The origin of electrooptical sensitivity of glassymaterials: crystal motifs in glasses

A.A. Lipovskii a,*, D.K. Tagantsev b, B.V. Tatarintsev b, A.A. Vetrov b

a St.-Petersburg State Technical University, Polytechnicheskaja 29, St.-Petersburg, 195251 Russiab 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 glass-

ceramics are presented. A niobium–lithium-silicate glass demonstrating a record Kerr coefficient (266� 10�16 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� 10�16 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 vcð1� vcÞ�2 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 bound-

aries. 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.

� 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,

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 glass-

ceramics [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

*Corresponding author. Fax: +7-812 552 7954.

E-mail address: lipovskii@phtf.stu.neva.ru (A.A. Lipovskii).

0022-3093/03/$ - see front matter � 2002 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0022-3093(02)01891-4

Journal of Non-Crystalline Solids 318 (2003) 268–283

www.elsevier.com/locate/jnoncrysol

by nature [28], and this allows evaluating potentialsuitability 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 demon-

strating only Kerr electrooptical phenomenon,

that is, a change of their refractive index underapplied electric field, with this change linearly de-

pending 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 ori-

entation and is equal to

Dn ¼ kBE2; ð1Þwhere 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

10�14 m/V2 [1–3,7,27]. Glass crystallization can

increase the Kerr coefficient of the medium up to

about 10�12 m/V2 (it is a result of the present

work), but it is not yet such a value that couldmeet 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 non-

linearity in poled 2 or crystallized glasses [8,10,13,

14,17,21,23–26,29–32]. From those studies it fol-

lows that the non-linearity of the glassy materials

though produced comes from the optical aniso-tropy resulting from either the oriented crystal

growth (in crystallized glasses) [13,23,33] or the

existence of structure singularities, which are sup-

posed to present themselves the regions with

crystal-like symmetry (structural motifs [25,32,34],clustering of NbO6 octahedra [35], groupings

[22,36,37], ferrons [38], and pseudocrystalline mi-

croheterogeneities related to the ferroelectric

crystal lattice [39]). However, among all these

works, there are practically no studies on electro-

optical Kerr sensitivity of as-prepared glasses

(glasses, which do not undergo any treatments), in

which only Kerr non-linearity can be revealed, aswell 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 under-

standing 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 tounderstand 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 microinhomoge-

neous 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 sev-

eral glass-forming systems, including well studied

before alkali-niobium-silicate systems, as well as

barium-titanate-silicate, and alkali-niobate-phos-

phate systems, was carried out by direct measure-

ments 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 scat-

tering (SAXS), densitometry, permittivity mea-

surements, and others. This study showed that

Kerr optical non-linearity of the investigated glassysystems 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.

1 For a material to be used in any optoelectronic chips, Kerr

coefficient must exceed 10�10 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-centersym-

metric media second harmonic generation [8,11–17,29,30].

Electrooptical sensitivity of those poled materials allows their

usage in optical modulators [18].

A.A. Lipovskii et al. / Journal of Non-Crystalline Solids 318 (2003) 268–283 269

In the discussion we try to find evidences thatthe 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 con-

dition high Kerr sensitivities of both the glasses andthe glass-ceramics formed from these glasses.

2. Experimental

2.1. Glasses

The compositions of the glasses studied in thiswork are presented in Table 1 where all of them

are sorted by series. Glass compositions werechosen 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 zeroelectrooptical response [3], we did not use com-

positions consisting of the mixtures of heavy

metals, for example, Ti and Pb. All the glasses are

synthesized using only chemically pure and high-

purity grade reagents.

The composition of the glasses of S-series can

be formalized as xNb2O5 � (66�x)SiO2 � 19Na2O �11K2O � 2B2O3 � 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 P2O5 Al2O3 Nb2O5 TiO2 BaO Na2O Li2O K2O CdO La2O3 B2O3 B� 1016

(m/V2)

