## 3 Results and Discussion  
In Figure 1a, the dependences r\({}_{\text{ab}}\)(T) obtained before and after irradiation with fast electrons at fluences from 0 (curve 1) to 86.3 \(\times\) 10\({}^{18}\) e/cm\({}^{2}\) (curve 8) are shown. These dependencies were analyzed in previous work [27]. The electrical resistivity of Y1-zPr\({}_{x}\)Ba\({}_{2}\)Cu\({}_{3}\)O\({}_{7-5}\) single crystals when the phenodynium content, z, changed from zero (curve 1) to z = 0.5 (curve 8) is shown in Figure 1b. As can be seen from Figure 1, in both cases, the curves are characterized by quasi-metallic behavior of electrical resistivity with a characteristic linear area of the dependence \(\rho\)(T) at high temperatures. Both at maximum irradiation fluences and at maximum Pr content, the \(\rho\)(T) curves acquired a characteristic S-shape, which indicates the appearance of a thermally activated region on the \(\rho\)(T) dependences, which will be discussed in more detail below. From Figure 1, it can be deduced that when the T dropped below T*, in the basal plane, on the \(\rho_{ab}\)(\(T\)) dependencies in the region of relatively high temperatures, an extended linear section was preserved even at for high irradiation fluences. Numerous theoretical models have been introduced to explain these dependences including the resonating valence band theory (RVB theory) [28] and the nearly antiferromagnetic Fermi liquid (NAFL) model [29]. Figure 1: (**a**). Temperature dependencies \(\rho_{\text{ab}}\)(T) of YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-8}\) single crystals prior to and after irradiation with electrons at fluences 0, 13.1, 24.7, 38.9, 55.7, 68.1, 79.2 and 86.3\(\cdot\)10\({}^{18}\) e/cm\({}^{2}\)—curves 1–8, respectively. Inset: dependence of the critical temperature, Tc (squares), and electrical resistivity at room temperature, \(\rho\)(300 K) (circles), on fluence for all samples. (**b**). Temperature dependences r(T) of Y1-zPr\({}_{x}\)Ba\({}_{2}\)Cu\({}_{3}\)O\({}_{7-8}\) single crystals for z 0.0, 0.05, 0.19, 0.23, 0.34, 0.43, 0.48 and 0.50—curves 1–8, respectively. Inset: dependence of the critical temperature, Tc (red circles), and electrical resistivity at room temperature, \(\rho\)(300 K) (green circles), on the Pr concentration for all samples. In the RVB theory, scattering in HTSC compounds occurs through the interaction of carriers (spinons and holons) [28]. Herewith, the T dependence of the electrical resistivity additionally to the linear T term introduces an additional term, proportional to 1/T [30], in both cases, as in longitudinal and as in transverse electrical resistivity:  
\[\rho(\text{T})=\text{AT}^{-1}+\text{BT} \tag{1}\]  
From Figure 2 (note: irradiation fluences up to \(\leq\)70 \(\times\) 10\({}^{18}\) cm\({}^{-2}\) or a low level of Pr doping, z \(<\) 0.25), it was observed that the dependences of the products \(\rho_{\text{ab}}\)(T)\(\cdot\)T on T\({}^{2}\) become close to linear. For medium and high fluences of \(\Phi\) > 100 \(\times\) 10\({}^{18}\) cm\({}^{-2}\) or in the case of medium and heavily Pr-doped samples z \(\geq\) 0.25, the experimental curves \(\rho_{\text{c}}\)(T) could not sufficiently be described by the dependence from Equation (1). Figure 3 shows the dependencies of the linearity parameters A and B in Equation (1) from fluence (\(\Phi\)) or praseodymium concentration (\(z\)). As inferred from the figure, the linearity of the \(\rho\)(T)\(\cdot\)T-T\({}^{2}\) dependence was directly related to the defectiveness of the structure of the experimental samples, since both the (linear) parameters increased rapidly by increasing \(\Phi\) or \(z\), i.e., by increasing the concentration of irradiation and impurity defects. Figure 3: A and B linearity parameters [Equation (1)] dependencies from (**a**) fluence (\(\Phi\)) and (**b**) praseodymium concentration (z). Figure 2: Temperature dependencies of electrical resistivity in \(\rho\)\(\cdot\)T–T\({}^{2}\) coordinates in the ab-plane.