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Effects of Sc2O3 addition on floating zone growth of rutile single crystals
Journal of Crystal Growth 125 (1992) 571—575 North-Holland
or.~
or
CRYSTAL GROWT H
Effects of Sc203 addition on floating zone growth of rutile single crystals Mikio Higuchi, Junichi Takahashi and Kohei Kodaira Department of Applied Chemistry, Faculty of Engineering, Hokkaido University, Sapporo 060, Japan Received 28 May 1992
Rutile single crystals doped with Sc203 were grown by the floating zone (FZ) method. The as-grown crystals were yellowish and transparent after the growth run, whereas an 3+ as-grown ions could puresubstitute rutile crystal Ti4+is sites dark-blue in theand rutile notstructure transparent to form evenoxygen if the crystal vacancies, growth via which is doneoxide underions an could oxygeneasily atmosphere. diffuse as The well Sc in Y 203-doped Zr02, and consequently transparent as-grown crystals were obtained. The formation of low-angle grain boundaries was appreciably suppressed, but not completely, with the addition of only Sc203. Simultaneous addition of 5c203 and Zr02 was effective to obtain transparent and grain-boundary-free rutile single crystals by the floating zone method.
1. Introduction Rutile single crystals belong to the most promising materials for polarizing devices owing to large refractive indices and larger birefringence [1]. Rutile is transparent in a wide range of wavelengths and is essentially pale-yellow because of the absorption edge at 420 nm. However, a rutile crystal grown from the melt is usually black dark-blue, since are a number of 3~ions andoroxygen vacancies formed at Ti temperatures [21. high We have successfully grown rutile single crystals by the floating zone (FZ) method in a previous study [3]. The optical quality of the FZ-grown crystals was superior to that of Verneuil-grown crystals. A relatively low oxygen partial pressure of up to iO~Pa was necessary to suppress the formation of low-angle grain boundaries. The asgrown crystals were also black or dark-blue as a result of growth under low oxygen partial pressure. Long-term annealing, for 10—20 days at 800°C in an oxidizing atmosphere, was usually necessary to diffuse oxide ions over the whole crystal so that transparent and pale-yellow rutile single crystals were obtained. 0022-0248/92/$05.OO © 1992
—
Recently, we found that the addition of a small quantity of Zr02 was very effective to suppress the formation of low-angle grain boundaries in FZ-grown rutile crystals [41.However, the asgrown crystals were also dark-blue, even if the crystal growth was carried out under an oxygen atmosphere. According to Arita et a!., the oxygen tracer diffusivity in Cr-doped rutile was 3 to 8 times larger et than a pure very rutilerapid singlediffusion crystal [51. Ikeda a!. that also inreported of oxide ions in an Al-doped and reduced rutile single crystal [61. These reports indicate that the addition of trivalent cations is very effective to enhance the diffusivity of oxide ions in rutile. In this study, we tried to grow Sc-doped rutile single crystals by the FZ method and investigated the effects of Sc 203 addition on decolorization of rutile single crystals.
2. Experimental procedure The starting materials used were Ti02 (99.9%; Toho Titanium Co., Ltd.), Sc203 (99.9%; Soekawa Kagaku Co., Ltd.) and Zr02 (reagent
Elsevier Science Publishers B.V. All rights reserved
572
M. Higuchi et a!.
/
Effects of Sc
203 addition on FZ growth of rutile single crystals
A
B
1 cm
1
ClU
Fig. 1. A-grown rutile crystals obtained by the floating zone method: (A) Sc-doped; (B) undoped.
grade; Daiichi Kigenso Kagaku Kogyo Co., Ltd.) powders. The addition of Sc203 was 0—0.5 at%. Some samples were added with Sc203 (0.1 at%) and Zr02 (0.4 at%), simultaneously. The procedures for preparation of feed rods and FZ crystal growth were essentially the same way as in previous studies [4,5]. The growth conditions were as follows: the growth rate was 5 mm/h, the rotation rate was 30 rpm for both feed rod and seed crystal, and the growth atmosphere was an oxygen stream of 2 liter/mm. Some samples were quenched by turning off the lamp power abruptly in the course of steady growth. After the observation of the color of as-grown crystals, they were cut perpendicular to the growth direction and polished. The specimen was exammed under a polarizing microscope with parallel and crossed nicols.
