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Homonuclear correlation spectroscopy (COSY) is a powerful technique used in Nuclear Magnetic Resonance (NMR) spectroscopy to study the correlations between nuclei of the same type within a molecule. It provides information about scalar couplings between adjacent nuclei, which helps determine connectivity and structural information. There are several COSY variants, each with its unique strengths and experimental parameters.
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Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
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Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is more complex than the packing of metal atoms that are the same size.
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Pairwise correlations in layered close-packed structures.

P M Riechers1, D P Varn1, J P Crutchfield1

  • 1Complexity Sciences Center and Physics Department, University of California, One Shields Avenue, Davis, California 95616, USA.

Acta Crystallographica. Section A, Foundations and Advances
|July 2, 2015
PubMed
Summary
This summary is machine-generated.

This study presents analytical expressions for layer correlations in close-packed structures using hidden Markov models. The findings offer a fast and accurate method for calculating these correlations, advancing materials science research.

Keywords:
X-ray diffractionpair distribution functionplanar disorderspectral decompositionstacking faultz-transformation

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Layered close-packed structures are fundamental in materials science.
  • Understanding stacking statistics is crucial for predicting material properties.
  • Previous methods for analyzing these structures can be computationally intensive.

Purpose of the Study:

  • To develop analytical expressions for pairwise correlation functions between layers in close-packed structures.
  • To provide an efficient computational method for analyzing stacking statistics.
  • To offer new relations and validate existing work in the field.

Main Methods:

  • Utilized a hidden Markov model (HMM) to describe stacking statistics.
  • Derived analytical expressions for pairwise correlation functions based on the HMM.
  • Applied the derived expressions to specific examples.

Main Results:

  • Developed explicit analytical functions for pairwise correlation functions.
  • Demonstrated that these functions can be computed quickly and accurately.
  • Achieved agreement with previously established results and derived novel relationships.

Conclusions:

  • The developed analytical expressions provide an efficient and accurate tool for studying layered close-packed structures.
  • This work offers a new perspective on analyzing stacking sequences using probabilistic models.
  • The findings have implications for materials design and understanding complex layered systems.