# Coupling a gas gun with an X-pinch x-ray source to perform x-ray diffraction under shock loading

Camille Chauvin, David Palma de Barros, Alice Delaunay, Thibaut de Rességuier

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Camille Chauvin, David Palma de Barros, Alice Delaunay, Thibaut de Rességuier. Coupling a gas gun with an X-pinch x-ray source to perform x-ray diffraction under shock loading. Review of Scientific Instruments, 2025, 96 (4), 10.1063/5.0245052. [https://doi.org/10.1063/5.0245052](https://doi.org/10.1063/5.0245052)

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# Coupling a gas gun with an X-Pinch X-ray source to perform X-ray diffraction under shock loading

C. Chauvin¹, D. Palma de Barros¹*, A. Delaunay¹, T. De Rességuier²

¹CEA, DAM, Gramat, F-46500 Gramat, France

²Institut P', CNRS, ENSMA. Université de Poitiers, 86961 Futuroscope, France

*corresponding author: david.palma-de-barros@cea.fr

## Abstract

X-ray diffraction is an appropriate technique to probe crystalline materials and better understand their response under shock loading, particularly when they experience phase transition. This technique was already used at various large-scale facilities. Here we present an alternative way to perform X-ray diffraction under shock loading at the laboratory scale by coupling an X-Pinch X-ray generator with a single stage gas gun. This X-ray source is capable of generating a single polychromatic X-ray flash shorter than 100 ns. Preliminary static diffraction tests gave promising results, then an experimental apparatus was set up to perform in-situ X-ray diffraction in a shock-loaded material. X-ray diffraction is performed in reflection, at the interface between the studied sample and an anvil window to ensure a homogeneous pressure state within the probed region. A specific target configuration was designed to synchronize the X-ray emission with the temporary shocked state. The synchronization is achieved by the use of a trigger chain which adjustable delay is chosen prior to the experiment based on the expected travel time of the shock wave throughout the target. The technique was successfully used to investigate the solid-solid phase transition of tin between β and γ phases. Results indicate a satisfying synchronization between the shock wave arrival and the X-ray emission. Diffractograms under shock loading show a disappearance of the static ambient figure (parent phase) and the development of new diffraction pattern (daughter phase).

## Introduction

The modelling of materials response under dynamic loading remains an issue of considerable interest both in materials science and various engineering applications. During the shock wave propagation, mechanical properties can be significantly modified over a very short time (nanosecond scale). These changes can be due to microstructure modifications such as phase transitions. The evaluation of material behaviour under these particular, highly dynamic conditions relies on numerical simulations involving physically-based models which are usually refined when compared to experimental results. [1] The limited time window of loading (from nanosecond to microsecond scale) has required the implementation of specific methods with very short time resolution: sound velocity measurements [2] [3], resistivity measurements [4], velocimetry (PDV, VISAR) [5] [6] [7] or temperature measurements. [6] These techniques enable to retrieve macroscopic properties of materials under shock loading. However, the simulations developed based on these measurements, coupled with static compression data, are not able to reproduce accurately the materials behaviour when a phase change occurs. In particular, the onset pressure for phase transitions in dynamic conditions is usually higher than expected from static data. This phenomenon was observed in various materials such as iron [8], bismuth [9], cadmium sulfide [10], titanium [11], zirconium [12], cerium [13] or tin [1]. Hence, transition kinetics must be implemented into simulations to match the experimental data [14] [15] [16] [17]. To improve such kinetic descriptions, which are still largely empirical, it is necessary to explore shock-induced transformations in-situ, at the atomic scale.

<footnote>This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0245052</footnote>
X-ray diffraction has successfully demonstrated its ability to probe both single crystals and polycrystalline materials in shock loading experiments. Depending on the microstructure of the sample to be studied, different types of X-ray emission can be used. A monochromatic radiation is more adapted to a polycrystalline analysis whereas a polychromatic beam is better suited for single crystals. These experiments require coupling short intense X-ray pulses with dynamic loading facilities. [18] [19] Such sources include synchrotron radiation, [20] [21] [22] plasma produced by the interaction of a high power laser pulse with a material (backlighter), [23] [24] and X-ray free electron lasers (XFEL). [25] [26] They all require access to large-scale facilities through beam time applications and program committees.

