  Accretion disks with masses ~0.001-0.1 Msun form during the merger of neutron
star (NS)-NS and black hole-NS binaries. Initially, such hyper-accreting disks
cool efficiently by neutrino emission and their composition is driven
neutron-rich by pair captures under degenerate conditions. However, as the disk
viscously spreads and its temperature drops, cooling becomes inefficient and
the disk becomes advective. Analytic arguments and numerical simulations
suggest that once this occurs, powerful winds likely drive away most of the
disk's remaining mass. We calculate the thermal evolution and nuclear
composition of viscously spreading accretion disks formed from compact object
mergers using one-dimensional height-integrated simulations. We show that
freeze-out from weak equilibrium necessarily accompanies the disk's late-time
transition to an advective state. As a result, hyper-accreting disks
generically freeze out neutron-rich (with electron fraction Ye ~ 0.2-0.4), and
their late-time outflows robustly synthesize rare neutron-rich isotopes. Using
the measured abundances of these isotopes in our solar system, we constrain the
compact object merger rate in the Milky Way to be < 1e-5 (M_d,0/0.1 Msun)^(-1)
per year, where M_d,0 is the average initial mass of the accretion disk. Thus,
either the NS-NS merger rate is at the low end of current estimates or the
average disk mass produced during a typical merger is << 0.1 Msun. We also show
that if most short duration gamma-ray bursts (GRBs) are produced by compact
object mergers, their beaming fraction must exceed f_b ~ 0.13(M_d,0/0.1 Msun),
corresponding to a jet half-opening angle > 30(M_d,0/0.1 Msun)^(1/2) degrees.
This is consistent with other evidence that short duration GRB outflows are
less collimated than those produced in long duration GRBs.
