We aim to quantify the chemical and kinematical properties of Galactic disks with a sample of 119,558 giant stars having abundances and 3D velocities taken or derived from the APOGEE DR17 and Gaia EDR3 catalogs. A Gaussian mixture model is employed to distinguish the high-{alpha} and low-{alpha} sequences along the metallicity by simultaneously using chemical and kinematical data. Four disk components are identified and quantified; they are named the h{alpha}mp, h{alpha}mr, l{alpha}mp, and l{alpha}mr disks and correspond to the high-{alpha} or low-{alpha}, and metal-poor or metal-rich properties. Combined with the spatial and stellar-age information, we confirm that they are well interpreted by the two-infall formation model. The first infall of turbulent gas quickly forms the hot and thick h{alpha}mp disk with consequent thinner h{alpha}mr and l{alpha}mr disks. Then the second gas accretion forms a thinner and outermost l{alpha}mp disk. We find that the inside-out and upside-down scenario does not only satisfy the overall Galactic disk formation of these two major episodes but is also presented in the formation sequence of the three inner disks. Importantly, we reveal the inverse age-[M/H] trend of the l{alpha}mr disk, which means its younger stars are more metal-poor, indicating that the rejuvenated gas from the second accretion gradually dominates later star formation. Meanwhile, the recently formed stars converge to [M/H]~-0.1dex, demonstrating a sufficient mixture of gas from two infalls.

Cone search capability for table J/ApJ/929/33/table2 (Chemical and kinematical data and membership probability of stars)