Review on structural, thermal, optical and ...

Review on structural, thermal, optical and spectroscopic properties of tellurium oxide based glasses for fibre optic and waveguide applications A. Jha*1, B. D. O. Richards1, G. Jose1, T. Toney Fernandez1, C. J. Hill2, J. Lousteau3 and P. Joshi4 This review focuses on the engineering of the structural, thermal, optical and spectroscopic properties of tellurium oxide (TeO2) glasses for their applications in fibre optic and waveguide devices. Unlike silica optical fibres, tellurium oxide glass fibres and light waveguides support propagation of light beyond y2 mm, where silica fibres become opaque. Silica fibres also have limited solubility for rare earth oxides due to silica’s structure, which is where tellurium oxide fibres and light waveguides can offer significant opportunities to engineer novel lasers and amplifiers for integrated optics. In this review, we compare the structural properties of TeO2 based glasses, modified by incorporating alkali, alkaline earth, and other oxide compounds. Based on Raman, UV, visible and infrared spectroscopic data, the structural aspects of tellurite glasses are discussed. The effects of compositional modification on the thermal and viscous flow properties are also compared and related with the resistance against devitrification. The significance of glass to crystal phase transformation during cooling and heating is explained in the context of preform and fibre fabrication. The review also reports on the characterisation of OH2 impurities in tellurite glasses. Recent developments in tellurite fibre lasers and femtosecond laser inscribed waveguide fabrication are discussed. Keywords: Tellurite, Glass, Fibre, Waveguides, Spectroscopy, Material characterisation, Photonics, Optics, Review

Introduction to tellurite glasses First discovered by Stanworth1 in 1952, the tellurite (TeO2) family of glasses are unique amongst oxide glasses, in which the main glass network is constituted predominantly of atoms of tellurium (Te) and oxygen (O), belonging to the group VIB in the periodic table of elements.2 This unique elemental combination from group VIB is manifested by the multi co-ordination of Te atoms in oxygen polyhedra, each of which carries a lone pair electron (LPE),3 and consequently contributes to a range of unusual spectroscopic, linear and nonlinear optical properties.4 For the last 20 years, the specific characteristic of TeO2 glass has been explored for 1

The Institute for Materials Research, Houldsworth Building, Clarendon Road, University of Leeds, Leeds LS2 9JT, UK Pilkington Technology Management Limited, Pilkington European Technical Centre, Hall Lane, Lathom L40 5UF, UK 3 Materials Science and Chemical Engineering Department, Corso Duca degli Abruzzi 2410129 Torino, Politecnico di Torino, Milano, Italy 4 Corporate Research Laboratory, Laird Technologies India Pvt Ltd, Unit-3, Fourth Floor, Navigator Building, ITPL, Whitefield Road, Bangalore560066, India 2

*Corresponding author, email [email protected]

ß 2012 Institute of Materials, Minerals and Mining and ASM International Published by Maney for the Institute and ASM International DOI 10.1179/1743280412Y.0000000005

spectroscopic and nonlinear optical properties for a range of applications in devices for light amplification and switching in optical communications networks.5–9 The large Te cation in oxygen polyhedra (pyramid, bipyramid and distorted pyramid) is also responsible for its extended multiphonon absorption edge beyond 4 mm in combination with the UV-visible cutoff edge in the region of 0?32–0?38 mm.4,7 The extended IR transparency in the TeO2 family of glasses is better than both germanium oxide (GeO2) and silicate (SiO2) glasses, as shown in Table 1.4,7,9 The tellurium oxygen bond is also responsible for its good thermal stability and corrosion resistance compared with the family of fluoride glasses.4 From Table 1, it is apparent that the corrosion resistance, determined by the solubility, of tellurium oxide is much better than that of fluoride and is comparable with GeO2 and highly alkaline silicates, but inferior to chalcogenide fibre materials. The low phonon energy (640–790 cm21 vibration bands for the trigonal pyramid, bipyramid and polyhedra) of tellurite glass is also attractive for designing near-IR and mid-IR lasers and amplifiers, and passive fibres for power delivery and sensor engineering. Worldwide interests in the engineering of fibre amplifiers emerged following the first significant results

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Spectroscopic properties of TeO 2 glasses

on the spectroscopic properties of rare earth ion doped fibres and bulk glasses reported by Wang and coauthors.4 Together with the analysis of spectroscopic and optical properties of rare earth doped tellurite glasses, Wang et al.4 also emphasised the importance of tellurite glass fibres for engineering ultra broadband amplifiers, which is not possible with standard rare earth doped silica fibres. This enhanced suitability of tellurite glass for applications in optical communications devices has been a major driver for research in this subject area since 1995. The first demonstration of an Er3z doped TeO2 glass fibre amplifier for multichannel amplification was at the NTT laboratory in Japan in 1997,5,6 which further accelerated worldwide interest7–9 for device engineering. In this review, we will discuss key applications in the section on ‘Applications of fibres and waveguides’ including those for optical communication. As is evident from the structural analysis of crystalline tellurium oxides, the LPE in the pyramid, bipyramid and polyhedron structures contribute to its large refractive index, and therefore affects the values of the Abbe number nD and nonlinear refractive index n2. The combinations of the optical, spectroscopic, physical and mechanical properties in Table 1 are attractive for developing both fibre and planar waveguide devices. ElMallawany10 authored a handbook on tellurite glass properties, which highlights the composition dependence of physical and optical properties. In this review, the objective is to discuss the control of material structure in fibres and waveguides, and their influence on device properties. The descriptions of structural, thermal and spectroscopic properties in the sections on ‘Introduction to tellurite glasses’ and ‘Optical properties of tellurite glasses’ are discussed in the context of fibre and planar waveguide engineering for optical signal amplification using the rare earth ions as dopants; laser engineering and the nonlinear parametric and Raman processes. The data compared in Table 1 show that tellurite fibres and waveguides can exhibit 25 times larger optical nonlinearity (n2) than either silicate or germanium oxides. Additionally, the materials engineering aspects of TeO2 glass leading to enhancements in laser gain and Raman amplification are also discussed.

1 Structural units in tellurite glass: TeO4 trigonal bipyramid (tbp) (left) and TeO3 trigonal pyramid (tp) (right)2,3

Glass formation, thermal and viscosity properties Glass formation and phase equilibria A vast majority of tellurite glass structure is based on its parent crystalline forms: the a and b allotropic forms, as described by Philippot,11 Sabadel et al.12 and CachauHerielatt et al.13 A number of investigations on the glass formation and structural analysis of binary and tellurite glasses have previously been reported.11–13 As described in literature,2,3,11–13 there are two basic structural units: TeO4 (trigonal bipyramid), TeO3 (trigonal pyramid), as well as the intermediate TeO3zd polyhedron. In a TeO4 unit, four oxygen atoms are coordinated with one tellurium atom to form a trigonal bipyramid (tbp) with one of the equatorial oxygen positions unoccupied, as shown in Fig. 1a. In the bipyramid structure, the two equatorial and two apical oxygen sites are called the bridging oxygens, whereas the third equatorial site is occupied by the LPEs in the valence band of tellurium. The LPE site is common to all three structural units, as shown in the trigonal pyramid (Fig. 1b) and polyhedron (not shown here). In the trigonal pyramid structure, there are two bridging oxygen sites and one nonbridging oxygen (NBO) which is a Te5O double bond.

