The dynamic diamond anvil cell (dDAC) is a recently developed experimental platform that has shown promise for studying the behavior of materials at strain rates ranging from intermediate to quasi-static and shock compression regimes. Combining dDAC with time-resolved x-ray diffraction (XRD) in the radial geometry (i.e., with incident x-rays perpendicular to the axis of compression) enables the study of material properties such as strength, texture evolution, and deformation mechanisms. This work describes a radial XRD dDAC setup at beamline P02.2 (Extreme Conditions Beamline) at DESY’s PETRA III synchrotron. Time-resolved radial XRD data are collected for titanium, zirconium, and zircon samples, demonstrating the ability to study the strength and texture of materials at compression rates above 300 GPa/s. In addition, the simultaneous optical imaging of the DAC sample chamber is demonstrated. The ability to conduct simultaneous radial XRD and optical imaging provides the opportunity to characterize plastic strain and deviatoric strain rates in the DAC at intermediate rates, exploring the strength and deformation mechanisms of materials in this regime.

High pressure research is a multidisciplinary field that provides insight into material properties such as phase stability, pressure–volume–temperature equations of state, superconductivity, chemical reactions, as well as strength and deformation mechanisms. High pressure loading, frequently under non-ambient temperature conditions, is also a common tool used in the synthesis of novel materials.1,2 High pressure techniques are commonly divided into two broad categories: quasi-static compression and dynamic (i.e., ramp or shock) compression. Quasi-static compression involves gradually changing the pressure using experimental platforms such as the diamond anvil cell (DAC) or large volume press apparatus. These devices typically achieve time-averaged strain rates, ε̇, on the order of 10−6–10−1 s−1.1 Alternatively, dynamic compression techniques such as split-Hopkinson pressure bars, gas guns, laser ramps, and shock compression may be used to compress materials at strain rates above 103 s−1.3 Material properties at strain rates between the quasi-static and dynamic compression regimes are less-commonly studied, at least partly because there are a limited number of techniques that can controllably load materials at these intermediate strain rates. However, these intermediate strain rates are important as they can be used to help understand large-scale events such as asteroid and meteorite impacts.4 Studying material properties at these intermediate strain rates can help resolve discrepancies in phase diagrams, phase transition boundaries, and deformation mechanisms between static and dynamic compression experiments. Several DAC based methods have been used to achieve these intermediate strain rates, including tightening the DAC screws using a gearbox, pneumatic membranes,5–9 and the dynamic diamond anvil cell (dDAC).10–12 

The dDAC utilizes a standard DAC that is dynamically compressed by a piezoelectric actuator that expands with the application of a user-defined electrical waveform.10–12 The compression (or strain) rate in a dDAC can be modified by tailoring the amplitude and shape of the voltage vs time function. Recently, dDACs have been employed to study the compression rate dependence of phase transitions in metals such as bismuth, cerium, praseodymium,13,14 hydrogen,15 and KCl.16 In these studies, the compression rate is observed to behave as a “third dimension” within a pressure–temperature phase diagram. Different compression rates may result in a shift in the phase transition pressure. The dDAC has also been used for other purposes, such as determining the bulk modulus of ice,17 observing the formation of ice under dynamic pressure, and characterizing its kinetics under shock growth.18,19 It has also been used to study the nitrogen phase diagram.10 Pressure cycling in the dDAC has been used to determine the bulk modulus of ferropericlase across its spin transition.20–22 

While the dDAC has demonstrated significant potential for studying materials under high pressure, it is most commonly coupled with x-ray diffraction (XRD) in the axial geometry (i.e., with incident x-rays parallel to the axis of compression), which does not allow for the determination of material strength, deformation mechanisms, or texture evolution. In the quasi-static compression regime, these properties are commonly studied in DACs using XRD in the radial geometry, with incident x-rays that are perpendicular to the axis of compression. In a radial DAC (rDAC) experiment, no pressure transmitting medium is included in the sample chamber, and the sample is subjected to near-axial stress. Due to the experimental geometry of an rDAC experiment, the x-rays probe crystal lattice planes that have a range of orientations with respect to the compression direction, from parallel to perpendicular. The radial geometry thus enables the extraction of information that cannot be determined from axial x-ray diffraction experiments, such as the lattice strain and texture (crystallographic preferred orientation) evolution. Texture and lattice strain evolution can be modeled using plasticity codes such as the ElastoViscoPlastic self-consistent (EVPSC) method to determine deformation mechanisms at high pressures.23 Lattice strains measured in rDAC can be combined with elastic properties to estimate the flow strength of a material at high pressures.

