X-ray diffraction of ramp-compressed aluminum to 475 GPa

Aluminum is predicted to undergo various solid–solid phase transformations to 10 TPa.¹ At ambient conditions, Al is a face-centered cubic (fcc) crystal. At 217 GPa and room temperature, fcc Al was observed to transform into a hexagonal close-packed (hcp) structure in diamond anvil cell (DAC) experiments.² The hcp phase was measured to be stable up to 333 GPa; beyond that, ab inito calculations are relied upon to predict the crystal structures of Al at extreme pressures and temperatures. Density-functional theory (DFT) predicts a transformation to body-centered cubic (bcc) Al at pressures between 316 GPa (Ref. 3) and 363 GPa,⁴ along the principal isentrope. A bcc Al polymorph was synthesized in a microexplosion and recovered,⁵ but the transformation pressure was not measured. The bcc phase was confirmed experimentally at 321 ± 12 GPa under dynamic compression,⁶ additional details of which are discussed here.

The high-pressure phase diagram of Al is illustrated in Fig. 1. Shock compression melts Al in the fcc phase at 125 GPa^8,9 due to an associated increase in entropy and temperature. Here, ramp compression is used to follow a nearly isentropic compression path in order to investigate the hcp and bcc phases of Al. At even higher pressures, Al is predicted to no longer arrange in simple, close-packed structures but transforms to open, incommensurate structures. The sequence of pressure-induced transitions is fcc–hcp [at 217 GPa, 298 K (Ref. 2)] hcp–bcc [at 321 GPa, ∼920 K (Ref. 6)] with the next phase transformation predicted at 3.2 TPa and 0 K to a Al16–I4/mcm host-guest structure.¹ 

The equation of state (EOS) of Al is important in high-energy-density (HED) experiments because it is used as a impedance-matching standard.^10–13 Al has been studied using DAC,² gas-gun,^14,15 nuclear explosion,¹⁶ pulsed-power,^17–19 and laser^20–23 drivers under static, shock, and quasi-isentropic compression. Better knowledge of the Al EOS is required to avoid the introduction of systematic errors in HED measurements.²⁴ 

Quasi-isentropic or ramp compression is used to compress materials to high pressures and lower temperatures than those accessible by shock compression.²⁵ The technique can use high-power lasers, pulsed-power, graded-density-impactors, etc., to compress samples from nanosecond (ns) to microsecond time scales. At these time scales, the pressure loading profiles and targets can be designed so that acoustic waves do not steepen to form a shock and Al may remain in the solid state at high-pressure where interesting phenomena are predicted, including solid–solid phase transformations. X-ray diffraction (XRD) measurements²⁶ have been developed at the OMEGA EP Laser Facility²⁷ that allow direct determination of lattice structure,^28,29 crystallographic texture,^30,31 and effects of material strength.³² 

This work probed the high-pressure crystal structure of Al up to 475 GPa using laser-driven ramp compression and in situ XRD. We observe a transformation from a fcc to an hcp structure at 216 ± 9 GPa. This measurement duplicates the fcc–hcp transition observed in static DAC experiments but at nanosecond time scales and slightly higher temperatures. At higher pressures, a transition to a bcc structure is observed at 321 ± 12 GPa.⁶ The bcc structure is measured to be stable to at least 475 GPa.

Pure Al and Al-6061 alloys have been shown to have profound differences in yield strength^19,23 and have distinct strain rate dependencies.³³ The existence and pressure onset for solid-solid phase transformations in 6061-Al alloy is essential for interpretation and analyses of previous and future ramp compression experiments.²⁴ We present the first observation of the fcc–hcp and hcp–bcc transformations in 6061-O (annealed) Al alloy at 175 ± 9 GPa and 333 ± 11 GPa, respectively.

The initial crystallographic texture of the rolled Al foils is characterized and studied through the observed phase transitions. The high-pressure texture suggests that close-packed and nearly closed-packed planes remain parallel during the fcc–hcp and hcp–bcc transformations.