A major challenge for X-ray diffraction in shock experiments relies on synchronizing the X-ray emission with the shock wave arrival into the probed region, in particular in impact experiments (gas gun of powder gun), where this arrival time cannot be anticipated accurately due to experimental uncertainties.

In this study, we present an alternative technique to perform X-ray diffraction at the laboratory scale by coupling an X-Pinch X-ray generator developed at CEA Gramat with a single stage gas gun. This paper first describes the experimental facility and setup. The specific target design and the corresponding synchronization system is then presented. Finally, a typical experiment is reported applied to the study of the polymorphic β-γ phase transition in shock-loaded tin.

## Experimental facility

### Gas gun

Shock loading is driven by the *Pyrene* [27] single stage gas gun capable of accelerating projectiles of 32 mm-diameter up to 850 m/s using helium. The projectile is composed of a polymer sabot (PVC or PP) on which an impactor of a chosen material is glued. Acceleration of the projectile starts upon opening of a pressurized reservoir by a quick valve. The pressure needed to accelerate the projectile is calculated with respect to its mass and the desired velocity. In order to avoid braking upon compression of an air cushion, primary vacuum is applied inside the barrel ($10^{-2}$ mbar). The impact velocity is measured by short-circuit probes inside the barrel located just before the target. Impact tilt has been previously characterized to be inferior to 5 mrad (using up to 6 piezoelectric pins).

### X-Pinch generator

The major originality in this work is the development of a specific X-ray source referred to as X-pinch. This source is sufficient to provide a diffraction pattern with a satisfying contrast, and it combines several advantages: it is compact, transportable, easy to use and tunable in energy. Thus, it is well suited to test experiments prior to applying for beam time on large scale facilities.

The X-ray emission of the X-Pinch system is generated by the implosion of thin metallic wires (X-Pinch load) crossed into an “X” shape between two metallic electrodes connected to a capacitor (Figure 1). [28] The capacitor used here (1.4 µF) is charged to a 75 kV voltage. Its discharge will generate a current pulse of 300 kA directly through the load. This pulse will induce fast heating of the wires but also strong compression due to an intense magnetic field, resulting into a plasma creation. The “X” shape enables to localize the plasma at the crossing point whereas a single wire would generate the plasma randomly along its length. This plasma constitutes a first micrometric source generating a ten-nanosecond timescale X-ray emission of “soft” X-rays photons of energies spreading up to 10 . The plasma instabilities at the crossing point lead to the formation of a gap several nanoseconds later, causing a voltage increase between the materials constituting the wires. Electrons will be accelerated towards this gap and their interaction with the plasma will generate an additional X-ray emission, creating a secondary source characterized by an isotropic photon emission with energies higher than 10 keV, useful for X-ray diffraction. The whole X-Pinch enclosure is maintained under a vacuum lower than $9×10^{-5}$ mbar.
<figure><img src="image_3.png" /></figure>

This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0245052

<figure><img src="image_4.png" /><figcaption>Figure 1: X-Pinch generator. The top schematic presents the temporal formation and evolution of the generated Pinch and X-ray flash. The bottom picture shows the practical design and dimensions.</figcaption></figure>

