- Email: [email protected]
The influence of dopants on the interface stability during Dy3Ga5O12 single crystal growth
CRYSTAL GROWTH FLSFVIFR
___________________________
Journal of Crystal Growth 143 ( l~)94)232—236
The influence of dopants on the interface stability during Dy3Ga5O12 single crystal growth V.V. Kochurikhin ‘,K. Shimamura
‘~,
T. Fukuda
Institute br Materials Research, /ohoku Unitersite, Katahira 2-i—I,,‘-loho—kii Sendat 950, Japan
Received 27 March 1994: manuscrIpt received in final form 3 June 994
Abstract Single crystals ot addition Dy3Ga5Owas , garnets (DGG)Ca: were grown by the method. suppression of spiral 2 ions investigated. DGG crystals hadCzochralski a strong brown color.The In order to suppress this growthTi4+ by Ca color, ions were added to the melt. The influence of dopants on the surface tension of garnet melts and spiral growth has been discussed.
1. Introduction At present gallium garnets single crystals are widely applied in devices of magnetic refrigeration [11. Among them, gadolinium gallium garnet (GGG) is the mostly used material because of its very good characteristics, such as high magnetic entropy and high thermal conductivity. Moreover, there is a well-elaborated growth technology of crystals with big size. However, dysprosium galhum garnet (DGG) seems to he more favorable than GGG, because of its higher magnetic entropy, and it may be useful as a working material for liquid and superfluid helium production in the temperature range below 20 K [2]. However, the application of DGG is still limited by growth difficulties preventing large crystal sizes due to
*
.
.
Corresponding author.
Permanent address: General Physics Institute, Vavilova Street 38, Moscow, Russian Federation,
the high tendency to the interface instability and spiral growth. Up to now the largest DGG single crystal which has been described in literature was 25 mm in diameter and 50 mm in length [31, hut it is well known [11 that industrial working elements of magnetic refrigeration require a cylindrical shape with at least a diameter of 50 mm. This means that in the case of conventional Czochralski technique crucibles with diameter of 80—100 mm are necessary. The use of such large crucihles promotes additional difficulties due to the small temperature gradients on the melt surface and intensification of spiral growth [41.However, in small crucibles. DGG single crystals still tend towards spiral growth. Therefore, Kimura et al. [21 have crystallized only 23% of the melt without spiral growth using a 47 mm diameter crucible. Thus, without special measures of the spiral growth suppression, the application of DGG single crystals is uncertain. There are some factors which create spiral growth in gallium garnets. One of them is the
1994 Elsevier Science By. All rights reserved SSDI 0022-0248(94)0036 I-fl 0022-0248/94/507.tl{)
V V Kochurikhin et a!. /Journal of Crystal Growth 143 (1994) 232—236
presence of different dopants in the melt [5]. Especially, according to some theories [4], noncompensated tetravalent ions (Si4~,Zr4~,Th4~) promote the spiral growth. Therefore, the addition of divalent ions (Ca2~,Mg2~)to the melt will result in the suppression of the spiral growth. In the present work the influence of dopants with different valence state on the phenomenon of spiral growth in DGG single crystals will be investigated.
2. Experimental procedure DGG single crystals were grown by the Czochralski technique using RF power supply of 60 kW. A cylindrical iridium crucible with diameter of 37 mm and height of 40 mm was used. The starting materials were Dy 203 (Nippon Yttrium C.), Ga203 (Mitsuwa’s Pure Chemicals) and CaCO3, Ti02 (High Purity Chemetals) of 99.99% purity. The stoichiometric Dy3Ga5O12 composition was used as initial melt. All crystals were grown in N2 + 2 vol% °2 atmosphere. A gas flow rate of 1 1/mm was used. A pulling rate of 3 mm/h of and17 rotation rate of 15 produced crystals mm in diameter. Therpm length of the boules depended on the beginning of spiral growth. The growth process was finished when the appearance of spiral symptoms had been clearly observed. The growth direction was (111). A diameter control system was not used. The lattice constant of the crystals was determined by the powder diffraction method with Cu Ka 1 radiation, using 8 diffraction lines, corresponding to Bragg angles 20 between 85° and 1150. The accuracy of lattice constant determination was = 1.0 X i0~ nm. The investigated samples were prepared by grinding of slices cut perpendicular to the growth directton. The stress-birefringence associated with facets was observed using an optical microscope with crossed nicols. Two wafers with a thickness of 3 mm each were cut from the top of an as-grown boule and from the section located at the beginning of spiral growth, respectively. Before the observation they were polished with a diamond paste.
