Low-temperature thermal expansion of the $α$ and $ω$ phases of titanium
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 $^\circ$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 $-0.71 \times 10^{-6}$ 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, $ω$-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 $427 \pm 5$ K and $409 \pm 12$ K and effective Grüneisen parameters of $1.33 \pm 0.04$ and $1.23 \pm 0.04$ for $α$-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.