| dc.description.abstract | One may now summarize the main findings of this work and also discuss a few additional points for further work. The first important result is that the critical exponent for the divergence of dR/dT in binary liquids has no appreciable dependence on the frequency used to measure the electrical resistance at least over the frequency range 10 Hz to 100 kHz. The possibility of a weak (logarithmic type) dependence of the frequency, however, cannot be ruled out at very high and very low frequencies. But measuring electrical resistance above 100 kHz is quite difficult. One can conclude that the dielectric dispersion contribution to the electrical resistivity is not at all appreciable.
Measurements of electrical resistivity in the critical region of the binary liquids when the pure system is doped with small (? 100 ppm) amounts of water impurities reveal no noticeable change in the critical exponent for dR/dT. Also, the amplitude ratio in the critical region is not affected very much. Of course, a shift in Tc occurs by adding impurities. The relevance of this study lies in the scale of the impurities chosen (a few parts in 10?–10?) as also its nature. As noted in text, this scale of impurities is analogous to the presence of defects or dislocations or non magnetic impurities in ferromagnets, antiferromagnets, metallic binary alloys, etc., defects or non ferroelectric impurities in ferroelectrics. Thus the above study simulates a likely physical picture in any system (undergoing second order phase transitions) and the consequent effect on the dR/dT anomaly. This does not seem to be affected appreciably by the impurities (or the related defects they may imply). In principle, this finding should hold even for the behaviour of dielectric constant in the critical region.
An analysis of the scattering of ions (even impurity ions) by the concentration fluctuations broadly explains the feature obtained experimentally for the binary liquids. The important point is to normalise the structure factor using spin sum rule to include large momentum transfer behaviour. This treatment gives the value of the exponent as 0.55. It also gives the order parameter temperature dependence for the resistance of the two phases as borne out experimentally. However, this theory does not give the + sign of coefficient of the singular term. Also it has some other limitations.
The insensitivity of the critical exponent (or at least a weak dependence) for dR/dT in binary liquids to the frequency and impurities places these anomalies on a firm footing. Before this study, such an impression was not possible. It seems that the exponent for dR/dT in binary liquids is close to 0.35 rather than to 1/8 (specific heat critical index). Most of the rigorous and recent theories of the critical scattering in magnetic materials (and allied systems) give ? exponent for dR/dT both above and below Tc. Though it seems to be held experimentally in a large number of systems, there does exist a different behaviour in a few systems. Nevertheless, the notion that dR/dT singularities follow specific heat type behaviour in most magnetic and related systems seems widespread. Binary liquids seem to defy this behaviour. It is shown that probing closer (? 1 mdeg) might still give an ? singularity cannot be ruled out. But one knows going too close to Tc is beset with problems - gravity effects which at present one does not know how to take care of accurately. Moreover, temperature range 10?² °C to 10?³ °C used for analysis of the experimental data in binary liquids gives reasonable values of exponents for other properties. It looks like one is still indeed a step away from realising universal behaviour in a dynamic property (or at least a static limit of it). | |
