  Biominerals such as seashells, corals skeletons, bone, and enamel are
optically anisotropic crystalline materials with unique nano- and micro-scale
organization that translates into exceptional macroscopic mechanical
properties, providing inspiration for engineering new and superior biomimetic
structures. Here we use particles of Seriatopora aculeata coral skeleton as a
model and demonstrate, for the first time, x-ray linear dichroic ptychography.
We map the aragonite (CaCO3) crystal c-axis orientations in coral skeleton with
35 nm spatial resolution. Linear dichroic phase imaging at the O K-edge energy
shows strong polarization-dependent contrast and reveals the presence of both
narrow (< 35{\deg}) and wide (> 35{\deg}) c-axis angular spread in
sub-micrometer coral particles. These x-ray ptychography results were
corroborated using 4D scanning transmission electron nano-diffraction on the
same particles. Evidence of co-oriented but disconnected corallite sub-domains
indicates jagged crystal boundaries consistent with formation by amorphous
nanoparticle attachment. Looking forward, we anticipate that x-ray linear
dichroic ptychography can be applied to study nano-crystallites, interfaces,
nucleation and mineral growth of optically anisotropic materials with sub-ten
nanometers spatial resolution in three dimensions.
