  We present a statistical fragmentation study of doubly charged alkali (Li,
Na, K) and antimony clusters. The evaporation of one charged trimer is the most
dominant decay channel (asymmetric fission) at low excitation energies. For
small sodium clusters this was quite early found in molecular dynamical
calculations by Landman et al. For doubly charged lithium clusters, we predict
Li$_{9}^{+}$ to be the preferential dissociation channel. As already seen
experimentally a more symmetric fission is found for doubly charged antimony
clusters. This different behavior compared to the alkali metal clusters is in
our model essentially due to a larger fissility of antimony. This is checked by
repeating the calculations for Na$_{52}^{++}$ with a bulk fissility parameter
set artificially equal to the value of Sb.
