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

Dinh Quoc Vuong; Nguyen Van Hung

doi:doi:10.11648/j.ajea.20160402.11

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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

Dinh Quoc Vuong, Nguyen Van Hung

Published in American Journal of Electromagnetics and Applications (Volume 4, Issue 2)

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), 2024. Published by Science Publishing Group

Keywords

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

References

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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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TY  - JOUR
T1  - Thermodynamic Properties of Bcc Crystals Studied Based on Their High-Order Expanded Debye-Waller Factors and XAFS Application to Ferrite Iron
AU  - Dinh Quoc Vuong
AU  - Nguyen Van Hung
Y1  - 2016/12/08
PY  - 2016
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
SP  - 14
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

Dinh Quoc Vuong

Quang Ninh Education & Training Department, Nguyen Van Cu, Ha Long, Quang Ninh, Vietnam
Nguyen Van Hung

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Thermodynamic Properties of Bcc Crystals Studied Based on Their High-Order Expanded Debye-Waller Factors and XAFS Application to Ferrite Iron
AU  - Dinh Quoc Vuong
AU  - Nguyen Van Hung
Y1  - 2016/12/08
PY  - 2016
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
SP  - 14
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  -

Copy | Download