  We use density-functional theory to study the structure of AlSb(001) and
GaSb(001) surfaces. Based on a variety of reconstruction models, we construct
surface stability diagrams for AlSb and GaSb under different growth conditions.
For AlSb(001), the predictions are in excellent agreement with experimentally
observed reconstructions. For GaSb(001), we show that previously proposed model
accounts for the experimentally observed reconstructions under Ga-rich growth
conditions, but fails to explain the experimental observations under Sb-rich
conditions. We propose a new model that has a substantially lower surface
energy than all (nx5)-like reconstructions proposed previously and that, in
addition, leads to a simulated STM image in better agreement with experiment
than existing models. However, this new model has higher surface energy than
some of (4x3)-like reconstructions, models with periodicity that has not been
observed. Hence we conclude that the experimentally observed (1x5) and (2x5)
structures on GaSb(001) are kinetically limited rather than at the ground
state.
