- Email: [email protected]
Macroclustering in liquid lithium niobate
ELSEVIER
Journal of Non-Crystalline
Macroclustering
Solids 205-207 (1996) 163-167
in liquid lithium niobate
P. Andonov as* , S. Kimura b, P. Palleau ’ ’ CNRS-LMVO,
Universite
de Versailles, 45 avenue des Etats his, Bat. Fermat, 78305 Versailles b NIRIM, I-l Namiki, Tsukuba-shi, Ibaraki, 305, Japan ’ ILL, BP 156, F 38042 Grenoble cedex 9, France
cedes France
Abstract The presence of microclusters in LiNbO, melt has been previously confiied from investigations by small angle X-ray scattering (SAXS) using synchrotron radiation. The evolution of clustersin the undercooled domain and the probable macroclustering near solidification had to be verified with a better accuracy. Using neutron scattering, the melt was studied by transmission through a sealed platinum container, avoiding the parasitic air scattering and the partial sample evaporation observed in the SAXS experiments, The results obtained from small angle neutron scattering (SANS) confirm that macroclusters are indeed present in molten LiNbO, with a radius of gyration increasing to 6 nm in the undercooled domain near solidification.
1. Introduction A behaviour characteristic of an expanding fluid has been detected in molten lithium metaniobate on cooling between 1590 and 1560 K and a marked increase of viscosity was observed below 1553 K [ 1,2]. These observations imply strong modifications in the liquid local and medium range ordering and a possible cluster formation [3]. Such behaviour, near the melting point (T, = 1526 K), might be correlated with the appearance of subgrain boundaries [4,.5] affecting the crystal growth. The structural studies carried out by high temperature X-ray and neutron diffraction [6,7] have confirmed a local ordering in the melt similar to the crystal up to the highest explored temperature (1623 K) with a persistent octahedral Nb coordination. The crystal belongs to the rhombohedral system with the space group R3c ES]which may become R3 or R% [8,9] at the Curie
point, T, just a few degrees below T,. Previous small angle X-ray scattering (SAXS) investigations El01 confirmed the presenceof scattering particles in the melt. From these different results, the microclusters can be described by an association of ,NbO, octahedra such as chains, small ReO,-type slabs or blocks constituted by two layers of four comer-shared octahedrainterlocked by a lithium atom. The number of these small particles is large enough to give an interference effect. By lowering the temperature, the particle size increases and, below 1550 K, macroclusters are probably present correlated to the rapid increase of viscosity. The deformation observed near origin in the SAXS curves could be explained by this ‘macroclustering’. To confirm this assumption, we present structural results obtained from small angle neutron scattering (SANS) experiments. 2. Experimental
* Corresponding author. Tel.: +33-l 45 07 50 76; fax: 45 07 58 22; e-mail: [email protected]. 0022-3093/96/$15.00 Copyright PI1 SOO22-3093(96)00436-X
0 1996 Elsevier
Science
+33-l
Monocrystals were prepared at Tsukuba (Japan) by the pulling Czochralski’s method [Ill from
B.V. All rights reserved.
