The Effect of Alkaline Earth (Ba, Sr and Ca) Doped Iron Bismuth Glasses on the Structural, Thermoelectric and Electrical Properties

Glasses with nominal composition 70Bi2O3–30Fe2O3 and 10X–60Bi2O3–30Fe2O3 (mol%); (X = Ba, Sr and Ca) were prepared by the conventional melt quenching technique. X-ray diffraction and differential scanning calorimeter confirm the amorphous nature of the glass samples. The iron-bismuth glass shows good solubility of alkaline earth elements ions. In temperatures range of 310–450 K, the dc conductivity of the glass samples containing alkaline earth elements enhanced. Glass sample containing Sr shows interesting electrical properties. All glass samples showed a transition from negative to positive Seebeck coefficient, this means that the conduction is mixed of electrons and holes charge carriers. The conduction mechanism of all samples obeys non-adiabatic small polaron hopping model of electron between iron ions. The calculated small polaron coupling constant, (γp) was found to be in the range of 10.25–17.28. Also, the calculated hopping mobility (μ) and carrier density (Nc) of glasses were in the range of 4.65 ×10-7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times {10}^{- 7}$$\end{document} to 4.11 ×10-3,cm2V-1s-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times {10}^{-3},\left({\mathrm{cm}}^{2}\,{\mathrm{V}}^{-1}\,{\mathrm{s}}^{-1}\right)$$\end{document} and 0.029–10 (×1017cm-3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\times {10}^{17}\,\mathrm{cm}}^{-3})$$\end{document} at 333 K, respectively. The conductivity of the present glasses was primarily determined by hopping carrier mobility.


Introduction
Recently multicomponent oxide glasses containing transition and/or heavy metal oxides attracted a considerable attention due to its possible applications. Among the heavy metal oxides, Bi 2 O 3 has attracted much attention because of its high optical properties such as density, IR transmission and polarizability so Bi 2 O 3 is used as layers for optoelectronic devices [1,2]. Presence of transition metal ions such as (Fe) in glasses lead to exciting electrical and optical properties with auspicious technological applications in electronic and optical devices [3]. The addition of iron oxide (Fe 2 O 3 ) to the bismuthate glasses is expected to enhance the electrical and optical properties. Several studies [4][5][6][7][8] have been made on the dc electrical conductivity mechanism of iron bismuthate glasses (BFO), which discussed on the bases of small polaron hopping (SPH) model between Fe 2+ and Fe 3+ sites. In addition, the electrical conductivity is found to be significantly depends on the interaction of an electron with its surroundings and the distance between the Fe-ions [9].
On the other hand, glasses with ionic conductivity attract much scientific attention because of their potential applications such as solid-state batteries, memory devices and sensors [10]. Recently, Moustafa [3], studied the electrical transport properties of iron bismuth glasses and revealed that, Fe 2 O 3 played a significant role in the electrical conduction enhancement. Bi 2 O 3 -Fe 2 O 3 glasses containing alkaline earth elements conductivity consist of ionic and electronic conduction. Ideally, the motion of alkaline earth ions and electrons are not dependent of each other [11,12]. Chu et al. [13], investigated the effect of the alkaline earth elements (Ca, Sr and Ba) addition on the electrical conduction for BiFeO 3 ceramics synthesized by solid state reaction method. Optical and magnetic properties of heterovalent ions, Ba, Sr and Ca, substituted BiFeO 3 was extensively studied [14][15][16]. With increase of ionic radius of the substituted ions, the magnetization increases. The magnetic properties enhancement could strongly relate to structural distortion caused by the substituent. Although the optical and magnetic properties comprehensively studied electrical properties revel shortage.

3
Based on the above, thermoelectrical and electrical properties of conventional melt quenching 70Bi 2 O 3 -30Fe 2 O 3 glass and heterovalent ions, Ba, Sr and Ca, substitution at the expense of bismuth required more investigation.