Experiments were performed on the OMEGA EP laser³⁴ at the University of Rochester's Laboratory for Laser Energetics. Figure 2 provides details about the experimental geometry. Ultraviolet 351-nm laser pulses were shaped to produce an irradiance profile that smoothly increases the applied pressure over 10 ns. The “ramped” pulse is designed for the specific target dimensions to avoid shock formation. An example of a delivered pulse shape is shown in Fig. 2(c). The peak drive laser intensities ranged from 1.5 × 10¹² to 3.4 × 10¹³ W/cm². A single drive beam irradiated the Al sandwich target at an angle of $23°$ with respect to the target normal. Distributed phase plates³⁵ were used to produce a focal spot with a super-Gaussian intensity distribution ${I=I0×exp[−2(r/550μm)8.0]}$⁠. Three different types of Al samples were used: 15- to 20‐μm-thick Al (99.999% purity) rolled foils from Goodfellow, 18‐μm-thick 6061-O (annealed) Al foils from ESPI metals (rolled from 76‐μm-thick stock), and electron-beam–deposited 15‐μm coatings on lithium fluoride (LiF). The rolling process resulted in a significant deviation from an “ideal” powder sample and produced strong preferred orientation (texture) of the crystal grains. The Al samples were sandwiched between plates of $⟨110⟩$-oriented 20‐μm-thick single-crystal diamond and $⟨100⟩$-oriented 100‐μm- or 150‐μm-thick LiF. The target stack was mounted on a high-Z tungsten, tantalum, or platinum plate (75–150 μm thick) with a 300‐μm-diameter pinhole aperture to provide collimation near the sample plane [Fig. 2(b)]. The 1100‐μm-diameter drive laser spot size is large relative to the 300‐μm-diameter collimating aperture in order to limit the XRD and velocimetry diagnostics' field of view to only the center of the compressed region of the sample.

An additional laser beam irradiated a backlighter foil with an irradiance of 2.5 × 10¹⁵ or 4.0 × 10¹⁵ W/cm² to optimize laser energy to x-ray conversion efficiency for a Ge or Cu backlighter foil, respectively. The 8.37-keV (Cu) and 10.25-keV (Ge) He-α x rays are generated over the duration of the laser pulse and emit as a quasi-monoenergetic source at an angle $23°$ with respect to the Al sandwich target normal. The drive and backlighter laser pulses are shown in Fig. 2(c).

X-rays scattered from interatomic lattice planes with spacings, d, constructively interfere when the Bragg condition, $λ=2d sin(θ)$⁠, is satisfied for an x-ray wavelength, λ, and x-ray incidence angle, θ. A “powdered” material (i.e., one with randomly orientated crystal grains) will produce uniform cones of diffracted x rays for each allowed lattice plane for the material crystal structure. Powder diffraction is used in these experiments to measure the scattering angle between the incident and diffracted beams, 2θ, to determine the crystal structure. Under compression, the 2θ for each lattice plane increases with decreasing interatomic spacing until a phase transformation occurs. When a new crystal structure is formed, an abrupt change in the scattering angles is observed as the symmetry, and therefore the structure factor, changes for the new atomic arrangement.

The in situ XRD diagnostic on OMEGA EP is called powder x-ray diffraction image plates (PXRDIP)²⁶ and is shown in Fig. 2. The Debye–Scherrer diffraction cones from both the compressed sample and ambient density high-Z pinhole trace out conic sections on the image plates (IP's)³⁶ lining the inside of a stainless steel box [shown in Fig. 2(a)]. Filters comprised of Cu or Al, for the Cu or Ge backlighters, respectively, are inserted in front of the IP's to attenuate background from the x-ray backlighter and from the ablation plasma. Diffraction from the pinhole material is used as a reference to precisely determine the diffraction geometry. The diffraction lines from the compressed sample are identified and their 2θ values are measured with respect to these reference lines.

The pressure of the Al sample is determined using the measured Al–LiF particle velocities. A line-imaging VISAR (velocity interferometer system for any reflector)³⁷ detects Doppler shifts of a 532-nm probe beam reflecting off the accelerating Al–LiF interface through the transparent LiF window. The Doppler shifts are manifested as shifts in the fringe pattern recorded in a 2-D interferogram. The fringe shifts are proportional to the changes in the velocity of the reflecting surface, allowing one to measure the Al-LiF interface velocity as a function of time. LiF was chosen as the window material because it is transparent under ramp compression up to 800 GPa³⁸ and is transparent under shock compression to 215 GPa.^39–41 In addition, the optical and mechanical responses of LiF under ramp compression are well known.^41,42 As seen in Fig. 2(a), a hole in the back of the PXRDIP box allows the VISAR probe to reflect off of the rear surface of the target mounted on the front of the box. The pressure determination from the measured particle velocities is discussed in Sec. III B.