164
P. Andonou
et al. / Journal
of Nou-Crystalline
LiNbO, rods obtained by sintering of Li,CO, and Nb,O, powders (natural abundance and purity = 99.99%) mixed in congruent composition and calcined for 5 h at 1273°C. The lamella are cut out of the crystal and thinned by polishing until a desired weight is obtained. The lamella are put in a container having platinum parallel faces with wall thickness 0.2 mm. The container is sealed with a sufficient free volume to avoid the deformation at high temperature and to maintain an oxidizing air atmosphere. The liquid sample dimensions (area 2 X 2 cm2, thickness d = 2 mm) optimize the neutron diffraction experiments with an absorption factor of the incident beam equal to 0.5. The experiments were carried out on the D17 spectrometer at the Institut Laue-Langevin in Grenoble (France). The melt temperature was controlled to +5 K. Crucible and heater were placed in an evacuated bell-jar to minimize air scattering. The angular range of the measurement was maintained within 0.528” I 2 13I 13.746” (20 = scattering angle). With a wavelength h = 1.1700 nm and K = (4nsin 9)/h, the explored K range extended from 0.049 to 1.285 nm-‘. The standard program ‘RNILS’, was used to produce the radial distribution function. The program ‘SPOLLY’ was applied to correct the sample spectrum. The neutron plus electronic background, I,,, was obtained from the run with a cadmium sample and the statistical error, SZc,, evaluated. The intensities scattered by an empty reference Pt container of same dimensions were also measured to study recrystallization effects on warming and then on cooling, at each temperature chosen for the study of the melt. Furnace, container scattering and sample self absorption were corrected using the values of the coherent scattering and absorption cross-sections as listed in the neutron diffraction tables [12,13]. The contribution of multiple scattering has been neglected. Finally the corrected sample scattering was normalized to the corrected V scattering for each K value. The corrected intensity can be expressed as folIows: I=$$-AS. f
4
A5 represents the incoherent and structure indepen-
Solids 205-207
(1996)
163-167
dent scattering and has to be subtracted from the corrected intensity. A, and A, refer to the vanadium and sample cross-sections respectively. They include: (i) the reduction by self absorption eZ(olald where &al is the macroscopic total cross-section of the sample, (ii) the cross-section term relative to the /di2)d. They are given by: A = samP1e (ax:dcattering td~~scattering/d”r2)de-~~~~~~~.The values S, and V, are obtained from the intensities scattered by the sample, I,, and the vanadium, I,, respectively and corrected for background and attenuation. They are given by: S, = Z, - Zcd - A,(Z,, - Zcd) and V, = Iv - Z,, A2&3 - Zcd) where A, and A, refer to the absorption of the sample and the vanadium respectively. ZsB is the background corresponding to the empty container in the furnace and ZVB the background corresponding to the furnace without container.
3. Results The intensities from the LiNbO, melt we&e measured at six temperatures, T increasing (T t) from 1529 to 1654 K by steps of 25 K and at 7 temperatures T decreasing (T J.) from 1654 to 1504 K with an undercoohng equal to 22 K. In Fig. 1, four curves of the corrected intensity, I(K), expressed in relative units, are plotted as a function of the wave vector for the highest temperature and for the other three values (T J,> at which a different evolution is observed. The zero on the intensity coordinate has been shifted for each different pattern. When K I 0.75 nm- * a sharp increase of the intensity is always observed as K goes to zero and the slope of the curves increases with decreasing temperature. For K2 1 nm-‘, the intensity shows a marked hump at 1579 K (T r>. This phenomenon subsists until 1604 K and disappears with increasing temperature. At the cooling, the same anomaly is reproduced with a weak hysteresis, totally vanished at 1554 K (T .J) and its maximum is observed at 1579 K (T 1). Then by lowering the temperature, a hollowing appears centred around 0.9 nm- ‘, followed by a noticeable rise for Kk 1 nm-’ until solidification. The present results are compared with those obtained by SAXS using the synchrotron radiation. In Fig. 2, the previous results are reported in a large K-range (0.20 nm-l I K < 14.00 nm-‘> for 12 different tempera-
P. Andonov
et aL/JoumaE
of Non-Crystalline
Solids 205-207
(19961 163-167
I cob relative
tures. The comparison is possible in the domain 0.20 mn-’ 5 K 2 1.28 run-‘. A good agreement is observed in the undercooled domain and up to T = 1579 K. In the low K-range, the slope of the curves varies as previously observed from the SAXS results and a shoulder is present at 1579 K. The differences appear at high temperature since the intensity is always increasing as K goes to zero and the lower-K side of the interference peak is not as marked as in the SANS curve except when T I 1554 K. To determine the size of the scattering particles, we have used the supplementary program ‘RGUIM’ (ILL), to attempt to fit a straight line to any corrected spectrum [14,15]. Five different functions of intensity vs. K 2 may. be fitted within a certain K-range which may be adjusted to optimize the region of K for which the model may be appropriate. We have tested the five options and retained the Guinier approximation to derive the radius of gyration, R,, of the not dense macroparticles because it gives the best fit in a large K-range. The interference effect relative
165
units
1513 1518 1523 1528 1538 1553 1573 1598 1823 1626 1648 1673 1
)
.