233
3. Results and discussion Five DGG crystals containing different dopants were grown (Table 1). All crystals were transparent, but their color changed from yellow to brown in dependence on the dopants concentration. Crystals Nos. 1—3 have been grown to study the influence of Ca2~ions on the spiral growth. Fig. 1 shows photographs of the boules No. 1 and No. 3. It can be seen that the addition of Ca2~ions to the melt increases the weight fraction of solid, crystallized without spiral symptoms (g~ 0),from 0.29 in the case2eofatoms undoped per formula DGG (Fig. unit (AFU) la) to 0.46 if 0.0036 Ca were added (Fig. ib). We did not try to grow crystals with higher Ca2~concentration because of the beginning of considerable coloration by deep brown. This effect may create additional growth difficulties by decreasing heat transfer and radiation and, therefore, decreasing the temperature gradient at the melt surface. The brown color results in generation of oxygen vacancies due to the presence of non-compensated ions with valence different from 3 [7]. In order to suppress the coloration, crystals4~ions. No. 4 and No.are5 There were grown withTi4~ addition Ti results [8] that ions ofsuppress the color of Ca-doped gadolinium scandium gallium garnet (GSGG) crystals without spiral formation. However, we have found that in the case of DGG, Ti4~ ions increase the spiral tendency very markedly. Although identical growth conditions were used for crystals No. 4 and No. 5, the value of g~ changed considerably. We think that in this case the small fluctuations of the crystal
Table 1 Dopant concentrations (CC.02c, CTI2c), weight fraction of solid crystallized without spiral symptoms (g~5) and lattice constants (acajc, a,,,ea,) of Ca,Ti:DGG crystals grown from stoichiometric melt (AFU = atoms per formula unit) No. i 2 3 4 5
CCa2* (AFU)
CTi~* (AFU)
—
—
0.00t2 0.0036 0.006 0.006
— —
0.006 0.006
g.~ 0.29 0.35 0.46 0.12 0.20
a . (nrn) 1.2320 t.2320 t.2320 1.2323 t.2323
a (tim) t.2321 1.2321 1.2321 1.2324 1.2324
VU Koshw’ikhin eta//Journal ~‘I t II sial (,,oiiih /4
234
diameter (0.2—0.3 mm) during growth promote the beginning of spiral growth. According to the X-ray powder diffraction analysis, all DGG crystals had a single phase garnet structure. The measured (a111~5)and calcu lated (a~1i~) values of the lattice constant are also added in Table 1. The calculated values were based on Shannon’s data of ionic radii [9], and an empirical formula [10] assuming that the Dy~ and Ca ions occupy dodecahedral, Ti sites -oc3 toctahedral and tetrahedral tahedral, Ga structure. The calculated values are of the garnet in good agreement with experimental data. This means that the assumption concerning ions sites is correct. Fig. 2 shows the cross-polarized light image of wafers cut perpendicular to the growth direction from the top part of crystal No. 3 (a) and from the part of beginning of spiral growth (h). In the top sample, three symmetric (211 ~ facets at the
1/003)
11
I. ______ -_____
‘~‘~
~
______ ~
~
-
~‘*5
(a)
-‘1’ -
.
