  While beta Pic is known to host silicates in ring-like structures, whether
the properties of these silicate dust vary with stellocentric distance remains
an open question. We re-analyze the beta Pictoris debris disk spectrum from the
Spitzer Infrared Spectrograph (IRS) and a new IRTF/SpeX spectrum to investigate
trends in Fe/Mg ratio, shape, and crystallinity in grains as a function of
wavelength, a proxy for stellocentric distance. By analyzing a re-calibrated
and re-extracted spectrum, we identify a new 18 micron forsterite emission
feature and recover a 23 micron forsterite emission feature with a
substantially larger line-to-continuum ratio than previously reported. We find
that these prominent spectral features are primarily produced by small
submicron-sized grains, which are continuously generated and replenished from
planetesimal collisions in the disk and can elucidate their parent bodies'
composition. We discover three trends about these small grains: as
stellocentric distance increases, (1) small silicate grains become more
crystalline (less amorphous), (2) they become more irregular in shape, and (3)
for crystalline silicate grains, the Fe/Mg ratio decreases. Applying these
trends to beta Pic's planetary architecture, we find that the dust population
exterior to the orbits of beta Pic b and c differs substantially in
crystallinity and shape. We also find a tentative 3-5 micron dust excess due to
spatially unresolved hot dust emission close to the star. From our findings, we
infer that the surfaces of large planetesimals are more Fe-rich and
collisionally-processed closer to the star but more Fe-poor and primordial
farther from the star.
