MATTER AT EXTREMES

32 ESRF

LIQUID LIQUID TRANSITION AND CRITICAL POINT IN SULFUR

The liquid liquid transition separating two liquids of the same substance is a rare and intriguing phenomenon that has changed perceptions of this state of matter. This study demonstrates the presence of such a transition in liquid sulfur, as well as providing the first evidence for the existence of a second critical point that has been actively searched for and predicted in water for almost 30 years.

Any substance can exist in liquid or gaseous state, and transform from one to another by varying the pressure (P) or temperature (T). For P and T conditions below the so-called critical conditions, the change of state is characterised by a sudden jump in density. As the critical conditions (which define a point in the P-T plane called the critical point) are approached and then exceeded, the density discontinuity decreases and then vanishes. The transformation from gas to liquid is continuous and the associated state is called the fluid or supercritical state. Near the critical point, matter hesitates between the liquid state and the gaseous state, producing large fluctuations in density: this is the phenomenon of critical opalescence. Supercritical fluids are used extensively in the chemical industry because they are excellent solvents.

In the 1990s, the existence of a second critical point was suggested in water from numerical simulations [1]. This critical point would exist at the terminal location of a transition line in the P-T plane separating two liquid phases. This hypothesis, strongly debated since, is a plausible scenario for explaining the anomalies of the thermodynamic properties of water, the best known being the maximum density at 4 °C. Unfortunately, this critical point would be located in an experimentally inaccessible domain where the liquid is highly unstable. Consequently, the efforts to demonstrate this experimentally have so far failed, and the very existence of this critical point in numerical water

models is still debated. A second critical point has also been proposed in other substances such as hydrogen and nitrogen. This time, it would be located in the liquid stability zone but the extreme P-T conditions to achieve (P ~ 1 Mbar, T ~ 1500-2500 K) represent a major obstacle for its observation.

In this study, the density and structure of liquid sulfur was investigated at beamline ID27 in the 0-30 kbar, 300-1100 K range. The phase diagram of sulfur has many similarities with that of phosphorus, in which a first-order transition (i.e., characterised by a discontinuous jump in density and entropy) separating two liquid phases was discovered [2]. This work demonstrated that such a liquid liquid transition also exists in sulfur and determined the transition line in the P-T plane by coupling X-ray absorption and diffraction measurements under high pressure and temperature (Figure 21). This discovery is already remarkable because this is only the second example of such liquid liquid transition observed in an element and in its thermodynamically stable liquid state.

But perhaps the most striking result resides in the discovery of a critical point terminating the transition line (point C in Figure 21). Indeed, by varying the pressure at a temperature higher than 1050 K, the density was observed to evolve continuously, unlike the jumps observed at lower temperature. This strongly indicates the presence of a critical point located around 21.5 kbar and 1035 K. The variation in density

Fig. 21: P-T phase diagram of sulfur in the liquid liquid transition region. LDL: low density liquid; HDL: high

density liquid; C: second critical point associated with the liquid liquid transition.