Figure 1 shows the XRD patterns for (Cu0.5Ag0.5)7SiS5I powders with different average particle size. It is shown that XRD patterns for (Cu0.5Ag0.5)7SiS5I powders are similar to diffractogram for (Cu0.5Ag0.5)7SiS5I solid solution crystal [25]. Comparison of diffractograms indicates that the lines broadening occurs with particle size decrease (Fig. 1). The results of microstructural analysis for prepared (Cu0.5Ag0.5)7SiS5I-based ceramics are presented in Fig. 2. From histograms of crystallites size distribution for different ceramic samples, obtained from powders which grinding in agate mortar and planetary ball mill for 30 min and 60 min, the size of crystallites after annealing was determined (Fig. 2).
It is shown that the ceramic samples prepared by sintering powders obtained by grinding in a planetary ball mill are characterized by a more homogeneous microstructure, characterized by the distribution of particles in a narrower range, in contrast to the samples obtained by sintering a microcrystalline powder with a particle size of 10–50 µm (Fig. 2). As a result of recrystallization process, the average size of crystallites for samples obtained from powders grinding in an agate mortar is ~ 12 µm, while for samples obtained from powders grinding in a planetary ball mill for 30 min and 60 min is ~ 5 µm and ~ 3 µm, respectively.
Figure 3 presents the frequency dependences of total electrical conductivity for (Cu0.5Ag0.5)7SiS5I-based ceramics. With frequency increase the electrical conductivity grows which is typical for materials with ionic conductivity in solid state [27]. The insert to Fig. 3 shows the dependence of the total electrical conductivity on the size of crystallites. It is revealed that at decrease of size of crystallites from 12 µm to 3 µm the decrease of total electrical conductivity for (Cu0.5Ag0.5)7SiS5I-based ceramic samples is observed.
For separation of the total electrical conductivity into ionic and electronic components, a standard approach using electrode equivalent circuits (EEC) [27, 28] and their analysis on Nyquist plots was used. The parasitic inductance of the cell (~ 2 × 10− 8 H) is taken into account during the analysis of all ceramic samples. It is shown that ceramic samples prepared on the basis of (Cu0.5Ag0.5)7SiS5I, are characterized by equal values of electronic and ionic components of electrical conductivity (σion ~ σel). At Z'-Z" dependences for (Cu0.5Ag0.5)7SiS5I-based ceramics with average crystallites size of 12 µm, 5 µm, and 3 µm two semicircles are observed.
The ЕЕС, which described the Nyquist plots, can be divided in two parts: one of them relates to ionic processes, another one to electronic processes. Low-frequency semicircles on the Nyquist plots correspond to the diffusion relaxation processes at the electrode/crystal boundary which is described by the capacity of the double diffusion layer Cdl and Warburg element of Wd, responsible for diffusion within the latter (Fig. 4). Serial to them were included the elements with Rgb/Cgb parameters which related to resistance and capacity of the grain boundaries of ceramic samples (the end of low-frequency semicircles) (Fig. 4). High-frequency semicircles correspond to the conductivity processes determined by the resistance of intra-grain boundaries, which is marked by Rdb on the EEC (Fig. 4). Thus, the ionic conductivity of (Cu0.5Ag0.5)7SiS5I-based ceramic samples is determined by the sum of the resistance of grain boundaries Rgb and the resistance limiting the ion diffusion WR. It should be noted that on EEC parallelly to the elements responsible for ion processes the electronic resistance Re is included and determined electronic conductivity of the samples (Fig. 4). With crystallites size decrease (12 µm →5 µm→ 3 µm) the low-frequency shift of low-frequency semicircle on EEC is observed. It may be related to the increasing of influence of diffusion ionic processes as well as increasing of ionic relaxation time due to the electronic conductivity decreasing.
Temperature studies have shown that with increasing temperature, the increase of electronic conductivity gradually eliminates the influence of diffusion ionic processes at the boundaries of ceramics crystallites, as evidenced by the decrease of the high-frequency semicircle at 323 K (Fig. 4, curve 2). With further increase of temperature up to 373 K (Fig. 4, curve 3) there is a further reduction of the influence of diffusion ionic processes, which, together with the decrease in the thickness of the double diffusion layer, and the complete disappearance of the high-frequency semicircle.
Figure 5a shows the dependences of the ionic and electronic components of electrical conductivity on the size of crystallites in (Cu0.5Ag0.5)7SiS5I-based ceramic samples. It is revealed that the decrease in the size of crystallites leads to monotonous decrease of ionic and electronic components of electrical conductivity, while their ratio remains unchanged (σion ~ σel).
The temperature dependences of the ionic and electronic components of electrical conductivity in the Arrhenius coordinates presents on Fig. 6. The linear behavior of above mentioned dependences was confirmed the thermoactivating character of electrical conductivity. From the presented temperature dependences of the ionic and electronic conductivity the activation energies were determined (Fig. 5b). It is shown that the activation energies of both components of electrical conductivity for (Cu0.5Ag0.5)7SiS5I-based ceramic samples nonlinearly depend on the size of crystallites (рис.5b). Thus, at the transition of the size of crystallites from 12 µm to 5 µm the slight increase of the activation energies of both components of electrical conductivity is observed, whereas at the transition of the size of crystallites from 5 µm to 3 µm the tendency to decrease of the activation energies of both components of electrical conductivity is revealed.
It should be noted that (Cu0.5Ag0.5)7SiS5I-based ceramics are characterized by disordered structure, which is associated with different reasons: (i) structural disordering, caused by the different size of crystallites; (ii) structural disordering, caused by the recrystallization process during annealing; (iii) compositional disordering, caused by the Cu+↔Ag+ cationic substitution. The combination of the above features in the final case leads to a change of the Nyquist plots for samples with different size of crystallites (Fig. 4) and causes the corresponding behavior of the total electrical conductivity (Fig. 3), its ionic and electronic components (Fig. 5), and its thermoactivation behavior (Figs. 6 and 7) for (Cu0.5Ag0.5)7SiS5I-based ceramics.
Comparison of the values of ionic and electronic conductivities, as well as their ratio for crystal and ceramic samples of (Cu0.5Ag0.5)7SiS5I solid solution have shown that the ionic conductivity and the ratio σion/σel of ceramic sample with an average crystallite size of 12 µm is slightly greater than that of crystal ones (σion = 2.2 × 10− 3 S/cm and σion/σel = 0.9 for crystal) [25]. Thus, studies show that (Cu0.5Ag0.5)7SiS5I-based ceramics is characterized by high electrical parameters, comparable or even higher than in the corresponding crystals. This, in turn, makes their use in solid ionic devices more promising due to their greater manufacturability and ease of production compared to crystals.