S-series S35 61 5 19 11 2 2 <0.5

S34 56 10 19 11 2 2 1.5

S33 51 15 19 11 2 2 9

S32 46 20 19 11 2 2 26

S31 41 25 19 11 2 2 71

S1 37 29 19 11 2 2 105

S2 35 31 19 11 2 2 117

S3 33 33 19 11 2 2 149

S4 31 35 19 11 2 2 169

S5 29 37 19 11 2 2 198

LiS-series LiS35 61 5 19 11 2 2 <0.5

LiS34 56 10 19 11 2 2 4

LiS33 51 15 19 11 2 2 39

LiS32 46 20 19 11 2 2 61

LiS31 41 25 19 11 2 2 110

LiS1 37 29 19 11 2 2 156

LiS2 35 31 19 11 2 2 195

LiS3 33 33 19 11 2 2 215

LiS4 31 35 19 11 2 2 266

BT-series BT7 30.2 15.6 19.3 35.0 <0.5

BT9 25.2 12.6 24.8 37.4 <0.5

BT11 20.1 10.0 30.0 40.0 <0.5

BT13 14.7 7.3 35.4 42.7 <0.5

P-series P1 66.7 5.6 5.6 22.2 <0.5

P2 56.3 12.5 12.5 18.7 <0.5

P3 50 16.7 16.7 16.7 1

P4 42.9 21.4 21.4 14.3 1.5

270 A.A. Lipovskii et al. / Journal of Non-Crystalline Solids 318 (2003) 268–283

priate 180-g batch in platinum crucible at 1450 �Cfor 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 corre-

sponding 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 andglass-ceramics produced from them is also de-

scribed in Ref. [1]. Within the frames of the present

work the lithium analogies of S glasses were syn-

thesized as well, and they differ from the glasses of

S-series only in containing lithium instead of so-

dium. 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 þAl2O3 þ2SiO2) 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–lanthanum-

niobate-phosphate ones. The glasses were synthe-

sized 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 diffrac-

tion

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 ofthe 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 ðKaÞ X-ray source and Ni filter.

XRD analysis did not show any crystallinephases 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

multicomponent glasses (10–20 �AA [42]) were re-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 chosenon the base of the DTA data (with heating inter-

rupted at different temperatures) of as-prepared

glasses and the XRD analysis of the probes ob-

tained 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 curvesof the glasses with a high content of niobium

(glasses S4-S31) have two exothermal maxima,

which move toward one another while niobium

content (or Nb2O5/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 par-

ticular, in ferroelectric form were revealed in the

glasses of S series in DTA heating in spite of 11

mol% of K2O contained in the glasses. The XRDanalysis of the probes of the S-series glasses re-

sulting from the DTA heating interrupted at

temperatures corresponding to the ends of the

high-temperature shoulder of the first (low tem-

perature) DTA peak (arrows in Fig. 1(a)) showed

that this peak was related to the precipitation of

A.A. Lipovskii et al. / Journal of Non-Crystalline Solids 318 (2003) 268–283 271

quasicubic sodium niobate only (Fig. 1(b)). Thisallowed us to choose heat treatment temperatures

to form monophase glass-ceramics (glass-ceramics

with only one crystalline phase) and to study ki-

netics of sodium niobate formation as well as, in

parallel, kinetics of other accompanying proper-

ties, such as Kerr coefficient, permittivity, density,

and others. The most comprehensive study of

glass-ceramics formation was performed for S2and 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.

2.4. Electrical (permittivity) and Kerr measure-

ments

The permittivity of the as-prepared and heat-

treated glasses was measured by the standard

technique of capacity measurements at 10 kHz

using copper electrodes deposited on the two op-

posite faces of glass or glass-ceramic samples. Thesamples were 20–30 mm long (and wide) and 2–3

mm thick. The same samples with polished end-

faces were used in Kerr measurements.

The measurements of electrooptical Kerr coef-

ficients 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 modu-lated 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 ac-

cording to the quadratic character of electroopti-

cal phenomenon the response of this modulator

was measured at the second harmonic of the in-

put frequency, i.e., at 10 kHz. To improve the

accuracy of the measurement a highly sensitivecalibrated 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 co-

efficient B, and this allowed us to avoid measuring

sample transparency, calibrating the circuit of the

photoreceiver, etc. This scheme gave rather highsensitivity due to the measurements taking place at

the frequency range free from typical noises, which

resulted in high signal selectivity. Besides, this al-

lowed compensating electrically the initial bire-

fringence, 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 commercialnitrobenzene. The measured value of Kerr coeffi-

cient coincided with literary data to within �0.5%.The accuracy was about �5% for BP 10�14 m/V2,

and it was �50% at lower limit of sensitivity

(B � 0:5� 10�16 m/V2), that was �5� 10�5 of Bvalue of nitrobenzene and �10�4 of B value of our

best glass-ceramics. Lower accuracy of the mea-

surements for the synthesized samples compared

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 tem-

peratures are marked by vertical arrows and they are 680 �C for

glass S4, 720 �C for glass S2, and 755 �C for glass S31.

