D.S. McLachlan

The AC and DC conductivity of nanocomposites

The microstructures of binary (conductor-insulator) composites, containing nanoparticles, will usually have one of two basic structures. The first is the matrix structure where the nanoparticles (granules) are embedded in and always coated by the matrix material and there are no particle-particle contacts. The AC and DC conductivity of this microstructure is usually described by the Maxwell-Wagner/Hashin-Shtrikman or Bricklayer model. The second is a percolation structure, which can be thought to be made up by randomly packing the two types of granules (not necessarily the same size) together. In percolation systems, there exits a critical volume fraction below which the electrical properties are dominated by the insulating component and above which the conducting component dominates. Such percolation systems are best analyzed using the two-exponent phenomenological percolation equation (TEPPE). This paper discusses all of the above and addresses the problem of how to distinguish among the microstructures using electrical measurements.

Measurements of universal and non-universal percolation exponents in macroscopically similar systems

Abstract Conductivity results and 1/f noise (Sv) measurements for percolation systems with a cellular structure (composites in which small conductor particles are embedded on the surface of larger regular shaped insulator particles) are given. The usual DC percolation parameters ( t, s and φc) were obtained from fitting the results to the percolation equations. φc 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. Flicker (1/f ) noise results on the systems give an additional exponent w from the relationship Sv/V2=KRw. For the systems measured so far, the exponent w is observed to take different values w1 close to and w2 further away from the conductor–insulator transition, for φ>φc. The very different values ( s, t and w), obtained for the various conducting powders, in the same macroscopic structure, indicates that the way the powders distribute themselves on the insulating particles, and the nature of the interparticle (cluster) contacts, is a major factor in determining the critical exponents. The results are compared with those obtained from random void models of percolation systems.

The temperature and volume fraction dependence of the resistivity of granular Al-Ge near the percolation threshold

Extensive measurements of the temperature and of the Al volume fraction dependence of the resistivity of granular Al-Ge have been made near the percolation threshold phi c. The results at 295 K are analysed using the percolation equations, as modified by Efros and Shklovskii, and by Straley, for systems where the two components have finite conductivity ratios, and by fitting the results to the general effective media (GEM) equation, which also takes into account the finite conductivities of both components. The parameters of these equations are the conductivities (resistivities) of the two components, the critical conductivity exponents s and t, and the critical (percolation) volume fraction phi c. The experimental value of phi c, obtained from resistivity and magnetoresistivity measurements at and below the superconducting transition temperature for Al, agrees remarkably well with the values obtained from the percolation and GEM equations. The observed exponents are found to be high, and the width of the critical region surprisingly large. Attempts to extend this type of analysis to lower temperatures proved unsuccessful, and it is concluded that the resistivity of the more insulating component, namely of the amorphous Al-doped Ge, depends on the total Al content of the sample. It is shown that phi c cannot be identified from the resistivity versus temperature curves between 5 and 295 K, nor from temperature derivatives of these curves. Graphs of the resistivity versus temperature of the amorphous Al-doped Ge for individual samples are extracted using the GEM equation.

Higher-order effects in the dielectric constant of percolative metal-insulator systems above the critical point

The dielectric constant of a conductor-insulator mixture shows a pronounced maximum above the critical volume concentration. Further experimental evidence is presented as well as a theoretical consideration based on a phenomenological equation. Explicit expressions are given for the position of the maximum in terms of scaling parameters and the (complex) conductances of the conductor and insulator. In order to fit some of the data, a volume-fraction-dependent expression for the conductivity of the more highly conductive component is introduced.

