Crystal-melt interface stresses: Atomistic simulation calculations for a Lennard-Jones binary alloy, Stillinger-Weber Si, and embedded atom method Ni

Molecular-dynamics and Monte Carlo simulations have been used to compute the crystal-melt interface stress $\left(f\right)$ in a model Lennard-Jones (LJ) binary alloy system, as well as for elemental Si and Ni modeled by many-body Stillinger-Weber and embedded-atom-method (EAM) potentials, respectively. For the LJ alloys the interface stress in the (100) orientation was found to be negative and the $f$ vs composition behavior exhibits a slight negative deviation from linearity. For Stillinger-Weber Si, a positive interface stress was found for both (100) and (111) interfaces: $f_{100}=(380\pm 30)\mathrm{mJ}∕{\mathrm{m}}^2$ and $f_{111}=(300\pm 10)\mathrm{mJ}∕{\mathrm{m}}^2$. The Si (100) and (111) interface stresses are roughly 80 and 65% of the value of the interfacial free energy $\left(\gamma \right)$, respectively. In EAM Ni we obtained $f_{100}=(22\pm 74)\mathrm{mJ}∕{\mathrm{m}}^2$, which is an order of magnitude lower than $\gamma$. A qualitative explanation for the trends in $f$ is discussed.

Figure 1

The temperature-composition $\left(x_2\right)$ phase diagram for the $ϵ=0.75$, $\sigma =1$ LJ alloy.

Figure 2

Top: the normal pressure minus the transverse pressure in units of ${ϵ}_{22}∕{\sigma }_{22}^3$ vs the distance normal to the crystal-melt interface. Data for six temperatures, corresponding to the six compositions shown in Fig. 1, are shown. The large negative peaks occur at the positions of the two interfaces in the periodic cell. Bottom: the normal pressure $P_{zz}$ vs position along the $z$ direction.

Figure 3

Crystal-melt interface stress for the $ϵ=0.75$, $\sigma =1$ LJ alloy vs the composition $x_2$. The dashed line represents a linear interpolation of the stresses for the two pure components.