Calculation of Temperature-Dependent Thermal Expansion Coefficient of Metal Crystals Based on Anharmonic Correlated Debye Model
Keywords:thermal expansion coefficient, metal crystals, anharmonic correlated Debye model
This study aims to calculate the anharmonic thermal expansion (TE) coefficient of metal crystals in the temperature dependence. The calculation model is derived from the anharmonic correlated Debye (ACD) model that is developed using the many-body perturbation approach and correlated Debye model based on the anharmonic effective potential. This potential has taken into account the influence on the absorbing and backscattering atoms of all their nearest neighbors in the crystal lattice. The numerical results for the crystalline zinc (Zn) and crystalline copper (Cu) are in agreement with those obtained by the other theoretical model and experiments at several temperatures. The analytical results show that the ACD model is useful and efficient in analyzing the TE of coefficient of metal crystals.
H. Liu, W. Sun, Z. Zhang, L. Lovings, and C. Lind, “Thermal Expansion Behavior in the A2M3O12 Family of Materials,” Solids, vol. 2, no. 1, pp. 87-107, February 2021.
J. W. Hwang, “Thermal expansion of nickel and iron, and the influence of nitrogen on the lattice parameter of iron at the Curie temperature,” Masters Theses, Department of Metallurgical Engineering, University of Missouri–Rolla, Rolla, Missouri, 1972.
V. A. Drebushchak, “Thermal Expansion of Solids: Review on Theories,” Journal of Thermal Analysis and Calorimetry, vol. 142, pp. 1097-1113, January 2020.
T. Dengg, V. Razumovskiy, L. Romaner, G. Kresse, P. Puschnig, and J. Spitaler, “Thermal Expansion Coefficient of WRe Alloys from First Principles,” Physical Review B, vol. 96, no. 3, pp. 035148, July 2017.
G. Laplanche, P. Gadaud, O. Horst, F. Otto, G. Eggeler, and E. P. George, “Temperature Dependencies of the Elastic Moduli and Thermal Expansion Coefficient of an Equiatomic, Single-Phase CoCrFeMnNi High-Entropy Alloy,” Journal of Alloys and Compounds, vol. 623, pp. 348-353, February 2015.
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, October 1981.
Z. K. Liu, Y. Wang, and S. Shang, “Thermal Expansion Anomaly Regulated by Entropy,” Scientific Reports, vol. 4, pp. 7043, November 2014.
Z. K. Liu, Y. Wang, and S. Shang, “Temperature-Dependent EXAFS Debye-Waller Factor of Distorted HCP Crystals,” Journal of the Physical Society of Japan, vo. 91, no. 5, pp.054703, April 2022.
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, March 1996.
T. S. Tien, “Effect of the Non-Ideal Axial Ratio C/A on Anharmonic EXAFS Oscillation of H.C.P. Crystals,” Journal of Synchrotron Radiation, vol. 28, pp. 1544-1557, September 2021.
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, September 2017.
N. V. Hung, C. S. Thang, N. B. Duc, D. Q. Vuong, and T. S. Tien, “Advances in Theoretical and Experimental XAFS Studies of Thermodynamic Properties, Anharmonic Effects and Structural Determination of FCC Crystals,” The European Physical Journal B, vol. 90, no.12, pp. 256, December 2017.
Y. S. Toukian, R. K. Kirby, R. E. Taylor, and P. D. Desai, Thermophysical Properties of Matter–Thermal Expansion: Metallic Elements and Alloys, New York: IFI/Plenum, 1975.
N. V. Hung, N. B. Trung, and B. Kirchner, “Anharmonic Correlated Debye Model Debye-Waller Factors,” Physica B: Condensed Matter, vol. 405, no. 11, pp. 2519-2525, June 2010.
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, December 2016.
T. S. Tien, “Analysis of EXAFS Oscillation of Monocrystalline Diamond-Semiconductors Using Anharmonic Correlated Debye Model,” European Physical Journal Plus, vol. 136, no.5, pp. 539, May 2021.
C. Y. Ho and R. E. Taylor, Thermal Expansion of Solids, Ohio: ASM International, 1998.
J. M. Tranquada, and R. Ingalls, “Extended X-Ray Absorption Fine-Structure Study of Anharmonicity in CuBr,” Physical Review B, vol. 28, no. 6, pp. 3520-3528, September 1983.
L. Tröger, T. Yokoyama, D. Arvanitis, T. Lederer, M. Tischer, and K. Baberschke, “Determination of Bond Lengths, Atomic Mean-Square Relative Displacements, and Local Thermal Expansion by Means of Soft-X-Ray Photoabsorption,” Physical Review B, vol. 49, no. 2, pp. 888-903, January 1994.
P. M. Morse, “Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels,” Physical Review, vol. 34, pp. 57-64, July 1929.
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, May 1959.
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, November 2008.
N. V. Hung and J. J. Rehr, “Anharmonic Correlated Einstein-Model Debye-Waller Factors,” Physical Review B, vol. 56, no. 1, pp. 43-46, July 1997.
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. 31, pp. 315303, June 2020.
N. V. Hung and P. Fornasini, “Anharmonic Effective Potential, Correlation Effects, and EXAFS Cumulants Calculated from a Morse Interaction Potential for FCC Metals,” Journal of the Physical Society of Japan, vol. 76, no. 8, article no. 084601, August 2007.
T. Yokoyama, T. Satsukawa, and T. Ohta, “Anharmonic Interatomic Potentials of Metals and Metal Bromides Determined by EXAFS,” Japanese Journal of Applied Physics, vol. 28, no. 10R, pp. 1905-1908, October 1989.
I. V. Pirog, T. I. Nedoseikina, I. A. Zarubin, and A. T. Shuvaev, “Anharmonic Pair Potential Study in Face-Centered-Cubic Structure Metals,” Journal of Physics: Condensed Matter, vol. 14, no. 8, pp. 1825-1832, February 2002.
N. V. Hung, T. S. Tien, N. B. Duc, and D. Q. Vuong, “High-Order Expanded XAFS Debye-Waller Factors of HCP Crystals Based on Classical Anharmonic Correlated Einstein Model,” Modern Physics Letters B, vol. 28, no. 21, pp. 1450174, August 2014.
J. Meija, T. B. Coplen, M. Berglund, W. A. Brand, P. D. Bièvre, M. Gröning, et al, “Atomic Weights of the Elements 2013 (IUPAC Technical Report),” Pure and Applied Chemistry, vol. 88, no. 3, pp. 265-291, February 2016.
How to Cite
Submission of a manuscript implies: that the work described has not been published before that it is not under consideration for publication elsewhere; that if and when the manuscript is accepted for publication. Authors can retain copyright in their articles with no restrictions. is accepted for publication. Authors can retain copyright of their article with no restrictions.
Since Jan. 01, 2019, AITI will publish new articles with Creative Commons Attribution Non-Commercial License, under The Creative Commons Attribution Non-Commercial 4.0 International (CC BY-NC 4.0) License.
The Creative Commons Attribution Non-Commercial (CC-BY-NC) License permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.