Combining the ability to generate intermediate strain rates in the dDAC with the ability to measure strength and texture development in the rDAC allows one to systematically study the rate dependence of strength and texture evolution under intermediate-rate loading conditions. Because the strain rate at which materials are loaded has been reported to affect the grain size of daughter phases after a phase transition,16 it is plausible that the strain rate may also affect the strength (i.e., through Hall–Petch strengthening24) of a material undergoing a phase transition. Many materials exhibit rate-sensitive deformation, and the use of intermediate strain rates allows one to study the plasticity and development of deformation microstructures during large scale phenomena such as meteor impacts.25–27 Intermediate strain rates also allow materials to remain metastable at higher pressures than observed in typical quasi-static DAC experiments.13,16 The presence of over-pressurized metastable phases allows the strength and texture of materials to be studied at pressures outside of their thermodynamically stable regimes. A final advantage of dDACs is that they are small enough to be portable, allowing for easy integration at synchrotron and X-ray Free Electron Laser (XFEL) user facilities.11,12,28–30

This work reports on the development and demonstration of an experimental platform combining the rDAC and dDAC to make a radial dDAC (RdDAC), enabling time-resolved XRD and optical studies of materials under intermediate strain rate loading conditions. In contrast to earlier experimental setups,5 this setup enables the simultaneous collection of optical images during radial XRD. Optical imaging enables the quantification of macroscopic plastic strain, a property that is typically unknown in DAC experiments. The present setup also allows for easy switching between axial and radial measurements with the same experiment. The current capabilities of the setup are described based on example dDAC compression experiments on titanium, zirconium, and zircon (ZrSiO4). Using this new platform, we achieved time-resolved radial XRD at compression rates above 300 GPa/s, in part due to the availability of faster detectors. This compression rate corresponds to a hydrostatic strain rate of ∼10° s−1 in titanium, where the hydrostatic strain was calculated using σ = ΔV/V0, where σ is the strain, V0 is the volume at 1 bar, and ΔV is the change in the lattice volume measured using XRD. While combining rDAC with motorized gearboxes or pneumatic membranes has been performed in the past, using the dDAC platform has several advantages. First are the higher compression rates that can be achieved with 160 TPa/s being recently reported using a dDAC10 and time-resolved XRD being achieved, at 87 TPa/s.27 The second advantage is the ability to choose arbitrary pressure vs time waveforms, such as a sinusoidal oscillation.22,31 This could be used to pressure cycle a material to investigate effects such as work hardening.

The RdDAC setup was designed based on the DESY dDAC previously described by Jenei et al.11, Figure 1 shows (a) 3D CAD models of the RdDAC setup and (b) a photograph of the experiment at the general purpose setup of the Extreme Conditions Beamline (ECB, P02.2) at PETRA III. The setup consists of a dDAC, an optical microscope system, a 2D x-ray detector, and the standard five axis sample positioning system of the beamline.32 

FIG. 1.

(a) CAD rendering of the RdDAC setup and the microscope setup. (b) Photograph of the RdDAC setup inside the ECB hutch.

FIG. 1.

(a) CAD rendering of the RdDAC setup and the microscope setup. (b) Photograph of the RdDAC setup inside the ECB hutch.

Close modal

The dDAC consists of a hardened stainless-steel canister, a piezoelectric actuator, and a BX-90 style DAC33 that has been modified to accommodate XRD in the radial geometry. Holes were cut out of the canister to allow for x-rays to pass through the dDAC assembly in the radial direction to accommodate XRD at angles up to 2θ = 35°. An additional cone is machined on the dDAC cylinder end cap for an optical microscope to view the sample. Adapter rings of different inner diameters are used to center DACs with different diameters in the dDAC housing. The piezoelectric actuator is used to compress the DAC from the opposite end of the dDAC canister in a controlled fashion. In the setup described here, a 96 mm long piezoelectric actuator (PI Ceramic GmbH) was used. The piezoelectric actuator is controlled with an arbitrary function generator located in the control room adjacent to the experimental hutch. Arbitrary functions with amplitudes up to 10 V are uploaded to the function generator using the Agilent Benchlink software package. The function generator is connected to a 1000 voltage amplifier (Piezosystem Jena GmbH), which ultimately drives the piezoelectric actuator and compresses the DAC.

