The origin of electrooptical sensitivity of glassy materials: crystal motifs in glasses

Journal of Non-Crystalline Solids 318 (2003) 268–283 www.elsevier.com/locate/jnoncrysol

The origin of electrooptical sensitivity of glassy materials: crystal motifs in glasses A.A. Lipovskii a

a,*

, D.K. Tagantsev b, B.V. Tatarintsev b, A.A. Vetrov

b

St.-Petersburg State Technical University, Polytechnicheskaja 29, St.-Petersburg, 195251 Russia b S. I. Vavilov State Optical Institute, Babushkina 36-1, St.-Petersburg, 193171 Russia Received 10 December 2001; received in revised form 16 July 2002

Abstract The results of studying electrooptical Kerr sensitivity in heavy metal silicate and phosphate glasses and glassceramics are presented. A niobium–lithium-silicate glass demonstrating a record Kerr coefficient (266
1016 m/V2 ) has been formed. Formation of the transparent glass-ceramics containing electrooptical sodium niobate microcrystals has been studied, and glass-ceramics demonstrating Kerr coefficients higher than 6000
1016 m/V2 have been elaborated. On the base of the effective medium approximation, it is shown that the Kerr coefficient of these glass-ceramics depends on the volume fraction of sodium niobate microcrystals, vc as a linear function of vc ð1  vc Þ2 A conception of the origin of electrooptical sensitivity of glasses is proposed. This conception is based on the hypothesis that in glasses there exist regions with exactly crystalline ordering within 2–3 coordination spheres, with these regions having no phase boundaries. These regions are named the crystal motifs (CM). Due to the highly effective mechanism of nuclear polarizability of the electrooptical crystals, the motifs with the symmetry of such crystals are responsible for high permittivity and Kerr sensitivity of the glasses, and they play a role of pre-nuclei while electrooptical glass-ceramics are forming under glass heat treatment. It has been found that synthesized barium-titanate-silicate and niobium–lithium-phosphate glasses demonstrate extremely low Kerr coefficients, and they do not form transparent glass-ceramics with any electrooptical precipitates. This contradicts literature data and is explained by the difference in the conditions of glass synthesis, which are supposed to be responsible for the formation of proper CMs. Ó 2002 Elsevier Science B.V. All rights reserved.

1. Introduction There is no need to refer to the fact that most crystals of ABO3 group, like LiNbO3 , BaTiO3 , and others, are widely used as electrooptical/non-linear optical media. Such crystals are produced in great amounts by industry nowadays. At the same time,

*

Corresponding author. Fax: +7-812 552 7954. E-mail address: [email protected] (A.A. Lipovskii).

however advanced the technology of those crystals is, many publications devoted to the study of electrooptical/non-linear optical properties of glasses [1–7], poled glasses [8–18] and glassceramics [1,6,7,13,19–27] constantly appear up today. Of all the reasons of those studies, the first one is a hope to replace crystalline materials with glassy ones because they are cheaper in production, more flexible in properties and allow substrates of unlimited size and shape. Generally, electrooptical and non-linear optical phenomena are the same

0022-3093/03/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0022-3093(02)01891-4

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by nature [28], and this allows evaluating potential suitability of materials for electrooptics on the base of knowledge on their non-linearity and vice versa. As to the electrooptical properties of glassy materials, their essential deficiency is insufficiently high response to the applied electric field. It is due to the glassy media being isotropic and demonstrating only Kerr electrooptical phenomenon, that is, a change of their refractive index under applied electric field, with this change linearly depending on the square of the field intensity. Kerr sensitivity of optical materials is characterized by Kerr coefficient, B, which can be experimentally determined by measuring the electric-field-induced birefringence, Dn ¼ ðnk  n? Þ, which for isotropic optical media does not depend on the sample orientation and is equal to Dn ¼ kBE2 ;

ð1Þ

where k is the light wavelength, and E is the dc electric field applied across the direction of the light beam propagation. For the best glasses the value of their Kerr coefficients achieves about 1014 m/V2 [1–3,7,27]. Glass crystallization can increase the Kerr coefficient of the medium up to about 1012 m/V2 (it is a result of the present work), but it is not yet such a value that could meet application requirements. 1 Most works on the optical non-linearity or electrooptical sensitivity of glassy materials are dedicated to the studies of the second-order nonlinearity in poled 2 or crystallized glasses [8,10,13, 14,17,21,23–26,29–32]. From those studies it follows that the non-linearity of the glassy materials though produced comes from the optical anisotropy resulting from either the oriented crystal growth (in crystallized glasses) [13,23,33] or the existence of structure singularities, which are supposed to present themselves the regions with 1

For a material to be used in any optoelectronic chips, Kerr coefficient must exceed 1010 m/V2 . 2 Another way to increase electrooptical response of glassy materials is to pole them under heating that results in the poled glasses and glass-ceramics demonstrating linear electrooptic effect (Pockels phenomenon) and typical for non-centersymmetric media second harmonic generation [8,11–17,29,30]. Electrooptical sensitivity of those poled materials allows their usage in optical modulators [18].

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crystal-like symmetry (structural motifs [25,32,34], clustering of NbO6 octahedra [35], groupings [22,36,37], ferrons [38], and pseudocrystalline microheterogeneities related to the ferroelectric crystal lattice [39]). However, among all these works, there are practically no studies on electrooptical Kerr sensitivity of as-prepared glasses (glasses, which do not undergo any treatments), in which only Kerr non-linearity can be revealed, as well as studies of changes in electrooptical Kerr coefficient in transferring glasses to glass-ceramics during heat treatment. An exclusion is several works [1,3–5,7,20,27], which do not allow understanding this topic completely. In spite of a small value of glass and glass-ceramics Kerr coefficients, a study of Kerr non-linearity of these materials has rather basic meaning because it could help us to understand the nature of the vitreous state. In our opinion, the data on Kerr non-linearity of glasses containing the components, which are the same as of known electrooptical crystals, like LiNbO3 , keep information about their microinhomogeneous structure, which appears to inherit the structure of these crystals and to condition high electrooptical sensitivity of the glasses. In this work, a study of Kerr sensitivity of several glass-forming systems, including well studied before alkali-niobium-silicate systems, as well as barium-titanate-silicate, and alkali-niobate-phosphate systems, was carried out by direct measurements of the Kerr coefficients of the glasses and glass-ceramics. The most comprehensive study was performed in the sodium–niobium-silicate systems, including systematic heat treatments of the glasses resulting in glass-ceramics with the highest Kerr sensitivity. In parallel, the crystallization process was studied by differential thermal analysis (DTA), X-ray diffraction (XRD), small-angle X-ray scattering (SAXS), densitometry, permittivity measurements, and others. This study showed that Kerr optical non-linearity of the investigated glassy systems was not directly dependent on the content of high-polarizable heavy ions, like Ba, Ti, and Nb, as was in the majority of the existing works on the topic involved. At the end of the article, reasons of Kerr optical non-linearity is discussed on the base of the obtained data and with allowance for other interpretations collected by the authors.

