Vol. 32 No. 4 (2022): Coming Issue

Analysis of Temperature-dependent Extended X-ray Absorption Fine Structure Oscillation of Distorted Crystalline Cadmium

Tong Sy Tien
Department of Basic Sciences, University of Fire Prevention and Fighting, 243 Khuat Duy Tien, Thanh Xuan, Hanoi 120602, Vietnam

Published 17-08-2022


  • crystalline cadmium,
  • anharmonic correlated Debye model,
  • Debye-Waller factor,
  • EXAFS oscillation

How to Cite

Sy Tien, T. (2022). Analysis of Temperature-dependent Extended X-ray Absorption Fine Structure Oscillation of Distorted Crystalline Cadmium. Communications in Physics, 32(4). https://doi.org/10.15625/0868-3166/16890


In this paper, the temperature-dependent extended X-ray absorption fine structure (EXAFS) of distorted crystalline cadmium has been analyzed using an efficient calculation-model. The analysis procedure is based on evaluating the influence of temperature on the phase shift and amplitude reduction of EXAFS oscillation that is expressed in terms of the EXAFS Debye-Waller factor. The anharmonic EXAFS cumulants are calculated by expanding the anharmonic correlated Debye model based on the anharmonic effective potential that depends on the structural characteristics of distorted crystalline cadmium. The numerical results satisfy well with those obtained using the experimental data and other models at various temperatures. The obtained results indicate that this theoretical model is useful for calculating and analyzing the experimental EXAFS data of distorted crystalline metals.


