Three-phase material mapping with incomplete X-ray diffraction spectral information

Area of Science:

• Materials Science
• Crystallography
• Solid Mechanics

Background:

• Equiatomic nickel-titanium alloys exhibit shape-memory properties driven by stress-induced phase transformations.
• Under uniaxial tensile load, these alloys transform from austenite (A) to rhombohedral (R) and then to martensite (M) variants.
• This transformation leads to spatial inhomogeneity due to pseudo-elasticity, complicating phase analysis.

Purpose of the Study:

• To develop a method for mapping the spatial distribution of phases in nickel-titanium alloys during tensile loading.
• To simultaneously determine unknown diffraction spectra for the R phase and quantify martensite detwinning.
• To address limitations in current in situ X-ray diffraction analyses.

Main Methods:

• In situ X-ray diffraction was performed on a nickel-titanium specimen under uniaxial tensile load.
• A novel algorithm utilizing proper orthogonal decomposition (POD) with inequality constraints was developed.
• The algorithm was designed to process diffraction data and resolve phase distribution and spectral information.

Main Results:

• The proposed algorithm successfully mapped the spatial distribution of austenite, R phase, and martensite variants.
• The method yielded previously unknown diffraction spectral information for the R phase.
• The extent of martensite detwinning was also determined, providing a comprehensive understanding of the transformation.

Conclusions:

• The novel POD-based algorithm effectively analyzes in situ X-ray diffraction data from stressed shape-memory alloys.
• This approach overcomes limitations in characterizing phase transformations and provides crucial missing spectral data.
• The methodology offers a powerful tool for understanding the complex behavior of nickel-titanium alloys under mechanical load.