<i>Ab initio</i>structural energetics of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>β</mml:mi><mml:mtext>−</mml:mtext><mml:msub><mml:mi>Si</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>surfaces

Motivated by recent electron microscopy studies on the Si3N4/rare-earth oxide interfaces, the atomic and electronic structures of bare beta-Si3N4 surfaces are investigated from first principles. The equilibrium shape of a Si3N4 crystal is found to have a hexagonal cross section and a faceted dome-like base in agreement with experimental observations. The large atomic relaxations on the prismatic planes are driven by the tendency of Si to saturate its dangling bonds, which gives rise to resonant-bond configurations or planar sp^2-type bonding. We predict three bare surfaces with lower energies than the open-ring (10-10) surface observed at the interface, which indicate that non-stoichiometry and the presence of the rare-earth oxide play crucial roles in determining the termination of the Si3N4 matrix grains.