Towards the extraction of the crystal cell parameters from pair distribution function profiles

Area of Science:

• Materials Science
• Crystallography
• Data Science

Background:

• The atomic pair distribution function (PDF) method has advanced structural analysis of nanomaterials, enabling short-range order investigations.
• However, ab initio crystal structure determination using PDF is challenging due to difficulties in identifying unit cell properties.

Purpose of the Study:

• To develop and validate a novel two-step method for estimating crystal cell parameters directly from PDF profiles.
• To improve the accuracy and feasibility of determining crystallographic properties for nano and quasi-amorphous materials.

Main Methods:

• A machine learning approach, specifically k-nearest neighbors, was employed to infer crystal cell types from PDF profiles.
• Multivariate analysis and vector superposition techniques were used to extract precise cell parameters.
• Recurrence quantitative analysis was utilized to derive descriptors from PDF profiles for machine learning input.

Main Results:

• The k-nearest neighbors classifier applied to whole PDF profiles demonstrated the highest performance in lattice determination.
• The cell parameter extraction step showed varying accuracy based on cell metric: 40% for monometric, 20% for dimetric, and 5% for trimetric cells.
• Promising results were achieved with real nanocrystals, identifying correct or near-correct unit cells even with significant crystalline impurities.

Conclusions:

• The presented method offers a significant advancement in determining crystallographic properties from PDF data, particularly for challenging nano and quasi-amorphous materials.
• This approach enhances the capability for ab initio crystal structure solution, broadening the application of PDF analysis in materials science.