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Abstract:
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We present the percolation-theory model for explanation of conductivity of perovskites based on the scaling property of grain boundary formation. Assuming a two-layer simple effective medium model, composed of the grain itself as a first layer and the boundary as a second layer, it was modeled that the net resistivity r of the medium depends on the average grain size L, boundary thickness L' and boundary fractal dimension D. The obtained formula was tested specifically for the perovskite system Ca$_{0.85}$Pr$_{0.15}$Mn$_{1-x}$Ru$_x$O$_3$ (x=0.00, 0.03, 0.05 and 0.07) whose structures and electric properties were reported earlier by these authors [VNU J. of Sci., XX, No.3 AP, 2004, p. 130-132]. The determination of fractal dimension was based on the standard length-area technique and was carried out using SEM images which were photographed at three magnification scales 2, 5 and 10$\mu$m. This dimension showed good correspondence to the small polaron hoping energy in high temperature region and gave very good fits to experimental data for T$ |