Absolute measurements of solid-material compressibility by magnetically driven shockless dynamic compression experiments to multi-megabar pressures have the potential to greatly improve the accuracy and precision of pressure calibration standards for use in diamond anvil cell experiments. To this end, we apply characteristics-based inverse Lagrangian analysis (ILA) to 11 sets of ramp-compression data on pure platinum (Pt) metal and then reduce the resulting weighted-mean stress-strain curve to the principal isentrope and room-temperature isotherm using simple models for yield stress and Grüneisen parameter. We introduce several improvements to methods for ILA and quasi-isentrope reduction, the latter including calculation of corrections in wave speed instead of stress and pressure to render results largely independent of initial yield stress while enforcing thermodynamic consistency near zero pressure. More importantly, we quantify in detail the propagation of experimental uncertainty through ILA and model uncertainty through quasi-isentrope reduction, considering all potential sources of error except the electrode and window material models used in ILA. Compared to previous approaches, we find larger uncertainty in longitudinal stress. Monte Carlo analysis demonstrates that uncertainty in the yield-stress model constitutes by far the largest contribution to uncertainty in quasi-isentrope reduction corrections. We present a new room-temperature isotherm for Pt up to 444 GPa, with 1-sigma uncertainty at that pressure of just under ± 1.2 % ; the latter is about a factor of three smaller than uncertainty previously reported for multi-megabar ramp-compression experiments on Pt. The result is well represented by a Vinet-form compression curve with (isothermal) bulk modulus K 0 = 270.3 ± 3.8 GPa, pressure derivative K 0 ′ = 5.66 ± 0.10 , and correlation coefficient R K 0 , K 0 ′ = − 0.843 .
Pulsed-power generators can produce well-controlled continuous ramp compression of condensed matter for high-pressure equation-of-state studies using the magnetic loading technique. X-ray diffraction (XRD) data from dynamically compressed samples provide direct measurements of the elastic compression of the crystal lattice, onset of plastic flow, strength–strain rate dependence, structural phase transitions, and density of crystal defects, such as dislocations. Here, we present a cost-effective, compact, pulsed x-ray source for XRD measurements on pulsed-power-driven ramp-loaded samples. This combination of magnetically driven ramp compression of materials with a single, short-pulse XRD diagnostic will be a powerful capability for the dynamic materials’ community to investigate in situ dynamic phase transitions critical to equation of states. Finally, we present results using this new diagnostic to evaluate lattice compression in Zr and Al and to capture signatures of phase transitions in CdS.
We present results from ramp compression experiments on high-purity Zr that show the α→ω, ω→β, as well as reverse β→ω phase transitions. Simulations with a multiphase equation of state and phenomenological kinetic model match the experimental wave profiles well. While the dynamic α→ω transition occurs ∼9GPa above the equilibrium phase boundary, the ω→β transition occurs within 0.9 GPa of equilibrium. We estimate that the dynamic compression path intersects the equilibrium ω-β line at P=29.2GPa, and T=490K. The thermodynamic path in the interior of the sample lies ∼100K above the isentrope at the point of the ω→β transition. Approximately half of this dissipative temperature rise is due to plastic work, and half is due to the nonequilibrium α→ω transition. The inferred rate of the α→ω transition is several orders of magnitude higher than that measured in dynamic diamond anvil cell (DDAC) experiments in an overlapping pressure range. We discuss a model for the influence of shear stress on the nucleation rate. We find that the shear stress sji has the same effect on the nucleation rate as a pressure increase δP=cϵijsji/(ΔV/V), where c is a geometric constant ∼1 and ϵij are the transformation shear strains. The small fractional volume change ΔV/V≈0.1 at the α→ω transition amplifies the effect of shear stress, and we estimate that for this case δP is in the range of several GPa. Correcting our transition rate to a hydrostatic rate brings it approximately into line with the DDAC results, suggesting that shear stress plays a significant role in the transformation rate.