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 $1.48times 10^{31}$ 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 $1.18times 10^{31}$ 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.
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