The temporal and spectral characteristics of the beam strongly depend on the material constituting the wires. The temporal shape of the pulse has been characterized over a series of calibration experiments. Figure 2 presents the results of two flashes made from gold wires of 25 µm-diameter. From shot to shot, the intensity emission profile is not reproducible (Figure 2a). However, the flash duration is always less than 100 ns, typically about 80 ns. Spectral analysis shows a weak Bremsstrahlung continuous emission and intense lines, characteristic of the material constituting the wires. The examples shown in Figure 2b clearly show the gold emission lines (L-series between 9 and 13 keV) and illustrate the good reproducibility of the spectra. A first study of the source size by point projection radiography showed that two sources could contribute to the radiation above 10 keV: a first source of a diameter slightly beneath 1 mm and another one less intense (10% ratio with the first one) with a diameter near 2 mm vertically shifted by about 1 mm. Further studies to characterize this source upon various wire materials and size are in progress.
<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>Figure 2: Emission characteristics for two X-Pinch flashes (red and blue) obtained with 25 µm-diameter gold wires: a) temporal shape of the pulses emitted above 10 keV, and b) spectral analyses of these same pulses with the vertical dashed lines corresponding to known gold emission L-series.</figcaption></figure>

Experimental arrangement

Diffraction layout

The typical configuration is shown in Figure 3. The x-ray source being isotropic, it is possible to implement various diagnostics all around. Typically, in shock experiments, diffraction and beam intensity measurement are used simultaneously. Due to the presence of a vacuum bell, the emitted beam must cross a 250 µm-thick mylar foil before any measurement.

Two diffraction arms are implemented to analyse two samples in the same configuration at each shot: the dynamic arm and the static arm, to perform X-ray diffraction of a shocked sample and a reference sample, respectively, with one same X-ray pulse. In both cases, diffraction is set in reflection geometry. Spatial shaping of the beams is made through adjustable tungsten slits so that only the center of the sample is illuminated. The crossing point of the wires is first aligned with the center of the sample using a camera. The slit is then inserted in the optical path and adjusted. According to the incidence angle, the X-ray spot will spread horizontally on the sample. The slit width is determined to minimize spreading around the center of the sample without compromising the alignment. The slit height is not sensitive to incidence angle and vertical spreading remains constant. At a fixed slit width, spreading is reduced by moving the source away from the slit (alignment more difficult) and by bringing the slit closer to the sample (not too close to avoid damage of the slit upon impact). In the classic experimental configuration, the distances are set 14 and 9 cm between the source-slit and slit-sample respectively. Considering a mm-size source, an illuminated zone of 10 mm width and 4 mm height is inferred on the sample. Diffraction patterns are collected on Fujifilm BA-MS image plates and digitized with a Typhoon FLA 7000 scanner (General Electrics). The detector is set with its normal making the same angle on the sample surface as the incident beam. Its distance from the sample is the same as the source to sample distance. The plates are protected from minor impacts with a 250 µm-thick mylar foil. The whole X-Pinch chamber is shielded with lead except holes for the direct beam. The diffraction being made in reflection, there is no direct illumination of the image plate by the source.

The emitted intensity is collected with two PIN diodes through a 250 µm-thick Al filter to measure only energies above 10 keV. The measured signal is used to verify the synchronization but also to compare the intensity between shots particularly when analysing the diffraction patterns. Such Al filters are not inserted in front of the image plates, since the samples are not expected to diffract at low energy and since the detector sensitivity, maximum at about 18 keV, decreases quickly below. [29]
<figure><img src="image_7.png" /><figcaption>Figure 3: Schematic of the experimental configuration. The source isotropy enables to analyse simultaneously the impacted sample and a reference sample in the same diffraction configuration. The combination of velocimetry and PIN diodes is used to retrieve the effective synchronization after the experiment.</figcaption></figure>

Because of geometrical practical limitations, the beam incidence angle (i in Figure 3) is limited between 10 and 30°. In the case of single crystals, the incidence angle of the X-ray beam can be determined to get the maximum diffraction spots over the entire spectral range of the probe. For instance, a particular attention can be brought to make crystallographic planes diffract at material lines which are the most reproducible. On the other hand, polycrystals diffraction is only detectable by the most intense material lines so that only those must be considered. Incidence angle is then determined to get the maximum peaks within the detector area. In the experiments reported next, given the image plate dimensions and location, the 2θ coverage from both polycrystals and single crystals is between 12° and 54°.

A specific numerical tool was developed to simulate the diffraction pattern that would be obtained considering the crystal parameters, the source energy range and the geometrical configuration. Two versions allow to simulate both single crystals and polycrystalline samples. Thanks to this tool, the crystallographic information can be identified by comparing the records with theoretical predictions.

