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Crystallization of ferroelectric bismuth vanadate in Bi2O3–V2O5–SrB4O7 glasses
Journal of Non-Crystalline Solids 226 Ž1998. 145–154
Crystallization of ferroelectric bismuth vanadate in Bi 2 O 3 –V2 O5 –SrB 4O 7 glasses M.V. Shankar 1, K.B.R. Varma
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Materials Research Centre, Indian Institute of Science, Bangalore 560 012, India Received 30 April 1997; revised 9 December 1997
Abstract Transparent glass samples with compositions 2 x Bi 2 O 3 –xV2 O5 – Ž100 y 3 x .SrB 4O 7 Ž15 F x F 25. have been fabricated via conventional melt–quenching technique. The as-quenched samples, of all the compositions under study, have been confirmed to be amorphous by X-ray powder diffraction ŽXRD. measurements. Differential thermal analyses of the glasses Ž x s 20 and 25. indicate a prominent exotherm in the 673 K to 683 K range and the XRD patterns of the samples, obtained by the heat treatment of the glasses at 683 K for 10 h, indicate crystallinity and all the crystalline peaks could be indexed to an orthorhombic ferroelectric bismuth vanadate, Bi 2VO5.5 ŽBiV. phase. High-resolution transmission electron microscopy on these samples confirm the presence of BiV crystallites dispersed in a continuous glass matrix. The dielectric properties of these glass–ceramics have been analysed by employing Maxwell’s model and various other dielectric mixture formulae. The study of the temperature dependence of e r of these glass–ceramics has revealed a dielectric maximum in the vicinity of the temperature at which crystalline BiV has a phase transition from the ferroelectric to paraelectric state. The compositional dependence of the optical properties of these transparent glass–ceramics has also been measured. q 1998 Elsevier Science B.V. All rights reserved. PACS: 42.70.-a; 77.22.-d; 78.20.-e
1. Introduction A large number of compounds belonging to the family of layered bismuth compounds w1–3x with the general formula wBi 2 O 2 x 2q wA ny1 B nO 3 nq1 x 2y, where A is in 12-fold coordination, B is 6-fold coordinated and n is an integer ranging from 1 to 5, were
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Corresponding author. Tel.: q91-80 309 2783r2600; fax: q91-080 334 1683; e-mail: [email protected]. 1 Presently at the Laboratory for Electro-Optic Systems ŽLEOS., Indian Space Research Organization ŽISRO., Bangalore.
synthesized w4–6x and the ferroelectricity in these compounds was described by Newnham et al. w7x. These structures are built up by an intergrowth of w B i 2 O 2 x 2 q layers and perovskite blocks wA ny1 B nO 3 nq1 x 2y. Bismuth vanadate, Bi 2VO5.5 ŽBiV. is a ferroelectric phase, recently identified, in the Bi 2 O 3 –V2 O5 binary system w8–10x. It has a crystal structure similar to that of the n s 1 member of the homologous series. It is orthorhombic with mean unit cell parameters a s 0.5543Ž1. nm, b s 0.5615Ž1. nm, and c s 1.5321Ž3. nm at 300 K w11x. Although this compound has been interesting from the viewpoint of dielectric and ferroelectric proper-
0022-3093r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 3 0 9 3 Ž 9 7 . 0 0 4 9 0 - 0
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M.V. Shankar, K.B.R. Varmar Journal of Non-Crystalline Solids 226 (1998) 145–154
ties, the ionic conductivity observed in the tetragonal phase, above 827 K, is a major constraint in exploiting this material for device applications. Our earlier investigations pertaining to the effect of microstructure on the dielectric and ferroelectric properties of BiV ceramic, indicated that the dielectric constant Ž e r ., as well as the dielectric loss Žtan d ., increases with increase in crystallite size w12x. Hence, it is evident that decreasing crystallite sizes within the nanometer range would lead to a reduction in tan d , a factor in consideration of BiV for various device applications. Although there exists numerous ways to achieve this goal w13,14x, the glass–ceramic route has been most effective, since amorphous solids offer a high degree of freedom in the topological and chemical arrangement of their constituent atoms w15x. Among the advantages of using glass–ceramics, in which a ferroelectric phase is crystallized by the devitrification of a glass matrix, is a decrease in porosity and dielectric loss. The properties of these glass–ceramics can be controlled by the microstructure and physical properties of the phases that crystallize in the glasses, upon heat treatment. Our recent investigations on strontium tetraborate, SrB 4 O 7 ŽSBO. glasses have indicated that SBO, by virtue of its favourable structural, thermal and optical properties, would be an ideal glass host matrix for dispersing various ferroelectric crystallites w16,17x. In the present paper, we report the results concerning the crystallization of the ferroelectric bismuth vanadate phase in the glassy matrix of the nominal compositions 2 x Bi 2 O 3 –xV2 O 5 – Ž1003 x .SrB 4 O 7 . Our studies indicate that the dielectric constant Ž e r . of these glass–ceramics can be accurately predicted by the use of dielectric mixture formulae. The optical transmission and the refractive indices of these transparent glass–ceramics are also reported in this paper.