ing growth run. However, cellular growth was also not observed in the case of 0.5 at%. Fig. 1 shows as-grown rutile crystal boules obtamed by the FZ method. The Sc-doped (0.1 at%) crystal (fig. 1A) is transparent and yellowish, which is close to a completely annealed rutile single crystal. The addition of 0.04 at% Sc203 was also effective to obtain a transparent as-grown crystal. On the other hand, the Sc-free crystal (fig. 1B) is dark-blue and translucent, although the crystal growth was carried out under an oxygen atmosphere. Fig. 2 shows a polished specimen cut from near the tip of the as-grown crystals. For the Sc-doped crystal (fig. 2a), the background letters “rutile” are clearly visible, while the Sc-free crystal (fig. 2b) is still dark-blue and translucent despite its thickness of approximately 1 mm.
3. Results and discussion Crystal growth of Sc-doped rutile crystals by the FZ method was successfully performed and cellular growth did not occur for Sc concentrations of up to 0.1 at%. On the other hand, the penetration of melt into the feed rod was observed in the latter half of the growth run for the crystal with high Sc concentration, e.g. 0.5 at%. This indicates that there was a large difference in Sc concentration between the melt and the feed rod. As mentioned later, the dissolution of Sc203 in rutile is very little, and hence Sc would be gradually concentrated in the melt with proceed-
ni
I a
a Fig. 2. Cross sections of the as-grown rutile crystals: (a) Sc-doped; (b) undoped.
M. Higuchi et a!.
/ Effects of Sc203
addition on FZ growth of ruti!e single crystals
~
-
Fig. 3. A quenched specimen of Sc-doped rutilc crystal. The specimen was moled in epoxy resin and cut so as to include the center of the crystal.
Fig. 3 shows more clearly the effect of Sc-doping on decoloration of a rutile crystal. The sample in fig. 3 was quenched in the course of a steady
At an early stage of annealing, oxide ions could easily diffuse via 3~ions, oxygen vacancies, which and as a result, are accompanied by Ti the peripheral region of the crystal readily becomes transparent and close to stoichiometric Ti0 2. After that, the diffusion of oxide ions through stoichiometric Ti02 region would be sluggish, and thus it takes a long-term annealing for 10—20 days to obtain a thoroughly transparent rutile single crystal. It is well known that Y- or Ca-doped Zr02, so-called stabilized Zr02, is a good ionic conductor, in which oxide ions are charge carriers and migrate easily via oxygen vacancies formed for the charge compensation [7]. In a similar way, oxide ions are expected to migrate easily in a .
3+
.
Sc-doped rutile 4~ sites singleincrystal. a rutile If Sccrystal, ions oxygen substitute the Ti vacancies will result: (1 —x) Ti0 2 +x Sc015
growth run. The frozen melt part is white and the grown crystal is, despite quenching, transparent and yellowish, except for the dark-blue region just below the melt zone. This crystal is in contrast with the Sc-free crystal in fig. 1B, which is dark-blue on the whole, although the crystal was not quenched but normally cooled to room ternperature. As stated above, the coloring of dark-blue or black in a pure rutile crystal grown from the melt can clearly be attributed to the reduction at high 3~, temperatures to formoxygen trivalent titaniumThe ions,reducTi and corresponding vacancies. tion is inevitable for the melt growth of rutile crystals. Accordingly, a transparent rutile crystal can be obtained by post-annealing in an oxidizing atmosphere to diffuse oxide ions over the whole crystal. The diffusion rate usually increases with increasing temperature, and thus it may be advantageous to anneal at as high temperatures as possible. However, the stability of Ti3 + increases with increasing temperature even under a high oxygen partial pressure. Therefore, annealing should be done at a relatively low temperature, which was empirically determined to be 800°Cfor the rutile single crystals grown under a low oxygen partial pressure of up to iO~Pa.
573
—~
Ti1~Sc~O2055V005,
where V0 is oxygen vacancy. The phase diagram for the TiO2—Sc2O3 systern has been investigated, and no solid solution is found at the Ti02-end region in the diagram [8]. Many researchers have reported, however, that a small quantity of Al203 can dissolve in Ti02 [7,9], although there is no solid solution region in the phase diagram for the Ti02—Al203 system [101.Accordingly, a small quantity of 5c203 is alsotype expected to dissolve in Ti02 to form the rutile solid solution. The oxygen vacancies introduced by the addition of Sc3~ions never disappear, even if Ti3~ ions are oxidized to Ti4t Quite rapid and continuous diffusion of oxide ions is therefore expected to occur on cooling, and transparent and yellowish rutile crystals were obtained in the as-grown state, as a result. Cracks were occasionally observed in transparent as-grown crystals as shown in fig. 1A. The cracks were formed spirally from tip to seed of the as-grown crystals on cooling to room temperature. The cause of the cracks is not clarified, but rapid diffusion of oxide ions may be responsible, since Sc-free rutile crystals, which are dark-blue, are never cracked. After the growth of a Sc-doped
574
a ~ ~
M Higuchi et a!.
