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Oxidizing effects of high temperature annealing in reducing atmosphere in Ca-doped YIG films
Journal of Magnetism and Magnetic Materials 20 (1980) 216-219 0 North-Holland Publishing Company
OXIDIZING EFFECTS OF HIGH TEMPERATURE ANNEALING IN REDUCING ATMOSPHERE CaDOPED YIG FILMS
IN
B. ANTONINI Luboratorio di Elettronica dell0 Stat0 Solid0 de1 CNR, Via Cineto Romano, 42, Roma, Italy
S.L. BLANK Bell Laboratories, Murray Hill, NJ 0 79 74, USA
S. LAGOMARSINO,
A. PAOLETTI,
P. PAROLI, F. SCARINCI and A. TUCCIARONE
Luboratorio di Elettronica dell0 Stato Solid0 de1 CNR Via Cineto Romuno, 42, Roma, Italy Received 15 August 1979; in revised form 10 December 1979
The existence of an oxidation mechanism is reported in Ca-doped YIG films, when high temperature annealing is carried out in Nz atmosphere. The annealings were performed at successively increasing temperatures, and optical absorption, lattice parameter and thermoelectric power were measured at each step. Optical absorption was observed going down to a minimum (T = 45O’C in one cycle of annealings, T = 400°C in a different cycle) and then rise again. The minimum in absorption corresponds to a maximum of the lattice parameter, while the thermoelectric power is always p-type. Analysis of the data leads to the conclusion that we are observing a reoxidation process, triggered both by temperature and oxygen vacancy concentration. This process is subject to exhaustion. Previous annealing experiments are analyzed in the light of these results.
1. Introduction
annealings giving rise to the highly absorbing Fe’+ centers. On the other hand, we have overwhelming evidence that, in our case, we are in the presence of a reoxidation mechanism, not previously reported, triggered both by temperature and vacancy concentration. Namely, the Fe4+ population goes down to a minimum, then there is an inversion of trend and it increases again. This conclusion is based on analysis of the absorption spectra, and on measurements of lattice parameter and of two thermoelectric power. Finally, the possible nature of the oxidation mechanism is discussed, together with its different bearing on the interpretation of the previously cited experiments [ 5,6].
Annealing in a reducing environment is a treatment widely used with iron garnet materials either for characterization purposes [l-6] or as a technique for changing properties of practical interest [7]. It is generally assumed that, when the temperature is high enough, an increasing number of oxygen vacancies can result from this treatment, thus decreasing, in the garnet, the valence of the cations that are less stable. Accordingly, in p-type yttrium iron garnet films, optical absorption due to the presence of Fe4+ centers has been generally observed to decrease under high temperature annealing in a reducing environment [3]. In this paper we report experiments of p-type Cadoped YIG films in which optical absorption, after successive annealings in Nz atmosphere at increasing temperatures, was observed to go down to a minimum and then increase again. A similar observation was previously reported by other authors [5,6] and attributed to the increasingly reducing
2. Experimental The iron garnet films were grown by the liquid phase epitaxial (dipping) technique utilizing super216
217
B. Antonini et al. / Oxidation of YIG: Ca in reducing atmosphere
cooled melts [8]. The apparatus and techniques used for growth have been discussed elsewhere [9,10]. Films used in this study were grown on GdsGas0r2 substrates from PbO-B20a fluxed melt. The film used to obtain the data shown in fig. 1 was grown on a (110) oriented substrate at 996°C at a growth rate of 0.38 I.cm/min and contained approximately 0.1 mol of divalent calcium per garnet formula unit as determined by calculations using the extrapolated distribution coefficient of divalent calcium in garnets. Axial rotation during growth was maintained at 100 rpm. The samples were first annealed in oxygen for 48 h at 1000°C. They were then annealed in nitrogen as indicated in table 1. The samples were quenched to room temperature in nitrogen after each anneal without being exposed to air. The absorption coefficients were determined from the relation Z = Zeema’ (t being the total film thickness), after the proper reflection corrections. The lattice parameters of the (110) films were measured using the high angle (Co radiation) reflection (12 6 2). The diffraction peaks of the film and the substrate were recorded simultaneously and an “apparent” lattice mismatch obtained from the relation As/a = (cotg 19)Ae. Two sets of planes, i.e. (12 2 6) and (12 6 2), were utilized in order to verify the merely elastic stress on the film [ 111, namely that the values of Au corresponding to the above sets of planes actually obey the law Aa = (af - a,)
e
,
cos2f$
Table 1 First cycle of annealings on one of the LPE films of Cadoped YIG Annealing number n
Atmosphere
Temperature (“C)
Time (h)
02
11000 300 350 400 450 500 550 600
48 18 4 4 4 4 4 4
N2 N2 N2 N2 N2 N2 N2
annealing in oxygen atmosphere (48 h being the saturating time) was devised in order to exhaust possible effects solely due to temperature. After the first annealing, the annealing times were not saturating anymore and, conservatively, their sum was designed to be less than 48 h. In fig. I the absorption spectra of the film are given, as measured after the annealings n = 1,2,5,7 and 8. We observe a minimum of the absorption at n = 5, corresponding to T = 450°C. The absorption at n = 8 (T = 600°C) goes back up to practically the same levels as n = 3 (T =
(1)
where 4 is the angle between the reflecting planes and the film surface, v is Poisson’s ratio (IJ = 0.30) and af - as is the relaxed “bulk” value of the fim-substrate lattice mismatch. Hence, the stress corrected af - a, is obtained from eq. (1). The thermoelectric power was measured along the [OOl ] direction in the film plane.
