Breakdown of the Stokes-Einstein relation in Stillinger-Weber silicon

We investigate the dynamical properties of liquid and supercooled liquid silicon, modeled using the Stillinger-Weber potential, to examine the validity of the Stokes-Einstein (SE) relation. Toward this end, we examine the relationship among various dynamical quantities, including (i) the macroscopic transport coefficients-self-diffusion coefficient D and viscosity η, (ii) relaxation time τα, and (iii) lengthscale dependent relaxation times τα(q) over a broad range of temperature T, pressure P, and density ρ covering both equilibrium and metastable liquid state points in the phase diagram. Our study shows a weak breakdown in the SE relation involving D and η, and the loci of the breakdown of the SE relation (SEB) are found in the high T liquid phase. The τα, when used as a proxy to η, shows a distinct breakdown in the SE relation, whose loci are found in the supercooled liquid phase. Interestingly, certain parts of the phase diagram show that the loci of onset of slow dynamics lie below the loci of SEB, suggesting a regime that exhibits Arrhenius but non-Fickian behavior. Computation of τα(q) enables us to extract the lengthscale associated with the Fickian to non-Fickian behavior using which we show that the breakdown of the SE relation occurs only below a specific lengthscale at a given temperature. Furthermore, we also compare the SEB loci with other features of the phase behavior, including the loci of compressibility maximum, density maximum, and diffusivity maximum.