Breakdown of Arrhenius law of 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-f and entropy S-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-f and H-f: in particular S-f = 16(2) k(B) is one order of magnitude larger compared to other elemental metals, and the experimental value of H-f is found to be more than three standard deviations off the theoretical one H-f = 1.46 eV (our DFT calculation for La at T = 0 K). A consistent explanation is given beyond the classical Arrhenius approach in terms of a temperature dependence of the vacancy formation entropy with S'(f) = 0.01119( 13) k(B)/K accounting for the anharmonic potential introduced by vacancies.