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Journal of Materials Science

, Volume 44, Issue 1, pp 40–46 | Cite as

Real and reciprocal space order parameters for porous arrays from image analysis

  • Forrest H. KaatzEmail author
  • Adhemar Bultheel
  • Takeshi Egami
Article

Abstract

A real space technique based on the pair distribution function (PDF) and a reciprocal space method utilizing a 2D fast Fourier transform (FFT) quantify the order in porous arrays. Porous arrays fabricated from nanoscience technology are analyzed. The PDFs are fit with a series of Gaussian curves and the widths of the Gaussian peaks are used to model the linear strain in the array. An order parameter is defined from the PDF and takes values from [0,1], where the value 1 represents an ideal array. The radial distribution function (RDF) is also determined for the porous arrays. The FFT of the porous arrays is used to generate an order parameter as a ratio of intensity to the full width at half maximum (σ) of the peaks. Defined as relative intensity \( I_{\text{r}} /\sigma \), this parameter takes values from [0,∞], where larger values represent more order in the array. We use a variety of available software to generate this data.

Keywords

Fast Fourier Transform Real Space Anodize Aluminum Oxide Radial Distribution Function Pair Distribution Function 

Notes

Acknowledgements

An iMac @ 2.4 GHz running Mac OS X 10.5.5 was used. Image SXM is a free download for the Mac OS available from Ref. [17]. MATLAB, the Curve Fitting Toolbox, Excel, and Kaleidagraph complete the software tools necessary to create and analyze the data. In Figs. 1 and 4 we have reprinted with permission from Ref. [1, 7], copyright [2003, 1998], American Institute of Physics and reprinted with permission from Ref. [3], copyright [2005], IOPP Publishing.

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Forrest H. Kaatz
    • 1
    Email author
  • Adhemar Bultheel
    • 2
  • Takeshi Egami
    • 3
    • 4
    • 5
  1. 1.Department of Mathematics and Life/Natural SciencesOwens Community CollegeToledoUSA
  2. 2.Department of Computer ScienceK.U.LeuvenHeverleeBelgium
  3. 3.Department of Materials Science and EngineeringThe University of TennesseeKnoxvilleUSA
  4. 4.Department of Physics and AstronomyThe University of TennesseeKnoxvilleUSA
  5. 5.Materials Science and Technology DivisionOak Ridge National LaboratoryOak RidgeUSA

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