/ E/6ci.v of Sc203
addition on FZ growth of rutile single crystals
_____
~
tI_______
_
,~jvF
~O~2 mm
1
mm
C
crystal, cooling under a low oxygen partial pressure and subsequent annealing were effective to avoid cracks. The duration of the annealing to obtain transparent crystals was very much shortened, i.e., 20 h at 800°C,as compared with the case for Sc-free crystals. Fig. 4 shows cross sections of the FZ-grown rutile crystals examined under a polarizing microscope with crossed nicols. A few low-angle grain boundaries are observed in a Sc-doped but Zr-free crystal (fig. 4b), which was doped with 0.5 at% Sc203. The number of the grain boundaries is considerably reduced as compared with a pure rutile crystal (fig. 4a). We found in a previous study that the number of low-angle grain boundaries in FZ-grown rutile crystals was reduced by4~ions the addition of a asmall would have role quantity of Zr02 [4].Zr to pin down the migration of dislocations (solution hardening) so that the formation of low-angle grain boundaries was suppressed. The ionic radius of Sc3~is 0.081 nm, which is close to that of Zr4~(0.079 nm). Accordingly, Sc3~was also expected to suppress the formation of low-angle grain boundaries. The number of grain boundaries was appreciably reduced, as shown in fig. 4b. in the case of ZrO 2, the addition of 0.5 at% was enough to grow rutile single crystals free from low-angle grain boundaries. In the case of 3~in Sc203,would rutile however, be much the quantity smallerofthan dissolved 0.5 at%, Sc and consequently a few low-angle grain boundaries were formed. Simultaneous addition of Zr0 2 (0.4 at%) and Sc203 (0.1 at%) was effective to obtain a grain-boundary-free rutile single crystal as shown in fig. 4c. The crystal was reasonably transparent and yellowish in the as-grown state.
4. Summary
1 mm
were rutile crystals
[-ig. 4. ( ross sections ot the as-grown observed with a polarizing microscope: (a) undoped; (b) Sc-doped; (c) Sc- and Zr-doped,
The addition of Sc203 was effective to obtain transparent and yellowish as-grown rutile single crystals by the floating zone method. Oxide ions could readily diffuse via oxygen vacancies, which introduced by the addition of Sc2O3. The formation of cracks was effectively avoided by cooling under a low oxygen partial pressure and .
.
.
-
M. Higuchi et al.
/ Effects of Sc203 addition
subsequent short-term annealing. The addition of Sc203 also had a role to reduce the number of low-angle grain boundaries, but a few boundaries were still observed in only Sc-doped crystal. Simultaneous addition of Sc2O3 and Zr02 was effective to obtain transparent and grainboundary-free rutile single crystals. References [1] M. Shirasaki and K. Asama, AppI. Opt. 21(1982) 4296. [2] H.B. Sachse, Anal. Chem. 33 (1961) 1349.
on FZ growth of rutile single crystals
575
[3] M. Higuchi, T. Hosokawa and S. Kimura, J. Crystal Growth 112 (1991) 354. [4] M. Higuchi and K. Kodaira, to be published. [5] M. Arita, M. Hosoya, M. Kobayashi and M. Someno, J. Am. Ceram. Soc. 62 (1979) 443.
[6] J.A.S.