r ‘
—
li~. 2. ( riss—pol.iiiisd light uli:igs’’, ~i~’t.il (“Ii. ~): (:i) 1111 I’.Irt: (h) ‘iii
,-
Iii
\1.IlsI’~at l)t 1
ssitli t’seiiiriiii’
~ITIeI~.’
sjlii.il
eii~ssiii
~IiI ~
center of the wafer are easily recognizable. On the other hand, in sample (h). one of the (211 ~ facets is considerably larger than the two others.
hut not reaching the edge of the houle, as reported in Ref. [11]. The effect of spiral suppression by adding of divalent ions for DGG is similar to other gallium garnets. Fig. 3 shows clearly the linear relationship between the weight fraction of solid, crystallized without spiral symptoms and the concentration of Ca ions. After Brandle et al. [5], the presence of the accidental tetravalent ions (Si3 Zr4 e, Th14) in the melt is the main reason of spiral growth. They supposed that these ions without valence compensation possess a distrihution coefficient less than unit and thus, they collect near the solid—liquid interface leading to the ‘
—~
I F Z
t’ I. ( ,achralski eiossn D( a, .,in~leer~st,ils: (a) ssithoiit dopant INo I): (h)( ‘a - DCIG crs~taI (No ~ U, 0036 atoms per formula unit),
increase of morphological instability. A critical
V. V Kochurikhin et a!. /Journal of Crystal Growth 143 (1994) 232—236
~
0.45
ferent compositions are characterized by different values of surface tension and, consequently, the influence of one dopant on the various melts may be differently. In the case of GSGG growth,
~
-
C
face tension and, therefore, the tendency to spiral
U
~-‘
growth. However, the influence of the same dopants on a LiNbO3 melt is reverse, i.e. with
0.35
-~
0) 0
235
0.25 0
~
0.002
I
0.004
concentration C Ca2~ (AFU) Fig. 3. Relationship between weight fraction of solid crystallized without spiral symptoms (g 25 concentration (AFU = atoms per formula unit) 15) and Ca
increasing ofin the 2~ dopant Mg2~decrease concentration, the the of surtenDGG dency If we to spiral melt assume comparison growth a and lower increases with surface GSGG, [13].tension then thea for example, Ca addition of Ti4~ions increases the surface tension of DGG melt and, consequently, the tendency towards spiral growth more markedly than in the case of GSGG. However, additional experiments are necessary to understand this phenomenon, exactly.
value of Si4~ ions in GSGG for spiral growth creation of 0.0016 AFU was detected [6]. The addition of 0.0012 AFU Ca2~ions to the GSGG melt resulted in the full suppression of spiral growth [8].However, we have found that a similar amount of Ca2~ in the case of DGG growth increases the value g~,but is not as effective as in GSGG (Table 1, No. 2). According to another theory [4], the spiral growth is mainly affected by the Marangoni flows due to a surface tension gradient. Such gradients can emerge in the melts of gallium garnets due to the evaporation of Ga 20 from the melt surface. The interaction thermoconvection Marangoni flows between at the melt surface affects and the interface stability. The dopants with 2- and 4-valence state influence the surface tension of gallium garnet melts differently. Divalent and tetravalent dopants decrease and increase this value, respectively. The suppression of spiral growth, observed by application of a high oxygen partial pressure [8], supports this hypothesis additionally. Moreover, it should be noted, that for gadolinium aluminum gallium garnet (GAGG) growth, where the evaporation of Ga 20 is less, spiral growth was not observed [12]. In virtue of this theory it is possible to explain 44 the of the influence of Tidifions marked on DGGdifference and GSGG melts. Obviously,
4. Conclusion In order to grow large size DGG crystals suitable for magnetic refrigeration by the Czochralski technique, the influence of Ca2~ and Ti4~ions on the growing interface stability was examined. The addition of 0.0036 AFU Ca2~ions increased the weight fraction of solid crystallized without spiral symptoms of growth from 0.29 to 0.45. The color of Ca : DGG crystals changed from yellow to brown with increasing Ca2~concentration. The attempts suppress the coloration adding 4~ions to were not successful due to by increasing Ti tendency of the spiral morphology.