3. Results and discussion A first cycle of successive annealings was carried out on one of the films described above. Table 1 shows, for each annealing, the respective atmosphere, the temperature and the time. The first high-temperature
Fig. 1. Successive absorption specfra of the film utilized in the first annealing cycle: n is the number of the annealing in the sequence, and the respective atmosphere, temperature and time are given in table 1.
B. Anionini et al. / Oxidation of YIG: Ca in reducing atmosphere
218
a.-a,mlO~a(em-‘) 0
I
6
12
16 I
-16
-6
05 0
12
6
a,-a,
16
-0
/
x iQ2hi’)
Fig. 2. (a) Decrease in absorption, ot - ck,r,after the nth annealing (n = 2,3), plotted against or - 0s the maximum observed decrease, at various wavelengths. The wavelengths run monotonically from 1.6 nm (corresponding to minimum Aa) to 0.55 flrn (corresponding to maximum AcY), namely, 1.6,1.5,1.4,1.3, 1.2, 1.1,1.0,0.91,0.84,0.77,0.71,0.67, 0.625,0.59 and 0.55 pm. The closely proportional behavior demonstrates that centers of the same species are successively destroyed by the annealings. These centers are the Fe@ centers. (b) on - 01s (n = 7,8) is the increase in absorption after the
minimum is reached at n = 5 in the annealing cycle, The increase in absorption is plotted against ot - os, the decrease observed previously in the cycle, at the same wavelengths as in (a). The closely proportional behavior demonstrates that the new centers produced by the nth annealing (n > 5) have the same spectral dependence as the centers previously destroyed, namely the Fe* impurities.
350°C). The successive decreases in absorption, between n = 1 and n = 5, may be compared (fig. 2a) and are found to have the same spectral dependence. This is consistent with the widely accepted assumption that centers of the same species, namely Fe4+ centers, are successively destroyed by the reducing annealings in N2 giving rise to oxygen vacancies. On the other hand, also the subsequent increase of the absorption after the minimum is reached (namely, (Y, - 0~swith n > S), have the same spectral dependence of the previous decrease (fig. 2b). Thus, from the optical data, there is a strong indication that the new absorbing,centers produced by the annealings n > 5, are the same as the ones destroyed by the
01 0.6
a6
1.0
1.2
1.4
1.6
1 (urn)
Fig. 3. The absorption spectrum of Fern(X),, as measured on the YIG (Si) (110) platelet of ref. 141, compared with the absorption spectrum of Fe& (e), namely a, - cts as derived from fii. 1.
previous annealings, namely Fe4+ centers. This would imply that we are in the presence of a reoxidation process. The evidence from the optical data is completed by fig. 3, where the difference between Fe4+ and Fe*+ absorption spectra is shown. We have repeated the annealing cycle on a second film specimen coming from the same wafer as the first film. The absorption spectra of the film during the cycle are shown in fig. 4; (a), (b), (c) and (d) are the successive steps of the cycle: (a) as grown; (b) 48 h in 0s at 6OO’C; (c) 8 h in Nz at 400°C; (d) 8 h in Nz at 600°C. Lattice parameter and thermoelectric power were measured at each step. The lattice parameter has a maximum coincident with the minimum in the absorption. The actual numbers for a, - ar are the following (+0.0002 A): 0.0068 A (as grown), 0.0072 A (0, annealing), 0.0052 A (minimum in OL),0.0066 W (last annealing). This inversion of trend is consistent with the picture of a reoxidation process pr.oducing the rise in absorption after the observed minimum. On the other hand, it seems difficult to make it compatible with a continuing reduction effect [2].