Before each dynamic loading experiment, a static diffraction pattern for each arm is recorded. The diffraction pattern of the static arm during the shot can be then compared to the pre-shot image (of the same sample) to identify a possible loss of diffraction spots due to fluctuations of the source intensity. If those patterns recorded from the reference sample before and during the shot are similar, the differences between the two diffraction patterns recorded in the dynamic arm from the shocked and ambient states can be unambiguously attributed to shock effects.

## Target design

To interpret the diffraction data, it is more relevant to try to probe the material under a homogeneous pressure state during the short duration of the X-ray flash. A promising way to achieve this goal is to investigate the shocked state of the sample of interest immediately after its impact on an anvil window transparent to X-rays mounted directly on a target holder in a configuration referred to as reverse impact experiment (Figure 4a). This way, the impactor/target interface can be kept at a constant state until the shock waves reflect from other interfaces or free surfaces and propagate back to the probed region. Piezoelectric pins passing through the target holder can be used to trigger the X-ray emission (Figure 4b). The pin length can be determined by comparing the internal machine delay generating the flash with the remaining flight distance before impact for an expected velocity.
However, this experiment cannot be performed easily in our facilities because of practical issues (e.g. vacuum). Moreover, if the studied sample is a single crystal, the fact that its orientation at the impact time will not be known (due to possible rotation of the projectile) will make data processing difficult.

<figure><img src="image_8.png" /><figcaption>Figure 4: Schematic of the reverse impact method. The studied sample constitutes the impactor so that it can be studied directly during the initial shocked state.</figcaption></figure>

Hence, an alternative configuration was chosen, where the sample is mounted between a target material (transfer plate) and an anvil window of known impedance (Figure 5a). Vacuum insulation is more easily achievable and crystal orientation is fixed. Although the probed state is still constant before reflected waves propagate back from distant surfaces, it is not directly the shocked state induced by the incident compression wave, but a secondary state governed by the impedance mismatch between the sample and the window material. It will be reached once the impact-driven shock wave has propagated through both the transfer plate and the sample thickness. In practice, trigger pins are inserted at a known depth within the transfer plate, so the transit time $\Delta t$ considered should be taken between their tips and the sample/window interface (Figure 5b). This transit time must be accurately anticipated since it conditions the trigger delay between the impact time and X-ray pulse. Note that this delay can be increased to probe later states during unloading and investigate the effects of pressure release in the material under study. Time-resolved PDV velocimetry is implemented (see further subsection) to detect shock breakout at the window free surface (which will validate the synchronization) and measure the free surface velocity (which will provide experimentally the pressure state in the sample based on impedance mismatch).

<figure><img src="image_9.png" /><figcaption>Figure 5: Chosen target configuration. The sample is directly mounted onto a transfer plate and studied in a secondary shocked state depending on the impedance mismatch with the anvil window.</figcaption></figure>
In our experiments, the transfer plate is a 5 mm-thick copper disk. This thickness allows to delay the shock wave arrival long enough to enable a triggering at different times of the shock event for various impact velocities. This plate also prevents the target from being curved by the vacuum applied in the barrel in the case of thin or soft materials. A 3 mm deep groove is machined onto the sample periphery to insert the trigger pins. The plate is fixed to the muzzle by nylon screws that will break upon impact. The whole system (impactor and target) is then caught in a catch tank after impact.

The anvil window must be chosen considering several major criteria. (1) Its material must not undergo any transformation during the shock. (2) Its shock impedance must be adapted to reach a certain pressure into the sample. (3) Its intrinsic X-ray absorption must be the smallest possible. (4) Its diffraction pattern must not overlap with that of the material under study, or this overlap should at least be limited. (5) Its thickness must maintain the shock state during the flash duration. As a result, this latest must be optimized to minimize X-ray absorption (thin) and maximise the time before release by reflected waves from its free surface (thick). The optical properties of the sample material under investigation must also be taken into account to determine the depth probed, which will be small for high absorption (high Z number). Care has to be taken to ensure that the whole probed volume is in a homogeneous state. Target and window dimensions must be designed to ensure that this pressure state will not be affected by additional perturbation from lateral release waves during the probing time. Their diameter have been set to 20 mm on the basis of both analytical estimations and 2D computations.

