Anisotropic Debye-Waller Factors and Debye Temperatures in Hexagonal Close-Packed Elements: A Comprehensive Compilation and Analysis

Open Access

Year : 2024 | Volume :11 | Special Issue : 12 | Page : 32-39
By

Dr. Purushotham Endla,

Endla AkhilBalaji,

  1. Associate Professor, Department of Physics,School of Sciences, SR University, Telangana, India
  2. Student, Computer Science and Engineering, Kakatiya Institute of Technology and Science, Telangana, India

Abstract

In this study, we have investigated the anisotropic behavior of Debye-Waller factors (DWFs) and Debye temperatures (DTs) in three distinct materials: hexagonal rhenium (Re), osmium (Os), and thallium (Tl). We conducted a comparative analysis, aligning our experimental data on directional Debye temperatures with theoretical calculations. This exercise provided valuable insights into the concurrence between practical and theoretical approaches, thereby offering a critical evaluation of the accuracy and reliability of theoretical predictions. For hexagonal close-packed (hcp) structures, deviations from the ideal c/a ratio of 1.633 reveal the nuanced interplay of forces along the hexagonal axis. In hcp metals, including our subjects, two principal DWFs, Ba and Bc, correspond to the ‘a’ and ‘c’ crystallographic directions. The relationship between these factors and atomic amplitudes offers profound insights into interatomic bonding, with the Bc/Ba ratio typically exceeding 1 for c/a ratios straying from the ideal 1.633 value. This study advances our understanding of anisotropic properties in hcp metals, sheds light on the structural nuances of the materials examined, and contributes significantly to crystallography, materials science, and solid-state physics.

Keywords: X-ray diffraction, Debye temperature, hcp element vacancy formation energy

[This article belongs to Special Issue under section in Journal of Polymer and Composites (jopc)]

How to cite this article:
Dr. Purushotham Endla, Endla AkhilBalaji. Anisotropic Debye-Waller Factors and Debye Temperatures in Hexagonal Close-Packed Elements: A Comprehensive Compilation and Analysis. Journal of Polymer and Composites. 2024; 11(12):32-39.
How to cite this URL:
Dr. Purushotham Endla, Endla AkhilBalaji. Anisotropic Debye-Waller Factors and Debye Temperatures in Hexagonal Close-Packed Elements: A Comprehensive Compilation and Analysis. Journal of Polymer and Composites. 2024; 11(12):32-39. Available from: https://journals.stmjournals.com/jopc/article=2024/view=131288


Full Text PDF

Browse Figures

References

R. Tynan et al., “Deuterium retention and thermal conductivity in ion-beam displacement-damaged tungsten,” Nucl. Mater. Energy, 12 (2017).
J. Olsen et al., “Investigation of defect clusters in ion-irradiated Ni and NiCo using diffuse X-ray scattering and electron microscopy,” J. Nucl. Mater., 471 (2016).N. Gopi Krishna and D.B. Sirdeshmukh, “Acta Crystallographica Section A,” 54, 513-514 (1998).
Shankar Narayana, N. Gopi Krishna, and D.B. Sirdeshmukh, “Acta Crystallographica Section A,” 57, 217-218 (2001).
B. Sirdeshmukh, L. Sirdeshmukh, and K.G. Subhadra, “Micro- and Macro-Properties of Solids (Springer Series in Materials Science),” 2006.
Singh and Y.P. Varshni, “Acta Crystallographica Section A,” 38, 854-858 (1982).
Pantea, I. Stroe, H. Ledbetter, J.B. Betts, Y. Zhao, L.L. Daemen, H. Cynn, and A. Migliori, “Physical Review B,” 80, 024112-1-024112-10 (2009).
Pantea, I. Stroe, H. Ledbetter, J.B. Betts, Y. Zhao, L.L. Daemen, H. Cynn, and A. Migliori, “Journal of Physics and Chemistry of Solids,” 69, 211-213 (2008).
H. Deng, W. Lu, Y.M. Hu, H.S. Gu, “Physica B,” 404, 1218-1221 (2009).
Geeta Krishna, K.G. Subhadra, and D.B. Sirdeshmukh, “Acta Crystallographica Section A,” 54, 253-258 (1998).
A. Gschneidner Jr., “Solid State Physics (USA),” 16, 275-426 (1964).
R. Glyde, “Journal of Physics and Chemistry of Solids (G.B),” 28, 2061-2065 (1967).
K. Tewary, “Journal of Physics F (GB),” 3, 704-708 (1973).
Shankar Narayana and N. Gopi Krishna, “Physica Status Solidi (a),” 202, No.14, 2731-2736 (2005).
Gopi Krishna, D.B. Sirdeshmukh, B.Rama Rao, B.J. Beandry, and K.A. Gschneidner Jr., “Physica Status Solidi (a),” 89, K37-K38 (1985).
Singh and Y.P. Varshni, “Physical Review B,” 24, 4340-4347 (1981).
Purushotham, E., “Title of the Paper,” Chemical Papers (Springer Nature, SCI Journal), 76, 7327–7331 (2022).
Purushotham E, Gopi Krishna N, “Title of the Paper,” Physica B (Elsevier): Condensed Matter, Volume 405, Issue 16, 3308-3311 (2010).
Purushotham E, Gopi Krishna N, “Title of the Paper,” Indian Journal of Physics (Springer), Volume 84, Issue 7, 887-893 (2010).
Purushotham E, Gopi Krishna N, “Title of the Paper,” Bulletin of Materials Science (Springer), Vol 36, Issue 6, 973-976 (2013).
Purushotham E and Gopi Krishna N, “Title of the Paper,” 2014, 7(1), 41-44, Link (2014).
Purushotham E, “Title of the Paper,” Journal of Engineering Science and Technology Review, Volume 6, Issue 1, 83-86 (2013).
Purushotham E, “Title of the Paper,” Bulletin of Material Science (SCI, Springer), 37 (4), 773-778, Link (2014).
Purushotham E, “Title of the Paper,” Journal of Nanoscience and Nanotechnology (SCI Journal), 16, No. 5(3), 2658-2662 (2016).
Purushotham E, “Title of the Paper,” Preparation and characterization of CuInSe2 nanoparticles, Rasayan Journal of Chemistry, 12(4), 1676 – 1680 (2019).
Purushotham E F, “Title of the Paper,” IOP Conference Series: Materials Science and Engineering (SCOPUS JOURNAL), 981 022085, 1-9 (2020).
Purushotham E, “Title of the Paper,” IOP Conference Series: Materials Science and Engineering, 1757-8981, 2020, 981 022086, 1-6 (2020).
Purushotham E, “Title of the Paper,” Lecture Notes on Data Engineering and Communications Technologies 63 (ISBN 978-981-16-0080-7, Vol-63, pg. No.297-304 (2021).
Purushotham E, “Title of the Paper,” IOP Conference Series: Materials Science and Engineering, 1757-8981, 1119 (2021) 012001, 1-5 (2021).
Purushotham E, “Title of the Paper,” Materials Today: Proceedings (Elsevier), Vol-47 (part 15), 5391-5394 (2021).
Purushotham E and Veerati Radhika, “Title of the Paper,” Materials Today: Proceedings (Elsevier), Vol-47 (part 15), 4993-4995 (2021).
Purushotham E, “Title of the Paper,” Materials Today: Proceedings (Elsevier), Vol- 47 (part 15), 5034-5037 (2021).


Special Issue Open Access Original Research
Volume 11
Special Issue 12
Received 30/10/2023
Accepted 20/12/2023
Published 15/01/2024