Phase diagrams supercooled silicon

Recently, extending the work of Sastiy and Angell [21], which provided evidence of a first-order liquid-liquid phase transition in silicon at zero pressure, Vasisht et al. [32,38] reported evidence of the existence of a negative pressure liquid-liquid critical point in SW silicon, based on extensive simulations of the SW model of silicon. These authors also constructed the complete phase diagram of supercooled silicon, which clearly demonstrates the interconnection between the various thermodynamic anomalies and the phase behavior of the liquid, as analyzed in previous works [16,46,58-60,69,88]. 

The complete phase behavior of supercooled silicon modeled by SW potential is summarized in Fig. 23. The phase diagram includes the liquid-liquid critical point, liquid-liquid coexistence line (obtained from identifying the jumps in density for small changes in temperature isobars generated using NPT MD simulations see... 

Figure 23. The ph ase diagram of supercooled silicon in pressure temperature (P, T) plane obtained from simulations using the SW potential. The phase diagram shows the location of (i) the liquid-crystal phase boundary [115]—thick solid line, (ii) the liquid-gas phase boundary and critical point—line and a star, (iii) the liquid-liquid phase boundaiy and critical point—filled diamond and a thick circle, (iv) the liquid splnodal—filled circle (v) the tensile limit—open circle (vi) the density maximum (TMD) and minimum (TMinD) lines— filled and open squares, and (vii) the compressibility maximum (TMC) and minimum (TMinC) line—filled and open circle. Lines joining TMD and TMinD (dot-dashed), TMC and TMinC (solid), Spinodal (black dotted line) are guides to the eye.

Dynamics One of the biggest challenges in the study of supercooled silicon is that, with deep undercooling the system, not only becomes prone to rapid crystallization but also the relaxation times increase very rapidly. Vasisht et al. studied the relaxation times at different parts of the phase diagram and found that ap proaching the liquid liquid transition line (below the critical temperature) and the compressibility maxima line (above the critical temperature), the relaxation time increases in a non Arrhenius manner. In Fig. 25a, the relaxation time as a function of temperature at two different pressme values (above — P = 0 GPa and below — P = —1.88 GPa critical point) is shown. Figure 25b shows relaxation times as a function of pressure for three different temperatures values. 

Figure 37. Phase diagram of supercooled silicon (in PT plane) at A. = 20.5, 21.0(5i) and 21.5 from MD simulations using the SW potential. The liquid-liquid transition points [100 are shown as filled diamonds, the density extrema points are shown as squares and compressibility maxima points are shown triangles. The values of X are stated over the symbols.

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