Journal of Non-Crystalline Solids 357 (2011) 3648–3653

Contents lists available at ScienceDirect

Journal of Non-Crystalline Solids

j ourna l homepage: www.e lsev ie r.com/ locate / jnoncryso l

Processing and characterization of transparent TeO2–Bi2O3–ZnO glass ceramics

Xiao Hu a, Guillaume Guery a, J. David Musgraves a,⁎, Don VanDerveer b, Joshua Boerstler a, Nathan Carlie a,Peter Wachtel a, Simon Raffy c, Roger Stolen a, Kathleen Richardson a

a School of Material Science and Engineering, Clemson University, Clemson, SC, USAb Department of Chemistry, Clemson University, Clemson, SC, USAc Department of Chemistry, Université Bordeaux 1, France

⁎ Corresponding author.E-mail address: jdm047@clemson.edu (J.D. Musgrav

0022-3093/$ – see front matter © 2011 Elsevier B.V. Adoi:10.1016/j.jnoncrysol.2011.06.032

a b s t r a c t

a r t i c l e i n f o

Article history:Received 7 May 2011Received in revised form 23 June 2011Available online 29 July 2011

Keywords:Tellurite glass ceramic;Transparent;Infrared optical property

Fabrication of TeO2–Bi2O3–ZnO glass ceramics with high transmittance in the near infrared (NIR) region isreported in the present work. Transparent tetragonal bipyramid crystals, tens of micrometers in size, with arefractive index closely matched to that of the glass matrix were formed using a two-step heat treatment.Nucleation- and growth-like curves for this crystal phase were determined using Differential ScanningCalorimetry (DSC). The crystalline phases present in the glass ceramics were identified via x-ray diffraction asa function of heat treatment. The lowest absorption coefficient of glass ceramic is approximately 0.5/cm in thenear infrared region (1.2 to 2.8 μm).

es).

ll rights reserved.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Due to their high transmittance from the visible to mid-infraredspectral regions, high refractive index, and non-linear opticalproperties such as second harmonic generation (SHG), telluriteglasses have received much attention in recent years and areconsidered promising materials for a variety of optical devices suchas optical switches, optical fibers and storage devices [1–3]. Adrawback to these materials is their lower mechanical stabilitywhen compared to other oxide glasses; one method to improvemechanical strength is through for formation of a glass ceramic bynucleating and growing a crystal phase in the base glass network.

Compared to the base glass, a glass ceramic containing crystalswith sizes between nanometers and micrometers can often havehigher strength, lower dielectric loss, and a lower coefficient ofthermal expansion [4]. However, the formation of these crystals in theglass matrix tends to decrease the optical transmittance because oflight scattering at the glass/crystal interface due to the refractiveindex mismatch between the phases. Two approaches can beemployed to obtain high-strength glass ceramic materials whilemaintaining high optical transmittance: the first is to reduce the sizeof the crystallites formed in the glass to well below the wavelength ofthe incident light, and the second is to form crystal phases which havea refractive index closely matched to that of the parent bulk glass [4].The present work reports results realized for a tellurite glass ceramicin the TeO2–Bi2O3–ZnO system which exhibits high transmittance inthe near-infrared region despite the formation of crystals with sizes

on the order of tens of micrometers. These crystals are tetragonalbipyramid in shape, highly uniform in size, and appear transparentwhen observed using a polarizing optical microscope, indicating asmall refractive index difference between the crystalline and glassphases. The optical properties of the glass phase, crystal phase, andthe combined glass ceramic are reported. The crystalline phase wasidentified by X-ray diffraction and the crystallization kinetics, used tounderstand crystallite formation and growth, were studied usingDifferential Scanning Calorimetry. These measurements allowednucleation- and growth-like curves for the glass system to bedetermined. Using these data, glass ceramic materials were preparedand their properties measured. High transmission in the infraredspectral region and potential optical functionality resulting from thecrystallization steps employed makes glass ceramics within thissystem promising for a variety of applications such as opticalcommunication and storage devices [5–7].

2. Experimental

Glasses with composition of 74TeO2–12Bi2O3–14ZnO were pre-pared using high purity raw materials: TeO2 (Alfa Aesar, Tech,99.999%), Bi2O3 (Alfa Aesar, Tech, 99.999%) and ZnO (Alfa Aesar,Tech, 99.0%). The raw materials were premixed and then melted in aplatinum crucible at 850 °C for 15 min. The glassmelt was then cast ona brass plate which had been pre-heated at 285 °C. Following casting,the glass was annealed at 285 °C for 8 h. A two-step heat treatment,described in detail below, was used to nucleate and then grow thecrystals in the glass matrix. Following this heat treatment, the glassceramic samples were cut and given an optical polish for furtherinvestigation.