Experimental
Glasses of 70Bi 2 O 3 -30Fe 2  The amorphous nature of the glasses was checked by Siemens D5000 X-ray diffractometer with nickel-filtered Cu K α radiation under accelerating voltage of 40 kV and current of 30 mA. The collected diffraction data was over a 2θ range of 5° to 60° at a scan rate of 3 degree per second. Thermal analysis was performed in the temperature range from room temperature to 850 K using differential scanning calorimetry NETZSCH DSC 204, with heating rate 10 K/min. The glass samples densities (ρ) were measured at room temperature by Archimedes method using Toluene as the immersion liquid of density 0.866 g/cm 3 . Glass samples were polished with emery paper to obtain parallel surfaces of ~ 1.5 mm thickness. Silver paste electrodes deposited on both faces of the polished samples. The dc conductivity of the glass samples was measured at temperatures between 310 and 450 K using Pico-ammeter type KEITHLEY 485. Hewlett Packard 34401A multimeter in temperature range 300-480 K was used for thermoelectric power measurements. Figure 1 shows the X-ray diffraction (XRD) patterns of the 70Bi 2 O 3 -30Fe 2 O 3 and 10X-60Bi 2 O 3 -30Fe 2 O 3 (mol%); (X = Ba, Sr and Ca) glass samples. It is observed that the quenched samples exhibit broad humps without any crystalline peaks which indicate the amorphous nature of the glass samples. Figure 2 shows, differential scanning calorimetry (DSC) curve of BFO sample with glass transition temperature (T g ) at 742 K followed by two exothermic crystallization peaks T C1 = 770 K and T C2 = 805 K. The thermal stability factor (ΔT = T C2 − T g ) usually employed to estimate the glass stability. The approximately large ΔT value (63 K) estimated from DSC data indicates high thermal stability of this glass. Other samples show a similar behavior.

Results and Discussion
The densities of the glass samples were measured by Archimedes method using the following equation [17,18]: where W a is the quenched glass sample weight in air, W L is the glass sample weight in Toluene and ρ L is the Toluene density at room temperature. The molar volume V m of the glass samples can be calculated according to the following equation [18]:  where M is the total molecular weight and ρ is the glass sample calculated density. As expected, opposite behavior of density and molar volume was observed, Fig. 3 and Table 1. The substitution of 10 mol% bismuth oxide (heavy) with heterovalent ions, Ba, Sr and Ca (light) show reduction in density values. While molar volume increases due to ionic radii increment. The ionic radius of Bi 3+ ions (= 0.103 nm) are substituted with Ca 2+ , Sr 2+ and Ba 2+ ions with the ionic radii of around 0.100, 0.118, and 0.135 nm, respectively [13].
The thermoelectric power or Seebeck coefficient (S) was evaluated when a temperature gradient was applied to both sides of the glass sample. The equation of Seebeck coefficient was described as S = ΔV/ΔT, where the major charge carrier becomes holes for a positive sign ( +) of Seebeck coefficient (S) and the major charge carrier becomes electrons for a negative sign (−) of Seebeck coefficient (S) [19,20].
It is observed from Fig. 4 that all glass samples display a transition from negative to positive sign of S, this means that the conduction is determined by the mix of electrons and holes. Thermoelectric power measurements are carried out to determine the fraction of reduced Fe ion, C = Fe 2+ / Fe total ,by the methods identified by Heikes et al. [21,22]. The relation between S and C obeys the following formula which depends on the ratio of low to high valence state of Fe [21,22]:  where k B is the Boltzmann's constant and e is the electron charge. Table 1 shows the C values for the present glass samples which estimated by using S. Figure 5 shows the variations of dc conductivity (σ) of glass samples as a function of reciprocal of the absolute temperature (T). It is clearly seen that a linear temperature dependence up to a certain temperature θ D /2 (θ D : Debye temperature). The activation energy (W) is temperature dependent and can be calculated from the slope of the linear fitting of the conductivity curve at higher temperature according to the following formula: where σ o is the pre-exponential factor and T is the absolute temperature. It is observed that σ smoothly increases with temperature, indicating a semiconducting nature of glass samples. The dc conductivity of the alkaline earth doped glasses is always higher than that of the BSFO sample. Figure 6 illustrates the dc conductivity and activation energy variation as a function of the composition. A general trend observed in this figure, is that the conductivity at fixed (4) = o exp −W∕k B T temperature (333 K) tends to be increased with alkaline earth elements addition and the maximum value observed with sample containing strontium while the opposite trend can be   [11,12,23]. The experimental conductivity data above θ D /2 were fitted with SPH model proposed by Mott [24]. The activation energy values are found to be 0.562 eV, 0.355 eV and 0.569 eV for XBFO (X = Ca, Sr and Ba) glass samples, respectively. The enhancement of conductivity and activation energy reduction agree with transition metal ion ratio values calculated from thermoelectric power measurements. The ionic conduction of the added alkaline earth elements could play a significant role in conductivity enhancement.
The hopping conductivity in oxide amorphous material containing transition metal (TM) ions was identified by Mott [24]. At sufficient higher temperatures, small polarons are created as result of the strong interaction between electrons and optical phonons [9]. The electron has an insignificant chance of making the transfer during each excitation for the non-adiabatic hopping regime. At high temperatures T > θ D /2, the dc conductivity (σ) of the nearest neighbor hopping is expressed as the following by where ʋ o represents the optical phonon frequency which is carried out from the electrical conductivity data according to the relation (k B θ D = h ʋ o ) the values of ʋ o are listed in Table. 1, α represents the tunneling factor, N represents the density of transition metal ion, R represents the mean distance between Fe ions, "e" represents the electronic charge and C represents the ratio of reduced Fe ions (C = Fe 2+ /Fe total ), The pre-exponential factor (σ o ) in Eq. 4 is expressed as

