  We investigate the energetics of the single-period and double-period core
reconstructions of the 90-degree partial dislocation in the homopolar
semiconductors C, Si, and Ge. The double-period geometry is found to be lower
in energy in all three materials, and the energy difference between the two
geometries is shown to follow the same trends as the energy gap and the
stiffness. Both structures are fully reconstructed, consisting entirely of
fourfold coordinated atoms. They differ primarily in the detail of the local
strains introduced by the the two reconstructions in the core region. The
double-period structure is shown to introduce smaller average bond-length
deviations, at the expense of slightly larger average bond-angle bending
distortions, with respect to the single-period core. The balance between these
two strain components leads to the lower energy of the double-period
reconstruction.