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  1. S. Shikata, K. Yamaguchi, A. Fujiwara, Y. Tamenori, K. Tsuruta, T. Yamada, S.S. Nicley, K. Haenen, S. Koizumi, X-ray absorption near edge structure and extended X-ray absorption fine structure studies of P doped (111) diamond, Diam. Relat. Mater. 105 (2020) 107769.
  2. DOI: https://doi.org/10.1016/j.diamond.2020.107769 DOI: https://doi.org/10.1016/j.diamond.2020.107769
  3. P. Fornasini, R. Grisenti, M. Dapiaggi, and G. Agostini, Local structural distortions in SnTe investigated by EXAFS, J. Phys.: Condens. Matter 33 (2021) 295404.
  4. DOI: https://doi.org/10.1088/1361-648X/ac0082 DOI: https://doi.org/10.1088/1361-648X/ac0082
  5. T.S. Tien, Temperature-Dependent EXAFS Debye–Waller Factor of Distorted HCP Crystals, J. Phys. Soc. Jpn. 91 (2022) 054703.
  6. DOI: https://doi.org/10.7566/JPSJ.91.054703 DOI: https://doi.org/10.7566/JPSJ.91.054703
  7. 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, Phys. Rev. B 53 (1996) 6111.
  8. DOI: https://doi.org/10.1103/PhysRevB.53.6111 DOI: https://doi.org/10.1103/PhysRevB.53.6111
  9. T. S. Tien, Effect of the non-ideal axial ratio c/a on anharmonic EXAFS oscillation of h.c.p. crystals, J. Synchrotron Rad. 28 (2021) 1544.
  10. DOI: https://doi.org/10.1107/S1600577521007256 DOI: https://doi.org/10.1107/S1600577521007256
  11. J. J. Rehr, F. D. Vila, J. J. Kas, N. Y. Hirshberg, K. Kowalski, and B. Peng, Equation of motion coupled-cluster cumulant approach for intrinsic losses in x-ray spectra, J. Chem. Phys. 152 (2020).
  12. DOI: https://doi.org/10.1063/5.0004865 DOI: https://doi.org/10.1063/5.0004865
  13. T. Yokoyama and S. Chaveanghong, Anharmonicity in elastic constants and extended x-ray-absorption fine structure cumulants, Phys. Rev. Materials 3 (2019) 033607.
  14. DOI: https://doi.org/10.1103/PhysRevMaterials.3.033607 DOI: https://doi.org/10.1103/PhysRevMaterials.3.033607
  15. R. B. Greegor and F. W. Lytle, Extended x-ray absorption fine structure determination of thermal disorder in Cu: Comparison of theory and experiment, Phys. Rev. B 20 (1979) 4902.
  16. DOI: https://doi.org/10.1103/PhysRevB.20.4902 DOI: https://doi.org/10.1103/PhysRevB.20.4902
  17. G. Bunker, Application of the ratio method of EXAFS analysis to disordered systems, Nucl. Instrum. Methods 207 (1983) 437.
  18. DOI: https://doi.org/10.1016/0167-5087(83)90655-5 DOI: https://doi.org/10.1016/0167-5087(83)90655-5
  19. J. J. Rehr and R. C. Albers, Theoretical approaches to x-ray absorption fine structure, Rev. Mod. Phys. 72 (2000) 621.
  20. DOI: https://doi.org/10.1103/RevModPhys.72.621 DOI: https://doi.org/10.1103/RevModPhys.72.621
  21. M. Newville, EXAFS analysis using FEFF and FEFFIT, J. Synchrotron Rad. 8 (2001) 96.
  22. DOI: https://doi.org/10.1107/S0909049500016290 DOI: https://doi.org/10.1107/S0909049500016290
  23. M. Newville, B. Ravel, D. Haskel, J. J. Rehr, E. A. Stern, and Y. Yacoby, Analysis of multiple-scattering XAFS data using theoretical standards, Physica B 208-209 (1995)154.
  24. DOI: https://doi.org/10.1016/0921-4526(94)00655-F DOI: https://doi.org/10.1016/0921-4526(94)00655-F
  25. A. L. Ankudinov, B. Ravel, J. J. Rehr, and S. D. Conradson, Real-space multiple-scattering calculation and interpretation of x-ray-absorption near-edge structure, Phys. Rev. B 58 (1998).
  26. DOI: https://doi.org/10.1103/PhysRevB.58.7565 DOI: https://doi.org/10.1103/PhysRevB.58.7565
  27. S. I. Zabinsky, J. J. Rehr, A. Ankudinov, R. C. Albers, and M. J. Eller, Multiple-scattering calculations of x-ray-absorption spectra, Phys. Rev. B 52 (1995) 2995.
  28. DOI: https://doi.org/10.1103/PhysRevB.52.2995 DOI: https://doi.org/10.1103/PhysRevB.52.2995
  29. J. J. Rehr, J. Mustre de Leon, S. I. Zabinsky, and R. C. Albers, Theoretical x-ray absorption fine structure standards, J. Am. Chem. Soc. 113 (1991) 5135.
  30. DOI: https://doi.org/10.1021/ja00014a001 DOI: https://doi.org/10.1021/ja00014a001
  31. T. S. Tien, Investigation of the anharmonic EXAFS oscillation of distorted HCP crystals based on extending quantum anharmonic correlated Einstein model, Jpn. J. Appl. Phys. 60 (2021) 112001.
  32. DOI: https://doi.org/10.35848/1347-4065/ac21b3 DOI: https://doi.org/10.35848/1347-4065/ac21b3
  33. G. Buxbaum and G. Pfaff, Industrial Inorganic Pigments, 3rd ed., Wiley-VCH, New York (2005). DOI: https://doi.org/10.1002/3527603735
