Thermal expansion and structural properties of some (PbO)x(ZnO)35−x(TeO2)65 glasses

The glasses (PbO)x(ZnO)35−x(TeO2)65 with 0 < x < 25 were prepared by conventional melting method. The substitution of ZnO by PbO leads to a decrease in the glass transition temperature (Tg) from 338 to 280 °C and an increase in the linear coefficient of thermal expansion (α) from 15.8 to 19.2 ppm K−1. A correlation between α and Tg has been confirmed by the Lindemann rule. The two prediction methods of the coefficient of thermal expansion (α) were compared with experimental values: the simple additivity model and the Mackenzie method. From Raman spectra, it is evident that the substitution of ZnO by PbO leads mainly to the conversion of TeO4 structural units to TeO3 structural units. This conversion leads to network depolymerization.


Introduction
Glasses based on TeO 2 are of interest from the materials promising for development in telecommunication applications. Those have a wide glass-forming region, a wide spectral region of optical transmittance, a high refractive index, a relatively low temperature of preparation, and the ability to host rare earth elements [1][2][3][4]. For a recent review related to TeO 2 based glasses, see Ref. [5]. In recent years, some attention was given to the preparation and study of the glasses of PbO-ZnO-TeO 2 system modified by rare earth elements, see e.g. [1,6], and also to the study of optical properties and structural arrangement in various glasses PbO-ZnO-TeO 2 system, see e.g. [7][8][9][10]. Despite some reservations to PbO due to its potential risk for an environment in several cases its application in glasses preparation gives still some benefits. For instance: (1) The addition of lead oxide to glass raises its refractive index and lowers its working temperature and viscosity. PbO based glasses have also acceptable corrosion properties and low processing temperatures. Even if a higher temperature of preparation is necessary, no darkening/coloration is observed while in Bi 2 O 3 glasses if melted close or above 1000 °C a darkening is observed due to termoreduction of Bi 2 O 3 entities [11].
(2) One advantage of PbO based glasses is also a possibility to omit alkaline oxides which, due to a possible motion of alkaline ions in the electrical field, leads to instability of electrical properties of those glasses [12].
From a recycling point of view, lead-containing waste glass can be used to produce anti-radiation materials or it can be decomposed into individual substances/elements that can be reused to produce new materials [16].
In Ref. [10] we examined the role of substitution of ZnO by PbO on the glass transition temperature (T g ), the optical band gap (E g ), and the structural arrangement inferred from the Raman spectroscopy. It was found that substitution of ZnO by PbO leads to a decrease in the T g and E g values, the density of Pb-O-Te linkages increases at  the expense of the density of Te-O-Te  Since there are several indications that PbO-ZnO-TeO 2 glasses have various interesting properties, we mentioned above, promising for potential application, this paper is devoted to the study of selected glasses from the system (PbO) x (ZnO) 35−x (TeO 2 ) 65 which complement the glasses studied in Ref. [10]. The main aim of this work is determination of the coefficient of the thermal expansion (α TMA ) and the structural arrangement inferred from the Raman spectroscopy results.

