Conductivity and Noise Measurements in 3D Percolative Cellular Structures
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Abstract Conductivity results and 1/f noise (Sav) measurements from some systems with a cellular structure (composites in which small conductor particles embed on the surface of larger and regular insulator particles) are given. The usual DC percolation parameters (*c,t &s) were obtained from fitting the results to the Percolation equations. values for the systems have been found to lie in the range 0.01 - 0.07, while both non-universal and close to universal values have been measured for the exponents s and t. In addition, 1/f or flicker noise results on the systems give an additional exponent o)from the relationship Swv/Vdc 2 = KR0 . For the systems measured so far, the exponent wois observed to take different values ml close to and o2 further away from the conductor-insulator transition, but on the conducting side (ý > +c). The very different values (s, t & wo),obtained for the various conducting powders, in the same macroscopic structure, indicates that the way the powders distribute themselves on the insulating particles is a major factor in determining the exponents.
*c
Introduction Since the 1970s extensive conductivity and dielectric studies of 2D (thin films) and 3D percolation systems have been made [1,2,3,4,5,6]. In some 3D systems the conducting particles tend to form three dimensional cellular structures, but no systematic study of this structure has previously been done. In this paper the first systematic study of the percolation properties of a series of 3D composites with a cellular structure (similar to the conductor being the 'soap film' of bubbles) will be presented, with the goal of learning more about what determines the percolation exponents. The composite consists of small particles of conductor coating a regular insulator matrix, made from larger particles.
Theory The critical volume fraction or percolation threshold (+c) of a conducting component is where a conductor-insulator transition occurs. The percolation conductivity equations that are used to characterise this behaviour are: am = ac((+ - +c )/(I"•c))t
conducting region (+ > +c)
(la)
am = ai((+c- +)/+c)- s
insulating region (+ < +c)
(lb)
am ~ I+ - cl-t/(t+s)
defines the crossover region (-~ +c);
357 Mat. Res. Soc. Symp. Proc. Vol. 500 ©1998 Materials Research Society
*
where is the volume fraction of the conductor component, ac and ai are the conductivities of the conducting and insulating components respectively; and am is the conductivity of the composite. The exponents t and s are for the conducting and insulating regions respectively. The modified GEM equation (7,8,9]: {(1- 4)(oail/- aml/s)/(ai1/s + Aaml/s} + {ý(a'cl/t- amllt)/(acl/t + Aaml)} = 0
(2)
where A = (1 - €c)/1 c , can equally well be used to fit the data and incorporates and
interpolates between eqs. (la) and (lb), where ai/ac is not extremely small(< 10-9). Several models have appeared in the literature explaining the behaviour of percolation systems near the critical or percolation threshold [10]. The Kusy model
(Figure 1(a)) shows that *c decreases
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