map of a volume of the sample would be
generated prior to the BCDI measurement
so that an interesting region could be se-
lected and optimal sets of Bragg peaks
could be predicted.
Fortunately, a variety of mesoscale x-ray
methods could perform this prescreening.
For example, pushing the near-field high-energy diffraction microscopy technique (4,
5) to its 1-µm resolution limit should allow
mapping of a 3D set of BCDI-compatible,
micrometer-sized grains sufficiently to determine relative locations and orientations,
even though detailed shapes would not be
determined (but the subsequent BCDI studies would reveal these). Submicrometer
beam size Laue diffraction using a differential aperture method (6) can map a 3D
distributed set of grains or, for film-based
samples, “simple” scanning microbeam
Laue can be used. These mesoscale methods
also complement emerging BCDI capabilities in that they track emergent behaviors
over thousands of grains in larger-grained,
application-relevant materials (7–11).
The recent development of “dark-field
x-ray microscopy” (12) offers an opportunity to “zoom” from the mesoscale down
to imaging of defect motions and behaviors in larger-sized grains than are easily
accessible to BCDI. Although not directly
measuring angstrom-scale atomic displacements seen in BCDI, this technique offers
the possibility of correlating responses on
different length scales in the same sample.
With continued development of both
coherent diffraction techniques and mesoscale measurements, the opportunity will
arise to understand quantitatively not only
individual defects but also how they respond to complex environments with complex boundary conditions and interact with
other defects present. However, a number
of limitations and complications should
be noted. The precise location of critical
events such as slip or twinning presumably
depends on nanoscale heterogeneities, such
as impurity and preexisting defect distributions. Correspondingly, there should exist a
distribution of critical stresses for a particular type of event. Nanoscale faceting of grain
boundaries may produce similar variations.
Truly rare events, such as crack or void initiation, can be critical for material reliability
but also remain difficult to predict because
they correspond to the tails of statistical
distributions. Model statistical distributions
may still have to be put into continuum mesoscale models in an ad hoc manner, ensembles of model calculations may be required,
or both approaches may be needed. Variations in model outcomes should reflect the
variations in properties in actual material
specimens of comparable size.
Further, most mesoscale models assume
smooth behavior, but mechanical deformation experiments on small samples and
single crystals (13, 14) show evidence for
avalanche or earthquake-like distributions
of events. Such events may well occur in
macroscopic samples as well. Similarly,
in thermally induced coarsening models,
grain boundaries are assumed to move
smoothly in time according to a curvature-induced driving force and an associated
mobility. However, pinning and depinning
may lead to intermittent dynamics instead.
In both cases, there may be limits to predictive capabilities, much like the limits to the
predictability of earthquakes.
The approaching upgrades of synchrotron sources around the world will accelerate and improve the flexibility of virtually
all the measurements described here. The
use of “multibend achromat” magnetic lattices to steer the electron beam leads to a
smaller and more isotropic source, which
in turn leads to multiple orders of magnitude increases in brilliance and coherent
flux, as well as increased coherence lengths
at all wavelengths. Measurements will become faster and applicable to larger grains.
Coupled with improved detectors, improved
reconstruction algorithms, and the ready
availability of high-performance computing,
these new sources could well lead to routine
coherent diffraction measurements com-
bined with mesoscale measurements, both
using higher-energy x-rays that penetrate
macroscopic dimensions through diverse
materials. There is every reason to believe
that we will find out just how predictive
“predictive modeling” will become. j
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Induced deformation connected to twin grains
pulled to apply
formation Mesoscale measurement over 0.4 mm3 volume
> 1 degree
Emergent properties observed at the mesoscale
Bragg coherent diffractive imaging by Yau et al. reveals nanoscale defect motions during thermal annealing.
These defect motions underlie mesoscale emergent behaviors studied by, for example, high-energy x-ray
diffraction microscopy (4, 5), as illustrated here.