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In the discussion we try to find evidences that the fluctuation microinhomogeneities peculiar to as-prepared glasses are the regions with exact crystalline symmetry, and that just those regions are the pre-nuclei of the crystallites, which form in glass-ceramics in heat treatment. Having the composition and the symmetry of some known electrooptical crystal, these regions appear to condition high Kerr sensitivities of both the glasses and the glass-ceramics formed from these glasses.

2. Experimental 2.1. Glasses The compositions of the glasses studied in this work are presented in Table 1 where all of them

are sorted by series. Glass compositions were chosen in such a way that they would contain components (oxides of alkaline metals, niobium, etc.) necessary to compose a certain electrooptical crystal, namely: BaTiO3 , LiNbO3 , NaNbO3 , KNbO3 . Because crystals containing different heavy metals can demonstrate either positive or negative electrooptical Kerr sensitivity, which due to the compensation effect could result in zero electrooptical response [3], we did not use compositions consisting of the mixtures of heavy metals, for example, Ti and Pb. All the glasses are synthesized using only chemically pure and highpurity grade reagents. The composition of the glasses of S-series can be formalized as xNb2 O5  (66x)SiO2  19Na2 O  11K2 O  2B2 O3  2BaO with x ranging from 5 to 37. The glasses were produced by melting an appro-

Table 1 Compositions (in mol%) and Kerr coefficient of studied glasses Glass

SiO2

S-series

S35 S34 S33 S32 S31 S1 S2 S3 S4 S5

61 56 51 46 41 37 35 33 31 29

5 10 15 20 25 29 31 33 35 37

LiS-series

LiS35 LiS34 LiS33 LiS32 LiS31 LiS1 LiS2 LiS3 LiS4

61 56 51 46 41 37 35 33 31

5 10 15 20 25 29 31 33 35

BT-series

BT7 BT9 BT11 BT13

30.2 25.2 20.1 14.7

P-series

P1 P2 P3 P4

P2 O5

Al2 O3

Nb2 O5

15.6 12.6 10.0 7.3 66.7 56.3 50 42.9

TiO2

Na2 O

Li2 O

19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19.3 24.8 30.0 35.4

5.6 12.5 16.7 21.4

BaO

B2 O3

B
1016 (m/V2 )

2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2

<0.5 1.5 9 26 71 105 117 149 169 198

2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2

<0.5 4 39 61 110 156 195 215 266

K2 O

CdO

11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

La2 O3

35.0 37.4 40.0 42.7

<0.5 <0.5 <0.5 <0.5 5.6 12.5 16.7 21.4

22.2 18.7 16.7 14.3

<0.5 <0.5 1 1.5

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priate 180-g batch in platinum crucible at 1450 °C for 2 h with stirring. The melts were poured onto a pre-heated brass plate, and each resultant glass was annealed for 2 h at the temperature corresponding to the glass viscosity equal to 1012 0:5 Pa s. For this series the anneal temperatures varied from 495 °C (for glass S35) to 585 °C (for glass S4). The study of Kerr optical non-linearity of similar glasses with x ranging from 29 to 35 and glass-ceramics produced from them is also described in Ref. [1]. Within the frames of the present work the lithium analogies of S glasses were synthesized as well, and they differ from the glasses of S-series only in containing lithium instead of sodium. These lithium analogies belong to the glasses of LiS-series. The compositions of the glasses of BT7, BT9, BT11, and BT13 belonging to BT-series can be formalized as xBaTiO3  (100  x)(BaO þ Al2 O3 þ 2SiO2 ) with x equal to 45, 55, 65 and 75. The glasses were produced by melting an appropriate 180-g batch in cristobalite crucible at 1500 °C for 2 h with stirring. The melts were also poured onto a massive brass plate, and resultant glasses were annealed for 2 h at temperature range 600–650 °C. The study of glass-ceramics formation in similar glass-forming system was already carried out by other researches and reported in Ref. [40]. The glasses of P-series are lithium–lanthanumniobate-phosphate ones. The glasses were synthesized in a platinum crucible at about 1400 °C for 2 h with stirring and in the amount of 180 g.

2.2. Differential thermal analysis and X-ray diffraction The glasses and glass-ceramics were studied by DTA using derivatograph Q-1500 D (MOM, Hungary, System: F. Paulik, J. Paulik, and L. Erdey). Heating rate was equal to 5 K/min within the temperature range 20–950 °C. The weight of the probes was equal to 0:7 0:05 g. As-prepared glasses, probes after DTA, and glass-ceramics formed at different temperatures were studied by XRD powder analysis. This analysis was performed using X-ray diffractometer DRON-2 with Cu ðKa Þ X-ray source and Ni filter.

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XRD analysis did not show any crystalline phases in all the as-prepared glasses. It should be noted that to be convinced that as-prepared glasses were free of any crystalline phase, they were selectively (generally, the glasses with high percentage of heavy metal ions) studied by SAXS [41]. This test confirmed the results of XRD analysis; only density fluctuations typical for  [42]) were remulticomponent glasses (10–20 A vealed indeed.

2.3. Heat treatments Heat treatments of the glasses were to produce glass-ceramic materials of high Kerr sensitivity due to precipitating grains of known electrooptical crystals. Heat treatment temperatures were chosen on the base of the DTA data (with heating interrupted at different temperatures) of as-prepared glasses and the XRD analysis of the probes obtained after DTA experiments. As an example, both DTA curves of several glasses of S series, with heating up to 950 °C, and XRD patterns of the probes resulting from DTA experiments are presented in Fig. 1. One can see that DTA curves of the glasses with a high content of niobium (glasses S4-S31) have two exothermal maxima, which move toward one another while niobium content (or Nb2 O5 /SiO2 ratio) decreases, and then they form one broad maximum or plateau (glasses S33 and S34). The XRD data show (Fig. 1(b)) that the glasses with low niobium content (S33-S35) crystallize with the only phase precipitating, namely: quasicubic sodium niobate, and in the glasses with high niobium content (S5-S31) more than one phase precipitate with sodium niobate being dominant. Those other phases were not identified. No potassium niobate crystals, in particular, in ferroelectric form were revealed in the glasses of S series in DTA heating in spite of 11 mol% of K2 O contained in the glasses. The XRD analysis of the probes of the S-series glasses resulting from the DTA heating interrupted at temperatures corresponding to the ends of the high-temperature shoulder of the first (low temperature) DTA peak (arrows in Fig. 1(a)) showed that this peak was related to the precipitation of

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2.4. Electrical (permittivity) and Kerr measurements

Fig. 1. DTA curves of several glasses of S-series (a), and XRD patterns of the probes of the same glasses obtained after such DTA experiments for glasses S5, S3, S1, S33, S34 and after DTA heating interrupted at temperatures corresponding to the end of the first DTA peak of each glass (b); in (a) these temperatures are marked by vertical arrows and they are 680 °C for glass S4, 720 °C for glass S2, and 755 °C for glass S31.

quasicubic sodium niobate only (Fig. 1(b)). This allowed us to choose heat treatment temperatures to form monophase glass-ceramics (glass-ceramics with only one crystalline phase) and to study kinetics of sodium niobate formation as well as, in parallel, kinetics of other accompanying properties, such as Kerr coefficient, permittivity, density, and others. The most comprehensive study of glass-ceramics formation was performed for S2 and S4 glasses. Heat treatments of these glasses were performed in air in the furnace with electrical heater on isothermal conditions at temperatures 655, 630, and 610 °C. Duration of the treatments was varied from 1 to 328 h.

