INTRODUCTION

Antimony oxide-based glasses, as a major family of heavy metal oxide glasses, show promising potential for applications in nonlinear optical devices such as ultrafast optical switches and/or power limiters [1–4]. They also have potential for application in broadband optical amplifiers operating around at 1.5 μm, and silicate glasses containing antimony were tested for optical amplification in communications in the C-band (1530–1560 nm) [5].

Stable binary glasses are formed in the (Sb2O3)1 – x–(PbCl2)x system [6, 7], which enables additions of other oxide compounds such as MoO3 or TeO2 and/ormetal halides (CuI, LiCl, ZnCl2), as related in other works [7–15].

The Sb2O3–PbCl2–AgCl glass system is particularly interesting due to its high ionic conductivity due to the presence of Ag. In addition to electrical conductivity, these glasses are transparent across a wide optical range (400 nm–6.5 µm) and they thus have a potential for applications in optoelectronics [16].

In this paper, the compositions of the investigated glasses belong to a wide range of compositions for which [Sb2O3] ∈ (45; 70), [PbCl2] ∈ (5; 40) and [AgCl] ∈ (5; 25). The glass transition temperatures of the prepared glasses are given. Moreover, the electrical and dielectric properties of the Sb2O3–PbCl2–AgCl glasses across a broad range of temperatures and frequencies are presented. This allows the temperature dependence of DC and AC conductivity as well as the dielectric properties of the glass samples to be investigated.

EXPERIMENTAL

The glasses were prepared using the standard processing steps of melting homogenised mixtures of the starting compounds, fining, cooling, melt casting, and annealing of glass bulks. Starting materials—99.9% Sb2O3 (Acros organics), 99% PbCl2 (Hichem), and 99.9% AgCl (Alfa Aesar)—were thoroughly mixed in an agate mortar and placed into a silica tube. Silica is not an ideal material for preparing this glass as it gradually dilutes in the glass melt. However, it is a better choice than platinum or gold, which both can be attacked by metallic particles resulting from oxidation-reduction reactions during heating of the batch and the glass melting process [16]. The contamination of the melt by SiO2 can be kept under the limit of detection by EDS semi quantitative chemical analysis if the melting time is kept as short as possible just to obtain a homogeneous glass melt [7]. During the melting process, the tube fills up with vapours from the glass melt which prevent the contact of the melt with ambient air and/or with combustion products from the flame used for heating.

After fining at about 850°C the melt was rapidly cooled down to approximately 600°C and poured on a brass plate preheated to 250°C (near the glass transition temperature Tg). After solidification, the sample was placed into an oven heated at Tg to remove thermally induced stresses. After a few hours at Tg, the temperature of the oven is slowly decreased down to room temperature [17].

The glass transition temperature Tg was measured by heating at a linear slope of 10°C/min using the TA Instruments DSC Q20 differential scanning calorimeter.

Samples for measurements of electrical and dielectric properties were cut and polished, and contact surfaces were coated with a conductive graphite layer. The DC conductivity was determined by measuring the electric current passing through the sample at a constant voltage of 10 V by Novocontrol Concept 90, across a temperature of 20–200°C. The current was measured by the Keithley 6517B picoammeter and the temperature was controlled by a Pt/PtRh thermocouple with an accuracy of ±1°C. Temperature dependence of the DC conductivity was measured during the phase when the temperature increased at a rate of 5°C/min [16].

The AC measurements (from 20 up to 150°C) were performed using the LCR Hi-tester Hioki 3522-50 at a frequency range 100 Hz–100 kHz. The measurements were performed in steps of 10°C after the temperature remained constant for 20 min [9, 18, 19]. Typically, as the frequency increases, the influence of electron transport processes increases, so at higher frequencies it is possible to see the influence of chemical elements for which different valence states are possible (Sb3+, Sb5+, W6+, W5+).