Table 1 Comparison of optical, thermal and spectroscopic properties of various glass families for device applications4,7,9 (some values may vary slightly depending on specific glass composition) Properties Optical properties Linear refractive index n Abbe number n Nonlinear index n2 (m2 W21) Transmission range (mm) Phonon energy (cm21) Band gap (eV) Theoretical minimum fibre loss (dB km21) and loss minimum wavelength/mm Physical properties Glass transition Tg (uC) Thermal expansion (61027uC21) Density/g cm23 Dielectric constant Predominant bonding Chemical stability

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GeO2

Silica

Fluoride

Chalcogenide

1.9–2.3 10–20 2.5610219 0.4–5 780 3 20 (2.8–3 mm)

1.7–1.8 25–40 10219 0.38–5 880 3.5–4

1.46 80 10220 0.2–2.5 1100 10 0.2 (1.55 mm)

1.4–1.6 60–100 10221 0.2–7 500–630 9–11 ,1 (2.5 mm)

2–3.3 Higher 0.45–11 350 1–3 0.4 (6.5 mm)

280–480 120–170 5.5 13–35 Covalent Good

450 100–130 6.4 … Covalent Good

1000 5 2.2 4.0 Covalent Excellent

270–300 150–200 5.0 … Ionic Moderate

300–420 140–210 4.5 … Covalent Moderate

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Although a LPE is equivalent to an oxide (O22) ion, the site for an oxide ion and a LPE during glass formation may therefore interchange mutually with four bridging oxygen sites when a glass network forms, offering bond deformation and packing of structural units. This is a unique structural characteristic of TeO2 glass, distinct from other network-forming glasses; e.g. silicates, phosphates, borates and germanates in which only the NBO and bridging oxygen exist as a part of the structural unit. The LPE site, depending upon the availability of a cation, may therefore contribute to a range of Coulombic distortions, allowing both apical and equatorial oxygen bonds to deform preferentially along the direction of strongest electrostatic interaction. This may provide a range of chemical environments for cations, e.g. the rare earth ions. The cationic link with a LPE site is an essential element of understanding the glass formation in the multicomponent system. In the bipyramid structure along the equatorial triangle, the perihelion Te–O bonds are shorter in length (0?185 nm) than that of the aphelion Te– O bonds (0?195 nm). The axial Te–O bond lengths are the largest and depending upon the cationic charge may vary between 0?205 and 0?215 nm.2,3,11–13 The known glass forming systems, as reported by Vogel2 and El-Mellawany,10 include (Li, Na, K, Rb, Cs, Tl)2O, (Mg, Ca, Sr, Ba, Zn, Cd, Pb)O, (B, Al, Ga, In, Bi, Ln)2O3, (Si, Ge, Ti, Zr, Hf, Ce)O2, (P, As, V, Nb, Ta, Sb)2O5 and (Cr, Mo, W)O3. Here the symbol ‘Ln’ designates the rare earth oxides. Besides these oxides, sulphates and SeO2 are also known to form glass. Many multicomponent glass forming systems have also been reported by Mazurin et al. on the compilation of non-silicate glass forming systems.14 An extensive list of tellurite halide glass compositions with glass forming ranges and their corresponding measured densities and molar volumes are reported in literature.2,10,14 It is interesting to note that a large number of strongly covalent glass forming oxides (B2O3, P2O5, GeO2) and conditional glass formers (WO3, Nb2O5, V2O5, ZrF4, etc.) combine with TeO2 due to a significant difference between the electronegativity of the constituent cationic elements. For example, borates and phosphates exhibit glass formation between 0?5 and 20 mol% relatively easily,2,10,14 whereas only a few percent of silica dissolves in tellurite liquids, which limits the glass forming range. By comparison, the conditional glass formers, namely, the tellurite–tungstate, tellurite–vanadate, and their ternary derivatives have more than 15 mol% glass forming solubility range in WO3 to almost 50 mol% in V2O5.15,16 The incorporation of fluorides2,10 is especially interesting for controlling the residual OH2 content in these glasses, for engineering low OH2 containing glass for devices which is discussed below in sections on ‘UV and IR absorption and intrinsic loss in tellurite glass es’ and ‘Purification chemistry and glass preform fabrication’. Little information on binary tellurium oxide phase equilibria is available. Dimitriev et al.15 were first to report a phase diagram in the ternary TeO2–Na2O–V2O5 system and supported the evidence for structural association of vanadate and tellurite networks in the 2TeO2.V2O5–Na2O.V2O5.2TeO2 composition. In the glass structure, both VO5 and VO4 structural units are observed together with TeO3 (pyramid) and TeO3zd (polyhedron) and TeO4 (pyramid) structural units. Dimitriev et al.15 concluded that ‘contrary to the crystal


phases, in V2O5 containing glasses the transition from VO5, toward VO4, does not proceed through the formation of new structural units of vanadium; but rather a gradual transition of the structure is observed with a change in the composition from 2TeO2, V2O5 to Na2O.V2O5.2TeO2’. The mixed glass forming networks depict a range of properties as a result of compositional dependence of the properties. A detailed phase diagram analysis on the sodiumtellurite system was investigated by Zhu et al.17 in which the authors demonstrated that the glass formation is more prevalent between 10 and 25 mol%Na2O, in which range the complexes of sodium tellurite coexist by forming low temperature eutectics mixtures. The presence of glass forming liquid in the vicinity of a eutectic invariant in a phase diagram has been well known,18,19 and in this context, only very few binary tellurite glass forming systems have been fully characterised. Known examples in the literature are TeO2–B2O3 with significant liquid–liquid phase immiscibility in the binary system with a monotectic invariant point at 661uC (934 K).20 A partial TeO2–PbO phase diagram is reported by Paul,18 with a known glass forming region up to 20 mol%PbO, which is above the eutectic point at around 25 mol%PbO at approximately 460uC. The phase transformation in a sodium tellurite system was investigated by Zhu et al.17 using isothermal heat treatment and phase identification using X-ray powder diffraction. It was reported that the 8TeO2.Na2O (NT8) structure decomposes to 4TeO2.Na2O (NT4) and TeO2 via the eutectoid reaction (equation (1)) in the temperature range of 335¡5uC. 8TeO2 :Na2 O(solid)~4TeO2 :Na2 O(solid)z4TeO2 (solid) (1) The structural changes in binary and ternary sodium– vanadate and sodium–tellurite were studied,16 and were subsequently confirmed by Ivanova21 using the pseudo ternary system 2TeO2.V2O5–GeO2. The ternary eutectic composition was found to be between 40 and 50 mol%2TeO2.V2O5. In summarising the phase diagram analysis, we conclude that only a score of binary tellurite compositions, compiled in the Phase Diagram for Ceramists,22 and ternary maps10,14 are available. In Table 2, the eutectic temperatures and compositions in the binary and ternary tellurite glass forming systems are summarised.