Due to the large size and weight of the RdDAC setup, the sample is aligned to the x-ray beam through the sample positioning system using the online optical microscope of beamline P02.2 s general purpose table. To accommodate radial diffraction, the sample stage is rotated by 90° from its standard setting. By simultaneously aligning a crosshair to the x-ray focus and the rotation center of the omega angle, the microscope can be aligned to focus on the position of the x-ray focus after the stage is rotated by 90°. The sample is then placed in the x-ray focus using the microscope, followed by a correction for the diamond index of refraction. The microscope camera is also used to collect images of the sample during compression, providing an estimate of the macroscopic plastic strain evolution in the sample.

High energy (25.6 and 42.7 keV) monochromatic XRD was collected at the ECB (P02.2) at the PETRA-III synchrotron at DESY. The x-ray beam size was tuned to 8.9 (h) × 5.3 (v) μm2 (25.6 keV) or 10.3 (h) × 5 (v) μm2 (42.7 keV) full-width at half of maximum using Compound Refractive Lenses (CRLs). The x-ray beam size was intentionally chosen to be larger than the standard focus of 8 (h) × 3 (v) μm2 to attempt to avoid the sample moving out of the beam during compression. The sample was also positioned such that the beam was at the edge of the sample along the axis of compression so that the sample moved into the beam as the piezo expanded. This defocusing and sample positioning resulted in the sample remaining in the beam for the vast majority of experiments. Depending on the desired compression rate, either a Perkin–Elmer (PE) XRD 1621 or 2.3 MPix GaAs LAMBDA area detector34 was used to collect 2D XRD images. Sample detector distance (SDD) as well as tilt and rotation of the Perkin–Elmer and LAMBDA detectors were calibrated with a Ce2O and Cr2O3 standard from NIST (SRN 676b) using the DIOPTAS software,35 respectively. The PE detector has a large, continuous collection area, allowing for excellent coverage of reciprocal space, but is limited in repetition rate to 15 Hz (frames/s), making it more ideal for slow compression experiments. At the time of these experiments, the GaAs LAMBDA detector had a maximum repetition rate of 2000 Hz, making it beneficial for collecting XRD during fast compression, but it had a more limited collection area of 10.1 × 8.5 cm2, with gaps between modules reducing the effective coverage to roughly 84% of this area. In the time since these experiments were performed, the ECB has upgraded its detectors to a maximum repetition rate of 24 kHz. The LAMBDA detector was triggered by an I/O signal from the beamline control computer, which also triggers the function generator. More details on the electronic setup can be found in Ref. 11. For the slower compressions, the Perkin–Elmer detector was manually started before triggering the waveform generator.

Figure 2(a) shows an example of a radial diffraction image of α-Ti collected using the LAMBDA detector with a 10 ms exposure time during a 300 GPa/s ramp. The compression function was a trapezoid profile with a 0.1 s compression (0–300 V on the piezoelectric actuator), a 0.1 s hold, and a 0.1 s decompression. The XRD pattern contains a series of diffraction rings of Ti. The radial coordinate of the rings (measured from the dark shadow of the beamstop just below the center of the image in Fig. 2) is related to the diffraction angle , and the coordinate around the azimuth of the ring is δ, where δ = 0° and 180° are the directions that are perpendicular to the direction of compression. Diffraction patterns collected during radial diffraction are typically integrated into 5° or 10° segments in δ to enable analysis of variations in the d-spacing and intensity around the diffraction rings.

FIG. 2.

(a) An example of a radial XRD image of α-Ti at 8 GPa collected with a 10 ms accumulation time at a 300 GPa/s compression rate using the LAMBDA detector. The red regions are a mask that was applied during integration to remove contributions from hot or dead pixels and regions between detector modules. (b) Shows the image in (a) integrated into 36 separate 10° sectors. The bottom half shows the integrated data, while the top half shows the full-profile refinement of the data performed using the Materials Analysis Using Diffraction (MAUD) software package. Red arrows indicate the axis of compression.

FIG. 2.

(a) An example of a radial XRD image of α-Ti at 8 GPa collected with a 10 ms accumulation time at a 300 GPa/s compression rate using the LAMBDA detector. The red regions are a mask that was applied during integration to remove contributions from hot or dead pixels and regions between detector modules. (b) Shows the image in (a) integrated into 36 separate 10° sectors. The bottom half shows the integrated data, while the top half shows the full-profile refinement of the data performed using the Materials Analysis Using Diffraction (MAUD) software package. Red arrows indicate the axis of compression.

