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

Open Access

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By

    Dr. Purushotham Endla

  1. 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

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Open Access Original Research
Volume
Received October 30, 2023
Accepted December 20, 2023
Published