Thermal stability and crystallisation properties of tellurite glasses The control of viscosity and crystal nucleation and growth is of paramount importance for minimising the extrinsic scattering loss due to the presence of crystals during glass preform and fibre fabrication. The scattering of light in the presence of crystals occurs due to the difference in the refractive indices of the matrix and the nucleating phase. However, if this index difference is minimised, then the scattering loss is minimal, and such materials are known as ‘transparent glass ceramics’ which often have a combination of properties related with both the glass matrix and nanoscale size crystals less than the wavelength of light (,100 nm). The applications of tellurite glass ceramic materials may be in thin film recording media23 such as compact disc


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drives, prompted by analysing the semiconducting properties of tellurium–vanadate glasses, reported by Flynn et al.;24 engineering of rare earth ion laser gain medium;25 and for frequency doubling via second and third harmonic generations.26,27 For data storage applications, the control of nucleation and crystal growth is essential for phase memory control, which is a manifestation of photo-induced phase transformation. For laser gain and second harmonic generation, the control of crystallites and orientation distribution respectively, is especially beneficial for maximising the gain.26,27 Besides the glass ceramic applications, the analysis of the temperature dependence of crystal nucleation and growth and viscosity is essential for the fabrication of fibre and planar waveguides. For the analysis of the thermal properties of materials, differential thermal analysers and differential scanning calorimeters are commonly used.28 Devitrification analysis may be performed both by isothermal and nonisothermal techniques, explained by Bansal et al.,29 with heating and cooling rates in the range of 2–500 K min21 in a differential scanning calorimeter applied. A systematic characterisation of the kinetics of devitrification was carried out by Liu et al.,30 using the methods described by Bansal et al.29 and Jordan and Jha.28 As an example, the glass transition and devitrification characteristics of two different families of glass forming systems: NZT [(902x)TeO2–10ZnO–xNa2O, x50, 10, 20 and 30)] and TZX [70TeO2–10ZnO–20X, X5ZnO, Li2O, Na2O and K2O] are reviewed in detail herein. The results for these two families of glasses are compared in Figs. 2 and 3, respectively. In a thermal scan, as shown in these two figures, we may be able to identify the following characteristic temperatures (K): the glass transition temperature Tg, the onset of crystallisation temperature Tx, peak temperature TP and the onset of melting Tm, which are often used to define the following glass stability parameters in equations (2a), (2b) and (3)31

DT~(Tx {Tg )

(2a)

DTp ~(Tp {Tx )

(2b)

S~

DT Tp {Tx DTDTp ~ Tg Tg

(3)

In general, the magnitude of a glass stability parameter indicates the resistance against devitrification and these were calculated and compared in Table 3. In Fig. 2, we find that with the increasing concentrations of Na2O in the NZT (902x mol%TeO2, 10 mol%ZnO, x mol%Na2O) compositions, the characteristic Tg and Tx temperatures decrease with respect to the X50 mol% composition. In order to have a meaningful understanding of the glass stability, additional stability parameters are required which have been especially defined in glass literature. In Table 3, a range of tellurite glass compositions are compared. From Table 3, we find that the absence of alkali (e.g. in N1 and RD1) tends to lower the thermal stability of a tellurite glass. By incorporating alkali oxide in the NZT and TZX families of compositions, the glass stability increases as determined by the values of the three stability parameters in equations (2a), (2b) and (3) in Table 3. Note that for N2, N3 and RD3, there are no values for DTp and S which imply that the exothermic peak for devitrification was negligibly small to account for any significant crystallisation. It is for this reason in Table 3 that ‘NF’ designates ‘not found’. It is evident that the presence of Na2O in the TZN glass system is essential for reducing the crystallisation tendency, however, when the TeO2/Na2O ratio approaches 2 : 1, the propensity for devitrification becomes greater, as can be shown from the data for N1…N4. A significant amount of evidence is borne out when the compositional

Table 2 List of binary and ternary tellurite glass forming eutectic compositions and temperatures10,14,18,19,22 Tellurite glass Eutectic compositions/ multicomponent system mol% of TeO2 TeO2–Na2O TeO2–Al2O3 TeO2–Er2O3 TeO2–Y2O3 TeO2–B2O3 TeO2–PbO

16.7, 28, 38 68.7, 85.0 97.5 98.5 y75, 5 75

458, 413, 420 650, 675 720 720 661, 432 460

TeO2–GeO2

67.0

685¡10

TeO2–MoO3

55.5

526

TeO2–P2O5

90.8

520

TeO2–VO2 TeO2–V2O5

80 y55, y75

625 475, 469

TeO2–V2O5–PbO

Ternary liquids 60 and 40 450–500 2mol%TeO2, 5–45 mol%V2O5 V2O5.2TeO2 and Na2O.V2O5.2TeO2 y415

TeO2–V2O5–Na2O

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Na2Te8O17, Na2Te4O9, Na2Te2O5 Al2Te3O9 Er2Te4O11 Y2Te4O11 Liquid–liquid immiscibility The melting points of PbTe4O9, PbTe2O5, Pb2Te3O8 and PbTeO3 are 585, 510, 605 and 560uC, respectively Metastable monotectic liquids exist above the eutectic temperature on the GeO2 rich side Congruently melting compound Te2MoO7 when cooled rapidly forms glass Te4P2O13, Te2P2O9, TeP2O7. There is the likelihood of a subeutectic immiscibility gap between 97 and 67 mol%TeO2 TeVO4 incongruent compound The Te2V2O9 phase melts congruently at 485uC, with a solid state phase transition at 323¡3uC Multiple binary compounds on PbO–TeO2 and Te2V2O9, and Pb2V2O7 Na2O.3V2O5.6TeO2

Jha et al.

