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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Waseda, Y., Matsubara, E., Shinoda, K.: X-Ray Diffraction Crystallography. Springer (2011)
Enzo, S., et al.: A profile-fitting procedure for analysis of broadened x-ray diffraction peaks. Journal of Applied Crystallography 21, 536–542 (1988)
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)
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1964)
Fogel, D.B., Back, T., Michalewicz, Z.: Evolutionary Computation 1. Basic Algorithms and Operators. IOP, Philadelphia (2000)
Golberg, D.E.: Genetic Algorithms. Addison-Wesley (1988)
Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Systems 9(3), 1–15 (1994)
Goldberg, D.E., Deb, K.: A comparative analysis of selection schemes used in genetic algorithms. Foundations of Genetic Algorithms 1, 69–93 (1991)
Deb, K.: Multi-objective optimization using evolutionary algorithms. Foundations of genetic algorithms. John Wiley & Sons (2001)
Storn, R., Price, K.: Differential evolution. A simple and efficient heuristic for global optimization over continuous spaces. J. Global Optimization 11, 341–359 (1997)
MacÃas, 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)
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)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-19222-2_42
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19221-5
Online ISBN: 978-3-319-19222-2
eBook Packages: Computer ScienceComputer Science (R0)