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Deconvolution of X-ray Diffraction Profiles Using Genetic Algorithms and Differential Evolution

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Abstract

Some optimization problems arise when X-ray diffraction profiles are used to determine the microcrystalline characteristics of materials, like the detection of diffraction peaks and the deconvolution process necessary to obtain the pure diffraction profile. After applying the genetic algorithms to solve satisfactorily the first problem, in this work we propose two evolutionary algorithms to solve the deconvolution problem. This optimization problem targets the objective of obtaining the profile that contains the microstructural characteristics of a material from the experimental data and instrumental effects. This is a complex problem, ill-conditioned, since not only there are many possible solutions, but also some of them lack physical sense. In order to avoid such circumstance, the regularization techniques are used, where the optimization of some of their parameters by means of intelligent computing permits to obtain the optimal solutions of the problem.

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References

  1. Waseda, Y., Matsubara, E., Shinoda, K.: X-Ray Diffraction Crystallography. Springer (2011)

    Google Scholar 

  2. Enzo, S., et al.: A profile-fitting procedure for analysis of broadened x-ray diffraction peaks. Journal of Applied Crystallography 21, 536–542 (1988)

    Article  Google Scholar 

  3. Pereira, S., Gómez, J.A., Vega, M.A., Sánchez, J.M., Sánchez, F.: Aplicación de los Algoritmos Genéticos y la Evolución Diferencial para la Optimización de Perfiles de Difracción de Rayos X. MAEB 2009, Malaga, Spain, February, 11–13, pp. 9–1 (2009)

    Google Scholar 

  4. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1964)

    Google Scholar 

  5. Fogel, D.B., Back, T., Michalewicz, Z.: Evolutionary Computation 1. Basic Algorithms and Operators. IOP, Philadelphia (2000)

    Google Scholar 

  6. Golberg, D.E.: Genetic Algorithms. Addison-Wesley (1988)

    Google Scholar 

  7. Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Systems 9(3), 1–15 (1994)

    MathSciNet  Google Scholar 

  8. Goldberg, D.E., Deb, K.: A comparative analysis of selection schemes used in genetic algorithms. Foundations of Genetic Algorithms 1, 69–93 (1991)

    MathSciNet  Google Scholar 

  9. Deb, K.: Multi-objective optimization using evolutionary algorithms. Foundations of genetic algorithms. John Wiley & Sons (2001)

    Google Scholar 

  10. Storn, R., Price, K.: Differential evolution. A simple and efficient heuristic for global optimization over continuous spaces. J. Global Optimization 11, 341–359 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  11. Macías, D., Olague, G., Méndez, E.R.: Inverse Scattering with Far-field Intensity Data: Random Surfaces that Belong to a Well-defined Statistical Class. Waves in Random and Complex Media 16(4), 545–560 (2006)

    Article  MATH  Google Scholar 

  12. Sánchez-Bajo, F., Cumbrera, F.L.: The use of the pseudo-Voigt function in the variance method of x-ray line-broadening analysis. Journal of Applied Crystallography 30(4), 427–430 (1997)

    Article  Google Scholar 

  13. Gomez, J., Sanchez, F., Pereira, S., Vega, M., Sanchez, J.: Custom Hardware Processor to Compute a Figure of Merit for the Fit of X-Ray Diffraction Peaks. X-Ray Optics and Instrumentation 2008, 1–7 (2008)

    Article  Google Scholar 

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Correspondence to Juan A. Gomez-Pulido .

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Santos, S.P., Gomez-Pulido, J.A., Sanchez-Bajo, F. (2015). Deconvolution of X-ray Diffraction Profiles Using Genetic Algorithms and Differential Evolution. In: Rojas, I., Joya, G., Catala, A. (eds) Advances in Computational Intelligence. IWANN 2015. Lecture Notes in Computer Science(), vol 9095. Springer, Cham. https://doi.org/10.1007/978-3-319-19222-2_42

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  • DOI: https://doi.org/10.1007/978-3-319-19222-2_42

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19221-5

  • Online ISBN: 978-3-319-19222-2

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