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 Hf and entropy Sf 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 Sf and Hf: in particular Sf=17(2)~kB is one order of magnitude larger compared to other elemental metals, and the experimental value of Hf is found to be more than three standard deviations off the theoretical one Hf=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 Sf=-0.0120(14)~kB/K accounting for the anharmonic potential introduced by vacancies.