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A Bayesian/Maximum Entropy Method for the Certification of a Nanocrystallite-Size NIST Standard Reference Material

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Diffraction Analysis of the Microstructure of Materials

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 68))

Abstract

A Bayesian/Maximum Entropy (MaxEnt) method for determining crystallite size distributions and morphologies from size-broadened X-ray line profiles is presented. This method will be used in certifying a nanocrystallite-size standard reference material (SRM) being developed at the National Institute of Standards and Technology (NIST). The proposed SRM will assist in ensuring that uniform procedures in quantifying the microstructure of nanocrystallites from X-ray line profile data are developed. This will become increasingly important as emerging nanotechnology applications begin to call for crystallites designed to have particular morphology and size distributions.

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References

  1. J.I. Langford and D. Louër: Rep. Prog. Phys. 59, 131 (1996)

    Article  ADS  Google Scholar 

  2. R. Vargas, D. Louër and J.I. Langford: J. Appl. Cryst. 16, 512 (1983)

    Article  Google Scholar 

  3. J.I. Langford and A.J.C. Wilson: J. Appl. Cryst. 11, 102 (1978)

    Article  Google Scholar 

  4. J.I. Langford and D. Louër: J. Appl. Cryst. 15, 20 (1982)

    Article  Google Scholar 

  5. J.I. Langford: NIST Spec. Pub. 846, 110 (1992)

    Google Scholar 

  6. C.E. Krill and R. Birringer: Phil. Mag. A77(3), 621 (1998)

    ADS  Google Scholar 

  7. J.I. Langford, D. Louër and P. Scardi: J. Appl. Cryst. 33, 964 (2000)

    Article  Google Scholar 

  8. N. Armstrong, W. Kalceff, J.P. Cline and J. Bonevich: J. Res. Nat. Inst. Stand. Techn. 2001 (Submitted); Proceedings of Accuracy in Powder Diffraction III, 22–25 April 2001, NIST, Gaithersburg, USA

    Google Scholar 

  9. R.K. Bryan: Eur. Biophys. J. 18, 165 (1990)

    Article  MathSciNet  Google Scholar 

  10. M. Jarrell and J.E. Gubernatis: Phys. Reports 269, 133 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  11. D. Louër and N. Audebrand (University of Rennes, 2001) For details see links at www.iucr.org/iucr-top/comm/cpd/projects/index.html

    Google Scholar 

  12. E.F. Bertaut: Acta Cryst. 3, 14 (1950)

    Article  Google Scholar 

  13. A. Guinier: X-ray diffraction in crystals, imperfect crystals and amorphous bodies. (Freeman, San Francisco 1963) Reprinted by Dover (New York), 1994

    Google Scholar 

  14. A.R. Stokes and A.J.C. Wilson: Proc. Camb. Phil. Soc. 38, 313 (1942)

    Article  ADS  Google Scholar 

  15. P. Scardi and M. Leoni: Acta Cryst. A 57, 604 (2001)

    Article  Google Scholar 

  16. D. Louër, J.P. Auffrédic and J.I. Langford: J. Appl. Cryst. 16, 183 (1983)

    Article  Google Scholar 

  17. J.I. Langford, A. Boultif, J.P. Auffrédic and D. Louër: Appl. Cryst. 26, 22 (1993)

    Article  Google Scholar 

  18. N. Armstrong: Application of the maximum entropy method to X-ray profile analysis. PhD thesis (Department of Applied Physics, University of Technology, Sydney, Australia 1999)

    Google Scholar 

  19. R. Kress: Linear integral equations. 2nd edn. (Springer, Berlin Heidelberg New York 1999)

    Book  MATH  Google Scholar 

  20. N. Armstrong and W. Kalceff: J. Appl. Cryst. 31, 453 (1998)

    Article  Google Scholar 

  21. R.T. Cox: Amer. J. Phys. 14(1), 1 (1946)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. D.S. Sivia: Data Analysis: A Bayesian Tutorial. (Oxford Science Pub., Oxford 1996)

    MATH  Google Scholar 

  23. K. Knuth: Inductive logic: From data analysis to experimental design. Presented at MaxEnt2001, APL John Hopkins Uuniversity, August 4–9, 2001. (URL: xxx.lanl.gov/list/physics.data-an/recent/0204068,2002)

    Google Scholar 

  24. G.B. Arfken and H.J. Weber: Mathematical Methods for Physicists. 4th edn. (Academic Press, San Diego 1996)

    Google Scholar 

  25. S.F. Gull: Developments in maximum entropy data analysis. In: Maximum Entopy and Bayesian Methods, ed. by J. Skilling (Kluwer Acad. Publ., Netherlands 1989) pp. 53–71