According to Austin and Mott [25] model for strong electron-phonon interaction, the hopping conduction activation energy (W) is given by;
where W H represents the hopping energy and W D represents the disorder energy. W D is defined as the average electronic energy change between two hopping sites Fe +2 ↔ Fe +3 .
where ɛ s represents the static dielectric constant and L is a constant (L = 0.3). The values of W D in the range of (0.11-0.25) eV. The electron makes transitions forward and backward more than once during excitation between hopping sites Fe +2 ↔ Fe +3 for the adiabatic hopping regime [9,24,25].
The polaron hopping mechanism nature (adiabatic or non-adiabatic) can be investigated from a plot of ln σ against W at a certain experimental temperature (T) according to the formula (lnσ = lnσ o − W/2.303kT) [26]. The hopping nature will be adiabatic if the estimated temperature (T e ) is close to experimental temperature T. Otherwise it is expected that the hopping nature will be non-adiabatic. Figure 7 displays the relationship between lnσ vs W for all the prepared glass samples at fixed temperature (333 K). The estimated temperature (T e = 247 K) is calculated from the slope of the plot is differ than the chosen temperature (T = 333 K) confirming that the conduction mechanism in the prepared glass samples is due to non-adiabatic small polaron hopping (SPH) of electrons [3]. The concentration of Fe ions per unit volume, N (cm −3 ) in the glass samples was calculated using the density by the relation [27] where N A is the Avogadro number, F w is the weight fraction of Fe 2 O 3 and M w is the molecular weight of Fe 2 O 3 and ρ is the density of the sample. The mean distance R between Fe ions in the glass samples was calculated from The values of R and N are given in Table 1. It is observed that as the distance between Fe ions increases the activation energy decreases. Furthermore, W depended on the mean Fe-ion spacing R for the glasses containing transition metal ions. These results suggested that the electrical conduction was due to SPH between Fe-ions. This result shows that there is a prominent positive correlation between W and R between transition metal ions.
In small polaron hopping (SPH) conduction, the bandwidth of polaron (J) obeys [28]: The values of (J) for all the prepared glass samples estimated from the right-hand side of the Eq. (12) or (13) at chosen temperature (333 K) are in the range of 0.015-0.018 eV depending on sample composition. Therefore, the condition for the existence of (SPH) is satisfied.
An unambiguous decision as to whether the polaron is actually in the adiabatic or in the nonadiabatic regime requires an estimate of the value of J, which can be obtained , where ε s and ε ∞ are the static and high frequencies dielectric constants of the samples, respectively. ε p is the effective dielectric permittivity. The calculated values of J are found to be in the range of 0.0002-0.010 eV, which are much smaller than those calculated from the R.H.S of Eq. (12) confirming the non-adiabatic hopping conduction at high temperature for these samples.
In adiabatic regime, the hopping energy W H is given using J as: where W p and Wʹ p represent the polaron binding energy and the maximum polaron binding energy, respectively. W H depends on R [29]. Otherwise, in non-adiabatic regime, W H , is given by: Using the values of W D and W, we obtained W H in the order of (0.30-0.55) eV. These values are near the W values for the present glass samples.
