  Highly accurate numerical results of phonon-induced two-electron spin
relaxation in silicon double quantum dots are presented. The relaxation,
enabled by spin-orbit coupling and the nuclei of $^{29}$Si (natural or purified
abundance), are investigated for experimentally relevant parameters, the
interdot coupling, the magnetic field magnitude and orientation, and the
detuning. We calculate relaxation rates for zero and finite temperatures (100
mK), concluding that our findings for zero temperature remain qualitatively
valid also for 100 mK. We confirm the same anisotropic switch of the axis of
prolonged spin lifetime with varying detuning as recently predicted in GaAs.
Conditions for possibly hyperfine-dominated relaxation are much more stringent
in Si than in GaAs. For experimentally relevant regimes, the spin-orbit
coupling, although weak, is the dominant contribution, yielding anisotropic
relaxation rates of at least two order of magnitude lower than in GaAs.
