"Trans-universal" dielectric response

The "universal" fractional power-law of frequency dependence of the complex dielectric susceptibility /spl chi//spl tilde/(/spl omega/)/spl equiv//spl epsi//spl tilde/(/spl omega/)-/spl epsi//sub /spl infin// with /spl chi/'(/spl omega/)=tan(n/spl pi//2)/spl chi/"(/spl omega/)/spl prop//spl omega//sup n-1/, has the limiting form of almost "flat" or frequency-independent loss widely observed in many low-loss solid dielectrics. The flat loss should correspond to the limit n/spl rarr/1 for which the ratio /spl chi/"(/spl omega/)//spl chi/'(/spl omega/)/spl rarr/0, but experimental evidence shows that the ratio is finite, typically in the range 10/sup -3/-10/sup -1/ and the fractional power law does not apply, especially to /spl chi/"(/spl omega/). Instead, it is found that in many cases the nearly "flat" loss follows the relation /spl epsi/"(/spl omega/)//spl epsi/'(/spl omega/). It has been proposed that the "flat" loss has an extension called "trans-universal law" which gives a nearly flat behaviour with a finite ratio /spl chi/"(/spl omega/)//spl chi/'(/spl omega/) in good agreement with experimental data. We illustrate this by the example of a low-loss ferroelectric-ceramic.