B. A.?tonini et al. / Oxidation of YIG: Ca in reducing atmosphere
219
high-temperature treatment, highly reducing and extended in time, may be safely assumed to have exhausted the’oxidation process [5]. Evaporation of some cation impurity in the garnet film is a reasonable candidate for the oxidation mechanism. Lead could be such an impurity. Boron, which is present in the melt, is another attractive possibility, Having established beyond reasonable doubt the existence of an oxidation process in our high temperature reduction experiment, singling out the specific mechanism remains an open problem for future work. 5 (pm)
Fig. 4. The absorption spectra of the fii utilized in the second annealing cycle; (a), (b), (c) and (d) are the successive steps of the cycle: (a) as grown; (b) 48 h in O2 at 600°C; (c) 8 h in Nz at 400°C; (d) 8 h in Nz at 600°C.
The thermoelectric power indicates that the film is always p-type, through all the cycle. The actual measured values are the following: 0.42 mV/“C (as grown), 0.52 mV/“C (0, annealing), 0.45 mV/‘C (minimum in CK), 0.65 mV/“C (last annealing). These values may be compared with 0.50, the thermoelectric power associated with Fe4+ in polycrystalline YIG with calcium substitutions [ 121. The observed oxidation process associated with the rise in absorption is triggered not only by temperature, but also by the oxygen vacancy concentration. This follows as pointed out above from having made the first annealing, in 02, at the highest temperature in the annealing cycle. Furthermore, we have experimentally verified that the oxidation mechanism is subject to exhaustion, so that, after an annealing treatment sufficiently extended in time, the reduction effect eventually prevails again. For example, in our optical absorption experiment, as we increase the annealing temperature, the absorption Q, after going through the minimum, is observed reaching a secondary maximum an-dhence decrease again. This it appears that, neglecting hightemperature oxidation mechanisms can possibly lead to serious errors of interpretation, particularly in annealing experiments in which such a double inversion of trend is observed [6]. On the other h&d, a
Acknowledgements
We gratefully acknowledge stimulating discussions with Prof. S. Geller. Also, we wish to thank Dr. L. Luther for the growth of the LPE films and L. Mastrogiacomo for expert technical assistance.
References [l] E.M. Gyorgy, J.F. Dillon, Jr. and J.M. Remeika, AIP Conf. Proc. 5 (1972) 680. [2] R. Metselaar and M.A.H. Huyberts, J. Phys.,Chem. Solids 34 (1973) 2257. [3] A. Akselrad, R.E. Novak and D.L. Patterson, AIP Conf. Proc. 25 (1974) 370. (41 B. Antonini, S. Geller, P. Paroli, A. Tucciarone and A.A. Colville, Appl. Phys. Lett. 27 (1975) 700. [S] R.C. Le Craw, E.M. Gyorgy, R.D. Pierce, J.W. Nielsen, S.L. Blank, D.C. Miller and R. Wolfe, Appl. Phys. Lett. 31 (1977) 243. [6] C. Borghese, R. Cosmi, P. De Gasperis and R. Tappa, Appl. Phys. Lett. 32 (1978) 344. [7] R.C. Le Craw, E.M. Gyorgy and R. Wolfe, Appl. Phys. Lett. 24 (1974) 573. [8] H.J. Levinstein, S.J. Licht, R.W. Landorf and S.L. Blank, Appl. Phys. Lett. 19 (1971) 486. [9 ] S.L. Blank and J.W. Nielsen, J. Crystal Growth 17 (1972) 302. [lo] S.L. Blank, J.W. Nielsen and W.A. Biolsi, J. Electrothem. Sot. 123 (1976) 856. [l l] See, for example, W. Tolksdorf, G. Bartels, P. Holst and W.T. Stacy, J. Crystal Growth 26 (1974) 122. [12] J. Verweel and B.J.M. Roovers, Solid State Phys. Electr. Telecommun. 3 (1960) 475.