Analytic scaling functions for percolative metal–insulator phase transitions fitted to AlxGe1−x data

Abstract The definition of the percolation scaling functions and an equation for the conductivity of a binary composite are combined to obtain two percolation scaling functions F + ( x + ) and F − ( x − ). F + ( x + ) is the function valid above the percolation threshold ( φ c ) and F − ( x − ) below. Using numerical simulation, it is then shown that these two functions display the principle properties required for them to be scaling functions. Previously reported experimental data on Al x Ge 1− x , where φ c was determined from superconductivity measurements, is replotted in the scaling form and shown to agree with the “best fit” F + ( x + ) and F − ( x − ).

Dielectric-constant measurements in a system of NbC grains near the percolation threshold

Measurements of the complex dielectric constant (e′ + ie″) on a series on NbC-KCl composites in a wide range of concentrations are performed as a function of φ (the volume fraction of the 1–3 μm NbC grains) at frequencies of 102, 103, 104 and 105 Hz. Frequency scaling of e = e′ + ie″ at the metal-insulator transition is different from one which follows from the scaling theory of an ideal percolation system. We observe two different values of the critical volume fraction of metal. The first critical concentration, φc1, is a cross-over point where the dielectric-constant frequency dependence changes and the loss factor is on the order of unity. The temperature behavior of the complex dielectric constant below the superconducting transition temperature Tc reveals a transformation of a system of isolated NbC grains into a system of weakly coupled tunneling junctions at φc1. The expected divergence of e′ is observed as the second critical volume concentration φc2 > φc1 is approached. At this concentration a cross-over from the capacitive tunneling junction medium to a truly metallic state occurs. At φ > φc2, e′ decreases rapidly as a function of φ and becomes negative at φ − φc2∼0.01, due to the negative effective real dielectric constant of the percolation metallic cluster which spans the system.

An analysis of dispersion measurements in percolative metal–insulator systems using analytic scaling functions

Abstract Continuous analytic scaling functions F+(ω/ωc+) and F−(ω/ωc−) for φ>φc and φ φc. These last two results are in conflict with the standard percolation theory.

The superconducting properties of PdHx≲1

Consecutive measurements of the magnetization curves and resistive transitions in magnetic fields have been made on PdHxT(x=H/Pd=0.9801−0.9957) foils between 2 and 10.4 K. The interpretation of the results is complicated by the fact that the magnetization curves are extremely irreversible and the hydrogen is distributed inhomogeneously in the samples. However, an analysis of the results shows PdH to probably be a type I superconductor with aTcof between 10.2 and 10.4 K, an HC(0) somewhat less than 900 G, and a κ of around 0.6 at absolute zero. Forx below about 0.995, PdHxbecomes a type II superconductor due to the increasing resistivity of the material.

Hard and Tough Boron Suboxide Based Composites

Boron Suboxide (B6O) powder was synthesized at temperatures of about 1400 oC from the reaction of boron and boric acid powders. The synthesized B6O powders were hot pressed at 1900 oC and at pressures of 50 MPa. Additionally to pure B6O materials, composites with Aluminum were prepared. The microstructure and properties of the sintered compacts were investigated. The addition of Aluminum in the composites results in the formation of an additional Aluminum Borate phase. The composites showed a similar hardness (~30GPa) as the pure B6O samples but an increased fracture toughness (~3.5MPa.m1/2).

Percolation exponents and threshold in two nearly ideal anisotropic continuum systems

Compressed discs made from graphite and, its mechanical but not electrical isomorph, boron nitride, as well as graphite-boron nitride powders, undergoing compression, are nearly ideal continuum percolation systems; as the ratio of their conductivities is 10−18 and the scatter of the experimental points near the critical volume fraction φc is very small. The following measurements, with the characteristic exponent(s) in brackets, are made on some or all of the samples in (axial) and at right angles (radial) to the direction of compression, as a function of the volume fraction of graphite (φ): DC conductivity (s and t), complex dielectric constant (s and t), magnetoresistivity (t⊥) and noise power (κ and w). The φcs obtained for all measurements are virtually the same in the axial and radial directions. The results for the exponents are less well understood. Where possible, these results are compared with theoretical predictions and previous experiments.