4
8
I
12
K (nm-')
Fig. 2. Coherent intensity, Icoh expressed in relative units, as a function of the wave vector K and plotted for twelve temperatures expressed in K. Results previously obtained from SAXS cl I].
Fig. 1. Corrected intensity, I expressed in relative units, as a function of the wave vector K and plotted for four temperatures expressed in K. Resulrs obtained from SANS.
to the small particles is assumed independent of the large particle distribution [ 111. The evolution of the linear fits is reported in Fig. 3. Large deviations are observed between the values obtained by heating (T t > and cooling (T J,> in the undercooled domain and at T = 1579 K. The R, values have been evaluated from the slopes of these fits, a, such as: R, = 6 and reported in the Table 1. For instance g 1554 K (T), from the Guinier approximation, R, = 3.31 i 0.30 nm which leads to: 0.40 I KR, I 1.81. Assuming spherical aggregates, the diameter of the macrocluters reaches a value Q, E 2igR, = 8.50 + 0.80 nm. The variations of R, with temperature is shown in Fig. 4 along with the SAXS results. At the same temperature, a difference is observed between the values obtained during heating and cooling, the size of particles being larger at the cooling. The evolution of R, determined from SANS is lower than the one from SAXS. The higher value reached at 1504 K is inferior to the one measured by SAXS
166
P. Andoaov
et al. / Journal
of Non-Crystalline
Solids 205-207
(1996)
163-167
Table 1 Values of the radius of gyration expressed in nm
Ln (1)
T (K)
R, (Tf)
1504
1529
3.09rto.40
1554
2.8OkOo.30 2.40F0.30 2.10+0.30 1.80*0.30 1.50+0.30
1579 1604 1629 16.54
R,(TJ) 6.20*0.40 3.85 rtO.40 3.3orto.30 2.80-10.30 2.35*0.30
1.95 & 0.30
at 1513 K. A sharp modification is not observed at 15.54 K and the radius of gyration progressively decreases up to 1654 K. The sudden rearrangement of microclusters assumed previously is not really confirmed. This difference can be explained by the large sample volume involved in the neutron diffraction and giving a high thermal inertia. 4. Conclusion
\, 15041
1 0
2
K *(nn?)
4
6
x10
-1
Fig. 3. Linear tits obtained from the Guinier approximation. Results obtained from SANS.
8
6 1 .
t\ 4
. .
0 a
Our present results has confirmed the presence in molten LiNbO, of macroclusters near solidification. The values of the radius of gyration of the scattering particles are similar to those obtained by SAKS. The differences are due to a progressive rearrangement of the clusters. The sudden aggregation of particles, revealed from previous SAKS results, does not show in the neutron diffraction results. The re-arrangement begins at a temperature larger than previously reported and continues as a progressive phenomenon. The sudden increase of viscosity observed near 1553 K cannot be explained by a rapid aggregation of particles or by a strong modification of the structure of the melt. Acknowledgements
0
2
The authors want to thank Dr R. Cubitt of ILL for discussions and experimental assistance.
~~ / 1500
I
1 1600
T (K)
Fig. 4. Radius of gyration, R,, expressed in nm, as a function of temperature from SANS: 0 at the heating; l at the cooling; previous results from SAXS [ll]: H. The lines are drawn as guides for the eye.
References El] S.A. Bol’shkov, V.P. Klyuev, N.N. Lyapushkin, A.P. Lyubimow and S.A. Fedulov, Inorg. Mater. (USSR) 5 (1969) 824.
