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Updated: Mar 26, 2026
11:17
Spark Plasma Sintering Apparatus Used for the Formation of Strontium Titanate Bicrystals
Published on: February 9, 2017
10.4K
Identifying the multiplicity of crystallographically equivalent variants generated by iterative phase transformations
Panagiotis Grammatikopoulos1, Robert Charles Pond2
1Nanoparticles by Design Unit, Okinawa Institute of Science and Technology (OIST) Graduate University, 1919-1 Tancha, Onna-son, Okinawa 904-0495, Japan.
Summary
Titanium (Ti) undergoes phase transformations between hexagonal close-packed and body-centered cubic structures. The Burgers Orientation Relationship governs these transitions, influencing texture evolution and variant multiplicity.
Area of Science:
- Materials Science
- Crystallography
- Solid-state Physics
Background:
- Phase transformations in titanium (Ti) involve transitions between hexagonal close-packed (h.c.p.) and body-centered cubic (b.c.c.) structures.
- These transformations are critical for understanding Ti's microstructure and properties.
- The Burgers Orientation Relationship (Burgers OR) is known to relate the crystallographic orientations of the h.c.p. and b.c.c. phases.
Purpose of the Study:
- To describe phase transformations in Ti purely from a crystallographic perspective.
- To analyze the evolution of crystallographic variants and texture during phase transitions.
- To quantify the multiplicity of variants and understand the role of symmetry operations.
Main Methods:
- Utilizing iterative heating and cooling cycles to induce phase transitions.
- Employing the four-dimensional Frank space for numerical manipulation of h.c.p. and b.c.c. structures.
- Performing crystallographic group decomposition to identify common symmetries and generating operations.
Main Results:
- Phase transitions between h.c.p. and b.c.c. structures in Ti were observed at 1155 K.
- The Burgers OR was confirmed to relate the crystallographic orientations of the two phases.
- Variant degeneracy was detected, reducing the number of potential variants in successive generations (e.g., from 72 to 57 in the second generation).
Conclusions:
- The crystallographic framework successfully describes Ti phase transformations and variant evolution.
- Understanding variant multiplicity is crucial for predicting and refining microstructural textures.
- Degeneracy in variant formation arises from specific alignments of symmetry operators dictated by the Burgers OR.
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