  We conisder the brittle versus ductile behavior of aluminum in the framework
of the Peierls-model analysis of dislocation emission from a crack tip. To this
end, we perform first-principles quantum mechanical calculations for the
unstable stacking energy $\gamma_{us}$ of aluminum along the Shockley partial
slip route. Our calculations are based on density functional theory and the
local density approximation and include full atomic and volume relaxation. We
find that in aluminum $\gamma_{us} = 0.224$ J/m$^2$. Within the Peierls-model
analysis, this value would predict a brittle solid which poses an interesting
problem since aluminum is typically considered ductile. The resolution may be
given by one of three possibilites: (a) Aluminum is indeed brittle at zero
temperature, and becomes ductile at a finite temperature due to motion of
pre-existing dislocations which relax the stress concentration at the crack
tip. (b) Dislocation emission at the crack tip is itself a thermally activated
process. (c) Aluminum is actually ductile at all temperatures and the
theoretical model employed needs to be significantly improved in order to
resolve the apparent contradiction.