Fig. 1. DSC thermogram of the base glass with composition 74TeO2–12Bi2O3–14ZnO.

3649X. Hu et al. / Journal of Non-Crystalline Solids 357 (2011) 3648–3653

All the characteristic temperatures of the base glass weremeasured with a Differential Scanning Calorimeter (DSC 2920, TAinstruments Inc) at a heating rate of 20 °C/min over the temperaturerange of 25–550 °C.

An improved understanding of the nucleation and the growthprocesses of the crystal phase is vital in controlling the crystallizationparameters used to obtain uniform, index-matched crystals. Therelative kinetics of these processes as a function of temperature isgiven by the nucleation- and growth-like curves [8] for the base glassunder controlled thermal treatment. The nucleation- and growth-likecurves for the glass composition of interest were determined usingthe method proposed by Marotta et al. and demonstrated by Masseraet al. [9,10] in a similar TBZ glass composition. The nucleation-likecurve for the 74TeO2–12Bi2O3–14ZnO glass composition was deter-mined using a Simultaneous DSC-TGA (SDT 2960, TA Instruments).For each data point obtained, 40 mg of glass was heated in the SDT inan open platinum pan at a rate of 20 °C/min, in order to minimize thepossibility of the formation of nuclei during the heating cycle, andthen held isothermally at the test temperature for 30 min with theexpectation that the number of nuclei formed in the glass at the testtemperature is dependent on the temperature of the soak. The shift ofthe maximum of the exothermal peak, as compared to the position ofthe peak when measured without the isothermal hold process,reflects the number of nuclei formed in the glass at this testtemperature. The temperature of the maximum of the exothermicpeak, Tp, in the thermogram was determined for each testtemperature.

The nucleation rate can be estimated by the following equation:

Ln I0ð Þ = EcR

1T

p

− 1T0p

!+ C ð1Þ

where I0 is the steady state nucleation rate and Ec is the activationenergy for crystallization, which represents the minimum amount ofenergy needed to initiate the crystallization reaction, R is the gasconstant [10], Tp is the maximum of the exothermic peak at a giventest temperature, and Tp

0 is the maximum of the exothermic peak withno nucleation hold. Therefore, by plotting (1/Tp−1/T0p) as a functionof temperature T, the nucleation-like curve can be obtained. This is notthe true nucleation curve as the constant C remains unknown.

The growth-like curve of the 74TeO2–12Bi2O3–14ZnO glasscomposition was measured with a Differential Scanning Calorimeter(DSC). Approximately 40 mg of glass, in a hermetically sealedaluminum pan, was heated from room temperature to a potentialgrowth temperature, T, at a heating rate of 20 °C/min. This ramp upwas followed by an isothermal hold for 5 min at a potential growthtemperature, the hold at this test temperature is designed to grow theextant crystals and increase the crystal fraction present in the matrix,which will be reflected in a decrease in the area of the crystallizationfeature, finally the temperature was ramped down to below the glasstransition temperature, Tg. The growth-like curve is obtained byplotting dA=A−AT as a function of temperature, where A is the areaof the exothermic peak of the thermogram of a glass powder whichdoes not undergo this isothermal hold, and AT is the area of theexothermic peak with the isothermal heat treatment described above,again, the variation of exothermic peak area (dA) reflects the extent ofcrystallization in the glass.

The transmittance of the base glass and the glass ceramics in thenear-infrared region was measured using Magna-IR 560 FourierTransformed Infrared Spectrometer from Nicolet. The system waspurged with dry N2 for 30 min before use to remove atmosphericwater and CO2 from the sample chamber. Then the absorptioncoefficient in NIR region was calculated based on the transmittance ofthe glass and glass ceramic samples considering the reflection at thesample surfaces. The refractive indices of the glass and glass ceramics

from 600 to 1100 nm were measured using an M-44 WVASESpectroscopic Ellipsometer (J. A. Woollam Co., Inc) with a resolutionof 10 nm.

X-Ray Diffraction (XRD) measurements were performed at roomtemperature on the glass and glass ceramic samples using Cu Kαradiation (Rigaku ULTIMA IV In.) at 40 kV and 40 mA. The XRDpatternswere comparedwith International Centre for Diffraction Data(ICDD) files to assess the crystal phases nucleated and grown in theglass ceramics resulting from the prescribed heat treatments.

