Investigation of Debye temperature and temperature-dependent EXAFS cumulants of Zn, Zr, a-Ti, Ru and Hf metals

Abstract In this work, the anharmonic Einstein model is developed to determine the Debye temperature and investigate the temperature effects on the extended x-ray absorption fine structure (EXAFS) cumulants of hexagonal close-packed (hcp) metals. We have derived the analytical expressions of the anharmonic effective potential, the effective force constant, the Debye temperature and the first four EXAFS cumulants as a function of axial ratio e = c / a . Numerical calculations have been conducted for hcp Zn, Zr, α -Ti, Ru and Hf metals up to temperature 800 K. Our findings indicate that the anharmonicity of thermal lattice vibrations significantly influences the EXAFS cumulants, particularly at high temperatures. Ru atoms have the strongest coupling force causing a phenomenon that Ru lattice shows a smaller thermal disorder, and Zn has a greater thermal disorder. Additionally, we highlight the significant contributions of thermal disorder to the mean-square relative displacement at high temperatures due to thermal lattice vibrations. Moreover, our Debye temperatures derived from the developed model align reasonably well with those reported in previous studies.