High pressure melt dynamics in shock-compressed titanium

Abstract

We study the high-pressure melting behavior of titanium using laser-driven shock compression with in situ femtosecond x-ray diffraction and molecular-dynamics simulations based on a machine-learned interatomic potential. The MD simulations predict the solid-liquid coexistence on the Hugoniot in the $\sim$$111-124$ GPa range. Experimentally, we observe the first evidence of liquid at 86 GPa. We also observe pronounced microstructural changes with pressure with strong grain refinement associated with the emergence of liquid, within the solid-liquid coexistence ($\sim$$110-126$ GPa). Above 126 GPa, we observe the persistence of residual levels of highly textured crystalline Ti to $\sim$$180$ GPa, well above the expected melt completion pressure. We discuss the accuracy that current laser-shock experimental platforms have at determining the melt onset and completion pressures.

Figures (23)

• Figure 1: Experimental setup for high pressure structural measurements on shock compressed Ti. (a) Target design consisting of polyimide/Ti/LiF layers. (b) VISAR interferogram records the Ti/LiF interface velocity as a function of time (yellow trace), which allows for a determination of sample pressure during the x-ray probe time (see Supplemental Materials). (c) X-ray diffraction pattern provides data on crystal structure, density and microstructural texture within the compressed Ti.
• Figure 2: Ti x-ray diffraction profiles. (a) Azimuthally-averaged diffraction pattern as a function of increasing shock pressure. The high pressure bcc $\beta-$phase is shaded in red, and the liquid diffraction signal is shaded in gray. Labels of experimental run number, pressure from VISAR, and $\beta-$phase density from XRD is labeled on each trace. The position of the uncompressed peaks (originating from regions of the sample ahead of the shock front) are highlighted by the vertical dashed lines. We observe the emergence of increased levels of liquid diffraction signal and a commensurate drop in scattering from the $\beta$-Ti (110) peak as a function of increasing shock pressure (see Fig. \ref{['fig:coexistence']} for the $\beta$, liquid phase fractions as a function of pressure). (b) Select regions of x-ray diffraction pattern show the evolution of intensity distribution in the $(110)$ ring of the $\beta$-phase as a function of pressure. At pressures below melt (Region 1) the $(110)$ reflection is highly localized around the Debye-Scheerer cones, consistent with large orientated grains. Powder-like diffraction is observed within solid-liquid coexistence (Region 2), consistent with microstructure refinement. Finally, above the MLMD determined melt line (Region 3), a residual amount of highly textured $\beta$-Ti $(110)$ reflection is observed with diminishing intensity as a function of pressure.
• Figure 3: Phase fraction as a function of pressure.$\beta$ and liquid phase fraction evolution as a function of pressure. Incipient melting is observed at 86 GPa (see Fig. \ref{['fig:Ti_Xray_profiles_zoom']}). The yellow band represents the the extent of the solid-liquid coexistence, under shock compression, as calculated by MLMD simulations. For the high pressure shots we report on the estimated thickness of $\beta$-Ti present, based on a measure of the compressed sample volume during the x-ray probe period. The highest-pressure shots are shown as translucent to indicate reduced confidence in the phase-fraction estimates due to sharp texture and potentially insufficient grain-sampling statistics.
• Figure 4: $P$-$T$ melt in titanium. The high pressure onset of melt has been constrained under static compression by Stutzmann et al.stutzmann2015 (open circles) and Errandonea et al.errandonea2001 (filled circles). The melt line as determined by our MLMD simulations are defined by the yellow squares. A fit to these data (with shaded uncertainties) is represented by the green curve. The calculated Hugoniot states are shown by the solid red line. The Hugoniot states from other EOS models shown are Kerley kerley2003, Cox cox2012 and Livermore-EOS (LEOS) model #220. The three $P$-$T$ regions with differing $\beta-$phase microstructure detailed in Fig. \ref{['fig:Waterfall_texture']}(b) are labeled here.
• Figure 5: Representation of potential contributors to $P$-$T$ gradients when using laser-shock experiments to determine solid-liquid coexistence. A $P$-$T$ phase map illustrating expected equilibrium behavior as the Hugoniot intersects with the melt line. Here, the red curve represents the region of solid (S) - liquid (L) coexistence. For each panel the black star represents an on-Hugoniot state, whereas the red star represents a portion of the sample which is off-Hugoniot. Potential experimental contributors include: (a) Preheating of sample due to laser-plasma x-rays, (b) Phase plate imprint gorman2022, (c) Temporally non-steady shock states, and (d) A $\sim$$\mu$m-thick epoxy layer resulting in a low-$T$ double-shock region coleman2022. See text for details.