X-Ray Diffraction of Solid Tin to 1.2 TPa

We report direct in situ measurements of the crystal structure of tin between 0.12 and 1.2 TPa, the highest stress at which a crystal structure has ever been observed. Using angle-dispersive powder x-ray diffraction, we find that dynamically compressed Sn transforms to the body-centered-cubic (bcc) structure previously identified by ambient-temperature quasistatic-compression studies and by zero-kelvin density-functional theory predictions between 0.06 and 0.16 TPa. However, we observe no evidence for the hexagonal close-packed (hcp) phase found by those studies to be stable above 0.16 TPa. Instead, our results are consistent with bcc up to 1.2 TPa. We conjecture that at high temperature bcc is stabilized relative to hcp due to differences in vibrational free energy.

Figure 1

Targets consist of $\sim 4\text{−}\mu \mathrm{m}$ Sn foil between single-crystal diamond plates of $\sim 20\mu \mathrm{m}$ (pusher) and $\sim 40\mu \mathrm{m}$ (tamper), joined by $1–2\text{−}\mu \mathrm{m}$ layers of epoxy. In some targets, the pusher is formed from two $\sim 15\text{−}\mu \mathrm{m}$ diamond plates sandwiching a $1–2\text{−}\mu \mathrm{m}$ Au preheat shield. The target is backed by a $300\text{−}\mu \mathrm{m}$-diameter Ta or Pt pinhole which collimates scattered x rays. The package is mounted on a box lined with image plates. ${\mathrm{He}}_{\alpha }$ x-ray radiation from a laser-ablated metal foil (incident at 45°) is diffracted off the target, and the Debye-Scherrer rings register as conic sections on the image plates.

Figure 2

X-ray diffraction measurements: (a) Omega EP 13742, (b) Omega 58709, (c) Omega 66028, and (d) Omega 68278. Rectangular image plates are digitally warped to map from detector planes to the azimuthal angle vs Bragg angle. Ideal peak positions for the reference material used for image plate calibration are shown in gray, and Sn ideal peak positions assuming a tetragonal (a) and bcc (b),(c) structure are shown with the red line segments. Suspected diamond peaks are labeled with an asterisk on the image plate lineouts shown in (e).

Figure 3

$d$ spacing of observed diffraction peaks (data in Table S1), compared with the density-functional theory (DFT) cold curve (red solid line) [1] and with the isothermal equation of state trends and phase transition known from static experiments (dotted lines) [1, 5], extrapolated above 180 GPa. The green lines represent the expected trend in diamond $d$ spacing [19] (dashed line, extrapolation above 800 GPa).

Figure 4

Top: Equation of state of Sn, assuming a bcc phase, compared to the DFT cold curve [1], Hugoniot data [26], and tabulated equation of state model SESAME 2161 [23]. Bottom: Phase diagram of Sn known from static and shock studies [1, 2, 27, 28, 29]. The thermodynamic path followed in this study is unknown, but the temperature is bounded by the gray hashed region.