A TEM study and non-isothermal crystallization kinetic of tellurite glass-ceramics

The theoretical basis for interpreting DTA results is provided by the formal theory of transformation kinetics as developed by Johnson and Mehl [13] and Avrami [14]. This theory describes the evolution with time, t, of the volume fraction crystallized, χ, in terms of the crystal growth rate u;where N ₀ is the number of pre-existing nuclei per unit volume, n and m are kinetic exponents, which depends on the dimensionality of the crystal growth. In the considered case, “site saturation” [15], the kinetic exponent is n = m. Assuming an Arrhenian temperature dependence for \( u = u_{0} {\text{e}}^{{E/RT^{\prime}}} \), and a heating rate, \( \beta = {\frac{{{\text{d}}T}}{{{\text{d}}t}}} \), Eq. 1 becomes:where E is the effective activation energy for crystal growth. By using the substitution \( y^{\prime} = {\frac{E}{{RT^{\prime}}}} \), the integral, I, can be represented, according to the literature [16], by the sum of the alternating series:

Considering that in this type of series the error produced is less than the first term neglected and bearing in mind that in most crystallization reactions \( y^{\prime} = \frac{E}{RT} \gg 1 \) [usually \( {\frac{E}{{RT^{\prime}}}} \ge 25 \)], it is possible to use the first term of this series, without making any appreciable error, and the above-mentioned integral becomes:if T ₀ = T (where T ₀ is the starting temperature) so that y ₀ is infinite. This assumption is justifiable for any thermal treatment that begins at a temperature where crystal growth is negligible, i.e., below the glass transition temperature, T _g [17].

Substituting Eq. 3 into Eq. 2, the volume fraction crystallized in a non-isothermal process is expressed as:where \( Q = g \cdot N_{0} \cdot \left( {\frac{R}{E}} \right)^{n} , \) a general expression for all values of the parameter n, which, as it is well known, in the case of “site saturation” depends on the mechanism of the crystal growth.

With the aim of calculating the kinetic parameters, the crystallization rate has been obtained by deriving Eq. 4 with respect to time, yielding:which has been assumed that the reaction rate constant is a time function through its Arrhenian temperature dependence. The maximum crystallization rate is found by making \( {\frac{{{\text{d}}^{2} x}}{{{\text{d}}t^{2} }}} = 0 \), thus the relationship:where the subscript, P, denotes the magnitude values corresponding to the maximum crystallization rate. Assuming the above-mentioned hypothesis \( {\frac{E}{{RT_{P} }}} \gg 1 \); the logarithmic form of Eq. 7 is written as:which is the equation of a straight line, whose slope and intercept give the activation energy, E, and the pre-exponential factor, \( q = Q^{{\frac{1}{n}}} \cdot K_{R} , \) respectively.

On the other hand, the quoted assumption, \( {\frac{E}{{RT_{P} }}} \gg 1, \) according to Eq. 4–6, allows us to express the maximum crystallization rate by the relationship:which makes it possible to obtain for each heating rate a value of the kinetic exponent, n. The corresponding mean value may be taken as the most probable value of the quoted exponent.

Glasses in the system (100 − x)TeO₂–5Bi₂O₃–xZnO and (100 − x)TeO₂–10Bi₂O₃–xZnO where x = 15, 20, 25 in mol% were prepared by mixing specified weights of raw material. Mixed batches were melted in gold crucible at 850 °C for ~30 min. The melt, which had a high viscosity, was cast at 700 °C in a graphite mold. Subsequently, the sample was transferred to an annealing furnace and kept for 2 h at 300 °C. Then, the furnace was switched off and the glass sample was allowed to cool. Samples for measurements of optical properties using DTA (Shimadzu DTA 50) curve of powdered specimen of about 30 mg were recorded in air at heating rate 3, 5, and 10 K min⁻¹, respectively, in Pt-crucible and using the same amount of Al₂O₃ as reference material in the range between 20 and 650 °C. The glass transition temperatures (T _g) is a selected as mid-point between the onset and the minimum temperature, where T _c is measured at the onset of crystallization, the T _p is measured at the peak of crystallization.

X-ray diffraction (XRD) investigation were carried out in Siemens D 5000 using (CuK_α radiation) diffractometer at 40 kV and 40 mV setting in 2θ range from 10° to 90°. The crystallized phases were identified by comparing the peak position and intensities with those in the JCPDS (Joint Committee on Powder Diffraction Standards) date files. The volume crystallized sample was studied by TEM (Hitachi H8100) using 200 kV and optical sample was coated with carbon for TEM study. Optical microscopy (OM) investigation were performed in Zeiss Optimas equipped with Nikon Coolpix 4.0 MP digital camera.

