“Trans-universal” dielectric response

The “universal” fractional power-law of frequency dependence of the complex dielectric susceptibility χ˜(ω)≡ε˜(ω)-ε_∞ with χ\´(ω)=tan(nπ/2)χ"(ω)∝ω^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→1 for which the ratio χ"(ω)/χ\´(ω)→0, but experimental evidence shows that the ratio is finite, typically in the range 10^-3-10^-1 and the fractional power law does not apply, especially to χ"(ω). Instead, it is found that in many cases the nearly “flat” loss follows the relation ε"(ω)/ε\´(ω). 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 χ"(ω)/χ\´(ω) in good agreement with experimental data. We illustrate this by the example of a low-loss ferroelectric-ceramic