ABRIDGED: METHODS: We have conducted a high-resolution spectroscopic study of 714 F and G dwarf and subgiant stars in the Solar neighbourhood. The star sample has been kinematically selected to trace the Galactic thin and thick disks to their extremes...... The determination of stellar parameters and elemental abundances is based on a standard 1-D LTE analysis using equivalent width measurements in high-resolution (R=40000-110000) and high signal-to-noise (S/N=150-300) spectra obtained with..... RESULTS: .... Our data show that there is an old and alpha-enhanced disk population, and a younger and less alpha-enhanced disk population. While they overlap greatly in metallicity between -0.7<[Fe/H]<+0.1, they show a bimodal distribution in [alpha/Fe]. This bimodality becomes even clearer if stars where stellar parameters and abundances show larger uncertainties (Teff<5400 K) are discarded, showing that it is important to constrain the data set to a narrow range in the stellar parameters if small differences between stellar populations are to be revealed. We furthermore find that the alpha-enhanced population has orbital parameters placing the stellar birthplaces in the inner Galactic disk while the low-alpha stars mainly come from the outer Galactic disk........... We furthermore have discovered that a standard 1-D, LTE analysis, utilising ionisation and excitation balance of Fe I and Fe II lines produces a flat lower main sequence. As the exact cause for this effect is unclear we chose to apply an empirical correction. Turn-off, and more evolved, stars, appears to be un-affected.
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