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Thermodynamic Properties of Bcc Crystals Studied Based on Their High-Order Expanded Debye-Waller Factors and XAFS Application to Ferrite Iron

Received: 24 October 2016     Accepted: 4 November 2016     Published: 8 December 2016
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Abstract

Thermodynamic properties of bcc crystals have been studied based on the anharmonic correlated Debye model high-order expanded Debye-Waller factors and X-ray absorption fine structure (XAFS). The many-body effects are taken into account in the present one-dimensional model based on the anharmonic effective potential that includes interactions of absorber and backscatterer atoms with their first shell near neighbors, where Morse potential is assumed to describe the single-pair atomic interaction. Analytical expressions for dispersion relation, correlated Debye frequency and temperature and four first temperature-dependent XAFS cumulants of bcc crystals have been derived using the many-body perturbation approach. The obtained cumulants are applied to calculating XAFS spectra and their Fourier transform magnitude. Numerical results for Fe, a ferrite crystal, are found to be in good agreement with experiment.

Published in American Journal of Electromagnetics and Applications (Volume 4, Issue 2)
DOI 10.11648/j.ajea.20160402.11
Page(s) 14-19
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Debye-Waller Factor, Effective Potential, Correlated Debye Model, XAFS, Iron

References
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[3] Stern A., P. Livins, and Zhe Zhang. (1991). Thermal vibration and melting from a local perspective Phys. Rev. B 43, 8850.
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[5] Hung N. V., Tien T. S., Duc N. B., Vuong D. Q. (2014). High-order expanded XAFS Debye-Waller factors of hcp crystals based on classical anharmonic correlated Einstein model. Mod. Phys. Lett. B 28, 1450174.
[6] Frenkel A. I. and Rehr J. J. (1993). Thermal expansion and x-ray-absorption fine-structure cumulants. Phys. Rev. B 48, 585.
[7] Miyanaga T., Fujikawa T. (1994). Quantum Statistical Approach to Debye-Waller Factor in EXAFS, EELS and ARXPS. III. Application of Debye and Einstein Approximation, J. Phys. Soc. Jpn. 63, 3683.
[8] Hung N. V. and Rehr J. J. (1997). Anharmonic correlated Einstein model Debye-Waller factors. Phys. Rev. B 56, 43.
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[10] Hung N. V., Tien T. S., Hung L. H., Frahm R. R. (2008). Anharmonic Effective Potential, Local Force Constant and EXAFS of HCP Crystals: Theory and Comparison to Experiment. Int. J. Mod. Phys. B 22, 5155.
[11] Daniel M., Pease D. M., Hung N. V., Budnick J. D. (2004). Local force constants of transition metal dopants in a nickel host: Comparison to Mossbauer studies. Phys. Rev. B 68, 134414.
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[13] Hung N. V., L. H. Hung L. H., Tien T. S., Frahm R. R. (2008). Anharmonic Effective Potential, Local Force Constant and EXAFS of HCP Crystals: Theory and Comparison to Experiment. Int. J. Mod. Phys. B 22, 5155.
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[16] Hung N. V., Hue T. T., Khoa H. D., Vuong D. Q. (2016). Anharmonic correlated Debye model high-order expanded interatomic effective potential and Debye-Waller factors of bcc crystals. Physica B 503, 174-178.
[17] V. Pirog I. V. and T. I. Nedoseikina T. I. (2003). Study of pair effective potentials in cubic metals. Physica B 334, 123.
[18] Mahan G. D., Many-Particle Physics (Plenum, New York, 1990) 2nd ed.
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  • APA Style

    Dinh Quoc Vuong, Nguyen Van Hung. (2016). Thermodynamic Properties of Bcc Crystals Studied Based on Their High-Order Expanded Debye-Waller Factors and XAFS Application to Ferrite Iron. American Journal of Electromagnetics and Applications, 4(2), 14-19. https://doi.org/10.11648/j.ajea.20160402.11

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    ACS Style

    Dinh Quoc Vuong; Nguyen Van Hung. Thermodynamic Properties of Bcc Crystals Studied Based on Their High-Order Expanded Debye-Waller Factors and XAFS Application to Ferrite Iron. Am. J. Electromagn. Appl. 2016, 4(2), 14-19. doi: 10.11648/j.ajea.20160402.11

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    AMA Style

    Dinh Quoc Vuong, Nguyen Van Hung. Thermodynamic Properties of Bcc Crystals Studied Based on Their High-Order Expanded Debye-Waller Factors and XAFS Application to Ferrite Iron. Am J Electromagn Appl. 2016;4(2):14-19. doi: 10.11648/j.ajea.20160402.11

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  • @article{10.11648/j.ajea.20160402.11,
      author = {Dinh Quoc Vuong and Nguyen Van Hung},
      title = {Thermodynamic Properties of Bcc Crystals Studied Based on Their High-Order Expanded Debye-Waller Factors and XAFS Application to Ferrite Iron},
      journal = {American Journal of Electromagnetics and Applications},
      volume = {4},
      number = {2},
      pages = {14-19},
      doi = {10.11648/j.ajea.20160402.11},
      url = {https://doi.org/10.11648/j.ajea.20160402.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajea.20160402.11},
      abstract = {Thermodynamic properties of bcc crystals have been studied based on the anharmonic correlated Debye model high-order expanded Debye-Waller factors and X-ray absorption fine structure (XAFS). The many-body effects are taken into account in the present one-dimensional model based on the anharmonic effective potential that includes interactions of absorber and backscatterer atoms with their first shell near neighbors, where Morse potential is assumed to describe the single-pair atomic interaction. Analytical expressions for dispersion relation, correlated Debye frequency and temperature and four first temperature-dependent XAFS cumulants of bcc crystals have been derived using the many-body perturbation approach. The obtained cumulants are applied to calculating XAFS spectra and their Fourier transform magnitude. Numerical results for Fe, a ferrite crystal, are found to be in good agreement with experiment.},
     year = {2016}
    }
    

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    AU  - Dinh Quoc Vuong
    AU  - Nguyen Van Hung
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    N1  - https://doi.org/10.11648/j.ajea.20160402.11
    DO  - 10.11648/j.ajea.20160402.11
    T2  - American Journal of Electromagnetics and Applications
    JF  - American Journal of Electromagnetics and Applications
    JO  - American Journal of Electromagnetics and Applications
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    EP  - 19
    PB  - Science Publishing Group
    SN  - 2376-5984
    UR  - https://doi.org/10.11648/j.ajea.20160402.11
    AB  - Thermodynamic properties of bcc crystals have been studied based on the anharmonic correlated Debye model high-order expanded Debye-Waller factors and X-ray absorption fine structure (XAFS). The many-body effects are taken into account in the present one-dimensional model based on the anharmonic effective potential that includes interactions of absorber and backscatterer atoms with their first shell near neighbors, where Morse potential is assumed to describe the single-pair atomic interaction. Analytical expressions for dispersion relation, correlated Debye frequency and temperature and four first temperature-dependent XAFS cumulants of bcc crystals have been derived using the many-body perturbation approach. The obtained cumulants are applied to calculating XAFS spectra and their Fourier transform magnitude. Numerical results for Fe, a ferrite crystal, are found to be in good agreement with experiment.
    VL  - 4
    IS  - 2
    ER  - 

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Author Information
  • Quang Ninh Education & Training Department, Nguyen Van Cu, Ha Long, Quang Ninh, Vietnam

  • Department of Physics, Hanoi University of Science, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

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