  Experimental phonon imaging in diamond anvils cell is demonstrated to be an
adequate tool to extract the complete set of elastic constants of
single-crystalline silicon up to the ZB$\rightarrow \beta-$Sn transition (10
GPa). Contrary to what was commonly admitted, we demonstrate that the
development of the strain-energy density in terms of strains cannot be stopped,
for silicon, after the terms containing the third-order elastic constants.
Nonlinear elasticity, degree of anisotropy and pressure-induced mechanical
stability of the cubic silicon structure are thus revisited and investigated in
more detail.
