A Novel Approach to Discovering and Describing Planar Disorder in
Close-Packed Structures from X-Ray Diffraction Spectra
Seminar, Center for the Study of Complex Systems
University of Michigan
November 2002
Abstract:
Polytypism is the phenomenon of a substance that can assume two or more
layer-like structures--each having the same stoichiometry--but differing only
in the manner of stacking. A substance particularly rich in observed
structures is zinc sulphide, with some crystalline structures having unit
cells extending over 100 layers. Also of interest are specimens that show
considerable disorder, often as a result of an arrested solid state
transformation between two crystalline structures. There can be regions in
the crystal that largely preserve the original crystalline structure
interspersed between regions containing more disorder or even different
crystal structures. It has been a challenge to characterize these disordered
samples on the basis of their diffraction spectra. I present a novel method
of detecting and describing planar disorder in close-packed structures from
their diffraction spectra which I demonstrate on experimental ZnS diffraction
patterns. Incorporating ideas originating from the study of dynamical
systems, I outline a method that provides the unique, minimal and most
compact model of the stacking disorder possible. From this model, I am able
to calculate physical parameters such as the average stacking fault energy
and the stacking entropy. I contrast this approach to more traditional views
of disorder such as the fault model, Jagodzinski's disorder theory and
reverse Monte Carlo techniques.