A Nikon Type 115 polarizing optical microscope was used toinvestigate the microstructure of glasses and glass ceramics. Bright-field images of the glass ceramic were recorded by a CCD camera. Theboundaries of the crystals on the focal plane were found using aMatlab program, and the areas enclosed by these boundaries werecalculated. The volume fraction of the crystals in the bulk was thenestimated from the area fraction of the crystals on the focal plane.

Scanning electron microscopy (SEM, Hitachi S-3400) was used toinvestigate the morphology of the crystalline phase in the glassceramics. The glass ceramic sample was etched in a 12.1 molar HClsolution for 1 min at room temperature before SEM investigation toprovide improved contrast during imaging.

3. Results

The characteristic temperatures of the base glass were obtainedfrom the DSC thermogram, which is shown in Fig. 1. The glasstransition temperature, Tg, was taken as the inflection point of theendotherm (obtained by taking the minimum of the first derivative ofthe curve), the crystallization temperature, Tp, is the maximum of theexothermic peak, and Tx is defined as the onset temperature of thecrystallization peak. ΔT is defined as the temperature differencebetween the glass transition and the onset of crystallization. Thesecharacteristic temperatures of the base glass are shown in Table 1, theaccuracy of the measurement was estimated to be ±2 °C.

The nucleation- and growth-like curves of the 74TeO2–12Bi2O3–

14ZnO glass are shown in Fig. 2. The lines connecting the measuredpoints are included only as a guide to the eye. In the nucleation-likecurve, the nucleation rate reaches a maximum at 360 °C, thendecreases after 360 °C because of the increased activation barrier fornucleation [4]. In the growth-like curve, the growth rate reaches itsfirst peak at around 350 °C and increases dramatically when thetemperature is higher than 370 °C.

Based on the nucleation- and growth-like curves, several two-stepheat treatments were used to form glass ceramics from the basetellurite glass. Glass ceramic (GC) sample 1 was heated at 340 °Cfor 17 h, then at 345 °C for 18 h; GC sample 2 was heated at 330 °C for18 h, then at 350 °C for 18 h; GC sample 3 was heated at 340 °C for

Table 1Characteristic temperatures of the base glass.

Characteristic Temperature Tg Tx1 Tp1 Tx2 Tp2 Tx3 Tp3 ΔT

°C±2 °C 324 355 368 372 381 428 456 31

3650 X. Hu et al. / Journal of Non-Crystalline Solids 357 (2011) 3648–3653

17 h, then at 350 °C for 18 h. Following these controlled heattreatments, the bulk glass ceramic remains transparent, as shown inFig. 3.

Optical microscopy images of the glass ceramics showing theevolution of the crystal phasewith treatment temperatures are shownin Fig. 4. As seen in the microscope images in Fig. 4, in each glassceramic sample crystals with uniform size were dispersed in the glassmatrix homogenously. Crystal volume fraction was estimated, usingthe method described above, to be 1%, 5% and 10% for glass ceramic(GC) sample 1, sample 2 and sample 3, respectively. The averagecrystal sizes are 20, 50 and 60 μm for GC samples 1, 2 and 3. Thecrystals, which have tetragonal bipyramid morphology, are transpar-ent in the optical microscope, which indicates a small refractive indexdifference between crystalline and glass phases.

Glass ceramic sample 3 was etched in a 12.1 molar HCl solution for1 min at room temperature for SEM observation, the micrographs ofwhich are shown in Fig. 5(a). The same area on the sample surfacewasalso investigated using an optical microscope, as shown in Fig. 5(b).The black area is the surface of the etched crystal, and the gray area isbase glass. It was observed that when etching the glass ceramicsurfaces, crystals were etched faster than the base glass afterimmersed in the acid solution. This indicates that the chemicalstability of the crystals is lower than that of the base glass in this acidsolution. The tetragonal bipyramid morphology of the crystals can beseen clearly after etching, and the average size is about 60 μm.

X-ray diffraction experiments were carried out using Cu Kαradiation for glass ceramics which had been heat treated at differenttemperatures to identify the crystal phases produced as a function oftemperature, these XRD patterns are shown in Fig. 6.