2 Isochronal (10 K min21) heating rate curves for N1…N4 family of glasses: (902x)TeO2–10ZnO–xNa2O [x50 (N1), 10 (N2), 20 (N3) and 30(N4)] glasses. The characteristic temperatures are the glass transition Tg, end of glass transition T’g , onset of crystallisation Tx, peak of crystallisation Tp and onset of melting Tm observed during a typical isochronal scan

dependence of alkali containing zinc–tellurite and boron–tellurite glasses are analysed by the Raman spectroscopic technique, which is discussed below in the section on ‘Structural properties of tellurite glass’ and in literature.25,32 More recently, the thermal stabilities and devitrification kinetics of the sodium tellurite family of glasses, having a composition range: (1002X)TeO2–XNa2O (mol%), where X varied between 5 and 25 mol%, were reported.32 The largest value of S (54?0) was found to be for X510 mol%, which then decreased to 3?4 and 2?5 for X515 and 20 mol% respectively. Besides the S parameter, the thermal stability can also be defined using the Hruby parameter HR in equation (4) HR ~

DT DTm

(4)

where DTm5Tm2Tx, where Tm is the melting point of devitrified material in a heating ramp. The differential


3 A comparison of the isochronal differential thermal analyser curves for the N3 and RD series of glasses 70TeO2–10ZnO–20X [X5ZnO (N3), Li2O (RD1), Na2O (RD2) and K2O (RD3)] glasses

temperature DTm is a direct measure of the overall growth rate of nucleated crystals, and as its magnitude becomes smaller, the propensity for the growth of crystals diminishes with the square of the magnitude of DTm.33 For a sodium–tellurite composition, the highest value of HR was found for X520 mol%, which is why this composition was modified by incorporating 10 mol% ZnO. The influence of ZnO was analysed by Kozukraov et al.34 by identifying the structural conjugation of ZnO6 units with TeO4 bipyramids, for which there was no proof.35 The presence of small crystallisation peaks in NZT compositions, as shown in Figs. 2 and 3, is due to the presence of ZnO, without which the devitrification dominates in the binary sodium–tellurite compositions as shown by Joshi and Jha.32 This is why some of the isochronal curves in Figs. 2 and 3 are featureless. Similar featureless thermal scans for Na2O and K2O can also be compared in Fig. 3. Liu et al.30 and Joshi and Jha32

Table 3 Comparison of characteristic temperatures (K) Tg, T’g , Tx, Tp, DT, DTp and S for the TZN: (902x)TeO2–10ZnO– xNa2O (x50, 10, 20 and 30) and TZX: 70TeO2–20X–10ZnO (X5ZnO, Li2O, Na2O and K2O) and boron oxide modified tellurite (BT) families of tellurite glasses ID

Composition (mol%)

Tg

Tg’

Tx

DT

Tp

DTp

S

N1 N2 N3 N4 RD1 RD2 RD3 BT-90 BT-80 BT-70 BT-60 BT-50

90TeO2–10ZnO 80TeO2–10ZnO–10Na2O 70TeO2–10ZnO–20Na2O 60TeO2–10ZnO–30Na2O 70TeO2–30ZnO 70TeO2–10ZnO–20Li2O 70TeO2–10ZnO–20K2O 90TeO2–10B2O3z5000 ppm Er2O3 80TeO2–10B2O3–10ZnOz5000 ppm Er2O3 70TeO2–20B2O3–10ZnOz5000 ppm Er2O3 60TeO2–20B2O3–20ZnOz5000 ppm Er2O3 50TeO2–20B2O3–20ZnO–10Na2Oz5000 ppm Er2O3

570 557 532 506 590 538 514 585 608 623 625 592

607 593 559 530 610 573 538 … … … … …

681 659 640 618 705 665 619 694 712 715 700 670

111 102 108 112 115 127 105 109 104 92 75 78

708

27 NF* NF 22 14 24 NF 24 16 15 20 30

10.1 NF NF 10.6 5.1 11.5 NF 8.4 5.0 4.0 4.2 7.3

640 719 689 … 718 728 730 720 700

*NF: designates that the Tp was difficult to determine, since the exothermic peak was very small in comparison with the onset of crystallisation.


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studied the kinetics of devitrification of tellurite glasses in detail. By employing the Kissinger and Avrami models,36,37 the findings30,32 showed that the values of the overall kinetic barrier for devitrification in sodium– tellurite compositions range between 190 and 220 kJ mol21. The magnitude of the kinetic barrier for glass to crystal transformation is therefore another quantitative thermal stability parameter, used for defining and quantifying the resistance against devitrification. The data for the kinetic barrier together with the volume of crystals transformed may also be used for the computation of time–temperature transformation curves, for which there is a large amount of literature on the inorganic glass forming systems.31,38–40

derived from viscosity differ significantly from 392 to 795 kJ mol21. These are considerably higher than the apparent activation energy for devitrification discussed above, suggesting that the rate processes involved in the thermal relaxation between Tg and Tx are different and should always be referred with the temperature range. Undoubtedly, the fragility model43,46 for tellurite glass is a convolution of the complex activation processes between Tg and Tx, which by comparing with fluorides and silicates, appears to exhibit an ‘intermediate fragility’46 during thermal and viscous relaxation.

Viscosity in transformation range

The thermal expansion coefficients of the tellurite family of glasses are usually measured using a dilatometer48 or DMA, along with measurements of viscosity, mechanical strength and modulii of elastic constants. Using a PerkinElmer DMA 7, the thermal expansion coefficients of the tellurite glasses in Table 4 were measured and are compared with the glass transition temperatures. In Table 4, we have also computed the values of B for those compositions for which we only know the data for a. The values of B, according to the Williams–Landel– Ferry49 model, is equal to the product of the volume expansion coefficient (3a) and the glass transition temperature (53aTg). For the vast majority of silicates, according to Angell43 and the Williams–Landel–Ferry theory,49 the values of B approach 0?025, which was also found to be true for some of the fluorides, reported by Clare and Parker.48 The constant value of 0?025 at Tg signifies that the molar volume change in the majority of glasses are of the order of 0?025,50 which then determines the relaxation and viscous flow of vitreous materials at Tg. The viscosity of a glass above Tg is manifested by the Adam–Gibbs model,51 in which the molar volume vf has an Arrhenius type dependence on temperature given by equation (6) where go is a pre-exponential and nf is the molar volume change at a given temperature. Bo is a constant. Bo (6) g~go exp vf

During the reheating process above Tg, a glass begins to relax to a thermodynamically more stable state compared to its as quenched state. For determining the viscosity, the approach proposed by Nemilov41 using penetration viscometry, was adopted for a range of annealed tellurite glasses. Using the thermal analysis technique discussed above, the relaxation of a glass between the onset of glass transition Tg and the end of transition T’g can be characterised after a careful calibration of the baseline using standards. Moynihan42 derived an empirical relationship for a range of network forming oxide glasses, namely, silicate, phosphate, borate and germanate glasses. According to his model, the viscosity g in the transformation range is expressed as equation (5) 14:2 log10 g~{5z 2 0:147 T{T’g = T’g 1=Tg {1=T’g z1 (5) 43

