where Δ G$_{f}$ is the bulk free energy difference between liquid and solid per unit volume. For the EAM Ni system studied here the temperature dependence of Δ G$_{f}$ is known accurately from previous studies. For the small range of temperatures considered in the MD simulations of width histograms, which are close to the bulk melting temperature, Δ G$_{f}$ can be accurately computed from the following expression: where L is the latent heat per unit volume, and Δ T$_{i}$ = T$_{M}$ − T$_{i}$ is the interface undercool- ing. From Eq. 7, the disjoining potential can be written in terms of the equilibrium width distribution as: where the a$_{i}$ are unknown constants related to C$_{i}$ in Eq. 7. These parameters lead to constant offsets when the quantity - k$_{B}$T$_{i}$ ln P ( w, T$_{i}$ ) /A$_{i}$ − Δ G$_{f}$w is plotted versus w for each interface temperature. To construct the disjoining potential a least squares fit is used to refine the values of the shift parameters ( a$_{i}$ ) along with the potential parameters (Δ γ and δ in Eq. 2 or Δ$_{1}$, δ$_{1}$ , Δ$_{2}$, and δ$_{2}$ in Eq. 3). In this procedure the initial values for the shift parameters were estimated “by eye” to give maximal overlap between the data, and the initial values for the potential parameters were obtained from an average of the independent fits to the data at separate temperatures (described above). The values of the parameters were then iteratively refined to minimize the square of the differences between the MD data and the analytical expressions for Ψ( w ). In the course of this work additional studies were also conducted to investigate the effects of the details of the simulation methodology on the resulting disjoining potentials. These additional analyses were performed for the Σ9 twist boundary in Ni as well as a series of 〈 100 〉 tilt boundaries in Ni and bcc Fe. The first issue addressed in these additional simulations was the effect of thermostat. Equation 7 assumes that the measured grain-boundary widths sample a canonical ensem- ble, and in order to achieve this by MD simulations we employed a standard Nose-Hoover Effects of Thermostat, System Size and Boundary Conditions 13 Δ G$_{f}$ = L (Δ T$_{i}$/T$_{M}$ ) (9) Ψ( w ) = − ( k$_{B}$T$_{i}$ ) lnP ( w, T$_{i}$ ) /A$_{i}$ − Δ G$_{f}$w + a$_{i}$ (10)