The permittivity of the as-prepared and heattreated glasses was measured by the standard technique of capacity measurements at 10 kHz using copper electrodes deposited on the two opposite faces of glass or glass-ceramic samples. The samples were 20–30 mm long (and wide) and 2–3 mm thick. The same samples with polished endfaces were used in Kerr measurements. The measurements of electrooptical Kerr coefficients of the glasses and glass-ceramics were performed with a specially designed apparatus at He–Ne laser wavelength k ¼ 0:63 lm [43]. The radiation going through the sample was modulated by ac voltage (5 kHz, up to 3.0 kV) applied to the electrodes of the sample. The samples were placed between two crossed polarizers, and according to the quadratic character of electrooptical phenomenon the response of this modulator was measured at the second harmonic of the input frequency, i.e., at 10 kHz. To improve the accuracy of the measurement a highly sensitive calibrated electrooptical modulator was placed between the input polarizer and the sample under study. The comparison of the voltages providing the same output signals for the modulator and for the sample gave the information about Kerr coefficient B, and this allowed us to avoid measuring sample transparency, calibrating the circuit of the photoreceiver, etc. This scheme gave rather high sensitivity due to the measurements taking place at the frequency range free from typical noises, which resulted in high signal selectivity. Besides, this allowed compensating electrically the initial birefringence, which appeared in all the experimental samples of laboratory as-prepared glasses. The accuracy of the measurements was proved by the experiment with liquid cell filled with commercial nitrobenzene. The measured value of Kerr coefficient coincided with literary data to within 0.5%. The accuracy was about 5% for B P 1014 m/V2 , and it was 50% at lower limit of sensitivity (B  0:5
1016 m/V2 ), that was 5
105 of B value of nitrobenzene and 104 of B value of our best glass-ceramics. Lower accuracy of the measurements for the synthesized samples compared

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with one of nitrobenzene was due to the possible non-uniformity and, sometimes, light scattering. 2.5. Viscosity and density measurements Glass viscosity was measured by the beambending method, with the bending base being 26.7 mm. The typical sample size was 30
6
2 mm3 . The measurements were performed on isothermal conditions, with the accuracy of temperature control being to within 0.5°. Glass and glassceramics density was determined at 20 °C using the Archimed principle with toluene as a reference liquid. The accuracy was equal to 0.001 g/cm3 . 2.6. Glass structure stabilization Glass structure stabilization was performed by annealing the glass samples at temperatures where their viscosity was equal to about 1014 0:1 Pa s, and Kerr coefficients of these stabilized glasses were measured and compared with ones measured for the as-prepared glasses, for which anneal temperatures corresponded to the viscosity equal to about 1012 0:5 Pa s. These heat treatments endured till glass viscosity ceased to change, which took about 10 days. Unchangeable in time viscosity indicated that structure relaxation was completed and glass structure was stabilized, that is, the structure had achieved metastable thermodynamic equilibrium at this temperature. The structure of the glasses though stabilized had the structural (fictive) temperature equal to the anneal temperature. Then, these glasses were quenched from the temperature corresponding to viscosity 1012 Pa s, and Kerr coefficients were measured again. The glass viscosity was monitored by the beam-bending technique using a separate sample, and the glass sample under annealing was placed adjacent to that separate sample just in the measurement cell of the viscometer furnace. 3. Results 3.1. As-prepared glasses In Table 1 the results of Kerr measurements of the glasses are presented. Comparing different

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glass-forming systems, one can see that there is not any correlation between heavy metal content and Kerr coefficient. The glasses of S-, LiS-, BT-, and P-series containing the same amount of corresponding heavy metal oxide (about 20 mol%) demonstrate Kerr coefficients equal to 26
1016 , 61
1016 , <0:5
1016 , and 1:5
1016 m/V2 , correspondingly. 3 However, within each separate glass-forming system Kerr coefficient either increases with a rise in heavy metal content (for glasses of S- and LiS-series, see Fig. 2) or remains constant to within the measurement accuracy (glasses of BT- and P-series, see Table 1). Kerr coefficient of all the studied glasses correlates with their permittivity; for S- and LiS-glasses this correlation is presented in Fig. 3, where parabolic fitting is used as the most appropriate one. DTA data combined with XRD ones showed that, the same way as was in the glasses of S-series (see Fig. 1), in the glasses of LiS-series the dominate phase precipitating was electrooptical, namely: microcrystals of lithium niobate. In Fig. 4 the examples of this study are presented. Asterisks over DTA peaks in Fig. 4(a) designate the temperatures of lithium niobate precipitation that was determined from XRD patterns (Fig. 4(b)) of the LiSglasses heated in DTA cell up to the temperatures marked by arrows in Fig. 4(a). The results of the DTA and XRD experiments with BT and P glasses are not presented here because X-ray analysis of the probes of these glasses obtained after DTA heating up to 950 °C did not show any ferroelectric phases. Two glasses, namely; S1 and S5, underwent the structural stabilization at temperatures where their viscosity was equal to about 1014 0:1 Pa s. These temperatures were 559 and 557 °C for S1 and S5 glasses, correspondingly. The progress in the viscosity change during heat treatment of S1 glass is shown in Fig. 5. After the stabilization at these temperatures, Kerr coefficients of the glasses increased by about 45% for S1 glass (from 105
1016 to 150
1016 m/V2 ) and by 30% for 3 For glasses S2, LiS2, and BT11, each containing about 30 mol% of corresponding heavy metal oxides, this tendency looks more evident. Kerr coefficients of these glasses are equal to 117
1016 , 195
1016 , and <0:5
1016 m/V2 .

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Fig. 2. Dependences of Kerr coefficient of S- and LiS-glasses on Nb2 O5 concentration. In inset: the same dependences, where Kerr coefficient is presented as a function of c=ð1  cÞ2 with c being Nb2 O5 molar concentration.

Fig. 4. DTA curves of several glasses of LiS-series (a), and XRD patterns of the probes of the same glasses obtained after DTA heating up to the temperatures marked in DTA curves by arrows (b). The dominant phase precipitating is ferroelectric crystals of lithium-niobate (black points).

Fig. 3. Kerr coefficient of S- and LiS-glasses via their permittivity (dash line corresponds to parabolic fitting).