Materials and methods
The studied materials (PbO) x (ZnO) 35−x (TeO 2 ) 65 , where x = 0; 5; 10; 15; 20 and 25 mol%, were prepared in batches of 20 g from oxides PbO, ZnO, and TeO 2 (purity > 99.9%; SIGMA-ALDRICH) in Pt crucible with a Pt lid. The stoichiometric amounts of oxides were mixed and inserted into a preheated electrical furnace at a temperature (T) 600 °C. The temperature was increased in the following step to melting temperature T ≈ 650-750 °C (depending on the chemical composition of the mixture). The obtained melts were homogenized for approximately 30 min. and after was poured onto a polished nickel plate preheated at 200 °C and then was cooled down to ambient temperature. The obtained glasses were annealed for one hour at a temperature close to their glass transition temperature (T g ). The glasses prepared were clear, slightly yellow with a shiny surface and the absence of XRD patterns confirmed the glassy nature of the samples prepared. The density (ρ) of the glasses was determined using the Archimedean method and distilled water was used as the referent liquid. The molar volume (V m ) was calculated according to the relation: V m = M/ρ, where M is the average molar weight of the glass. The values of ρ and V m were determined with a relative error ± 0.5%. The values of the dilatometric glasstransition temperature (T g ), the dilatometric deformation temperature (T d ), and the coefficient of thermal expansion (α TMA ) were estimated employing a thermo-mechanical analysis of the samples. The cubes of glasses 5 × 5 × 5 mm were heated at a heating rate of 5 K min −1 under 10 N force loading (TMA CX04 equipment, R.M.I. Pardubice, Czech Republic). The values of T g were determined with relative error ± 0.5%, T d and α TMA values were determined with relative error ± 1.5%.
Raman spectra were measured at room temperature on the natural shiny surface of the bulk samples with a Horiba-Jobin Yvon LaBRam HR Spectrometer. The spectra were recorded in back-scattering geometry under excitation with Nd-YAG laser radiation (532 nm) at a power of 10 mW taking 10 scans with an exposition time of 2 s. The spectra were reduced using the Shuker-Gammon relation [17] and their intensities were normalized. Reduced and normalized spectra were decomposed using LabSpec 5 software (Horiba Jobin Yvon).

Coefficient of the thermal expansion (α)
In the relevant literature, the methods proposed for the prediction of α values were derived especially for silicate glasses, see e.g. [18][19][20][21][22][23][24]. We have used two methods for the studied tellurite glasses: 1. The simple additivity model, see e.g. [24] which is a linear combination (LC) of the α values of oxides forming the glass. The coefficient of the thermal expansion of glass is given by the relation: where i is the volume fraction and α i is the value of the thermal expansion of the i-th oxide of a glass. The values of α i for relevant oxides are tabulated in Table 1. 2. Mackenzie method (M) was developed by Mackenzie, Makishima and Yaman, see e.g. [25]. This method relates the values of α to several properties like the packing density of mass particles present and their bond strengths. In the method of Mackenzie, Makishima, and Yaman, the expression for the coefficient of the thermal expansion of a glass (α M ) is given by the relation [25,26]: where ρ is the experimental density; V t is packing density; r M is ionic radius of metal; r O is ionic radius of oxygen (1.35 × 10 -10 m); f B,I is fraction of the number of bonds in i-th oxide; c p,i is specific heat; f i is molar fraction of oxide; k is constant (23.9); e V,i is dissociation energy related to 1 mol; M r is relative molecular mass.
Packing density V t is function of V c m : where V i is the factor of the spatial packing of the relevant oxide and V mi is the molar volume of the i-th oxide of the glass. The fraction of bonds in i-th oxide f B,i is done: where m M is the number of cations in oxide (M m O n ); y i is coordination number of element M (in i-th oxide), B t is the total number of metal-oxygen bonds in a concrete glass For a calculation of the linear coefficient of the thermal expansion by LC and M-methods, we used the literature parameters [26][27][28][29][30] summarized in Table 1.   Table 1. A quite small increase in V m may be associated with the fact that at a lower PbO content, Pb could mainly be incorporated into the empty space of a glass network and hence it behaves rather as a network modifier. The Zn 2+ ions usually connect the chain ends, hence the ZnO substitution with PbO, up to about x = 25 mol%, where PbO acts mainly as a network modifier [31], leads to a further network depolymerization and to a decrease in the T g and T d values as    Table 2. The values of RD (V m ) and RD (ρ), are smaller than 1%, although they rise with an increase in PbO content, see Table 2.