Acknowledgements The authors are indebted to Professor P. Rudolph for discussion and critical reading of the manuscript.
References [11Y. Hakuraku 140.
and H. Ogata, Jap. J. AppI. Phys. 25 (1986)
236
V V Koehurikhin et a!. /.Iournal o( Crvstal Grout/i /43 (/994) 232— 236
[2] H. Kimura, H. Macda and M. Sato, J. Mater. Sci. 23 (1988) 809. [31T. Numazawa, H. Kimura, M. Sato and H. Maeda. (‘rvogenie Eng. 28 (1993) 588 (in Japenesel. [41 SE. Stokowski, MN. Randles and R.S. Morris, IEEE J. Quantum Electron. QE—24 (1988) 934. [51F.J. Bruni. Crystals for Magnetic Application (Spinger. Berlin, 1978) p. 61.). [6] V.J. Fratello, CD. Brandle, A.J. Valcntino and SE. Stokowski J. Crystal Growth 85 (1987) 229. [7] M. Padvari-Horvath, 1. Foldvali, 1. Fellegvari. L. Gosztonyi and J. Paitz. Phys. Status Solidi (a) 84 (1984) 547.
[8] C’.D. Brandle, V.J. Fratcllo and i\.J. Valentino. J. (rss)al Growth 85 (1987) 223. [9] RD. Shannon. Acta tryst. 32A (1976) 751. [Ill] B. Stroeka. P. HoIst and W. Tolksdorf, Philips J. kcs. 33 (1978) 186. [II] H. Kimura, ‘1’. Numaza’,sa. M. Sato tad il Macd:i, 1. Crystal Growth 87 (1988) 523. [12] 1-1. Kimura, H. Maeda ~ind M. Sato. J. (‘rvs)ul I irowili 74 (1986)187. [13] S. Erdei and V.’!. (iahrieljan. (rvstal Res. ‘t’cclinol. 24 (1989) 987.
___________________________
Journal of Crystal Growth 143 ( l~)94)232—236
The influence of dopants on the interface stability during Dy3Ga5O12 single crystal growth V.V. Kochurikhin ‘,K. Shimamura
‘~,
T. Fukuda
Institute br Materials Research, /ohoku Unitersite, Katahira 2-i—I,,‘-loho—kii Sendat 950, Japan
Received 27 March 1994: manuscrIpt received in final form 3 June 994
Abstract Single crystals ot addition Dy3Ga5Owas , garnets (DGG)Ca: were grown by the method. suppression of spiral 2 ions investigated. DGG crystals hadCzochralski a strong brown color.The In order to suppress this growthTi4+ by Ca color, ions were added to the melt. The influence of dopants on the surface tension of garnet melts and spiral growth has been discussed.
1. Introduction At present gallium garnets single crystals are widely applied in devices of magnetic refrigeration [11. Among them, gadolinium gallium garnet (GGG) is the mostly used material because of its very good characteristics, such as high magnetic entropy and high thermal conductivity. Moreover, there is a well-elaborated growth technology of crystals with big size. However, dysprosium galhum garnet (DGG) seems to he more favorable than GGG, because of its higher magnetic entropy, and it may be useful as a working material for liquid and superfluid helium production in the temperature range below 20 K [2]. However, the application of DGG is still limited by growth difficulties preventing large crystal sizes due to
*
.
.
Corresponding author.
