Temperature-dependent High-order XAFS Cumulants of Gaseous Bromine Calculated Based on the Classical Statistical Theory
Main Article Content
Abstract
The anharmonic X-ray absorption fine structure (XAFS) cumulants of gaseous bromine (Br2) in an expansion to the 4th order have been calculated under the influence of thermal disorder. The thermodynamic parameters of Br2 have considered the influence of nearest neighbors on the backscattering and absorbing atoms. The temperature-dependent XAFS cumulants were calculated explicitly and simply from the calculation model developed based on the classical statistical theory within the correlated Einstein model. The obtained numerical results of Br2 at temperatures from 0 to 600 K fit with those obtained from the experimental XAFS data and other theoretical approaches at various temperatures. These results indicate that the present theoretical model helps analyze experimental XAFS signals of gaseous bromine and other gases.
Keywords:
High-oder XAFS cumulants, thermal disorders, gaseous bromine, classical statistics, correlated Einstein model.
References
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https://doi.org/10.1103/PhysRevMaterials.3.033607.
[3] P. Fornasini, R. Grisenti, M. Dapiaggi, G. Postini, Local Structural Distortions in SnTe Investigated by EXAFS, Journal of Physics: Condensed Matter, Vol. 33, 2021, pp. 295404, https://doi.org/10.1088/1361-648X/ac0082.
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[6] T. Yokoyama, K. Kobayashi, T. Ohta, 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, 1996, pp. 6111-6122, https://doi.org/10.1103/PhysRevB.53.6111.
[7] G. Dalba, P. Fornasini, M. Grazioli, Local Disorder in Crystalline and Amorphous Germanium, Physical Review B, Vol. 52, No. 15, 1995, pp. 11034-11043, https://doi.org/10.1103/PhysRevB.52.11034.
[8] T. S. Tien, Temperature-Dependent EXAFS Debye-Waller Factor of Distorted HCP Crystals, Journal of the Physical Society of Japan, Vol. 91, No. 5, 2022, pp. 054703, https://doi.org/10.7566/JPSJ.91.054703.
[9] K. J. Szabo, N. Selander, Organofluorine Chemistry: Synthesis, Modeling, and Applications, Wiley-VCH, Weinheim, 2021, https://doi.org/10.1002/9783527825158.
[10] T. Yokoyama, Path-integral Effective-potential Method Applied to Extended X-ray-absorption Fine-structure Cumulants, Physical Review B, Vol. 57, No. 6, 1998, pp. 3423-3432, https://doi.org/10.1103/PhysRevB.57.3423.
[11] H. K. Hieu, N. M. Hai, Application of Path-integral for Studying EXAFS Cumulants, Communications in Physics, Vol. 14, No. 3S1, 2014, pp. 40-44, https://doi.org/10.15625/0868-3166/24/3S1/5075.
[12] 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, 2020, pp. 315303,
https://doi.org/ 10.1088/1361-6463/ab8249.
[13] N. B. Duc, V. Q. Tho, T. S. Tien, D. Q. Khoa, H. K. Hieu, Pressure and Temperature Dependence of EXAFS Debye-Waller Factor Of Platinum, Radiation Physics and Chemistry, Vol. 149, 2018, pp. 61-64, https://doi.org/10.1016/j.radphyschem.2018.03.017.
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[15] T. S. Tien et al., High-order EXAFS Cumulants of Diamond Crystals Based on A Classical Anharmonic Correlated Einstein Model, Journal of Physics and Chemistry of Solids, Vol. 134, 2019, pp. 307-312, https://doi.org/10.1016/j.jpcs.2019.06.020.
[16] E. A. Stern, P. Livins, Z. Zhang, Thermal Vibration and Melting from A Local Perspective, Physical Review B, Vol. 43, No. 11, 1991, pp. 8850-8860, https://doi.org/10.1103/PhysRevB.43.8850.
[17] J. Freund, R. Ingalls, E. D. Crozier, Extended X-ray-absorption Fine-structure Study of Copper Under High Pressure, Physical Review B, Vol. 39, No. 17, 1989, pp. 12537-12547, https://doi.org/10.1103/PhysRevB.39.12537.
[18] N.V. Hung, J.J. Rehr, Anharmonic correlated Einstein-model Debye-Waller factors, Physical Review B, Vol. 56, No. 1, 1997, pp. 43–46, https://doi.org/10.1103/PhysRevB.56.43.
[19] N. V. Hung, T. S. Tien, N. B. Duc, 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, 2014, pp. 1450174, https://doi.org/10.1142/S0217984914501747.
[20] K. P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure, IV: Constants of Diatomic Molecules, Springer New York, New York, 1979, https://doi.org/10.1007/978-1-4757-0961-2.