The XRD patterns were compared with ICDD data files andliterature sources [11–13] to identify the crystalline phases present.Fig. 6(a), (b) and (c) correspond to the glass ceramic (GC) samples 1,2, and 3 which were shown in Fig. 4. In all three of the GC samplesBi0.864Te0.136O1.568 is the only crystal phase detected. Considering theheating process of GC 1, 2 and 3, this crystal type corresponds to thefirst crystallization peak in Fig. 1 (Tx1=355 °C, Tp1=368 °C). In Fig. 6(d), the glass was heated at 330 °C for 20 h, then 350 °C for 40 h, thesame heat treatment temperatures as those used for GC sample 2shown in pattern (b), but with the crystal growth time prolonged to40 h. The glass ceramic remains transparent, and the main crystal

300 350 400 450

0

20

40

60

80

100

120

140

0

20

40

60

80

100

120

140

dA

(m

W)

1/T

p-1/

Tp0

(x1

0-5 °

C-1

)

Temperature (°C)

Nucleation-like curve Growth-like curve

Fig. 2. Nucleation and growth-like curves of 74TeO2–12Bi2O3–14ZnO glass.

phases are Bi0.864Te0.136O1.568 and ZnO (ICDD PDF #13-0311), thecrystal size reaches about 100 μm. The difference between patterns(d) and (b) indicates that ZnO appears as a second crystal phase whenthis composition is held at 350 °C for sufficient time; In Fig. 6(e), theglass is totally devitrified after heating at 370 °C for 20 h, the maincrystal phase is Bi2Te4O11 (ICDD PDF #81-1330) with a secondaryBi0.864Te0.136O1.568 phase (ICDD PDF #38-0865), indicating theevolution of the crystal phases in the glass matrix as a function oftemperature. The formation of Bi2Te4O11 and Bi0.864Te0.136O1.568

crystal phases may correspond to the second crystallization peak inDSC curve shown in Fig. 1 with Tx2=372 °C and Tp2=381 °C.

The transmittance of the base glass and glass ceramic samples wasmeasured from 3500 to 8000 cm−1 (1.25 to 2.85 μm) using a FourierTransform Infrared Spectrometer. Samples were ground to a thicknessof 2 mm and then optically polished. The transmission spectra areshown in Fig. 7. The highest transmittance of the base glass is 75%,while that of glass ceramic sample 1 is 69%, sample 2 is 65% andsample 3 is 43%. Compared with base glass, the decrease oftransmission in GC sample 1 and sample 2 is less than 15%.

To estimate the refractive index of the crystalline phases, therefractive indices of a glass ceramic and the base glass were measuredusing Spectroscopy Ellipsometery. Glass ceramic (GC) sample 3 waschosen to be compared with base glass because of its highest crystalvolume fraction which is approximately 10%. Refractive indices of tenpoints on the sample surface were measured, and the average valuewas calculated. The result is shown in Fig. 8.

4. Discussion

An improved measure of the real crystal growth rate was obtainedby subjecting glass samples to varying heat treatments andmeasuringthe sizes of the crystals formed. These results demonstrate that boththe nucleation and growth processes are much faster at 360 °C than350 °C: these experiments show that the crystals can grow to 50 μm in3 h at 360 °C, giving a crystal growth rate of approximately 0.3 μm/min, while it takes 18 h at 350 °C for the crystals to reach 50 μm,giving a growth rate of approximately 0.05 μm/min; this result is inagreement with the nucleation- and growth-like curves shown inFig. 2. However, simultaneously high nucleation and growth rates alsomake the crystallization process difficult to control and can lead touncontrolled devitrification. In addition, higher heating temperatureslead to the formation of multiple crystal phases, as shown in the XRDpatterns in Fig. 6. Based on these facts, the nucleation temperatures of330 and 340 °C, with associated growth temperatures of 345 and350 °C were employed, and the influence of these treatmenttemperatures on the crystallization behavior was studied.

Among the three glass ceramic samples, sample 2 was treated atthe lowest nucleation temperature, 330 °C, leading to a low density ofcrystals compared to the other samples shown in Fig. 4. As thenucleation rate is determined by the treatment temperature [4], ahigher temperature will result in a higher nucleation rate, and whenthe heating time is fixed, will lead to higher density of nuclei. Duringthe growth step of the heat treatment, sample 1 was heated at a lowertemperature than samples 2 and, as shown in Fig. 4(a), the crystalsproduced in sample 1 have a diameter of approximately 20 μm, whichis much smaller than those present in sample 2 (50 μm) and sample 3(60 μm), confirming that the growth rate and resultant crystal sizewill increase as the function of the growth temperature. In summary,for this TBZ glass ceramic, the number density and the size of thecrystals are controllable via heating treatment temperatures.

