A Theoretical Model for the Several Common Stacked Crystals in Arrangement of the Stacking Sequence of Parallel Atomic Layers in a Simple Crystal Solid

Abstract

By the use of position vectors and Ising spin, model Hamiltonians for several common stacked crystals are introduced in the light of the stacking sequences. Due to the stacking sequences each metal atom resides in one of a number of physical equivalent positions per lattice point in a stacking layer. Introducing position vectors which point to respective metal atoms in the stacking layers, the common structures along the stacking sequence are represented by the way in which the position vectors rotate. Ising spin is employed to describe the difference of rotation angle between the position vectors residing in nearest neighboring layers along the stacking sequence. The common structures are represented by their respective orderings of Ising spin along the stacking sequences which correspond to arrangements of the stacking layers.