Inferring Pattern and Disorder in Close-Packed Structures from X-ray Diffraction Studies, Part II: Structure and Intrinsic Computation in Zinc Sulphide

In the previous paper of this series [D. P. Varn, G. S. Canright, and J. P. Crutchfield, Physical Review B, submitted] we detailed a procedure--epsilon-machine spectral reconstruction--to discover and analyze patterns and disorder in close-packed structures as revealed in x-ray diffraction spectra. We argued that this computational mechanics approach is more general than the current alternative theory, the fault model, and that it provides a unique characterization of the disorder present. We demonstrated the efficacy of computational mechanics on four prototype spectra, finding that it was able to recover a statistical description of the underlying modular-layer stacking using epsilon-machine representations. Here we use this procedure to analyze structure and disorder in four previously published zinc sulphide diffraction spectra. We selected zinc sulphide not only for the theoretical interest this material has attracted in an effort to develop an understanding of polytypism, but also because it displays solid-state phase transitions and experimental data is available. With the first spectrum we find qualitative agreement with earlier fault-model analyses, although the reconstructed epsilon machine detects structures not previously observed. In the second spectrum, the results cannot be expressed in terms of weak faulting and so no direct comparison between the fault model and the reconstructed epsilon machine is possible. Nonetheless, we show that the epsilon machine gives substantially better experimental agreement and a number of structural insights. In the third spectrum, the fault model fails completely due to the high degree of disorder present, while the reconstructed epsilon machine reproduces the experimental spectrum well. In the fourth spectrum, we again find good quantitative agreement with experiment but find that the epsilon machine has difficulty reproducing the shape of several Bragg-like peaks. We discuss the reasons for this. Using the epsilon machines reconstructed for each spectrum, we calculate a number of physical parameters--such as,stacking energies, configurational entropies, and hexagonality--and several quantities--including statistical complexity and excess entropy--that describe the intrinsic computational properties of the stacking structures.