physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

and

electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

, the universal dielectric response, or UDR, refers to the observed emergent behaviour of the

dielectric In electromagnetism, a dielectric (or dielectric medium) is an Insulator (electricity), electrical insulator that can be Polarisability, polarised by an applied electric field. When a dielectric material is placed in an electric field, electric ...

properties exhibited by diverse solid state systems. In particular this widely observed response involves

power law In statistics, a power law is a Function (mathematics), functional relationship between two quantities, where a Relative change and difference, relative change in one quantity results in a relative change in the other quantity proportional to the ...

scaling of dielectric properties with

frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

under conditions of

alternating current Alternating current (AC) is an electric current that periodically reverses direction and changes its magnitude continuously with time, in contrast to direct current (DC), which flows only in one direction. Alternating current is the form in w ...

, AC. First defined in a landmark article by A. K. Jonscher in ''

Nature Nature is an inherent character or constitution, particularly of the Ecosphere (planetary), ecosphere or the universe as a whole. In this general sense nature refers to the Scientific law, laws, elements and phenomenon, phenomena of the physic ...

'' published in 1977, the origins of the UDR were attributed to the dominance of many-body interactions in systems, and their analogous RC network equivalence. The universal dielectric response manifests in the variation of AC Conductivity with frequency and is most often observed in complex systems consisting of multiple phases of similar or dissimilar materials. Such systems, which can be called heterogenous or composite materials, can be described from a dielectric perspective as a large network consisting of resistor and capacitor elements, known also as an RC network. At low and high frequencies, the dielectric response of heterogeneous materials is governed by percolation pathways. If a heterogeneous material is represented by a network in which more than 50% of the elements are capacitors,

percolation In physics, chemistry, and materials science, percolation () refers to the movement and filtration, filtering of fluids through porous materials. It is described by Darcy's law. Broader applications have since been developed that cover connecti ...

through capacitor elements will occur. This percolation results in conductivity at high and low frequencies that is directly proportional to frequency. Conversely, if the fraction of capacitor elements in the representative RC network (P_c) is lower than 0.5, dielectric behavior at low and high frequency regimes is independent of frequency. At intermediate frequencies, a very broad range of heterogeneous materials show a well-defined emergent region, in which power law correlation of

admittance In electrical engineering, admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the multiplicative inverse, reciprocal of Electrical impedance, impedance, analogous to how Electrical resistanc ...

to frequency is observed. The power law emergent region is the key feature of the UDR. In materials or systems exhibiting UDR, the overall dielectric response from high to low frequencies is symmetrical, being centered at the middle point of the emergent region, which occurs in equivalent RC networks at a frequency of :

\omega = (RC)^

. In the power law emergent region, the admittance of the overall system follows the general power law proportionality

Y\propto\omega^

, where the power law exponent α can be approximated to the fraction of capacitors in the equivalent RC network of the system α≅P_c.

Significance of the UDR

The power law scaling of dielectric properties with frequency is valuable in interpreting impedance spectroscopy data towards the characterisation of responses in emerging ferroelectric and multiferroic materials.

References

{{Reflist, 30em Dielectrics Electric and magnetic fields in matter Condensed matter physics Electrical engineering Electronic engineering