Determining stacking order in close-packed structures from interlayer correlation functions

What is it about?

It is shown how to reconstruct the stacking sequence from the pairwise correlation functions between layers in close-packed structures. First, of theoretical interest, the analytical formulation and solution of the problem are presented when the exact pairwise correlation counts are known. In the second part, the practical problem is approached. A simulated annealing procedure is developed to solve the problem using as initial guess approximate solutions from previous treatments. The robustness of the procedure is tested over synthetic data followed by an experimental example. The developed approach performs robustly over different synthetic and experimental data comparing favorably to other reported methods.

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Why is it important?

We provided a numerical solution to the inverse inference problem for close-packed structures by using a simulated annealing procedure which we call numerical stacking reconstruction (NSR). The method does not rely on any extra assumption besides the PCPs themselves. In this sense, it yields results as close as the numerical procedure is capable of. A key aspect of the developed procedure is the educated guess of the initial sequences used as input to the simulated annealing stage. The convergence and reliability of the result depended heavily on it. NSR incorporates the knowledge of previous models into its framework to advance initial guesses. This has the important implication that even in the worst scenario, NSR performs as well as previous approaches. This also implies that it is amenable to further extension with other models as previous guesses. Yet in all the numerical test performed, there was no need for additional models than the ones considered. In all cases, the convergence of the NSR the procedure was below seven minutes for a general purpose desktop computer with 8M of RAM and a Dual core Pentium processor.

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