  A novel liquid-liquid phase transition has been proposed and investigated in
a wide variety of pure substances recently, including water, silica and
silicon. From computer simulations using the Stillinger-Weber classical
empirical potential, Sastry and Angell [1] demonstrated a first order
liquid-liquid transition in supercooled silicon, subsequently supported by
experimental and simulation studies. Here, we report evidence for a
liquid-liquid critical end point at negative pressures, from computer
simulations using the SW potential. Compressibilities exhibit a growing maximum
upon lowering temperature below 1500 K and isotherms exhibit density
discontinuities below 1120 K, at negative pressure. Below 1120 K, isotherms
obtained from constant volume-temperature simulations exhibit non-monotonic,
van der Waals-like behavior signaling a first order transition. We identify Tc
~ 1120 +/- 12 K, Pc -0.60 +/- 0.15 GPa as the critical temperature and pressure
for the liquid-liquid critical point. The structure of the liquid changes
dramatically upon decreasing the temperature and pressure. Diffusivities vary
over 4 orders of magnitude, and exhibit anomalous pressure dependence near the
critical point. A strong relationship between local geometry quantified by the
coordination number, and diffusivity, is seen, suggesting that atomic mobility
in both low and high density liquids can usefully be analyzed in terms of
defects in the tetrahedral network structure. We have constructed the phase
diagram of supercooled silicon. We identify the lines of compressibility,
density extrema (maxima and minima) and the spinodal which reveal the
interconnection between thermodynamic anomalies and the phase behaviour of the
system as suggested in previous works [2-9]
