We used the spectroscopic and astrometric data provided from the GALactic Archaeology with HERMES (GALAH) Data Release (DR2) and Gaia DR2, respectively, for a large sample of stars to investigate the behaviour of the [ $\alpha$ /Fe] abundances via two procedures, that is, kinematically and spectroscopically. With the kinematical procedure, we investigated the distribution of the [ $\alpha$ /Fe] abundances into the high-/low-probability thin disc, and high-/low-probability thick-disc populations in terms of total space velocity, [Fe/H] abundance, and age. The high-probability thin-disc stars dominate in all sub-intervals of [ $\alpha$ /Fe], including the rich ones: [ $\alpha$ /Fe] $\,>\,0.3$ dex, where the high-probability thick-disc stars are expected to dominate. This result can be explained by the limiting apparent magnitude of the GALAH DR2 ( $V \lt 14$ mag) and intermediate galactic latitude of the star sample. Stars in the four populations share equivalent [ $\alpha$ /Fe] and [Fe/H] abundances, total space velocities, and ages. Hence, none of these parameters can be used alone for separation of a sample of stars into different populations. High-probability thin-disc stars with abundance $-1.3 \lt {\rm[Fe/H]}\leq -0.5$ dex and age $9 \lt \tau\leq13$ Gyr are assumed to have different birth places relative to the metal-rich and younger ones. With the spectroscopic procedure, we separated the sample stars into $\alpha$ -rich and $\alpha$ -poor categories by means of their ages as well as their [ $\alpha$ /Fe] and [Fe/H] abundances. Stars older than 8 Gyr are richer in [ $\alpha$ /Fe] than the younger ones. We could estimate the abundance [ $\alpha$ /Fe] = 0.14 dex as the boundary separating the $\alpha$ -rich and $\alpha$ -poor sub-samples in the [ $\alpha$ /Fe] $\,\times\,$ [Fe/H] plane.

Radial metallicity gradients measured today in the interstellar medium (ISM) and stellar components of disk galaxies are the result of chemo-dynamical evolution since the beginning of disk formation. This makes it difficult to infer the disk past without knowledge of the ISM metallicity gradient evolution with cosmic time. We show that abundance gradients are meaningful only if stellar age information is available. The observed gradient inversion with distance from the disk mid-plane seen in the Milky Way can be explained as the effect of inside-out disk formation and disk flaring of mono-age populations. A novel recent method is presented for constraining the evolution of the Galactic ISM metallicity with radius and time directly from the observations, while at the same time recovering the birth radii of any stellar sample with precise metallicity and age measurements.