2. Experimental 2.1. Glass preparation Glass samples, with the compositions 2 x Bi 2 O 3 – xV2 O5 – Ž100-3 x .SrB 4 O 7 Ž x s 15, 20, and 25., have been prepared from reagent-grade Bi 2 O 3 , V2 O5 , and SrB 4 O 7 . Strontium tetraborate ŽSrB 4 O 7 ., used in the
present study, was prepared via a solid-state synthesis route, by heating a stoichiometric mixture of SrCO 3 and H 3 BO 3 at 8008C for 12 h, with intermediate grinding and sintering. Homogeneous mixtures of stoichiometric compositions were melted in a platinum crucible at 1373 K for 1 h in air. Transparent reddish grey, flat plates were obtained by pouring the liquid onto a stainless steel plate Žheated to 373 K. and pressed quickly with another plate. Long glass rods Ž3 mm in diameter, 30 mm in length. of various compositions could also be fabricated by pouring the liquid into a heated stainless steel mould. The glasses were, subsequently, annealed at 3008C for 12 h, at heating and cooling rates of 18C miny1 . 2.2. X-ray powder diffraction (XRD) and electron microscopy The crushed powders of the as-quenched samples Žaverage particle size ranged from 15 to 20 nm. and the heat-treated Žaverage particle size ranged from 25 to 30 nm. samples were examined by XRD using Cu-K a radiation. The XRD patterns obtained were analyzed and the Bi 2VO5.5 phase formation was confirmed by comparing the lattice parameters computed based on these XRD patterns with the values reported in the literature w11x for BiV, prepared by conventional ceramic methods. High-resolution transmission electron microscope ŽHRTEM. ŽJEOL 200 CX. was employed to examine the amorphousrcrystalline states of the powders of the as-quenched samples. Selected-area electron diffraction ŽSAED. studies were carried out on the heat treated glass–ceramics to estimate the lattice parameters of the crystalline phase embedded in the glass matrix. 2.3. Thermal analysis and density measurements The glassy state of the as-quenched samples was confirmed by subjecting the powders Žweighingf 20 mg. to differential thermal analysis ŽDTA., in the temperature range 300 K to 1273 K. A heating rate of 20 K miny1 was employed for the thermal analyses. Three samples of each composition were subjected to differential thermal analyses and the average value of glass-transition temperature ŽTg ., temperature of onset of crystallization ŽTcr . and the
M.V. Shankar, K.B.R. Varmar Journal of Non-Crystalline Solids 226 (1998) 145–154
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melting point ŽTmp . were determined Ž"28C accuracy.. The volume fractions of the crystalline phase, in the heat treated samples, were computed based on their densities measured by the Archimedean method. 2.4. Dielectric and optical studies The capacitance and the dielectric loss Žtan d . measurements, in two-probe configuration Ž"2% accuracy., on the annealed glass and the glass–ceramic samples Žtypical dimensions: length, 6 to 7 mm, breadth, 3 to 4 mm, and thickness, 0.8 to 1.0 mm. were carried out in the frequency range of 100 Hz to 100 kHz at a signal strength of 0.5 V rms ŽKeithley 3330 LCZ meter.. For this purpose, the surfaces of the annealed plates of the glass and the glass–ceramic samples were sputtered with gold and silver epoxy was used to bond leads to the sample. The dielectric constants Ž"5% accuracy. were calculated based on the capacitance measurements and by measuring the electrode area and the thickness of the samples. The samples were held at each fixed temperature for a few minutes Ž5 min., till the temperature stabilizes, before making the electrical measurements. The annealed glasses and the transparent glass– ceramics were polished prior to optical measurements. The optical transmissions of these samples were measured in the wavelength range 500 nm to 2500 nm, using a spectrophotometer ŽHitachi U3400.. The refractive indices of the transparent glass–ceramics were estimated by the Brewster angle measurement technique, at 632.8 nm, using a He–Ne laser.
3. Results 3.1. DTA of the 2xBi 2 O3 –xV2 O5 – (100 y 3x)SrB4 O7 glasses Typical DTA curves obtained for the powder of the as-quenched glasses corresponding to the compositions x s 15, 20, 25 are shown in Fig. 1a–c, respectively. The differential thermogram, for a representative sample with the composition x s 25, has an exotherm at 683 K and an endotherm at 803 K followed by another exotherm at 988 K before melting around 1033 K. The sample, with the composi-
Fig. 1. The DTA traces of the Ža. x s15, Žb. x s 20, and Žc. x s 25 glass samples.
tion x s 25, heat treated at a temperature close to the first exotherm Ž683 K. for 10 h did not exhibit any exothermic peak around that temperature when subsequently subjected to DTA. 3.2. X-ray powder diffraction and phase identification in the glass–ceramics The XRD patterns of the as-quenched samples, for the compositions with x of 15, 20, and 25, depicted in Fig. 2a–c, confirm their amorphous state. The broad peak observed around 2 u f 288, corresponds to the most intense Bragg peak of BiV; its width decreases with increase in x ŽFig. 2c.. To identify the crystalline phase associated with the first exotherm observed in the DTA, the optically transparent glasses heat treated at 683 K for 12 h, were subjected to XRD measurement. The Bragg peaks in the XRD of the x s 15, 20 and 25 samples, heat treated at 683 K for 12 h ŽFig. 2d–f. could be indexed to an orthorhombic Bi 2VO5.5 ŽBiV. phase with the lattice parameters a s 0.5543Ž1. nm, b s 0.5615Ž1. nm, and c s 1.5321Ž3. nm. These are in good agreement with values reported in the literature w11x. At this stage, as evident from Fig. 2d–f, no peaks attributable to crystalline strontium tetraborate,
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exotherm. for 12 h, revealed the crystallization of both BiV and SBO. The Bragg peaks corresponding to SBO and BiV phases are indicated by S and B in Fig. 3. The lattice parameters for SBO, computed based on this XRD pattern are in agreement with the literature values w18x. However, the samples, at this stage, lose their visual transparency completely. 3.3. Transmission electron microscopy
Fig. 2. The XRD patterns of the as-quenched samples wŽa., Žb., and Žc.x and the glass–ceramic samples wŽd., Že., and Žf.x with compositions x s15, 20 and 25.
SrB 4 O 7 ŽSBO. or any other mixed phase could be identified. However, the XRD ŽFig. 3. for a x s 25 sample heat treated at 1000 K Žbeyond the second
The high resolution transmission electron micrograph of an as-quenched sample with the composition x s 25 is depicted in Fig. 4a. The SAED pattern, shown in the inset, clearly demonstrates the amorphous state. The electron micrograph ŽFig. 4b., along with the SAED pattern recorded for the sample heat treated at 683 K for 12 h, indicates the presence of spherical crystallites of varied sizes Ž10 to 15 nm. dispersed in a continuous glass matrix. However, the glass heat treated at 773 K for 48 h consists of spherical crystallites of fairly uniform size, evenly dispersed in the glass matrix ŽFig. 4c.. A high resolution lattice image of this sample is shown in Fig. 4d. The fringe spacing, observed in the crystallite, is 0.76 nm, which corresponds to one-half of the cparameter of bismuth vanadate.
Fig. 3. The XRD pattern of a glass sample, with composition x s 25, heat-treated at 1000 K.
M.V. Shankar, K.B.R. Varmar Journal of Non-Crystalline Solids 226 (1998) 145–154
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Fig. 4. Transmission electron micrographs of the samples corresponding to x s 25 composition: Ža. as-quenched sample; Žb. glass–ceramic sample, obtained by heat treating the glass sample at 683 K, 12 h; Žc. glass–ceramic sample obtained by heat treating the glass sample at 773 K, 48 h; Žd. The lattice image recorded for the sample heat-treated at 773 K.
