Anharmonicity in elastic constants and extended x-ray-absorption fine structure cumulants

Abstract

We have investigated temperature dependence of the elastic constants and higher-order EXAFS (extended x-ray-absorption fine structure) cumulant moments, both of which originate from vibrational anharmonicity. We focus our attention on how the third- or fourth-order anharmonicity contributes to these physical quantities. Although it may be believed that the fourth-order anharmonicity should dominantly contribute to the fourth-order EXAFS cumulant through the first-order quantum statistical perturbation theory, it is consequently found that the experimental fourth-order EXAFS cumulant observed in fcc Ni, Cu, and stainless steel 316 are described mainly by the third-order anharmonicity through the second-order perturbation. In case of the elastic constants, such a situation is more prominent, and the contribution of the fourth-order anharmonicity is negligibly small for the estimation of temperature dependence of the elastic constants. We have also observed significant lattice strains on Cr and Mo in stainless steel 316 through the Fe, Ni, Cr, and Mo K-edge EXAFS measurements: a compressive lattice strain on Cr associated with larger thermal fluctuations and a more significant compressive lattice strain on Mo without enhanced thermal fluctuation. Such a characteristic dissimilarity may be caused by the differences in the atomic weights and the cohesive energies between Cr and Mo. Moreover, we have performed path-integral effective classical potential and classical Monte-Carlo simulations to describe the bulk moduli of the Invar and Elinvar alloys that show noticeable anomalies due to the so-called Invar effect. Appropriate temperature dependence of the bulk moduli is successfully obtained for the Invar, Elinvar, and stainless steel 304 and 316 alloys as well as elemental fcc Cu and Ni metals.