Role of phonon anharmonicity and electronic free energy on thermodynamic properties of fcc ytterbium

Abstract

Although many thermophysical properties of lanthanide family members are similar, ytterbium is an exception. The coefficient of thermal expansion for Yb is almost three times as large as the coefficients for other rare-earth metals, a clear manifestation of anharmonicity. In the present study, therefore, the influence of the phonon anharmonicity and the electronic free energy on thermal expansion and other thermodynamic properties of ytterbium has been investigated from absolute zero to the melting temperature (T). We used first principles density functional perturbation theory combined with thermal perturbative treatment for including intrinsic anharmonicity. Modeling Yb as an anharmonic oscillator as suggested by Oganov and Dorogokupets [J. Phys. Condens. Matter 16, 1351 (2004)], an anharmonic vibrational contribution is included in a parametric way. It has allowed us to unveil the effect of anharmonicity connecting the low-temperature quantum correction up to the high-temperature classical value. Furthermore, due to the complex behavior of 4f-shell electrons, the electronic excitation was computed through the fixed electronic density-of-state approximation. It remains two orders of magnitude higher than the anharmonic lattice term. Combining these contributions, we can evaluate several T-dependent but zero-pressure thermodynamic properties of Yb in its fcc phase. Since, at lower pressure, anharmonicity increases with temperature, one of the objectives of this study is to examine the importance of anharmonicity in determining these properties. For instance, an excellent agreement is found for the linear thermal expansion for the entire temperature range, whereas other properties such as entropy, bulk moduli, thermal Grüneisen parameter, and the phonon frequency shifts are also in agreement with the reported findings; notably, the discrepancy observed in the enthalpy and specific heats at high-T is discussed. A detailed analysis has suggested that an additional contribution from point defects is needed, like vacancy formation, for an accurate calculation of specific heat, while higher-order terms in temperature-dependent perturbative series are mandatory for enthalpy. Electronic contribution remains positive for caloric properties. The theory of anharmonic phonon-phonon interaction and computed thermal expansion of the crystal was finally used to analyze renormalized phonon frequency. The significant objective of the study is to elucidate the role of electronic agitations and intrinsic phonon thermal stress as a physical mechanism over and above the dominating volume expansion effect, which is responsible for restricting an overwhelming quasi-harmonic thermal expansion and a rapid decrease in bulk moduli close to melting. We propose that a quantitative agreement for entropy and enthalpy requires a delicate balance between T2-dependent and higher-order terms in an anharmonic perturbation series.