P. Andonov
et al./JournaE
of Non-Crystalline
[2] K. Shigematsu, Y. Anztii, S. Morita, M. Yamada and H. Yokoyama, Jpn. J. Appl. Phys. 26 (12) (1987) 1988. [3] A.R. Ubbelohde, The Molten State of Matter (Wiley, Chichester, 1978). [4] N. Niizeki, T. Yamada and H. Toyoda, Jpn. J. Appl. Phys. 6 (2-3) (1967) 151 and 318. [51 Y.S. Luh, R.S. Feigelson, M.M. Fejer and R.J. Byer, J. Cry% Growth, 78 (1986) 135; 85 (1987) 264. [61 K. SugiyamB, K. Nomura, Y. Waseda, P. Andonov, S. Kimura and K. Shigematsu, 2. Naturforsch, 45a (1990) 1325. 171 P. Audonov, P. Chieux and S. Kimura, J. Phys.: Condens. Matter 5, (1993) 1. [8] S.C. Abrahams, J.M. Reddy and J.L. Bernstein, J. Phys. Chem. Solids 27 (1966) 997; S.C. Abrahams, WC. Hamilton and J.M. Reddy, J. Phys. Chem. Solids 27 (1966) 1013; SC.
Solids 21X-207
(1996)
163-167
167
Abrahams, H.J. Levinstein and J.M. Reddy, J. Phys. Chem. Solids 27 (1966) 1019. 191 H. Boysen and F. Altofer, Acta Crystallogr. B.50 (1994) 405. [lOI P. Andonov, S. Kimura and T. Sawada, J. Non-Cry& Solids 156-158 (1993) 783. [ll] A.A. Ballmann, J. Am. Ceram. Sot. 48 (1965) 112. [12] L. Koester and W.B. Yelon, Neutron Diffraction Newsletters (The Neutron Diffraction Commission of the International Union of Crystallography, 1983). [I31 V.F. Sears, AECL, Report 8490 (1984). 1141 A. Guinier and G. Foumet, Small Angle Scattering of X-Rays, (Wiley, New York, 1955). El51 0. Glatter and 0. Kratky, Small-Angle X-Ray Scattering (Academic Press, London, 1982).
Journal of Non-Crystalline
Macroclustering
Solids 205-207 (1996) 163-167
in liquid lithium niobate
P. Andonov as* , S. Kimura b, P. Palleau ’ ’ CNRS-LMVO,
Universite
de Versailles, 45 avenue des Etats his, Bat. Fermat, 78305 Versailles b NIRIM, I-l Namiki, Tsukuba-shi, Ibaraki, 305, Japan ’ ILL, BP 156, F 38042 Grenoble cedex 9, France
cedes France
Abstract The presence of microclusters in LiNbO, melt has been previously confiied from investigations by small angle X-ray scattering (SAXS) using synchrotron radiation. The evolution of clustersin the undercooled domain and the probable macroclustering near solidification had to be verified with a better accuracy. Using neutron scattering, the melt was studied by transmission through a sealed platinum container, avoiding the parasitic air scattering and the partial sample evaporation observed in the SAXS experiments, The results obtained from small angle neutron scattering (SANS) confirm that macroclusters are indeed present in molten LiNbO, with a radius of gyration increasing to 6 nm in the undercooled domain near solidification.