S5 glass (from 195
1016 to 250
1016 m/V2 ). Then, S1 glass was quenched from 580 °C that corresponded to viscosity 1012 Pa s, and, after quenching, Kerr coefficient of the glass proved to be 120
1016 m/V2 . 3.2. Glass-ceramics As mentioned above, the most comprehensive study of glass-ceramics formation has been performed on the base of the glasses of S-series. The glass-ceramics made of the glasses of S-series with

Fig. 5. The progress in the viscosity change of S1 glass during the glass structure stabilization. Glass structure stabilization at the viscosity equal to 1013:9 Pa s increased Kerr coefficient of the glass by 45%. The same experiment with S5 glass led to 30% increase in its Kerr coefficient.

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niobium oxide content exceeding 29 mol% demonstrated a high transparency and a monotonic increase with subsequent saturation in Kerr coefficient, permittivity, and density with a rise in the duration of heat treatment (Fig. 6). Scattered heat treatments of LiS glasses gave very similar results for the glasses contained less than 29 mol% niobium oxide. LiS glasses with niobium oxide content exceeding 29 mol% formed two-phase glass-ceramics, with lithium niobate being one of them. At the same time the glass-ceramics made of the glasses of BT- and P-series did not demonstrate such a behavior; all attempts to form transparent glass-ceramics failed, no increase in Kerr sensitivity was found, and no electrooptical phases precipitated. The rise in Kerr coefficient in S and LiS glass-ceramics was accompanied with precipitating

electrooptical microcrystals; quasicubic sodium niobate in S glass-ceramics and lithium niobate in LiS glass-ceramics. Estimation of volume fractions of crystalline phase in the formed glass-ceramics, vc , was performed by processing XRD pattern [44], but due to the low intensities of the diffraction peaks, this estimation showed low accuracy. To determine vc more precisely sets of the glasses with relative weight deficits of NaNbO3 in the batch (or deficit of Na2 O þ Nb2 O5 ) corresponding to different amounts of these components incorporated by sodium niobate microcrystals were synthesized and the densities of these glasses were measured (Fig. 7). Two such sets were synthesized, namely: the glasses with sodium niobate deficit in S2 and in S4 glass. We designated the glasses of those sets as MðS2Þ and MðS4Þ glasses (or simply M-glasses) and considered that their densities, qm ðwÞ, were equal to the densities of the glassy parts of the glassceramics, qg ðwÞ, produced from the corresponding S glasses, that is, for each glass-ceramics, produced from S2 or S4 glass, qm ðwÞ ¼ qg ðwÞ. Here, w is the above-mentioned weight deficit of sodium niobate, which, in accordance with our assumption, is the same as the weight fraction of sodium niobate in the correspondent glass-ceramics. It is easy to derive equations to calculate the magnitudes of vc using the dependence of the M-glass densities on w, that is, qm ðwÞ; these equations are

Fig. 6. Permittivity (a), Kerr coefficient (b), and density (c) of S2 glass-ceramics formed at 610 °C via processing time.

Fig. 7. Permittivity and density of MðS4Þ glasses via molar deficit (by batch) of NaNbO3 .

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w¼

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ðqm ðwÞ  qÞqc ; ðqm ðwÞ  qc Þq

vc ¼ w

q ; qc

ð2Þ

where qm ðwÞ is the polynomial approximation of the M-glass density (see Fig. 7, dash line), q is the measured glass-ceramics density, qc is the density of crystalline sodium niobate. This calculation gave an overestimate of value w (and vc ) that ensued from the maximal possible weight fractions of sodium niobate crystals, which could form in ac-

Fig. 9. Kerr coefficient of the glass-ceramics produced from S4 (1,2) and S2 (3,4) glasses at 630 °C (1,3) and 610 °C (2,4) for different time of heat treatment via volume fraction of crystalline sodium niobate. Solid line corresponds to the effective medium approximation. In inset: Glass-ceramics density via volume fraction of sodium-niobate microcrystals.

Fig. 8. DTA of S2 glass-ceramics formed at 610 °C for different times (a). The decrease in the height of the peak in the vicinity of 680 °C, which corresponds to the precipitation of sodium niobate microcrystals, and its disappearance evidence that the glassy part of glass-ceramics is exhausted with niobium ions (see inset in (a), where H is the relative height of the peak and t is the time of glass-ceramics formation). At the same time, the properties of the glass-ceramics are similarly related to the height of this DTA peak (b), and this corroborates that it is sodium niobate precipitates, which actually are the only cause responsible for all the properties of these glass-ceramics. The motion of the DTA peak at 680 °C towards low temperatures is explained by decreasing the viscosity of the glassy part of glassceramics resulting from decreasing niobium content in the course of crystal phase formation.

cordance with the glass batches. It was likely to be due to the glassy part of glass-ceramics, which includes Ôglass–crystalÕ interfaces, having density lower as compared with the density of the glasses of the same composition, which are synthesized by conventional melting. The absolute values of vc were corrected by normalizing the saturated values of vc to the ones, which could be maximally achieved in accordance with the weight compositions of the initial glasses. The saturation times could be identified not only through the time dependences of Kerr coefficient, permittivity, and density, but also by DTA of the glass-ceramics formed for different times (Fig. 8(a)). This DTA monitored just saturation in the crystallization process rather than in the glassceramics properties. Note, that the height of DTA peak in the region of 680 °C, which is responsible for sodium niobate precipitation, decreases with the heat treatment time the same way as an increase in Kerr coefficient, permittivity, and density (Fig. 8(b)). This actually proves that the changes in all these characteristics are exclusively caused by the sodium niobate precipitates, and the contribution of the glassy part to the non-linear properties of the glass-ceramics is negligible. The correctness of our estimations of values vc was also

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confirmed by the relation between these values and the glass-ceramics densities (Fig. 9, inset).

4. Discussion Let us use the effective medium approximation [45] (in its simplest formulation) to understand the increase of Kerr coefficient with heat treatment time, quantitatively. In accordance with the approximation the average (microscopic) electric field in a continuous heterogeneous medium consisting of two dielectrics, which in case of glassceramics are glassy matrix and microcrystals embedded into this matrix, can be written as X E¼ v i Ei ¼ v c Ec þ v g Eg ; ð3Þ i

where vc and vg are the volume fractions of the crystalline and glassy parts of the medium and Ec and Eg are the electric fields in those parts. The difference of the electric fields in the crystalline and glassy parts is caused by the difference of their permittivities. The electric field E is the average field applied to the material, which in case of a plate sample is equal to U =D, where U is the applied voltage and D is the sample thickness. Allowing for the relation vg þ vc ¼ 1 and the electrical induction (eE) of a medium being constant, that is, ec Ec ¼ eg Eg where ec and eg are the permittivities of the microcrystals and the glassy part of the glass-ceramics, from Eq. (3) it follows that   U ec ¼ vc þ ð1  vc Þ Ec : ð4Þ D eg In Kerr measurements, the monitored signal is proportional to the product BE2 L, where B is the Kerr coefficient of glass-ceramics, E is the electric field applied to the sample (equal to U =D), and L is the sample length or the path, which light passes through the sample. If the contribution to the Kerr sensitivity of the glass-ceramics related to the glassy part of the material is neglected, and this sensitivity is due to the sodium niobate microcrystals only, it is possible to represent the signal through Kerr coefficient of the crystalline phase, that is, Kerr coefficient of polycrystalline sodium

