## 3 Results and Discussion
### Dielectric Constant Fractal Correction  
Complex fractal correction is presented as  
\[\alpha_{f}=\alpha_{S}+\alpha_{P}+\alpha_{M},\]  
where each \(\alpha\) represents fractal correction induced by grain surface, inside pore surface and particles' Brownian motion, respectively. Fractal correction based on Brownian motion of particles, \(\alpha_{M}\), is not  
Figure 11: Scaled reliability function of normal distribution for KZM100-MOD-Y. Figure 12: Inverted Dirac Delta function for BT02-MOD-Y. included in this analysis because of its minor influence (in comparison to \(\alpha_{S}\) and \(\alpha_{P}\)) and to provide less complicated further analysis. Here in this part, we applied fractal corrections \(\alpha_{\text{s}}\) (grain surface) and \(\alpha_{\text{p}}\) (inside pore surface) to Curie-Weiss law, introduced in References [22; 23]. \[\varepsilon_{r}(T_{f},\alpha)=\frac{C_{c}}{T-T_{c}}==\frac{C_{c}}{\frac{T_{f }}{\alpha}-T_{c}}\]  
\[C_{c}\text{-}10^{5}.\]  
Sintering temperature T for modified BaTiO\({}_{3}\)-ceramics must be influenced by three factors forming fractal corrective factor \(\alpha_{f}\), making the real ceramic temperature \(T_{f}\), which is a corrected \(T\); the two temperatures are connected using equation \(T_{f}=\alpha_{f}\text{-}T\) and \(\alpha_{f}\) is a complex fractal correction. In all of these ceramics and general materials science formulas, absolute temperature is present. So, in our experiments and discussed samples and results, we have absolute temperature \(T\), as temperature in all processes and structures. \(T\) is a measure of thermal relations in all of these processes and phenomena. The present thermal effects are in strong connection with the structural constituents grains and pores, especially their surfaces and related characteristics of intergranular-pores contacts relations and phenomena, also the ecranization effects of electronic properties influence from one to another side of the grain boundaries. So complex fractal correction \(\alpha_{f}\) will be temperature fractal correction that is, \(T_{f}=\alpha_{f}\text{-}T\). In this case, the microfractality and associate complex fractal correction \(\alpha_{f}\) have very important role on that submicrolevel and also influence on local and in summary the samples thermal effects. As we neglected fractal correction \(\alpha_{\text{M}}\), total fractality impact is equally distributed over \(\alpha_{s}\) and \(\alpha_{p}\)  
\[\alpha=\frac{\alpha_{p}+\alpha_{s}}{2}\]  
\[\varepsilon_{r}(T_{f},\alpha_{p},\alpha_{s})=\frac{C_{c}}{\frac{2T_{f}}{ \alpha_{p}+\alpha_{s}}-T_{c}}\]  
\[\varepsilon_{r}(T_{f},\alpha_{p},\alpha_{s})=\frac{C_{c}}{\frac{2T_{f}}{0.34 045+0.263}-T_{c}}=\frac{C_{c}}{\frac{2T_{f}}{0.60345}-T_{c}}=\frac{C_{c}}{3.31 43T_{f}-T_{c}}.\]  
The known dependence of capacitance on \(\varepsilon_{r}\) can be presented with equation:  
\[C=\varepsilon_{r}\varepsilon_{0}\frac{S}{d}\]  
where \(\varepsilon_{0}\) stands for absolute dielectric constant, S is the sample surface and d represents sample thickness. Including values for \(T_{f}\) (25 \({}^{\circ}\)C), \(S\) (3 mm) and \(d\) (0.75 mm), a function showing relation between capacitance (C) and \(T_{c}\) can be obtained for our experimental data:  
\[C=3.54\times 10^{-14}\frac{C_{c}}{936.6-T_{c}}\]  
In this way, influence of DC bias on capacitance change can also give the insight in \(T_{c}\) change, which is very important for the investigation of capacitor stability under different operational conditions. According to the literature, \(C_{c}\) of pure BaTiO\({}_{3}\) is the order of magnitude \(10^{5}\), so it can be assumed that modified BaTiO\({}_{3}\) could have the similar values, obtaining the dependence [27]:Tables 3-6 present data used for fractal correction of the Curie-Weiss equation. The data were read from the curve that has been produced by the device for capacitance stability measurement.