3.4. Dielectric studies The frequency response of the dielectric constant Ž e r ., at 300 K, for the as-quenched samples Ž x s 15, 20 and 25. is depicted in Fig. 5. e r decreases with increasing frequency, in the 100 Hz to 100 kHz frequency range. e r was found to increase with increase in the Bi 2 O 3 –V2 O5 content of the asquenched samples at all the frequencies under study. The frequency response of e r of the glass–ceramics, obtained by heating the glasses at 773 K Ž12 h., which is higher than the first crystallization temperature, is shown in Fig. 6. The dispersion of e r with frequency also increases with increase in Bi 2 O 3 – V2 O5 content. It is observed that tan d for the glasses and glass–ceramics of all the compositions under study have a dielectric loss Ž0.003 to 0.11 " 0.001.; much less than that of BiV ceramic Ž1.2 " 0.05 to 0.8 " 0.05. prepared by conventional ceramic processing w19x.
Fig. 5. The variation of e r as a function of the frequency, for the glass samples Žlines are drawn as guides for the eyes..
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M.V. Shankar, K.B.R. Varmar Journal of Non-Crystalline Solids 226 (1998) 145–154
Fig. 6. The variation of e r with frequency for the glass–ceramic samples Žlines are drawn as guides for the eyes..
Fig. 8. The variation of e r with time for a x s 25 sample maintained at 683 K Žlines are drawn as guides for the eyes..
The frequency dispersion of the dielectric loss, tan d , is small Ž4 = 10y3 F tan d F 8 = 10y3 . for the glass samples. Fig. 7 which shows the frequency response of tan d , for the glass–ceramics of three representative compositions x of 15, 20, and 25, indicates that tan d of the glass–ceramic sample increases with increase in Bi 2 O 3 –V2 O5 content. The frequency dispersion of tan d is comparatively larger in the glass–ceramic samples than in the glass samples. The larger frequency dispersion of tan d in the glass–ceramics is attributed to the presence of the crystalline BiV phase dispersed in the glass matrix.
In fact, polycrystalline BiV, obtained by conventional ceramic route, has a frequency dispersion in both e r and tan d : e r Ž100 Hz. f 1600 and e r Ž100 kHz. f 90, tan d 100 Hz f 1.2 and tan d 100 kHz f 0.2. The crystallization of BiV in these samples was monitored in situ, by measuring e r as a function of time, for a glass maintained at 683 K. We observed that e r increases with increasing time ŽFig. 8.. The variation of e r with temperature, at various frequencies, for the glass–ceramic sample with the composition x s 25, is shown in Fig. 9. e r increases with increase in temperature at all the frequencies under
Fig. 7. The variation of tan d with frequency for the glass–ceramic samples Žlines are drawn as guides for the eyes..
Fig. 9. The variation of e r Žat different frequencies. with temperature for a x s 25 glass–ceramic sample.
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matrix. We confirmed that this exotherm is a consequence of the onset of crystallization of monophasic bismuth vanadate in the SBO glass. We attribute the endotherm at 803 K to the glass-transition temperature of the glass, which constitutes the matrix. The second exotherm in the DTA, indicates the onset of crystallization of SBO phase. The DTA, supported by XRD analysis, carried out on the samples heattreated at 683 K for 10 h, suggests that the time required for the process of BiV crystallization in SBO glass matrix is around 10 h.
Fig. 10. The optical transmission spectra of the glass–ceramic samples with composition x s15, 20 and 25.
study Ž100 Hz to 100 kHz.. A peak in e r is observed around 750 K, which is about 20 K higher than the phase transition temperature reported for crystalline BiV w11x. 3.5. Optical studies The optical transmissions Žuncorrected for scattering and other reflection losses. of the glass–ceramic samples with compositions x of 15, 20, and 25 in the wavelength range 500 to 2500 nm are depicted in Fig. 10. The optical transmissions of the glass– ceramic samples with compositions x of 25 and 20 are similar. The transmission decreases by more than half the maximum value below 1500 nm, continues to decrease in the entire range of 700 nm to 1500 nm and the transmission ceases beyond f 700 nm. The refractive indices of these glass–ceramics increase with increase in x. The refractive indices of the glass–ceramic samples with compositions x of 15, 20, and 25 are 1.86 " 0.02, 2.15 " 0.02, and 2.17 " 0.02, respectively.
4. Discussion 4.1. Crystallization of BiV in the glassy matrix of SBO The DTA data shows the occurrence of crystallization of a single phase around 683 K in the glass
4.2. Dielectric properties of the glass–ceramics The glass–ceramic samples, obtained in the present studies, have dielectric constants larger than those of the glass samples, owing to a contribution from crystalline BiV phase. The increase in e r with time, for the glass sample maintained at 683 K, is attributed to an increase in the fraction of the crystalline phase present in these samples. The crystallization process is complete in 10 h, as confirmed by the absence of a crystallization peak at 683 K in the DTA for the sample heat treated at this temperature for 10 h. Therefore, the further increase in e r after 10 h Žsee Fig. 8. is attributed to an increase in the volume fraction of the crystalline phase. The peak in e r , exhibited by these glass–ceramics ŽFig. 9., near the phase-transition temperature of crystalline BiV, is suggestive of their polar nature. The magnitude of the peak, which is smaller than that observed in the case of crystalline BiV, may be attributed to the presence of interpenetrating residual glass of lesser dielectric constant. The shift in the curie point ŽTc . may arise due to the effects of the elastic and the electrostrictive forces exerted by the surrounding glass matrix on the crystallites participating in the phase transition. It is interesting to note that the BiV crystallites embedded in the glass matrix exhibit a phase transition, unhindered by the presence of an interpenetrating glassy-phase of smaller e r . 4.2.1. Application of dielectric mixture formulae Dielectric mixture formulae are applied to predict the dielectric constant of the glass–ceramic samples containing bismuth vanadate crystallites, with dielec-
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tric constant, e 1 and volume fraction d 1 , dispersed in a strontium tetraborate glass matrix, with dielectric constant, e 2 and volume fraction d 2 Žs 1 y d 1 . has yielded accurate values. The validity of the prediction is demonstrated for a glass–ceramic sample with composition x s 25, in which the BiV phase Žwith dielectric constant, e 1 s 90 Žat 100 kHz.. occupies a volume fraction d 1 s 0.53. The glass matrix SBO Žwith dielectric constant, e 2 s 10 Žat 100 kHz.. occupies a volume fraction d 2 Žs 1 y d 1 . s 0.47. In the classical Claussius–Mossotti treatment of a mixture of dielectrics composed of spherical dielectric inclusions dispersed in a continuous loss less dielectric medium w20x, assuming that each inclusion is polarized in the same way as if others are absent, i.e., taking no account of interaction, the effective dielectric constant Ž eeff . of the composite is given by the expression:
eeff s e 2 1 q 3 d 1
Ž e1 y e2 . Ž e1 q 2 e2 .
