Percolation silicon

Fig. 2.9.10 Maps of the temperature and of the experimental data. The right-hand column convection flow velocity in a convection cell in refers to numerical simulations and is marked Rayleigh-Benard configuration (compare with with an index 2. The plots in the first row, (al) Figure 2.9.9). The medium consisted of a and (a2), are temperature maps. All other random-site percolation object of porosity maps refer to flow velocities induced by p = 0.7 filled with ethylene glycol (temperature thermal convection velocity components vx maps) or silicon oil (velocity maps). The left- (bl) and (b2) and vy (cl) and (c2), and the hand column marked with an index 1 represents velocity magnitude (dl) and (d2).

Figure 8.4 Typical variation of the standard NMR parameter, %c, as a function of the variable of percolation e the different states of gelation were obtained by quenching the polymer in ice, at different times during the kinetics of synthesis of the network which occurs at 150 °C. The polymer is a slightly modified silicone chain which bears randomly distributed vinyl groups as comonomeric units (the mean number of vinyl groups along one chain is Cvi = 2 x 10"3). Links are created between vinyl and methyl groups the three symbols correspond to different catalyst concentrations (redrawn from [18])...

Thus, the non-Debye dielectric behavior in silica glasses and PS is similar. These systems exhibit an intermediate temperature percolation process associated with the transfer of the electric excitations through the random structures of fractal paths. It was shown that at the mesoscale range the fractal dimension of the complex material morphology (Dr for porous glasses and porous silicon) coincides with the fractal dimension Dp of the path structure. This value can be obtained by fitting the experimental DCF to the stretched-exponential relaxation law (64). 

More detailed calculations of the elastic properties of model networks have confirmed Phillips model. The coordination dependence of the elastic modulus is shown in Fig. 2.12 (He and Thorpe 1985). Both the modulus Cn and the number of zero frequency vibrational modes, /, drop to zero at the critical coordination of 2.4, as predicted by Eq. (2.17). The properties are explained in terms of percolation of rigidity. The coordination of 2.4 represents the lowest network coordination for which locally rigid structmes are fully connected, so that the entire network is rigid, but only just so. The elastic modulus is therefore non-zero and continues to increase as the network becomes more connected. The four-fold amorphous silicon network is far from the critical coordination and is very rigid. 

Figure 7. Silicon oxide cluster aggregate distribution below and above percolation volume fraction threshold...

---