Breakdown of the Arrhenius Law of the Temperature Dependent Vacancy Concentration in fcc-Lanthanum

Abstract

We measured the temperature dependent equilibrium vacancy concentration using in-situ positron annihilation spectroscopy in order to determine the enthalpy $H_{\text{f}}$ and entropy $S_{\text{f}}$ of vacancy formation in elementary fcc-La. The Arrhenius law applied for the data analysis, however, is shown to fail in explaining the unexpected high values for both $S_{\text{f}}$ and $H_{\text{f}}$: in particular $S_{\text{f}}=17(2)k_{\text{B}}$ is one order of magnitude larger compared to other elemental metals, and the experimental value of $H_{\text{f}}$ is found to be more than three standard deviations off the theoretical one $H_{\text{f}}=1.46\text{eV}$ (our \acs{dft} calculation for La at $T=0\text{K}$). A consistent explanation is given beyond the classical Arrhenius approach in terms of a temperature dependence of the vacancy formation entropy with $S_{\text{f}}^{\prime }=-0.0120(14)k_{\text{B}}/\text{K}$ accounting for the anharmonic potential introduced by vacancies.

5 pages, 3 figures