Understanding the mechanism of structural phase transitions in rare-earth elements is a fundamental challenge in condensed matter physics, with significant implications for materials science applications. In this study, we present a systematic investigation of the phase transitions of yttrium under pressure conditions ($<30\mathrm{GPa}$) focusing on the hcp, Sm-type, and double hcp phases. A comparative study between the generalized gradient approximation (GGA) and meta-GGA functionals reveals that the Perdew-Burke-Ernzerhof functional significantly underestimates the phase transition pressures, whereas the restored regularized strongly constrained and appropriately normed functional (${\mathrm{r}}^2\mathrm{SCAN}$) provides accurate predictions of phase transition pressures which are in excellent agreement with experimental data. The results confirm that the experimentally observed phase transitions in yttrium are driven by vibrational instabilities, as evidenced by the emergence of soft acoustic modes in the phonon dispersion curves for both hcp and Sm-type phases. The analysis of the soft mode further reveals a different intermediate phase of $P\overline{6}2c$ symmetry occurring during the transition between the hcp and Sm-type phases. A transition from the centrosymmetric space group $P{6}_3/mmc$ (hcp) to the $t$-type subgroup $P\overline{6}2c$ involves loss of inversion symmetry and a reduction in point group symmetry from $D_{6h}$ to $D_{3h}$. Additionally, calculations of elastic properties confirm mechanical softening at the phase boundaries, particularly in the hcp phase, suggesting a strong correlation between elastic softening and structural transitions. These findings indicate that the pressure-induced modifications of electronic bonding, reflected in gradual $s$ to $d$ charge transfer and accompanied by phonon softening and mechanical weakening near the transition pressures, play a central role in driving the structural phase transitions in yttrium.

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• High-pressure studies
• Phase transitions
• Density functional theory
• Meta-GGA