ii
ABSTRACT
Percolation phenomena involving the electrical conductivity, dielectric constant,
Hall coefficient, magnetoconductivity, relative magnetoresistivity, 1/ f noise and thermoelectric power are investigated in graphite (G) and hexagonal boron-nitride (BN)
powder mixtures. Two kinds of systems are used in the experiments: highly compressed
discs and parallelepipeds, cut from these discs, as well as 50%G-50%BN and 55%G-45%BN powder mixtures undergoing compression.
The measured DC conductivities follow the power-laws 0"( <p, 0) ex: (<p-<Pc)t (<p > <Pc)
and O"(<p, 0) ex: (<Pc-<Pti (<p < <Pc), and the low frequency (lOOHz & 1000Hz) dielectric constant varies as c( <p, W ~ 0) ex: (<Pc - <P )-S( <P < <Pc), where <Pc is the percolation threshold, t and s are the conductivity exponents, and s is the dielectric exponent.
Near the percolation threshold and at high frequencies, the AC conductivity varies with frequency as 0"( <p, w) ex: WX and the AC dielectric constant varies as c( <p, w) ex: w-Y,
where the exponents x and y satisfy the scaling relation x + y = 1. The crossover frequency We scales with DC conductivity as Wc ex: O"q( <p, 0) (<p > <Pc), while on the
insulating side, Wc ~ 1, resulting in q ~O for the three G-BN systems. The loss tangent tan t5( <p, w) (<p < <Pc) is found to have a global minimum, in contrary to the results of computer simulations.
The Hall constant could not be measured using existing instrumentation. The measured magnetoconductivity and relative magnetoresistivity follow the power-laws - 6. 0" ex: (<p - <Pc)3.08 and 6.R/ R ex: (<p - <Pc)O.28 respectively. These two exponents, iii 3.08 and 0.28, are not in agreement with theory.
The 1/ f noise was measured for the conducting discs and parallelepipeds. The normalized 1/ f noise power varies as Sv I V2 ex RW with the exponents w = 1.47 and
1.72 for the disc and parallelepiped samples respectively. Furthermore, the normalized
noise power near the percolation threshold is, for the first time, observed to vary
inversely with the square-root of sample volume.
Based on the Milgrom-Shtrikman-Bergman-Levy (MSBL) formula, thermoelectric
power of a binary composite is shown to be a linear function of the WiedemanFranz
ratio. A scaling scheme for the Wiedeman-Franz ratio for percolation systems
is proposed, which yields power-law behavior for the thermoelectric power. The
proposed power-laws for the thermoelectric power can be written as (Sm - Md ex
(<p - <Pc)h 1 for <P > <Pc and as (Sm - /~1d ex (<Pc - <p)-h2 for <p < <Pc, where Sm is
the thermoelectric power for the composites, Afl is a constant for a given percolation
system, and hI and h2 are the two critical exponents. The experimental thermoelectric
power data for the G-BN conducting parallelepipeds was fitted to the above powerlaw
for <p > <Pc. A least squares fit yielded the exponent hI = -1.13 and parameter
MI =9.511l V I I< respectively.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/19443 |
| Date | 23 January 1997 |
| Creators | Wu, Junjie |
| Publisher | University of the Witwatersrand |
| Source Sets | South African National ETD Portal |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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