Ž 1.
where e 1 and e 2 are the dielectric constants of the dispersed phase and the host matrix phase respectively and d 1 is the volume-fraction of the dispersed phase. The Claussius–Mossotti formula for a dispersion of spheres is given by Reynolds and Hough w21x as
eeff s
Ž 1 y d 1 . 2 e 22 q Ž 1 q 2 d 1 . e 1 e 2 . Ž 1 y d1 . e1 q Ž 2 q d1 . e2
Ž 2.
Using Reynolds and Hough’s adaptation of the Claussius–Mossotti formula, we calculate the dielectric constant Ž eeff . of the glass–ceramic sample to be 28.8 " 60.5 Žat 100 kHz., which is comparable with the experimentally measured number Žbased on capacitance measurements. of 29 " 0.5 Žat 100 kHz.. The agreement of the calculated and experimentally measured values may be due to the spherical shape of the crystalline inclusions, in the present case. When the dispersed phase occupies a significant volume fraction Ž) 0.25., the spacing between the dispersed crystallites is small, allowance for electrostatic interaction between the crystallites must be made, while modelling the dielectric behaviour. w22x and Bruggeman w23x incorporated interBottcher ¨ action effects by assuming, in the calculation of the effective polarizing field, that the spheres of dielec-
tric constant e 1 are immersed in a medium of dielectric constant eeff . The Bottcher–Bruggeman formula ¨ is given by Reynolds and Hough as two separate formulae, eeff y e 2 e1 y e2 s d1 , Ž 3a . 3 eeff e 1 q 2 eeff e 1 y eeff e 2 y eeff d1 q d2 s0 Ž 3b . e 1 q 2 eeff e 1 q 2 eeff where e 1 , e 2 and d 1 have the usual meanings and d 2 refers to the volume fraction of the host matrix phase. A similar formula has been proposed by Niesel w24x, 1 1r2 eeff s N q Ž N 2 q 8 e1 e2 . Ž 4. 4 where N s Ž3 d 1 y 1. e 1 q Ž2 y 3 d 1 . e 2 . Odelevski has demonstrated the validity of such a formula for a mixture of two dielectric constituents with large difference Žat least 1 order of magnitude. in their dielectric permittivity w25x. Application of Niesel’s formula is relevant in the present case as there is a large difference in the dielectric constant of the SBO glass matrix Ž e 2 s 10. and the dispersed BiV crystallites Ž e 1 s 90.. According to Niesel’s formula, the dielectric constant of the glass–ceramic sample is 39.88, which is much larger than the experimentally measured value of f 29 " 0.5 Žat 100 kHz.. The logarithmic mixture rule w26,27x, given by log eeff s d 1 log e 1 q d 2 log e 2 Ž 5. could also be applied to the present system. It predicts 32.04 for the glass–ceramic sample, which is larger than the experimentally measured value. The high resolution transmission electron micrographs of the glass–ceramic samples ŽFig. 4b and c. clearly demonstrate the presence of spherical crystallites dispersed in a continuous host matrix. This observation has prompted us to employ Maxwell’s model which describes a two-phase dielectric mixture comprising of spherical particles with higher dielectric constant dispersed in a matrix of smaller dielectric constant w28x. According to Maxwell’s model, the dielectric constant of such a composite is given by d 2 e 2 Ž 2r3 q e 1r3 e 2 . q d 1 e 1 eeff s . Ž 6. d 2 Ž 2r3 q e 1r3 e 2 . q d 1
M.V. Shankar, K.B.R. Varmar Journal of Non-Crystalline Solids 226 (1998) 145–154
As per this model, the calculated value of eeff is 28.8 which is close to the experimentally measured 29 " 0.5. Based on the close agreement between the predicted and the experimentally measured values, we propose that the dielectric properties of SBO–BiV glass–ceramics are adequately described by the Maxwell model. 4.3. Optical properties of the transparent glass– ceramics In explaining the effect of composition of the glass on the refractive index, we shall base our considerations upon theoretically proven relationships between molar refraction Ž R m . and refractive index Ž n., derived by Volf w29x, Lorentz w30x, and Lorenz w31x: Rm s
Ž n2 y 1. M Ž n2 q 2. r
Ž 7.
where n is the refractive index Žat 632.8 nm., r is the density and M is the molecular weight of the glass–ceramic sample. The importance of the molar refraction lies in its relationship to the structure of the glass. Molar refraction, R m , is proportional to the polarizability of the material, a m , according to the relationship,
am s
3 4pN
Rm
Ž 8.
where N is the number of polarizable ions per mole, assumed to be equal to Avogadro’s number. The value of R m and a m , evaluated using Eqs. Ž7. and Ž8. are: 29.9 " 0.1 cm3 moly1 and Ž11.85 " 0.01. = 10y2 4 cm3 for the glass–ceramic sample with x s 15 and R m s 37.5 " 0.1 cm3 moly1 and a m s Ž14.87 " 0.01. = 10y2 4 cm3 for the glass–ceramic sample with x s 25. The increase of polarizability is accompanied by an increase in molar refraction and hence by an increase in the refractive index. The refractive index was found to depend not only upon polarizability but also upon molar volume, Mrr ; it increases when the molar volume decreases, viz. when the structure gets denser. The compositional dependence of nonlinear optical properties of these glass– ceramics can be estimated by employing the empirical relation between the linear optical polarizability
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a opt and third-order NLO susceptibility Ž x 3 ., as proposed by Wang w32x. The relation between a m and x 3 is given by: 3
x 3 s CX Ž n2 q 2 . Ž n 2 y 1 . a m where CX is a constant, n is the linear refractive index and a m is the linear optical polarizability. The x 3 values for the SBO–BiV glass–ceramics, estimated based on the values of n and a m , indicate that the x 3 increases steadily with increase in Bi 2 O 3 – V2 O5 content. For instance, the x 3 value predicted for the glass–ceramic sample with x s 25 composition is nearly four times that of the sample with the composition x s 15. It has already been demonstrated w33x that the optical transmission properties of these glass– ceramics could be tailored by adjusting the BiV content. Studies are under progress to explore the possibility of enhancing the electro-optic response of these glass–ceramics, at wavelengths near the optical absorption edge.
