The ideal strength of silicon is predicted along various loading paths using density functional theory. Stress-strain curves are calculated under uniaxial tension, relaxed shear, and uniaxial deformation conditions. In order to check the stability of the deformation paths, the phonon spectra and the stiffness tensors are computed within density-functional perturbation theory. A second-order phase transition is found to occur before the elastic instability when applying a $\left\{111\right\}⟨\overline{1}\overline{1}2⟩$ relaxed shear. In all the other deformation conditions, the first predicted instabilities are located at the center of the Brillouin zone. Finally, the crystallographic nature of the instabilities is investigated by the calculation of the phonon eigendisplacements and by the decomposition of the stiffness tensors.

• Received 10 April 2006

DOI:https://doi.org/10.1103/PhysRevB.74.235203