Permanent address: General Physics Institute, Vavilova Street 38, Moscow, Russian Federation,
the high tendency to the interface instability and spiral growth. Up to now the largest DGG single crystal which has been described in literature was 25 mm in diameter and 50 mm in length [31, hut it is well known [11 that industrial working elements of magnetic refrigeration require a cylindrical shape with at least a diameter of 50 mm. This means that in the case of conventional Czochralski technique crucibles with diameter of 80—100 mm are necessary. The use of such large crucihles promotes additional difficulties due to the small temperature gradients on the melt surface and intensification of spiral growth [41.However, in small crucibles. DGG single crystals still tend towards spiral growth. Therefore, Kimura et al. [21 have crystallized only 23% of the melt without spiral growth using a 47 mm diameter crucible. Thus, without special measures of the spiral growth suppression, the application of DGG single crystals is uncertain. There are some factors which create spiral growth in gallium garnets. One of them is the
1994 Elsevier Science By. All rights reserved SSDI 0022-0248(94)0036 I-fl 0022-0248/94/507.tl{)
V V Kochurikhin et a!. /Journal of Crystal Growth 143 (1994) 232—236
presence of different dopants in the melt [5]. Especially, according to some theories [4], noncompensated tetravalent ions (Si4~,Zr4~,Th4~) promote the spiral growth. Therefore, the addition of divalent ions (Ca2~,Mg2~)to the melt will result in the suppression of the spiral growth. In the present work the influence of dopants with different valence state on the phenomenon of spiral growth in DGG single crystals will be investigated.
2. Experimental procedure DGG single crystals were grown by the Czochralski technique using RF power supply of 60 kW. A cylindrical iridium crucible with diameter of 37 mm and height of 40 mm was used. The starting materials were Dy 203 (Nippon Yttrium C.), Ga203 (Mitsuwa’s Pure Chemicals) and CaCO3, Ti02 (High Purity Chemetals) of 99.99% purity. The stoichiometric Dy3Ga5O12 composition was used as initial melt. All crystals were grown in N2 + 2 vol% °2 atmosphere. A gas flow rate of 1 1/mm was used. A pulling rate of 3 mm/h of and17 rotation rate of 15 produced crystals mm in diameter. Therpm length of the boules depended on the beginning of spiral growth. The growth process was finished when the appearance of spiral symptoms had been clearly observed. The growth direction was (111). A diameter control system was not used. The lattice constant of the crystals was determined by the powder diffraction method with Cu Ka 1 radiation, using 8 diffraction lines, corresponding to Bragg angles 20 between 85° and 1150. The accuracy of lattice constant determination was = 1.0 X i0~ nm. The investigated samples were prepared by grinding of slices cut perpendicular to the growth directton. The stress-birefringence associated with facets was observed using an optical microscope with crossed nicols. Two wafers with a thickness of 3 mm each were cut from the top of an as-grown boule and from the section located at the beginning of spiral growth, respectively. Before the observation they were polished with a diamond paste.
233
3. Results and discussion Five DGG crystals containing different dopants were grown (Table 1). All crystals were transparent, but their color changed from yellow to brown in dependence on the dopants concentration. Crystals Nos. 1—3 have been grown to study the influence of Ca2~ions on the spiral growth. Fig. 1 shows photographs of the boules No. 1 and No. 3. It can be seen that the addition of Ca2~ions to the melt increases the weight fraction of solid, crystallized without spiral symptoms (g~ 0),from 0.29 in the case2eofatoms undoped per formula DGG (Fig. unit (AFU) la) to 0.46 if 0.0036 Ca were added (Fig. ib). We did not try to grow crystals with higher Ca2~concentration because of the beginning of considerable coloration by deep brown. This effect may create additional growth difficulties by decreasing heat transfer and radiation and, therefore, decreasing the temperature gradient at the melt surface. The brown color results in generation of oxygen vacancies due to the presence of non-compensated ions with valence different from 3 [7]. In order to suppress the coloration, crystals4~ions. No. 4 and No.are5 There were grown withTi4~ addition Ti results [8] that ions ofsuppress the color of Ca-doped gadolinium scandium gallium garnet (GSGG) crystals without spiral formation. However, we have found that in the case of DGG, Ti4~ ions increase the spiral tendency very markedly. Although identical growth conditions were used for crystals No. 4 and No. 5, the value of g~ changed considerably. We think that in this case the small fluctuations of the crystal
