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

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.