Fig. 2: Heterogeneous distribution of Peierls-like distortions is an equilibrium property and is observed in the supercooled-liquid.

The potential energy for the model with a mass density of 5.9 g cm⁻³ is shown in dependence of temperature during melt-quenching in ab-initio MD simulations with a quenching rate of 9.5 K ps⁻¹ (dark line). At several different temperatures, branches with constant temperature are created. Here, color indicates the time starting at departure from the melt-quenching trajectory. While full equilibration is observed directly after quenching at 600 K and 700 K, the system begins to deviate from the supercooled-liquid line at approximately 500 K. Note that the quenching rate used here is approximately 14 orders of magnitude larger than the rate typically used to determine a glass transition temperature in DSC measurements. This is why the system falls out of equilibrium at a higher temperature. \({T}_{{{{\rm{m}}}}}^{{{{\rm{LD}}}}}\) marks the (experimental) melting point of antimony at a density of 6.49 g cm⁻³. The dashed lines indicate the approximated dependence of potential energy on temperature of the supercooled liquid in equilibrium at high and low temperatures and a linear extrapolation of the low-temperature behavior of the glassy phase. An approximation of the supercooled liquid line at lower temperatures is obtained by a linear fit of the potential energies at 400 K to 600 K after equilibration. Note that the system is probably not fully equilibrated after 100 ps at 400 K and this datapoint should be at slightly lower energies. For visual clarity, the data in the main area were smoothed using a Savitzky–Golay filter. The raw data for constant temperatures between 300 K and 700 K are depicted in the inset. The gray area indicates an upper bound estimate of the energy of the crystal, which is obtained from the recrystallized sample at 400 K.