Next, by using the values of R, in Table 1, the polaron radius (r p ) is given by relation: The values of r p are listed in Table 2. It is observed that the values of the hopping energy W H decrease and hence the values of the polaronic radius increase (as r p is inversely proportional to W H ).
The density of states at Fermi level N(E F ) values are estimated in term of W as [30,31]: The values of N(E F ) for all the prepared glass samples are summarized in Table 2. It is clear that, the N(E F ) values are of the order of 10 21 (eV −1 cm −3 ). The values of the density of states N(E F ) are logical for the localized states [30,32].
The electron-phonon interaction in oxide amorphous material is represented by the small polaron coupling constant γ p, . The values of (γ p ) given by were also calculated for all the prepared glass samples [7]. The calculated values of γ p are listed in Table 2. The values of γ p > 4 for all the prepared glass samples usually suggest a strong electron-phonon interaction [32]. From results listed in Table 2, It is noticed that the γ p has minimum value at the highest conductivity sample (BSFO). The hopping carrier mobility values in the non-adiabatic regime are given by the following equation [25].
Also, the carrier density (N c ) value is calculated from the following relation [33].
The calculated values of μ and N c for all the prepared glass samples at 333 K are listed in Table. 3. Because the condition of the localized for hopping electrons is generally for μ < 0.01 (cm 2 V −1 s −1 ) [9,31,34], the results show that electrons in these samples are localized at the Fe-ion sites. The formation of small polaron (SP) for all the prepared glass samples is reconfirmed. Also the constant N c ∼ 10 17 means that the conductivity of prepared glass samples is determined by hopping mobility [30].
We will apply the law suggested by Greaves at intermediate temperature (below θ D /2) [35] as a modification of Mott's variable range hopping (VRH) model [25]. The expression for the DC conductivity (σ) according to Greaves's VRH model is given by following formula: where A and B are constants, and we get B by following formula A plot of ln(σ T 1/2 ) versus T −1/4 is shown in Fig. 8 to calculate the factor α. The calculated values of α and N(E F ) are acceptable for the localized states [25,36].

Conclusion
Glasses of 70Bi 2 O 3 -30Fe 2 O 3 and 10X-60Bi 2 O 3 -30Fe 2 O 3 (mol%); (X = Ba, Sr and Ca) were prepared by the conventional melt quenching technique. From the XRD and DSC results all the glass samples were fully amorphous in nature. DC conductivity was found to depend on the type of the added alkaline earth element. The conductivity enhancement and activation energy reduction agree with transition metal ion ratio values calculated from thermoelectric power measurements. The DC electrical conductivity of the glass samples was obeying the nonadiabatic small polaron hopping (SPH) model of electron between Fe-ions. The electron-phonon interaction coefficient, (γ p ) was calculated and found to be in the range of 10.25-17.28. The nearly constant of carrier density (Nc) ~ 10 17 cm −3 indicates that the conductivity is determined by the hopping mobility.