  Axions and axion-like pseudoscalar particles with dimension-5 couplings to
photons exhibit coherent Primakoff scattering with ordered crystals at keV
energy scales, making for a natural detection technique in searches for solar
axions. We find that there are large suppressive corrections, potentially
greater than a factor of $\mathcal{O}(10^3)$, to the coherent enhancement when
taking into account absorption of the final state photon. This effect has
already been accounted for in light-shining-through-wall experiments through
the language of Darwin classical diffraction, but is missing from the
literature in the context of solar axion searches that use a matrix element
approach. We extend the treatment of the event rate with a heuristic
description of absorption effects to bridge the gap between these two
languages. Furthermore, we explore the Borrmann effect of anomalous absorption
in lifting some of the event rate suppression by increasing the coherence
length of the conversion. We study this phenomenon in Ge, NaI, and CsI crystal
experiments and its impact on the the projected sensitivities of SuperCDMS,
LEGEND, and SABRE to the solar axion parameter space. Lastly, we comment on the
reach of multi-tonne scale crystal detectors and strategies to maximize the
discovery potential of experimental efforts in this vein.
