Experimental observation of nonuniversal behavior of the conductivity exponent for three-dimensional continuum percolation systems

Current Percolation and Anisotropy in PolycrystallineMgB2

“…This has been confirmed by SEM investigations. Other experimental data range from 0.17 in pressed mixtures of conducting spheres and Teflon powder [24], to 0.31 in systems consisting of silver coated and uncoated glass beads [22] or 0.47 in granular W-Al 2 O 3 films [23]. Experimental data on the unirradiated bulk sample at higher temperatures and the fitted J c (B) curves are plotted in Fig.…”

“…During this transition the system can be considered as a mixture of normal and superconducting grains. Systems consisting of two materials with different resistances (conducting/insulating [21,22,23,24] or normal/superconducting [25,26]) have been investigated experimentally and are well understood in the framework of percolation theory. In mixtures of normal and superconducting powders the resistivity remains finite as long as the probability p, that a grain is superconducting (i.e.…”

“…There, the current in a network consisting of equal resistors with a current voltage law U ∝ I α is given near the percolation threshold by I = σ ef f U 1/α , with the conductivity σ ef f ∝ (p − p c ) t [29] and t = (d − 1)ν + (ζ − ν)/α [30], where d denotes the dimensionality of the system, ζ is about one and the correlation exponent ν is 0.88 in 3D systems [31]. Most experimental data were obtained on systems consisting of normal conducting (α = 1) and insulating particles [8,22,23,24]. In this case, the above power law for σ ef f was found to be an excellent approximation and t to be in reasonable agreement with the theoretical prediction (t = 1.88).…”

Hole-doping dependence of percolative phase separation inPr0.5−δCa0.2+δNiebieskikwiat1, Sánchez2, Morales3 et al. 2002Phys. Rev. B13090View full textAdd to dashboardCite

“…26,27,29,30 However, it has been shown that the conductivity exponent is nonuniversal, 31 and specific geometrical configurations of the contacts between percolating clusters could shift t to much higher values, e.g. by the formation of narrow necks.…”

Model of transport nonuniversality in thick-film resistors

“…Typical examples of nonuniversal systems are carbon-black-polymer composites, 20 and materials constituted by insulating regions embedded in a continuous conducting phase. 14,16 Despite that TFRs have been historically among the first materials for which transport nonuniversality has been reported, 3 the microscopic origin of their universality breakdown has not been specifically addressed so far. In this letter we show that the cross-over between universality and nonuniversality reported in Fig.1 can be explained within a single model whose basic features are the peculiar microstructure of TFRs and the tunneling processes between conducting grains.…”