atoms, divided by the area of the boundary. The dimensions of the computational cell used in these energy minimizations and in the subsequent MD simulations are given in Table I. 

## Molecular-Dynamics Simulations 

Finite temperature simulations were performed by MD employing the LAMMPS code [42]. All simulations were performed with a constant number of atoms, constant volume and temperature (NVT ensemble). The temperature was maintained by using a Nose- Hoover thermostat [43] with a thermostat relaxation time of 0.1 ps, employing a time-step of 1 fs. The simulations began with the optimized zero-temperature geometry, which was equilibrated at different temperatures. Prior to each simulation at a given temperature, the periodic lengths parallel to the grain boundary plane were expanded according to the finite- temperature value of the lattice constant for the bulk crystal (determined separately). These periodic lengths were then held constant in all of the NVT MD simulations. The atoms in the slabs that were held fixed during the energy minimization procedure were made dynamic for the finite-temperature simulations, and the boundary conditions were modified such that both the grains terminated in free surfaces. 

As discussed in the next sub-section, two types of analysis were conducted on the simu- lated systems to study their premelting behavior. The first was a calculation of the excess volume as a function of temperature. In the simulations used for this analysis equilibration times were a few ns. The system volume was sampled over a total time of at least 10 ns at a frequency of 10 ps. 

The second analysis involved the calculation of equilibrium grain boundary width his- tograms. For these analyses, the simulations started at a given temperature with an equili- bration lasting 10 ns. Statistics were then obtained for the boundary width histograms from a total of 4000 snaphsots, sampled at a frequency of 10 ps. As discussed below, this number of snapshots and sampling rate ensured that at least a hundred statistically independent samples were obtained at each of the temperatures studied for the histogram analysis. 