Close modal

In a conventional axial diffraction dDAC setup, simultaneously collecting optical images and x-ray diffraction of the sample is not possible because the objective would block the x-rays. In radial dDAC experiments, the presence of the microscope objective that is used to align the sample may also be used to collect optical images of a sample during compression to assess the sample and gasket deformation on the macroscopic scale.

Imaging of the sample during an experiment was enabled by replacing the beamline’s standard Prosilica camera with a pco.edge 4.2 WAT CLHS camera on the online microscope. These data are saved in an HDF5 format (*.nxs) and can be further processed using software, such as in image J, after the completion of the data collection. The Pioneering in Cameras and Optoelectronics (PCOs) edge camera in these experiments is the master and simultaneously triggers XRD data collection. While the LAMBDA detectors have no readout time, the PE XRD 1621 has a readout time of 67 ms. The PCO edge 4.2 can operate at a maximum frequency of 100 Hz. Due to relatively low light levels, the exposure time used for the experiments described below was 100 ms. Time stamps of the images (XRD and optical) enable synchronization of the two data streams during post-compression processing.

For the slower compression rate experiments, several commercially available amorphous metallic glass gaskets were tested due to their high strength and lack of crystalline diffraction peaks. The amorphous metallic glass used in the work reported here was composed of Co0.70/Si + B0.23/Mn0.05/Fe + Mo0.02 and was procured from GoodFellow. Because the amorphous metallic glass gaskets result in relatively high intensity broad background peaks, amorphous boron powder and epoxy mixtures, pressed into a Kapton retaining ring, were used for some of the experiments.36 Diamonds with 200 µm or 300 µm diameter flat culets were employed in all experiments.

The sampling frequency in these experiments was limited not by the detector but rather by the flux of the diffracted beam. We note that a sample with a high atomic number and high symmetry should diffract sufficiently well to collect XRD data at 2000 Hz, the maximum repetition rate of the detector at the time that these experiments were performed. The experiments reported here used elemental Ti and Zr, as well as zircon, spanning compression rates from roughly 4–300 GPa/s. Table I presents the experimental parameters for each of the experiments studied in this work.

TABLE I.

Summary of the experimental parameters for the compressions studied.

CuletXRDPeakCompression/
diameteraccumulationvoltagedecompressionHoldPressureCompression
Sample(μm)Gasket materialtime (s)(V)time (s)time (s)(GPa)rate (GPa/s)Detector
Ti 300 Boron epoxy mix 0.01 400 0.1 0.15 0–25 300 LAMBDA 
Ti 300 Boron epoxy mix 0.20 500 4.5 3–21 3.7 PE 
Zr 200 Co0.70/Si + B0.23/Mn0.05/Fe + Mo0.02 0.10 600 2.4 2.9 1–40 16.5 PE 
Zircon 200 Boron epoxy mix 0.03 450 0.6 0.57 5–35 56.7 LAMBDA 
CuletXRDPeakCompression/
diameteraccumulationvoltagedecompressionHoldPressureCompression
Sample(μm)Gasket materialtime (s)(V)time (s)time (s)(GPa)rate (GPa/s)Detector
Ti 300 Boron epoxy mix 0.01 400 0.1 0.15 0–25 300 LAMBDA 
Ti 300 Boron epoxy mix 0.20 500 4.5 3–21 3.7 PE 
Zr 200 Co0.70/Si + B0.23/Mn0.05/Fe + Mo0.02 0.10 600 2.4 2.9 1–40 16.5 PE 
Zircon 200 Boron epoxy mix 0.03 450 0.6 0.57 5–35 56.7 LAMBDA 

The XRD area detector images collected [Fig. 2(a)] can be analyzed to determine lattice strains and unit cell volumes and to quantify texture development.

To quantify strain and texture evolution, the masked image in Fig. 2(a) was sliced and integrated in steps of 10° in azimuth (δ), resulting in 36 1-D diffraction patterns. The 36 integrated patterns for a Ti compression are shown as a contour plot in the lower half of Fig. 2(b), with regions of high intensity in red and those of low intensity in blue. The position of the Ti diffraction peaks can be seen to vary sinusoidally with δ, indicating a difference in lattice strain along the axis of compression (δ = 90, 270°) and perpendicular to the axis of compression (δ = 0, 180°).

