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 disk , 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 ] \sim 0 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 .