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

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.