High-pressure melting curve of sulfur up to 65 GPa

The melting curve of elemental sulfur was measured to pressures of 65 GPa in a laser-heated diamond-anvil cell using ex situ textural analyses combined with spectroradiometry and benchmarked with laser-power-temperature functions. The melting curve reaches temperatures of $\sim 1800\mathrm{K}$ by 65 GPa and is smooth in the range of 23–65 GPa with a Clapeyron slope of $\sim 14\mathrm{K}/\mathrm{GPa}$ at 23 GPa. This is consistent with melting of a single tetragonal sulfur structure in this range, which is confirmed by in situ x-ray diffraction. An updated equation of state for tetragonal sulfur is determined, and the high-pressure, high-temperature stability region of tetragonal sulfur is reassessed.

Figure 1

Mapping melt texture to 2D temperature maps. (a) A sample heated to a peak temperature of 1370 K at 51 GPa showing no melt bleb. (b) A sample heated to a peak temperature of 1680 K at 51 GPa showing a distinct melt bleb. (c) Zoom in of dotted region in (b) of a sulfur melt bleb and its boundary. (d) Melt boundary superimposed on the temperature map which is integrated to determine a melting temperature of $1600(\pm 100)\mathrm{K}$.

Figure 2

SEM image of a melt spot on a sample heated at 34 GPa to a peak temperature of 1630 K showing holes where KBr fell into the melt and was dissolved with water after quenching. The melt boundary is outlined in red, and the holes are outlined in black dashes.

Figure 3

Laser power-temperature relationships during heating of a sulfur sample at 23 GPa using KCl as thermal insulation. Samples were heated from both sides using a CW infrared laser and slowly ramping up the power. Temperatures are determined by fitting Planck radiation the blackbody radiation at 600–800 nm from a spatially selected area $\sim 4\mu \mathrm{m}$ in diameter on the heated sample [20]. Temperature increases rapidly and nearly linearly below the melting point. Once the melting point is reached, the temperature fluctuates around a plateau (grey shaded region) before the temperature begins to increase again. The entire heating duration was 26 minutes. Open symbols are those for which raw diffraction patterns are shown in Fig. S7.

Figure 4

The extended high-pressure melting curve of sulfur. Diamonds are melting points from textural mapping, and grey shaded bars are laser power-temperature inferred melting temperatures. “$\times$” symbols are samples heated to temperatures which did not show any textural evidence of melting. The curve is a Simons-Glatzel fit to the textural data $T_m=T_{m,\mathrm{ref}}{\left(\frac{P-P_{\mathrm{ref}}}{a}+1\right)}^{\frac{1}{c}}$ with $a=64.84$ and $c=1.41$.

Figure 5

Room-temperature tetragonal sulfur volumes as a function of pressure. Filled (open) symbols are shown for volumes collected on compression (decompression) for this study (circles), Refs. [8] (squares), [7] (diamonds). A third-order Birch-Murnaghan equation of state fit to only our data is shown as a black curve. Extrapolation to higher and lower pressures agree remarkably well with existing data in Ref. [7, 8].

Figure 6

Examples of integrated tetragonal sulfur diffraction patterns at high temperatures with corresponding raw images shown inset. Grey ticks mark the fitted peaks for sulfur in the $\mathrm{I}{4}_1/acd$ structure (16 atoms per unit cell). Asterisks (integrated patterns) and dashed circles (raw images) denote diffraction from the insulation/pressure media (Ne at 44 GPa, KCl at 23 GPa). Pressures are derived from the pressure medium and neglect the effect of thermal pressure.

Figure 7

Selected heating patterns of tetragonal sulfur using B2 KCl insulation (top panels) and solid Ne insulation (bottom panels). The right panels show a zoom-in of the dashed regions with insulation and sulfur peaks. Volumes of these patterns from fitting 8–10 peaks for sulfur and 3 peaks for KCl/Ne are shown in Table S2. A discussion of the pressure change may be found in the Supplemental Material [29].

Figure 8

The $P,T$ diagram of sulfur to 70 GPa. Phases reported below 1 GPa (e.g., monoclinic) are not displayed due to a comparatively small stability field. The melt boundary above 26 GPa (black solid line) and the plus symbols indicating the tetragonal form of sulfur are from this study. Other melting data points and curves are from Refs. [16] (grey circles), [17] (thin dashed line), [2] (black circles). The liquid-liquid transitions $L-L^{\prime }$ and $L^{\prime }-L^{\prime \prime }$ are from Refs. [2, 3]. The trigonal-rhombohedral (“rh”) and rhombohedral-tetragonal boundaries are from Ref. [9], the orthorhombic-trigonal transition boundary (grey dashed line) is from Ref. [39], and the trigonal-tetragonal boundary (thick dashed line) is inferred from Refs. [9, 13]. The asterisks on the trigonal-tetragonal boundary are discrete transition points from Ref. [13]. Solid phase boundaries that are shown in dashed lines are speculative due to few points or discrepancies between studies. The filled squares at room temperature represent reported transition to tetragonal sulfur from this study (plus symbol), Refs. [8] (black), [7] (grey), [5] (grey with black outline).