Angell analysed a large family of glasses using equation (5), and showed the difference between a category of strong network glasses and those with weak or fragile networks. This important distinction is depicted by determining the slope of the viscosity against the reduced temperature (Tg/T) curves. Using Tg and T’g values summarised in Table 3 for different types of tellurite glasses and equation (4), the values of viscosities in the transformation range were computed and plotted against temperature in Fig. 4 for the NTZ and TZX families of glasses respectively. From Fig. 4a, it is evident that as the molar concentration of sodium oxide increases, the viscosity of TZN glass drops at a given temperature. The drop in the viscosity is also related to the increasing proportions TeO3 structural units, as explained using the data from Raman spectroscopy, discussed below in the section on ‘Structural properties of tellurite glass’. The slopes of the curves in Fig. 4a are comparable and seem to be almost parallel for each composition. By comparison, the compositional dependence of viscosities in Fig. 4b shows that at a given temperature, the TZX glass with zinc oxide has the highest viscosity, and that with K2O manifests the lowest viscosity. The compositional dependence of viscosities bear strong correlation to the relative proportions of TeO4 bipyramid, TeO3 pyramid and TeO3zd structural units, which will be brought together in a discussion at the end of the Raman spectroscopy section. The viscosity and thermal relaxation properties above Tg have also been investigated in detail by Zhu et al.43–46 and Zhang et al.,47 and the activation energy values

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Coefficients of thermal expansion of tellurite glasses

From equation (6), the larger the value of nf, the smaller the viscosity at a given temperature. In this respect, the expansion coefficient of a glass bears an important relationship with the viscosity, via the molar volume model originally proposed by Eyring52 and later on adopted by many investigators in the field of physics of liquids and glass science.

Structural properties of tellurite glass Raman spectroscopic analysis of tellurite glasses and glass ceramics A large body of Raman spectroscopic analysis of tellurite glasses is credited to Sekiya et al,53 who analysed the structural changes in binary and ternary tellurite glasses modified with the oxides of elements from groups IA to VIA and VIB.54–57 Using X-ray photoelectron and Raman spectroscopic techniques, Himei et al. also analysed the structures of TeO2 and binary sodium–tellurite materials.58,59 The complex tellurites, e.g. 4TeO2.Na2O, have large structural units, with sheet-like structures as reported by Tagg et al.60,61

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4 Viscosity versus temperature relationships in the transformation ranges of two families of tellurite glasses: a N series: (902x)TeO2–10ZnO–xNa2O (x50, 10, 20 and 30) glasses and b RD series: 70TeO2–10ZnO–20X (X5ZnO, Li2O, Na2O and K2O). The transformation range represents a temperature range between Tg and Tx

The two adjacent sheets are separated by a layer of sodium ions. Within the sheet, both the TeO4 and TeO3 link together and decrease the Te–Te distance (0?3165 nm), compared to the Te–Te distances in the b-TeO2 structures (0?317 nm). The sheet-like structure in 4TeO2.Na2O compares well with the sheets of sodium–tellurite–vanadate structure in Na2O.V2O5.2 TeO2.15,16 Within the vanadate–tellurite glass, the VO4 tetrahedron units link up with the TeO4 bipyramids, and the Naz ions reside between the sheets in a large coordination field of oxygen atoms, where the average coordination number may vary between 7 and 8. The structure of tellurite glass, in which the TeO3 and TeO4 units have lone pair electrons, offers bond deformation and flexibility by accommodating a range of small and large tetrahedron units from strongly

covalent glass formers, namely silicates, borates, phosphates and germanates.3 The solubility of silicates in tellurite in the absence of alkali ions is much smaller than when alkalis are present in more than 5 mol% concentrations. Vogel2 reported that the refractive indices of the binary and ternary glasses, which depend on the density of constituent oxides, vary in the range of 1?9–2?2 with a corresponding density range of 4?4– 6?0 g cm3. Empirical evidence shows that the accommodative character of trigonal bipyramid and pyramid combinations diminishes in terms of enhancing the structural packing density of tellurite glasses when larger octahedral units of tantalate and rare earth ions are present in the structure, as discussed in the phase diagram section in Table 2. From this table, we find that phase separation can occur in rare-earth doped binary

Table 4 Compositional dependence of coefficient of thermal expansion and glass transition temperatures in tellurite glasses:14 all compositions are in mol%; B53aTg TeO2

BaO

Bi2O3 PbO

68.13 58.92 50.03 63.5 31.4 33.41 69.27 66.64 80 80 75 75 70 70 65 65 60 80 73.07 65 80

… … … … 15.0 … 23.05 … 15 10 20 15 25 20 30 25 30 … … … …

… … … … … … … … 5 10 5 10 5 10 5 10 10 … … … …

16.24 14.04 16.62 22.2 … 16.65 … 16.68 … … … … … … … … … … … … …

WO3

MoO3 V2O5

As2O5 Nb2O5 Er2O3 B2O3 Na2O ZnO a/1027 K21 Tg/K B53aTg

15.63 27.04 33.35 … … … … … … … … … … … … … … … 16.76 … …

… … … 14.3 … … … … … … … … … … … … … … … … …

… … … … … … 7.68 … … … … … … … … … … … … … …

… … … … 53.61 49.94 … … … … … … … … … … … … … … …

… … … … … … … 16.68 … … … … … … … … … … … … …

… … … … … … … … … … … … … … … … … … 10.17

… … … … … … … … … … … … … … … … … … … 15 10

… … … … … … … … … … … … … … … … … 10 … 20 …

… … … … … … … … … … … … … … … … … 10 … … 10

151.2 125 127 180 135 140 145 115 … 173.9 … 159 … 100 … 187 179 185 112 221 173


586 627 … 588 558 … … … 617 600 622 613 630 621 639 644 659 558 705 582 608

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5 a A comparison of low frequency (Boson) Raman spectra in the 10–200 cm21 range for a range of N1…N4 glasses: (902x)TeO2–xNa2O–10ZnO (x50, 10, 20 and 30 mol%). lpump5514 nm. b Raman spectra in 10–200 cm21 range of (702x)TeO2–10ZnO–20X [X5ZnO, RD1 (Li2O), RD2 (Na2O) and RD3 (K2O)] glasses lpump5514 nm

tellurite glasses. In Table 5, the phonon energies of structural units present in a range of binary tellurite glasses are summarised with the vibrational assignments.

