Derivation of the Model Hamiltonian for HCP and FCC Structures from the Pairwise Interaction Model and Low Temperature Analysis of the Model Hamiltonian

Abstract

The model Hamiltonians for several common stacked crystals are well described by introducing the position vector and Ising spin in the previous paper. From the pairwise interaction model the model Hamiltonian for the hcp and the fcc structures is derived. Interactions of second neighboring atom pairs along the stacking sequence contribute mainly to construction of the hcp and the fcc structures. Physical meanings of the coupling constant J between Ising spins and that V between the position vectors are made clear. The behavior of the model Hamiltonian at low temperatures is analyzed on the basis of a systematic series expansion procedure. The structural phase transition from the fcc to the hcp structures with increasing temperature occurs in case where J is positive.