To obtain glass ceramics with high transmittance, reduction oflight scattering during propagation is a critical issue. One method toreduce light scattering is to reduce crystal sizes below the wavelengthof the incident light, typically implying nano-sized crystals; in thiscase the losses due to light scattering can be estimated by Raleigh–Debye theory [14]. Another method to reduce light scattering is to

base glass GC sample 1 GC sample 2 GC sample 3

340°C 17h

330°C 18h340°C 17h

Fig. 3. Glass and glass ceramics in 74TeO2–12Bi2O3–14ZnO system glass ceramic.

(b)1

200µm

Sample 2

(b)2

Sample 2 50µm

(a)2

50µmSample 1

(a)1

200µm

Sample 1

Sample 3

(c)2

50µm

(c)1

200µm

Sample 3

Fig. 4. Optical microscope images of glass ceramic samples: (a)1 and (a)2 are images of GC sample 1 captured with 5× objective and 50× objective, respectively; (b)1 and b(2) areimages of GC sample 2 captured with 5× objective and 50× objective, respectively;.(c)1 and (c)2 are images of GC sample 3 captured with 5× objective and 50× objective,respectively.

3651X. Hu et al. / Journal of Non-Crystalline Solids 357 (2011) 3648–3653

(b)

(a)

50µm

50µm

Fig. 5. (a) SEM image of GC sample 3 after etched in 12.1 mol/L HCl for 1 min, (b) microscope image of the same area on GC sample 3 after etched in 12.1 mol/L HCl for 1 min.

3652 X. Hu et al. / Journal of Non-Crystalline Solids 357 (2011) 3648–3653

produce crystals with a refractive index closely matched to that of theglass matrix. As seen in Figs. 4 and 5, the crystals sizes are much largerthan thewavelength of the incident light, meaning that Raleigh theorycannot be applied to this system, and the non-spherical shape of thecrystals cannot be ignored because of their large size, meaning thatMie theory, which focuses on scattering by spherical particles, is alsonot suitable for this situation [15]. Therefore the impact of lightscattering has been estimated by geometrical optics. The scattering inthe glass ceramic is primarily the result of reflection at the interfacebetween the glass matrix and the crystals. The orientation of the

Fig. 6. XRD patterns of glass ceramics in the 74TeO2–12Bi2O3–14ZnO system underdifferent heating treat conditions. XRD patterns (c), (d), (e) correspond to the glassceramic samples 3, 2, 1 shown in Fig. 4. ×−−——— Bi0.864Te0.136O1.568; ○—————ZnO;●———Bi2Te4O11.

crystals is distributed randomly throughout the matrix, implying thatthe incident angle of the light at the interface will be similarlydistributed, so the reflection is expressed by the following equa-tion [16]:

R =12

sin2 i1−i2ð Þsin2 i1 + i2ð Þ +

tan2 i1−i2ð Þtan2 i1 + i2ð Þ

" #ð2Þ

where R is the reflection at the interface between crystalline and glassphases, i1 is the incident angle of the light at the interface, and i2 is therefracted angle. This relation implies that in the glass ceramicsstudied, if the refractive indices of glass and crystalline phases areclose, i1 and i2 will be close, and the reflection R will be small. Smallreflection implies low levels of light scattering during propagation inthe glass ceramic, decreasing the attenuation. Therefore, it can beconcluded that when the crystal size and distribution in the glassceramic is fixed, if the refractive indices of the glass and crystallinephases are close, the scattering will be limited, and it will lead to smallattenuation and thus high transmission of light in glass ceramics.

The refractive indices of the base glass and glass ceramic sample 3are shown in Fig. 8. The refractive index of the base glass and glassceramic sample 3 at 632 nm are 2.11 and 2.13, respectively, and at1064 nm they are 2.08 and 2.09, respectively. The refractive indexdifference between base glass and glass ceramic sample 3 is less than0.03. The linear refractive index of the crystal phase can be estimatedusing the lever rule [17]:

ngc = xnc + yng ð3Þ

where ngc is the refractive index of the glass ceramic, nc is therefractive index of the crystal phase, ng is the refractive index of the

Fig. 7. Transmittance and calculated absorption coefficients of the base glass and glass ceramic (GC) samples from 3500 to 8000 cm−1.

3653X. Hu et al. / Journal of Non-Crystalline Solids 357 (2011) 3648–3653

glass phase, x is the volume fraction of crystalline phase, and y is thevolume fraction of glass phase.