XRD data were used to measure the density of the compressed Al, detect phase transformations, identify the crystal structure, and measure the high-pressure crystallographic texture. The direct x-ray source (XRS) image and reference diffraction calibration lines are identified and assigned their known 2θ values. A least-squares minimization routine determines best-fit values for the experimental geometry including image plate, XRS, and pinhole locations. The IP's are projected into 2θ‐ϕ space, where ϕ is the azimuthal angle around the Debye–Scherrer ring. Background subtracted 2θ‐ϕ projections of Al in the fcc (c), hcp (b), and bcc (a) phases are shown in Fig. 3. The x-rays originating from the ablation plasma create a smoothly varying background across the image plates, and the background levels are higher at higher pressures, as seen in Fig. 3(a). The background subtraction is performed in the 2θ‐ϕ space with a nonlinear peak clipping algorithm.⁴³ The IP's show four diffraction lines from Al in the fcc phase at 0 GPa [Fig. 3(c)], three lines in the hcp phase at 291 GPa [Fig. 3(b)], and one line in the bcc phase at 466 GPa [Fig. 3(a)]. Additional features are visible on the IP's due to single-crystal Laue diffraction from the diamond and LiF windows, edges of the IP's, and filter edges. Azimuthally averaged lineouts of the 2θ‐ϕ projections are plotted versus Q [Q = (4π/λ)sin(θ)], for x-ray wavelength, λ, in Fig. 4.

Two distinct changes in crystal symmetry are observed in the XRD data with increasing pressure, indicative of two structural phase transformations. The XRD pattern for undriven pure Al foil is shown in Figs. 3(c) and 4(c). This pattern shows strong initial texture; for example, the fcc (111) line is present only at azimuthal angles, $±150°$⁠. The texture is also apparent in the fcc (200), (220), and (311) lines. When pressure is increased to 291 GPa [Figs. 3(b) and 4(b)], the fcc (200) peak disappears, and the hcp (100) peak and hcp (101) peak form the characteristic hcp triplet along with the hcp (002) peak. At the highest pressures, the hcp peaks disappear and a single intense peak is observed. The single peak, labeled in Figs. 3(a) and 4(a), is consistent with the bcc (110) diffraction line and shows significantly less texture than the initial rolled foil. A summary of these data were presented previously in Ref. 6. In a similar experiment performed on Al at the National Ignition Facility, three lines corresponding to bcc Al (110), (200), and (211) were observed under ramp-compression above 400 GPa.⁴⁴ The observation of three reflections from the bcc phase confirms the single reflection in the OMEGA data, indicating that Al is a bcc metal above 321 ± 12 GPa. The NIF XRD platform has a greater x-ray brightness than the OMEGA XRD platform and recorded two additional higher-angle peaks.

Accurate pressure measurements are facilitated with the use of transparent LiF windows that allows one to directly measure of the Al–LiF interface velocity using VISAR. With the knowledge of the optical and mechanical response of LiF under ramp compression,^38,41,42 the pressure at the Al–LiF interface can be deduced. To determine the mean pressure within the finite-thickness Al sample, a correction is applied to Al–LiF pressure using the method of characteristics. Previous studies used single-crystal diamond windows which become opaque under ramp-compression above ∼100 GPa.^28,29 The use of a transparent LiF window eliminates the need to back-propagate a free-surface velocity and the systematic errors associated with the diamond EOS, strength effects, and assumptions of wave interactions within the window. The use of a LiF window additionally improves the accuracy of the pressure determination because it has a wave-impedance much closer to that of Al compared to diamond; thus, only a small correction to the interface pressure is needed to obtain the pressure inside the sample. This method could also provide additional information about the reflectivity under ramp compression.

The pressure determination for shot 22477 is outlined in Fig. 5. The Al–LiF interface velocity as a function of time is measured with an accuracy of ∼5% of the velocity per fringe (VPF). The VPF's used in the two interferometers were 1.64 and 2.74 μm/ns fringe; the two velocities are shown in Fig. 5(b) overlaid on the VISAR interferogram.