OXIDIZING EFFECTS OF HIGH TEMPERATURE ANNEALING IN REDUCING ATMOSPHERE CaDOPED YIG FILMS
IN
B. ANTONINI Luboratorio di Elettronica dell0 Stat0 Solid0 de1 CNR, Via Cineto Romano, 42, Roma, Italy
S.L. BLANK Bell Laboratories, Murray Hill, NJ 0 79 74, USA
S. LAGOMARSINO,
A. PAOLETTI,
P. PAROLI, F. SCARINCI and A. TUCCIARONE
Luboratorio di Elettronica dell0 Stato Solid0 de1 CNR Via Cineto Romuno, 42, Roma, Italy Received 15 August 1979; in revised form 10 December 1979
The existence of an oxidation mechanism is reported in Ca-doped YIG films, when high temperature annealing is carried out in Nz atmosphere. The annealings were performed at successively increasing temperatures, and optical absorption, lattice parameter and thermoelectric power were measured at each step. Optical absorption was observed going down to a minimum (T = 45O’C in one cycle of annealings, T = 400°C in a different cycle) and then rise again. The minimum in absorption corresponds to a maximum of the lattice parameter, while the thermoelectric power is always p-type. Analysis of the data leads to the conclusion that we are observing a reoxidation process, triggered both by temperature and oxygen vacancy concentration. This process is subject to exhaustion. Previous annealing experiments are analyzed in the light of these results.
1. Introduction
annealings giving rise to the highly absorbing Fe’+ centers. On the other hand, we have overwhelming evidence that, in our case, we are in the presence of a reoxidation mechanism, not previously reported, triggered both by temperature and vacancy concentration. Namely, the Fe4+ population goes down to a minimum, then there is an inversion of trend and it increases again. This conclusion is based on analysis of the absorption spectra, and on measurements of lattice parameter and of two thermoelectric power. Finally, the possible nature of the oxidation mechanism is discussed, together with its different bearing on the interpretation of the previously cited experiments [ 5,6].
Annealing in a reducing environment is a treatment widely used with iron garnet materials either for characterization purposes [l-6] or as a technique for changing properties of practical interest [7]. It is generally assumed that, when the temperature is high enough, an increasing number of oxygen vacancies can result from this treatment, thus decreasing, in the garnet, the valence of the cations that are less stable. Accordingly, in p-type yttrium iron garnet films, optical absorption due to the presence of Fe4+ centers has been generally observed to decrease under high temperature annealing in a reducing environment [3]. In this paper we report experiments of p-type Cadoped YIG films in which optical absorption, after successive annealings in Nz atmosphere at increasing temperatures, was observed to go down to a minimum and then increase again. A similar observation was previously reported by other authors [5,6] and attributed to the increasingly reducing
2. Experimental The iron garnet films were grown by the liquid phase epitaxial (dipping) technique utilizing super216
217
B. Antonini et al. / Oxidation of YIG: Ca in reducing atmosphere
cooled melts [8]. The apparatus and techniques used for growth have been discussed elsewhere [9,10]. Films used in this study were grown on GdsGas0r2 substrates from PbO-B20a fluxed melt. The film used to obtain the data shown in fig. 1 was grown on a (110) oriented substrate at 996°C at a growth rate of 0.38 I.cm/min and contained approximately 0.1 mol of divalent calcium per garnet formula unit as determined by calculations using the extrapolated distribution coefficient of divalent calcium in garnets. Axial rotation during growth was maintained at 100 rpm. The samples were first annealed in oxygen for 48 h at 1000°C. They were then annealed in nitrogen as indicated in table 1. The samples were quenched to room temperature in nitrogen after each anneal without being exposed to air. The absorption coefficients were determined from the relation Z = Zeema’ (t being the total film thickness), after the proper reflection corrections. The lattice parameters of the (110) films were measured using the high angle (Co radiation) reflection (12 6 2). The diffraction peaks of the film and the substrate were recorded simultaneously and an “apparent” lattice mismatch obtained from the relation As/a = (cotg 19)Ae. Two sets of planes, i.e. (12 2 6) and (12 6 2), were utilized in order to verify the merely elastic stress on the film [ 111, namely that the values of Au corresponding to the above sets of planes actually obey the law Aa = (af - a,)
e
,
cos2f$
Table 1 First cycle of annealings on one of the LPE films of Cadoped YIG Annealing number n
Atmosphere
Temperature (“C)
Time (h)
02
11000 300 350 400 450 500 550 600
48 18 4 4 4 4 4 4
N2 N2 N2 N2 N2 N2 N2
annealing in oxygen atmosphere (48 h being the saturating time) was devised in order to exhaust possible effects solely due to temperature. After the first annealing, the annealing times were not saturating anymore and, conservatively, their sum was designed to be less than 48 h. In fig. I the absorption spectra of the film are given, as measured after the annealings n = 1,2,5,7 and 8. We observe a minimum of the absorption at n = 5, corresponding to T = 450°C. The absorption at n = 8 (T = 600°C) goes back up to practically the same levels as n = 3 (T =
(1)
where 4 is the angle between the reflecting planes and the film surface, v is Poisson’s ratio (IJ = 0.30) and af - as is the relaxed “bulk” value of the fim-substrate lattice mismatch. Hence, the stress corrected af - a, is obtained from eq. (1). The thermoelectric power was measured along the [OOl ] direction in the film plane.
