Using a sample of 69,919 red giants from the SDSS-III/APOGEE Data Release 12, we measure the distribution of stars in the [$alpha$/Fe] vs. [Fe/H] plane and the metallicity distribution functions (MDF) across an unprecedented volume of the Milky Way d
isk, with radius $3<R<15$ kpc and height $|z|<2$ kpc. Stars in the inner disk ($R<5$ kpc) lie along a single track in [$alpha$/Fe] vs. [Fe/H], starting with $alpha$-enhanced, metal-poor stars and ending at [$alpha$/Fe]$sim0$ and [Fe/H]$sim+0.4$. At larger radii we find two distinct sequences in [$alpha$/Fe] vs. [Fe/H] space, with a roughly solar-$alpha$ sequence that spans a decade in metallicity and a high-$alpha$ sequence that merges with the low-$alpha$ sequence at super-solar [Fe/H]. The location of the high-$alpha$ sequence is nearly constant across the disk, however there are very few high-$alpha$ stars at $R>11$ kpc. The peak of the midplane MDF shifts to lower metallicity at larger $R$, reflecting the Galactic metallicity gradient. Most strikingly, the shape of the midplane MDF changes systematically with radius, with a negatively skewed distribution at $3<R<7$ kpc, to a roughly Gaussian distribution at the solar annulus, to a positively skewed shape in the outer Galaxy. For stars with $|z|>1$ kpc or [$alpha$/Fe]$>0.18$, the MDF shows little dependence on $R$. The positive skewness of the outer disk MDF may be a signature of radial migration; we show that blurring of stellar populations by orbital eccentricities is not enough to explain the reversal of MDF shape but a simple model of radial migration can do so.
We present Galactic mean metallicity maps derived from the first year of the SDSS-III APOGEE experiment. Mean abundances in different zones of Galactocentric radius (0 < R < 15 kpc) at a range of heights above the plane (0 < |z| < 3 kpc), are derived
from a sample of nearly 20,000 stars with unprecedented coverage, including stars in the Galactic mid-plane at large distances. We also split the sample into subsamples of stars with low and high-[{alpha}/M] abundance ratios. We assess possible biases in deriving the mean abundances, and find they are likely to be small except in the inner regions of the Galaxy. A negative radial gradient exists over much of the Galaxy; however, the gradient appears to flatten for R < 6 kpc, in particular near the Galactic mid-plane and for low-[{alpha}/M] stars. At R > 6 kpc, the gradient flattens as one moves off of the plane, and is flatter at all heights for high-[{alpha}/M] stars than for low-[{alpha}/M] stars. Alternatively, these gradients can be described as vertical gradients that flatten at larger Galactocentric radius; these vertical gradients are similar for both low and high-[{alpha}/M] populations. Stars with higher [{alpha}/M] appear to have a flatter radial gradient than stars with lower [{alpha}/M]. This could suggest that the metallicity gradient has grown steeper with time or, alternatively, that gradients are washed out over time by migration of stars.
