Fractal dimensions in switching kinetics of ferroelectrics

Scott, J. F. (2007) Fractal dimensions in switching kinetics of ferroelectrics. Ferroelectrics, 349. pp. 157-162. DOI https://doi.org/10.1080/00150190701260934

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Abstract

Early work by the author with Prof. Ishibashi [Scott et al., J. Appl. Phys. 64, 787 (1988)] showed that switching kinetics in ferroelectrics satisfy a constraint on current transients compatible with d = 2.5 dimensionality. At that time with no direct observations of the domains, it was not possible to conclude whether this was a true Hausdorff dimension or a numerical artefact caused by an approximation in the theory (which ignored the dependence of domain wall velocity upon domain diameter). Recent data suggest that the switching dimensionality is truly fractal with d = 2.5. The critical exponent b characterizing the order parameter P(T) can be written as a continuous function of dimension d as b(d) = [n(d)/2] [d+h(d)-2], which is exact within hyperscaling; here n and h are the exponents characterizing the pair correlation function G(r,T) and the structure factor S(q,T). For d=2.5 the estimate is that b is approximately ¼.

Item Type:	Article
Uncontrolled Keywords:	2007 AREP 2007 P IA54
Subjects:	03 - Mineral Sciences
Divisions:	03 - Mineral Sciences
Journal or Publication Title:	Ferroelectrics
Volume:	349
Page Range:	pp. 157-162
Identification Number:	https://doi.org/10.1080/00150190701260934
Depositing User:	Sarah Humbert
Date Deposited:	16 Feb 2009 13:03
Last Modified:	23 Jul 2013 10:08
URI:	http://eprints.esc.cam.ac.uk/id/eprint/670

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