Raman spectroscopic analysis of tellurite glasses and glass ceramics Shen and Jha62 studied the structural changes in TeO2 glass which were measured and compared with compositions modified with different oxides. In the ternary 70TeO2–10ZnO–20X glass system, where X represents ZnO, Li2O, Na2O and K2O, the corresponding compositions are designated as N3, RD1, RD2 and RD3 respectively. In Figs. 5 and 6, the effect of sodium ions on the low (5–200 cm21) and high (300–1000 cm21) frequency Raman spectra for the sodium zinc–tellurite (902X)TeO2–10ZnO–XNa2O family of glasses is compared. By comparison, in Fig. 6, the effect of the size of alkali ions in the (902X)TeO2–10ZnO–XR2O glasses is analysed, which was pioneered and initiated by Sekiya et al.53–57 The depolarisation ratio is defined as r5IHV/ IHH, where IHV and IHH are the intensities of scattered radiation at an arbitrary frequency v in the HV and HH spectra. This ratio r is related to the symmetry of the

structural vibration units. From Fig. 5, it is evident that there is a small but discernible shift in the Boson (low frequency Raman) peaks when the effect of Kz ions are compared with those of Naz and Liz ions. The observed shift in peak positions to higher frequencies is consistent with the reduced mass m and force constant f relationship of a linear harmonic oscillator, having a fundamental mode as described in equation (7) 1 f 1=2 n~ (7) 2p m A similar trend in the peak positions is also observed in the optical phonon spectra shown in Fig. 6, for the cations considered above. In Table 6, the observed values of the Boson peak frequencies and the depolarisation ratios r at three different optical phonon frequencies are compared. From such a comparison, we find that the depolarisation ratio at the Boson peaks for ZnO and alkali containing tellurite glasses decrease in the following manner of magnitude of charge and ion mass: ZnO, Li2O, Na2O and K2O. Furthermore, since the alkali elements have identical charge, the decrease in

Table 5 Comparison of optical phonon frequency in binary tellurite glasses (compositions in mol%: N1: 90TeO2–10ZnO, N2: 80TeO2–10ZnO–10Na2O, N4: 60TeO2–10ZnO–30Na2O)* n/cm21 Assigned vibrational modes in TeO2 glass

a-TeO2 n/cm21

N1

N2

N4

Peak A: Stretching vibrations of Te–O in TeO3zd and TeO3 Peak B: Symmetric bending vibrations of Te–O–Te formed by sharing vertices of TeO4, TeO3zd and TeO3. The non-bridging Te–O nbo in TeO3zd, and Te5O nbo in TeO3 Peak C: Antisymmetric or coupled symmetric vibrations along Te–O–Te axes in TeO3zd/TeO4, TeO4/TeO3, and TeO3/TeO3zd pairs in the directions of apices and equatorial combinations of directions Peak D: Continuous network consisting of TeOn (n54, 3zd, 3) Peak E: Symmetric and bending vibrations of Te–O–Te linkages at corner sharing sites

773 716

778 730

768 717

793 765

659

664

657

681

611 450

591 440

601 421

582 450

*Maximum phonon energies (cm21) of oxides which are also conditional glass formers, as tellurite glasses: PO4 (1200), WO3 (910), BO3 and BO4 units (810, 1400), MoO3 (950), GeO2 (880).

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6 a A comparison of high frequency Raman spectra in the 300–1000 cm21 range for a range of N1…N4 family of glasses: (902x)TeO2–xNa2O–10ZnO (x50, 10, 20 and 30 mol%). lpump5514 nm. b Raman spectra in the 300–1000 cm21 range of (702x)TeO2–10ZnO–20X [X5ZnO, RD1 (Li2O), RD2 (Na2O) and RD3 (K2O)] glasses. lpump5514 nm

the values of r is due to the size of the cations, which increases from Liz to Kz. The effects of cationic size and charge are therefore consistent with the polarisation dependence of Raman intensities, especially in the acoustic phonon region. In the context of developing an understanding of the structure of sodium–zinc–tellurite glass, Joshi et al.63 analysed the results of Raman spectroscopy for such glasses which were modified with B2O3 to increase the non-radiative rates between the 4I11/2 and 4I13/2 levels in Er3z ions. Doping with B2O3 is particularly interesting considering that boron oxide containing glasses, depending upon the boron concentration, may have either a (BO3)32 dominated pyramid type structure, or a (BO4)52/ (BO3)32 tetrahedron/pyramid structure. The phonon energy spectra for the boroxyl ring (constructed from (BO3)32 pyramids) and the tetrahedron structures were studied in detail.64–66 The preponderance of (BO4)52/ (BO3)32 units as a function of alkali concentrations in the boron oxide glasses were studied by Krogh-Moe64 and Bray and O’Keefe67 which showed that the 4-fold coordinated boron concentrations increased monotonically for alkali modified glasses, except for the Liz modified structure where a maximum was observed at around 40 mol% of Li2O. The data analysis presented in literature64,67 is relevant for the analysis of boron-oxide modified tellurite glasses, shown in Fig. 7, where we see the high energy shoulder at around 808 cm21 is increasing with B2O3 composition in various glasses, listed in Table 3 as BT80…BT50 glasses. The optical phonon

peaks A to G, identified in Fig. 7, have been assigned with the same vibrational nomenclature as shown in Table 5.

Table 6 Boson peak frequency and depolarisation ratio r in 70TeO2–20X–10ZnO (X5ZnO, Li2O, Na2O and K2O) glass system62

7 Raman spectra of B2O3–TeO2 glasses when excited with a 633 nm laser. The range 900–1600 cm21 part is smoothened for five points and magnified by five times.63 At around 450 and 750 cm21 are two important Raman vibrational signatures which are strongly dependent on the sodium or alkali oxide concentrations. The intensity of bridging mode vibrations between 2 tbps at 450 cm21 reduces with increasing alkali, whereas the intensity of tp increases with alkali concentrations

Boson peak v¡1 cm21 r¡0.02 at Boson peak r¡0.02 at 455 cm21 r¡0.02 at 660 cm21 r¡0.02 at 780 cm21

ZnO

Li2O

Na2O

K2O

43 0.82 0.48 0.43 0.35

44 0.56 0.23 0.16 0.11

41 0.54 0.37 0.34 0.28

36 0.54 0.26 0.19 0.15


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8 Raman spectra of barium–bismuth–tellurite glasses

It is evident that the presence of B2O3 with alkali proportionately increases the peak intensities of optical phonon components with respect to the otherwise dominant 650 cm21 peak due to the symmetric and anti-symmetric structural vibrations of the structural units TeO4, TeO3zd and TeO3. Since the characteristic optical phonon frequencies for BO4 units is in the 1300– 1400 cm21 range, the evidence for the presence of such units was also examined, and it was concluded that the intensities due to BO4 units might be extremely weak, at least 20–25 times less intense than the boroxyl ring at 808 cm21. From Fig. 7, it becomes apparent that the minimum ratio of B2O3/Na2O required for boroxyl rings to dominate the boron oxide modified tellurite structure is B2O3/Na2O52 : 1. The preponderance of boroxyl rings thus seems to be consistent with the phase immiscibility observed in the B2O3–TeO2 phase diagram, discussed in Table 2. This implies that the structural continuity between the tellurite and the boroxyl networks might prevail through the alkali ions occupying the nonbridging sites in the vicinity of TeO4–TeO3zd–TeO3 and the boroxyl chain. The presence of ZnO in the BT family of glasses appears similar to that without boron oxide glasses, (N1…N4 compositions in Table 3), in which the ZnO4 tetrahedra may occupy sites between the LPE and NBO, as explained elsewhere.35 The characterisation of vibrational spectra using Raman spectroscopy is extremely beneficial for the engineering of tellurite glasses for a range of active and passive applications. For example, the substitution of ZnO and Na2O with Bi2O3 and BaO (BaF2) was analysed by Hill and Jha,68 as shown in Fig. 8, and demonstrated that such glasses are suitable for extended mid-IR transmission. The importance of compositional control in tellurite glasses for tailoring the Raman gain were also demonstrated.69–71 Between 20 and 40 times enhancement in the Raman gain coefficient in niobate, tungstate and tantalate modified tellurite glasses were observed, when compared with pure silica.69–71 For enhancing the solubility of rare earth ions, the tellurite glasses were modified with WO372 and P2O573 for thin film fabrication and further optical integration of waveguide circuits with polymer and semiconductor