The relationship between a measured lattice plane spacing, dm(hkl), and ψ [where cosψ=cosθcos(δ)] at azimuthal angle δ and diffraction angle θ can be fit using
dm(hkl)=dPhkl[1+(13cos2ψ)Q(hkl)].
(1)
Here, dp(hkl) is the lattice plane spacing predicted under hydrostatic compression, and Q(hkl) is given by
Qhkl=t3[α2GRhkl1+1αGV1],
(2)
where GR is the shear modulus at the Reuss limit, GV is the shear modulus at the Voigt limit, and α is a weighting factor.37,38 The experimental value of the shear modulus has empirically been found to be well-approximated by the average of GR and GV, implying a value of α = 1/2.37 When ψ = 54.7°, Eq. (1) reduces to dm(hkl)=dPhkl, meaning that observed diffraction at this azimuthal angle can be used to determine the d-spacing under hydrostatic compression. Further information about this model, including its derivation, can be found in Refs. 37–39. The differential stress, t, which provides a lower bound for yield strength, can be determined using
t=6GQ(hkl).
(3)
Quantitative analysis of the integrated radial diffraction images was performed using the Materials Analysis Using Diffraction (MAUD) Rietveld refinement software package [Fig. 2(b)].40 The refinement process in this procedure is outlined in Ref. 41. Rietveld refinement provides the unit cell parameters, the lattice strains, and the texture of the sample.

Titanium (Ti, Z = 22) is a relatively low-Z metal that is commonly used in the automotive and aerospace industries. At ambient conditions, Ti crystallizes in a hexagonal close packed (hcp, P63/mmc) structure (α-Ti) and, at high pressure, transforms to ω-Ti with an open hexagonal structure (P6/mmm). Under quasi-static compression, the α→ω phase transition begins at pressures between 2.9 and 11 GPa, depending on factors such as shear stress, the quantity and nature of impurities present, and grain size.42–45 Under shock loading, Ti has been found to remain in the α-Ti phase at pressures as high as 12 GPa,46 suggesting a compression rate dependence of the α → ω phase transformation. A previous study has shown that at an intermediate compression rate of 73 GPa/s, the α-Ti to ω-Ti transition is observed between the phase transition pressures of static and shock compression experiments.47 

Multiple mechanisms for the α-Ti to ω-Ti phase transition have been proposed, such as the TAO-148 and Silcock mechanisms.49 A previous study using radial XRD to study the texture of Zr at high pressure, which also has an α→ω structural phase transition similar to that in Ti, found that the α to ω phase transition of Zr proceeds by the Silcock mechanism.50 Performing a similar study of titanium is, therefore, useful to verify the phase transition mechanism in Ti.

As an example, we studied the effect of compression rate on lattice strains and the texture change in Ti with pressure. Figure 3(a) shows the relationship between pressure and Q(hkil) for α-Ti up to 13 GPa for two different compression rates: 3.7 GPa/s (hollow symbols) and 300 GPa/s (solid symbols). The pressure was determined using the lattice parameters obtained from refinement at the so called magic angle (ψ = 54.7°), where conditions are hydrostatic, and a previously published equation of state for Ti.51 

FIG. 3.

(a) The relationship between Q(hkil) and the pressure of α-Ti at 300 GPa/s (solid symbols) and 3.7 GPa/s (open symbols). Lines are to guide the eye. (b) The relationship between pressure and the differential stress, t, for two different compression rates. (c) Inverse pole figures show the texture of α-Ti along the axis of compression when compressed at 300 GPa/s at 1 and 8 GPa. Texture intensity is given in multiples of random distribution (mrd). Note that the 3.7 GPa/s experiment had a higher starting pressure than the 300 GPa/s.

FIG. 3.

(a) The relationship between Q(hkil) and the pressure of α-Ti at 300 GPa/s (solid symbols) and 3.7 GPa/s (open symbols). Lines are to guide the eye. (b) The relationship between pressure and the differential stress, t, for two different compression rates. (c) Inverse pole figures show the texture of α-Ti along the axis of compression when compressed at 300 GPa/s at 1 and 8 GPa. Texture intensity is given in multiples of random distribution (mrd). Note that the 3.7 GPa/s experiment had a higher starting pressure than the 300 GPa/s.