Table 1 Dopant concentrations (CC.02c, CTI2c), weight fraction of solid crystallized without spiral symptoms (g~5) and lattice constants (acajc, a,,,ea,) of Ca,Ti:DGG crystals grown from stoichiometric melt (AFU = atoms per formula unit) No. i 2 3 4 5
CCa2* (AFU)
CTi~* (AFU)
—
—
0.00t2 0.0036 0.006 0.006
— —
0.006 0.006
g.~ 0.29 0.35 0.46 0.12 0.20
a . (nrn) 1.2320 t.2320 t.2320 1.2323 t.2323
a (tim) t.2321 1.2321 1.2321 1.2324 1.2324
VU Koshw’ikhin eta//Journal ~‘I t II sial (,,oiiih /4
234
diameter (0.2—0.3 mm) during growth promote the beginning of spiral growth. According to the X-ray powder diffraction analysis, all DGG crystals had a single phase garnet structure. The measured (a111~5)and calcu lated (a~1i~) values of the lattice constant are also added in Table 1. The calculated values were based on Shannon’s data of ionic radii [9], and an empirical formula [10] assuming that the Dy~ and Ca ions occupy dodecahedral, Ti sites -oc3 toctahedral and tetrahedral tahedral, Ga structure. The calculated values are of the garnet in good agreement with experimental data. This means that the assumption concerning ions sites is correct. Fig. 2 shows the cross-polarized light image of wafers cut perpendicular to the growth direction from the top part of crystal No. 3 (a) and from the part of beginning of spiral growth (h). In the top sample, three symmetric (211 ~ facets at the
1/003)
11
I. ______ -_____
‘~‘~
~
______ ~
~
-
~‘*5
(a)
-‘1’ -
.
r ‘
—
li~. 2. ( riss—pol.iiiisd light uli:igs’’, ~i~’t.il (“Ii. ~): (:i) 1111 I’.Irt: (h) ‘iii
,-
Iii
\1.IlsI’~at l)t 1
ssitli t’seiiiriiii’
~ITIeI~.’
sjlii.il
eii~ssiii
~IiI ~
center of the wafer are easily recognizable. On the other hand, in sample (h). one of the (211 ~ facets is considerably larger than the two others.
hut not reaching the edge of the houle, as reported in Ref. [11]. The effect of spiral suppression by adding of divalent ions for DGG is similar to other gallium garnets. Fig. 3 shows clearly the linear relationship between the weight fraction of solid, crystallized without spiral symptoms and the concentration of Ca ions. After Brandle et al. [5], the presence of the accidental tetravalent ions (Si3 Zr4 e, Th14) in the melt is the main reason of spiral growth. They supposed that these ions without valence compensation possess a distrihution coefficient less than unit and thus, they collect near the solid—liquid interface leading to the ‘
—~
I F Z
t’ I. ( ,achralski eiossn D( a, .,in~leer~st,ils: (a) ssithoiit dopant INo I): (h)( ‘a - DCIG crs~taI (No ~ U, 0036 atoms per formula unit),
increase of morphological instability. A critical
V. V Kochurikhin et a!. /Journal of Crystal Growth 143 (1994) 232—236
~
0.45
ferent compositions are characterized by different values of surface tension and, consequently, the influence of one dopant on the various melts may be differently. In the case of GSGG growth,
~
-
C
face tension and, therefore, the tendency to spiral
U
~-‘
growth. However, the influence of the same dopants on a LiNbO3 melt is reverse, i.e. with
0.35
-~
0) 0
235
0.25 0
~
0.002
I
0.004
concentration C Ca2~ (AFU) Fig. 3. Relationship between weight fraction of solid crystallized without spiral symptoms (g 25 concentration (AFU = atoms per formula unit) 15) and Ca
increasing ofin the 2~ dopant Mg2~decrease concentration, the the of surtenDGG dency If we to spiral melt assume comparison growth a and lower increases with surface GSGG, [13].tension then thea for example, Ca addition of Ti4~ions increases the surface tension of DGG melt and, consequently, the tendency towards spiral growth more markedly than in the case of GSGG. However, additional experiments are necessary to understand this phenomenon, exactly.