Ikeda, Y.-M. Chiang and B.D. Fabes, J. Am. Ceram. Soc. 73 (1990) 1633. 17] W.D. Kingery, J. Pappis, ME. Doty and D.C. Hill, J. Am. Ceram. Soc. 42 (1959) 393. [8] L.N. Komissarova B.!. Pokrovskii and V.V. Nechaeva, Dokl. Akad. Nauk SSSR 168 (1966) 1079. 19] J. Yahia, Phys. Rev. 130 (1963) 1711. [10] AM. Lejus, D. Goldberg and A. Revcolevschi, Compt. Rend. (Paris) C 263 (1966) 1223.
or.~
or
CRYSTAL GROWT H
Effects of Sc203 addition on floating zone growth of rutile single crystals Mikio Higuchi, Junichi Takahashi and Kohei Kodaira Department of Applied Chemistry, Faculty of Engineering, Hokkaido University, Sapporo 060, Japan Received 28 May 1992
Rutile single crystals doped with Sc203 were grown by the floating zone (FZ) method. The as-grown crystals were yellowish and transparent after the growth run, whereas an 3+ as-grown ions could puresubstitute rutile crystal Ti4+is sites dark-blue in theand rutile notstructure transparent to form evenoxygen if the crystal vacancies, growth via which is doneoxide underions an could oxygeneasily atmosphere. diffuse as The well Sc in Y 203-doped Zr02, and consequently transparent as-grown crystals were obtained. The formation of low-angle grain boundaries was appreciably suppressed, but not completely, with the addition of only Sc203. Simultaneous addition of 5c203 and Zr02 was effective to obtain transparent and grain-boundary-free rutile single crystals by the floating zone method.
1. Introduction Rutile single crystals belong to the most promising materials for polarizing devices owing to large refractive indices and larger birefringence [1]. Rutile is transparent in a wide range of wavelengths and is essentially pale-yellow because of the absorption edge at 420 nm. However, a rutile crystal grown from the melt is usually black dark-blue, since are a number of 3~ions andoroxygen vacancies formed at Ti temperatures [21. high We have successfully grown rutile single crystals by the floating zone (FZ) method in a previous study [3]. The optical quality of the FZ-grown crystals was superior to that of Verneuil-grown crystals. A relatively low oxygen partial pressure of up to iO~Pa was necessary to suppress the formation of low-angle grain boundaries. The asgrown crystals were also black or dark-blue as a result of growth under low oxygen partial pressure. Long-term annealing, for 10—20 days at 800°C in an oxidizing atmosphere, was usually necessary to diffuse oxide ions over the whole crystal so that transparent and pale-yellow rutile single crystals were obtained. 0022-0248/92/$05.OO © 1992
—
Recently, we found that the addition of a small quantity of Zr02 was very effective to suppress the formation of low-angle grain boundaries in FZ-grown rutile crystals [41.However, the asgrown crystals were also dark-blue, even if the crystal growth was carried out under an oxygen atmosphere. According to Arita et a!., the oxygen tracer diffusivity in Cr-doped rutile was 3 to 8 times larger et than a pure very rutilerapid singlediffusion crystal [51. Ikeda a!. that also inreported of oxide ions in an Al-doped and reduced rutile single crystal [61. These reports indicate that the addition of trivalent cations is very effective to enhance the diffusivity of oxide ions in rutile. In this study, we tried to grow Sc-doped rutile single crystals by the FZ method and investigated the effects of Sc 203 addition on decolorization of rutile single crystals.
2. Experimental procedure The starting materials used were Ti02 (99.9%; Toho Titanium Co., Ltd.), Sc203 (99.9%; Soekawa Kagaku Co., Ltd.) and Zr02 (reagent
Elsevier Science Publishers B.V. All rights reserved
572
M. Higuchi et a!.
/
Effects of Sc
203 addition on FZ growth of rutile single crystals
A
B
1 cm
1
ClU
Fig. 1. A-grown rutile crystals obtained by the floating zone method: (A) Sc-doped; (B) undoped.
grade; Daiichi Kigenso Kagaku Kogyo Co., Ltd.) powders. The addition of Sc203 was 0—0.5 at%. Some samples were added with Sc203 (0.1 at%) and Zr02 (0.4 at%), simultaneously. The procedures for preparation of feed rods and FZ crystal growth were essentially the same way as in previous studies [4,5]. The growth conditions were as follows: the growth rate was 5 mm/h, the rotation rate was 30 rpm for both feed rod and seed crystal, and the growth atmosphere was an oxygen stream of 2 liter/mm. Some samples were quenched by turning off the lamp power abruptly in the course of steady growth. After the observation of the color of as-grown crystals, they were cut perpendicular to the growth direction and polished. The specimen was exammed under a polarizing microscope with parallel and crossed nicols.
ing growth run. However, cellular growth was also not observed in the case of 0.5 at%. Fig. 1 shows as-grown rutile crystal boules obtamed by the FZ method. The Sc-doped (0.1 at%) crystal (fig. 1A) is transparent and yellowish, which is close to a completely annealed rutile single crystal. The addition of 0.04 at% Sc203 was also effective to obtain a transparent as-grown crystal. On the other hand, the Sc-free crystal (fig. 1B) is dark-blue and translucent, although the crystal growth was carried out under an oxygen atmosphere. Fig. 2 shows a polished specimen cut from near the tip of the as-grown crystals. For the Sc-doped crystal (fig. 2a), the background letters “rutile” are clearly visible, while the Sc-free crystal (fig. 2b) is still dark-blue and translucent despite its thickness of approximately 1 mm.