3. Results and discussion A first cycle of successive annealings was carried out on one of the films described above. Table 1 shows, for each annealing, the respective atmosphere, the temperature and the time. The first high-temperature
Fig. 1. Successive absorption specfra of the film utilized in the first annealing cycle: n is the number of the annealing in the sequence, and the respective atmosphere, temperature and time are given in table 1.
B. Anionini et al. / Oxidation of YIG: Ca in reducing atmosphere
218
a.-a,mlO~a(em-‘) 0
I
6
12
16 I
-16
-6
05 0
12
6
a,-a,
16
-0
/
x iQ2hi’)
Fig. 2. (a) Decrease in absorption, ot - ck,r,after the nth annealing (n = 2,3), plotted against or - 0s the maximum observed decrease, at various wavelengths. The wavelengths run monotonically from 1.6 nm (corresponding to minimum Aa) to 0.55 flrn (corresponding to maximum AcY), namely, 1.6,1.5,1.4,1.3, 1.2, 1.1,1.0,0.91,0.84,0.77,0.71,0.67, 0.625,0.59 and 0.55 pm. The closely proportional behavior demonstrates that centers of the same species are successively destroyed by the annealings. These centers are the Fe@ centers. (b) on - 01s (n = 7,8) is the increase in absorption after the
minimum is reached at n = 5 in the annealing cycle, The increase in absorption is plotted against ot - os, the decrease observed previously in the cycle, at the same wavelengths as in (a). The closely proportional behavior demonstrates that the new centers produced by the nth annealing (n > 5) have the same spectral dependence as the centers previously destroyed, namely the Fe* impurities.
350°C). The successive decreases in absorption, between n = 1 and n = 5, may be compared (fig. 2a) and are found to have the same spectral dependence. This is consistent with the widely accepted assumption that centers of the same species, namely Fe4+ centers, are successively destroyed by the reducing annealings in N2 giving rise to oxygen vacancies. On the other hand, also the subsequent increase of the absorption after the minimum is reached (namely, (Y, - 0~swith n > S), have the same spectral dependence of the previous decrease (fig. 2b). Thus, from the optical data, there is a strong indication that the new absorbing,centers produced by the annealings n > 5, are the same as the ones destroyed by the
01 0.6
a6
1.0
1.2
1.4
1.6
1 (urn)
Fig. 3. The absorption spectrum of Fern(X),, as measured on the YIG (Si) (110) platelet of ref. 141, compared with the absorption spectrum of Fe& (e), namely a, - cts as derived from fii. 1.
previous annealings, namely Fe4+ centers. This would imply that we are in the presence of a reoxidation process. The evidence from the optical data is completed by fig. 3, where the difference between Fe4+ and Fe*+ absorption spectra is shown. We have repeated the annealing cycle on a second film specimen coming from the same wafer as the first film. The absorption spectra of the film during the cycle are shown in fig. 4; (a), (b), (c) and (d) are the successive steps of the cycle: (a) as grown; (b) 48 h in 0s at 6OO’C; (c) 8 h in Nz at 400°C; (d) 8 h in Nz at 600°C. Lattice parameter and thermoelectric power were measured at each step. The lattice parameter has a maximum coincident with the minimum in the absorption. The actual numbers for a, - ar are the following (+0.0002 A): 0.0068 A (as grown), 0.0072 A (0, annealing), 0.0052 A (minimum in OL),0.0066 W (last annealing). This inversion of trend is consistent with the picture of a reoxidation process pr.oducing the rise in absorption after the observed minimum. On the other hand, it seems difficult to make it compatible with a continuing reduction effect [2].