The X-ray emission sequence is initiated by a voltage peak provoked by the shock wave interacting with the piezoelectric pins (DYNASEN) placed into grooves behind the material of interest. Several pins may be used, regularly distributed around the target, to account for a possible tilt at impact. However, using numerous pins could prejudice the diffraction measurement by intercepting the X-rays. Next, two piezoelectric pins are inserted on a diameter. Because of impact time uncertainties from the firing device (response time of the quick valve) and from the flight time of the projectile, it is necessary to implement a triggering system as close as possible to the target.

## Trigger chain

As mentioned above, the time interval between the pins activation and the arrival of the shock wave at the sample-window interface is used to let the triggering system initiate the X-ray emission. The trigger signal then propagates during the shock wave transit. The entire chronology of the experiment is illustrated in Figure 6. The shock propagation time can be inferred for various impact velocities using the Rankine-Hugoniot equations or hydrocode simulations, assuming that the material parameters are known for all constituents. Phase transformations within the sample under investigation may affect these parameters and subsequent wave velocities, which will introduce some uncertainty in the transit times. The trigger propagation is also known by characterizing the internal delay of the machines used in the chain. For a good synchronization, the entire X-ray illumination must occur during the homogeneous state between the shock breakout at the sample-anvil interface and before the free surface release waves.
<figure><img src="image_10.png" /><figcaption>Figure 6: Chronology of the trigger chain based on the shock wave propagation analysis. Each major event of the wave propagation are identified with dashed lines.</figcaption></figure>

A specific trigger chain has been designed to meet the above requirements, its general scheme is shown in Figure 7. In order to keep a certain flexibility on the time of interest, the transfer plate thickness is oversized. This way, the shock travel time exceeds the internal delay of the components used in the beam generation chain so that a delay device can be implemented.

<figure><img src="image_11.png" /><figcaption>Figure 7: The different systems involved into trigger system scheme. The two initial pins are activated by the shock propagating in the transfer plate</figcaption></figure>

The chain is composed of several stages, each dedicated to treat and shape the signal before the X-ray emission. Each device and connection cables introduce a delay of the propagated signal that must be taken into account to configure the trigger chain prior to each shot. The use of two piezoelectric pins implies the implementation of a specific equipment that will calculate the median time of impact according to the two signals. Several output signals are recorded along the triggering chain to ensure its good operation during shock experiments. This chain is composed of 4 different devices:

* Low noise copier: Upon shock wave arrival, the pins deliver a high voltage pulse, up to 80 V. However, this signal is very noisy and might trigger the Median Delay Generator at the wrong time (trigger threshold at 0.3 V). To avoid this problem, a low noise pulse is generated by this device upon receiving an input exceeding 3V, preventing the next stage from being activated by noise.

* Median delay generator (Greenfield Technology): it calculates the median time between both pin signals and adds a time delay prescribed by the user (Figure 8).
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.
PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0245052

<figure><img src="image_12.png" /><figcaption>Figure 8: a) Ideal and b) deteriorated cases for the median delay generator. Pm represents the theoretical time of shock arrival at the center of the target, considered as the median time between the two external pin signals P1 and P2. The Sensor Range S.R. is used instead of Pm in case a pin fails (no Pm) or if Δt=P2-P1 is longer than expected.</figcaption></figure>

