Unraveling strongly entropic effect on β-relaxation in metallic glass: Insights from enhanced atomistic samplings over experimentally relevant timescales

The Johari-Goldstein secondary $(\ensuremath{\beta})$ relaxation is an intrinsic feature of glasses, which is crucial to many properties of disordered materials. One puzzling feature of $\ensuremath{\beta}$-relaxation is its wide relaxation peak, which could imply a critical role of entropy. Here we quantify the activation entropy related to the $\ensuremath{\beta}$-relaxation in metallic glass via well-tempered metadynamics simulations. The activation free energy of the $\ensuremath{\beta}$-relaxation drastically decreases with increasing temperature, indicating a strongly entropic effect that may contribute a multiplication prefactor up to several orders of magnitude to the frequency. We further argue the entropic effect by linear extrapolation of the temperature-dependent activation free energy to 0 K, which gives rise to activation energy, in agreement with the barrier spectrum explored by the activation-relaxation technique. The entropic effect signifies the multiplicity of activation pathways which agrees with the experimentally found wide frequency domain of the $\ensuremath{\beta}$-relaxation.