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niobate (Bc ), the electric field applied to the crystals Ec and the effective length of the crystalline phase of the glass-ceramics sample, which, in case of a parallelepiped sample, is obviously equal to 2 vc L. Thus, we can write that BE2 L ¼ Bc ðEc Þ vc L, and then, using Eq. (4), express B through the volume fraction of the crystalline phase vc as 2 follows: B ¼ Bc vc ½a þ vc ð1  aÞ . If a  1 we have " # Bc vc B¼ 2 ; ð5Þ a ð1  vc Þ2 where a ¼ ec =eg . In case eg is known this dependence allows estimating value Bc or Kerr coefficient of dense sodium niobate ceramics, which is the same. In general, value eg is not a constant and it depends on vc because when microcrystals form, the glassy part of the material is exhausted with niobium, which is responsible for the glass permittivity (see Table 1). Variations of eg were determined from the measurements of permittivities of the M-glasses (see Fig. 7 for MðS4Þ glasses), and they proved to be described by the linear dependence eg ¼ e  18vc for the glass-ceramics formed from both S2 glass and S4 one. Here e is the permittivity of the glasses S2 or S4, which is equal to 29 2 for both glasses. Taking for sodium niobate ec ¼ 80, we got Bc  600 000
1016 m/V2 , which was consistent with the data reported in Ref. [20]. The assumption a  1 gave an error, which could not exceed 30% of the determined magnitude of Bc From Fig. 9, one can see that the same curve suits all the glass-ceramics formed, and this corroborates the validity of this deduction, for this curve should be the same indeed, if the crystalline phase precipitating in heat treatments is the same for different glasses of about the same permittivity. Thus, Kerr sensitivity of electrooptical glassceramics is uniquely related to the volume fraction of electrooptical crystalline phase only, which, generally speaking, is consisted of ordered regions with crystalline symmetry. This result can be used to interpret the origin of Kerr sensitivity of the initial glasses as follows. From the data on Kerr measurements it follows that electrooptical sensitivity of the S and LiS glasses increases with niobium content (Fig. 2),

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and at the same time such a correlation is absent for the glasses of BT- and P-series (Table 1), where independently on the glass composition Kerr coefficient remained unchangeably small. Kerr coefficients of the glasses of these series differ by one–two orders in spite of these glasses containing about equivalent and high amounts of ions with high polarizability. It should be noted here that our data on Kerr sensitivity of the glasses of BTseries and glass-ceramics produced from these glasses contradict literature data. The authors of Ref. [3] reported a high Kerr sensitivity of Ticontained glasses, and the author of Ref. [40] reported BaTiO3 microcrystals precipitating in heat treatment of the glasses of the same compositions as the glasses of BT-series. In accordance with our data, these glasses demonstrate extremely low Kerr sensitivity and can be crystallized only at temperatures higher 850 °C, with the crystalline phase not being barium titanate. 4 The same results were obtained for the glasses of P-series, that is, low Kerr sensitivity and incapacity of forming electrooptical sodium niobate crystals under heat treatment. Such behavior cannot be understood if Kerr sensitivity is caused by the electronic polarizability only, which in case of the glasses under study can mainly result from the high content of such ions as Ti4þ , Ba2þ , and Nb5þ . As was mentioned above, the glasses of S-, LiS-, BT-, and P-series containing the same amounts (20 mol%) of the corresponding heavy metal oxide demonstrate Kerr coefficients equal to 26
1016 , 61
1016 , <0:5
1016 (measurement accuracy), and 1:5
1016 m/V2 , correspondingly. However, within each separate glass-forming system Kerr coefficient either increases with a rise in heavy metal content (glasses of S- and LiS-series) or remains constant to within the measurement accuracy (glasses of BT- and P-series). To explain this behavior of different glass-forming systems, we have used the crystallite hypothesis [46] and accumulated modern knowledge about glass structure [42,47–49] and gener-

4

We discuss this contradiction below. In our experiments several crystalline phases precipitated in heat treatments at about 900 °C for 2 h, and those phases could not be identified.

alized several conceptions of the origin of the electrooptical sensitivity of glasses, which are independently developed by the authors of this article [6,7,27] and other authors (conceptions of structural motifs [32,34], clustering of NbO6 octahedra [35], groupings [22,36,37], ferrons [38], and microheterogeneities with pseudocrystalline symmetry [39]). Our conception is based on the following statements and inferences: 1. High polarizability of a medium gives rise to its high optical non-linearity and, therefore, electrooptical sensitivity, which in glassy materials, due to their isotropy, can reveal itself only in Kerr electrooptical effect. In particular, the relation between polarizability and non-linearity comes from Fig. 3, where one can see that Kerr coefficient increases with a rise in glass permittivity, which, in its turn, directly related to the medium polarizability. 2. We suggest the fluctuation density inhomogeneities peculiar to the glasses to be the ordered regions with exactly crystalline symmetry, the regions having no phase boundaries. Specific size of these ordered regions corresponds to the characteristic scale of the density fluctua), which, in the case under contions (10–20 A sideration, averages 2–3 coordination spheres in accordance with the size of the elementary  [50]. unit cell of sodium niobate, that is, 3.9 A However, the results obtained in [34] allow thinking that glasses can inherit not only the short-range order from the crystal, but also the intermediate-range one, which means that specific size of the ordered regions can achieve . The existence of such ordered regions 50–100 A ensues from the data on light [42], X-ray [51], and small-angle X-ray [52] scattering, on Raman and absorption spectroscopy [35], on disturbance of Newton character of the glass viscosity at extra low loading, at which the glass behaves like Bingham rheological body [53] as well as on the analysis of thermodynamic functions of glasses at 0 K [47], and others [54–57]. We will call these regions the crystal motifs (CM). 3. The electronic contribution to the polarizability is exclusively related to the deformation of

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electron shells of the atoms comprising glassy matrix, and, in the materials involved, its value is very small, because the glasses containing the same amounts of high-polarizable heavy metals, for example Nb, demonstrated Kerr coefficients differing by one–two orders. However, if the structure (composition and symmetry) of the motifs corresponds to the structure of any electrooptical (ferroelectric) crystal, the main contribution to the polarization is caused by the effective mechanism of nuclear (ionic) polarizability of the medium through the deformation of the ionic lattice of CMs. This, in its turn, ensures a high value of Kerr coefficient of the glass. Theoretical calculations of the local electric field (Lorenz field) in ferroelectric crystals with allowance for their local structure (the exact positions of atoms in the unit cell) argues in favour of the conception of CMs. These calculations predict the high polarizability of ferroelectric crystals being revealed only due to their specific symmetry (perovskite structure), for which the local field at the central atom of the unit cell can exceed the one calculated in accordance with the macroscopic approximation of isotropic medium by one order and more. According to Slater [58], this is the essential reason of the ferroelectricity of perovskite-like crystals. For example, he showed that the Lorenz field at titanium atoms in ferroelectric barium titanate lattice was equal to ð30 þ 4p=3ÞP rather than 4pP =3 (where P is the polarization) coming from the macroscopic approximation of isotropic medium, and that weak divergences from the crystal symmetry led to a dramatic decrease in the local field. 5 Taking into account that the macroscopic electric field within some inclusions of permittivity notably exceeding one of their surrounding is essentially weakened (see Eq. (4)), this result looks like one having a great importance for the problems discussed here because, in our conception, the corresponding CMs (in case of as-quenched glasses) and nano- or microcrystals (in case of glass5

Within the frames of the ferrons conception [38], which looks like most prospective, the local field is considered equal to 4pP =3.

