Ultrafast visualization of crystallization and grain growth in shock-compressed SiO2

Nature Communications 6: Article number: 8191 doi: (2015); Published 4 September 2015; Updated 13 October 2015 An incorrect version of the Supplementary Information was inadvertently published with this Article and did not show axes labels for Supplementary Figs 2–4. The HTML has now been updated toinclude the correct version of the Supplementary Information.

GPa shots are shown here as panels (A) and (B)) and on CeO 2 standard (panel (C)).
Pixels associated with the spaces in between ASICs of the CSPADs have been removed for refinement. show consistency in sample intensity over several runs and across 12-hour shifts (e.g., 3 and 4). Examples of dark patterns are also shown to give ~2000 counts. Note that some ASICs show an apparent, artificial offset in intensity for the dark patterns (e.g., 45-57°).
Inset: Graph of incident X-ray photon energy as a function of runs listed for the X-ray only fused silica patterns. On average, 10 12 photons per pulse per shot were recorded for this experiment.

VISAR Analysis Details
Velocity Interferometer System for Any Reflector (VISAR) 3 data was collected simultaneously for each drive intensity and XFEL delay combination. The applied pressures listed in this paper are determined using the transit time through the sample package to calibrate a pressure-irradiance scaling law for the GDP ablator, and then using the scaling law exponent provided in Swift and Kraus 4 to determine the sample pressure for the lower energy shots. This method is preferred to using the transit times at the lower stress states to directly determine the shock pressure from an inferred wave velocity because of the complicated compressive response of fused silica below ~25 GPa.
The variation in strain for the material involved in this style of compression is significant, however, the volume fraction is less than 10%.
To determine the transit time through the entire sample, the drive laser was accurately co-timed with the streak cameras used for the VISAR diagnostic. Possibly due to break-up of the fused silica material upon breakout of the shock-wave at the free surface, it was impossible to determine the free surface velocity of the fused silica.
Instead, we measure a total transit time through the GDP ablator and the fused silica sample.
The Hyades Radiation Hydrodynamics code 5 was used to model the wave propagation through the GDP ablator and the fused silica sample. SESAME 7592 and 7386 equations of state were used for the GDP ablator and fused silica, respectively 6  considering the same drive conditions were used) and within the uncertainty of the VISAR derived stress value of 33.6 ± 5.0 GPa. No preferred orientation corrections in GSAS were required to provide a match of (110), (101), (111) and (210) peak intensities to previously published powder data found in the crystallographic information file (cif) 8 .
This cif provided the starting phase information for GSAS. From this comparison to Ross et al. 8 peak intensities, we find our diffraction data lack preferred orientation. Note that the right most ASICs (at the highest 2θ) for each time slice show significant damage (e.g., not recording any intensities at all, damaged pixels, shadowing). Therefore, only peak position is recorded for (211) due to difficulties extracting reliable relative intensities in these quadrants. It should be noted that for our refinements, no amorphous component was considered when fitting the background. Since the goal was to refine the crystalline peak position and intensity, we decided not to include the diffuse component in the refinement fitting and the background was fit with a Chebyshev polynomial in GSAS irrespective of the location of the shock front in the sample and percent shocked or unshocked material. We also note that the largest contribution to the reduced-χ 2 value is derived from the (110) peak straddling the edge of ASICs such that if we artificially fill in those intensities the reduced-χ 2 value decreases significantly.
To calibrate our sample-to-detector distances, detector tilts and determine instrumental broadening we used a NIST Standard Reference Material (SRM) 674b CeO 2 powder. A Rietveld refinement (Supplementary, Fig. 2) of CeO 2 powder shows much narrower peaks than for the stishovite grown during shock compression.

Diffraction Interpretation Details
We find the compressed fused silica peak is centered at ~2.10(5) Å -1 . If we assume 4-fold coordination for this glass (i.e., comparing to work from Sato and Funamori 10 for a low density amorphous (LDA) phase), the pressure estimate is 19.7 (+/-1.4) GPa. This contrasts the (110) peak position of stishovite and VISAR data (in combination with the pressure-irradiance scaling) suggesting a much lower applied pressure of 4.7(8) GPa. We speculate the glass component is transitioning from a 4-fold to 6-fold coordination and a strict comparison to a pressure derived from only a 4-fold glass structure would be unfair and manifest as an inconsistency. In other words, a density or pressure comparison would only be valid if we: a) knew the structure of our glass phase, and b) found that structure to be comparable to the findings of Sato and Funamori 10 . However, given the 2θ coverage of our data, we cannot assess the glass structure and therefore a pressure comparison is not appropriate. Furthermore, the stress conditions we explore in this experiment are within the "mixed phase region" of fused silica which makes interpretation of these data complex and in no way are we indicating these findings are definitive, rather a starting place for exploring new physics. In an effort to provide a metric for identification (or classification) of behaviors as a function of pressure we decide to use the crystalline diffraction/VISAR applied pressure value of 4.7 GPa for the rest of the paper.
The development of stishovite peaks at longitudinal stresses of 4.7 and 7.6 GPa is contradictory to the SiO 2 P-T phase diagram as determined from static compression experiments 11 . In our experiments, diffraction peaks matching coesite are never seen. To the best of our knowledge, coesite has not been produced or recovered from shock wave experiments 12 due to the quenching path necessary to form metastable coesite 13 . We explain this by the sluggish nature of the transition quartz to coestite and the over-driven pressure conditions on a reduced timescale allowing the higher symmetry, metastable stishovite phase to form first. In other words, if the transition from fused silica is kinetically inhibited from going to coesite then it may be thermodynamically consistent to transition to stishovite in the coesite stability region. A similar phenomenon has been observed in water-ice. Metastable ice VII forms from the liquid in the ice VI stability regime and metastable ice VII forms from the high density amorphous phase in the ice VI stability regime 14,15 . Phases of simpler symmetry can be seen in the stability regime of less symmetric phases and indicates a kinetic-control process influenced by a low interface free energy.

Grain Size Determination
We cross-check our estimate of grain size against the commonly used Scherrer Equation which does not contain a strain broadening term 16 : , where σ = grain size; K = dimensionless shape factor (commonly set to 0.9); λ = X-ray wavelength; β = line broadening at full width at half maximum (FWHM) minus instrumental broadening (0.03°); θ = Bragg angle. Since this equation is suited for a single Bragg peak, after calculating the grain size for each peak in a given trace, we average these values together to determine a single grain size per trace. The uncertainty extracted from each fit is also averaged to determine a total Scherrer uncertainty for the trace. As expected, we find remarkable agreement (grain size values are identical within uncertainties) compared to the Warren-Averbach 17 method using the prescription of Hawreliak et al. 18 . However, we note that the Warren-Averbach 17 method does not discriminate between inter-grain and intra-grain strain broadening.

Grain Growth Mode
In order to assume the simplest model possible, using the expression D = k(t-t 0 ) 1/n , we fix n to single value and let k and t 0 be free parameters. We tested a range of n values but found the curvature of the model trend did not match the data points well if we forced n ≤ 4. At n = 6 or 8 the t 0 values were reasonable, but find the best fit for all datasets was at n = 7 (±1). A table of our fitting parameters is as follows: For the 33.6 and 18.9 GPa data, the t 0 values are indistinguishable with the uncertainty, therefore we group them together to give an average nucleation time of 1.4 (4) ns. Note that for the 4.7 GPa trend, we have only 2 data points so the fitting is not well-constrained.