Monte Carlo Simulation of Modulated Phases

Abstract

Modulated phases exist over a wide range of material classes. In general, the term ’modulated phases’ refers to the existence of an ordered array of multiple constituent elements of the material. These elements are typically either atoms of different Z or blocks of different phases. A good example of the former are intermetallics, such as the LI2 structure Ni3Al which consists of four interpenetrating simple cubic lattices (one occupied by Al and the other three by Ni) If we ignore chemical type, this structure is simply face centered cubic. Materials such as SiC are also ordered, but unlike Ni3Al it exhibits a wide range of phases, some with unit cells as large as 1200 nm on an edge1 The existence of multiple ordered structures of the same material is known as polytypism and has been observed for such disparate materials as metal iodides, micas, chalcogenides, opal, and graphite1. Different polytypes are often related to each other by the presence of periodic arrays of planar defects such as stacking faults or antiphase boundaries. Recent work2 has suggested that spin models, such as the Axial Next Nearest Neighbor Ising (ANNNI) model provide a reasonable description of polytypism. In two dimensions, this model exhibits3 both ferromagnetic and ordered (alternating two spin wide stripes — ↑↑↓↓↑↓↓↑↓↓↑↓↓) phases at low temperatures. In addition to a low temperature ferromagnetic phase, the three dimensional ANNNI model has a large number of different ordered phases at different temperatures and magnitudes of the frustration parameter.