Nguyen Thi Minh Thuy
Faculty of Fundamental Sciences, University of Fire Prevention and Fighting, Hanoi 120602, Vietnam
DOI : https://doi.org/10.47191/ijmra/v7-i06-54Google Scholar Download Pdf
ABSTRACT:
The anharmonic X-ray absorption fine structure (XAFS) Debye-Waller (DW) factor of the crystalline tungsten (W) has been investigated in the temperature-dependent. This DW factor is calculated in explicit forms using the quantum anharmonic correlated Einstein model developed from the correlated Einstein model based on the anharmonic effective potential and the quantum statistical theory. The numerical results of W in the temperature range from 0 to 900 K are in good agreement with those obtained by the other theoretical models and experiments at several temperatures. The analytical results show that the anharmonic correlated Einstein model is suitable for analyzing the experimental XAFS data of metals.
KEYWORDS:XAFS DW factor, thermal disorders, crystalline tungsten, Einstein model
REFERENCES:1. P. Fornasini, R. Grisenti, M. Dapiaggi, G. Agostini, and T. Miyanaga, “Nearest-neighbour distribution of distances in crystals from extended X-ray absorption fine structure,” Journal of Chemical Physics, Vol. 147, No. 4, pp. 044503, 2017.
2. P. A. Lee, P. H. Citrin, P. Eisenberger, and B. M. Kincaid, “Extended x-ray absorption fine structure its strengths and limitations as a structural tool,” Reviews of Modern Physics, Vol. 53, No. 4, pp. 769-806, 1981.
3. P. Eisenberger and G. S. Brown, “The study of disordered systems by EXAFS: Limitations,” Solid State Communications, Vol. 29, No. 6, pp. 481-484, 1979.
4. I.V. Pirog and T.I. Nedoseikina, “Study of effective pair potentials in cubic metals,” Physica B: Condensed Matter, Vol. 334, No. 2, pp. 123-129, 2003.
5. M. Newville, “Fundamentals of XAFS,” Reviews in Mineralogy & Geochemistry, Vol. 78, No. 1, pp. 33-74, 2014.
6. R. B. Greegor and F. W. Lytle, “Extended x-ray absorption fine structure determination of thermal disorder in Cu: Comparison of theory and experiment,” Physical Review B, Vol. 20, No. 12, pp. 4902-4907, 1979.
7. N. V. Hung, C. S. Thang, N. B. Duc, D. Q. Vuong, and T. S. Tien, “Temperature dependence of theoretical and experimental Debye-Waller factors, thermal expansion and XAFS of metallic Zinc,” Physica B: Condensed Matter, Vol. 521, pp. 198-203, 2017.
8. E. Lassner, W. D. Schubert, E. Lüderitz, and H. U. Wolf, Tungsten, Tungsten Alloys, and Tungsten Compounds, Weinheim: Wiley-VCH, 2000.
9. K. Turrell, Tungsten (Elements), New York: Benchmark Books, 2004.
10. John Emsley, Nature's Building Blocks: An AZ Guide to the Elements, 2nd ed. New York: Oxford University Press, 2011.
11. N. V. Hung, T. T. Hue, H. D. Khoa, and D. Q. Vuong, “Anharmonic correlated Debye model high-order expanded interatomic effective potential and Debye-Waller factors of bcc crystals,” Physica B: Condensed Matter, Vol. 503, pp. 174-178, 2016.
12. T.S. Tien, “Temperature dependence of EXAFS spectra of BCC crystals analyzed based on classical anharmonic correlated Einstein model,” Journal of Theoretical and Applied Physics, Vol. 14, No. 3, pp. 295-305, 2020.
13. T.S. Tien, “Advances in studies of the temperature dependence of the EXAFS amplitude and phase of FCC crystals,” Journal of Physics D: Applied Physics, Vol. 53, No. 11, pp. 315303, 2020.