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ceramics) should be regarded just as such inclusions. Therefore, an appreciable electrooptical response of the medium can be revealed only if those inclusions possess crystalline symmetry of known electrooptical crystals, where this suppressed and weakened macroscopic field could cause rather high medium polarization due to the high local field. 6 The importance of the local factor to explain the origin of the third order non-linear susceptibility of the niobiumcontained glasses is also emphasized in Ref. [35]. 4. It is known that, due to the clamping, crystalline inclusions in an elastic medium can stay in non-equilibrium, relatively to a free large crystal, state, and their phase transition temperatures (including Curie temperature) may be shifted by more than 100 K [59]. It means that both in glass formation by quenching and in cooling crystallized glasses, contrary to expectations, the crystalline inclusions (CMs or microcrystals) can be in the phase different from the equilibrium one, and, therefore, this can appreciably change electrooptical sensitivity of the material. For instance, to explain a high Kerr sensitivity of sodium niobate glass-ceramics at room temperature the authors of Ref. [1] concluded that NaNbO3 microcrystals were in ferroelectric phase in spite of free NaNbO3 crystals being non-ferroelectric. Additionally, it was found that, BaTiO3 crystallites precipitating in glass 15BaO–15TiO2 –70TeO2 was in paraelectric cubic phase rather than ferroelectric tetragonal one [60] and that in the formation of glass-ceramics from PbO–BaO–TiO2 –B2 O3 glass, the lattice strain between glass matrix and precipitated cubic PbTiO3 crystallites restricted the phase transition of lead titanate crystal into ferroelectric phase [61]. Thus, the clamping should be allowed for in choosing glass compositions and conditions of heat treatments to form a highly sensitive electrooptical glassy material. 6 In [3] it was assumed that in glass-ceramic materials the local and external fields were equal. If it were correct, why would different uniform glasses with the same content of highly polarizable ions show different Kerr sensitivity?

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5. An increase in the total volume fraction of the ordered regions with a proper crystalline symmetry (like one of ferroelectric crystals) leads to an increase in the electrooptical sensitivity of the material. In this work and other ones, for example [1,7,20,24,39,62], this was demonstrated by the experiments on glass crystallization, and, in our opinion, was due to the effective nuclear mechanism of polarization dominating all the other ones. However, in accordance with the modern view on the structure of vitreous state, there must be another way to increase Kerr sensitivity of glasses. Following this view [47,48,63], the lower structural (fictive) temperature of the glass, the higher extent of the glass structure ordering. This ensues from the fact that configuration contributions to the free energy and the entropy of any glass must be vanished in approaching glass structure towards the one corresponding to the Kauzmann temperature [49]. It means that the stabilization of glass structure by long anneals at temperatures below the glass transition temperature should increase the total volume fraction of CMs resulting in an increase in Kerr coefficient of the glass. It is that increase in Kerr coefficient that is revealed after low-temperature stabilization of S1 and S5 glasses (Fig. 5). That it is not crystallization is confirmed by the reversibility of Kerr coefficients of the glasses in stabilization-quenching circles. Unfortunately, this way to increase Kerr sensitivity is restricted by the fact that the state, when the glass structure has the fictive temperature equal to the Kauzmann one and thermodynamically is equivalent to the crystal structure (in our terms, this means volume fraction of CMs being equal to 1), is not allowed by the thermodynamics [49] and by the phase transition theory, which forbids smooth phase transitions between structures with different space dimensions (fractal in glasses and discrete in crystals) [64]. 6. CMs should be considered as crystal pre-nuclei because the structure of CMs is already ordered, so that the balance between surface and bulk free energies to form stable nuclei is achieved faster and seems to be shifted towards lower temperatures, and, therefore, the forma-

tion of stable nuclei is facilitated. From this assumption it follows that the composition of the expected crystalline phase, which precipitates in heat treatment, should be the same as general composition of the CMs. If this composition coincides with one of electrooptical crystals and, therefore, Kerr coefficient of the glass is rather high, one can expect a high sensitive electrooptical glass-ceramics to form, with the microcrystals being of the same composition, which CMs had. Our experiments corroborate this inference. Indeed, the glasses of S- and LiS-series demonstrated highest Kerr sensitivity, and after crystallization they formed high effective electrooptical glass-ceramics with electrooptical phases of NaNbO3 and LiNbO3 . However, no electrooptical phases were found after crystallization of the glasses of BT- and P-series, which initially demonstrated extremely low Kerr coefficients as well. In accordance with the proposed conception, this indicates that in BT- and Pglasses the CMs did not have a proper symmetry. The structure of CMs appearing to form in quenching and melting processes strongly depends on the thermal-temporal conditions of glass synthesis. The latter appears to explain the difference in the result obtained in the present research and the ones reported in [3,40], where electrooptical titanate glasses and glassceramics with barium titanate microcrystals as precipitates were formed. The explanation proposed in [3], where authors did not receive high Kerr coefficients in mixed Ti–Pb glasses due to the compensation effect (positive and negative sign of Kerr coefficient for titanate and lead structural entities), is valid as well. In terms of the proposed conception, the lack of Kerr sensitivity in those glasses seemed to be caused by the fact that two types of crystalline motifs, which actually gave opposite contributions to the electrooptical sensitivity of the material, were formed indeed. In brief, in our opinion, glasses contain specific structural entities, which possess the exactly crystalline symmetry within 2–3 (and maybe more) coordination spheres, with these entities having no phase boundaries. We call these entities the CMs,

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and consider them to be responsible for Kerr sensitivity of glasses, if their compositions and structure coincide with one of known electrooptical crystals. This approach can give us only qualitative explanation of the origin of Kerr sensitivity of glasses because today there is not clear perception of the structure and role of the interfaces between CMs and surrounding amorphous glassy matrix. However, looking at Figs. 2 and 9, one can see that the characters of the dependences of Kerr coefficient on the niobium content in the glass and on the volume fraction of sodium niobate crystalline phase in the glass-ceramics are similar, that is, both curves demonstrate acceleration in the rise of Kerr coefficient. Being presented as a function 2 of variable A ¼ c=ð100  cÞ where c is the molar percentage of niobium oxide in the glasses, Kerr coefficient of S and LiS glasses demonstrates a linear increase with A (see the inset in Fig. 2). 7 These linear dependences suggest applying the effective medium approximation to describe electrooptical behavior of the glasses, the same way as was in case of the glass-ceramics. The only thing which one has to do is to replace vc in Eq. (5) with c. This qualitative consideration implies that value c for these glasses plays the same role as value vc for glass-ceramics, and that the volume fraction of sodium niobate CMs is a linear function of the niobium oxide content. All this allows the glasses to be treated as a continuous heterogeneous medium (mixture) consisting of two dielectrics, one of them being the amorphous network and another one being CMs. Thus, the CMs conception looks like the external reality.

