content_image/363824.jpg
numerous previous MD studies of grain-boundary premelting performed over the past three decades [21–34]. The technique for calculating disjoining potentials by MD is based on an analysis of the equilibrium distribution of the widths of premelted intergranular films, which are related to the underlying disjoining forces through the fluctuation-dissipation theorem. The purpose of this paper is to describe the technical details surrounding the implementa- tion of this method, and to demonstrate its application in the study of two distinct classes of grain boundary premelting behavior. Specifically, we consider the premelting behavior of a high and intermediate energy boundary in elemental Ni where the widths of the premelted layers continuously increase or remain finite, respectively, as the melting point is approached from below. It is shown that the former behavior is consistent with an interfacial free energy (Ψ) that decreases exponentially with increasing width ( w ) of the premelted layer, while the latter behavior can be quantitatively modeled with a dependence of Ψ on w that features a weak attractive minimum at nanometer-scale widths. This minimum is accompanied by a grain boundary structure with alternating solid bridges and disordered regions that bears strong similarities to the type of structure found to be associated with such a minimum in a recent phase-field-crystal study [19]. 

The remainder of this paper is outlined as follows. In the next section we review a continuum, sharp-interface formalism for the thermodynamic properties underlying grain- boundary premelting and coalescence, based on the definition of the so-called “disjoining potential,” the (negative) derivative of which is the disjoining pressure referred to above. Section III discusses the technical details underlying the calculation of the disjoining poten- tial by MD, as well as the details of the simulations undertaken in the current application of the method to the study of high-temperature grain boundaries in fcc Ni. The results are presented in section IV, followed by a summary and discussion of the findings in the context of previous theoretical studies in section V. 

## DISJOINING POTENTIAL 

The equilibrium width of a premelted grain-boundary is governed by a competition be- tween bulk and interfacial thermodynamic factors, which can be represented mathematically as follows: 

<img src='content_image/363824.jpg'>

