  The spatial structure of stellar populations with different chemical
abundances in the Milky Way contains a wealth of information on Galactic
evolution over cosmic time. We use data on 14,699 red-clump stars from the
APOGEE survey, covering 4 kpc <~ R <~ 15 kpc, to determine the structure of
mono-abundance populations (MAPs)---stars in narrow bins in [a/Fe] and
[Fe/H]---accounting for the complex effects of the APOGEE selection function
and the spatially-variable dust obscuration. We determine that all MAPs with
enhanced [a/Fe] are centrally concentrated and are well-described as
exponentials with a scale length of 2.2+/-0.2 kpc over the whole radial range
of the disk. We discover that the surface-density profiles of low-[a/Fe] MAPs
are complex: they do not monotonically decrease outwards, but rather display a
peak radius ranging from ~5 kpc to ~13 kpc at low [Fe/H]. The extensive radial
coverage of the data allows us to measure radial trends in the thickness of
each MAP. While high-[a/Fe] MAPs have constant scale heights, low-[a/Fe] MAPs
flare. We confirm, now with high-precision abundances, previous results that
each MAP contains only a single vertical scale height and that low-[Fe/H],
low-[a/Fe] and high-[Fe/H], high-[a/Fe] MAPs have intermediate (h_Z~300 to 600
pc) scale heights that smoothly bridge the traditional thin- and thick-disk
divide. That the high-[a/Fe], thick disk components do not flare is strong
evidence against their thickness being caused by radial migration. The
correspondence between the radial structure and chemical-enrichment age of
stellar populations is clear confirmation of the inside-out growth of galactic
disks. The details of these relations will constrain the variety of physical
conditions under which stars form throughout the MW disk.
