Pressure-softening of zone-edge TA phonons and the fourfold to sixfold phase change

The observed tendency in tetrahedral solids for the pressure-induced softening of zone-edge TA phonons to correlate with the threshold pressure ${P}_{T}$ of the fourfold to sixfold phase change is examined for 25 materials. A strong correlation is found for an effective pressure shift obtained by using a simple tight-binding model to exclude the frequency-stiffening non-central-force contribution to the zone-edge TA modes. The correlation is further improved by accounting for the material's shear rigidity. A parameter ${P}_{T}^{\mathrm{correl}}$ is defined that correlates linearly to ${P}_{T}$ with near-unity slope and high quality factor up to the transition of BP at \ensuremath{\sim}1.6 Mbar. The pressure-softening of the zone-edge TA modes is driven by the negative tension produced in the bonds by compression. This tension originates from increased electron-overlap repulsion, which modifies the metallic and ionic character of the bonding, leading eventually to the phase change. This is the underlying mechanism that links the pressure-softening of the zone-edge TA phonons to the phase transition.