, the diusion constant will continuously increase since the viscosity decreases with annealing time. This property of diusion induced by annealing time is useful for KNbO3 single crystal growth from the liquid. A detailed analysis on the data of K2 O±Nb2 O5 molten system has been reported in Ref. [8]. The temperature dependence of viscosity, g, can be described by the Arrhenius equation Ea ; 3 g A exp RT where A is a constant, Ea is the activation energy of viscosity, R is the gas constant and T is the absolute temperature. Fig. 4(a) shows the temperature dependence of the viscosity in the Ar-
rhenius plot of 1/T versus viscosity g, for liquids of BaB2 O4 , BaB2 O4 with NaF and Na2 O ¯ux at temperatures of about 910°C±1150°C. For comparison with other experiment on pure BaB2 O4 melt, the viscosity data from Ref. [10] are also plotted in Fig. 4(a). Considering the time-dependent viscosity of BaB2 O4 liquid, we ®nd the results obtained by dierent methods coincide. As predicted by Ref. [11], the viscosity of BaB2 O4 liquid is as large as 197.2 mPa s at the growth temperature (1050°C) of b-BaB2 O4 crystal growth by the Czochralski method. It can be seen that both of the ¯uxes, Na2 O and NaF, decrease the viscosity of BaB2 O4 liquid. In terms of Stokes±Einstein relation, Eq. (2), we conclude that the liquid with ¯ux has a relative bigger diusion constant than the pure BaB2 O4 liquid. This larger diusivity of b-BaB2 O4 increases crystal growth since the larger viscosity of the BaO±B2 O3 system decreases the b-BaB2 O4 crystal growth. It is noteworthy that the viscosity of BaB2 O4 liquid is not ®tted by an Arrhenius relation of Eq. (3), i.e. the viscosity as shown in the ®gure increases more quickly while temperature reduces down to the region of b-BaB2 O4 crystal growth. In other words, the activation energy, corresponding to the slope of the curve, increases from 122.4 to 137.6 KJ/mol. This fact indicates that the microstructure of the liquid in the normal and super-
X. Hong, K. Lu / Journal of Non-Crystalline Solids 250±252 (1999) 111±115
cooling region, respectively, dier. Fig. 4(b) shows the viscosity of ¯uid Hg in a plot of 1/T versus viscosity, g, which is taken from Ref. [12]. Unlike the reduction of viscous activation energy of BaB2 O4 liquid from supercooling to normal liquid region, the viscosity of ¯uid Hg cannot be ®t with an Arrhenius relation because of the activation energy increasing from 2.49 to 3.56 KJ/mol with temperature increasing into the range of the Hg expanded region. Further work on the expanded region, especially during the M±NM transition, will be important and of interesting. 5. Conclusions In summary, we conclude that the double-wire torsion pendulum is a useful tool for viscosity measurement especially for liquids at temperatures 1000°C, and has potential for studying the relationship between the viscosity and composition, atmosphere, temperature, and annealing history of a liquid. Acknowledgements The authors are grateful to Professors Y.Q. Zhao, Z.A. Wu, Z.G. Zhu, S.S. Yi, X. Wu and T.S. Ke for their assistance in the experiment and
115
valuable discussions. One of the authors, X.H., would like to express his appreciation to Professor Dr W. Freyland for his help during X.H.'s stay in Karlsruhe. This work was supported by the Chinese Natural Science Foundation and a grant for Key Research Project in Climbing Program from the State Science and Technology Commission of China. References [1] Y. Anzai, S. Kimura, T. Sawada, T. Rudolph, K. Shigematsu, J. Cryst. Growth 134 (1993) 227. [2] H. Kouta, Y. Kuwano, K. Ito, F. Marumo, J. Cryst. Growth 114 (1991) 676. [3] Iida, R.I.L. Guthrie, The Physical Properties of Liquid Metals, Clarendon Press, Oxford, 1988, p. 147. [4] T'ing-Sui Ke, M. Ross, Rev. Sci. Instrum. 20 (1949) 795. [5] T.S. Ke, Phys. Rev. 71 (1947) 533. [6] Xinguo Hong, Kunquan Lu, Rev. Sci. Instrum. 66 (1995) 4318. [7] Xinguo Hong, Kunquan Lu, J. Cryst. Growth 152 (1995) 334. [8] Xinguo Hong, Y.F. Chen, J. Cryst. Growth 165 (1996) 81. [9] T.E. Morrisson, L.J. Zapas, T.W. Dewitt, Rev. Sci. Instrum. 26 (1955) 351. [10] C.-T. Chen, B.-C. Wu, A.-D. Jiang, G.-M. You, Sci. Sinica B 28 (1985) 235. [11] S. Imoto, S. Kimura, Y. Anzai, Y. Kuwano, J. Cryst. Growth 135 (1994) 279. [12] H.v. Tippelskirch, E.U. Frank, F. Hensel, J. Kestin, Berichte der Bunsen-gesellschft bd.79 Nr. 10 (1975) 889.