Homogeneous and transparent glasses were prepared in the system (100 − x)TeO₂–5Bi₂O₃–xZnO and (100 − x)TeO₂–10Bi₂O₃–xZnO, where x = 15, 20, 25 in mol%. Differential thermal analysis (DTA) investigation was conducted on the as-cast prepared glasses. Figure 1 shows that, the glass transition temperature increase with increasing ZnO content, and also it increases with increasing Bi₂O₃ content in the glass matrix. T _g as a function of composition can reveal a transformation of the glass structure. We expect that, ZnO and Bi₂O₃ break down the TeO₄ network structure creating TeO₃₊₁ and TeO₃ phase built in the glass matrix that results in the structural rearrangements of the glasses due to the transfer of the bridging oxygen into elongate bridging oxygen and non-bridging oxygen. The values of bond Te–O have four different kinds; Te–NBO_ax, Te–NBO_eq, Te–BO_ax, and Te–BO_eq, which is due to NBO with axial position, NBO with equatorial position, BO with axial position, and BO with equatorial position. This explains why, the glass transition temperature increase with both increasing ZnO and Bi₂O₃ content in the network glass TeO₂/Bi₂O₃/ZnO. Figure 2a illustrates the respective DTA thermograms of as-cast 70TeO₂–10Bi₂O₃–20ZnO glass sample scanned at heating rate of 10 °C/min. The glass transition (T _g), the two peaks crystallization temperature (T _p1 and T _p2), and melting temperature (T _m) are marked on the thermograms. As seen in Fig. 1, DTA scan exhibits a small exothermic peak corresponding to the glass transition (T _g), and two exothermic peaks corresponds to the formation and/or transformation of crystalline phase. Onset crystallization temperature (T _c) and peak temperature of crystallization (T _P) is given in Table 1. Figure 1b depicts the DTA traces for the first crystallized peak of 70TeO₂/10Bi₂O₃/20ZnO at β = 10 K/min, besides the fraction, χ (crystallized at a given temperature T) given by χ = A _T/A, where A is the total area of the exothermic peak between the temperatures, T _i (the onset of crystallization) and T _f (the full crystallization). A _T is the area between T _i and T. The graphical representation of the crystallized volume fraction shows the typical sigmoid curve as a function of temperature for different heating rates for the first crystallization curve 70TeO₂/10Bi₂O₃/20ZnO (Fig. 2a, b) based on mentioned work elsewhere [18, 19]. Figure 3 shows the plots \( \ln \left( {{\frac{{T_{\text{g}}^{2} }}{\beta }}} \right) \) versus \( \left( {{\frac{1}{{T_{\text{g}} }}}} \right) \) for the glass powder displaying the linearity of the equations used. The values of the activation energy obtained for the glass transition are 460.7 kJ mol⁻¹. The crystallization maximum temperature is observed to increase with the increase in heating rate (see Table 1). The crystallization maximum in DTA scans corresponds to the temperature at which the rate of transformation of the viscous liquid into crystals becomes maximum. This means that, the number of nucleation site is increased by using slower heating rates and the peak maximum will occur at a temperature which the melt viscosity is higher at lower temperature.

The ratio between the ordinates of the DTA curve and the total area of the peak gives the corresponding crystallization rates, which makes it possible to build the curves of the exothermal peaks depicted in Fig. 4a, b. It was observed that, the values of (dx/dt)_p increase with the increase in the heating rate. From the experimental values of the (dx/dt)_p, one can calculate the kinetic exponent n from Eq. 9 . The value of kinetic exponent, n, for both the phases at each of the experimental heating rates is given in Table 1. The value of n depends on the mechanism of the transformation reaction.

Plot \( \ln \left( {{\frac{{T_{P}^{2} }}{\beta }}} \right) \) versus \( \left( {{\frac{1}{{T_{P} }}}} \right) \) for crystallization of the glass is shown in Fig. 5. A linear plot indicates the validity of Kissinger method [17]. The activation energy for crystallization of first phase is 305.8 kJ mol⁻¹, and second phase is 197 kJ mol⁻¹ (see Table 2).

