Low-temperature thermal expansion of the $\alpha$ and $\omega$ phases of titanium

Abstract

We investigated the low-temperature thermal expansion of the $\alpha$ phase and the $\omega$ 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 $\omega$-Ti was synthesized at 7.7 GPa and 500 ${}^{\circ }$C and recovered to ambient pressure. Although the two phases exhibit very similar volumetric thermal expansion, their axial responses are markedly different. In $\alpha$-Ti, the $c$-axis thermal expansion coefficient becomes negative below approximately 50 K and reaches a minimum of $-0.71\times 10^{-6}$ 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, $\omega$-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 $\alpha$-Ti decreases with increasing temperature. Debye-Grüneisen analysis yielded Debye temperatures of $427\pm 5$ K and $409\pm 12$ K and effective Grüneisen parameters of $1.33\pm 0.04$ and $1.23\pm 0.04$ for $\alpha$-Ti and $\omega$-Ti, respectively. The first-principles calculations reproduce the volumetric thermal expansion of both phases and capture the overall trends of their axial responses.

28 pages, 2 tables, 6 Figures