1. Introduction A behaviour characteristic of an expanding fluid has been detected in molten lithium metaniobate on cooling between 1590 and 1560 K and a marked increase of viscosity was observed below 1553 K [ 1,2]. These observations imply strong modifications in the liquid local and medium range ordering and a possible cluster formation [3]. Such behaviour, near the melting point (T, = 1526 K), might be correlated with the appearance of subgrain boundaries [4,.5] affecting the crystal growth. The structural studies carried out by high temperature X-ray and neutron diffraction [6,7] have confirmed a local ordering in the melt similar to the crystal up to the highest explored temperature (1623 K) with a persistent octahedral Nb coordination. The crystal belongs to the rhombohedral system with the space group R3c ES]which may become R3 or R% [8,9] at the Curie
point, T, just a few degrees below T,. Previous small angle X-ray scattering (SAXS) investigations El01 confirmed the presenceof scattering particles in the melt. From these different results, the microclusters can be described by an association of ,NbO, octahedra such as chains, small ReO,-type slabs or blocks constituted by two layers of four comer-shared octahedrainterlocked by a lithium atom. The number of these small particles is large enough to give an interference effect. By lowering the temperature, the particle size increases and, below 1550 K, macroclusters are probably present correlated to the rapid increase of viscosity. The deformation observed near origin in the SAXS curves could be explained by this ‘macroclustering’. To confirm this assumption, we present structural results obtained from small angle neutron scattering (SANS) experiments. 2. Experimental
* Corresponding author. Tel.: +33-l 45 07 50 76; fax: 45 07 58 22; e-mail: [email protected]. 0022-3093/96/$15.00 Copyright PI1 SOO22-3093(96)00436-X
0 1996 Elsevier
Science
+33-l
Monocrystals were prepared at Tsukuba (Japan) by the pulling Czochralski’s method [Ill from
B.V. All rights reserved.
164
P. Andonou
et al. / Journal
of Nou-Crystalline
LiNbO, rods obtained by sintering of Li,CO, and Nb,O, powders (natural abundance and purity = 99.99%) mixed in congruent composition and calcined for 5 h at 1273°C. The lamella are cut out of the crystal and thinned by polishing until a desired weight is obtained. The lamella are put in a container having platinum parallel faces with wall thickness 0.2 mm. The container is sealed with a sufficient free volume to avoid the deformation at high temperature and to maintain an oxidizing air atmosphere. The liquid sample dimensions (area 2 X 2 cm2, thickness d = 2 mm) optimize the neutron diffraction experiments with an absorption factor of the incident beam equal to 0.5. The experiments were carried out on the D17 spectrometer at the Institut Laue-Langevin in Grenoble (France). The melt temperature was controlled to +5 K. Crucible and heater were placed in an evacuated bell-jar to minimize air scattering. The angular range of the measurement was maintained within 0.528” I 2 13I 13.746” (20 = scattering angle). With a wavelength h = 1.1700 nm and K = (4nsin 9)/h, the explored K range extended from 0.049 to 1.285 nm-‘. The standard program ‘RNILS’, was used to produce the radial distribution function. The program ‘SPOLLY’ was applied to correct the sample spectrum. The neutron plus electronic background, I,,, was obtained from the run with a cadmium sample and the statistical error, SZc,, evaluated. The intensities scattered by an empty reference Pt container of same dimensions were also measured to study recrystallization effects on warming and then on cooling, at each temperature chosen for the study of the melt. Furnace, container scattering and sample self absorption were corrected using the values of the coherent scattering and absorption cross-sections as listed in the neutron diffraction tables [12,13]. The contribution of multiple scattering has been neglected. Finally the corrected sample scattering was normalized to the corrected V scattering for each K value. The corrected intensity can be expressed as folIows: I=$$-AS. f
4
A5 represents the incoherent and structure indepen-
Solids 205-207
(1996)
163-167
dent scattering and has to be subtracted from the corrected intensity. A, and A, refer to the vanadium and sample cross-sections respectively. They include: (i) the reduction by self absorption eZ(olald where &al is the macroscopic total cross-section of the sample, (ii) the cross-section term relative to the /di2)d. They are given by: A = samP1e (ax:dcattering td~~scattering/d”r2)de-~~~~~~~.The values S, and V, are obtained from the intensities scattered by the sample, I,, and the vanadium, I,, respectively and corrected for background and attenuation. They are given by: S, = Z, - Zcd - A,(Z,, - Zcd) and V, = Iv - Z,, A2&3 - Zcd) where A, and A, refer to the absorption of the sample and the vanadium respectively. ZsB is the background corresponding to the empty container in the furnace and ZVB the background corresponding to the furnace without container.