value of Si4~ ions in GSGG for spiral growth creation of 0.0016 AFU was detected [6]. The addition of 0.0012 AFU Ca2~ions to the GSGG melt resulted in the full suppression of spiral growth [8].However, we have found that a similar amount of Ca2~ in the case of DGG growth increases the value g~,but is not as effective as in GSGG (Table 1, No. 2). According to another theory [4], the spiral growth is mainly affected by the Marangoni flows due to a surface tension gradient. Such gradients can emerge in the melts of gallium garnets due to the evaporation of Ga 20 from the melt surface. The interaction thermoconvection Marangoni flows between at the melt surface affects and the interface stability. The dopants with 2- and 4-valence state influence the surface tension of gallium garnet melts differently. Divalent and tetravalent dopants decrease and increase this value, respectively. The suppression of spiral growth, observed by application of a high oxygen partial pressure [8], supports this hypothesis additionally. Moreover, it should be noted, that for gadolinium aluminum gallium garnet (GAGG) growth, where the evaporation of Ga 20 is less, spiral growth was not observed [12]. In virtue of this theory it is possible to explain 44 the of the influence of Tidifions marked on DGGdifference and GSGG melts. Obviously,
4. Conclusion In order to grow large size DGG crystals suitable for magnetic refrigeration by the Czochralski technique, the influence of Ca2~ and Ti4~ions on the growing interface stability was examined. The addition of 0.0036 AFU Ca2~ions increased the weight fraction of solid crystallized without spiral symptoms of growth from 0.29 to 0.45. The color of Ca : DGG crystals changed from yellow to brown with increasing Ca2~concentration. The attempts suppress the coloration adding 4~ions to were not successful due to by increasing Ti tendency of the spiral morphology.
Acknowledgements The authors are indebted to Professor P. Rudolph for discussion and critical reading of the manuscript.
References [11Y. Hakuraku 140.
and H. Ogata, Jap. J. AppI. Phys. 25 (1986)
236
V V Koehurikhin et a!. /.Iournal o( Crvstal Grout/i /43 (/994) 232— 236
[2] H. Kimura, H. Macda and M. Sato, J. Mater. Sci. 23 (1988) 809. [31T. Numazawa, H. Kimura, M. Sato and H. Maeda. (‘rvogenie Eng. 28 (1993) 588 (in Japenesel. [41 SE. Stokowski, MN. Randles and R.S. Morris, IEEE J. Quantum Electron. QE—24 (1988) 934. [51F.J. Bruni. Crystals for Magnetic Application (Spinger. Berlin, 1978) p. 61.). [6] V.J. Fratello, CD. Brandle, A.J. Valcntino and SE. Stokowski J. Crystal Growth 85 (1987) 229. [7] M. Padvari-Horvath, 1. Foldvali, 1. Fellegvari. L. Gosztonyi and J. Paitz. Phys. Status Solidi (a) 84 (1984) 547.
[8] C’.D. Brandle, V.J. Fratcllo and i\.J. Valentino. J. (rss)al Growth 85 (1987) 223. [9] RD. Shannon. Acta tryst. 32A (1976) 751. [Ill] B. Stroeka. P. HoIst and W. Tolksdorf, Philips J. kcs. 33 (1978) 186. [II] H. Kimura, ‘1’. Numaza’,sa. M. Sato tad il Macd:i, 1. Crystal Growth 87 (1988) 523. [12] 1-1. Kimura, H. Maeda ~ind M. Sato. J. (‘rvs)ul I irowili 74 (1986)187. [13] S. Erdei and V.’!. (iahrieljan. (rvstal Res. ‘t’cclinol. 24 (1989) 987.