3. Results and discussion Crystal growth of Sc-doped rutile crystals by the FZ method was successfully performed and cellular growth did not occur for Sc concentrations of up to 0.1 at%. On the other hand, the penetration of melt into the feed rod was observed in the latter half of the growth run for the crystal with high Sc concentration, e.g. 0.5 at%. This indicates that there was a large difference in Sc concentration between the melt and the feed rod. As mentioned later, the dissolution of Sc203 in rutile is very little, and hence Sc would be gradually concentrated in the melt with proceed-
ni
I a
a Fig. 2. Cross sections of the as-grown rutile crystals: (a) Sc-doped; (b) undoped.
M. Higuchi et a!.
/ Effects of Sc203
addition on FZ growth of ruti!e single crystals
~
-
Fig. 3. A quenched specimen of Sc-doped rutilc crystal. The specimen was moled in epoxy resin and cut so as to include the center of the crystal.
Fig. 3 shows more clearly the effect of Sc-doping on decoloration of a rutile crystal. The sample in fig. 3 was quenched in the course of a steady
At an early stage of annealing, oxide ions could easily diffuse via 3~ions, oxygen vacancies, which and as a result, are accompanied by Ti the peripheral region of the crystal readily becomes transparent and close to stoichiometric Ti0 2. After that, the diffusion of oxide ions through stoichiometric Ti02 region would be sluggish, and thus it takes a long-term annealing for 10—20 days to obtain a thoroughly transparent rutile single crystal. It is well known that Y- or Ca-doped Zr02, so-called stabilized Zr02, is a good ionic conductor, in which oxide ions are charge carriers and migrate easily via oxygen vacancies formed for the charge compensation [7]. In a similar way, oxide ions are expected to migrate easily in a .
3+
.
Sc-doped rutile 4~ sites singleincrystal. a rutile If Sccrystal, ions oxygen substitute the Ti vacancies will result: (1 —x) Ti0 2 +x Sc015
growth run. The frozen melt part is white and the grown crystal is, despite quenching, transparent and yellowish, except for the dark-blue region just below the melt zone. This crystal is in contrast with the Sc-free crystal in fig. 1B, which is dark-blue on the whole, although the crystal was not quenched but normally cooled to room ternperature. As stated above, the coloring of dark-blue or black in a pure rutile crystal grown from the melt can clearly be attributed to the reduction at high 3~, temperatures to formoxygen trivalent titaniumThe ions,reducTi and corresponding vacancies. tion is inevitable for the melt growth of rutile crystals. Accordingly, a transparent rutile crystal can be obtained by post-annealing in an oxidizing atmosphere to diffuse oxide ions over the whole crystal. The diffusion rate usually increases with increasing temperature, and thus it may be advantageous to anneal at as high temperatures as possible. However, the stability of Ti3 + increases with increasing temperature even under a high oxygen partial pressure. Therefore, annealing should be done at a relatively low temperature, which was empirically determined to be 800°Cfor the rutile single crystals grown under a low oxygen partial pressure of up to iO~Pa.
573
—~
Ti1~Sc~O2055V005,
where V0 is oxygen vacancy. The phase diagram for the TiO2—Sc2O3 systern has been investigated, and no solid solution is found at the Ti02-end region in the diagram [8]. Many researchers have reported, however, that a small quantity of Al203 can dissolve in Ti02 [7,9], although there is no solid solution region in the phase diagram for the Ti02—Al203 system [101.Accordingly, a small quantity of 5c203 is alsotype expected to dissolve in Ti02 to form the rutile solid solution. The oxygen vacancies introduced by the addition of Sc3~ions never disappear, even if Ti3~ ions are oxidized to Ti4t Quite rapid and continuous diffusion of oxide ions is therefore expected to occur on cooling, and transparent and yellowish rutile crystals were obtained in the as-grown state, as a result. Cracks were occasionally observed in transparent as-grown crystals as shown in fig. 1A. The cracks were formed spirally from tip to seed of the as-grown crystals on cooling to room temperature. The cause of the cracks is not clarified, but rapid diffusion of oxide ions may be responsible, since Sc-free rutile crystals, which are dark-blue, are never cracked. After the growth of a Sc-doped
574
a ~ ~
M Higuchi et a!.
