After the magma ocean state, secondary atmospheres build up via early volcanic degassing of planetary interiors. The terrestrial planets Venus, Earth, and Mars are believed to have originated from similar source material but reveal distinct present-day atmospheric compositions, pressures, and temperatures. To investigate how such diverse atmospheres emerge, we have built a three-step model coupling mantle and atmospheric composition. The model incorporates mantle melting, melt ascent, and volcanic degassing. Additionally, it includes atmospheric equilibrium chemistry, taking into account processes such as water condensation and hydrogen escape. Key parameters such as mantle oxygen fugacity, melt production rates, surface temperature, and volatile abundance in the mantle, were varied to understand their impact on atmospheric composition and pressure. For reduced mantles with redox states below IW +1, atmospheric pressures remain strongly limited to a maximum of 2 bar due to the outgassing of predominantly light species that are prone to atmospheric escape or condensation. Above IW +1, atmospheric pressure can reach several tens of bars depending on the outgassing efficiency. For high-pressure atmospheres, CO2 is the main atmospheric species observed in our models. For oxidized low-pressure atmospheres, depending on temperature, atmospheres can be either waterrich or also CO2-dominated. For reducing atmospheres, nitrogen species tend to dominate the atmospheres, with NH3 for colder atmospheres and N2 for warmer atmospheres. CH4 becomes dominant only in a narrow parameter space at redox states around IW +0.5 to IW +2 and is favored by lower atmospheric temperatures.