A characteristics algorithm is used to map the pressure in the Al sample in space and time, shown in Fig. 5(c).^45,46 The characteristics solver assumes that the thermodynamic quantities under isentropic compression propagate at the local sound speed along hydrodynamic characteristics.⁴⁷ Therefore, the fluid flow can be solved as a grid of forward- and backward-propagating characteristics.

The boundary condition at the Al–LiF interface is the continuity of particle velocity and normal stress. An EOS model for the Al sample and window material is used. The inputs into the characteristics-propagation algorithm used here include the measured apparent Al–LiF particle velocity, EOS SESAME 7271 and 7271v3^41,42 for LiF, Kerley 3700 EOS for Al,⁷ refractive index models for LiF,^38,40 Al sample thickness, and the XRS probe time and duration.

From the characteristics code, the average pressure throughout the thickness of the Al over the duration of the x-ray probe can be determined [Fig. 5(d)]. To assess the errors, the characteristics calculation was performed 2000 times for each shot, varying the individual experimental parameters within their uncertainties. The Monte Carlo (MC) routine randomly calls either the SESAME 7271 or the more-compressible 7271v3 to include error in the LiF EOS. The MC routine also randomly uses either a power law or linear refractive-index correction proposed by Refs. 40 and 38, respectively, to include error in the refractive-index correction. The power law method proposed by Rigg et al. captures the non-linear refractive index behavior of LiF measured by Davis et al. The linear refractive-index correction gives a systematically higher velocity than the non-linear refractive index correction which results in up to a 3% higher pressure.

The mean and standard deviation, σ_P, from the MC error analysis are given as the value and error for the measured pressure during the x-ray exposure. The standard deviation, σ_P, of the mean pressure state in the sample ranged from 3.2% to 6.5% of the mean pressure. In addition to the histogram of mean pressure values from the MC ensemble, there is a range of pressure values during the x-ray exposure due to pressure gradients in the sample, as shown in the inset of Fig. 5(d). The average standard deviation, Δ_P, from the MC analysis of the pressure state in the sample due to pressure gradients ranged from 0.6% to 15.3% of the mean pressure.

Shocks were observed only in experiments above 405 GPa with a jump of 1.6 km/s in the particle velocity (∼33 GPa, ∼790 K) being the strongest shock due to the diamond Hugoniot elastic limit (HEL) wave,⁴⁸ assuming the jump is a signature of shock formation. Data that do not lie on the principal isentrope in Fig. 1 are at an elevated temperature due to these small shocks and are plotted on their shock-ramp path.

A pressure scan was performed with 26 shots for pure Al to measure the pressure onset for the fcc–hcp and hcp–bcc phase transitions. A plot of these data is shown in Fig. 6 as the lattice d spacing and density versus pressure. The data are plotted as black (fcc), red (hcp), and blue (bcc) points. The data are compared to the Kerley 3700 principle isentrope (black, red, and blue lines) using the ideal c/a ratio for hcp phase in Fig. 6(a).⁷ The vertical dashed black lines are plotted at the measured onset pressure for the fcc–hcp and hcp–bcc phase transitions. Compression in the fcc phase is consistent with the Al isentrope (black curves) to 216 ± 9 GPa, where an additional peak from hcp (101) is first observed. A region of coexistence is observed to 238 ± 9 GPa, and the hcp (100) and (002) diffraction peaks are also detected. The diffraction data are consistent with the hcp phase until 321 ± 12 GPa, where the bcc (110) peak is observed. Another region of coexistence is observed up to 363 ± 14 GPa. At higher pressures, the hcp peaks eventually disappear and a single diffraction peak from bcc (110) is observed to 475 ± 16 GPa. Figure 6(b) plots the best-fit density for the assigned crystal structure as a function of pressure. These data are summarized in Table I.