272 A.A. Lipovskii et al. / Journal of Non-Crystalline Solids 318 (2003) 268–283

with one of nitrobenzene was due to the possiblenon-uniformity and, sometimes, light scattering.

2.5. Viscosity and density measurements

Glass viscosity was measured by the beam-

bending method, with the bending base being 26.7

mm. The typical sample size was 30� 6� 2 mm3.

The measurements were performed on isothermalconditions, with the accuracy of temperature

control being to within �0.5�. Glass and glass-

ceramics 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, andKerr coefficients of these stabilized glasses were

measured and compared with ones measured for

the as-prepared glasses, for which anneal temper-

atures corresponded to the viscosity equal to about

1012�0:5 Pa s. These heat treatments endured tillglass 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) tem-

perature equal to the anneal temperature. Then,these glasses were quenched from the temperature

corresponding to viscosity 1012 Pa s, and Kerr co-

efficients 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 sep-

arate 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

glass-forming systems, one can see that there is notany correlation between heavy metal content and

Kerr coefficient. The glasses of S-, LiS-, BT-, and

P-series containing the same amount of corre-

sponding heavy metal oxide (about 20 mol%)

demonstrate Kerr coefficients equal to 26� 10�16,61� 10�16, <0:5� 10�16, and 1:5� 10�16 m/V2,

correspondingly. 3 However, within each separate

glass-forming system Kerr coefficient either in-creases 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 cor-

relation 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 domi-

nate phase precipitating was electrooptical, namely:

microcrystals of lithium niobate. In Fig. 4 the ex-

amples of this study are presented. Asterisks over

DTA peaks in Fig. 4(a) designate the temperatures

of lithium niobate precipitation that was deter-mined from XRD patterns (Fig. 4(b)) of the LiS-

glasses 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 vis-

cosity change during heat treatment of S1 glass is

shown in Fig. 5. After the stabilization at these

temperatures, Kerr coefficients of the glasses in-creased by about 45% for S1 glass (from

105� 10�16 to 150� 10�16 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� 10�16, 195� 10�16, and <0:5� 10�16 m/V2.

A.A. Lipovskii et al. / Journal of Non-Crystalline Solids 318 (2003) 268–283 273

S5 glass (from 195� 10�16 to 250� 10�16 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� 10�16 m/V2.

3.2. Glass-ceramics

As mentioned above, the most comprehensive

study of glass-ceramics formation has been per-

formed on the base of the glasses of S-series. The

glass-ceramics made of the glasses of S-series with

Fig. 3. Kerr coefficient of S- and LiS-glasses via their permit-

tivity (dash line corresponds to parabolic fitting).

Fig. 2. Dependences of Kerr coefficient of S- and LiS-glasses on

Nb2O5 concentration. In inset: the same dependences, where

Kerr coefficient is presented as a function of c=ð1� cÞ2 with cbeing Nb2O5 molar concentration.

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.

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).

274 A.A. Lipovskii et al. / Journal of Non-Crystalline Solids 318 (2003) 268–283

niobium oxide content exceeding 29 mol% dem-onstrated a high transparency and a monotonic

increase with subsequent saturation in Kerr coef-

ficient, 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-phaseglass-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 sensitiv-

ity was found, and no electrooptical phases pre-

cipitated. The rise in Kerr coefficient in S and LiS

glass-ceramics was accompanied with precipitating

electrooptical microcrystals; quasicubic sodiumniobate 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 withrelative weight deficits of NaNbO3 in the batch (ordeficit of Na2OþNb2O5) corresponding to dif-

ferent 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) andconsidered that their densities, qmðwÞ, were equalto the densities of the glassy parts of the glass-

ceramics, qgðwÞ, produced from the corresponding

S glasses, that is, for each glass-ceramics, produced

from S2 or S4 glass, qmðwÞ ¼ qgðwÞ. 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 inthe correspondent glass-ceramics. It is easy to de-

rive equations to calculate the magnitudes of vcusing the dependence of the M-glass densities on

w, that is, qmðwÞ; 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.

