High-pressure–high-temperature phase diagram of tin

The high-pressure–high-temperature behavior of tin has been measured with x-ray diffraction and laser-heated diamond anvil cells up to 225 GPa at 300 K and to 110 GPa and $\sim 4000$ K. Temperature has been measured using conventional point pyrometry as well as a four-color mapping pyrometer. The stability fields of Sn liquid and solid phases $(\beta \text{−}\mathrm{Sn}, \mathrm{bct} \gamma \text{−}\mathrm{Sn}, \mathrm{bcc}\text{−}\mathrm{Sn}, \mathrm{hcp}\text{−}\mathrm{Sn})$ have been constrained. The high-pressure hcp-Sn phase has been observed but at higher pressure than under hydrostatic compression. The bcc-bct transition conditions are measured, up to a bcc-bct-liquid triple point at 18.9 GPa/1410 K. A lower bound for bcc-Sn melting line is proposed (Simon equation): $T_m=581{((P-2.86)/6.44+1)}^{0.71}$ ($P$ in GPa, $T_m$ in Kelvin).

Figure 1

Sn room temperature EoS. Pressure-volume points have been collected under nonhydrostatic compression above 15 GPa. The EOS from Refs. [9, 10] (quasihydrostatic - black) and Ref. [11] (nonhydrostatic - red) are plotted as dashed lines. (Botton) Difference in percents between current and [9, 10, 11] EOS volumes. S11, S13, and G17 correspond to Refs. [9], [10], and [11], respectively.

Figure 2

Sn $\beta$-bct transition. Relative amount of bct-Sn measured during run Sn30. Dashed arrows identify compression-decompression cycles. (Inset) Diffraction spots for $\beta$-Sn at 4 GPa/300 K during run Sn30. Strained/unstrained crystals are shown with red/black arrows. For clarity, the data at 425 K have been shifted by 70%.

Figure 3

Sn bct-bcc transition at 300 K. (a) XRD patterns for run Sn39. Red squares: bct-Sn, blue stars: bcc-Sn and gray disks: KI. (b) Relative amount of bcc-Sn measured for compression and decompression, estimated using the intensity ratio between ${\left(110\right)}_{\mathrm{bct}}$ and ${\left(110\right)}_{\mathrm{bcc}}$ peaks. Dashed arrows identify compression-decompression cycles.

Figure 4

Sn bcc-hcp transition at 300 K. (a) X-ray diffraction patterns collected during compression ($\uparrow$)/decompression ($\downarrow$) during run Sn34. Blue stars: bcc-Sn, green diamonds: hcp-Sn, gray circles: KCl and purple hexagons: Re. (b) Evolution of the fraction of hcp-Sn. For clarity, fraction of hcp-Sn was multiplied by 2 on the graph. Data from Refs. [9, 11] are also plotted; pressure transmitting medium are indicated in the legend.

Figure 5

Comparison between 4C point pyrometry and pyrometry data. (a) temperatures measured with point pyrometry and 4C pyrometry on the location of the x-ray spot for one heating ramp in run Sn34 at $\sim 106$ GPa. Maximum temperature is also plotted. (b) comparison between Wien fits for two different times during this ramp. (c) Temperature maps calculated by 4C pyrometer for another heating ramp. They show the progressive deviation of the maximum temperature from the x-ray location, indicated by the purple arrows and disk. The disk size is the approximate x-ray spot size on the sample.

Figure 6

Sn bcc-bct transition at HT. (a) Evolution of XRD patterns on $T$ increase ($\uparrow$)/decrease ($\downarrow$) at $\sim 38$ GPa. Red squares: bct-Sn, blue stars: bcc-Sn and gray circles: KCl. (b) PT chart in the 0–60 GPa/300–1500 K range. Combined data from our experiments (laser heating) and from Ref. [15] (resistive heating). The two gray lines correspond to Eqs (2) and (3). Black arrows identify XRD patterns plotted in (a).

Figure 7

Sn melting evidenced with x-ray diffraction. Stack of integrated XRD patterns collected during a laser heating ramp at (a) $\sim 41$ GPa in run Sn37 and (b) $\sim 46$ GPa in run Sn48.

Figure 8

Reaction between Sn and PTM during run Sn46. (a) XRD signal before and after laser heating at $\sim 90$ GPa, showing the appearance of new XRD spots indicated in yellow. (b) Integrated XRD pattern showing ${\mathrm{SnI}}_4$ (lattice parameter $a=4.099$ Å), Sn and KI after chemical reaction at 90 GPa.

Figure 9

Cross-calibration of our data during three heating ramps: (a) at $\sim 65$ GPa, run Sn46. Temperature below 3000 K are validated. (b) at $\sim 55$ GPa, run Sn47. A good agreement between calculated and experimental volume is observed. The black arrow shows time/temperature where diffuse scattering indicative of melting was observed. (c) At $\sim 100$ GPa, run Sn43. This ramp is represented in Fig. 5.

Figure 10

Conditions where solid/liquid phases of Sn have been observed. Error bars are only presented for ($P,T$) points where liquid was observed to increase lisibility of the diagram. Data from literature [15, 18, 20, 49] are added for direct comparison.