Atomistic simulations of 2:1 clay minerals based on parameterized forcefields have been applied successfully to provide a detailed description of the interfacial structure and dynamics of basal planes and interlayers, but have made limited progress in exploring the edge surfaces of these ubiquitous layer-type aluminosilicates. In the present study, molecular dynamics simulations and energy-minimization calculations of the edge surfaces using the fully flexible CLAYFF forcefield are reported. Pyrophyllite provides an ideal prototype for the 2:1 clay-mineral edge surface because it possesses no structural charge, thus rendering the basal planes inert, while crystal-growth theory can be applied to identify two major candidates for the structure of the edge surfaces. Models based on these candidate structures reproduced bulk crystal bond distances accurately when compared to X-ray data and ab initio molecular simulations, and the predicted edge surface bond distances were in agreement with those determined via ab initio simulation. The calculated surface free energy and surface stress led to an accurate prediction of pyrophyllite nanoparticle morphology, while surface excess energies calculated for the edge surfaces were always negative. These results are consistent with the observed pyrophyllite nanoparticle morphology, with the concept of negative interfacial energies, and conditions that may give rise to them including a role in the stabilization of layer-type nanoparticulate minerals. Molecular dynamics simulations of hydrated nanoparticle edge surfaces indicated five reactive surface oxygen sites on the dominant candidate edge, in agreement with a recent model of proton titration data for 2:1 clay minerals. These promising results illustrate the potential for classical mechanical atomistic simulations that explore edge surface phenomena at much greater length- and times-scales than are currently possible with computationally expensive ab initio methods.

In this paper we are interested in the microscopic modelling of a two-dimensional two-well problem that arises from the square-to-rectangular transformation in (two-dimensional) shape-memory materials. In this discrete set-up, we focus on the surface energy scaling regime and further analyse the Hamiltonian that was introduced by Kitavtsev et al. in 2015. It turns out that this class of Hamiltonians allows for a direct control of the discrete second-order gradients and for a one-sided comparison with a two-dimensional spin system. Using this and relying on the ideas of Conti and Schweizer, which were developed for a continuous analogue of the model under consideration, we derive a (first-order) continuum limit. This shows the emergence of surface energy in the form of a sharp-interface limiting model as well the explicit structure of the minimizers to the latter.