The data are compared to various models in Fig. 6(b) including the chemical model-based Kerley 3700 principal isentrope,⁷ the 3-active-electron DFT-based SESAME 3722 multiphase principal isentrope,⁴ and the room-temperature DAC data.² The multiphase description is required in the EOS model for agreement with the density jump observed in our data for the bcc phase. Sjostrom et al. predicted the fcc-to-hcp transition to occur at 195 GPa (780 K) and the hcp-to-bcc transition at 363 GPa (920 K) along the principle isentrope.⁴ Kudasov et al. calculated the same transitions at 198 and 320 GPa, respectively.³ The onset pressures calculated by Kudasov et al. using an all-electron DFT model are in excellent agreement with the measured onset pressures. Their calculated transition pressures are 8% lower and 0.3% lower than the measured onset pressures for the fcc–hcp and hcp–bcc transitions, respectively. A plot of the best-fit c/a ratios for the hcp phase is shown in Fig. 7. The weighted mean, 1.65 ± 0.01, is larger than the ideal ratio, 1.633. This is also larger than the c/a ratio used by Kudasov et al., 1.615; however, that c/a ratio was optimized independent of temperature.

We observe a coexistence of fcc–hcp and hcp–bcc phases near the transition pressures. The spatial and temporal gradients within the Al sample are not large enough to explain the coexistence observed over 22-GPa and 43-GPa ranges. For the two shots with fcc–hcp coexistence, the maximum standard deviation in pressure due to spatial gradients, Δ_P, is 12 GPa compared to 22 GPa. And for the three shots with hcp–bcc coexistence, the maximum standard deviation in pressure due to spatial gradients, Δ_P, is 12 GPa compared to 43 GPa. The fcc–hcp coexistence has been observed in other materials, including Xe,⁴⁹ due to the development of stacking disorder in the fcc lattice to form hcp. Coexistence and hysteresis are observed in the α(bcc)–ϵ(hcp) transition for iron, and it is attributed to a large elastic strain energy.⁵⁰ 

Previous authors have observed significant differences in yield strength in pure Al and Al 6061 alloy under ramp compression.^19,23 Additional experiments reported that the difference in the yield strength was most likely due to the difference in impurity levels and strain rate effects.³³ Due to the distinct properties of pure and alloy Al, we performed an independent study of the fcc–hcp and hcp–bcc phase transformations in Al 6061-O (annealed temper).

Al 6061 was chosen because it has been widely studied under ramp and shock compression,^13,19,24 including studies of yield strength⁵¹ and the onset of plastic flow.³³ Pulsed-power experiments by Lemke et al.²⁴ used magnetically driven Al 6061 cylindrical liner implosions to infer pressure-density data in various samples. Systematic differences in their measured and simulated velocities were conjectured to be caused by solid-solid phase transitions occurring in the Al-6061 liners, but there have not been any direct measurements of these transitions before this work.

In these experiments, the alloy stock was composed of 97.39% Al, 0.92% magnesium, 0.61% silicon, and 0.53% iron by weight, with other less-abundant elements. A summary of the Al-6061-O data (black, red, and blue points) is shown in Fig. 8 along with the pure Al data (white points). The fcc–hcp and hcp–bcc phase transformations are shown for the Al alloy. The hcp (101) peak is first observed at 175 ± 9 GPa and the bcc (110) peak at 333 ± 11 GPa. Similar to pure Al, regions of coexistence are observed over a 52-GPa range for fcc and hcp and a 42-GPa range for hcp and bcc. For the two shots with fcc–hcp coexistence, the maximum standard deviation in pressure due to spatial gradients, Δ_P, is 11 GPa, and for the two shots with hcp–bcc coexistence, the maximum standard deviation in pressure due to spatial gradients, Δ_P, is 9 GPa. Therefore, the coexistence is not due to the spatial gradients in the sample.

The pressure onset for the hcp phase in the alloy is 40 GPa lower than in the pure Al. Additional data are needed to make the same comparison for the hcp–bcc transformation. This pressure onset difference is unexpected based on the results by Smith et al.³³ Smith et al. found that the Al 6061-T6 peak elastic precursor stress was insensitive to the strain rate at the onset of plastic flow compared to pure Al. This difference in the rate dependence of peak elastic precursor stress suggests that the onset stress for the fcc–hcp and hcp–bcc phase transformations would be lower in pure Al than Al 6061 for strain rates in the thermal activation regime. Otherwise, the phase-transformation onset stress would be the same for pure and alloy Al if the strain rate is in the phonon-drag–dominated regime. Based on the sample thicknesses and loading rates used in this study, pure and alloy Al have the same onset stress for plasticity; therefore, one would not expect the phase boundaries to shift for the pure and alloy Al. This is because the Peierls stress would be the same for both materials.⁵² Unexpectedly, the measured pressure onset for the hcp phase in the alloy is lower than in the pure Al. However, the alloy investigated here was a different temper than used by Smith et al., which can cause differences in the distribution of precipitates in the Al matrix and can affect its mechanical properties. In diffusional phase transformations, the precipitates can act as heterogeneous nucleation sites for the hcp phase, but more data are required before conclusions on the kinetics of plastic flow and phase transformations can be drawn.