A.A. Lipovskii et al. / Journal of Non-Crystalline Solids 318 (2003) 268–283 275

w ¼ ðqmðwÞ � qÞqcðqmðwÞ � qcÞq

; vc ¼ wqqc

; ð2Þ

where qmðwÞ is the polynomial approximation of

the M-glass density (see Fig. 7, dash line), q is the

measured glass-ceramics density, qc is the densityof crystalline sodium niobate. This calculation

gave an overestimate of value w (and vc) that en-sued from the maximal possible weight fractions of

sodium niobate crystals, which could form in ac-

cordance with the glass batches. It was likely to be

due to the glassy part of glass-ceramics, which

includes �glass–crystal� interfaces, having density

lower as compared with the density of the glassesof the same composition, which are synthesized by

conventional melting. The absolute values of vcwere corrected by normalizing the saturated values

of vc to the ones, which could be maximally

achieved in accordance with the weight composi-

tions of the initial glasses.

The saturation times could be identified not

only through the time dependences of Kerr coef-ficient, 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 glass-

ceramics 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 in-crease 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 contri-

bution of the glassy part to the non-linear prop-

erties of the glass-ceramics is negligible. The

correctness of our estimations of values vc was also

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 isthe 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 glass-

ceramics resulting from decreasing niobium content in the

course of crystal phase formation.

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 crystal-

line sodium niobate. Solid line corresponds to the effective

medium approximation. In inset: Glass-ceramics density via

volume fraction of sodium-niobate microcrystals.

276 A.A. Lipovskii et al. / Journal of Non-Crystalline Solids 318 (2003) 268–283

confirmed by the relation between these values andthe 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 treatmenttime, quantitatively. In accordance with the ap-

proximation the average (microscopic) electric

field in a continuous heterogeneous medium con-

sisting of two dielectrics, which in case of glass-

ceramics are glassy matrix and microcrystals

embedded into this matrix, can be written as

E ¼Xi

viEi ¼ vcEc þ vgEg; ð3Þ

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 andglassy 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 ap-

plied voltage and D is the sample thickness. Al-

lowing for the relation vg þ vc ¼ 1 and the

electrical induction (eE) of a medium being con-

stant, that is, ecEc ¼ egEg where ec and eg are thepermittivities of the microcrystals and the glassy

part of the glass-ceramics, from Eq. (3) it follows

that

UD

¼ vc

�þ ecegð1� vcÞ

�Ec: ð4Þ

In Kerr measurements, the monitored signal is

proportional to the product BE2L, where B is the

Kerr coefficient of glass-ceramics, E is the electric

field applied to the sample (equal to U=D), and L isthe sample length or the path, which light passesthrough 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 micro-

crystals only, it is possible to represent the signal

through Kerr coefficient of the crystalline phase,

that is, Kerr coefficient of polycrystalline sodium

niobate (Bc), the electric field applied to the crys-

tals 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

vcL. Thus, we can write that BE2L ¼ BcðEcÞ2vcL,and then, using Eq. (4), express B through

the volume fraction of the crystalline phase vc asfollows: B ¼ Bcvc½aþ vcð1� aÞ��2. If a � 1 wehave

B ¼ Bc

a2vc

1� vcð Þ2" #

; ð5Þ

where a ¼ ec=eg. In case eg is known this depen-

dence allows estimating value Bc or Kerr coeffi-

cient of dense sodium niobate ceramics, which is

the same. In general, value eg is not a constant andit depends on vc because when microcrystals form,

the glassy part of the material is exhausted with

niobium, which is responsible for the glass per-

mittivity (see Table 1). Variations of eg were de-termined from the measurements of permittivities

of the M-glasses (see Fig. 7 for MðS4Þ glasses), andthey proved to be described by the linear depen-

dence eg ¼ e� 18vc for the glass-ceramics formed

from both S2 glass and S4 one. Here e is the per-mittivity 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 � 60000� 10�16 m/V2, whichwas 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 corrobo-

rates the validity of this deduction, for this curve

should be the same indeed, if the crystalline phase

precipitating in heat treatments is the same fordifferent glasses of about the same permittivity.