3. Results The intensities from the LiNbO, melt we&e measured at six temperatures, T increasing (T t) from 1529 to 1654 K by steps of 25 K and at 7 temperatures T decreasing (T J.) from 1654 to 1504 K with an undercoohng equal to 22 K. In Fig. 1, four curves of the corrected intensity, I(K), expressed in relative units, are plotted as a function of the wave vector for the highest temperature and for the other three values (T J,> at which a different evolution is observed. The zero on the intensity coordinate has been shifted for each different pattern. When K I 0.75 nm- * a sharp increase of the intensity is always observed as K goes to zero and the slope of the curves increases with decreasing temperature. For K2 1 nm-‘, the intensity shows a marked hump at 1579 K (T r>. This phenomenon subsists until 1604 K and disappears with increasing temperature. At the cooling, the same anomaly is reproduced with a weak hysteresis, totally vanished at 1554 K (T .J) and its maximum is observed at 1579 K (T 1). Then by lowering the temperature, a hollowing appears centred around 0.9 nm- ‘, followed by a noticeable rise for Kk 1 nm-’ until solidification. The present results are compared with those obtained by SAXS using the synchrotron radiation. In Fig. 2, the previous results are reported in a large K-range (0.20 nm-l I K < 14.00 nm-‘> for 12 different tempera-
P. Andonov
et aL/JoumaE
of Non-Crystalline
Solids 205-207
(19961 163-167
I cob relative
tures. The comparison is possible in the domain 0.20 mn-’ 5 K 2 1.28 run-‘. A good agreement is observed in the undercooled domain and up to T = 1579 K. In the low K-range, the slope of the curves varies as previously observed from the SAXS results and a shoulder is present at 1579 K. The differences appear at high temperature since the intensity is always increasing as K goes to zero and the lower-K side of the interference peak is not as marked as in the SANS curve except when T I 1554 K. To determine the size of the scattering particles, we have used the supplementary program ‘RGUIM’ (ILL), to attempt to fit a straight line to any corrected spectrum [14,15]. Five different functions of intensity vs. K 2 may. be fitted within a certain K-range which may be adjusted to optimize the region of K for which the model may be appropriate. We have tested the five options and retained the Guinier approximation to derive the radius of gyration, R,, of the not dense macroparticles because it gives the best fit in a large K-range. The interference effect relative
165
units
1513 1518 1523 1528 1538 1553 1573 1598 1823 1626 1648 1673 1
)
.
4
8
I
12
K (nm-')
Fig. 2. Coherent intensity, Icoh expressed in relative units, as a function of the wave vector K and plotted for twelve temperatures expressed in K. Results previously obtained from SAXS cl I].
Fig. 1. Corrected intensity, I expressed in relative units, as a function of the wave vector K and plotted for four temperatures expressed in K. Resulrs obtained from SANS.
to the small particles is assumed independent of the large particle distribution [ 111. The evolution of the linear fits is reported in Fig. 3. Large deviations are observed between the values obtained by heating (T t > and cooling (T J,> in the undercooled domain and at T = 1579 K. The R, values have been evaluated from the slopes of these fits, a, such as: R, = 6 and reported in the Table 1. For instance g 1554 K (T), from the Guinier approximation, R, = 3.31 i 0.30 nm which leads to: 0.40 I KR, I 1.81. Assuming spherical aggregates, the diameter of the macrocluters reaches a value Q, E 2igR, = 8.50 + 0.80 nm. The variations of R, with temperature is shown in Fig. 4 along with the SAXS results. At the same temperature, a difference is observed between the values obtained during heating and cooling, the size of particles being larger at the cooling. The evolution of R, determined from SANS is lower than the one from SAXS. The higher value reached at 1504 K is inferior to the one measured by SAXS
166
P. Andoaov
et al. / Journal
of Non-Crystalline
Solids 205-207
(1996)
163-167
Table 1 Values of the radius of gyration expressed in nm
Ln (1)
T (K)
R, (Tf)
1504
1529
3.09rto.40
1554
2.8OkOo.30 2.40F0.30 2.10+0.30 1.80*0.30 1.50+0.30
1579 1604 1629 16.54
R,(TJ) 6.20*0.40 3.85 rtO.40 3.3orto.30 2.80-10.30 2.35*0.30
1.95 & 0.30
at 1513 K. A sharp modification is not observed at 15.54 K and the radius of gyration progressively decreases up to 1654 K. The sudden rearrangement of microclusters assumed previously is not really confirmed. This difference can be explained by the large sample volume involved in the neutron diffraction and giving a high thermal inertia. 4. Conclusion
\, 15041
1 0
2
K *(nn?)