5. Conclusions Precipitation of a crystalline phase of polar Bi 2VO5.5 was accomplished by the controlled heattreatment of glasses of the composition 2 x Bi 2 O 3 – xV2 O5 – Ž100 y 3 x .SrB 4 O 7 Ž15 F x F 25.. The experimentally determined dielectric constants of the glass–ceramics were fitted to various dielectric mixture formulae and these results are found to be in agreement with those predicted by Maxwell’s model. The optical properties of these glass–ceramics suggest that these novel glass composites are promising materials for nonlinear optical applications.
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Crystallization of ferroelectric bismuth vanadate in Bi 2 O 3 –V2 O5 –SrB 4O 7 glasses M.V. Shankar 1, K.B.R. Varma
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Materials Research Centre, Indian Institute of Science, Bangalore 560 012, India Received 30 April 1997; revised 9 December 1997
Abstract Transparent glass samples with compositions 2 x Bi 2 O 3 –xV2 O5 – Ž100 y 3 x .SrB 4O 7 Ž15 F x F 25. have been fabricated via conventional melt–quenching technique. The as-quenched samples, of all the compositions under study, have been confirmed to be amorphous by X-ray powder diffraction ŽXRD. measurements. Differential thermal analyses of the glasses Ž x s 20 and 25. indicate a prominent exotherm in the 673 K to 683 K range and the XRD patterns of the samples, obtained by the heat treatment of the glasses at 683 K for 10 h, indicate crystallinity and all the crystalline peaks could be indexed to an orthorhombic ferroelectric bismuth vanadate, Bi 2VO5.5 ŽBiV. phase. High-resolution transmission electron microscopy on these samples confirm the presence of BiV crystallites dispersed in a continuous glass matrix. The dielectric properties of these glass–ceramics have been analysed by employing Maxwell’s model and various other dielectric mixture formulae. The study of the temperature dependence of e r of these glass–ceramics has revealed a dielectric maximum in the vicinity of the temperature at which crystalline BiV has a phase transition from the ferroelectric to paraelectric state. The compositional dependence of the optical properties of these transparent glass–ceramics has also been measured. q 1998 Elsevier Science B.V. All rights reserved. PACS: 42.70.-a; 77.22.-d; 78.20.-e
1. Introduction A large number of compounds belonging to the family of layered bismuth compounds w1–3x with the general formula wBi 2 O 2 x 2q wA ny1 B nO 3 nq1 x 2y, where A is in 12-fold coordination, B is 6-fold coordinated and n is an integer ranging from 1 to 5, were
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Corresponding author. Tel.: q91-80 309 2783r2600; fax: q91-080 334 1683; e-mail: [email protected]. 1 Presently at the Laboratory for Electro-Optic Systems ŽLEOS., Indian Space Research Organization ŽISRO., Bangalore.
synthesized w4–6x and the ferroelectricity in these compounds was described by Newnham et al. w7x. These structures are built up by an intergrowth of w B i 2 O 2 x 2 q layers and perovskite blocks wA ny1 B nO 3 nq1 x 2y. Bismuth vanadate, Bi 2VO5.5 ŽBiV. is a ferroelectric phase, recently identified, in the Bi 2 O 3 –V2 O5 binary system w8–10x. It has a crystal structure similar to that of the n s 1 member of the homologous series. It is orthorhombic with mean unit cell parameters a s 0.5543Ž1. nm, b s 0.5615Ž1. nm, and c s 1.5321Ž3. nm at 300 K w11x. Although this compound has been interesting from the viewpoint of dielectric and ferroelectric proper-
0022-3093r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 3 0 9 3 Ž 9 7 . 0 0 4 9 0 - 0
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ties, the ionic conductivity observed in the tetragonal phase, above 827 K, is a major constraint in exploiting this material for device applications. Our earlier investigations pertaining to the effect of microstructure on the dielectric and ferroelectric properties of BiV ceramic, indicated that the dielectric constant Ž e r ., as well as the dielectric loss Žtan d ., increases with increase in crystallite size w12x. Hence, it is evident that decreasing crystallite sizes within the nanometer range would lead to a reduction in tan d , a factor in consideration of BiV for various device applications. Although there exists numerous ways to achieve this goal w13,14x, the glass–ceramic route has been most effective, since amorphous solids offer a high degree of freedom in the topological and chemical arrangement of their constituent atoms w15x. Among the advantages of using glass–ceramics, in which a ferroelectric phase is crystallized by the devitrification of a glass matrix, is a decrease in porosity and dielectric loss. The properties of these glass–ceramics can be controlled by the microstructure and physical properties of the phases that crystallize in the glasses, upon heat treatment. Our recent investigations on strontium tetraborate, SrB 4 O 7 ŽSBO. glasses have indicated that SBO, by virtue of its favourable structural, thermal and optical properties, would be an ideal glass host matrix for dispersing various ferroelectric crystallites w16,17x. In the present paper, we report the results concerning the crystallization of the ferroelectric bismuth vanadate phase in the glassy matrix of the nominal compositions 2 x Bi 2 O 3 –xV2 O 5 – Ž1003 x .SrB 4 O 7 . Our studies indicate that the dielectric constant Ž e r . of these glass–ceramics can be accurately predicted by the use of dielectric mixture formulae. The optical transmission and the refractive indices of these transparent glass–ceramics are also reported in this paper.