Thus, Kerr sensitivity of electrooptical glass-

ceramics 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),

A.A. Lipovskii et al. / Journal of Non-Crystalline Solids 318 (2003) 268–283 277

and at the same time such a correlation is absentfor 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 BT-series and glass-ceramics produced from these

glasses contradict literature data. The authors of

Ref. [3] reported a high Kerr sensitivity of Ti-

contained glasses, and the author of Ref. [40] re-

ported 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 Kerrsensitivity and can be crystallized only at temper-

atures higher 850 �C, with the crystalline phase notbeing barium titanate. 4 The same results were

obtained for the glasses of P-series, that is, low

Kerr sensitivity and incapacity of forming elec-

trooptical sodium niobate crystals under heat

treatment.

Such behavior cannot be understood if Kerrsensitivity 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� 10�16, 61� 10�16, <0:5� 10�16

(measurement accuracy), and 1:5� 10�16 m/V2,

correspondingly. However, within each separate

glass-forming system Kerr coefficient either in-

creases 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 crystallitehypothesis [46] and accumulated modern knowl-

edge about glass structure [42,47–49] and gener-

alized several conceptions of the origin of theelectrooptical sensitivity of glasses, which are in-

dependently developed by the authors of this ar-

ticle [6,7,27] and other authors (conceptions of

structural motifs [32,34], clustering of NbO6 oc-

tahedra [35], groupings [22,36,37], ferrons [38], and

microheterogeneities with pseudocrystalline sym-

metry [39]). Our conception is based on the fol-

lowing statements and inferences:

1. High polarizability of a medium gives rise to its

high optical non-linearity and, therefore, elec-

trooptical sensitivity, which in glassy materials,

due to their isotropy, can reveal itself only in

Kerr electrooptical effect. In particular, the rela-

tion between polarizability and non-linearity

comes from Fig. 3, where one can see that Kerrcoefficient increases with a rise in glass permit-

tivity, which, in its turn, directly related to the

medium polarizability.

2. We suggest the fluctuation density inhomogene-

ities peculiar to the glasses to be the ordered re-

gions with exactly crystalline symmetry, the

regions having no phase boundaries. Specific

size of these ordered regions corresponds tothe characteristic scale of the density fluctua-

tions (10–20 �AA), which, in the case under con-

sideration, averages 2–3 coordination spheres

in accordance with the size of the elementary

unit cell of sodium niobate, that is, 3.9 �AA [50].

However, the results obtained in [34] allow

thinking that glasses can inherit not only the

short-range order from the crystal, but alsothe intermediate-range one, which means that

specific size of the ordered regions can achieve

50–100 �AA. The existence of such ordered regionsensues 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 glassbehaves like Bingham rheological body [53] as

well as on the analysis of thermodynamic func-

tions 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 polarizabil-

ity is exclusively related to the deformation of

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.

278 A.A. Lipovskii et al. / Journal of Non-Crystalline Solids 318 (2003) 268–283

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 elec-trooptical (ferroelectric) crystal, the main con-

tribution to the polarization is caused by the

effective mechanism of nuclear (ionic) polariz-

ability of the medium through the deformation

of the ionic lattice of CMs. This, in its turn, en-

sures a high value of Kerr coefficient of the

glass. Theoretical calculations of the local elec-

tric field (Lorenz field) in ferroelectric crystalswith allowance for their local structure (the

exact positions of atoms in the unit cell) argues

in favour of the conception of CMs. These cal-

culations predict the high polarizability of fer-

roelectric 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 ac-cordance with the macroscopic approximation

of isotropic medium by one order and more.

According to Slater [58], this is the essential rea-

son of the ferroelectricity of perovskite-like

crystals. For example, he showed that the Lo-

renz field at titanium atoms in ferroelectric bar-

ium titanate lattice was equal to ð30þ 4p=3ÞPrather 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 de-

crease 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 agreat importance for the problems discussed

here because, in our conception, the corre-

sponding CMs (in case of as-quenched glasses)

and nano- or microcrystals (in case of glass-

ceramics) should be regarded just as such inclu-

sions. Therefore, an appreciable electrooptical

response of the medium can be revealed only

if those inclusions possess crystalline symmetry

of known electrooptical crystals, where this sup-

pressed and weakened macroscopic field could

cause rather high medium polarization due to

the high local field. 6 The importance of thelocal factor to explain the origin of the third

order non-linear susceptibility of the niobium-

contained glasses is also emphasized in Ref.

