Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Materials Science Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Choi J, Luo Y, Wehrspohn RB, Hillebrand R, Schilling J, Gösele U (2003) J Appl Phys 94(8):4757

    Article  CAS  Google Scholar 

  2. Asoh H, Nishio K, Nakao M, Tamamura T, Masuda H (2001) J Electrochem Soc 148(4):B152

    Article  CAS  Google Scholar 

  3. Krishnan R, Nguyen HQ, Thompson CV, Choi WK, Foo YL (2005) Nanotechnology 16:841

    Article  CAS  Google Scholar 

  4. Hulteen JC, Treichel DA, Smith MT, Duval ML, Jensen TR, Van Duyne RP (1999) J Phys Chem B 103:3854

    Article  CAS  Google Scholar 

  5. Blanford CF, Carter CB, Stein A (2004) J Microsc 216(3):263

    Article  CAS  Google Scholar 

  6. Campbell M, Sharp DN, Harrison MT, Denning RG, Turberfield AJ (2000) Nature 404(6773):53

    Article  CAS  Google Scholar 

  7. Li AP, Müller F, Birner A, Nielsch K, Gösele U (1998) J Appl Phys 84:6023

    Article  CAS  Google Scholar 

  8. Masuda H, Fukuda K (1995) Science 238:1466

    Article  Google Scholar 

  9. Sun F, Cai W, Li Y, Cao B, Lei Y, Zhang L (2004) Adv Funct Mater 14(3):283

    Article  CAS  Google Scholar 

  10. Shang XF, Wang M, Qu SX, Zhao R, Zhou JJ, Xu XB, Tan MQ, Li ZH (2008) Nanotechnology 19:065708

    Article  Google Scholar 

  11. Sellmyer DJ, Zheng M, Skomski R (2001) J Phys Condens Matter 13:R433

    Article  CAS  Google Scholar 

  12. Lei Y, Cai W, Wilde G (2007) Prog Mater Sci 52:465

    Article  CAS  Google Scholar 

  13. Li J, Papadopoulos C, Xu JM, Moskovits M (1999) Appl Phys Lett 75:367

    Article  CAS  Google Scholar 

  14. Park KH, Lee S, Koh KH, Lacerda R, Teo KBK, Milne WI (2005) J Appl Phys 95:024311

    Article  Google Scholar 

  15. Shingubara S, Okino O, Sayama Y, Sakaue H, Takahagi T (1997) Jpn J Appl Phys 36:7791

    Article  CAS  Google Scholar 

  16. Egami T, Billinge SJL (2003) Underneath the Bragg peaks: structural analysis of complex materials. Pergamon, Amsterdam

    Book  Google Scholar 

  17. Barrett S (2008) The website of Image SXM is at https://doi.org/www.liv.ac.uk/~sdb/ImageSXM/. Accessed November 2008

  18. Kaatz FH (2006) Naturwissenschaften 93:374

    Article  CAS  Google Scholar 

  19. Kaatz FH, Bultheel A, Egami T (2008) Naturwissenschaften 95:1033

    Article  CAS  Google Scholar 

  20. Kodama K, Iikubo S, Taguchi T, Shamoto S (2006) Acta Crystallogr A 62:444

    Article  Google Scholar 

  21. Mason G (1968) Nature (London) 217:733

    Article  Google Scholar 

  22. Kashi MA, Ramazani A (2005) J Phys D Appl Phys 38:2396

    Article  CAS  Google Scholar 

  23. Ba L, Li WS (2000) J Phys D Appl Phys 33:2527

    Article  CAS  Google Scholar 

  24. Rao YL, Anandan V, Zhang G (2005) J Nanosci Nanotechnol 5:2070

    Article  CAS  Google Scholar 

  25. Kashi MA, Ramazani A, Rahmandoustand M, Noormohammadi M (2007) J Phys D Appl Phys 40:4625

    Article  CAS  Google Scholar 

  26. Sulka GD, Parkoaa KG (2006) Thin Solid Films 515:338

    Article  CAS  Google Scholar 

  27. Frigo M, Johnson SG (2005) Proc IEEE 93(2):216

    Article  Google Scholar 

  28. Reis PM, Ingale RA, Shattuck MD (2006) Phys Rev Lett 96:258001

    Article  CAS  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Department of Mathematics and Life/Natural Sciences, Owens Community College, Toledo, OH, 43699, USA

    Forrest H. Kaatz

  2. Department of Computer Science, K.U.Leuven, Celestijnenlaan 200A, 3001, Heverlee, Belgium

    Adhemar Bultheel

  3. Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN, 37996, USA

    Takeshi Egami

  4. Department of Physics and Astronomy, The University of Tennessee, Knoxville, TN, 37996, USA

    Takeshi Egami

  5. Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA

    Takeshi Egami

Authors
  1. Forrest H. Kaatz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Adhemar Bultheel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Takeshi Egami
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Forrest H. Kaatz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kaatz, F.H., Bultheel, A. & Egami, T. Real and reciprocal space order parameters for porous arrays from image analysis. J Mater Sci 44, 40–46 (2009). https://doi.org/10.1007/s10853-008-3154-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10853-008-3154-4

Keywords

Search

Navigation