Breakdown of Arrhenius law of 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 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 = 17(2) kB 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 = −0.0120(14) kB/K accounting for the anharmonic potential introduced by vacancies.

Theoretical insights into non-Arrhenius behaviors of thermal vacancies in anharmonic crystals

“…where g 0 , g 1 , g 2 , and g 3 are fitting parameters. Indeed, applying eqn (16) to existing DD data 45 gives g 0 = 1.37 eV. This figure is close to G f 0K = 1.38 eV derived from the SMM and G f 0K = 1.40 eV deduced from the two-stage upsampled thermodynamic integration using Langevin dynamics (TU-TILD).…”

“…However, the fitted value of H f can be appreciably larger than its DFT counterpart. 16 Besides, the generation of vacancies in many metallic substances does not obey the classical Arrhenius ansatz. 17 These anomalous phenomena have raised persistent controversies in the physics community.…”

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[(CH3)2NH2]2PdBr4, a layered hybrid halide perovskite semiconductor with improved optical and electrical properties

“…The obtained values of bulk resistance ( R g ), corresponding to the grain, are used to determine the electrical conductivity σ g as follows: 37 where e is the thickness of the sample and S is the area of one flat face of the pellet. The thermal dependence of R g and the electrical conductivity ln( σ g ) versus (1000/ T ) is displayed in Fig.…”