7 That these linear dependences start only from 11 mol% Nb2 O5 is explained by the presence of potassium oxide in the glasses. In accordance with our data on Raman spectroscopy of these glasses [65], potassium ions are the first ones, which occupy niobium ions forming no electrooptical CMs, so that the S and LiS glasses containing up to 11 mol% Nb2 O5 do not contain an essential quantity of electrooptical sodium niobate CMs. Moreover, the non-electrooptical nature (composition and symmetry) of CMs containing both potassium and niobium is corroborated by the data on XRD and the data on glassceramics formation, where neither ferroelectric KNbO3 nor other electrooptical potassium contained phases were found.

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5. Conclusion Sets of niobate sodium and lithium-silicate, barium-titanate-silicate and niobium–lithiumphosphate glasses were synthesized, and composition dependences of density, permittivity and Kerr coefficient of all these glasses were studied. The niobium alkaline glasses demonstrated highest permittivity and Kerr sensitivity. The lithium silicate glasses demonstrated record Kerr coefficients (266
1016 m/V2 ). It was shown that Kerr coefficient of niobium alkaline silicate glasses increased with a rise in niobium content, and that the barium-titanate-silicate and niobium–lithiumphosphate glasses did not possess any appreciable Kerr sensitivity. Kinetics of the formation of transparent monophase glass-ceramics with electrooptical sodium-niobate microcrystals were studied. Kerr coefficient higher than 6000
1016 m/V2 was obtained for sodium-niobate glass-ceramics produced from the glass containing 35 mol% of Nb2 O5 . Using the effective medium approximation, it was shown that Kerr coefficient of these glass-ceramics depended on the volume fraction of sodium-niobate microcrystals precipitated as a linear function of vc ð1  vc Þ2 where vc was the volume fraction. The relation between glassceramics Kerr coefficient and permittivity appears to be parabolic. A conception of the origin of electrooptical sensitivity of glasses is proposed. The conception is based on the hypothesis that in glasses there are regions with exactly crystalline ordering within 2–3 coordination spheres, with these regions having no phase boundaries. These regions were called the CMs. The motifs with the symmetry of some electrooptical crystal caused high Kerr sensitivity of the glasses, and they play a role of pre-nuclei while electrooptical glass-ceramics are forming by glass heat treatment. In accordance with the proposed conception, low-temperature stabilization of the glasses should lead to the development of the CMs resulting in an increase in Kerr coefficient of the glass, and this has been corroborated experimentally, when after glass stabilization Kerr coefficient of sodium niobate glasses increased by 30–45%.

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Synthesized barium-titanate-silicate and niobium–lithium-phosphate glasses did not form transparent glass-ceramics with any electrooptical precipitates. This contradicts literature data and is explained by the difference in the conditions of glass synthesis, which are supposed to be responsible for the formation of proper CMs. Acknowledgements The research has been supported by International Science and Technology Center (Grant #979). The authors appreciate Dr V. Golubkov for SAXS characterization of the glasses. References [1] G.O. Karapetyan, Yu.G. Korolyov, L.V. Maksimov, S.V. Nemilov, Fiz. Khim. Stekla (Rus) 12 (5) (1986) 598. [2] N.F. Borrelli, W.H. Dumbaugh, Electro- and magnetooptic effects in heavy metal oxide glasses, Proc. SPIE, vol. 843, 1987, p. 6. [3] N.F. Borrelli, B.G. Aitken, M.A. Newhous, D.W. Hall, J. Appl. Phys. 70 (5) (1991) 2774. [4] T. Hashimoto, H. Uchida, I. Takagi, H. Nasu, K. Kamiya, J. Non-Cryst. Solids 253 (1–3) (1999) 30. [5] S. Smolorz, I. Kang, F. Wise, B.G. Aitken, N.F. Borrelli, J. Non-Cryst. Solids 256&257 (1–3) (1999) 310. [6] A.A. Zhilin, G.O. Karapetyan, A.A. Lipovskii, L.V. Maksimov, G.T. Petrovsky, D.K. Tagantsev, Glass Phys. Chem. 26 (3) (2000) 242. [7] G.O. Karapetyan, A.A. Lipovskii, V.V. Loboda, L.V. Maksimov, D.V. Svistunov, D.K. Tagantsev, B.V. Tatarintsev, A.A. Vetrov, Electrooptic glasses and glass-ceramics for elements controlling laser radiation, Proc. SPIE, vol. 4353, 2001, p. 23. [8] S. Horinouchi, H. Imai, G.J. Zhang, K. Mito, K. Sasaki, Appl. Phys. Lett. 68 (25) (1996) 3552. [9] G. Bonfrate, V. Pruneri, P.G. Kazansky, P. Tapster, J.G. Rarity, Appl. Phys. Lett. 75 (16) (1999) 2356. [10] S. Montant, A. Le Calvez, E. Freysz, A. Ducasse, V. Nazabal, E. Fargin, G. Le Flem, Appl. Phys. Lett. 74 (18) (1999) 2623. [11] V. Pruneri, G. Bonfrate, P.G. Kazansky, H. Takebe, K. Morinaga, M. Kohno, K. Kuwasaki, T. Takeuchi, Appl. Phys. Lett. 74 (18) (1999) 2578. [12] A. Narazaki, K. Tanaka, K. Hirao, N. Soga, J. Appl. Phys. 85 (4) (1999) 2046. [13] A. Narazaki, K. Tanaka, K. Hirao, Appl. Phys. Lett. 75 (21) (1999) 3399. [14] V. Nazabal, E. Fargin, C. Labrugere, G. Le Flem, J. NonCryst. Solids 270 (1–3) (2000) 223.