The output time is the median pin trigger time, corresponding to the shock wave arrival at the target center, delayed by a user delay plus an internal delay (Figure 8a). In a correct experiment, after the first pin signal is detected, the second must be detected in a certain time interval considering an impact tilt. The maximum impact tilt combined with the projectile velocity will determine the maximum possible delay. The user delay is set by subtracting all internal delays of the whole chain from the estimated transit time of the shock wave between the pins plane and the targeted event time. A deteriorated scenario must be considered (Figure 8b) in the case when one pin fails (pin default) or when the second pin signal arrives later than expected (pin default, incorrect configuration of the synchronization chain, unusual impact tilt). Then, in order to ensure the output signal generation, an additional feature can be adjusted by the user: the sensor range (S.R.). Usually this sensor range is set considering the maximum expected delay due to the impact tilt introduced previously. As a result, in this deteriorated case, the device will use the sensor range to calculate the median time instead of the pin interval. If the missing signal is the later of the two, this failure will be compensated assuming the worst possible tilt. On the contrary, if the earlier pin signal fails, the flash will suffer from non-negligible delay.

* Signal amplification (Stanford): the 5 V amplitude output signal from the median delay generator is too low to activate the X-ray generator, it must be amplified at least above 10 V.

* The X-ray generator also possesses an internal rise time between the trigger signal and the flash generation. It seems to depend on the nature of the load wires (different electric behaviour). For instance, this delay has been characterized for 25 µm-diameter gold wires to be 460 ns with a 10 ns jitter over almost 100 flashes.

Before beginning impact experiments, numerous tests were performed by using a pulse generator delivering voltage impulsion into the triggering chain to simulate pins activation. Several scenarios were tested to check the triggering system operation and its reproducibility. All records showed a good consistency with theory within the devices jitter. The global jitter of the whole chain was estimated to 20 ns.
Time-resolved velocimetry

As stated earlier, it is essential to accurately record the velocity evolution at a position close to the sample surface, both to check the synchronization and to determine the shock pressure in the probed material. To this end, PDV measurements [30] [31] are performed at the anvil free surface because of its opacity to the laser wavelength. This technique relies on a displacement interferometer on which one arm is used as reference and the other one targets the sample. The reflected light of each arm is then combined again and creates interferences while the target is in motion. The interferences are detected by a photodiode and acquired though an oscilloscope. The output signal forms a sinusoidal on which each oscillation corresponds to a motion of half the laser wavelength. By proceeding a windowed Fourier transform on the signal, it is then possible to retrieve its frequency at each time step and deduce the target velocity by multiplying the frequency by half the laser wavelength. For instance a velocity of 1000 m/s leads to an oscillating signal of 1.29 GHz for a 1550 nm laser. Pressure applied to the material can then be retrieved through classical shock equations by using the free surface approximation or impact velocity combined with impedance matching relations at the sample-anvil interface.

Application to the impact behaviour of tin

The setup described in the previous sections, coupling impact loading with in-situ X-ray
diffraction using an original X-ray source, has been applied to investigate shock-induced structural
modifications in single-crystal tin at the atomic scale. Due to its low fusion temperature, a low pressure
solid-solid phase transition, and a relatively well-documented thermodynamic behaviour, this metal is
a good candidate for preliminary studies prior to investigating materials with more complex phase
diagrams. Under quasi-static loading, tin undergoes several structural transformations with increasing
pressure. The ambient double body-centered tetragonal structure (β-tin) transforms into γ-tin with a
body-centered tetragonal structure between 9 and 10 GPa at ambient temperature. [32] [33] [34] [35]
[36]

Under shock loading, which implies non-negligible heating, the β-y transition pressure is expected to be lowered near 7.5 GPa. However, experiments carried out on tin under impact loading suggested a phase transition occurring between 8.5 and 9.5 GPa, [1] [6] [22] about 1 GPa higher than the 7.5 GPa expected. Several hypotheses exist about the governing mechanism of the transition and its kinetics. In this context, in-situ analysis of the crystal configuration during shock compression would be of major interest, particularly to identify the new phase appearance.

