ε-Machine spectral reconstruction theory: a direct method for inferring planar disorder and structure from X-ray...

Area of Science:

• Materials Science
• Solid State Physics
• Computational Mechanics

Background:

• Planar disorder in close-packed structures presents challenges in characterization.
• Previous work introduced a technique for analyzing diffraction patterns to identify disorder.

Purpose of the Study:

• To provide the theoretical framework for analyzing planar disorder.
• To adapt computational mechanics for describing one-dimensional structure in materials.

Main Methods:

• Developed a statistical model, the epsilon-machine (ε-machine), based on computational mechanics.
• Applied the ε-machine to analyze stacking structures and diffraction patterns.
• Utilized power spectra data for structural analysis.

Main Results:

• The ε-machine model quantifies memory, structural complexity, and configurational entropy.
• Demonstrated the theoretical basis for the previously introduced disorder analysis technique.
• Established a link between diffraction patterns and fundamental material properties.

Conclusions:

• The developed theoretical framework enables direct analysis of planar disorder from diffraction data.
• The ε-machine provides a robust method for quantifying material structure and complexity.
• This approach is adaptable to various experimental systems with power spectra data.