    Google Scholar 

  26. J.E. Shore and R.W. Johnson: IEEE Trans. IT 26(1), 26 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  27. R.W. Johnson and J.E. Shore: IEEE Trans. IT 26(6), 942 (1983)

    Article  MathSciNet  Google Scholar 

  28. Y. Tikochinsky, N.Z. Tishby and R.D. Levine: Phys. Rev. Lett. 52(16), 1357 (1984)

    Article  ADS  Google Scholar 

  29. S.F. Gull and J. Skilling: IEE Proc. F131, 646 (1984)

    Google Scholar 

  30. J. Skilling: The eigenvalues of mega-dimensional matrices. In: Maximum Entropy and Bayesian Methods, ed. by J. Skilling (Kluwer Acad. Pub., Netherlands 1989) pp. 455–566

    Google Scholar 

  31. J. Skilling: Quantified Maximum Entropy. In: Maximum Entropy and Bayesian Methods, ed. by P.F. Fougére (Kluwer Acad. Pub., Netherlands 1990) pp. 341–350

    Chapter  Google Scholar 

  32. F. Goambo and E. Gassiat: Annals Stat. 25(1), 328 (1997)

    Article  Google Scholar 

  33. J. Skilling and R.K. Bryan: Mon. Not. R. astr. Soc. 211, 111 (1984)

    ADS  MATH  Google Scholar 

  34. D.M. Titterington: Astron. Astrophys. 144, 381 (1985)

    MathSciNet  ADS  Google Scholar 

  35. E.T. Jaynes: Phys. Rev. 106(4), 620 (1957)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  36. B.R. Frieden: J. Opt. Soc. Am. 62(4), 511 (1972)

    Article  ADS  Google Scholar 

  37. A.R. Stokes: Proc. Phys. Soc. London A 61, 382 (1948)

    Article  ADS  Google Scholar 

  38. D.S. Sivia, (Private communication 1999)

    Google Scholar 

  39. J.J.K. O’Ruanaidh and W.J. Fitzgerald: Numerical Bayesian methods applied to signal processing. Springer, Berlin Heidelberg New York 1996)

    Book  MATH  Google Scholar 

  40. R.W. Cheary and J.P. Cline: Adv. X-ray Anal. 38, 75 (1995)

    Article  Google Scholar 

  41. J.A. Blackman, B.L. Evans and A.I. Maaroof: Phys. Rev. B 49(19), 13863 (1994)

    Article  ADS  Google Scholar 

  42. L.B. Kiss, J. Söderland, G.A. Niklasson and C.G. Granqvist: Nano-Struct. Mater. 12, 327 (1999)

    Article  Google Scholar 

  43. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller: J. Chem. Phys. 21, 1087 (1953)

    Article  ADS  Google Scholar 

  44. W.K. Hastings: Biometr. 57, 97 (1970)

    Article  MATH  Google Scholar 

  45. S.E. Koonin and D.C. Meredith: Computational physics: Fortran version. (Wesly, New York 1990)

    MATH  Google Scholar 

  46. S. Geman and D. Geman: IEEE Trans. Pattern Anal. Mach. Intell. 6(6), 721 (1984)

    Article  MATH  Google Scholar 

  47. L. Kirkup, Private communication, Department of Applied Physics, UTS 11 July, 2002

    Google Scholar 

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Authors
  1. N. Armstrong
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  2. W. Kalceff
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  3. J. P. Cline
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  4. J. Bonevich
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Editor information

Editors and Affiliations

  1. Max Planck Institute for Metals Research, Heisenbergstrasse 3, 70569, Stuttgart, Germany

    Eric J. Mittemeijer

  2. Dipartimento di Ingegneria dei Materiali e Tecnologie Industriali, Università di Trento, Facoltà di Ingegneria, Via Mesiano 77, 38050, Mesiano, Italy

    Paolo Scardi

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Armstrong, N., Kalceff, W., Cline, J.P., Bonevich, J. (2004). A Bayesian/Maximum Entropy Method for the Certification of a Nanocrystallite-Size NIST Standard Reference Material. In: Mittemeijer, E.J., Scardi, P. (eds) Diffraction Analysis of the Microstructure of Materials. Springer Series in Materials Science, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06723-9_8

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  • DOI: https://doi.org/10.1007/978-3-662-06723-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07352-6

  • Online ISBN: 978-3-662-06723-9

  • eBook Packages: Springer Book Archive

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