[15] L.C. Triques, M.B. Cordeiro, V. Balestrieri, B. Lesche, W. Margulis, C.S. Carvalho, Appl. Phys. Lett. 76 (18) (2000) 2496. [16] Z. Xu, L. Liu, Y. Fei, P. Yang, Z. Hou, L. Xu, W. Wang, Appl. Phys. Lett. 77 (1) (2000) 70. [17] J. Arentoft, K. Pedersen, S.I. Bozhevolnyi, M. Kristensen, P. Yu, C.B. Nielsen, Appl. Phys. Lett. 76 (1) (2000) 25. [18] X.-C. Long, S.R.J. Brueck, IEEE Photon. Technol. Lett. 9 (6) (1997) 767. [19] N.F. Borrelli, A. Herczog, R.D. Maurer, Appl. Phys. Lett. 7 (5) (1965) 117. [20] N.F. Borrelli, M.M. Layton, J. Non-Cryst. Solids 6 (1971) 197. [21] Y. Ding, Y. Miura, A. Osaka, J. Mater. Res. 11 (2) (1996) 495. [22] E.B. de Araujo, J.A.C. de Paiva, J.A. Freitas Jr., A.S.B. Sombra, J. Phys. Chem. Solids 59 (5) (1998) 689. [23] Y. Ding, Y. Miura, S. Nakaoka, T. Nanba, J. Non-Cryst. Solids 259 (1–3) (1999) 132. [24] P. Pernice, A. Aronne, V.N. Sigaev, P.D. Sarkisov, V.I. Molev, S.Yu. Stefanovich, J. Am. Ceram. Soc. 82 (12) (1999) 3447. [25] P. Pernice, A. Aronne, V.N. Sigaev, M.V. Kupriyanova, J. Non-Cryst. Solids 275 (3) (2000) 216. [26] Y. Takahashi, Y. Benino, V. Dimitrov, T. Komatsu, J. Non-Cryst. Solids 260 (1–2) (1999) 155. [27] A.A. Lipovskii, D.K. Tagantsev, B.V. Tatarintsev, A.A.Vetrov, Formation of sodium niobate glass-ceramics, Electroceramics VII-2000, International Conference on Electroceramics and their Applications, Portoroz, Slovenia, 3–6 September 2000, Abstract Book, 2000, p. 96. [28] A. Yariv, P. Yeh, Optical Waves in Crystals, Wiley, New York, 1984. [29] T.G. Alley, S.R.J. Brueck, M. Wiedenbeck, J. Appl. Phys. 86 (12) (1999) 6634. [30] V. Pruneri, F. Samoggia, G. Bonfrate, P.G. Kazansky, G.M. Yang, Appl. Phys. Lett. 74 (17) (1999) 2423. [31] M.V. Shankar, B.R. Varma, J. Non-Cryst. Solids 243 (2–3) (1999) 192. [32] V.N. Sigaev, Glass Phys. Chem. 24 (4) (1998) 295. [33] K. Gerth, C. Russel, R. Keding, P. Schleevoigt, H. Dunken, Phys. Chem. Glasses 40 (3) (1999) 135. [34] E.N. Smelyanskaya, V.N. Sigaev, A.A. Volkov, V.V. Voitsekhovskii, G.A. Komandin, V.D. Shigorin, A.A. Kaminskii, Glass Phys. Chem. 23 (4) (1997) 303. [35] T. Cardinal, E. Fargin, G. Le Flem, S. Leboiteux, J. NonCryst. Solids 222 (1997) 228. [36] E.B. de Araujo, J.A.C. de Paiva, A.S.B. Sombra, J. Phys.: Condens. Matter 7 (1995) 9723. [37] J.S. de Andrade, A.G. Pinheiro, I.F. Vasconcelos, M.A.B. de Araujo, M.A. Valente, A.S.B. Sombra, J. Phys. Chem. Solids 61 (6) (2000) 899. [38] Y. Xu, J.D. Mackenzie, J. Non-Cryst. Solids 246 (1999) 136. [39] M.M. Layton, A. Herczog, J. Am. Ceram. Soc. 50 (7) (1967) 369. [40] A. Herczog, J. Am. Ceram. Soc. 47 (3) (1964) 107.

A.A. Lipovskii et al. / Journal of Non-Crystalline Solids 318 (2003) 268–283 [41] E.A. Porai-Koshits, N.S. Andreyev, J. Soc. Glass Technol. 43 (213) (1959) 235T. [42] G.O. Karapetyan, L.V. Maksimov, O.V. Yanush, Glass Phys. Chem. 18 (6) (1992) 412. [43] A.A. Vetrov, A.A. Lipovskii, D.K. Tagantsev, Instrum. Exp. Techn. 45 (4) (2002) 550. [44] A.A. Zhilin, T.I. Chuvaeva, M.P. Shepilov, Glass Phys. Chem. 26 (1) (2001) 20. [45] L.D. Landau, E.M. Lifshitz, P. Pitaevski, Electrodynamic of Continuous Media, Pergamon, Oxford, 1984. [46] A.A. Lebedev, Writings GOI (Trudy GOI) 2 (1921) 1. [47] S.V. Nemilov, Fiz. Khim. Stekla (Rus) 8 (1) (1982) 11. [48] S.V. Nemilov, Thermodynamic and Kinetic Aspects of the Vitreous State, CRC, Boca Raton, FL, 1995. [49] S.V. Nemilov, Glass Phys. Chem. 25 (5) (1999) 377. [50] S.P. SolovÕev, Yu.N. Venevtsev, G.S. Zhdanov, Kristallografija (Rus) 6 (2) (1961) 217. [51] E. Rat, M. Foret, E. Courtens, R. Vacher, M. Arai, Phys. Rev. Lett. 83 (7) (1999) 1355. [52] V.V. Golubkov, E.A. Porai-Koshits, Fiz. Khim. Stekla (Rus) 7 (3) (1981) 278. [53] G.M. Berteniev, A.S. Eremeeva, Vysokomolec. Soedin. (Rus) 3 (1961) 740.

283

[54] V.N. Sigaev, E.N. Smelyanskaya, V.G. Plotnichenko, V.V. Koltashev, A.A. Volkov, P. Pernice, J. Non-Cryst. Solids 248 (2–3) (1999) 141. [55] S.P. Zhdanov, B.T. Kolomiest, V.M. Lyubin, V.K. Malinovsky, Phys. Stat. Sol. (a) 59 (1979) 621. [56] S.P. Zhdanov, V.K. Malinovsky, PisÕma ZhTF (Rus) 3 (1977) 943. [57] D.K. Tagantsev, Fiz. Khim. Stekla (Rus) 13 (6) (1987) 839. [58] J.C. Slater, Phys. Rev. 78 (6) (1950) 748. [59] N.A. Pertsev, K.H. Salje, Phys. Rev. B 61 (2) (2000) 902. [60] K. Tanaka, H. Kuroda, A. Narazaki, K. Hirao, N. Soga, J. Mater. Sci. Lett. 17 (13) (1998) 1063. [61] S.M. Lynch, J.E. Shelby, J. Am. Ceram. Soc. 67 (1984) 424. [62] J.D. Jain, IETE Tech. Rev. 2 (7) (1985) 238. [63] S.V. Nemilov, Fiz. Khim. Stekla (Rus) 7 (5) (1981) 575. [64] L.D. Landau, E.M. Lifshitz, Statistical Physics, Nauka (Rus), Moscow, 1964. [65] A.A. Lipovskii, D.K. Tagantsev, A.A. Vetrov, O.V. Yanush, Raman spectroscopy and the origin of electrooptical Kerr phenomenon in niobium alkali-silicate glasses, Opt. Mater. (2002) in press.