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S stars are transition objects between M-type giants and carbon stars on theasymptotic giant branch (AGB). They are characterized by overabundances ofs-process elements. Roughly half of them are enhanced in technetium (Tc), ans-process element with no stable isotope, while the other half lack technetium.This dichotomy arises from the fact that Tc-rich S stars are intrinsicallyproducing s-process elements and have undergone third dredge-up (TDU) events,while Tc-poor S stars owe their s-process overabundances to a past pollution bya former AGB companion. Our aim is to analyse the abundances of S stars andgain insights into their evolutionary status and on the nucleosynthesis ofheavy s-process elements taking place in their interior. In particular, thelocation of extrinsic and intrinsic S stars in the HR diagram will be comparedwith the theoretical onset of the TDU on the thermally-pulsing AGB. A sample of19 S-type stars was analysed by combining HERMES high-resolution spectra,accurate Gaia Data Release 2 (GDR2) parallaxes, stellar-evolution models, andnewly-designed MARCS model atmospheres for S-type stars. Combining the derivedparameters with GDR2 parallaxes allows a joint analysis of the location of thestars in the Hertzsprung-Russell diagram and of their surface abundances. Forall 19 stars, Zr and Nb abundances are derived, complemented by abundances ofother s-process elements for the three Tc-rich S stars. These abundances agreewithin the uncertainties with nucleosynthesis predictions for stars ofcorresponding mass, metallicity and evolutionary stage. Most extrinsic S starslie close to the tip of the red giant branch (RGB), and a few are located alongthe early AGB. The location of intrinsic S stars in the HR diagram iscompatible with them being thermally-pulsing AGB stars.

S stars and s-process in the Gaia era I. Stellar parameters and chemical abundances in a sub-sample of S stars with new MARCS model atmospheres