www.elsevier.com/locate/jnoncrysol
Viscosity measurement with an improved torsion pendulum method Xinguo Hong *, Kunquan Lu Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080, People's Republic of China
Abstract In this paper, we report an improved torsion pendulum method for the viscosity measurement on molten K2 O±Nb2 O5 system and BaB2 O4 melts, with and without ¯ux, at high temperature in air ambient atmosphere. In K2 O±Nb2 O5 molten system, the viscosity shows time-dependence, indicating that the annealing process of the liquid is useful for crystal growth from the liquid. The viscosity of BaB2 O4 melt has a dierent property between the normal and supercooling region. For the purpose of comparison, the viscous property of ¯uid Hg from the reference from the normal to expanded region has been discussed. The improved torsion pendulum method shows high potential to the study of the relationship between the viscosity and composition, atmosphere, temperature and history of a liquid. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction In the ®eld of crystal growth, viscosity is important not only for the proper control of crystal growth from a liquid, but also for better understanding on liquid properties concerning specially the defects and inhomogeneity [1]. It is known that the growth of b-BaB2 O4 single crystal, a new nonlinear optical material, is aected by heat treatments including the melting process [2]. To understand the kinetics of reaction in a liquid and control the level of defects in a crystal, accurate viscosity measurement is necessary. The viscosity of liquids at room temperature is relatively easy to measure with sucient accuracy by choosing a proper technique such as capillary method, rota-
* Corresponding author. Present Address: c/o Prof. K. Tamura, Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima, 739-8521, Japan. Tel.: +81 824 24 6555; fax: +81 824 24 0757.
tion method, oscillating plate method and the oscillating vessel method. A review of these methods has been made recently by Iida and Guthrie [3]. Unfortunately, it is still dicult to measure viscosity at high temperature, for instance of oxide liquids with low viscosity, although much eort has been made in last decades. The purpose of this report is to present an improved method on torsion pendulum and some results on KNbO3 and BaB2 O4 liquids at temperatures >1000°C.
2. Experiment The schematic diagram of the instrument, which is based on the principle of a torsion pendulum [4,5], is illustrated in Fig. 1. The operation of this apparatus is as follows: while the platinum cylinder being immersed into a liquid, an equal but opposite torque oered by a couple of electromagnets turns the torsion pendulum a small angle
0022-3093/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 2 9 1 - 4
112
X. Hong, K. Lu / Journal of Non-Crystalline Solids 250±252 (1999) 111±115
Fig. 1. Schematic diagram of the double-wire torsion pendulum method.
and then is released. Unless the liquid is highly viscous, the torsion pendulum system will oscillate; thus the viscosity of the liquid can be determined from the calculation on this damped oscillating process. We call this method the double-wire torsion pendulum method since there are two torsion wires used in the apparatus [6]. This improvement increases both the anti-disturbance and the repeatability of the experiment, and makes it possible to measure the viscosity of oxide liquids in air ambience. For a more detailed description and some experimental results, please see Refs. [6±8].
