  This is the second in a series of three papers in which we study a
two-dimensional lattice gas consisting of two types of particles subject to
Kawasaki dynamics at low temperature in a large finite box with an open
boundary. Each pair of particles occupying neighboring sites has a negative
binding energy provided their types are different, while each particle has a
positive activation energy that depends on its type. There is no binding energy
between particles of the same type. At the boundary of the box particles are
created and annihilated in a way that represents the presence of an infinite
gas reservoir. We start the dynamics from the empty box and are interested in
the transition time to the full box. This transition is triggered by a critical
droplet appearing somewhere in the box. In the first paper we identified the
parameter range for which the system is metastable, showed that the first
entrance distribution on the set of critical droplets is uniform, computed the
expected transition time up to and including a multiplicative factor of order
one, and proved that the nucleation time divided by its expectation is
exponentially distributed, all in the limit of low temperature. These results
were proved under three hypotheses, and involve three model-dependent
quantities: the energy, the shape and the number of critical droplets. In this
second paper we prove the first and the second hypothesis and identify the
energy of critical droplets. The paper deals with understanding the geometric
properties of subcritical, critical and supercritical droplets, which are
crucial in determining the metastable behavior of the system. The geometry
turns out to be considerably more complex than for Kawasaki dynamics with one
type of particle, for which an extensive literature exists. The main motivation
behind our work is to understand metastability of multi- type particle systems.