2. Experimental 2.1. Glass preparation Glass samples, with the compositions 2 x Bi 2 O 3 – xV2 O5 – Ž100-3 x .SrB 4 O 7 Ž x s 15, 20, and 25., have been prepared from reagent-grade Bi 2 O 3 , V2 O5 , and SrB 4 O 7 . Strontium tetraborate ŽSrB 4 O 7 ., used in the
present study, was prepared via a solid-state synthesis route, by heating a stoichiometric mixture of SrCO 3 and H 3 BO 3 at 8008C for 12 h, with intermediate grinding and sintering. Homogeneous mixtures of stoichiometric compositions were melted in a platinum crucible at 1373 K for 1 h in air. Transparent reddish grey, flat plates were obtained by pouring the liquid onto a stainless steel plate Žheated to 373 K. and pressed quickly with another plate. Long glass rods Ž3 mm in diameter, 30 mm in length. of various compositions could also be fabricated by pouring the liquid into a heated stainless steel mould. The glasses were, subsequently, annealed at 3008C for 12 h, at heating and cooling rates of 18C miny1 . 2.2. X-ray powder diffraction (XRD) and electron microscopy The crushed powders of the as-quenched samples Žaverage particle size ranged from 15 to 20 nm. and the heat-treated Žaverage particle size ranged from 25 to 30 nm. samples were examined by XRD using Cu-K a radiation. The XRD patterns obtained were analyzed and the Bi 2VO5.5 phase formation was confirmed by comparing the lattice parameters computed based on these XRD patterns with the values reported in the literature w11x for BiV, prepared by conventional ceramic methods. High-resolution transmission electron microscope ŽHRTEM. ŽJEOL 200 CX. was employed to examine the amorphousrcrystalline states of the powders of the as-quenched samples. Selected-area electron diffraction ŽSAED. studies were carried out on the heat treated glass–ceramics to estimate the lattice parameters of the crystalline phase embedded in the glass matrix. 2.3. Thermal analysis and density measurements The glassy state of the as-quenched samples was confirmed by subjecting the powders Žweighingf 20 mg. to differential thermal analysis ŽDTA., in the temperature range 300 K to 1273 K. A heating rate of 20 K miny1 was employed for the thermal analyses. Three samples of each composition were subjected to differential thermal analyses and the average value of glass-transition temperature ŽTg ., temperature of onset of crystallization ŽTcr . and the
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melting point ŽTmp . were determined Ž"28C accuracy.. The volume fractions of the crystalline phase, in the heat treated samples, were computed based on their densities measured by the Archimedean method. 2.4. Dielectric and optical studies The capacitance and the dielectric loss Žtan d . measurements, in two-probe configuration Ž"2% accuracy., on the annealed glass and the glass–ceramic samples Žtypical dimensions: length, 6 to 7 mm, breadth, 3 to 4 mm, and thickness, 0.8 to 1.0 mm. were carried out in the frequency range of 100 Hz to 100 kHz at a signal strength of 0.5 V rms ŽKeithley 3330 LCZ meter.. For this purpose, the surfaces of the annealed plates of the glass and the glass–ceramic samples were sputtered with gold and silver epoxy was used to bond leads to the sample. The dielectric constants Ž"5% accuracy. were calculated based on the capacitance measurements and by measuring the electrode area and the thickness of the samples. The samples were held at each fixed temperature for a few minutes Ž5 min., till the temperature stabilizes, before making the electrical measurements. The annealed glasses and the transparent glass– ceramics were polished prior to optical measurements. The optical transmissions of these samples were measured in the wavelength range 500 nm to 2500 nm, using a spectrophotometer ŽHitachi U3400.. The refractive indices of the transparent glass–ceramics were estimated by the Brewster angle measurement technique, at 632.8 nm, using a He–Ne laser.
3. Results 3.1. DTA of the 2xBi 2 O3 –xV2 O5 – (100 y 3x)SrB4 O7 glasses Typical DTA curves obtained for the powder of the as-quenched glasses corresponding to the compositions x s 15, 20, 25 are shown in Fig. 1a–c, respectively. The differential thermogram, for a representative sample with the composition x s 25, has an exotherm at 683 K and an endotherm at 803 K followed by another exotherm at 988 K before melting around 1033 K. The sample, with the composi-
Fig. 1. The DTA traces of the Ža. x s15, Žb. x s 20, and Žc. x s 25 glass samples.
tion x s 25, heat treated at a temperature close to the first exotherm Ž683 K. for 10 h did not exhibit any exothermic peak around that temperature when subsequently subjected to DTA. 3.2. X-ray powder diffraction and phase identification in the glass–ceramics The XRD patterns of the as-quenched samples, for the compositions with x of 15, 20, and 25, depicted in Fig. 2a–c, confirm their amorphous state. The broad peak observed around 2 u f 288, corresponds to the most intense Bragg peak of BiV; its width decreases with increase in x ŽFig. 2c.. To identify the crystalline phase associated with the first exotherm observed in the DTA, the optically transparent glasses heat treated at 683 K for 12 h, were subjected to XRD measurement. The Bragg peaks in the XRD of the x s 15, 20 and 25 samples, heat treated at 683 K for 12 h ŽFig. 2d–f. could be indexed to an orthorhombic Bi 2VO5.5 ŽBiV. phase with the lattice parameters a s 0.5543Ž1. nm, b s 0.5615Ž1. nm, and c s 1.5321Ž3. nm. These are in good agreement with values reported in the literature w11x. At this stage, as evident from Fig. 2d–f, no peaks attributable to crystalline strontium tetraborate,
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exotherm. for 12 h, revealed the crystallization of both BiV and SBO. The Bragg peaks corresponding to SBO and BiV phases are indicated by S and B in Fig. 3. The lattice parameters for SBO, computed based on this XRD pattern are in agreement with the literature values w18x. However, the samples, at this stage, lose their visual transparency completely. 3.3. Transmission electron microscopy
Fig. 2. The XRD patterns of the as-quenched samples wŽa., Žb., and Žc.x and the glass–ceramic samples wŽd., Že., and Žf.x with compositions x s15, 20 and 25.
SrB 4 O 7 ŽSBO. or any other mixed phase could be identified. However, the XRD ŽFig. 3. for a x s 25 sample heat treated at 1000 K Žbeyond the second
The high resolution transmission electron micrograph of an as-quenched sample with the composition x s 25 is depicted in Fig. 4a. The SAED pattern, shown in the inset, clearly demonstrates the amorphous state. The electron micrograph ŽFig. 4b., along with the SAED pattern recorded for the sample heat treated at 683 K for 12 h, indicates the presence of spherical crystallites of varied sizes Ž10 to 15 nm. dispersed in a continuous glass matrix. However, the glass heat treated at 773 K for 48 h consists of spherical crystallites of fairly uniform size, evenly dispersed in the glass matrix ŽFig. 4c.. A high resolution lattice image of this sample is shown in Fig. 4d. The fringe spacing, observed in the crystallite, is 0.76 nm, which corresponds to one-half of the cparameter of bismuth vanadate.
Fig. 3. The XRD pattern of a glass sample, with composition x s 25, heat-treated at 1000 K.
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Fig. 4. Transmission electron micrographs of the samples corresponding to x s 25 composition: Ža. as-quenched sample; Žb. glass–ceramic sample, obtained by heat treating the glass sample at 683 K, 12 h; Žc. glass–ceramic sample obtained by heat treating the glass sample at 773 K, 48 h; Žd. The lattice image recorded for the sample heat-treated at 773 K.
