Clustering in the LiNbO3 melt

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Journal of Non-Crystalline Solids 156-158 (1993) 783-786 North-Holland

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Clustering in the LiNbO 3 melt P. A n d o n o v a, S. Kimura b and T. Sawada b CNRS - LMMM, I place Aristide Briand, 92195 Meudon c~dex, France h NIRIM, 1-1 Namiki, Tsukuba-shi, Ibaraki 305, Japan

Structural analysis of the LiNbO 3 melt has been carried out by means of the small angle scattering of X-rays using the synchrotron radiation and the high temperature diffraction using X-ray and neutron radiations. The usual methods were used to analyze the intensity data. A local order was defined. The radius of gyration, the interparticle distance, and form and size of the scattering particles were obtained. The clustering phenomenon is described using the diffraction results and the data of viscosity and density previously published. Formation and evolution of the particles are followed from 1673 to 1513 K including the undercooling domain. Microclusters are correctly represented by chains of two, three or four NbO 6 octahedra and blocks constituted by two layers of four corner-shared niobium oxide moles tightened by a lithium atom. Macroclusters, formed by regrouping of microclusters, appear from 1550 K onwards; this fact would explain the very rapid increase of the viscosity. The physical parameters determined in this work from different methods are in good agreement with each other and also with the results obtained from the viscosity and density measurement.

1. Introduction Large sub-grain free LiNbO 3 crystals are used in non-linear optics, piezoelectricity, acoustics or modulaion of light [1,2]. Density, viscosity and surface tension of the melt have been investigated as a function of temperature [3,5] in order to seek the best conditions for crystal synthesis using the Czochralski method. The authors explain the anomalous viscosity change by the presence of clusters in the liquid. The complete transformation of the spectrum obtained by high temperature Raman spectroscopy [6] was explained by a Nb coordination change. Tetrahedra {NbO4} would be present in the liquid and rearranged before solidification to obtain octahedral {NbO6}. The structure, resolved in the ferroelectric phase [7], belongs to the ilmenite family and the thermal expansion of atomic bonds is similar to that of niobates belonging to the perovskite family [8]. In order to confirm these previous assumptions, Correspondence to: Dr P. Andonov, Centre National de la Recherche Scientifique, Laboratoire de Magnetisme et Mat6riaux Magnetiques, 1 place Aristide Briand, 92195 Meudon c~dex, France. Tel: +33-1 45 07 50 76. Telefax: + 33-1 45 07 58 22.

the local order was investigated in the same temperature domain using the high temperature diffraction method by X-rays [9] and by neutrons [10] and the presence of spatial heterogeneities was controlled by the small angle X-ray scattering

(SAXS). 2. Samples and experiments The samples were prepared in the NIRIM, Tsukuba. The starting material was sintered LiNbO 3 obtained from Li2CO 3 and Nb20 5 powders of high purity (99.99%) and natural isotopic abundance mixed in the congruent composition [11]. High temperature X-ray experiments were carried out on the theta-theta diffractometer in the Senken at the University of Sendal The wave vector, Q, varied from 0.6 to 13.5 ~,~ and three temperatures were studied: T = 1548, 1573 and 1598 K. High temperature neutron experiments were carried out on the D4B spectrometer at the o 1 ILL-Grenoble. Q varied from 0.27 to 16.26 A - ; sixteen temperatures were studied from 1593 to 1460 K. The SAXS was carried out on the BL-10C of the KEK in Tsukuba; an original furnace

0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved

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P. Andonov et aL / Clustering in the LiNbO 3 melt

maintains thin liquid samples in vertical position without container. Q varied from 0.020 to 1.400 .~-1 and T from 1673 to 1513 K. 1513

3. Results

1518

3.1. High temperature diffraction

1523

Usual analysis is applied to the data obtained from methods of high temperature diffraction

1528 1538

• 1¢

ROFx.ray s- RDF

1553

neutronsl

1573

relative units

1598

el liquid

1623 1626 1648 1673

~-1) .4

-10

.8

1.2

Fig. 2. Coherent intensities, Icoh = f(Q), plotted at different temperatures expressed in K.

