Rheology of liquid fcc metals: Equilibrium and transient-time correlation-function nonequilibrium molecular dynamics simulations

Abstract

Using classical molecular dynamics simulation together with the quantum-corrected Sutton-Chen many-body embedded-atom model, we study the rheology of several liquid fcc metals (Pb, Pt, Ir, Ag, and Rh) at ambient pressure and at four temperatures ranging from 5% below the melting temperature to 75% above the melting temperature. We first carry out equilibrium molecular dynamics simulations and determine, using Green-Kubo's formalism, the shear viscosity ${\ensuremath{\eta}}_{\text{GK}}$, the shear modulus ${G}_{\ensuremath{\infty}}$, and the Maxwell relaxation time ${\ensuremath{\tau}}_{M}$. By scaling the shear stress autocorrelation function or, equivalently, the time-dependent viscosity $\ensuremath{\eta}(t)$ by ${\ensuremath{\eta}}_{\text{GK}}$ and the time $t$ by ${\ensuremath{\tau}}_{M}$, we show that the scaled time-dependent viscosity for all metals collapses onto the same curve. This demonstrates that the relaxation behavior is the same for all metals studied here. We then apply transient-time correlation-function nonequilibrium molecular dynamics simulations to determine the response of liquid metals subjected to shear rates ranging from $10\text{ }{\text{s}}^{\ensuremath{-}1}$ to $5\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }{\text{s}}^{\ensuremath{-}1}$. We show that for all metals, the shear rate-dependent viscosity $\ensuremath{\eta}(\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}})$ (scaled by ${\ensuremath{\eta}}_{\text{GK}}$) as a function of the applied shear rate $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}$ (scaled by the inverse of ${\ensuremath{\tau}}_{M}$) collapses onto the same curve. We obtain the same result for the shear rate-dependent pressure $P(\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}})$ (scaled by ${G}_{\ensuremath{\infty}}$) and for the potential energy (scaled by its equilibrium value). Fits to power-law expressions show that $\ensuremath{\eta}(\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}})$ follows the prediction of mode-coupling theory and that nonanalytic exponents are found for the shear rate dependence of pressure and potential energy.