*3.4. Electric and Dielectric Properties*

The dielectric constant values (*ε*') of the AFS samples fluctuated between 6.324 for sample AFS2 at 8 MHz and 11.988 for sample AFS8 at 50 Hz (Figure 8), while the electric conductivity values (*σ*) varied from 0.0105 μS/cm for sample AFS1 at 50 Hz to 43.57 μS/cm for sample AFS8 at 8 MHz (Figure 9). Based on the *ε*' values, the AFS samples can be grouped in descending order into two groups: group 1 (AFS8, AFS9, AFS7, AFS5, AFS6 samples) and group 2 (AFS3, AFS4, AFS1, AFS2 samples), as can be seen in Figure 8. The dielectric constant decreased with increasing applied AC frequency, while electric conductivity increased dramatically with increasing AC frequency, a common behavior recorded by many authors [35,36,51]. Following Nabawy and Rochette [38], the increase in conductivity with increasing frequency passes through three stages: (A) a steady stage with negligible increase in *σ*, (B) a transitional stage, and (C) a last stage with a dramatic increase in *σ* (Figure 9).

The imaginary electric modulus for samples AFS4, AFS2, and AFS1 was relatively high at 50 Hz (0.1388–0.0145), whereas it was lower for the other samples with different slopes, causing an inflection point in the frequency range of 2.5–3.0 MHz (Figure 10). These different dipolar relaxations were attributed to different relaxations for *ε*' and *ε*" at higher frequencies and to the crystal surfaces, which become more active at higher frequencies [52–55].

Based on the *σ* classification of Khater et al. [35,36], differentiation of *σ* values is difficult at low frequency values (*σ* = 0.01–0.181 μS/cm, *f* < 1500 kHz, Figure 9) and refers to poor semiconductors (0.01–1.0 μS/cm, Khater et al. [35,36]), whereas *σ* values are higher at high frequency values (*σ* = 0.181–43.57 μS/cm, *f* ≥ 1500 kHz) referring to poor (0.01–1.0 μS/cm) to fair semiconductors (1.0–1000 μS/cm, Khater et al. [35,36]). The measured electric and dielectric parameters are presented graphically as a function of the AC frequency in Figures 8–10.

**Figure 8.** Plotting the dielectric constant of the samples versus the applied frequency.

**Figure 9.** Plotting the electric conductivity of the samples versus the applied frequency.

**Figure 10.** Plotting the imaginary part of the complex electric modulus of the samples versus the applied frequency.

Effect of Sintering Temperatures on Electric Properties

Increases in the crystallization grade were the primary variable affecting the electric and dielectric properties of sample AFS5, as shown in Figure 11. It is indicated that the crystal size was smaller for AFS5 sintered at 1050 ◦C. At 1100 ◦C, the crystal size was well-developed with reduced pore volume, which caused a decrease in the electric and dielectric parameters. Sintering at this temperature enhanced dielectric properties, such that it could be considered a more appropriate semiconductor material than the samples sintered at 1050 ◦C and 1150 ◦C (Figure 11).