1

LI-O

t

04)

1

t

Nb-Nb

0-0

b) c r y s t a l

... Li-Li __ Li-Nb ... Li-O - - Nb-Nb

v

,

.... Nb-O

j

I t I i t

- - O-O Li NbOa

1

2

3

4

6

II

Fig. 1. RDF(r)x.ray s -RDF(r)ncutrons: (a) experimental curve; (b) curve calculated with the crystalline distances.

to determine the radial distribution function, RDF(r). Figures l(a) and (b) show the experimental and theoretical differences ((RDF(r)x_rays)-(RDF(r)neutrons)). A comparison of curves gives the mean interatomic, rip distances of some pairs without doubt. The theoretical curve is obtained finding the sum of the crystalline distances calculated from the coordinates published for the ferroelectric phase at 300 K and adjusted by an expansion coefficient. Each rij distance is represented by a Gaussian having a half peak width equal to the resolution due to Fourier transformation and Im~x weighted by AW~j, the mean difference of the contributions W/j of radiations and by the number of pairs in which i-j are separated by a distance, %. From the distances r~Nb_O, r~Li_O, r~o_ o a n d r~Nb_Nb obtained in this way the first two peaks of RDF(r) are fitted and the coordination numbers nij were deduced. At 1573 K, n o _ o is nearly equal to the crystalline value, 7.60 instead of 8.00 . The value

P. Andonov et al. / Clustering in the LiNbO 3 melt

hiLl_ o = 2.76 can be explained only if numerous Li atoms are linked with three O atoms. These values increase near the solidification. The first values rlNb_ o = 1.933 + 0.003 A, nlr,rb_o = 6.00 ___ 0.05, and nLLi_O confirm the octahedrally coordinated niobium units tightened by Li atoms in the molten LiNbO 3.

11 (A) Ic to

785

t T

o sample • sample

I II

o

3.2. Small angle scattering The coherent intensity obtained after usual corrections is plotted versus Q in fig. 2. The curves show three well defined regions: (1) a sharp increase of the intensity as Q goes to zero; (2) a maximum in I(Q) at somewhat larger values of Q; and (3) a slowly decreasing profile typical of single-particle scattering. After normalization in electron units and Fourier transformation of I(Q), the results were analyzed in the real space. In this way, the function p(r) of the interparticle distance distribution was obtained.

4. Discussion

The zone (1) was explained in terms of scattering by macroclusters, the radius of gyration, Rg, of which was computed using the Guinier law [12]. The zone (2) was interpreted in terms of interference of micro clusters of which the mean radius of gyration, R0m, was obtained using the Hosemann method [13]; their mean distance, d, and their mean size were determined according to Ehrenfest [14]. Using several methods of Porod [15], the correlation length, lc, was calculated; the tail of the curves I(Q) was used to determine the total surface area of clusters and, from the limiting values of intensity, some parameters of the particles were controlled such as volume, crosssection and thickness. Fig. 3 shows the obtained results versus T. A sharp change of Rg is observed specially in the undercooling domain but R0m varies slowly with T. Two types of particle exist in the melt near the solidification. For T > 1630 K, a linear increase of d confirms a weak change in the size and the number of microclusters at high temperature. The relative change of

8

~

"',,

di 7

~

i Rom

It

,

,

1500

1550

1600

, T(,°K) 1650

1~00

Fig. 3. Cluster characteristics obtained experimentally.

2.4 × 1 0 - 4 / K corresponds to a third of the relative density change given by Shigematsu [4]. The local order makes the presence of {NbO 4} unit in the liquid impossible. So we assume that the clusters are constituted by {NbO 6} units (crystalline unit) such as octahedra chains, ReO 3 blocks, aggregate built by two layers of four corner-shared NbO 6 moles linked by a Li atom (see fig. 4), etc. The parameters of these models, assumed to be like elementary revolution shapes, were calculated and compared with the SAXS results. Only some of them can be retained to be contained in the experimental limit sizes. The trend of peaks of p(r) and f(r)=p(r)/r confirms the chosen cluster forms. NbO 6 moles are probably present in the melt at high T and dimers could appear from T - 1700 K onwards. Then chains of at most three or four octahedra and blocks of 2 × 2 × 1 octahedra could

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P. Andonov et al. / Clustering in the LiNbO 3 melt

5. Conclusions

N,b9

ZX (a)

(bl

(c)

Fig. 4. Microcluster models: (a) chains of 3 N b O 6 octahedra; (b) ReO 3 blocks 3 x 2 x 1; and (c) regular aggregates 2 x 2 x 2.

