<i>Ab initio</i>thermodynamics of oxide surfaces:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mn/><mml:mo>(</mml:mo><mml:mn>0001</mml:mn><mml:mo>)</mml:mo><mml:mn/></mml:math>

The oxygen coverage, structure, and thermodynamic stability of (0001) surfaces of ${\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ (hematite) as a function of temperature and oxygen pressure are investigated by ab initio density functional theory with the generalized gradient approximation. Spin-polarized total energy and force calculations are performed using the projector augmented wave method as implemented in the Vienna ab initio simulation package. At high chemical potentials of oxygen (i.e., high pressure or low temperature), the most stable (0001) surface of hematite is completely covered with oxygen atoms. At low chemical potentials, a structure with one surface iron atom per two-dimensional unit cell is found to be the most stable surface termination. Around 800 K at an oxygen partial pressure of 0.2 bar, this reactive surface iron atom can bind and release an oxygen atom, thus switching between formal oxidation states (III) and (V), i.e., between stoichiometric and ferrate-like states. The fully reduced (iron terminated) surface is found to be thermodynamically unstable and dissociates adsorbed oxygen molecules spontaneously.