Enthalpy-entropy compensation of atomic diffusion originates from softening of low frequency phonons

Abstract

Experimental data accumulated over more than 120 years show not only that diffusion coefficients of impurities ordinarily obey the Arrhenius law in crystalline solids, but also that diffusion pre-exponential factors measured in a same solid increase exponentially with activation energies. This so-called compensation effect has been argued to result from a universal positive linear relationship between entropic contributions and energy barriers to diffusion. However, no physical model of entropy has ever been successfully tested against experimental compensation data. Here, we solve this decades-old problem by demonstrating that atomistically computed harmonic vibrational entropic contributions account for most of compensation effects in silicon and aluminum. We then show that, on average, variations of atomic interactions along diffusion reaction paths simultaneously soften low frequency phonons and stiffen high frequency ones; because relative frequency variations are larger in the lower region of the spectrum, softening generally prevails over stiffening and entropy ubiquitously increases with energy.

Defect Spectroscopy in Halide Perovskites Is Dominated by Ionic Rather than Electronic Defects

“…45 Therefore, N1 has been interpreted as continuum of donor states at the CIS surface 42 or an injection/extraction barrier. 46,47 In view of the evidence for Cu migration in CIS, N1 showing up with same rates for τ 1 and τ 2 independent of any transport layers, and ionic defects often following the Meyer−Neldel rule, 7 we propose that the N1 signal in CIS corresponds to ionic migration, likely to Curelated defects.…”

“…Using iodide partial pressure investigations, it was deduced that the halide ion is the most mobile. 4,5 Furthermore, it was shown that the mobile ions follow the Meyer−Neldel rule 6,7 and that HaPs are capable of self-healing after being damaged. 8,9 As a result, Rakita et al 10 stated that HaPs "are likely an example of a class of materials that cannot support static bulk defect densities significantly above thermodynamically-dictated densities.…”

Temperature-Dependent Ionic Conductivity and Properties of Iodine-Related Defects in Metal Halide Perovskites

“…46,55 The physical origin of this dependence of diffusion prefactor on activation energy is still not resolved, although recently an explanation based on compensation effect due to loosening of crystalline lattices' elastic moduli at transition states (Zener's model) has been proposed. 56 Because of the presence of an internal electric field, ions accumulate at the interfaces between the perovskite active layer and the transport layers, 57 which leads to the formation of Debye layers at these interfaces. When anions and cations are present, 46 Debye layers form at both interfaces to the transport layers.…”

Vacancy diffusion in palladium hydrides

“…The compensation effect has been largely ascribed to softening of low-frequency m modes at the transition state relative to the initial state based on diffusion studies in silicon and aluminum. 31 In the present case, however, the change in was mainly determined by 0 the change in the entropy of vacancy formation, which in turn had a significant contribution from the vibrational entropy of hydrogen (Supplementary Fig. 2).…”