RESULTS

The acronyms of the respective glass compositions and their corresponding compositions expressed in molar percentages are shown in Table 1. The table summarizes also the electric and dielectric properties described in following text. The dependencies of the transition temperature Tg on the AgCl content in the studied Sb2O3–PbCl2–AgCl glasses are shown in Fig. 1. The Tg values decrease with increasing AgCl content in glasses with both 50 and 70 mol % Sb2O3. The temperature dependence of DC conductivity, σdc, of the investigated glasses is presented in Fig. 2. At temperature sranging between room temperature and 200°C the observed dependences follow Arrhenius-like equation

$${{\sigma }_{{{\text{dc}}}}} = {{\sigma }_{0}}\exp \left( {{{{{E}_{{{\text{dc}}}}}} \mathord{\left/ {\vphantom {{{{E}_{{{\text{dc}}}}}} {kT}}} \right. \kern-0em} {kT}}} \right),$$
(1)

where σ0 is the pre-exponential factor, Edc is the conduction activation energy, k is the Boltzmann constant, and T is the thermodynamic temperature. The determined parameters of Eq. (1) for the linear parts of the recorded temperature dependences of DC conductivity are summarized in Table 1.

Table 1. Parameters of Sb2O3–PbCl2–AgCl glasses: glass composition acronym, composition in mol %, conduction activation energies (Edc), pre-exponential factors (σ0), and electrical conductivity (σdc) at 150°C, AC conductivity frequency dependency parameters calculated by using the approximation of equation σac(f) = σ01 + A f n from measurement values at 150°C
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Fig. 1.
figure 1

Glass transition temperature Tg dependence for two glass series: (Sb2O3)50–(PbCl2)50 – x–(AgCl)x and (Sb2O3)70–(PbCl2)30 – x–(AgCl)x as a function of AgCl concentration.

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Fig. 2.
figure 2

DC conductivity temperature dependency curves of Sb2O3–PbCl2–AgCl glasses measured at a temperature range of 25–200°C. Glass samples corresponding to the individual plotted data are indicated in the figure.

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The AC conductivity σac of Sb2O3–PbCl2–AgCl glasses increases with increasing temperature and frequency. In Fig. 3, frequency dependencies of AC conductivity measured at 150°C are presented. AC conductivity frequency dependency can be described using the following formula

$${{\sigma }_{{{\text{ac}}}}} = {{\sigma }_{{01}}} + A{{f}^{n}},$$
(2)

where f is the frequency, and A and n are the parameters. The value of σ01 corresponds to DC conductivity, and its values for the temperature of 150°C are shown in Table 1. The value of σ01 is subject to an error due to the fact that it is an extrapolated value and also that the contribution of other carriers of electric charge (for example electrons) is more pronounced at higher frequencies in AC measurements than in DC measurements (mainly ionic conductivity in the investigated glasses). Therefore in some cases the σdc and σ01values may differ significantly from each other. The parameter A increases and the exponent n slightly decreases with increasing PbCl2 and AgCl contents.

Fig. 3.
figure 3

AC conductivity frequency dependency curves of Sb2O3–PbCl2–AgCl glasses measured at 150°C. Glass samples corresponding to the individual plotted data are indicated in the figure.

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The dielectric response was studied using modular spectroscopy. Complex electrical modulus M* was introduced [20–22] as the reciprocal value of the complex permittivity ε* by the equation

$$M\text{*} = M'\,\, + jM'' = {{\left( {\varepsilon _{{\text{r}}}^{*}} \right)}^{{ - 1}}}.$$
(3)

The measured modular spectra, i.e. the dependencies of complex electrical modulus in complex plane, are shown in Fig. 4. At lower AgCl content, the shapes of modular spectra can be characterized as semicircles with a centre just below the real axis with linear tails appearing at high frequencies. In these cases, dielectric relaxation can be characterized by a relatively narrow range of relaxation times. At higher AgCl content, the centres of the semicircles shift more under real axis. Consequently, the range of relaxation times expands.

Fig. 4.
figure 4

Modular diagrams of Sb2O3–PbCl2–AgCl glasses at 150°C. Glass samples corresponding to the individual plotted data are indicated in the figure.

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The relaxation times as a function of temperature τ = τ(T) were calculated as reciprocal value of angular frequency 1/(2πfm), where fm is the frequency of maxima M " obtained from frequency dependency of the imaginary part of complex electric modulus. As an example, Fig. 5 shows these dependencies of M " for glass E30-15 at various temperatures. For glasses where relaxation time values could be determined, the temperature dependencies of relaxation times follows the Arrhenius equation (see Fig. 6).

Fig. 5.
figure 5

Frequency dependency of the imaginary part of complex electric modulus M ′′ for (Sb2O3)55–(PbCl2)30–(AgCl)15 glass (E30-15) at various temperatures. Colours in the figure correspond to different temperatures.