B. A.?tonini et al. / Oxidation of YIG: Ca in reducing atmosphere
219
high-temperature treatment, highly reducing and extended in time, may be safely assumed to have exhausted the’oxidation process [5]. Evaporation of some cation impurity in the garnet film is a reasonable candidate for the oxidation mechanism. Lead could be such an impurity. Boron, which is present in the melt, is another attractive possibility, Having established beyond reasonable doubt the existence of an oxidation process in our high temperature reduction experiment, singling out the specific mechanism remains an open problem for future work. 5 (pm)
Fig. 4. The absorption spectra of the fii utilized in the second annealing cycle; (a), (b), (c) and (d) are the successive steps of the cycle: (a) as grown; (b) 48 h in O2 at 600°C; (c) 8 h in Nz at 400°C; (d) 8 h in Nz at 600°C.
The thermoelectric power indicates that the film is always p-type, through all the cycle. The actual measured values are the following: 0.42 mV/“C (as grown), 0.52 mV/“C (0, annealing), 0.45 mV/‘C (minimum in CK), 0.65 mV/“C (last annealing). These values may be compared with 0.50, the thermoelectric power associated with Fe4+ in polycrystalline YIG with calcium substitutions [ 121. The observed oxidation process associated with the rise in absorption is triggered not only by temperature, but also by the oxygen vacancy concentration. This follows as pointed out above from having made the first annealing, in 02, at the highest temperature in the annealing cycle. Furthermore, we have experimentally verified that the oxidation mechanism is subject to exhaustion, so that, after an annealing treatment sufficiently extended in time, the reduction effect eventually prevails again. For example, in our optical absorption experiment, as we increase the annealing temperature, the absorption Q, after going through the minimum, is observed reaching a secondary maximum an-dhence decrease again. This it appears that, neglecting hightemperature oxidation mechanisms can possibly lead to serious errors of interpretation, particularly in annealing experiments in which such a double inversion of trend is observed [6]. On the other h&d, a
Acknowledgements
We gratefully acknowledge stimulating discussions with Prof. S. Geller. Also, we wish to thank Dr. L. Luther for the growth of the LPE films and L. Mastrogiacomo for expert technical assistance.
References [l] E.M. Gyorgy, J.F. Dillon, Jr. and J.M. Remeika, AIP Conf. Proc. 5 (1972) 680. [2] R. Metselaar and M.A.H. Huyberts, J. Phys.,Chem. Solids 34 (1973) 2257. [3] A. Akselrad, R.E. Novak and D.L. Patterson, AIP Conf. Proc. 25 (1974) 370. (41 B. Antonini, S. Geller, P. Paroli, A. Tucciarone and A.A. Colville, Appl. Phys. Lett. 27 (1975) 700. [S] R.C. Le Craw, E.M. Gyorgy, R.D. Pierce, J.W. Nielsen, S.L. Blank, D.C. Miller and R. Wolfe, Appl. Phys. Lett. 31 (1977) 243. [6] C. Borghese, R. Cosmi, P. De Gasperis and R. Tappa, Appl. Phys. Lett. 32 (1978) 344. [7] R.C. Le Craw, E.M. Gyorgy and R. Wolfe, Appl. Phys. Lett. 24 (1974) 573. [8] H.J. Levinstein, S.J. Licht, R.W. Landorf and S.L. Blank, Appl. Phys. Lett. 19 (1971) 486. [9 ] S.L. Blank and J.W. Nielsen, J. Crystal Growth 17 (1972) 302. [lo] S.L. Blank, J.W. Nielsen and W.A. Biolsi, J. Electrothem. Sot. 123 (1976) 856. [l l] See, for example, W. Tolksdorf, G. Bartels, P. Holst and W.T. Stacy, J. Crystal Growth 26 (1974) 122. [12] J. Verweel and B.J.M. Roovers, Solid State Phys. Electr. Telecommun. 3 (1960) 475.