We observe significant correlations in the high-pressure texture between the fcc, hcp, and bcc phases of Al.⁶ In Fig. 9(a), pole figures [(111) and (200)] for the rolled foils used in these experiments show strong initial texture; the initial preferred orientation is nearly fiber textured which is ideal for studying mechanisms of atomic rearrangement.⁵³ The pole figures were collected using a Philips X'Pert High Resolution Materials Research diffractometer. The pole figures show the (200)_fcc plane normals are nearly parallel (⁠$0°$–$15°$⁠) to the pressure-loading axis. The initial texture of the (200) fcc planes can be seen in Fig. 9(b) in a diffraction pattern from an undriven shot where the (200) diffraction ring has limited azimuthal extent on the IP's. Also shown in Fig. 9(a), the (111)_fcc plane normals have a preferred orientation of $40°$–$60°$ with respect to the pressure-loading direction. The (111) diffraction ring in Fig. 9(b) is only visible on a single IP (left).

The crystallographic texture was tracked through the fcc–hcp and hcp–bcc phase transformations. Lineouts along the azimuthal angle of the most close-packed Debye–Scherrer rings are shown in Fig. 9(c) in the fcc, hcp, and bcc phases. The yellow-shaded regions of Fig. 9(c) highlight the peaks in the texture that persist in the three phases for the fcc (111), hcp (002), and bcc (110) planes. The persistence of the initial texture in the close-packed planes suggests that the close-packed planes remain parallel through the transformations. Therefore, these data are consistent with the Shoji–Nishiyama orientation relation (OR)⁵⁴ for the fcc–hcp transition and the Burgers OR⁵⁵ for the hcp–bcc transition. These OR's provide the relationship between specific planes and directions in parent and child crystals. The texture can also be seen in Fig. 3 in the 2θ‐ϕ projections. In Fig. 3(a), the bcc (110) shows less texture than the original sample due to the atomic rearrangement from multiple phase transformations; however, the peaks at $±150°$ persist to 466 GPa.

In summary, we report x-ray diffraction data on solid pure and 6061-O Al compressed to 475 GPa⁶ and 479 GPa, respectively. The fcc–hcp transition onset is observed at 216 ± 9 GPa in pure Al⁶ and at 175 ± 9 GPa in 6061 Al. This duplicates the observation, in static compression, of the fcc–hcp transition under dynamic compression conditions, nanosecond time scales, and high strain rates. We observed the fcc–hcp phase transition at a 40-GPa lower pressure in the 6061 Al than in pure Al. This is unexpected from the previously observed discrepancy in the rate dependence of the peak elastic precursor between pure and 6061 Al,³³ and suggests that the impurities do not cause the phase boundaries to shift to higher pressures. The hcp–bcc transition onset is observed at 321 ± 12 GPa in pure Al,⁶ and 333 ± 11 GPa in the alloy. The stress–density data are in better agreement with the all-electron DFT isentrope by Kudasov et al.³ than the conductive-electron DFT SESAME 3722 isentrope⁴ and the chemical model-based Kerley 3700 isentrope.⁷ The initial texture of the rolled foils is maintained in the high-pressure texture of the close-packed planes, suggesting that the close-packed planes remain parallel through the fcc–hcp and hcp–bcc transitions.

The authors thank the OMEGA EP team for laser operation and diagnostic support. We would like to thank M. Bonino, K. Lintz, C. Sorce, N. Whiting, J. Tellinghusien, A. Sorce, J. Kendrick, and R. Boni at LLE.

This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award No. DE-NA0001944, the University of Rochester, and the New York State Energy Research and Development Authority.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.

Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under Contract No. DE-NA0003525.

This report was prepared as an account of work sponsored by an agency of the U.S. Government. Neither the U.S. Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the U.S. Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the U.S. Government or any agency thereof.