3.4. Dielectric studies The frequency response of the dielectric constant Ž e r ., at 300 K, for the as-quenched samples Ž x s 15, 20 and 25. is depicted in Fig. 5. e r decreases with increasing frequency, in the 100 Hz to 100 kHz frequency range. e r was found to increase with increase in the Bi 2 O 3 –V2 O5 content of the asquenched samples at all the frequencies under study. The frequency response of e r of the glass–ceramics, obtained by heating the glasses at 773 K Ž12 h., which is higher than the first crystallization temperature, is shown in Fig. 6. The dispersion of e r with frequency also increases with increase in Bi 2 O 3 – V2 O5 content. It is observed that tan d for the glasses and glass–ceramics of all the compositions under study have a dielectric loss Ž0.003 to 0.11 " 0.001.; much less than that of BiV ceramic Ž1.2 " 0.05 to 0.8 " 0.05. prepared by conventional ceramic processing w19x.
Fig. 5. The variation of e r as a function of the frequency, for the glass samples Žlines are drawn as guides for the eyes..
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Fig. 6. The variation of e r with frequency for the glass–ceramic samples Žlines are drawn as guides for the eyes..
Fig. 8. The variation of e r with time for a x s 25 sample maintained at 683 K Žlines are drawn as guides for the eyes..
The frequency dispersion of the dielectric loss, tan d , is small Ž4 = 10y3 F tan d F 8 = 10y3 . for the glass samples. Fig. 7 which shows the frequency response of tan d , for the glass–ceramics of three representative compositions x of 15, 20, and 25, indicates that tan d of the glass–ceramic sample increases with increase in Bi 2 O 3 –V2 O5 content. The frequency dispersion of tan d is comparatively larger in the glass–ceramic samples than in the glass samples. The larger frequency dispersion of tan d in the glass–ceramics is attributed to the presence of the crystalline BiV phase dispersed in the glass matrix.
In fact, polycrystalline BiV, obtained by conventional ceramic route, has a frequency dispersion in both e r and tan d : e r Ž100 Hz. f 1600 and e r Ž100 kHz. f 90, tan d 100 Hz f 1.2 and tan d 100 kHz f 0.2. The crystallization of BiV in these samples was monitored in situ, by measuring e r as a function of time, for a glass maintained at 683 K. We observed that e r increases with increasing time ŽFig. 8.. The variation of e r with temperature, at various frequencies, for the glass–ceramic sample with the composition x s 25, is shown in Fig. 9. e r increases with increase in temperature at all the frequencies under
Fig. 7. The variation of tan d with frequency for the glass–ceramic samples Žlines are drawn as guides for the eyes..
Fig. 9. The variation of e r Žat different frequencies. with temperature for a x s 25 glass–ceramic sample.
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matrix. We confirmed that this exotherm is a consequence of the onset of crystallization of monophasic bismuth vanadate in the SBO glass. We attribute the endotherm at 803 K to the glass-transition temperature of the glass, which constitutes the matrix. The second exotherm in the DTA, indicates the onset of crystallization of SBO phase. The DTA, supported by XRD analysis, carried out on the samples heattreated at 683 K for 10 h, suggests that the time required for the process of BiV crystallization in SBO glass matrix is around 10 h.
Fig. 10. The optical transmission spectra of the glass–ceramic samples with composition x s15, 20 and 25.
study Ž100 Hz to 100 kHz.. A peak in e r is observed around 750 K, which is about 20 K higher than the phase transition temperature reported for crystalline BiV w11x. 3.5. Optical studies The optical transmissions Žuncorrected for scattering and other reflection losses. of the glass–ceramic samples with compositions x of 15, 20, and 25 in the wavelength range 500 to 2500 nm are depicted in Fig. 10. The optical transmissions of the glass– ceramic samples with compositions x of 25 and 20 are similar. The transmission decreases by more than half the maximum value below 1500 nm, continues to decrease in the entire range of 700 nm to 1500 nm and the transmission ceases beyond f 700 nm. The refractive indices of these glass–ceramics increase with increase in x. The refractive indices of the glass–ceramic samples with compositions x of 15, 20, and 25 are 1.86 " 0.02, 2.15 " 0.02, and 2.17 " 0.02, respectively.
4. Discussion 4.1. Crystallization of BiV in the glassy matrix of SBO The DTA data shows the occurrence of crystallization of a single phase around 683 K in the glass
4.2. Dielectric properties of the glass–ceramics The glass–ceramic samples, obtained in the present studies, have dielectric constants larger than those of the glass samples, owing to a contribution from crystalline BiV phase. The increase in e r with time, for the glass sample maintained at 683 K, is attributed to an increase in the fraction of the crystalline phase present in these samples. The crystallization process is complete in 10 h, as confirmed by the absence of a crystallization peak at 683 K in the DTA for the sample heat treated at this temperature for 10 h. Therefore, the further increase in e r after 10 h Žsee Fig. 8. is attributed to an increase in the volume fraction of the crystalline phase. The peak in e r , exhibited by these glass–ceramics ŽFig. 9., near the phase-transition temperature of crystalline BiV, is suggestive of their polar nature. The magnitude of the peak, which is smaller than that observed in the case of crystalline BiV, may be attributed to the presence of interpenetrating residual glass of lesser dielectric constant. The shift in the curie point ŽTc . may arise due to the effects of the elastic and the electrostrictive forces exerted by the surrounding glass matrix on the crystallites participating in the phase transition. It is interesting to note that the BiV crystallites embedded in the glass matrix exhibit a phase transition, unhindered by the presence of an interpenetrating glassy-phase of smaller e r . 4.2.1. Application of dielectric mixture formulae Dielectric mixture formulae are applied to predict the dielectric constant of the glass–ceramic samples containing bismuth vanadate crystallites, with dielec-
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tric constant, e 1 and volume fraction d 1 , dispersed in a strontium tetraborate glass matrix, with dielectric constant, e 2 and volume fraction d 2 Žs 1 y d 1 . has yielded accurate values. The validity of the prediction is demonstrated for a glass–ceramic sample with composition x s 25, in which the BiV phase Žwith dielectric constant, e 1 s 90 Žat 100 kHz.. occupies a volume fraction d 1 s 0.53. The glass matrix SBO Žwith dielectric constant, e 2 s 10 Žat 100 kHz.. occupies a volume fraction d 2 Žs 1 y d 1 . s 0.47. In the classical Claussius–Mossotti treatment of a mixture of dielectrics composed of spherical dielectric inclusions dispersed in a continuous loss less dielectric medium w20x, assuming that each inclusion is polarized in the same way as if others are absent, i.e., taking no account of interaction, the effective dielectric constant Ž eeff . of the composite is given by the expression:
eeff s e 2 1 q 3 d 1
Ž e1 y e2 . Ž e1 q 2 e2 .