/ E/6ci.v of Sc203
addition on FZ growth of rutile single crystals
_____
~
tI_______
_
,~jvF
~O~2 mm
1
mm
C
crystal, cooling under a low oxygen partial pressure and subsequent annealing were effective to avoid cracks. The duration of the annealing to obtain transparent crystals was very much shortened, i.e., 20 h at 800°C,as compared with the case for Sc-free crystals. Fig. 4 shows cross sections of the FZ-grown rutile crystals examined under a polarizing microscope with crossed nicols. A few low-angle grain boundaries are observed in a Sc-doped but Zr-free crystal (fig. 4b), which was doped with 0.5 at% Sc203. The number of the grain boundaries is considerably reduced as compared with a pure rutile crystal (fig. 4a). We found in a previous study that the number of low-angle grain boundaries in FZ-grown rutile crystals was reduced by4~ions the addition of a asmall would have role quantity of Zr02 [4].Zr to pin down the migration of dislocations (solution hardening) so that the formation of low-angle grain boundaries was suppressed. The ionic radius of Sc3~is 0.081 nm, which is close to that of Zr4~(0.079 nm). Accordingly, Sc3~was also expected to suppress the formation of low-angle grain boundaries. The number of grain boundaries was appreciably reduced, as shown in fig. 4b. in the case of ZrO 2, the addition of 0.5 at% was enough to grow rutile single crystals free from low-angle grain boundaries. In the case of 3~in Sc203,would rutile however, be much the quantity smallerofthan dissolved 0.5 at%, Sc and consequently a few low-angle grain boundaries were formed. Simultaneous addition of Zr0 2 (0.4 at%) and Sc203 (0.1 at%) was effective to obtain a grain-boundary-free rutile single crystal as shown in fig. 4c. The crystal was reasonably transparent and yellowish in the as-grown state.
4. Summary
1 mm
were rutile crystals
[-ig. 4. ( ross sections ot the as-grown observed with a polarizing microscope: (a) undoped; (b) Sc-doped; (c) Sc- and Zr-doped,
The addition of Sc203 was effective to obtain transparent and yellowish as-grown rutile single crystals by the floating zone method. Oxide ions could readily diffuse via oxygen vacancies, which introduced by the addition of Sc2O3. The formation of cracks was effectively avoided by cooling under a low oxygen partial pressure and .
.
.
-
M. Higuchi et al.
/ Effects of Sc203 addition
subsequent short-term annealing. The addition of Sc203 also had a role to reduce the number of low-angle grain boundaries, but a few boundaries were still observed in only Sc-doped crystal. Simultaneous addition of Sc2O3 and Zr02 was effective to obtain transparent and grainboundary-free rutile single crystals. References [1] M. Shirasaki and K. Asama, AppI. Opt. 21(1982) 4296. [2] H.B. Sachse, Anal. Chem. 33 (1961) 1349.
on FZ growth of rutile single crystals
575
[3] M. Higuchi, T. Hosokawa and S. Kimura, J. Crystal Growth 112 (1991) 354. [4] M. Higuchi and K. Kodaira, to be published. [5] M. Arita, M. Hosoya, M. Kobayashi and M. Someno, J. Am. Ceram. Soc. 62 (1979) 443.
[6] J.A.S.
Ikeda, Y.-M. Chiang and B.D. Fabes, J. Am. Ceram. Soc. 73 (1990) 1633. 17] W.D. Kingery, J. Pappis, ME. Doty and D.C. Hill, J. Am. Ceram. Soc. 42 (1959) 393. [8] L.N. Komissarova B.!. Pokrovskii and V.V. Nechaeva, Dokl. Akad. Nauk SSSR 168 (1966) 1079. 19] J. Yahia, Phys. Rev. 130 (1963) 1711. [10] AM. Lejus, D. Goldberg and A. Revcolevschi, Compt. Rend. (Paris) C 263 (1966) 1223.