14. T.S. Tien, “Investigation of the anharmonic EXAFS oscillation of distorted HCP crystals based on extending quantum anharmonic correlated Einstein model,” Japanese Journal of Applied Physics, Vol. 60, No. 11, pp. 112001, 2021.
15. T. S. Tien, N. V. Nghia, C. S. Thang, N. C. Toan, and N. B. Trung, “Analysis of temperature-dependent EXAFS Debye-Waller factor of semiconductors with diamond crystal structure,” Solid State Communications, Vol. 352, pp. 114842, 2022.
16. N. V. Hung, L. H. Hung, T. S. Tien, and R. R. Frahm, “Anharmonic effective potential, effective local force constant and EXAFS of hcp crystals: Theory and comparison to experiment,” International Journal of Modern Physics B, Vol. 22, No. 29, pp. 5155-5166, 2008.
17. N. V. Hung and J. J. Rehr, “Anharmonic correlated Einstein-model Debye-Waller factors,” Physical Review B, Vol. 56, No. 1, pp. 43-46, 1997.
18. S. H. Simon, The Oxford Solid State Basics, 1st ed. Oxford: Oxford University Press, 2013.
19. I. L. Shabalin, Ultra-High Temperature Materials I, New York: Springer, 2014.
20. P. M. Morse, “Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels,” Physical Review, Vol. 34, pp. 57-64, 1929.
21. T. Yokoyama, K. Kobayashi, T. Ohta, and A. Ugawa, “Anharmonic interatomic potentials of diatomic and linear triatomic molecules studied by extended x-ray-absorption fine structure,” Physical Review B, Vol. 53, No. 10, pp. 6111-6122, 1996.
22. E. Sevillano, H. Meuth, and J. J. Rehr, “Extended x-ray absorption fine structure Debye-Wailer factors. I. Monatomic crystals,” Physical Review B, Vol. 20, No. 12, pp. 4908-4911, 1979.
23. N. W. Ashcroft and N. D. Mermin, Solid State Physics, 1st ed. New York: Holt-Rinehart & Winston, 1976.
24. L. A. Girifalco and V. G. Weizer, “Application of the Morse Potential Function to Cubic Metals,” Physical Review, Vol. 114, No. 3, pp. 687-690, 1959.
Volume 07 Issue 06 June 2024
There is an Open Access article, distributed under the term of the Creative Commons Attribution – Non Commercial 4.0 International (CC BY-NC 4.0) (https://creativecommons.org/licenses/by-nc/4.0/), which permits remixing, adapting and building upon the work for non-commercial use, provided the original work is properly cited.
Our Services and Policies
Authors should prepare their manuscripts according to the instructions given in the authors' guidelines. Manuscripts which do not conform to the format and style of the Journal may be returned to the authors for revision or rejected.
The Journal reserves the right to make any further formal changes and language corrections necessary in a manuscript accepted for publication so that it conforms to the formatting requirements of the Journal.
International Journal of Multidisciplinary Research and Analysis will publish 12 monthly online issues per year,IJMRA publishes articles as soon as the final copy-edited version is approved. IJMRA publishes articles and review papers of all subjects area.
Open access is a mechanism by which research outputs are distributed online, Hybrid open access journals, contain a mixture of open access articles and closed access articles.
International Journal of Multidisciplinary Research and Analysis initiate a call for research paper for Volume 07 Issue 07 (July 2024).
PUBLICATION DATES:
1) Last Date of Submission : 26 July 2024 .
2) Article published within a week.
3) Submit Article : editor@ijmra.in or Online
Why with us
1 : IJMRA only accepts original and high quality research and technical papers.
2 : Paper will publish immediately in current issue after registration.
3 : Authors can download their full papers at any time with digital certificate.
The Editors reserve the right to reject papers without sending them out for review.
Authors should prepare their manuscripts according to the instructions given in the authors' guidelines. Manuscripts which do not conform to the format and style of the Journal may be returned to the authors for revision or rejected. The Journal reserves the right to make any further formal changes and language corrections necessary in a manuscript accepted for publication so that it conforms to the formatting requirements of the Journal.