Ž 1.
where e 1 and e 2 are the dielectric constants of the dispersed phase and the host matrix phase respectively and d 1 is the volume-fraction of the dispersed phase. The Claussius–Mossotti formula for a dispersion of spheres is given by Reynolds and Hough w21x as
eeff s
Ž 1 y d 1 . 2 e 22 q Ž 1 q 2 d 1 . e 1 e 2 . Ž 1 y d1 . e1 q Ž 2 q d1 . e2
Ž 2.
Using Reynolds and Hough’s adaptation of the Claussius–Mossotti formula, we calculate the dielectric constant Ž eeff . of the glass–ceramic sample to be 28.8 " 60.5 Žat 100 kHz., which is comparable with the experimentally measured number Žbased on capacitance measurements. of 29 " 0.5 Žat 100 kHz.. The agreement of the calculated and experimentally measured values may be due to the spherical shape of the crystalline inclusions, in the present case. When the dispersed phase occupies a significant volume fraction Ž) 0.25., the spacing between the dispersed crystallites is small, allowance for electrostatic interaction between the crystallites must be made, while modelling the dielectric behaviour. w22x and Bruggeman w23x incorporated interBottcher ¨ action effects by assuming, in the calculation of the effective polarizing field, that the spheres of dielec-
tric constant e 1 are immersed in a medium of dielectric constant eeff . The Bottcher–Bruggeman formula ¨ is given by Reynolds and Hough as two separate formulae, eeff y e 2 e1 y e2 s d1 , Ž 3a . 3 eeff e 1 q 2 eeff e 1 y eeff e 2 y eeff d1 q d2 s0 Ž 3b . e 1 q 2 eeff e 1 q 2 eeff where e 1 , e 2 and d 1 have the usual meanings and d 2 refers to the volume fraction of the host matrix phase. A similar formula has been proposed by Niesel w24x, 1 1r2 eeff s N q Ž N 2 q 8 e1 e2 . Ž 4. 4 where N s Ž3 d 1 y 1. e 1 q Ž2 y 3 d 1 . e 2 . Odelevski has demonstrated the validity of such a formula for a mixture of two dielectric constituents with large difference Žat least 1 order of magnitude. in their dielectric permittivity w25x. Application of Niesel’s formula is relevant in the present case as there is a large difference in the dielectric constant of the SBO glass matrix Ž e 2 s 10. and the dispersed BiV crystallites Ž e 1 s 90.. According to Niesel’s formula, the dielectric constant of the glass–ceramic sample is 39.88, which is much larger than the experimentally measured value of f 29 " 0.5 Žat 100 kHz.. The logarithmic mixture rule w26,27x, given by log eeff s d 1 log e 1 q d 2 log e 2 Ž 5. could also be applied to the present system. It predicts 32.04 for the glass–ceramic sample, which is larger than the experimentally measured value. The high resolution transmission electron micrographs of the glass–ceramic samples ŽFig. 4b and c. clearly demonstrate the presence of spherical crystallites dispersed in a continuous host matrix. This observation has prompted us to employ Maxwell’s model which describes a two-phase dielectric mixture comprising of spherical particles with higher dielectric constant dispersed in a matrix of smaller dielectric constant w28x. According to Maxwell’s model, the dielectric constant of such a composite is given by d 2 e 2 Ž 2r3 q e 1r3 e 2 . q d 1 e 1 eeff s . Ž 6. d 2 Ž 2r3 q e 1r3 e 2 . q d 1
M.V. Shankar, K.B.R. Varmar Journal of Non-Crystalline Solids 226 (1998) 145–154
As per this model, the calculated value of eeff is 28.8 which is close to the experimentally measured 29 " 0.5. Based on the close agreement between the predicted and the experimentally measured values, we propose that the dielectric properties of SBO–BiV glass–ceramics are adequately described by the Maxwell model. 4.3. Optical properties of the transparent glass– ceramics In explaining the effect of composition of the glass on the refractive index, we shall base our considerations upon theoretically proven relationships between molar refraction Ž R m . and refractive index Ž n., derived by Volf w29x, Lorentz w30x, and Lorenz w31x: Rm s
Ž n2 y 1. M Ž n2 q 2. r
Ž 7.
where n is the refractive index Žat 632.8 nm., r is the density and M is the molecular weight of the glass–ceramic sample. The importance of the molar refraction lies in its relationship to the structure of the glass. Molar refraction, R m , is proportional to the polarizability of the material, a m , according to the relationship,
am s
3 4pN
Rm
Ž 8.
where N is the number of polarizable ions per mole, assumed to be equal to Avogadro’s number. The value of R m and a m , evaluated using Eqs. Ž7. and Ž8. are: 29.9 " 0.1 cm3 moly1 and Ž11.85 " 0.01. = 10y2 4 cm3 for the glass–ceramic sample with x s 15 and R m s 37.5 " 0.1 cm3 moly1 and a m s Ž14.87 " 0.01. = 10y2 4 cm3 for the glass–ceramic sample with x s 25. The increase of polarizability is accompanied by an increase in molar refraction and hence by an increase in the refractive index. The refractive index was found to depend not only upon polarizability but also upon molar volume, Mrr ; it increases when the molar volume decreases, viz. when the structure gets denser. The compositional dependence of nonlinear optical properties of these glass– ceramics can be estimated by employing the empirical relation between the linear optical polarizability
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a opt and third-order NLO susceptibility Ž x 3 ., as proposed by Wang w32x. The relation between a m and x 3 is given by: 3
x 3 s CX Ž n2 q 2 . Ž n 2 y 1 . a m where CX is a constant, n is the linear refractive index and a m is the linear optical polarizability. The x 3 values for the SBO–BiV glass–ceramics, estimated based on the values of n and a m , indicate that the x 3 increases steadily with increase in Bi 2 O 3 – V2 O5 content. For instance, the x 3 value predicted for the glass–ceramic sample with x s 25 composition is nearly four times that of the sample with the composition x s 15. It has already been demonstrated w33x that the optical transmission properties of these glass– ceramics could be tailored by adjusting the BiV content. Studies are under progress to explore the possibility of enhancing the electro-optic response of these glass–ceramics, at wavelengths near the optical absorption edge.
5. Conclusions Precipitation of a crystalline phase of polar Bi 2VO5.5 was accomplished by the controlled heattreatment of glasses of the composition 2 x Bi 2 O 3 – xV2 O5 – Ž100 y 3 x .SrB 4 O 7 Ž15 F x F 25.. The experimentally determined dielectric constants of the glass–ceramics were fitted to various dielectric mixture formulae and these results are found to be in agreement with those predicted by Maxwell’s model. The optical properties of these glass–ceramics suggest that these novel glass composites are promising materials for nonlinear optical applications.
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