  Some anisotropy in both mechanical and thermodynamical properties of bismuth
is expected. A combination of density functional theory total energy
calculations and density functional perturbation theory in the local density
approximation is used to compute the elastic constants at 0 K using a finite
strain approach and the thermal expansion tensor in the quasiharmonic
approximation. The overall agreement with experiment is good. Furthermore, the
anisotropy in the thermal expansion is found to arise from the anisotropy in
both the directional compressibilities and the directional Gr\"uneisen
functions.