Close modal

During the lower compression rate (3.7 GPa/s) experiment, the values of Q(hkil) range between 3.2 × 10−3 and 4.2 × 10−3 at the starting pressure of 3.4 GPa, with Q(0002) having the highest value and Q101̄1 having the lowest value. For the higher 300 GPa/s compression rate experiment, Q(hkil) for all hkil starts below 0.001 at 0.4 GPa and increases to values between 0.0025 and 0.0030 at 2 GPa. Note that this experiment has a lower starting pressure than the lower compression rate experiment; hence, there are datapoints below 3.4 GPa. Above 2 GPa, the values of Q(hkl) start to diverge for the higher compression rate data due to the onset of plastic yielding. Similar to the low compression rate data, Q(0002) has the highest value, and Q101̄2 has the lowest value of Q(hkil). The difference in the lowest Q(hkil) values between the high and low compression rate experiments is within the uncertainty of the values of Q(hkl). Similar to the low compression rate experiment, Q(hkil) in the high compression rate experiment decreases in value during the phase transition. These high and low compression rate data demonstrate that Q(hkil) can be measured at different compression rates up to 300 GPa/s for Ti and potentially at higher compression rates for higher Z materials with high symmetry space groups. The Q(hkil) values continue to increase in value until ∼10 GPa, at which point they start to decrease, coinciding with the α-Ti to ω-Ti phase transition.

The differential stress (t) vs pressure for both the low and high compression rates is provided in Fig. 3(b). These values were determined using Eq. (3), using the values of G given in Ref. 52. At the lower compression rate, t is found to slowly increase with pressure between the starting pressure of 3.4 GPa and the start of the phase transition pressure and then decrease. For the high compression rate, t rapidly increases until 2 GPa and then increases at a slower rate, similarly to the low compression rate data, until the phase transition. This change in the rate of increase in t is likely due to the onset of plastic yielding in the material.

Figure 3(c) shows inverse pole figures of the sample compressed at 300 GPa/s at 1 and 8 GPa. At 1 GPa, the sample has nearly random orientations. When the pressure increases to 8 GPa, it develops a 0001 texture maximum in the compression direction. These data demonstrate both the lattice strains and texture of Ti can be determined at compression rates up to 300 GPa/s.

Similar to Ti, zirconium (Zr) is a group IV transition metal that has a hcp (α-Zr, P63/mmc) structure at ambient conditions. At 5–12 GPa (depending on factors such as hydrostaticity and the level of impurities), the Zr phase transforms to ω-Zr, which has an open hexagonal (P6/mmm) structure.53 Upon further compression to 30–35 GPa, the ω-Zr phase transforms into the body centered cubic β-Zr structure.54–56 Radial DAC and deformation-DIA experiments have been performed on Zr at quasi hydrostatic compression.50 This previous study observed 0001α112̄0ω correspondence in the textures of α-Zr and ω-Zr. Modeling indicated that 112̄0101̄0 prismatic slip combined with (1000)101̄0 basal slip leads to texture development in Zr.50 

Studying Zr using a dDAC was motivated by the literature suggesting that Zr exhibits strain rate dependent behavior where higher phase transition pressures are observed at dynamic strain rates compared to quasistatic strain rates. At quasistatic strain rates, nanosized grains of α-Zr held at pressures between 4.1 and 5.1 GPa transforms to ω-Zr over a period of ∼40 min.57 Under dynamic loading conditions (3 × 106ε̇ ≤ 108 s−1), the α to ω transition overshoots the phase boundary by ∼9 GPa.58 

Figure 4(a) shows an x-ray intensity vs time plot of Zr compressed from 0.5 to 40.2 GPa using the RdDAC setup with an average compression rate of 16.5 GPa/s. Figure 4(b) shows XRD patterns at various times during the experiment. Initially, the Zr sample is in the α-Zr phase at 0.5 GPa. During the ramp (0–2.4 s), the α-Zr phase transform into ω-Zr between 0.3 and 0.5 s (7.6–11.8 GPa). The end of this phase transition is shown by the XRD patterns labeled 0.4 and 0.5 s in Fig. 4(b), where the α-Zr (0002) peak at Q = 2.32 Å−1 disappears. For this dataset, the pressure is determined using the EOS of Zr published by Anzellini et al.59 (α and ω) and Pigott et al. (β).54 The sample remains in the ω-Zr phase until ∼1.9 s, when the (0001) and (0002) peaks, marked with black arrows, disappear. This can be seen more clearly in Fig. 4(b) at 1.8 and 2.0 s; however, the (0001) and (0002) peaks are very weak, likely due to them being very low intensity peaks. The disappearance of these peaks indicates that the β-Zr phase has formed. The β-Zr phase remains present through the “hold” section of the compression profile (∼40.2 GPa in pressure) before reverting back to ω-Zr at 6.4 s (∼35 GPa) [see the 5.9 s and 6.2 s XRD patterns in Fig. 4(b)]. The (0001) and (0002) peaks of ω-Zr are very weak on decompression and are not visible on some of the diffraction patterns after 6.2 s. This is likely due to a combination of preferred orientation and the sample moving with respect to the x-ray beam due to the contraction of the RdDAC housing.