3. Results Fig. 2 shows the results of molten KNbO3 measured by the double-wire torsion pendulum and the conventional torsion pendulum method, respectively. There is only one torsion-wire in the conventional torsion pendulum including the oscillation vessel method. It can be seen that the experimental points, measured with the doublewire torsion pendulum, are in good agreement
with the exponential functions ®tted to the data even at high temperature and in air. In contrast, with the conventional torsion pendulum, which is similar to the apparatus of Morrisson and coworkers [9], except for water at room temperature, the situation at high temperature is much dierent. Modulation of the amplitudes produces the data of molten KNbO3 with bad reproducibility (Fig. 2). No matter what precaution against the convection from melt and air is employed in the experiment, the background noise aects amplitudes and is so serious that no reproducible results can be drawn from the experimental data. This scatter in data is why the kind of apparatus based on conventional torsion pendulum method cannot be used for the viscosity measurement at high temperatures in air. It is then reasonable to place the apparatus based on torsion pendulum in a thermostat [9]. In this case, the torsion pendulum was successfully used to measure the viscosity of liquid helium. We can conclude that the conventional torsion pendulum method is no longer adequate in the case of high temperature and in air, and the lower torsion wire shown in Fig. 1 is important and makes it possible to measure the viscosity of a liquid in air. The logarithmic attenuation factor (damping factor), a, is obtained by ®tting the equation, a ÿ ln AN =A0 =N to the data. From our previous work on the double-wire torsion pendulum method, the following relation was suggested [6,8] g Cakl ;
1
where g is the viscosity of liquid, C is an apparatus constant, al represents the damping factor due to the viscous damping of liquid and k a function of the shape of immersing head, is a constant near unity. From the experiment on a series of standard oils, the C and k are 4.276 ´ 103 and 1.076, respectively. We then calculate the molten viscosity from al by Eq. (1). The still open problem is why a liquid with excess K2 O must be annealed at temperatures > the melting point before KNbO3 single crystal begins to grow. To ®nd the experimental clue about this open problem, we carried out the viscosity measurement for the ®rst time with the double-wire torsion pendulum [8]. Fig. 3 shows
X. Hong, K. Lu / Journal of Non-Crystalline Solids 250±252 (1999) 111±115
113
Fig. 2. The amplitude AN versus the number of oscillation periods N for molten KNbO3 at 1150°C with the improved method and conventional torsion pendulum method, respectively. Diamond with the improved method. Square, circle, up and down triangles, and star with the conventional method.
Fig. 3. Annealing eects on the damping factor and viscosity of molten K2 O±Nb2 O5 system. Down triangle, circle, open circle and open square are the melts with 50, 51, 52 and 56 mol% K2 O, respectively. Lines are drawn as guide for the eye.
the annealing eect on the damping factors of the double-wire torsion pendulum. The right y-axis of Fig. 3 are the viscosities calculated with Eq. (1). It
can be seen that the viscosities of the melts with 50 and 51 mol% K2 O increase markedly with annealing time, but continuously decrease for the melts with 52 and 56 mol%. BaB2 O4 (BBO) exists in two crystalline phases, a-phase (high temperature phase) and b-phase (low temperature phase). b-BaB2 O4 has nonlinear optical properties [7]. Since BaB2 O4 melts congruently at 1095°C whereas the phase transition occurs at 925°C, the investigation, considering the dierence between properties of the normal melt and those of the supercooled liquid, will be essential to understanding the growth of b-BaB2 O4 single crystal. Nevertheless, the viscosity of bBaB2 O4 has only partly been investigated so far [11], without covering the range of the reported growth temperature (1050°C) and the supercooling region below 1050°C. The ¯ux method has been adopted widely by using a ¯ux to grow the low temperature phase of b-BaB2 O4 single crystals at a temperature below the phase transition. There is no reliable data of the fundamental
114
X. Hong, K. Lu / Journal of Non-Crystalline Solids 250±252 (1999) 111±115
Fig. 4. The temperature dependence of viscosity in Arrhenius plot of 1/T versus logarithmic viscosity g (mPa s). (a) For the melts of BaB2 O4 (circle, open circle, S. Imoto et al.), BaB2 O4 ±NaF (square) and BaB2 O4 ±Na2 O (up triangle). (b) For ¯uid Hg (from Ref. [11].)
physical properties such as viscosity of the melt containing ¯ux. Fig. 4(a) shows the viscosity of BBO melts.
