Session V2: CM.2 Phase Transitions: Tin and Germanium

Phase Diagram of Sn into the Megabar Pressure Range

The melting curve of Sn has previously been studied using shock techniques up to P $\sim$50 GPa, and recent diamond anvil cell experiments showed flat melting temperatures between 40 and 68 GPa. We performed new melting experiments using laser-heated diamond anvil cell techniques combined with \textit{in situ} synchrotron X-ray diffraction, revealing a steep rise in melting slope above 70 GPa up to a maximum T$_{m}$ $\sim$5500 $\pm$ 500 K at 1.05 Mbar. Those results immediately paved the way for laser driven shock experiments that could probe both the melting relation following shock compression and the solidus below the melting curve in the 1-10 Mbar pressure range via ramp compression and diffraction techniques. We also performed room temperature experiments to 1.4 Mbar using the diamond anvil cell with near hydrostatic conditions (He loadings) and synchrotron X-ray diffraction. Our results at room temperature reveal a previously unreported distortion of the body centered tetragonal phase (\textit{I4/mmm}) to an orthorhombic structure (\textit{Immm}) at 32 GPa. Between 40 and 70 GPa, the X-ray diffraction patterns reveal two structures that can be assigned to this body centered orthorhombic structure and the second to the previously reported bcc (\textit{Im-3m}) phase. The phase diagram spreading across 2 Mbar and 6000 K will be discussed.   

Sound velocity under shock compression and bct-bcc transition of Tin

The longitudinal sound velocity of material can be resolved from the particle velocity of window profile under shock loading. Two analysis methods are proposed. One is name for the speedy change derivative of sound velocity versus time and the other is the continue lowering of velocity plateau. We carefully analysis the experimental data from the direct reverse-impact configuration and the new sound velocity data are provided. The results show the experimental points of the longitudinal sound velocity against shock pressure are dispersive and the range of transition pressure from bct-bcc under dynamic compression is difficult to obtain.   

Powder diffraction from solids in the terapascal regime

A method of obtaining powder diffraction data on dynamically-compressed solids has been implemented at the Jupiter and OMEGA laser facilities. Thin powdered samples are sandwiched between diamond plates, and ramp compressed in the solid phase using a gradual increase in the drive-laser intensity. The pressure history in the sample is determined by back-propagation of the measured diamond free-surface velocity. A pulse of x-rays is produced at the time of peak pressure by laser illumination of a thin Cu or Fe foil, and collimated at the sample plane by a pinhole cut in a Ta substrate. The diffracted signal is recorded on x-ray sensitive material, with a typical d-spacing uncertainty of approximately 0.01 {\AA}. This diagnostic has been used up to 1.2 TPa (12 Mbar) to verify the solidity, measure the density, constrain the crystal structure, and evaluate the strain-induced texturing of a variety of compressed samples spanning atomic numbers from 6 (carbon) to 82 (lead).   

A new polymorph of germanium

The behavior of germanium under high pressure has been studied for many decades using diamond-anvil cells (DACs). A series of metal-metal transitions has been observed after the initial transition to the metallic $\beta $-Sn structure at $\sim$10 GPa. More recently, evidence for the semiconductor-metal transition has also been reported from point loading (indentation) experiments. Particularly pure amorphous Ge as starting material can be reliably phase transformed. These transitions are not reversible however, and meta-stable crystalline phases can be recovered upon pressure release. In this study we report experimental evidence from both point loading and in-situ DAC experiments for a new polymorph of Ge with the r8 structure, the same as observed for silicon. In the point loading case, the final phases after unloading are characterized using Raman spectroscopy in conjunction with computations employing density functional theory. In the DAC case, in-situ X-ray diffraction using synchrotron radiation was employed. This combination of two such very different methods for pressure application yields a more comprehensive picture of the phase behavior of Ge.   

Germanium Multiphase Equation of State

A new SESAME multiphase Germanium equation of state (EOS) has been developed utilizing the best experimental data and theoretical calculations. The equilibrium EOS includes the GeI (diamond), GeII (beta-Sn) and liquid phases. We will also explore the meta-stable GeIII (tetragonal) phase of germanium. The theoretical calculations used in constraining the EOS are based on quantum molecular dynamics and density functional theory phonon calculations. We propose some physics rich experiments to better understand the dynamics of this element.   

Phase Stability and Equation of State of Vanadium and V-Ti alloys to 220 GPa

Experimental studies of vanadium found that during compression it undergoes a phase transition from the low pressure body centered cubic crystal structure to a rhombohedral phase at 65 GPa when compressed under quasihydrostatic conditions and as low as 30 GPa under uniaxial compression (PRB 83, 054101). Theoretical studies are in reasonable agreement with the transition pressure and predict that upon further compression above 200 GPa the bcc phase becomes stable again. The latest study (PRL 103, 235501) predicts that alloying vanadium with small amounts of the neighboring elements can increase or decrease the stability of the bcc phase relative to the rhombohedral phase. We performed powder x-ray diffraction experiments in diamond anvil cell of pure vanadium and V-Ti alloys at ambient temperature up to 220 GPa. In this paper we will discuss our findings related to the stability of the high pressure rhombohedral phase of the pure vanadium and the equation of state, and the influence of the alloying on the EOS.   

Embedded atom model for tin and MD simulation of tin shock loading and melting

The goal of the work was to develop an interatomic potential, that can be used in large-scale classical MD simulations to predict tin properties near the melting curve, the melting curve itself, and the kinetics of melting and solidification when shock and ramp loading. According to phase diagram, shocked tin melts from bcc-phase, and since the main objective was to investigate melting, the EAM was parameterized for bcc-phase. The EAM was optimized using isothermal compression data (experimental at T$=$300K and ab initio at T$=$0K for bcc, fcc, bct structures), experimental and QMD data on the Hugoniot and on the melting at elevated pressures. The Hugoniostat calculations centered at $\beta $-tin at ambient conditions showed that the calculated Hugoniot is in good agreement with experimental and QMD data above $\beta $-BCT transition pressure. A series of calculations of overcooled liquid in pressure range corresponding to bcc-phase showed crystallization into bcc-phase. Since the principal Hugoniot of tin originates from the $\beta $-tin that is not described by this EAM the special initial state of bcc samples was constructed to perform large-scale MD simulations of shock loading.