FIG. 4.

(a) A contour plot of the time evolution of integrated XRD patterns of Zr during an RdDAC experiment. The black arrows indicate the positions of the ω-Zr (0001) and (0002) peaks. (b) Selected XRD patterns of Zr at various times during the Zr experiment.

FIG. 4.

(a) A contour plot of the time evolution of integrated XRD patterns of Zr during an RdDAC experiment. The black arrows indicate the positions of the ω-Zr (0001) and (0002) peaks. (b) Selected XRD patterns of Zr at various times during the Zr experiment.

Close modal

A selection of the optical images collected during the same experiment is shown in Fig. 5(a). These images show the gasket and sample at different times during the experiment. The width and height of the sample chamber [shown as L1 and L2 in Fig. 5(a)] were measured using the “Plot Profile” tool of ImageJ.60 The area of the sample chamber [the region in Fig. 5(a) circled in a dashed line labeled “A”] is approximated using the area of an ellipse; A=π4L1L2. Figure 5(b) shows the change in length, ΔL=LL0L0 for L1 and L2 over time, where L0 is the initial length and the change in area ΔA=AA0A0 of the sample chamber over time, where A0 is the initial area. Between 0 and 0.25 s, lightning in the sample’s appearance is observed. This change in appearance coincides with the α-Zr to ω-Zr phase transition. Measurement of the sample chamber shows the sample chamber decreases in size due to the unfilled space in the sample chamber being closed. Between 0.25 and 1.35 s, during compression, the sample chamber increases in size, with the sample chamber extruding to the left of the image, before decreasing slightly during the ω-Zr to β-Zr phase transition. During the holding period of the experiment, no macroscopic change in the sample was observed. Upon decompression, the sample chamber expands. After decompression (time = 7.75 s, P = 25 GPa), the DAC moved slightly due to the piezoelectric actuator contracting and no longer holding the DAC in place. The sample chamber increases in width more than in height, indicating that the deformation of this sample has a component of pure shear. This information can provide important constraints on the sample strain state for plasticity modeling and the fitting of lattice strain in the DAC, both of which typically assume an axial compression geometry.

FIG. 5.

(a) Optical images of Zr contained in an amorphous metal gasket were collected during the experiment. (b) The change in the width (L1), height (L2), and area (A) of the sample chamber with time.

FIG. 5.

(a) Optical images of Zr contained in an amorphous metal gasket were collected during the experiment. (b) The change in the width (L1), height (L2), and area (A) of the sample chamber with time.

Close modal

Zircon (ZrSiO4) is a nesosilicate that is found in the Earth’s crust and has been used to quantify conditions generated during meteor impacts.27 The presence of twins and reidite, a high-pressure polymorph of zircon, is interpreted to be characteristic of high-pressure shock deformation.61 However, the phase transition into reidite as well as the deformation mechanisms in zircon and reidite are still poorly understood. For example, the phase transition into reidite should theoretically begin at 5 GPa,62 but static experiments document the transition at around 20 GPa63–66 and shock experiments at 30–40 GPa.61,67 The higher onset of the zircon to reidite phase transition during shock experiments suggests the strain rate plays an important role in the phase transition. The bulk of deformation that occurs during an asteroid impact has been estimated to occur at strain rates of 102 to 103 s−1.25,26 These strain rates are intermediate to strain rates generated during static compression and shock compression but are achievable using the RdDAC. Thus, the RdDAC has great potential for understanding impact processes.

In this study, the effect of the compression rate on the phase transition, lattice strain, and texture development was explored. An experiment using the RdDAC with a compression rate of 56.7 GPa/s is compared to an experiment done with the quasi-static rDAC that was continuously compressed at a rate of 1.7 × 10−3 GPa/s using a gas membrane. The latter experiment was performed at the High-Pressure Collaborative Access Team (HP-CAT), Sector 16, at the Advanced Photon Source.

In contrast to previous experiments indicating that higher strain rate experiments exhibit a higher transition pressure, we do not observe a significant change in pressure for the onset of the phase transition [Fig. 6(a)]. Surprisingly, the RdDAC experiment has a higher reidite volume fraction compared to the rDAC experiment for the same pressures [Fig. 6(a)]. Example data and its refinement are provided in Fig. 6(b). At 25 GPa, the RdDAC sample has ∼6% reidite, whereas the rDAC sample does not have any reidite yet. At 35 GPa, the RdDAC sample was ∼50% reidite, with the rDAC sample having only ∼20% reidite. We speculate that there may be other factors contributing to this discrepancy, such as the higher differential stress that occurs in the RdDAC.

