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We have investigated the metallicity distributions of mono-age stellarpopulations across the disc of $6 \lesssim R \lesssim 12$\,kpc and $|Z|\lesssim 2$\,kpc using samples selected from the main-sequence turn-off andsub-giant (MSTO-SG) stars targeted by the LAMOST Galactic Spectroscopicsurveys. Both the mean values and the profiles of the distributions exhibitsignificant variations with age and position. We confirm that the oldest($>11$\,Gyr) stars have nearly flat radial [Fe/H] gradients at all heightsabove the disc but show negative vertical [Fe/H] gradients. For stars youngerthan 11\,Gyr, the radial [Fe/H] gradients flatten with $|Z|$, while thevertical [Fe/H] gradients flatten with $R$. Stars of 4--6\,Gyr exhibit steepernegative radial [Fe/H] gradients than those of either younger or older ages.Values of [$\alpha$/Fe] of mono-age stellar populations also show significantradial and vertical gradients, with patterns varying with age. The [Fe/H]distribution profiles of old ($>8$\,Gyr) stars vary little with $R$, whilethose of younger stars exhibit strong radial variations, probably a consequenceof significant radial migration. The [$\alpha$/Fe] radial distribution profilesshow opposite patterns of variations with age compared to those of [Fe/H]. Wehave also explored the impacts of stellar mixing by epicycle motions (blurring)on the [Fe/H] and [$\alpha$/Fe] distributions, and found that blurring mainlychange the widths of the distribution profiles. Our results suggest that thedisc may have experienced a complex assemblage history, in which both the"inside-out" and "upside-down" formation processes may have played an importantrole.

Metallicity distributions of mono-age stellar populations of the Galactic disc from the LAMOST Galactic spectroscopic surveys