X-ray diffraction of molybdenum under shock compression to 450 GPa

Molybdenum (Mo) is a body-centered-cubic (bcc) transition metal that has widespread technological applications. Although the bcc transition elements are used as test cases for understanding the behavior of metals under extreme conditions, the melting curves and phase transitions of these elements have been the subject of stark disagreements in recent years. Here we use x-ray diffraction to examine the phase stability and melting behavior of Mo under shock loading to 450 GPa. The bcc phase of Mo remains stable along the Hugoniot until 380 GPa. Our results do not support previous claims of a shallow melting curve for molybdenum.

Figure 1

Experimental setup for x-ray diffraction of shock-compressed molybdenum. The locations of the target package (white square), drive beams, x-ray source, and VISAR laser are indicated. The x-ray source is generated by laser ablation of a Cu foil shown in the upper left. A schematic of the target package is shown below. The x-ray diagnostic box lined with image plate detectors is shown here unfolded illustrating representative diffraction images. White arrows point to diffraction lines, and the orange dashed-dotted line traces a representative diffraction peak across a series of image plates at a constant diffraction angle 2θ. The panels are labeled L, R, U, D, and B corresponding to the left, right, up, down, and back image plates.

Figure 2

Representative VISAR interferogram recording the velocity at the interface between Mo and LiF for a calculated Mo pressure of 367(20) GPa (shot No. 72418) (top panel). Blurring of the shock breakout is due to wave reverberation into the epoxy layer used to glue the Mo foil to the LiF window. Bottom panel: Extracted Mo/LiF velocity history from the top panel. Small variations in interface velocity arise from fluctuations in the laser drive. The orange shaded area indicates the time the x rays were generated relative to the wave propagation into the target package. Diffraction was measured before the wave breaks out into the LiF window, and thus only part of the Mo sample is compressed. The inset shows additional representative extracted Mo/LiF velocities history from the VISAR interferogram for calculated Mo pressures of 250(16) GPa (blue), 338 (18) GPa (green), and 450 (25) GPa (red). The time axis for each shot is normalized to shock arrival at Mo/LiF interface.

Figure 3

(a)–(f) Representative x-ray diffraction images from six Mo shock-compression experiments (left panel of Fig. 1). No background subtraction has been performed. The feature at the top and lower left indicated by blue arrows are artifacts from the filters inside the enclosure. The numbers indicate the assignments of the diffraction lines. 1: unshocked molybdenum, 2: shocked molybdenum (orange arrow), and 3: unshocked Ta. Single-crystal x-ray diffraction spots are suspected to arise from the LiF window. The green, blue, and red curves in (a) show representative contours of constant 2θ at 50°, 74°, and 94°.

Figure 4

Representative x-ray diffraction data for shock-compressed Mo projected into 2θ-$\varphi$ space [43], where $\varphi$ is the azimuthal angle around the incident x-ray direction [panels (a), (c), (e), and (g)]. In these coordinates diffraction peaks are straight lines of constant 2θ. The vertical solid red lines and dashed green lines show positions of ambient-pressure Mo and Ta peaks, respectively. The orange arrows point to the location of the compressed Mo (110) peak for pressures below 380 GPa and diffuse scattering at higher pressures. The panels on the right [(b), (d), (f ), and (h)] show the corresponding background-subtracted one-dimensional x-ray diffraction patterns for the window regions defined by the horizontal blue lines in the corresponding left-hand panel. The diffraction peaks are assigned to uncompressed Mo (red labels), compressed Mo (black labels), and Ta pinhole (green labels). Intensities in the right-hand panels are in photostimulated luminescence (PSL) units.

Figure 5

Pressure vs density for molybdenum. Black circle shows x-ray densities from this study. Static diamond-anvil cell data [13, 21] are shown as red triangles, and Hugoniot measurements [16, 17, 18, 48, 50] from gun experiments are shown as gray diamonds. Densities are also shown for the fcc, hcp, dhcp, and ω phases at selected pressures by assigning the indicated diffraction line to the observed Mo diffraction peak. For hexagonal phases (hcp, dhcp, and ω), the $c/a$ ratios are taken to be 1.633, 3.154, and 0.622, respectively [63, 64]. Uncertainties are shown for bcc only and are similar for other structures.

Figure 6

(a) FWHM of diffraction peaks vs pressure for shocked and unshocked Mo. The blue diamonds show values from the diffraction feature near 2θ ≈ 45° [the (110) peak up to 380 GPa and the diffuse scattering at high pressures]. The FWHM of the shocked Mo (110) peak weakly increases from 1.6° to 1.9° from 250 to 380 GPa and exhibits a sudden jump to values greater than 4° above 390 GPa. The red diamonds show the FWHM of the corresponding unshocked Mo (110) peaks. (b) Intensity variations along the azimuthal direction ($\varphi$) relative to the incident x-ray beam for selected pressures. The red curves show the intensity variations of the (110) peak for the uncompressed regions of the Mo sample reflecting the texture of the starting foils. Azimuthal intensity variations of the compressed samples are shown as blue curves. At 250 GPa, the (110) peak of the compressed sample exhibits textural changes relative to the uncompressed sample. At 380 GPa, the compressed sample retains a reduced texture, but no texturing can be observed at 390 GPa and above. Traces are offset for clarity with zero intensity values indicated by dashed black lines for offset traces. (c) Representative diffraction image (250 GPa) showing region of line out (vertical red and blue dashed lines) between 2θ values of 38°–40° and 45°–47° used in panel (b). Background correction was performed by subtracting the intensity from an equal-sized line out from immediately above or below the measured feature. The vertical solid red lines and dashed green lines show positions of ambient-pressure Mo and Ta peaks, respectively.

Figure 7

Phase diagram of molybdenum. Black circles represent our experimentally measured shock pressures and calculated shock temperatures [57], and the gray band shows the estimated uncertainty. The purple shaded region shows the range of calculated melting curves for Mo [4, 8, 24, 57]. The red triangles show DAC melting data [1, 3], and the green bars indicate the location of previously reported 210- and 390-GPa discontinuities with their uncertainties [2]. The black arrow points to where shock melting is observed from our diffraction data at 390 GPa. The solid-liquid coexistence region is estimated from Ref. [57].

Figure 8

Compressional ($V_P$), bulk ($V_B$), and shear ($V_S$) sound velocities in shocked molybdenum as a function of pressure. Blue, open, and gray symbols are data obtained under shock compression from gas-gun measurements using the optical analyzer technique [2, 9, 37]. The red dashed lines are from ab initio molecular dynamics calculations [28]. The black squares show 1-bar velocities. The solid black line shows bulk sound velocities calculated from the Hugoniot slope [2]. The blue arrows point to the location of reported discontinuities at 210 and 390 GPa [2]. More recent sound velocity data [9] provide additional evidence in support of the 390-GPa discontinuity, consistent with our x-ray diffraction results (black dashed line) but do not support the existence of the 210-GPa discontinuity.