FIG. 6.

(a) Volume fraction of zircon vs reidite as a function of pressure. The RdDAC experiment is depicted with open symbols; the rDAC is depicted with closed symbols. (b) XRD data of zircon at 30 GPa during the zircon–reidite phase transition. The middle shows the integrated data, while the top third shows the full-profile refinement of the data. The bottom shows the refinement of a single XRD pattern.

FIG. 6.

(a) Volume fraction of zircon vs reidite as a function of pressure. The RdDAC experiment is depicted with open symbols; the rDAC is depicted with closed symbols. (b) XRD data of zircon at 30 GPa during the zircon–reidite phase transition. The middle shows the integrated data, while the top third shows the full-profile refinement of the data. The bottom shows the refinement of a single XRD pattern.

Close modal

The higher strain-rate dataset generally has higher lattice strains overall (Fig. 7), and the order of the lattice strains is different as well. Q(200) has the highest values for the rDAC experiment but the lowest values for the RdDAC experiment, indicating that different deformation mechanisms are active.

FIG. 7.

Relationship between Q(hkl) and pressure (GPa) for zircon with the rDAC at the Advanced Photon Source (closed symbols) vs the RdDAC at the ECB (open symbols). Corresponding colored lines are best fit to the data, with dotted lines for the RdDAC experiment and solid lines for the rDAC experiment.

FIG. 7.

Relationship between Q(hkl) and pressure (GPa) for zircon with the rDAC at the Advanced Photon Source (closed symbols) vs the RdDAC at the ECB (open symbols). Corresponding colored lines are best fit to the data, with dotted lines for the RdDAC experiment and solid lines for the rDAC experiment.

Close modal

Texture evolution also exhibits changes with the compression rate (Fig. 8). The rDAC experiment exhibits texture development characterized by a maximum at (110) between 10 and 25 GPa. At higher pressures, this shifts to a maximum of (100). In the RdDAC experiment, the maximum is instead at (001), and it exhibits a stronger texture than the rDAC experiment (1.8 vs 1.4 mrd). Differences in lattice strains and texture evolution indicate the zircon has rate sensitive deformation mechanisms over these strain rates.

FIG. 8.

Inverse pole figures of the compression direction showing the texture evolution of zircon with increasing pressure from 5 to 35 GPa.

FIG. 8.

Inverse pole figures of the compression direction showing the texture evolution of zircon with increasing pressure from 5 to 35 GPa.

Close modal

A setup at the Extreme Conditions Beamline (ECB, P02.2) that allows for radial XRD in a dDAC was developed. This setup allows for the simultaneous collection of radial XRD and optical images of the sample at compression rates up to 300 GPa/s. This setup enables the strength and texture development to be studied at intermediate strain rates.

This work was supported by the Laboratory Directed Research and Development program of Los Alamos National Laboratory (LANL) and the Dynamic Materials Properties Program under the LANL Office of Experimental Sciences. LANL is operated by Triad National Security, LLC, for the DOE-NNSA under Contract No. 89233218CNA000001. L.M. acknowledges support from the NSF (Grant Nos. EAR-1654687 and EAR-2054993) and the US Department of Energy National Nuclear Security Administration through the Chicago-DOE Alliance Center (Grant No. DE-NA0003975). We acknowledge DESY (Hamburg, Germany), a member of the Helmholtz Association HGF, for the provision of experimental facilities. Parts of this research were carried out at beamline P02.2 (Extreme Conditions Beamline) at PETRA III.

The authors have no conflicts to disclose.

L. Q. Huston: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (lead); Writing – review & editing (equal). L. Miyagi: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal). R. J. Husband: Data curation (equal); Investigation (equal); Writing – review & editing (equal). K. Glazyrin: Conceptualization (equal); Data curation (equal); Investigation (equal). C. Kiessner: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (lead); Writing – review & editing (equal). M. Wendt: Conceptualization (equal); Resources (equal). H. P. Liermann: Conceptualization (lead); Data curation (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (lead); Supervision (equal); Writing – review & editing (equal). B. T. Sturtevant: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (lead); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data presented in this paper are available upon reasonable request from the corresponding author.

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