appear below 1670 K. If T decreases, linear blocks of 3 × 2 × 1 octahedra and 2 × 2 × 2 regular or deformed aggregates [5] could subsist in a large T-range; nmc (the microcluster number) is sufficient to give an interference effect in all the domain of T. Near 1553 K, large dispersions are observed in the R0m and l c values; this fact was explained by the appearance of macroclusters described as a sudden association of microclusters. According to the limiting values of I(Q), lamellar particles cannot describe the macroclusters which are assumed of spherical form. The anomalous increase of viscosity below 1553 K was described as a 'clustering' by Ubbeholde [16] who connects the viscosity, rh, with the volume fraction, qbi, of the clusters at a temperature, Ti. The relationship ~ / = f ( T ) is a logarithmic expression; a mean cluster volume can be obtained by extrapolation of the slope of the curve In(~7) =f(1/T). Shigematsu et al. [4] have determined the ~i values at different temperatures and a cluster volume equal to 7.4 × 104 ~3 at 1553 K. The SAXS results explain the evolution of the viscosity. When T decreases then nmc increases, which causes the bump observed around T---1600 K in the curve "0 = f ( T ) . A clustering of the microclusters begins when nmc = 10.5 X 1018/cm 3. The number of macroclusters, NMc, and their volume were determined from Rg and ~7. NMc remains always inferior to nmc and the macrocluster volume increases rapidly when the melting point is approached while nm¢ and the microcluster volume do not change really. The volume fraction of clusters is equal to 18% at Tm=1526 K and 24% at 1513 K just before the solidification in the undercooling domain.

Formation and evolution of clusters have been studied in the molten LiNbO 3. Our results are in good agreement with the viscosity data. Diffraction experiments coupled with the conventional viscosity measurements make a very effective tool to study the clustering in the pre-solidification domain. Help by Professor Y. Waseda of Tohoku University, which made this collaboration work possible, is greatly appreciated. The authors would like to thank P. Chieux (ILL) and K. Sugiyama (SENKEN) for their help in the neutron and X-ray experiments. P.A. acknowledges the financial support by JISTEC. This work was partially supported by the Special Coordination Fund for Promoting Science and Technology of STA Japan.

References [1] A.A. Ballman, J. Am. Ceram. Soc. 48 (1965) 112. [2] S.A. Fedulov, Z.I. Shapiro and P.B. Ladyzhinskii, Sov. Phys. Crystallogr. 10 (1965) 218 and 268. [3] S.A. Bol'shvov, V.P. Klyuev, N.N. Lyapushkin, A.P. Lyubimov and S.A. Fedulov, Inorg. Mater. (USSR) 5 (1969) 824. [4] K. Shigematsu, Y. Anzai, S. Morita, M. Yamada and H. Yokoyama, Jpn. J. Appl. Phys. 26 (1987) 1988. [5] J.A.S. Ikeda, V.J. Fratello and C.D. Brandle, J. Cryst. Growth 92 (1988) 271. [6] Yu.K. Voronko, A.B. Kudryavtsev, V.V. Osiko and A.A. Sobol, in: Growth of Crystals, Vol. 16, ed. Kh.S. Bagdasarov and E.L. Lube (Consultants Bureau, New York, 1988) p. 199. [7] S.C. Abrahams, H.J. Levinstein and J.M. Reddy, J. Phys. Chem. Solids 27 (1966) 1019. [8] H.D. Megaw, Acta Crystallogr. A24 (1968) 583. [9] K. Sugiyama, K. Nomura, Y. Waseda, P. Andonov, S. Kimura and K. Shigematsu, Z. Naturforsch. 45a (1990) 1325. [10] P. Andonov, P. Chieux and S. Kimura, to be published in J. Phys.: Condens. Matter. [11] P. Lerner, C. Legras and J.P. Dumas, J. Cryst. Growth 3&4 (1968) 231. [12] A. Guinier and G. Fournet, Small-Angle Scattering of X-rays (Wiley, New York, 1955). [13] R. Hosemann, Z. Phys. 128 (1950) 465. [14] P. Ehrenfest, Proc. Amsterdam Acad. 17 (195) 1132 and 1184. [15] G. Porod, Kolloid. Z. 124 (1949) 83; 125 (1952) 51 and 109. [16] A.R. Ubbeholde, The Molten State of Matter (Wiley, New York, 1977).