[35].

4. It is known that, due to the clamping, crystal-

line inclusions in an elastic medium can stay

in non-equilibrium, relatively to a free large

crystal, state, and their phase transition temper-atures (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 expecta-

tions, the crystalline inclusions (CMs or micro-

crystals) can be in the phase different from the

equilibrium one, and, therefore, this can appre-

ciably change electrooptical sensitivity of thematerial. For instance, to explain a high Kerr

sensitivity of sodium niobate glass-ceramics at

room temperature the authors of Ref. [1] con-

cluded that NaNbO3 microcrystals were in fer-

roelectric phase in spite of free NaNbO3

crystals being non-ferroelectric. Additionally,

it was found that, BaTiO3 crystallites precipitat-

ing in glass 15BaO–15TiO2–70TeO2 was in para-electric cubic phase rather than ferroelectric

tetragonal one [60] and that in the formation

of glass-ceramics from PbO–BaO–TiO2–B2O3

glass, the lattice strain between glass matrix

and precipitated cubic PbTiO3 crystallites re-

stricted the phase transition of lead titanate

crystal into ferroelectric phase [61]. Thus, the

clamping should be allowed for in choosingglass compositions and conditions of heat treat-

ments to form a highly sensitive electrooptical

glassy material.

5 Within the frames of the ferrons conception [38], which

looks like most prospective, the local field is considered equal to

4pP=3.

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?

A.A. Lipovskii et al. / Journal of Non-Crystalline Solids 318 (2003) 268–283 279

5. An increase in the total volume fraction of the

ordered regions with a proper crystalline sym-

metry (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 demon-

strated by the experiments on glass crystalliza-

tion, and, in our opinion, was due to theeffective nuclear mechanism of polarization

dominating all the other ones. However, in ac-

cordance 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 fromthe fact that configuration contributions to the

free energy and the entropy of any glass must

be vanished in approaching glass structure to-

wards the one corresponding to the Kauzmann

temperature [49]. It means that the stabilization

of glass structure by long anneals at tempera-

tures below the glass transition temperature

should increase the total volume fraction ofCMs resulting in an increase in Kerr coefficient

of the glass. It is that increase in Kerr coefficient

that is revealed after low-temperature stabiliza-

tion of S1 and S5 glasses (Fig. 5). That it is not

crystallization is confirmed by the reversibility

of Kerr coefficients of the glasses in stabiliza-

tion-quenching circles. Unfortunately, this way

to increase Kerr sensitivity is restricted by thefact that the state, when the glass structure

has the fictive temperature equal to the Kauz-

mann 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 differ-ent space dimensions (fractal in glasses and dis-

crete in crystals) [64].

6. CMs should be considered as crystal pre-nuclei

because the structure of CMs is already or-

dered, 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 as-

sumption 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 co-

incides with one of electrooptical crystals and,

therefore, Kerr coefficient of the glass is rather

high, one can expect a high sensitive electroop-tical glass-ceramics to form, with the microcrys-

tals being of the same composition, which CMs

had. Our experiments corroborate this infer-

ence. Indeed, the glasses of S- and LiS-series

demonstrated highest Kerr sensitivity, and after

crystallization they formed high effective elec-

trooptical glass-ceramics with electrooptical

phases of NaNbO3 and LiNbO3. However, noelectrooptical phases were found after crystalli-

zation of the glasses of BT- and P-series, which

initially demonstrated extremely low Kerr coef-

ficients as well. In accordance with the proposed

conception, this indicates that in BT- and P-

glasses the CMs did not have a proper symme-

try. The structure of CMs appearing to form in

quenching and melting processes strongly de-pends on the thermal-temporal conditions of

glass synthesis. The latter appears to explain

the difference in the result obtained in the pre-

sent research and the ones reported in [3,40],

where electrooptical titanate glasses and glass-

ceramics with barium titanate microcrystals as

precipitates were formed. The explanation pro-

posed in [3], where authors did not receive highKerr 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 sensi-

tivity in those glasses seemed to be caused by

the fact that two types of crystalline motifs,

which actually gave opposite contributions tothe electrooptical sensitivity of the material,

were formed indeed.

