Differentiability breaking and Schwarz theorem violation in an aging material
Abstract
Dielectric constant measurements are performed in the frequency range from 1 kHz to 1 MHz on a disordered material with ferroelectric properties (KTa_{1x}Nb_{x}O_{3} crystals) after isothermal aging at the plateau temperature T_{pl}≅10 K. They show that the derivatives of the complex capacitance with respect to temperature and time present two very peculiar behaviors. The first point is that the first and second derivatives against temperature are not equal on the two sides of T_{pl}; this is differentiability breaking. The second point is that the two crossed second derivatives against temperature and time are not equal (indeed they have opposite signs); this is a violation of Schwarz theorem. These results are obtained on both the real part and the imaginary part of the capacitance. A model, initially imagined for aging and memory of aging, attributes the timedependent properties to the evolution (growth and reconformations) of the polarization domain walls. It is shown that it can also explain the observed differentiability breaking (and in particular its logarithmic increase with the plateau duration t_{pl}) and the violation of Schwarz theorem.
 Publication:

Physical Review B
 Pub Date:
 July 2002
 DOI:
 10.1103/PhysRevB.66.024105
 Bibcode:
 2002PhRvB..66b4105D
 Keywords:

 77.22.Gm;
 78.30.Ly;
 Dielectric loss and relaxation;
 Disordered solids