[abridged] Beryllium is a pure product of cosmic ray spallation. This implies a relatively simple evolution in time of the beryllium abundance and suggests its use as a time-like observable. We study the evolution of Be in the early Galaxy and its dependence on kinematic and orbital parameters. We investigate the formation of the halo and the thick disk of the Galaxy and the use of Be as a cosmochronometer. Beryllium abundances are determined from high resolution, high signal to noise UVES spectra with spectrum synthesis in the largest sample of halo and thick disk stars analyzed to date. We present our observational results in various diagrams. 1) In a log(Be/H) vs [Fe/H] diagram we find a marginal statistical detection of a real scatter, above what expected from measurement errors, with a larger scatter among halo stars. The detection of the scatter is further supported by the existence of pairs of stars with identical atmospheric parameters and different Be abundances. 2) In an log(Be/H) vs [alpha/Fe] diagram, the halo stars separate into two components; one is consistent with predictions of evolutionary models, while the other has too high alpha and Be abundances and is chemically indistinguishable from thick disk stars. This suggests that the halo is not a single uniform population where a clear age-metallicity relation can be defined. 3) In diagrams of Rmin vs [alpha/Fe] and log(Be/H) the thick disk stars show a possible decrease of [alpha/Fe] with Rmin, whereas no dependence of Be with Rmin is seen. This anticorrelation suggests that the star formation rate was lower in the outer regions of the thick disc, pointing towards an inside-out formation. The lack of correlation for Be indicates that it is insensitive to the local conditions of star formation.
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