4. Discussion In terms of Stokes±Einstein equation D
kT ; 6pga
2
where D is the diusion constant and a is a molecular length. In the compositions of 52 and 56 mol% K2 O, the diusion constant will continuously increase since the viscosity decreases with annealing time. This property of diusion induced by annealing time is useful for KNbO3 single crystal growth from the liquid. A detailed analysis on the data of K2 O±Nb2 O5 molten system has been reported in Ref. [8]. The temperature dependence of viscosity, g, can be described by the Arrhenius equation Ea ; 3 g A exp RT where A is a constant, Ea is the activation energy of viscosity, R is the gas constant and T is the absolute temperature. Fig. 4(a) shows the temperature dependence of the viscosity in the Ar-
rhenius plot of 1/T versus viscosity g, for liquids of BaB2 O4 , BaB2 O4 with NaF and Na2 O ¯ux at temperatures of about 910°C±1150°C. For comparison with other experiment on pure BaB2 O4 melt, the viscosity data from Ref. [10] are also plotted in Fig. 4(a). Considering the time-dependent viscosity of BaB2 O4 liquid, we ®nd the results obtained by dierent methods coincide. As predicted by Ref. [11], the viscosity of BaB2 O4 liquid is as large as 197.2 mPa s at the growth temperature (1050°C) of b-BaB2 O4 crystal growth by the Czochralski method. It can be seen that both of the ¯uxes, Na2 O and NaF, decrease the viscosity of BaB2 O4 liquid. In terms of Stokes±Einstein relation, Eq. (2), we conclude that the liquid with ¯ux has a relative bigger diusion constant than the pure BaB2 O4 liquid. This larger diusivity of b-BaB2 O4 increases crystal growth since the larger viscosity of the BaO±B2 O3 system decreases the b-BaB2 O4 crystal growth. It is noteworthy that the viscosity of BaB2 O4 liquid is not ®tted by an Arrhenius relation of Eq. (3), i.e. the viscosity as shown in the ®gure increases more quickly while temperature reduces down to the region of b-BaB2 O4 crystal growth. In other words, the activation energy, corresponding to the slope of the curve, increases from 122.4 to 137.6 KJ/mol. This fact indicates that the microstructure of the liquid in the normal and super-
X. Hong, K. Lu / Journal of Non-Crystalline Solids 250±252 (1999) 111±115
cooling region, respectively, dier. Fig. 4(b) shows the viscosity of ¯uid Hg in a plot of 1/T versus viscosity, g, which is taken from Ref. [12]. Unlike the reduction of viscous activation energy of BaB2 O4 liquid from supercooling to normal liquid region, the viscosity of ¯uid Hg cannot be ®t with an Arrhenius relation because of the activation energy increasing from 2.49 to 3.56 KJ/mol with temperature increasing into the range of the Hg expanded region. Further work on the expanded region, especially during the M±NM transition, will be important and of interesting. 5. Conclusions In summary, we conclude that the double-wire torsion pendulum is a useful tool for viscosity measurement especially for liquids at temperatures 1000°C, and has potential for studying the relationship between the viscosity and composition, atmosphere, temperature, and annealing history of a liquid. Acknowledgements The authors are grateful to Professors Y.Q. Zhao, Z.A. Wu, Z.G. Zhu, S.S. Yi, X. Wu and T.S. Ke for their assistance in the experiment and
115
valuable discussions. One of the authors, X.H., would like to express his appreciation to Professor Dr W. Freyland for his help during X.H.'s stay in Karlsruhe. This work was supported by the Chinese Natural Science Foundation and a grant for Key Research Project in Climbing Program from the State Science and Technology Commission of China. References [1] Y. Anzai, S. Kimura, T. Sawada, T. Rudolph, K. Shigematsu, J. Cryst. Growth 134 (1993) 227. [2] H. Kouta, Y. Kuwano, K. Ito, F. Marumo, J. Cryst. Growth 114 (1991) 676. [3] Iida, R.I.L. Guthrie, The Physical Properties of Liquid Metals, Clarendon Press, Oxford, 1988, p. 147. [4] T'ing-Sui Ke, M. Ross, Rev. Sci. Instrum. 20 (1949) 795. [5] T.S. Ke, Phys. Rev. 71 (1947) 533. [6] Xinguo Hong, Kunquan Lu, Rev. Sci. Instrum. 66 (1995) 4318. [7] Xinguo Hong, Kunquan Lu, J. Cryst. Growth 152 (1995) 334. [8] Xinguo Hong, Y.F. Chen, J. Cryst. Growth 165 (1996) 81. [9] T.E. Morrisson, L.J. Zapas, T.W. Dewitt, Rev. Sci. Instrum. 26 (1955) 351. [10] C.-T. Chen, B.-C. Wu, A.-D. Jiang, G.-M. You, Sci. Sinica B 28 (1985) 235. [11] S. Imoto, S. Kimura, Y. Anzai, Y. Kuwano, J. Cryst. Growth 135 (1994) 279. [12] H.v. Tippelskirch, E.U. Frank, F. Hensel, J. Kestin, Berichte der Bunsen-gesellschft bd.79 Nr. 10 (1975) 889.