Boron Carbide (B₄C) seems to be the best candidate for anvil windows behind shock-loaded tin. Indeed, its shock impedance is very close to (slightly higher than) that of tin and it possesses a good X-ray transmission over the considered spectrum. However, its high sound speed implies fast wave propagation reducing the time of observation. Thanks to its high Hugoniot Elastic Limit between 14 and 19 GPa [37] [38] [39] [40] [41], B₄C remains elastic over the whole range of shock pressures applied in the experiments. Besides, it is opaque to the laser wavelength (1550 nm) used for PDV measurements, so that records provide the anvil free surface velocity. In the experiments, 750 µm-thick disks with a 20 mm-diameter of compressed boron carbide powder were used as anvil windows (ACAL BFI).

According to possible orientation relation proposed between the β and γ phases [42] and the
spectral range of emission, two β-tin single crystal orientations are well suited to observe the γ phase
easily, in the hypothesis of a single crystal conservation: (100) and (110). Samples of single crystal tin
of 20 mm-diameter and 1 mm-thickness (Goodfellow, Princeton, 99.999% purity) were used in the
experiments. Over the considered spectral range, tin is highly absorbent. For example, its penetration
depth dₚ at 30 keV is about 34 µm. Because of the low incidence angle i on the sample in our geometry,
typically 11°, and because both incident and diffracted beams must travel through the probed volume,
the effective penetration depth to be considered, about ½ dₚ sin(i), amounts to only a few µm beneath
the sample-anvil interface. Therefore, the pressure state within this probed volume can be considered
<figure><img src="image_13.png" /></figure>

This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0245052

homogeneous. Tin crystals were oriented with a Laue diffractometer. They were glued onto copper transfer plates and anvil windows were glued on the other side (Araldite AY103). The whole target was then mounted on the gun muzzle. The same configuration was used on the static arm of the experiment.

One-dimensional hydrocode simulations were performed to determine the time window of observation at the interface between tin and boron carbide. A satisfactory synchronization will be considered if the flash covers the entire duration over which the new phase is expected, around 100 ns. The flash duration was estimated to be typically near 80 ns. According to simulations, it must be emitted 60 ns before the anvil free surface velocity plateau. This can be checked by comparing the free surface velocity with the PIN diode records.

In the following example, a tungsten impactor was accelerated to a velocity of 720 m/s onto a target made of a copper transfer plate and a (100) tin single crystal backed with a boron carbide anvil window. A shock pressure of 15 GPa was reached in tin, leading to a 17.4 GPa pressure at the interface with B₄C. The particle velocity at this interface is about 590 m/s. Thus, during the X-ray pulse of about 100 ns, the probed volume beneath the interface moves about 60 µm in the impact direction. Given the incidence angle, this motion is expected to shift laterally the intersection point with the X-ray beam, which should gradually shift the positions of the diffraction spots on the image plate. However, simulations indicate that this shift will remain very small with respect to the detector resolution.

Results are presented in Figure 9. The experimental uncertainty on the velocity measurement has been estimated to ± 0.4 m/s. In Fig. 9c, a fair consistency is found between the measured and simulated velocity profiles, despite some discrepancies that may be attributed to the limitations of the constitutive laws (for both tin and boron carbide) and to the poor reflectivity of the anvil free surface. The comparison between the X-ray pulse (diode output) and these velocity profiles shows a good synchronization of the X-ray emission with the time window of the compressed state within the probed region as inferred from the simulation.

<figure><img src="image_14.png" /><figcaption>Figure 9. Impact loading of a (100) single crystal tin: diffraction patterns recorded before the shot with corresponding Miller indices (a) and during shock compression with debris impacts circled in red, the ambient spot in purple and the new one in green (b) and comparison between the free surface velocity record (black), the simulated profile in dotted lines and the X-ray pulse (red) showing good synchronization (c).</figcaption></figure>

The resulting ambient diffraction pattern matches that of a (100) tin single crystal (Figure 9a). Miller indices of the diffracting planes according to the simulation are indicated next to each diffraction spot. The diffraction pattern originating from the B₄C anvil window (rings, due to the polycrystalline nature) is also visible twice because of intense Lα and Lβ lines of gold.

