Fractal Dimension of Thin‐film Surfaces Obtained by Fourier Spectral Analysis

Zahn, W.; Zösch, Antje

doi:10.1002/(sici)1096-9918(199706)25:7/8<488::aid-sia255>3.3.co;2-e

Cited by 2 publications

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“…The band gap of about 1.4 eV indicates the presence of Cr(OH) 3 and Cr 2 O 3 . I(z) measurements show the existence of an oxide layer whose thickness exceeds a critical value only after in-situ experiments in the EC STM.…”

Section: Discussionmentioning

confidence: 99%

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STS investigations to describe corrosion procedures on thin CrN layers

2003

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To represent the corrosion characteristics of thin hard material layers, CrN layers, which were magnetron sputtered, have been exposed to solutions with chloride or sulfate ions. The alterations of the layer surfaces were examined. Static immersion tests were carried out ex-situ in 1 mol L(-1) NaCl or 1 mol L(-1) Na(2)SO(4) solution over a period of 14 months. For in-situ measurements, the layers were inserted into the electrochemical cell of an EC STM as the working electrode. The sample potential was altered cyclically. At the same time, voltammograms were taken and the topography alteration was observed. Alterations in the surface structure were documented as hybrid information resulting from changes in topography and the chemical consistency or the thickness of the oxide layers. These modifications were demonstrated with scanning tunnelling spectroscopy before and after the treatment with solutions. Several chemical phases (initial state and oxide layers) were distinguished with raster tunnelling spectroscopy (measurements I(V) and I(z)). The evaluation of the I(z) spectroscopy showed that the tip was in mechanical contact with the sample if an oxide layer of greater thickness has existed. Exemplary XPS investigations demonstrated corrosive alterations of the CrN layers due to oxidation. Asymmetry and peak locations suggest that in addition to Cr(2)O(3) and CrN a complex mixture of different chromium oxides such as Cr(2)O(3) and Cr(OH)( x) exists.

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Section: Discussionmentioning

confidence: 99%

“…A planar magnetron was used for layer deposition on Si single crystal wafers [3,4]. Before coating, the substrates were charged in order to be cleaned in an argon atmosphere at a pressure of about 5 Pa by feeding a voltage of about 1.2 kV.…”

Section: Layer Preparationmentioning

confidence: 99%

STS investigations to describe corrosion procedures on thin CrN layers

2003

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“…The images may be digital or have to be digitalized and sometimes need to be processed so that the features of fractal objects can be extracted. There are many methods for extraction of fractal dimension from an image all including numerous variations (Pentland, 1984;Clarke, 1986;Dubuc et al, 1989;Theiler, 1990;Miller and Reifenberger, 1992;Chen et al, 1993;Molteno, 1993;Sarkar and Chaudhuri, 1994;Van Put et al, 1994;Douketis et al, 1995;Vazquez et al, 1995;Zahn and Zösch, 1997;Brewer and Di Girolamo, 2006;Oczeretko et al, 2008;Li et al, 2009;Liu et al, 2010).…”

Section: Determination Of Fractal Dimension From Gray-scale Imagesmentioning

confidence: 99%

“…Power spectrum method (Saupe, 1988;Zahn and Zösch, 1997) Method is based on the power spectrum dependence of fractional Brownian motion…”

Section: Determination Of Fractal Dimension From Gray-scale Imagesmentioning

confidence: 99%

“…Although the fractal approach is very useful, calculating quantitative properties like fractal dimension from an image is still elusive and challenging. Different algorithms have been proposed and tested (Pentland, 1984;Clarke, 1986;Chen et al, 1989;Molteno, 1993;Sarkar and Chaudhuri, 1994;Van Put et al, 1994;Liu and Chang, 1997;Zahn and Zösch, 1997;Chen et al, 2003;Losa et al, 1994Losa et al, -2005Sun et al, 2006;Lopes and Betrouni, 2009;Li et al, 2009) and many studies have been developed to investigate the reliability of fractal dimension estimation with different algorithms applied to different fractal functions. Several studies have reported that different methods (dimension estimators) often yield significantly different results in a manner that makes interpretation difficult (Dubuc et al, 1989;Douketis et al, 1995;Vazquez et al, 1995;Chen et al, 2003;Brewer and Di Girolamo, 2006;Oczeretko et al, 2008;Liu et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

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Performance assessment of methods for estimation of fractal dimension from scanning electron microscope images

Risović

Pavlović²

2013

Scanning

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Processing of gray scale images in order to determine the corresponding fractal dimension is very important due to widespread use of imaging technologies and application of fractal analysis in many areas of science, technology, and medicine. To this end, many methods for estimation of fractal dimension from gray scale images have been developed and routinely used. Unfortunately different methods (dimension estimators) often yield significantly different results in a manner that makes interpretation difficult. Here, we report results of comparative assessment of performance of several most frequently used algorithms/methods for estimation of fractal dimension. To that purpose, we have used scanning electron microscope images of aluminum oxide surfaces with different fractal dimensions. The performance of algorithms/methods was evaluated using the statistical Z-score approach. The differences between performances of six various methods are discussed and further compared with results obtained by electrochemical impedance spectroscopy on the same samples. The analysis of results shows that the performance of investigated algorithms varies considerably and that systematically erroneous fractal dimensions could be estimated using certain methods. The differential cube counting, triangulation, and box counting algorithms showed satisfactory performance in the whole investigated range of fractal dimensions. Difference statistic is proved to be less reliable generating 4% of unsatisfactory results. The performances of the Power spectrum, Partitioning and EIS were unsatisfactory in 29%, 38%, and 75% of estimations, respectively. The results of this study should be useful and provide guidelines to researchers using/attempting fractal analysis of images obtained by scanning microscopy or atomic force microscopy.

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Fractal Dimension of Thin‐film Surfaces Obtained by Fourier Spectral Analysis

Cited by 2 publications

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STS investigations to describe corrosion procedures on thin CrN layers

STS investigations to describe corrosion procedures on thin CrN layers

Performance assessment of methods for estimation of fractal dimension from scanning electron microscope images

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