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9 A comparison of Raman spectra for the annealed sodium–tellurite glass ceramic with a glassy composition 10 mol%Na2O–90 mol%TeO2. The pump excitation wavelength chosen was 633 nm

devices respectively. Vibrational spectroscopic data, together with thermal and spectroscopic properties, are detailed in literature.69–73 Besides vibrational spectroscopic analysis of tellurite glass structures, in this review article, we also present a comparison of Raman spectroscopic data for binary sodium–tellurite glasses and glass ceramic structures caused by phase transformation in the sodium–tellurite glass. This is discussed below to demonstrate the structure–property relationship for engineering Er3z ion gain media.25 To the best of our knowledge, there is no spectroscopic data in the glass literature which considers the influence of polymorphic phase transformation on the Raman spectra, and its consequential implication on the strength and line shape of a rare earth ion optical transition for device engineering. For such a comparison of Raman and X-ray spectra of a tellurite glass ceramic with the parent glass, we selected a composition with 89?5 mol%TeO2–10?0 mol%Na2O with 0?5 mol%Er2O3 which lies in the vicinity of a sodium–tellurite complex crystal, NT8 (Na2O.8TeO2), identified by Zhu et al.17 The glass composition is similar to the composition of the NT8 complex, which on reheating the sodium–tellurite glass might devitrify polymorphically and form NT8 crystals and may eventually decompose above 342uC by forming crystalline TeO2 and NT4 phases. Further confirmation of phase changes in the glass ceramic materials were studied25 using Raman spectroscopic analysis, (lex5633 nm), which is ideal for Er3z doped materials as there are no absorption peaks for the dopant at this wavelength. A significant difference in the optical phonon structure is evident in Fig. 9 between the two different ranges of annealing temperatures. The details of changes in Raman and X-ray spectra are discussed25 together with the doubling of the full width half maximum of the Er3z spectra at 1510–1650 nm and visible wavelengths. The properties of tellurite glass ceramics are interesting in terms of engineering laser gain and solid state light sources. The optical phonon spectra in the range 400– 780 cm21 in Fig. 9 appear to be strongly dependent on the heat treatment temperature. The Raman and the

Jha et al.

X-ray spectroscopic analyses agree well with the phase transformation studies by Zhu et al.17

Relationship between thermal stability and glass structure using Raman spectroscopy In this section, we attempt to introduce another way of examining the thermal and structural stability of tellurite glass networks by analysing the Boson peak data for a range of glass forming systems. In the Boson peak models for the vitreous networks,74–80 the presence of the peak represents the frequency distribution of inelastic scattering of low frequency phonons or the acoustic phonon modes. The model thus suggests that a wider frequency distribution of acoustic phonons represents a larger number of modes, supporting the weaker coupling between the modes for their propagation, and vice versa. Thus, a glass with a narrow width of acoustic phonon modes has a deeper vibrational density of acoustic phonon states, as compared with the shallower distribution function. The distribution of phonon states follows the Bose–Einstein energy distribution as a function of temperature.74,78 On the other hand, the peak of the acoustic phonon distribution curve yields the values of correlation length 2R (nm) which is the mean free path length between the subsequent scattering of low frequency phonons and is given by the Martin–Brenig model (equation (8))74 2R~

Vt pCvBP

(8)

In equation (8), the constant C and vBP are the velocity of light and peak frequency in wave numbers (cm21) of Boson distribution curve respectively. Vt is the transverse acoustic phonon velocity in the medium. The value of 2R derived from equation (8) is much larger than the average Te–O, Te5O and Te–Te distances in the structural units, and therefore, the values of 2R represents the average spatial (radius) distribution in the glass network, within which might exist an intermediate range order connecting all the short range order structural units for sustaining acoustic phonons. Thus, a smaller value of 2R represents a shorter mean free path length, and vice versa. In a tellurite glass of similar composition, the average sound velocity79 was measured and found to be in the range of 2?06105–3?46105 cm s21, which can be used as an approximation for the transverse velocity Vt for determining the structural correlation length 2R, as shown in Table 7, in which we have also compared the values of 2R for silica and related glass forming systems. The acoustic phonon velocities in silica and fluoride glasses were measured and found to be 3800 and 2100 m s21 respectively.80 The derived values of 2R


from equation (8) are of the order of 0?81 and 0?53 nm respectively which was reported by Almeida.80 Almeida pointed out that the length scales correspond to the bridging and dihedral angle distribution. He suggested that the larger values of 2R might correspond to extended intermediate range order. Since the 2R value of 0?81 nm in silica corresponds to the acoustic phonon mean free path length, which is nearly five times larger than the Si–O distance in the SiO4 tetrahedra, such an extended length scale may explain why such materials depict high viscosity and thermal diffusivity in comparison with any other inorganic glass systems.10 Since a significant component of the overall acoustic phonon propagation is supported via the shear modes, the magnitude of mean free path length or the structural correlation length, 2R, may be able to point out the shear mode interaction for viscous flow above glass transition temperature. Based on the estimated values of 2R in Table 7 for tellurite glasses, it is possible to propose that the length scales between 0?53 and 0?65 nm correspond to a volume, within which the various structural units of TeO2 with a range of configurations are present. The presence of different sizes of cations affects the values of the 2R length scales, and therefore, the estimated and measured viscosities in Fig. 4 and the thermal expansion coefficients in Table 4. In the case of the tellurite glasses described above, we find that the values of the constant B near Tg range from 0?019 to 0?035, which is the effective molar volume at the glass transition temperature. The comparison of B values in Table 4 suggests that the glasses with a higher degree of structural modification, i.e. those compositions with greater proportions of TeO3 and TeO3zd, as determined from the Raman spectroscopic analysis above in Fig. 5a–9, will in effect have larger free volume at Tg. This is because the TeO3 and TeO3zd units are less likely to bridge with the dominant TeO4 bipyramid structures and provide the required network continuity, which is evident when the overall alkali content of alkali–zinc–tellurite or alkali–boron–tellurite increases. The normalised Raman intensities of peaks at around 780 and 710 cm21 increase proportionately at the expense of the peaks at 650 and 450 cm21.35,62 It is for this reason that for the compositions with a larger proportion of TeO2 in Table 4 have values of B which are systematically lower than those with higher concentrations of alkali and alkaline earth oxides. This may explain why the NZT family of tellurite glasses have B values approaching 0?035. By comparison in Table 4, the BaO–Bi2O3 modified tellurite depicts a much lower value of B at 0?019. Also in Bi2O3, the Bi3z ions have