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Fig. 6.
figure 6

Relaxation times of selected Sb2O3–PbCl2–AgCl glasses in dependence on temperature. Glass samples corresponding to the individual plotted data are indicated in the figure.

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Activation energy Eτ for Arrhenius-type dielectric relaxation was determined using the expression

$$\tau = {{\tau }_{0}}\exp \left( {{{ - {{E}_{\tau }}} \mathord{\left/ {\vphantom {{ - {{E}_{\tau }}} {kT}}} \right. \kern-0em} {kT}}} \right),$$
(4)

where τ0 is the pre-exponential factor, Eτ is the conduction activation energy, k is the Boltzmann constant, and T is the thermodynamic temperature. The value of Eτ correlates with the value of Edc (Table 1), i.e. the activation energy of the dielectric relaxation is affected by transport of the same type of electric charge.

DISCUSSION

The decrease of Tg values with increasing AgCl content in investigated glasses corresponds to the AgCl roleplays as a modifier in the antimonite glass network. According to [16], the increase in the molar concentration of AgCl leads to decrease of Tg values due to the formation of weaker Ag–Cl chemical bonds instead of stronger Sb–O bonds. The glass can accept only certain amount of modifiers without deterioration of the glassy network stability. As a consequence, the glass stability and density decrease significantly at high AgCl concentrations. As far as DC conductivity is concerned, temperature dependencies can be well described by the Arrhenius law with a single dominant mechanism of electric charge transport. In terms of the glass composition, polaronic conductivity Sb3+–Sb5+ and/or ionic conductivity by means of Ag+, or Cl– ions, respectively, could be considered as probable transport mechanisms. Transition from polaronic conductivity to ion conductivity mediated by Ag+ ions at lower concentrations of AgO (>0.1 mol %) has been reported recently [23]. It could be assumed that Ag+ ions are dominant charge carriers in Sb2O3–PbCl2–AgCl glasses. The DC conductivity values increase and the DC conductivity activation energy decreases with increasing AgCl content. The contribution of Cl– ions to DC conductivity is probably not significant. The DC conductivity values also increase with higher PbCl2 content. It is important, that this compound causes the increase of mobility of ions due to a relaxation of the glass network and an increase of the molar volume [16]. The authors investigated the possibility of electric transport using Cl– ions in detail in a similar glass system of Sb2O3–PbCl2–LiCl [14]. Their analysis showed that the influence of Cl– ions on electrical conductivity is negligible. It means that the DC conductivity increases at higher AgCl and PbCl2 contents due to the expansion of the glass network lead to an increase of the ion mobility. Moreover, in the case of AgCl an increase of the concentration of charge carriers occurs. The glass network relaxation is connected with a decrease of activation energies of DC conductivity in an interval ranging from 1 eV (A45-05) to 0.56 eV (A25-25). The A25-25 glass also reaches the highest value of conductivity at 150°C.

At measured temperatures, AC conductivity increases with increasing angular frequency and changes according to the power-law described by relation (2). The changing values of σ01 and A shown in Table 1 suggest that the dominant underlying mechanism of AC conductivity is the transport of the same type of electric charge as in the case of DC conductivity (σdc (150°C) in Table 1). The shape of the measured modular spectra (Fig. 4) indicates significant influence of ion movement. Also the activation energy of dielectric relaxation corresponds to the activation energy of DC conductivity. This also means that the influence of Ag+ ions transport is significant.

CONCLUSIONS

The results obtained by electrical measurements and the observed dependencies of the parameters of the studied materials show that the conductivity of Sb2O3–PbCl2–AgCl glasses show an Arrhenius-type behaviour. The dominant mechanism of charge transport in the investigated glasses is an ionic mechanism involving Ag+ ions. On the other hand, the contribution of Cl– ions and/or electrons to the transport of electric charge in these materials is less significant.

The values of direct electric conductivity are spread across a range spanning 5 orders of magnitude. The highest value of DC conductivity, around 3.6 × 10−5 S m−1 at 150°C with a corresponding activation energy of 0.56 ± 0.03 eV, was obtained for the (Sb2O3)50–(PbCl2)25–(AgCl)25 glass. Positive influence of the addition PbCl2 on electric mobility of the charge carrier Ag+ has been highlighted. The transport of electric charge by Ag+ ions has also an effect on values of alternate electric conductivity and dielectric relaxation of glasses.