Low-temperature thermal expansion of the α and ω phases of titanium
Abstract
We investigated the low-temperature thermal expansion of the α phase and the ω phase, a high-pressure polymorph of titanium, by X-ray diffraction measurements from approximately 5 to 300 K, together with first-principles calculations. Single-phase bulk polycrystalline ω-Ti was synthesized at 7.7 GPa and 500 ∘C and recovered to ambient pressure. Although the two phases exhibit very similar volumetric thermal expansion, their axial responses are markedly different. In α-Ti, the c-axis thermal expansion coefficient becomes negative below approximately 50 K and reaches a minimum of −0.71 × 10−6 K−1 at 20 K. Both experiment and theory indicate substantially smaller c-axis negative thermal expansion than previously reported from single-crystal length measurements. In contrast, ω-Ti expands nearly isotropically along the a and c axes, and its c/a ratio remains nearly temperature independent and close to the ideal bcc-derived value. The c/a ratio of α-Ti decreases with increasing temperature. Debye-Grüneisen analysis yielded Debye temperatures of 427 ± 5 K and 409 ± 12 K and effective Grüneisen parameters of 1.33 ± 0.04 and 1.23 ± 0.04 for α-Ti and ω-Ti, respectively. The first-principles calculations reproduce the volumetric thermal expansion of both phases and capture the overall trends of their axial responses.
Related
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BibTeX
@misc{nishiyama2026lowtemperature,
title = {{Low-temperature thermal expansion of the $α$ and $ω$ phases of titanium}},
author = {Norimasa Nishiyama and Atsushi Togo and Yoshitaka Matsushita},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33302},
eprint = {2609.33302},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33302},
}
RIS
TY - UNPB
TI - Low-temperature thermal expansion of the α and ω phases of titanium
AU - Norimasa Nishiyama
AU - Atsushi Togo
AU - Yoshitaka Matsushita
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33302
UR - https://arxiv.org/abs/2609.33302
AB - We investigated the low-temperature thermal expansion of the α phase and the ω phase, a high-pressure polymorph of titanium, by X-ray diffraction measurements from approximately 5 to 300 K, together with first-principles calculations. Single-phase bulk polycrystalline ω-Ti was synthesized at 7.7 GPa and 500 ^∘C and recovered to ambient pressure. Although the two phases exhibit very similar volumetric thermal expansion, their axial responses are markedly different. In α-Ti, the c-axis thermal expansion coefficient becomes negative below approximately 50 K and reaches a minimum of −0.71 × 10^−6 K^−1 at 20 K. Both experiment and theory indicate substantially smaller c-axis negative thermal expansion than previously reported from single-crystal length measurements. In contrast, ω-Ti expands nearly isotropically along the a and c axes, and its c/a ratio remains nearly temperature independent and close to the ideal bcc-derived value. The c/a ratio of α-Ti decreases with increasing temperature. Debye-Grüneisen analysis yielded Debye temperatures of 427 ± 5 K and 409 ± 12 K and effective Grüneisen parameters of 1.33 ± 0.04 and 1.23 ± 0.04 for α-Ti and ω-Ti, respectively. The first-principles calculations reproduce the volumetric thermal expansion of both phases and capture the overall trends of their axial responses.
ER -