4
6
x10
-1
Fig. 3. Linear tits obtained from the Guinier approximation. Results obtained from SANS.
8
6 1 .
t\ 4
. .
0 a
Our present results has confirmed the presence in molten LiNbO, of macroclusters near solidification. The values of the radius of gyration of the scattering particles are similar to those obtained by SAKS. The differences are due to a progressive rearrangement of the clusters. The sudden aggregation of particles, revealed from previous SAKS results, does not show in the neutron diffraction results. The re-arrangement begins at a temperature larger than previously reported and continues as a progressive phenomenon. The sudden increase of viscosity observed near 1553 K cannot be explained by a rapid aggregation of particles or by a strong modification of the structure of the melt. Acknowledgements
0
2
The authors want to thank Dr R. Cubitt of ILL for discussions and experimental assistance.
~~ / 1500
I
1 1600
T (K)
Fig. 4. Radius of gyration, R,, expressed in nm, as a function of temperature from SANS: 0 at the heating; l at the cooling; previous results from SAXS [ll]: H. The lines are drawn as guides for the eye.
References El] S.A. Bol’shkov, V.P. Klyuev, N.N. Lyapushkin, A.P. Lyubimow and S.A. Fedulov, Inorg. Mater. (USSR) 5 (1969) 824.
P. Andonov
et al./JournaE
of Non-Crystalline
[2] K. Shigematsu, Y. Anztii, S. Morita, M. Yamada and H. Yokoyama, Jpn. J. Appl. Phys. 26 (12) (1987) 1988. [3] A.R. Ubbelohde, The Molten State of Matter (Wiley, Chichester, 1978). [4] N. Niizeki, T. Yamada and H. Toyoda, Jpn. J. Appl. Phys. 6 (2-3) (1967) 151 and 318. [51 Y.S. Luh, R.S. Feigelson, M.M. Fejer and R.J. Byer, J. Cry% Growth, 78 (1986) 135; 85 (1987) 264. [61 K. SugiyamB, K. Nomura, Y. Waseda, P. Andonov, S. Kimura and K. Shigematsu, 2. Naturforsch, 45a (1990) 1325. 171 P. Audonov, P. Chieux and S. Kimura, J. Phys.: Condens. Matter 5, (1993) 1. [8] S.C. Abrahams, J.M. Reddy and J.L. Bernstein, J. Phys. Chem. Solids 27 (1966) 997; S.C. Abrahams, WC. Hamilton and J.M. Reddy, J. Phys. Chem. Solids 27 (1966) 1013; SC.
Solids 21X-207
(1996)
163-167
167
Abrahams, H.J. Levinstein and J.M. Reddy, J. Phys. Chem. Solids 27 (1966) 1019. 191 H. Boysen and F. Altofer, Acta Crystallogr. B.50 (1994) 405. [lOI P. Andonov, S. Kimura and T. Sawada, J. Non-Cry& Solids 156-158 (1993) 783. [ll] A.A. Ballmann, J. Am. Ceram. Sot. 48 (1965) 112. [12] L. Koester and W.B. Yelon, Neutron Diffraction Newsletters (The Neutron Diffraction Commission of the International Union of Crystallography, 1983). [I31 V.F. Sears, AECL, Report 8490 (1984). 1141 A. Guinier and G. Foumet, Small Angle Scattering of X-Rays, (Wiley, New York, 1955). El51 0. Glatter and 0. Kratky, Small-Angle X-Ray Scattering (Academic Press, London, 1982).