Table 7 Values of structural correlation length 2R in a sodium–zinc–tellurite ternary (902x)TeO2–xNa2O–10ZnO (x50, 10, 20 and 30) and alkali–zinc–tellurite 70TeO2–20X–10ZnO (X5Li2O, Na2O, K2O and ZnO) glass system x50 v ¡1 cm21 2R¡0.01 nm Alkali v ¡1 cm21 2R¡0.01 nm Silica80 Fluoride glass80

x510

x520

38 40 41 0.58 0.55 0.54 Na2O K2O Li2O 44 41 36 0.50 0.54 0.61 SiO2 glass Boson peak at cm21, 2R¡0.01 nm50.81 Fluoride glass Boson peak at cm21, 2R¡0.01 nm50.53

x530 42 0.53 ZnO 43 0.51


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any alkali–zinc–tellurite glasses, since nf!B. The mixed oxide glass formers, namely, WO3, MO3, and V2O5, with TeO2 also exhibit significantly lower values of B than in alkali and boron oxide modified tellurite glasses, suggesting that the presence of a second network former appears to reduce the effective molar volume.

Optical properties of tellurite glasses Refractive indices and dispersion characteristics of tellurite glasses

10 The relationship between gD and nD (Abbe number) for a range of tellurite glasses

octahedral packing, which might provide additional configurational rearrangement of TeO4 bipyramids, TeO3 pyramids, and polyhedral. Limited phase equilibrium data22 shows that there are potentially intermediate complexes in the bismuth and barium–tellurite binary mixtures which might reflect on the complex Coulombic interaction in the glassy structure. The estimated molar volume data B in Table 4 for Bi2O3– BaO and alkali–zinc–tellurite glasses suggest that in the transformation range, the glass viscosity from equation (6), will be much higher than that for the sodium or

The refractive index of tellurite glass is strongly dependent on the composition because of the polarisability of the constituent ions. The compositional dependence of the refractive index of tungsten–tellurite glasses are summarised in Table 8 below, compiled from literature,10,14 and shows the effects of monovalent, divalent, trivalent, and pentavalent oxides. The values of the refractive indices range from 1?932 to 2?304, and the corresponding values of Abbe number nD are between 23 and 14?4. The Abbe number nD of a material is defined in equation (9) where nD, nF and nC designate the refractive indices of tellurite glasses at the Fraunhofer wavelengths, (the D-, F- and C-spectral lines at 589?2, 486?1 and 656?3 nm respectively). nD ~

nD {1 nF {nC

(9)

Low dispersion (low chromatic aberration) tellurite glasses in Table 8 have high values of nD and vice versa. The dispersive properties, represented by the Abbe number, of tellurite glasses are plotted in Fig. 10, in

Table 8 Refractive indices and Abbe numbers of tungsten–tellurite glasses, which has been recompiled from data in literature10,14

368

Composition/mol%

nD

40TeO2–10Li2O–50WO3 15TeO2–30Li2O–55WO3 20TeO2–25Li2O–55WO3 64.17TeO2–4.23Tl2O–31.60WO3 68.60TeO2–6.54Tl2O–24.86WO3 69.58TeO2–16.30Tl2O–14.21WO3 78.45TeO2–11.24Tl2O–10.31WO3 79.60TeO2–3.85Tl2O–16.54WO3 83.33TeO2–13.67BaO–3.00CdO 83.33TeO2–10.67BaO–6.00CdO 83.33TeO2–13.67BaO–3.00ZnO 83.33TeO2–10.67BaO–6.00ZnO 83.33TeO2–7.67BaO–9.00ZnO 83.33TeO2–4.67BaO–12.00ZnO 83.33TeO2–1.67BaO–15.00ZnO 83.33TeO2–13.67BaO–3.00Sc2O3 83.33TeO2–13.67BaO–3.00Ga2O3 83.33TeO2–13.67BaO–3.00Y2O3 83.33TeO2–13.67BaO–3.00La2O3 83.33TeO2–13.67BaO–3.00Gd2O3 83.33TeO2–13.67BaO–3.00As2O3 72.13TeO2–3.85BaO–24.02WO3 69.44TeO2–7.41BaO–23.15WO3 79.34TeO2–4.76BaO–15.88WO3 83.74TeO2–5.66BaO–10.60WO3 63.77TeO2–4.82BaO–31.41WO3 82.70TeO2–8.65Bi2O3–11.04Nb2O5 47.55TeO2–17.07Bi2O3–35.38Nb2O5

2.046 1.971 1.932 2.1916 2.1801 2.1969 2.1955 2.1698 2.0835 2.0767 2.0819 2.0624 2.0530 2.0441 2.0358 2.0686 2.0480 2.0512 2.0706 2.0694 2.0866 2.0725 2.1143 2.1738 2.1507 2.1742 2.2362 2.3014


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nD

715.4 728.0 791.4 740.8 617.5 578.9 564.8 575.2 553.7 539.9 529.6 518.8 552.5 523.5 567.9 551.4 550.2 575.6 602.7 676.0 691.8 665.4 712.3 782.0 906.0

20 22 23 16.6 16.2 15.1 16.1 18.9 18.72 19.06 18.81 19.91 19.50 19.71 19.96 19.35 20.02 18.51 19.41 19.44 18.88 17.8 16.9 17.0 17.3 16.5 15.8 14.4

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refractive index with wavelength in equation (11) is negative, the value of ng for a given wavelength is larger than the leading wave, and therefore depicts a slower group velocity. The group velocity, from equations (10) and (11), can be expressed as equation (12) Vg ~

c c ~ ng n{lðdn=dlÞ

(12)

The refractive indices of the tellurite family of glasses are much larger than the silicates (1?45–1?52), which mean that the values of Abbe numbers ranging from 14 to 23 represent highly dispersive media. It should also be noted that the values of n in a high index medium are also dependent on the absorption k which represents the complex part of the refractive index (equation (13)) n~no zik 11 The wavelength dependence of the refractive indices of the TeO2–BaO–Bi2O3 family of glasses. In the legend, the numbers in figure legends correspond to the percentage molar concentrations of TeO2–BaO–Bi2O3. For example, the 80 : 10 : 10 represents a composition with 80 mol%TeO2, 10 mol%BaO and 10 mol%Bi2O3

(13)

The absorption k becomes dominant when n becomes large approaching absorption edges, where the index of refraction is given by the Kramers–Kronig relationship (equation (14))85 Dn(v’)~

c p

? ð 0

which the values of the Abbe numbers are plotted against the corresponding refractive indices, showing the inverse relationship between refractive index and dispersion. The phase velocity V in a medium is given by equation (10) and is dependent on the value of the refractive index, n, and the velocity of light in vacuum, c