In crystals, where sequences of diffusive events are usually dominated by a single-jump mechanism, D is proportional to the product of the average rate at which jumps are activated and the concentration of defects possibly mediating jumps. 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.Ītomic diffusion in solids proceeds via sequences of thermally activated atomic jumps, which, in the presence of chemical inhomogeneities, induce a flux of atoms that can be described at the mesoscopic level by the diffusion coefficient D 1, 2. 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. However, no physical model of entropy has ever been successfully tested against experimental compensation data. This so-called compensation effect has been argued to result from a universal positive linear relationship between entropic contributions and energy barriers to diffusion. 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.
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