Schematic of transient x-ray diffraction from a single crystal sample, illustrating diffraction from different points at different compressions.
Schematic of shock generation by laser ablation. In the polycrystalline diffraction experiments, important processes included the transport and deposition (via conductivity) of the laser energy, the formation and expansion of the ablation plume (including its conductivity, dictating the position of the critical surface where the laser energy is absorbed), and the emission and transport of thermal radiation from the ablation plasma.
Schematic of experimental layout (not to scale). The slit in each x-ray streak camera was in the plane of the diagram.
Orientation maps of crystal planes in foils thick. Each circular figure is a stereographic projection, showing a gray scale map of the distribution of normals to one plane. The center of the circle is the normal to the sample; the circumference is the set of directions lying in the plane of the sample. Crystals in the foils are oriented so that the [00.1] direction is predominantly normal to the surface of the foil, with a distribution around 30° wide. The directions lie predominantly in the plane of the foil, with a similar out-of-plane distribution. Thus the foils are polycrystalline, but with significant texturing.
Reusable clamp-type target holder (“Ortiz holder”).
X-ray spectrum from laser-heated Ti foil.
Simulated powder pattern for polycrystalline Be with isotropic distribution of orientations. For the Be foils in the diffraction orientation used, the (0002) peak would be greatly enhanced compared with the others. On compression, peaks move to higher angles. If the compression is isotropic, the fractional change in lattice parameter is the same for all planes. If the pressure is isotropic (no strength), the fractional change varies as the equilibrium ratio for Be changes with pressure. For pure uniaxial compression (no plastic flow), the change in lattice parameter depends on the orientation of a given grain with respect to the loading direction, which can be found from the orientation of the diffraction line in the azimuthal direction (i.e., about the axis of the incident x-ray beam). For uniaxial compression with plastic flow, the difference in compression measured using different lines can be used to investigate the degree of elastic compression.
Simulated powder pattern for polycrystalline Be (range of angles captured by detectors). For the Be foils in the diffraction orientation used, the (0002) peak would be greatly enhanced compared with the others.
Example x-ray streak camera record from a static (unshocked) trial: TRIDENT shot 13664. The spots and star-shaped markings at the outside were caused by arcing from the pulsed high voltage in the streak tube. The circular image intensifier is clearly evident. There is evidence of a weak line, probably from the or planes.
Example x-ray film record from a static (unshocked) trial: TRIDENT shot 15004. For any plane, diffraction from grains of different orientations falls into a cone with apex on the sample and axis coaxial with the incident x-rays. The curved locus on the film is the intersection of the diffraction cone with the film. The locus appears mottled as it comprises diffraction from a finite set of grains.
Example x-ray film record from a shocked sample: TRIDENT shot 15002. The relative position of some higher-intensity mottles changes from unshocked to shocked material, which is presumably caused by the difference in distribution between unshocked and shocked texture, generally allowing different fractions of the grains to diffract over the region illuminated by x-rays; it is not caused by bulk motion of the sample as this is negligible over the duration of the x-ray pulse. Both shocked and unshocked signals include low-intensity tails in Bragg angle which remain overlapped at these compressions.
Example x-ray streak camera record from a shocked sample: TRIDENT shot 15002. Diffraction from unshocked material is evident until the shock reaches the rear surface of the sample, when released material is observed instead. Diffraction from shocked material is evident before and after the onset of release, as the x-rays penetrate deep into the sample (for which reason, the rise time of the shock cannot be determined here). Diffraction from shocked material decreases as release from the rear surface propagates back through the sample, releasing the pressure.
Irradiance and drive pressure history from an example of a dynamic loading experiment (TRIDENT shot 15002). The optimum laser pulse shape was chosen with the aid of radiation hydrodynamics simulation, designed to induce a constant ablation pressure during the pulse. The actual pulse shape on any shot deviated from the ideal shape, giving some variation in the pressure history applied to the sample. The applied pressure history propagates through the sample, the instantaneous variation in compression appearing as a distribution in instantaneous Bragg angles.
Wave structure of free surface velocity history. Left: schematic of idealized waves. The elastic precursor travels at the longitudinal sound speed and its arrival time depends on the bulk and shear moduli of the sample material. The amplitude of the elastic precursor depends on the flow stress in the sample, which is strongly affected by the microstructure. The plastic wave travels at the bulk sound speed, but does not appear as a single velocity jump at the surface because the faster elastic wave reverberates between the free surface and the approaching plastic wave, accelerating the surface in a series of steps. The peak free surface velocity depends on the driving pressure. Following the velocity peak, the surface decelerates (elastic waves on release are omitted for simplicity) until internal tension in the sample results in spallation. Right: example free surface velocity histories from a shocked sample: TRIDENT shots 12182 (mean irradiance of ) and 12 184 . The timing of the elastic and plastic waves is consistent with continuum dynamics predictions using the published equation of state and shear modulus of Be, and the amplitude of the plastic wave is consistent with the measured irradiance.
Dependence of (0002) Bragg angle in Be on shock pressure, for limiting assumptions about the deformation symmetry of the lattice.
Dependence of (0002) Bragg angle in Be on shock pressure, for limiting assumptions about the deformation symmetry of the lattice (detail at lower pressures). The heavy line on the isotropic curve shows the expected range of plastically relaxed states in shot 13002. The heavy line on the uniaxial curve shows the observed range of elastic precursor states in foils of this thickness. The error bar shows the range of Bragg angles measured by polycrystal diffraction on the same shot, with the pressure range taken from the irradiance history. The heavy dashed line shows the range of uniaxial compressions inferred from surface velocimetry on thinner foils and (0001) crystals, which may represent uniaxial compression at early times in each grain.
Lattice parameters expected and observed in an example polycrystalline diffraction experiment (TRIDENT shot 15002).
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