  34. M. Hou, L. Li,, and M. Zhuang, Research on application mechanism of cadmium in new energy vehicle charging group, IOP Conf. Ser.: Earth Environ. Sci. 227 (2019) 052046.
  35. DOI: https://doi.org/10.1088/1755-1315/227/5/052046 DOI: https://doi.org/10.1088/1755-1315/227/5/052046
  36. A. M. Kadim, Applications of Cadmium Telluride (CdTe) in Nanotechnology, IntechOpen, London (2019). DOI: https://doi.org/10.5772/intechopen.85506
  37. N. E. Galushkin, N. N. Yazvinskaya, and D. N. Galushkin, Nickel-cadmium batteries with pocket electrodes as hydrogen energy storage units of high-capacity, Journal of Energy Storage 39 (2021) 102597.
  38. DOI: https://doi.org/10.1016/j.est.2021.102597 DOI: https://doi.org/10.1016/j.est.2021.102597
  39. N. V. Hung, L. H. Hung, T. S. Tien, and R. R. Frahm, Anharmonic effective potential, local force constant and EXAFS of HCP crystals: Theory and comparison to experiment, Int. J. Mod. Phys. B 22 (2008) 5155.
  40. DOI: https://doi.org/10.1142/S0217979208049285 DOI: https://doi.org/10.1142/S0217979208049285
  41. 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, Mod. Phys. Lett. B 28 (2014) 1450174.
  42. DOI: https://doi.org/10.1142/S0217984914501747 DOI: https://doi.org/10.1142/S0217984914501747
  43. N. V. Hung, N. B. Trung, and B. Kirchner, Anharmonic correlated Debye model Debye–Waller factors, Physica B 405 (2010) 2519.
  44. DOI: https://doi.org/10.1016/j.physb.2010.03.013 DOI: https://doi.org/10.1016/j.physb.2010.03.013
  45. N. B. Duc, N. V. Hung, H. D. Khoa, D. Q. Vuong, and T. S. Tien, Thermodynamic Properties and Anharmonic Effects in XAFS Based on Anharmonic Correlated Debye Model Debye–Waller Factors, Adv. Mater. Sci. Eng. 2018 (2018) 3263170.
  46. DOI: https://doi.org/10.1155/2018/3263170 DOI: https://doi.org/10.1155/2018/3263170
  47. N. B. Duc, V. Q. Tho, T. S. Tien, D. Q. Khoa, and H. K. Hieu, Pressure and temperature dependence of EXAFS Debye-Waller factor of platinum, Radiat. Phys. Chem. 149 (2018) 61.
  48. DOI: https://doi.org/10.1016/j.radphyschem.2018.03.017 DOI: https://doi.org/10.1016/j.radphyschem.2018.03.017
  49. T. S. Tien, Analysis of EXAFS oscillation of monocrystalline diamond-semiconductors using anharmonic correlated Debye model, Eur. Phys. J. Plus. 136 (2021) 539.
  50. DOI: https://doi.org/10.1140/epjp/s13360-021-01378-z DOI: https://doi.org/10.1140/epjp/s13360-021-01378-z
  51. E. D. Crozier, J. J. Rehr, and R. Ingalls, X-ray Absorption: Principles, Applications, Techniques of EXAFS, SEXAFS, XANES, edited by D. C. Koningsberger and R. Prins, Chap. 9, Wiley, New York (1988).
  52. T. S. Tien, Advances in studies of the temperature dependence of the EXAFS amplitude and phase of FCC crystals, J. Phys. D: Appl. Phys. 53 (2020) 315303.
  53. DOI: https://doi.org/10.1088/1361-6463/ab8249 DOI: https://doi.org/10.1088/1361-6463/ab8249
  54. N. V. Hung, T. S. Tien, and L. H. Hung, High-order anharmonic effective potentials and EXAFS cumulants of FCC crystals calculated from a Morse interaction potential, Communications in Physics 18 (2008) 75.
  55. 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, Phys. Rev. B 49 (1994) 888.
  56. DOI: https://doi.org/10.1103/PhysRevB.49.888 DOI: https://doi.org/10.1103/PhysRevB.49.888
  57. A. Sanson, On the neglecting of higher-order cumulants in EXAFS data analysis, J. Synchrotron Radiat. 16 (2009) 864.
  58. DOI: https://doi.org/10.1107/S0909049509037716 DOI: https://doi.org/10.1107/S0909049509037716
  59. 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, J. Chem. Phys. 147 (2017) 044503.
  60. DOI: https://doi.org/10.1063/1.4995435 DOI: https://doi.org/10.1063/1.4995435
  61. P. M. Morse, Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels, Phys. Rev. 34 (1929) 57.
  62. DOI: https://doi.org/10.1103/PhysRev.34.57 DOI: https://doi.org/10.1103/PhysRev.34.57
  63. L. A. Girifalco and V. G. Weizer, Application of the Morse Potential Function to Cubic Metals, Phys. Rev. 114 (1959) 687.
  64. DOI: https://doi.org/10.1103/PhysRev.114.687 DOI: https://doi.org/10.1103/PhysRev.114.687
  65. N. V. Hung and J. J. Rehr, Anharmonic correlated Einstein-model Debye-Waller factors, Phys. Rev. B 56 (1997) 43.
  66. DOI: https://doi.org/10.1103/PhysRevB.56.43 DOI: https://doi.org/10.1103/PhysRevB.56.43
  67. P. Enghag, Encyclopedia of the elements: Technical data, history, processing, applications, Wiley-VCH, Weinheim (2004). DOI: https://doi.org/10.1002/9783527612338