Method for computing short-range forces between solid-liquid interfaces driving grain boundary premelting

We present a molecular dynamics based method for accurately computing short-range structural forces resulting from the overlap of spatially diffuse solid-liquid interfaces at wetted grain boundaries close to the melting point. The method is based on monitoring the fluctuations of the liquid layer width at different temperatures to extract the excess interfacial free energy as a function of this width. The method is illustrated for a high-energy $\Sigma 9$ twist boundary in pure Ni. The short-range repulsion driving premelting is found to be dominant in comparison to long-range dispersion and entropic forces and consistent with previous experimental findings that nanometer-scale layer widths may be observed only very close to the melting point.

Figure 1

Calculated excess volumes versus temperature for four grain boundaries in elemental Ni.

Figure 2

(Color online) Snapshots from a MD simulation at an undercooling of $2\mathrm{K}$, illustrating the dynamic nature of the GB width. The red (blue) areas indicate regions of solid- (liquid)like liquid order. The liquidlike regions at the far left- and right-hand sides represent premelting of the free surfaces of the simulation cell, while that in the middle corresponds to the premelted grain boundary.

Figure 3

(Color online) Distribution function $P\left(w\right)$ vs $w$ from the MD simulations (symbols) versus the least-squares fits of the premelting model of Eqs. (1, 2).

Figure 4

(Color online) Illustration of the histogram method used to extract the disjoining potential. The inset plots the right-hand side of Eq. (4) with the constants $a_i$ set to zero. The main plot merges the individual histograms of data and reproduces the complete disjoining potential $\Psi \left(w\right)$. The solid line is a best fit to the exponential decay given in Eq. (2).