The glass transformation temperature and coefficient of thermal expansion
The values of the glass transformation temperature (T g ), the deformation temperature (T d ), and the linear coefficient of thermal expansion (α TMA ; for the temperature range of 100-200 °C) are collected in Table 3. As evident with the increasing content of PbO replacing ZnO, the values of T g and T d decrease and the values of α TMA simultaneously increase. The calculated values of α M and α LC differ from the experimental values α TMA in the range of − 14.58 to +11.39%, while the average relative deviation of the Mackenzie method is + 5% and the method of linear combination is − 11%. It is obvious that for investigated glasses the prediction methods used are the limiting ones, as documented in Fig. 1. We suppose that at a low concentration of PbO up to 5-10 mol%, this one is modifier only and in the concentration region 5-20 mol% PbO acts in both its roles, i.e. modifying and network forming [10].
A correlation between the linear coefficient of thermal expansion and the glass-transition temperature was explained e.g. in Ref. [32] with the help of the Lindemann rule. There are also some indications that both the linear coefficient of the thermal expansion and the glass-transition temperature can be correlated with the cohesive energy of a network, see e.g. Refs. [33,34], respectively. For simplicity, as a measure of the cohesive energy of our glasses network, we use the average single bond strength (B) of the glass, see e.g. Ref. [35]. Here

Raman spectra
The Raman spectra of the glasses studied are shown in Figs. 3 and 4 is shown and the typical decomposed spectrum of (PbO) 15 (ZnO) 20 (TeO 2 ) 65 glass. The compositional dependence of the relative band intensity (rbi) for the studied glasses is shown in Fig. 5. The bands assignment is summarized in Table 4.
In Fig. 5 is shown compositional dependence of the relative band intensity (rbi) for studied glasses.   It is evident that rbi at 786 cm −1 decreases while rbi at 738 cm −1 increases. The changes in rbi are inverse and seem to be correlated since rbi 786 + rbi 738 varies in a narrow region from 57.6 (x = 0) to 60.9 (x = 25). Hence, the substitution of ZnO by PbO similarly as in the other TeO 2 glasses [9] leads to a conversion of TeO 4 and or TeO 3+1 units (trigonal bipyramids-tbp) to TeO 3 units (trigonal pyramids-tp). Contrary to changes in rbi 786 and rbi 738 , the changes in the other Raman band intensities are quite subtle. The rbi at 670 cm −1 increases while the rbi at 618 cm −1 , Fig. 2 Dependence of the glass transition temperature (T g ; relative error ± 0.5%) and linear coefficient of the thermal expansion (α TMA ; relative error ± 1.5%) on the average single bond strength. For better clarity, the experimental values of α TMA are multiplied by 10  Table 3. The quite small increase in rbi 335 and rbi 112 with an increase in PbO content is of interest. We assume that the Raman band at around 335 cm −1 and its rbi increase mainly reflects the formation of some Te-O-Pb linkages. The Raman band at around 112 cm −1 has in all probability a dual origin. Usually, in Pb containing oxide glasses the Raman response at around 100 cm −1 is attributed to the vibration of Pb atoms respectively to the vibration of Pb 2+ ion, see e.g. [39,40]. This band was observed, however, for our glass where x = 0 ((ZnO) 35 (TeO 2 ) 65 ). Jaba et al. [41] found similar rbi in (ZnO) 30 (TeO 2 ) 70 glasses and it is tentatively attributed to a symmetric stretching vibration of Te-O. It should be noted that Raman activity at around 112 cm −1 could in all probability also be attributed to the librational modes of TeO 4 units [42]. The exact assignment of this Raman band in the studied glasses needs further study. An increase in rbi 112 with an increase in PbO content and simultaneous decrease in ZnO content indicates, however, that this Raman band for x > 0 can also be attributed to the vibration activity of Pb atoms. The results obtained are in harmony with our recent results [10] except for the compositional trend in rbi 600 . In both recently studied glasses (PbO) x (ZnO) 30−x (TeO 2 ) 70 and (PbO) x (ZnO) 40−x (TeO 2 ) 60 the rbi 600 slightly increases with an increase in PbO content. We do not currently have a reasonable explanation for this discrepancy.

Conclusions
The thermal expansion coefficient (α) and structure of (PbO)x(ZnO)35-x(TeO 2 )65 (0 ≤ x ≤ 25) glass system were studied. The possibility prediction of α was studied using two methods: the simple additivity model and the Mackenzie method. The increasing content of PbO leads to an increase in α and a decrease in the glass-transition temperature. A correlation between these through the cohesive energy of a network was verified. The Raman spectra show on depolymerization of the TeO 2 glass network with increasing concentration of PbO, which primarily acts mainly as a glass modifier in the concentrations used.
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