Non-affine fields in solid-solid transformations: the structure and stability of a product droplet.

Area of Science:

• Materials Science
• Solid-State Physics
• Crystallography

Background:

• Solid-solid transformations involve complex microstructural changes.
• Understanding the nucleation and growth of phases like martensite is crucial for materials design.
• Elastic interactions and deformation mechanisms significantly influence transformation pathways.

Purpose of the Study:

• To investigate the microstructure, morphology, and growth dynamics of martensite droplets forming within austenite.
• To analyze the role of non-affine deformations in solid-solid transformations.
• To identify and characterize different stable solutions for martensite droplet structures.

Main Methods:

• Utilized Landau theory incorporating both affine and non-affine deformations.
• Employed variational calculations to determine stable solutions.
• Analyzed the behavior of the non-affine field (φ) and its relation to stress and mobility.

Main Results:

• Identified three distinct stable solutions (I, II, III) for martensite droplet structure.
• Characterized solutions by the profile and localization of the non-affine field φ.
• Observed a specific relationship between twin width (l) and size (W) in solution I (l ∝ √W), which differs in solutions II and III.
• Developed a dynamical phase diagram illustrating these solutions.

Conclusions:

• The three identified solutions represent distinct solid-state microstructures.
• Non-affine deformation plays a critical role in mediating strain incompatibility and screening elastic interactions.
• The findings provide insights into the fundamental mechanisms governing phase transformations in solids.