Universal dielectric response: Difference between revisions
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The Universal Dielectric Repsonse 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_circuit|RC network]]. <ref>{{cite journal| last1=McCullen | first1= Nicholas J. | title= The robustness of the emergent scaling property of random RC network models of complex materials | journal= . Journal of Physics D: Applied Physics | year=2009 | volume=42 | issue=6 |
The Universal Dielectric Repsonse 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_circuit|RC network]]. <ref>{{cite journal| last1=McCullen | first1= Nicholas J. | title= The robustness of the emergent scaling property of random RC network models of complex materials | journal= . Journal of Physics D: Applied Physics | year=2009 | volume=42 | issue=6 |
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| page=064001| }}</ref>. 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]] through capacitor elements will occur. This percolation results in conductivity at high and low frequencies that is directly proportional to frequency. Conversely, if fewer than 50% of elements in the representative RC network are capacitors, dielectric behavior at low and high frequencies 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]] to frequency is observed. The power law emergent region is they 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 :<math>\omega = (RC)^{-1} </math>. In the power law emergent region, the conductivity of the overall system |
| page=064001| }}</ref>. 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]] through capacitor elements will occur. This percolation results in conductivity at high and low frequencies that is directly proportional to frequency. Conversely, if fewer than 50% of elements in the representative RC network are capacitors, dielectric behavior at low and high frequencies 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]] to frequency is observed. The power law emergent region is they 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 :<math>\omega = (RC)^{-1} </math>. In the power law emergent region, the conductivity of the overall system follows the general power law proportionality <math> Y\propto\omega^{\alpha} </math>, where the power law exponent α can be approximated to the fraction of capacitors in the equivalent RC network of the system. <ref > {{cite journal| title= Universality of the emergent scaling in finite random binary percolation networks| journal= PLOS One | year=2017 | volume=12 |issue=2 | pages= e0172298|url= http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0172298 | doi=10.1371/journal.pone.0172298}} </ref> |
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== Significance of the UDR == |
== Significance of the UDR == |
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In domains of physics and electrical engineering, the Universal Dielectric Response, or UDR, refers to the observed emergent behaviour of the dielectric properties exhibited by diverse solid state systems. In particular this widely observed response involves power law scaling of dielectric properties with frequency under conditions of alternating current, AC. First defined in a landmark article by A. K. Jonscher in Nature published in 1977[1], the origins of the UDR were attributed to the dominance many-body interactions in systems, and their analogous RC network equivalence.[2]
The Universal Dielectric Repsonse 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. [3]. 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 through capacitor elements will occur. This percolation results in conductivity at high and low frequencies that is directly proportional to frequency. Conversely, if fewer than 50% of elements in the representative RC network are capacitors, dielectric behavior at low and high frequencies 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 to frequency is observed. The power law emergent region is they 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 :. In the power law emergent region, the conductivity of the overall system follows the general power law proportionality , where the power law exponent α can be approximated to the fraction of capacitors in the equivalent RC network of the system. [4]
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.[5][6]
References
- ^ Jonscher, Andrew K. (1977). "The 'universal'dielectric response". Nature. 267 (5613): 673. Bibcode:1977Natur.267..673J. doi:10.1038/267673a0.
- ^ Jonscher, Andrew K. (1992). "The universal dielectric response and its physical significance". ." IEEE Transactions on Electrical Insulation. 27 (3): 407.
- ^ McCullen, Nicholas J. (2009). "The robustness of the emergent scaling property of random RC network models of complex materials". . Journal of Physics D: Applied Physics. 42 (6): 064001.
{{cite journal}}: Cite has empty unknown parameter:|1=(help) - ^ "Universality of the emergent scaling in finite random binary percolation networks". PLOS One. 12 (2): e0172298. 2017. doi:10.1371/journal.pone.0172298.
{{cite journal}}: CS1 maint: unflagged free DOI (link) - ^ MacDonald, J.R. (1985). "Generalizations of universal dielectric responseand a general distribution‐of‐activation‐energies model for dielectric and conducting systems". Journal of applied physics. 58 (5): 1971. Bibcode:1985JAP....58.1971M. doi:10.1063/1.336004.
- ^ Pattanayak, Samita (2014). "Generalizations of Effect of Dy-substitution on structural, electrical and magnetic properties of multiferroic BiFeO3 ceramics". Ceramics International. 40 (6): 7983.
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