High-Energy Coherent X-Ray Diffraction Microscopy of Polycrystal Grains: Steps Toward a Multiscale Approach

We present proof-of-concept imaging measurements of a polycrystalline material that integrate the elements of conventional high-energy x-ray diffraction microscopy with coherent diffraction-imaging techniques, and that can enable in situ strain-sensitive imaging of lattice structure in ensembles of deeply embedded crystals over five decades of length scale upon full realization. We demonstrate that the combination of these two characterization methods enables a more complete picture of the crystal-lattice strain than either method is capable of providing individually. Such complementary imaging capabilities are critical to addressing questions in a variety of research areas such as materials science and engineering, chemistry, and solid-state physics. Towards this eventual goal, the following key aspects are demonstrated: (1) high-energy Bragg coherent diffraction imaging (HE BCDI) of submicron-scale crystallites at 52 keV at current third-generation synchrotron light sources, (2) HE BCDI performed in conjunction with far-field high-energy diffraction microscopy (FF HEDM) on the grains of a polycrystalline sample in a smoothly integrated manner, and (3) the orientation information of an ensemble of grains obtained via FF HEDM used to perform complementary HE BCDI on multiple Bragg reflections of a single targeted grain. The imaged structures are seen to be $477\pm 50$ nm or smaller in size, with an estimated strain resolution of $2.5\times {10}^{-4}$. These steps lay the foundation for integration of HE BCDI, which typically provides a spatial resolution tens of nanometers, into a broad suite of well-established HEDM methods, extending HEDM beyond the few-micrometer resolution bound and into the nanoscale, and positioning the approach to take full advantage of the orders-of-magnitude improvement of x-ray coherence expected at fourth-generation light sources presently being built and commissioned worldwide.

Figure 1

(a) Simplified schematic of Beamline 1-ID-E at the Advanced Photon Source, showing the essential components in the laboratory frame of reference. The $X$ axis goes into the plane of the figure. Only the top sawtooth lens is used to provide focus. See Appendix pp1 for details on why this configuration is chosen. (b) Central slice of the partially coherent three-dimensional (3D) diffraction signal from the gold submicroparticle. Color scale denotes photon count. (c)–(e) Amplitude cross sections of the gold submicroparticle after phase retrieval. Color scale denotes the amplitude of the reconstructed complex-valued object in arbitrary units. See Appendix pp5 for the spatial resolution of this measurement. (f) Lattice strain profile on the surface of the 3D submicroparticle. The arrow indicates the positive $X$ direction in the laboratory frame. (g) Profile of the Gaussian coherence function along the direction of the arrow shown in (f). The half-width at half-maximum is an estimate of the $X$-transverse coherence length of the beam.

Figure 2

Schematic of the multiscale measurement technique with the HEDM and BCDI components. The FF HEDM measurement is made at a scattering distance of 1 m while the HE BCDI measurement is made at a scattering distance of 6 m. The detector images, respectively, denote the relatively coarse resolution of the Bragg peaks from the grains in the sample (FF HEDM), and the finer details of the fringe pattern in the vicinity of one such peak. We note that the beam dimensions shown here only correspond to the FF HEDM measurement. The beam size is actually set to $1.5\times 50\mu {\mathrm{m}}^2$ for all HE BCDI measurements.

Figure 3

Scatter plot of the reciprocal lattice points corresponding to the Bragg peaks from the illuminated grains, acquired during the FF HEDM measurement. Shown here is a subset of the observed Bragg reflections, up to the $⟨311⟩$ reflection for fcc crystals. The bold markers denote a Friedel pair of $⟨111⟩$ reflections from a single grain. Also shown are the enlarged central slices of the measured partially coherent diffraction signal in the vicinity of these reflections (reoriented to emphasize the centrosymmetry about the line denoted by the two arrows, corresponding to reciprocal lattice vector directions $\pm {\mathbf{Q}}_{111}$, respectively).

Figure 4

(a) Reconstructed isosurface image of the grain of interest from the polycrystalline film (isovalue 20% of the maximum amplitude of the reconstructed object), obtained from the HE BCDI data set corresponding to the $\left[111\right]$ reflection. The phase field as determined by phase retrieval, is superposed on the grain surface. The raw phase is smoothed twice with a Gaussian kernel of size $1\times 1\times 1$ pixels in order to reduce the effects of pixelation prior to differentiation. This minimizes the effect of kernel-induced spreading while preserving the salient features. We provide images of the raw, unprocessed phase in Fig. 10 of the appendix, in which the pixelation artifacts are clearly visible. We see that the spatially resolved phase in one image is correspondingly inverted in the other image. The black arrow depicts the direction of the incident x-ray beam in the Bragg condition. (b) The same grain imaged from the data set corresponding to the $\left[\overline{1}\overline{1}\overline{1}\right]$ reflection. (c),(d) The corresponding lattice strain-field components, computed after kernel smoothing the phase field. The red arrow denotes the reciprocal lattice vectors $\mathbf{Q}=\left[111\right]$ and $\mathbf{Q}=\left[\overline{1}\overline{1}\overline{1}\right]$, respectively. All isosurface axis dimensions are in nanometers. (e)–(g) Strain-profile cross section of the grain reconstruction shown in (a), through the center of the grain. These images represent three mutually perpendicular slices of size $60\times 60$ pixels in the numeric array (IJ, JK, KI). (h)–(j) Corresponding strain profile obtained from the reconstruction in (b).

Figure 5

Distributions of the strain component of the three BCDI reconstructions, taking into account only the internal voxels (far away from the grain boundaries) where strain is nominally zero. For all three reconstructions, the half-widths of the strain distributions are around $2.5\times {10}^{-4}$, which gives the estimated strain resolution of the nominally well-ordered lattices.

Figure 6

The four diffraction spots, taken in order, correspond to configurations 1, 2, 3 and 5 from Table 2 respectively.

Figure 7

(a) The amplitude $\left|\mathit{\rho }\right|$ of the polycrystal grain as determined from phase retrieval. (b) Variation of $\left|\mathit{\rho }\right|$ along the line in (a) (from the exterior to the interior of the grain), along with the error function fit to the rising edge. (c),(d) The corresponding plots for a cross section of the gold submicroparticle, with an estimated spatial resolution of 52 nm.

Figure 8

Spatially resolved strain component along the surface of the smaller of the two chosen grains.

Figure 9

Variation of the detector integrated intensity, as a function of scatterer position along the rocking direction. For each successive scan over the same angular interval, we see that the position of the Bragg reflection (indicated by the central, bright peak of the rocking curve) remains at the same angular position (approximately the 35th angular step). This indicates that there is no appreciable rotation of the isolated submicroparticle on its substrate for the duration of the measurement.

Figure 10

Isosurface of the reconstructed raw phase of the thin-film grain (from the $[111]$ reflection). The pixelation artifacts are highlighted.

Figure 11

(Top) Histograms of the internal phases of the Friedel-pair reconstructions. The phases are weighted with weights proportional to the reconstructed object amplitude at each pixel, and the units of the $Y$ axis are arbitrary. The two plots indicate that the phases recovered from phase retrieval are indeed negatives of each other. (Bottom left) The central strain profile cross section of the grain in Fig. 4 from the main manuscript (i.e., reconstructed from the $[111]$ reflection), with the color range rescaled to highlight the strain values of the internal voxels. (Bottom right) The corresponding rescaled cross-section image for Fig. 4 in the main paper (from the $[\overline{1}\overline{1}\overline{1}]$ reflection).