In brief, in our opinion, glasses contain specific

structural entities, which possess the exactly crys-

talline symmetry within 2–3 (and maybe more)

coordination spheres, with these entities having no

phase boundaries. We call these entities the CMs,

280 A.A. Lipovskii et al. / Journal of Non-Crystalline Solids 318 (2003) 268–283

and consider them to be responsible for Kerrsensitivity of glasses, if their compositions and

structure coincide with one of known electroopti-

cal crystals. This approach can give us only qual-

itative explanation of the origin of Kerr sensitivity

of glasses because today there is not clear percep-

tion 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 crys-

talline phase in the glass-ceramics are similar, that

is, both curves demonstrate acceleration in the rise

of Kerr coefficient. Being presented as a function

of variable A ¼ c=ð100� cÞ2 where c is the molarpercentage 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 ef-

fective medium approximation to describe elec-

trooptical 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) withc. This qualitative consideration implies that value

c for these glasses plays the same role as value vcfor 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 me-

dium (mixture) consisting of two dielectrics, one of

them being the amorphous network and anotherone being CMs. Thus, the CMs conception looks

like the external reality.

5. Conclusion

Sets of niobate sodium and lithium-silicate,

barium-titanate-silicate and niobium–lithium-

phosphate glasses were synthesized, and composi-

tion dependences of density, permittivity and Kerr

coefficient of all these glasses were studied. The

niobium alkaline glasses demonstrated highestpermittivity and Kerr sensitivity. The lithium sili-

cate glasses demonstrated record Kerr coefficients

(266� 10�16 m/V2). It was shown that Kerr coef-

ficient of niobium alkaline silicate glasses increased

with a rise in niobium content, and that the

barium-titanate-silicate and niobium–lithium-

phosphate glasses did not possess any appreciable

Kerr sensitivity.Kinetics of the formation of transparent

monophase glass-ceramics with electrooptical so-

dium-niobate microcrystals were studied. Kerr

coefficient higher than 6000� 10�16 m/V2 was

obtained for sodium-niobate glass-ceramics pro-

duced from the glass containing 35 mol% of

Nb2O5. Using the effective medium approxima-

tion, it was shown that Kerr coefficient of theseglass-ceramics depended on the volume fraction of

sodium-niobate microcrystals precipitated as a

linear function of vcð1� vcÞ�2 where vc was the

volume fraction. The relation between glass-

ceramics Kerr coefficient and permittivity appears

to be parabolic.

A conception of the origin of electrooptical

sensitivity of glasses is proposed. The conception isbased 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 byglass heat treatment. In accordance with the pro-

posed conception, low-temperature stabilization

of the glasses should lead to the development of

the CMs resulting in an increase in Kerr coeffi-

cient of the glass, and this has been corroborated

experimentally, when after glass stabilization Kerr

coefficient of sodium niobate glasses increased by

30–45%.

7 That these linear dependences start only from 11 mol%

Nb2O5 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% Nb2O5 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 glass-

ceramics formation, where neither ferroelectric KNbO3 nor

other electrooptical potassium contained phases were found.

A.A. Lipovskii et al. / Journal of Non-Crystalline Solids 318 (2003) 268–283 281

Synthesized barium-titanate-silicate and nio-bium–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 respon-

sible for the formation of proper CMs.

Acknowledgements

The research has been supported by Interna-

tional 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 magneto-

optic 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. Tata-

rintsev, A.A. Vetrov, Electrooptic glasses and glass-ceram-

ics 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. Non-

Cryst. 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, Slove-

nia, 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. Non-

Cryst. 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.

282 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. Solov�ev, Yu.N. Venevtsev, G.S. Zhdanov, Kris-

tallografija (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.

[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. Mal-

inovsky, Phys. Stat. Sol. (a) 59 (1979) 621.

[56] S.P. Zhdanov, V.K. Malinovsky, Pis�ma 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 electroop-

tical Kerr phenomenon in niobium alkali-silicate glasses,

Opt. Mater. (2002) in press.

A.A. Lipovskii et al. / Journal of Non-Crystalline Solids 318 (2003) 268–283 283