Year: 2025
Type: article
Abstract: Isotopic effects in the Debye temperature and in the temperature-dependent extended X-ray absorption fine structure (EXAFS) cumulants have been predicted based on the developed anharmonic Einstein model in the case of non-ideal axial ratio of hexagonal close-packed (hcp) zirconium isotopes. We derive analytical expressions for the force constants, the Debye temperature, and the first three EXAFS cumulants as functions of the axial ratio e = c/a. Numerical calculations are conducted for the isotopes 90Zr, 91Zr, 92Zr, 94Zr, and 96Zr up to a temperature of 700 K. Our findings reveal that the effects of isotopic mass differences are clearly evident at low temperatures, particularly below 100 K, where quantum effects predominate. At higher temperature, the anharmonicity caused by thermal lattice vibrations significantly influences the EXAFS cumulants, and reduces the isotopic effects in EXAFS cumulants. Furthermore, our derived Debye temperatures from the developed model exhibit reasonable agreement with experimental value measured by X-ray diffraction.
Source: Romanian Journal of Physics
Authors: TAM NGUYEN TRONG, HIEU HO KHAC, HONG NGUYEN THI
Institutions: Vietnam Maritime University, Duy Tan University
Language: English
Subfield: Radiation
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4408994261