Pushing the limits of crystallography.

Area of Science:

• Crystallography
• Materials Science
• Condensed Matter Physics

Background:

• Crystal structure refinement is crucial for understanding materials.
• A known issue is the bias between calculated and measured diffraction intensities, especially for weak reflections.
• This bias is linked to factors correcting for atomic vibrations (phonons) and disorder (phasons), particularly in quasicrystals.

Purpose of the Study:

• To investigate the cause of bias in crystal structure refinement.
• To address the limitations of current phason correction methods in quasicrystals.
• To propose and validate a novel statistical approach for phason correction.

Main Methods:

• Analysis of corrective factors for phonons and phasons in diffraction intensity calculations.
• Evaluation of the standard exponential Debye-Waller factor for phasons in quasicrystals.
• Development and application of a new statistical method for calculating phason correction factors.
• Testing the method on model quasiperiodic systems.

Main Results:

• The bias in diffraction intensities is significantly influenced by phason and phonon corrective factors.
• The standard Debye-Waller factor is inadequate for phasons in quasicrystals.
• The proposed statistical method successfully describes phasonic perturbations.
• High-quality refinement fits were achieved using the novel correction method.

Conclusions:

• Phason and phonon dynamics are key to understanding diffraction intensity bias.
• A new statistical approach offers a reliable method for phason correction in quasicrystals.
• This advancement facilitates more accurate crystal structure refinements for quasiperiodic materials.