Shear melting at the crystal-liquid interface: Erosion and the asymmetric suppression of interface fluctuations

The influence of an applied shear on the planar crystal-melt interface is modeled by a nonlinear stochastic partial differential equation of the interface fluctuations. A feature of this theory is the asymmetric destruction of interface fluctuations due to advection of the crystal protrusions on the liquid side of the interface only. We show that this model is able to qualitatively reproduce the nonequilibrium coexistence line found in simulations. The impact of shear on spherical clusters is also addressed.

Figure 1

Nonequilibrium coexistence line in the space of the reduced supercooling $\mathrm{\Delta }/Q^{1/2}$ and the square of the reduced shear stress ${\widehat{\sigma }}^2$. The solid line corresponds to the empirical fit in Eq. (11)), while the dashed line is a straight line fit to the data at small ${\widehat{\sigma }}^2$, included for comparison. Inset: Coexistence curve, plotted as $T_m-T$, vs the squared shear stress ${\sigma }^2$ obtained from molecular dynamics simulations of the Lennard-Jones crystal in the presence of shear [10]. The dashed line is a straight line fit to the low-stress data.

Figure 2

Variance $\langle {(h-\langle h\rangle )}^2\rangle /Q$ of the interface height fluctuations along the coexistence line as a function of ${\widehat{\sigma }}^2$ for three different values of $Q$.

Figure 3

Plot of the crystal growth rate $\upsilon /Q^{1/2}$ vs $[\mathrm{\Delta }-{\mathrm{\Delta }}_{\mathrm{coex}}\left(\widehat{\sigma }\right)]/Q^{1/2}$ for a range of choices of the reduced stress $\widehat{\sigma }$ and the noise amplitude $Q^{1/2}$.