Computational mechanics of Close Packed Structures with individual layer interaction

What is it about?

This is the second contribution in a series of papers dealing with dynamical models in equilibrium theories of polytypism. Instead of using an Ising model over spins defined by the Hagg coding, a Hamiltonian considering direct interaction between the close packed layers is assumed. Results of the phase diagram and the appearance of disorder are compared with the previous analysis using the Ising model. Computational mechanics is the framework under which the analysis is performed.

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Why is it important?

In this second article we explore a Hamiltonian introduced by Ahmad and Khan where interaction is taken between actual pair of layers in contrast with the usual Ising models which is based in the Hagg coding. Ahmad-Khan has been mostly overlooked in the literature in spite of its more sound physical interpretation. Computational mechanics is a tool developed in the area of complexity analysis by Prof. Crutchfield and coworkers, and introduced to the study of polytypism by D. P. Varn and coworkers. The insight given by Computational Mechanics to the analysis of polytypism has a number of advantages from the mathematical and physical point of view which has been emphasized in the first contribution. In this article we focus on the consequence of the Ahmad-Khan Hamiltonian summarized as: 1) is shown that Ahmad-Khan Hamiltonian has a more direct physical interpretation in terms of the interactions of real physical entities than the usual Ising approach. It is mathematically simpler and physically sounder. 2) Ahmad-Khan model reproduces all the results given by the Ising models but includes new possible long range polytype at the boundaries of the stable phases. Some of this new polytypes haven been reported experimentally. 3) The occurrence of disorder within the model is analyzed and compared to the same analysis done for the Ising model. Ahmad-Khan model shows in much cases greater stability of the boundary phases as well as higher probabilities compared to the Ising model. This in turn, accommodates better to the experimental results.