  Tests on $B-L$ symmetry breaking models are important probes to search for
new physics. One proposed model with $\Delta(B-L)=2$ involves the oscillations
of a neutron to an antineutron. In this paper a new limit on this process is
derived for the data acquired from all three operational phases of the Sudbury
Neutrino Observatory experiment. The search was concentrated in oscillations
occurring within the deuteron, and 23 events are observed against a background
expectation of 30.5 events. These translate to a lower limit on the nuclear
lifetime of $1.48\times 10^{31}$ years at 90% confidence level (CL) when no
restriction is placed on the signal likelihood space (unbounded).
Alternatively, a lower limit on the nuclear lifetime was found to be
$1.18\times 10^{31}$ years at 90% CL when the signal was forced into a positive
likelihood space (bounded). Values for the free oscillation time derived from
various models are also provided in this article. This is the first search for
neutron-antineutron oscillation with the deuteron as a target.