Using the data obtained from glass ceramic sample 3, Fig. 8, andassuming the volume fraction of the crystal phase is 10%, estimatedfrom Fig. 4, the refractive index of the crystals is calculated to be 2.3 at632 nm and 2.2 at 1064 nm. The refractive index difference betweencrystalline and glass phase at 632 nm is about 0.2, at 1064 nm is about0.1. As analyzed above, the compatible refractive indices of glass andcrystals lead to small scattering and therefore high transmission.

The transmission spectra of glass and glass ceramics in NIR region,shown in Fig. 7 above, can be used to calculate the absorptioncoefficient of the glass and glass ceramics. As tellurite glasses exhibit ahigh refractive index, the reflection at the surface is typically high andcannot be ignored, therefore, the absorption coefficient can becalculated based on the following equations [16]:

α = −1tln

T1−Rð Þ2 ð4Þ

R =n−1n + 1

� �2ð5Þ

where α is the absorption coefficient of the sample, T is thetransmission of the sample, R is the reflection on the sample surfaces,n is the refractive index, and t is the thickness. Using these equations,the absorption coefficient α can be calculated considering the

Fig. 8. Refractive index of base glass and glass ceramic sample 3.

reflection of the incident light at the sample surfaces, this result isalso shown in Fig. 7.

In Fig. 7, for GC sample 1, the absorption coefficient isapproximately 0.5/cm, while that for GC sample 2 is roughly 0.9/cm,both are very close to that of the base glass. The absorption coefficientof GC sample 3 is higher than that of the base glass, about 2.8/cm. Itcan be seen that as the crystal volume fraction in the glass ceramicsincreases, the attenuation of light increases, indicating that lightscattering by the crystals is the main source of loss during the lightpropagation in the glass ceramics, therefore, to reduce the light loss inorder to apply these glass ceramics in fiber devices, crystal size anddistribution should be well controlled.

5. Conclusion

In summary, glass ceramics in the TeO2–Bi2O3–ZnO system withhigh transparency in NIR region were obtained, optical propertieswere characterized, and the crystal phases under different heatingtemperatures were identified. With high transparency in NIR anduniform crystal phase, this glass ceramic could become a goodcandidate for various IR optical devices.

Acknowledgements

Funding support for this work has been provided by the USNational Science Foundation (NSF AWARD #0807016).

References

[1] Tanaka Katsuhisa, Narazaki Aiko, et al., J. Non-Cryst Solids 203 (1996) 49–54.[2] G. Senthil Murugan, E. Fargin, et al., J. Non-Cryst Solids 344 (2004) 158–166.[3] Jonathan Massera, Nucleation and Growth of Tellurite based glasses suitable for

Mid-Infrared Application, PhD dissertation, Clemson University, US, 2009.[4] Robert H. Doremus, Glass Science, 2nd edition John Wiley & Sons, 1994.[5] A. Jha, P. Joshi, S. Shen, Opt. Express 16 (2008) 13526–13533.[6] Kazuhide Shioya, Takayuki Komatsu, et al., J. Non-Cryst. Solids 189 (1995) 16–24.[7] M. Niyaz Ahamad, et al., J. Non-Cryst. Solids 355 (2009) 1517–1520.[8] Chandra S. Ray, Kisa S. Ranasinghe, Delbert E. Day, Solid. State. Sci 3 (2001)

727–732.[9] A. Marotta, A. Buri, F. Branda, J. Mater. Sci 16 (1981) 341–344.

[10] J. Massera, J. Remond, J. Musgraves, M.J. Davis, S. Misture, L. Petit, K. Richardson, J.Non-Crys. Solids 356 (2010) 2947–2955.

[11] Gy. A. Lovas, I. Dodony, et al., J. Solid. State. Chem. 135 (1998) 175–181.[12] Masai Hirokazu, Toda Tatsuya, et al., Appl. Phys. Lett 94 (1–3) (2009) 151908.[13] E.I. Sayed Yousef, A.E. Al-salami, et al., J. Mater. Sci 45 (2010) 5929–5936.[14] S. Hendy, Appl. Phys. Lett 81 (2002) 1171–1173.[15] Robert W. Hopper, J. Non-Cryst Solids 70 (1985) 111–142.[16] Born Max, Wolf Emil, “Principles of Optics”, Seventh Edition the University Press,

Cambridge, 2002 with correction.[17] Sakamoto Akihiko, Yamamoto Shigeru, Jpn. J. Appl. Phys 45 (2006) 6969–6973.