Percolatoin And Fractal Analysis On Cu/Cu₂O Cermets

Cu/Cu₂O cermet materials were prepared with hot pressing and hot pressing re-duction methods. The Cu/Cu₂O cermets prepared with hot pressing technology wereproduced by hot pressing the spherical and Cu₂O powders or branched Cu and Cu₂Opowders. The hot pressing reduction method was hot pressing C and Cu₂O powders.Using C to reduce Cu₂O matrix into Cu as the conductor. The dc electrical conductiv-ity of Cu/Cu₂O cermets, with different volume content, structure, and distribution, weretested. The percolation and fractal behavior were analyzed, and the relationship betweenmicrostructure and properties has been found.The percolation thresholds with different conductor structure and distribution wereobtained by the dc electrical conductivity test. The highest percolation threshold was theone prepared with 75μm spherical Cu. The percolation thresholds of Cu/Cu₂O cermetsprepared with different sizes of spherical Cu were very close, they were all about 0.22.The percolation threshold of Cu/Cu₂O cermet prepared with branched Cu was the lowest,it was about 10%. The percolation threshold of Cu/Cu₂O cermets prepared with hotpressing reduction method was close to the one prepared with spherical Cu, it was about22% as well. By the lattice analysis, it can be concluded that the percolation thresholddecreases with increasing of aspect ratio and decreasing of size of conductors, and thevariation rate of the percolation threshold based on aspect ratio dependence is faster thanthe one based on size dependence. By comparing the Cu/Cu₂O cermets prepared withsame volume content of Cu, it was found that the Cu/Cu₂O cermets with branched Cuhas the highest dc electrical conductivity, and the Cu/Cu₂O cermets with spherical Cuhas the lowest dc electrical conductivity.By the analyzing of the Cu/Cu₂O cermets prepared by the hot pressing reductionmethod, the electrical conductivity percolation critical exponent lower than the univer-sal value, t = 0.87±0.1, was firstly obtained in real conductor/insulator composites.The definition of the backbone density was introduced into the percolation system, andpresuming the conductors were obeyed the Poisson distribution. A model predicting thepercolation critical exponent were given and demonstrated that the percolation thresh-old is proportional to the backbone density. A"structure factor"was introduced into themodel. The more complex the conductor structure, the lower the structure factor. Nearthe percolation threshold, the critical exponent was not a constant but has a ?uctuation, which means the backbone density was not linearly increasing with increasing of volumecontent of conductors. It was also found that the increasing rate of the dc electrical con-ductivity, with same increasing rate of volume content of conductor, was different withdifferent structure and distribution of conductors. The Cu/Cu₂O cermets prepared withbranched Cu has the highest increasing rate, and the one prepared with reduction methodhas the lowest increasing rate.The fractal dimensions of all Cu/Cu₂O cermets increase with increasing volumecontent of the conductors. The fractal dimension of those prepared with spherical andbranched Cu have a ?uctuation near the percolation threshold. This means the complexityof the conductor's structure varied near the percolation threshold. Cu/Cu₂O cermets withsame conductor volume content but different structure and distribution leads to differentfractal dimensions. Those prepared with branched Cu has lower fractal dimension, andthose prepared with spherical Cu and reduction method have higher fractal dimensions.The fractal dimension of those prepared with spherical Cu decreases with decreasing sizeof conductors. The increasing rates of the fractal dimension were different with differentstructure and distribution of conductors. Those prepared with branched Cu was higherthan those prepared with spherical Cu, and the increasing rate of those prepared withreduction method is close to zero.By the quantitative calculation of the 2d square lattice percolation system, it wasfound that the quantities of infinite cluster and backbone increase with increasing vol-ume content of conductors, but the backbone density has a ?uctuation near the perco-lation threshold. by the quantitative calculation of the percolation critical exponent, italso found that near the percolation threshold, the percolation critical exponent has a?uctuation as well.