  The merger of two white dwarfs (WDs) has for many years not been considered
as the favoured model for the progenitor system of type Ia supernovae (SNe Ia).
But recent years have seen a change of opinion as a number of studies, both
observational and theoretical, have concluded that they should contribute
significantly to the observed type Ia supernova rate. In this paper, we study
the ignition and propagation of detonation through post-merger remnants and we
follow the resulting nucleosynthesis up to the point where a homologous
expansion is reached. In our study we cover the entire range of WD masses and
compositions. For the emergence of a detonation we study three different
setups. The first two are guided by the merger remnants from our earlier
simulations (Dan et al. 2014}, while for the third one the ignitions were set
by placing hotspots with properties determined by spatially resolved
calculations taken from the literature. There are some caveats to our approach
which we investigate. We carefully compare the nucleosynthetic yields of
successful explosions with SN Ia observations. Only three of our models are
consistent with all the imposed constraints and potentially lead to a standard
type Ia event. The first one, a $0.45\,M_\odot\ {\rm helium\ (He)} + 0.9
\,M_\odot$ carbon-oxygen (CO) WD system produces a sub-luminous, SN 1991bg-like
event while the other two, a $0.45\,M_\odot\ {\rm He} + 1.1\,M_\odot$
oxygen-neon (ONe) WD system and a $1.05+1.05\,M_\odot$ system with two CO WDs,
are good candidates for common SNe Ia.
