Figure 1

Examples of spectra across the first-order transition encountered by varying pressure at constant temperature (left panel) or by varying temperature at (almost) constant pressure (right panel). The upper (lower) spectra refer to the polymeric (molecular) phase. The upper spectra have been vertically shifted by 2, for clarity.Reuse & Permissions

Figure 2

The $S(q)$ pattern corresponding to the coexistence point on the transition line at 0.72 GPa and 1450 °C (middle plot, full line) compared with a pattern in the molecular phase (lower plot, vertically displaced by $-1$) and one in the polymeric phase (upper plot, vertically displaced by 1). The pattern at coexistence compares well with a linear combination of 35% of the upper polymeric pattern and 65% of the lower molecular one (middle plot, grey line, vertically displaced by $-0.2$).Reuse & Permissions

Figure 3

(a) The high-$p$ high-$T$ portion of the phase diagram of phosphorus in the region where the first-order phase transition is located. Stars correspond to coexistence points; solid circles and open squares correspond to data in the polymeric and in the molecular phase, respectively (only data close to the transition line are reported). The black line is the 2nd order polynomial that best represents the transition line. Solid and open triangles correspond to literature data for the polymeric and the molecular phase, respectively [11]. Open diamonds and the grey line refer to the melting line of black phosphorus [12, 23]. (b) A simplified version of the phase diagram of phosphorus in semilog scale in order to put the low and high pressure data in a unified picture. At room conditions the orthorhombic black crystal is the stable phase which, on increasing $T$, sublimes to the molecular ${\mathrm{P}}_4$ gas [16] (solid line). At high pressure, together with our results on the high-$T$ high-$p$ phase transition (solid line), we sketch previous results on: the melting line and the high-$T$ high-$p$ phase transition (grey line) [11, 12]; the orthorhombic to rhombohedral (rhomb.) crystal transition [24]; and the orthorhombic, rhombohedral, and liquid triple point (open triangle) [23]. At low $p$, the boiling line of the metastable molecular ${\mathrm{P}}_4$ liquid is also reported (dashed line) [16]. The critical point at the end of this line is calculated to be at 695 °C and 8.2 MPa (open circle) [16]. The ensemble of these data allows us to conclude that the high-$p$ high-$T$ transition is a first-order transition between a dense molecular fluid and a polymeric liquid.Reuse & Permissions