In order to fabricate 70TeO₂–10Bi₂O₃–20ZnO glass-ceramic, we applied heat treatment condition which led to the precipitation of crystalline phases. On the basis of DTA results, X-ray diffractometry scans were carried out to verify the nature of crystallizing phases in the glass network at temperature above T _g for prepared glasses. The XRD patterns for this sample at different heating temperature are shown in Figs. 6, 7. First, the 70TeO₂–10Bi₂O₃–20ZnO glass tempered at 350 °C for 3 h [see Fig. 6 (chart a)] and 350 °C for 4 h [see Fig. 6 (chart b)], it has one crystalline phase Bi_3.2Te_0.8O_6.4 (ICDD card: 00-049-1761). The important Bi_3.2Te_0.8O_6.4 was of the best solid-state oxygen ion conductors. Also, the X-ray diffractogram estimates that the same crystalline phase appears in our prepared glass tempered at 375 °C for 1.5 h [see Fig. 7 (chart a)]. When the prepared glass tempered at 375 °C for 3 h, two phases Bi_3.2Te_0.8O_6.4 and Zn₂Te₃O₈ were obtained as shown in Fig. 7 (chart b), and three crystalline phases Bi_3.2Te_0.8O_6.4, Zn₂Te₃O₈ (ICDD card: 20-1270), Bi₂Te₄O₁₁ (ICDD card: 01-081-1330), respectively, were obtained, when it tempered 375 °C for 4.5 h as shown in Fig. 8 (chart c). Furthermore, heat treatment at higher temperature leads to the complete reaction of Bi₂O₃ with TeO₂ to form the stoichiometric compound Bi₂Te₄O₁₁. Senthil Murugan et al. [12] estimated the primary phase Bi_3.2Te_0.8O_6.4 which belongs to the cubic (centro symmetric) phase along with traces of Bi₂TeO₅ in the 70TeO₂–15Bi₂O₃–15ZnO glass heat treated at 350 °C/6 h. Also, they were found only major phase Bi₂Te₄O₁₁ in the same sample heat treated at 500 °C/6 h. Kozhukharov et al. [20] estimated the phase of α-TeO₂ at the temperature 435 °C and Te₃Zn₂O₈ at 479 °C for 80 mol% TeO₂ and 20 mol% ZnO composition and concluded the crystallizing Zn₂Te₃O₈ phase only at 432 ° in the 60 mol% TeO₂ and 40 mol% ZnO, which corresponds to single crystallization peak. It is well known that in the Zn₂Te₃O₈ structure \( _{\infty }^{1} \left[ {{\text{Te}}(4){\text{Te}}_{2} (3 + 1){\text{O}}_{8} } \right] \) chains are formed where for one TeO₄ polyhedron, there are two TeO₃ trigonal pyramids. Popple et al. [21] detected Bi₂Te₄O₁₁ phase in the Bi₂O₃–TeO₂. Moreover, the TeO₂ evaporates onto the Bi₂O₃ grains producing TeO₂ layer, and hence this TeO₂ layer reacts with the Bi₂O₃ by bulk diffusion forming Bi₂Te₄O₁₁ reactions. From the previous reported data, we conclude that, Bi_3.2Te_0.8O_6.4, Zn₂Te₃O₈, and Bi₂Te₄O₁₁reactions also are taking place by bulk diffusion in our glasses, not new crystalline phases appeared in prepared glass. Furthermore the activation energy of obtained crystalline phases in the prepared glass are 305.8 and 197 kJ mol⁻¹ and the kinetic parameter, n, for both crystallization exotherms closed to 1.0 (i.e., one dimensional growth from surface to inside).

The prepared glasses are high homogeneity transparent glass-ceramics depending on the heat treatment condition. Therefore, it is easy to take the photos of crossed polarized transmission microscope for the 70TeO₂–10Bi₂O₃–20ZnO glass at different heating temperature are shown in Fig. 9a–e. It has high-nucleation density of crystallites when tempered at 350 °C at different times 1, 2, 3, and 4 h. (see Fig 9a–e). Also, the grain size of crystallites increases with increasing the time of sample thermally treated. The prepared sample was examined under transmission electron microscope (TEM) after sputtering a thin carbon film on the prepared glass for conduction. The TEM micrographs for this sample were shown in Fig. 10a–d, which indicate that the scattered crystallites are uniform size in range 5 μm in the prepared sample tempered at 350 °C/4 h. Also, Fig. 10a revealed centrosymmetric tridymite crystal in the matrix of the prepared glass. Figure 10b is TEM micrograph of the sample 70TeO₂–10Bi₂O₃–20ZnO heated 400 °C for 0.5 h, which reveals crystalline phase, droplet-free halos and amorphous glassy regions in the microstructure. When Bi₂O₃ is added in tellurite glasses, it contributes the following effects: (i) incorporation of holes and defects between two chains, (ii) formation of strong Te–O–M ion covalent bonds, and (iii) strong influence on the Te–axOeq–Te angle between two polyhedra and distorted in TeO_3±1 unit followed by a creation of regular TeO₃ trigonal pyramid units leaving non-bridging oxygen atoms and due to the formation of Te–O–Bi kingies in the glass matrix [22‐25]. So, we are suggest that when addition of Bi₂O₃ to the TeO₂–ZnO glasses causes splitting of O–Te–O and Zn–O–Zn bonds and hence, the bridging oxygens (BO) are converted into non-bridging oxygens (NBO) and the electronic shell of O²⁻ ion is affected by polarizing action of modifying ions, since Bi³⁺ ions are highly polarizing with Te⁴⁺. This is due to droplet holes formed in the glass-ceramic matrix of present sample.

At temperature 375 °C for 3 h, the matrix of glass has high dense needle shaped crystal is shown in Fig. 10c. Finally, we found that, Bi³⁺ played an important role to get crystallization in the tellurite glass-ceramic by using mapping TEM of glassy ceramic matrix of 70TeO₂–10Bi₂O₃–20ZnO.