Editing Fractal dimension (section)

== Fractal surface structures ==
[[File:Wiki df figure.png|thumb|upright=1.5|Figure 7: Illustration of increasing surface fractality. Self-affine surfaces (left) and corresponding surface profiles (right) showing increasing fractal dimension ''D<sub>f</sub>''.]]
The concept of fractality is applied increasingly in the field of [[Surface Science|surface science]], providing a bridge between surface characteristics and functional properties.<ref>{{Citation |last=Pfeifer |first=Peter |chapter=Fractals in Surface Science: Scattering and Thermodynamics of Adsorbed Films |date=1988 |volume=10 |pages=283–305 |editor-last=Vanselow |editor-first=Ralf |publisher=Springer Berlin Heidelberg |doi=10.1007/978-3-642-73902-6_10 |isbn=9783642739040 |editor2-last=Howe |editor2-first=Russell |title=Chemistry and Physics of Solid Surfaces VII |series=Springer Series in Surface Sciences}}.</ref> Numerous surface descriptors are used to interpret the structure of nominally flat surfaces, which often exhibit self-affine features across multiple length-scales. Mean [[surface roughness]], usually denoted R<sub>A</sub>, is the most commonly applied surface descriptor, however, numerous other descriptors including mean slope, [[root-mean-square]] roughness (R<sub>RMS</sub>) and others are regularly applied. It is found, however, that many physical surface phenomena cannot readily be interpreted with reference to such descriptors, thus fractal dimension is increasingly applied to establish correlations between surface structure in terms of scaling behavior and performance.<ref>{{Cite journal |last1=Milanese |first1=Enrico |last2=Brink |first2=Tobias |last3=Aghababaei |first3=Ramin |last4=Molinari |first4=Jean-François |date=December 2019 |title=Emergence of self-affine surfaces during adhesive wear |journal=Nature Communications |volume=10 |issue=1 |pages=1116 |doi=10.1038/s41467-019-09127-8 |issn=2041-1723 |pmc=6408517 |pmid=30850605 |bibcode=2019NatCo..10.1116M}}</ref> The fractal dimensions of surfaces have been employed to explain and better understand phenomena in areas of [[contact mechanics]],<ref>[https://www.researchgate.net/publication/318345969_Contact_stiffness_of_multiscale_surfaces_by_truncation_analysis Contact stiffness of multiscale surfaces], In the International Journal of Mechanical Sciences (2017), 131.</ref> [[friction | frictional behavior]],<ref>[https://www.researchgate.net/publication/283675011_Static_friction_at_fractal_interfaces Static Friction at Fractal Interfaces], Tribology International (2016), vol.&nbsp;93.</ref> [[electrical contact resistance]]<ref>{{cite journal |first1=Zhai |last1=Chongpu |first2=Hanaor |last2=Dorian |first3=Proust |last3=Gwénaëlle |first4=Gan |last4=Yixiang |title=Stress-Dependent Electrical Contact Resistance at Fractal Rough Surfaces |journal=Journal of Engineering Mechanics |volume=143 |issue=3 |pages=B4015001 |year=2017 |doi=10.1061/(ASCE)EM.1943-7889.0000967 }}</ref> and [[transparent conducting oxide]]s.<ref>{{Cite journal |last1=Kalvani |first1=Payam Rajabi |last2=Jahangiri |first2=Ali Reza |last3=Shapouri |first3=Samaneh |last4=Sari |first4=Amirhossein |last5=Jalili |first5=Yousef Seyed |date=August 2019 |title=Multimode AFM analysis of aluminum-doped zinc oxide thin films sputtered under various substrate temperatures for optoelectronic applications |journal=Superlattices and Microstructures |volume=132 |pages=106173 |doi=10.1016/j.spmi.2019.106173 |s2cid=198468676 }}</ref>