Crystal-Structure Matches in Solid-Solid Phase Transitions.

Area of Science:

• Materials Science
• Crystallography
• Computational Materials Science

Background:

• Solid-solid phase transitions involve complex atomic rearrangements between crystal structures.
• Current methods for describing crystal-structure matches (CSM) are limited and often rely on supercells, introducing uncertainty.
• Understanding CSM is crucial for predicting and controlling phase transformations.

Purpose of the Study:

• To develop a robust theoretical framework for describing and classifying all possible crystal-structure matches (CSM).
• To provide a systematic and comprehensive method for exploring solid-solid phase transition mechanisms.
• To identify novel CSMs, particularly for the martensitic transformation in steel.

Main Methods:

• Developed a theoretical framework leveraging the Hermite normal form for integer matrices.
• Utilized translational and rotational symmetries for a supercell-independent description of CSM.
• Implemented an enumeration algorithm to exhaustively identify all potential CSMs.

Main Results:

• Identified numerous candidate CSMs for the martensitic transformation in steel with lower strains than known mechanisms.
• Unveiled two previously elusive CSMs corresponding to the Kurdjumov-Sachs and Nishiyama-Wassermann orientation relationships.
• Demonstrated the framework's ability to comprehensively enumerate CSMs beyond conventional optimization schemes.

Conclusions:

• The proposed theoretical framework offers a comprehensive and efficient strategy for researching solid-solid phase transition mechanisms.
• The Hermite normal form provides a powerful tool for systematic analysis of crystal structure relationships.
• This approach promises to advance the understanding and prediction of phase transformations in materials.