The image recorded during the shocked state (dynamic arm) is shown in Figure 9b. A dark diffuse cloud is observed in the upper right part of the image. It results from a parasitic illumination of the screen, likely coming from diffused radiation generated by the interaction of the incident beam with some collimating device (slit, slit stand or supporting rod, see Fig. 3). The marked black spots
inside the red oval correspond to collisions of fragments ejected upon impact. Such collisions leave hollow prints in the image plate surface which can be identified after the shot and, in most cases, differentiated from diffraction spots. However, in case the distinction between an impact and a diffraction spot is difficult, the doubtful spot is not taken into account in the pattern analysis. The disappearance of the most ambient (100) pattern (which was clearly detected in the static arm) is observed while the B₄C diffraction rings are still present. The ambient (30-1) spot is still visible (purple ring) revealing that the ambient phase may be still present in the probed zone in reduced quantity. The diffuse elongated spot in the middle remains at the same location as the ambient (200). However, a new diffraction spot is also observed in the green circle. This one could be attributed to a (31-4) plane following the Katzke relation. An additional spot of the phase corresponding to the (110) plane also fits into the diffuse elongated spot which cannot be attributed to a specific phase. According to these results, a mixed phase region might be inferred.

Further investigations are needed to confirm if the new pattern corresponds to the newly formed γ phase. Indeed, more diffraction spots are required to assess unambiguously its presence.

## Conclusion

We have developed an original setup to couple a gas gun launcher with an X-Pinch X-ray generator to perform in-situ X-ray diffraction under shock loading. It includes the implementation of a modular trigger chain of major importance. It also requires a specific target design and complementary instrumentation and devices to shape and delay the X-ray emission at the right time. Through the selection of an adapted material regarding its optical and mechanical properties used as an anvil window, a homogeneous state could be probed in the material under investigation.

An X-ray pulse of duration about 80 ns and energies above 10 keV is generated by a source referred to as X-pinch, then collimated to the center of the sample. An appropriate diffraction angle, distances and image plate positioning can be dimensioned thanks to a simulation tool. To ensure the best diffraction conditions, the emission of the source is monitored and its time interval is compared to the velocity evolution of the target free surface recorded with a PDV interferometer. A static equivalent target is used at each shot to compare its reference diffraction pattern with that obtained under shock loading. Because of the low impact tilt, only two pins are necessary to trigger the X-ray emission. This manner they can be located outside the optical path of the X-ray beam.

The trigger chain involves specific devices to reduce the noise from the pin output. The calculated median time in the target is first determined and then delayed to perform the X-ray emission at the right time. The well characterised internal delay of each device permits to determine the correct delay to introduce into the chain to succeed the synchronization, over a wide range of impact velocities. A correct amplification then allows to activate the final emission.

First experiments permitted to successfully investigate the phase change of tin under dynamic loading. Static images showed that both tin single crystal and boron carbide polycrystal used as an anvil window can be identified by diffraction. The diffraction pattern under shock loading shows a clear modification of the diffraction pattern indicating a crystal evolution, i.e. the quasi-disappearance of the initial β phase and the emergence of a new spot likely related to the formation of the high-pressure γ phase. A mixed phase region is then inferred.

Complementary experiments are planned by using several crystallographic orientations or polycrystalline samples. In parallel, similar shock experiments are planned at a synchrotron facility in order to compare the results between both types of X-ray source.

## Acknowledgements

This work was supported by the Commissariat à l'énergie atomique et aux énergies alternatives (CEA). The authors thank the different CEA Gramat teams who were involved in the project and took part in its realization. In particular, O. Chaumeil, O. Lassalle, L. Renault, F. Sinatti, P. Violle for their support in plate impact experiments. The team would also like to thank F. Zucchini for useful
<figure><img src="image_15.png" /></figure>

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0245052

discussions and his help on the X-Pinch generator but also S. Bergey and L. Travichon for their work on
the synchronization system and on the experimental setup.

**Author declarations**

The authors have no conflicts to disclose.

**Data Availability Statement**

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

<footnote>This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.</footnote>
<figure><img src="image_16.png" /></figure>

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