  In this work, we study by means of simulations of hard spheres the
equilibrium between a spherical solid cluster and the fluid. In the NVT
ensemble we observe stable/metastable clusters of the solid phase in
equilibrium with the fluid, representing configurations that are global/local
minima of the Helmholtz free energy. Then, we run NpT simulations of the
equilibrated system at the average pressure of the NVT run and observe that the
clusters are critical because they grow/shrink with a probability of 1/2.
Therefore, a crystal cluster equilibrated in the NVT ensemble corresponds to a
Gibbs free energy maximum where the nucleus is in unstable equilibrium with the
surrounding fluid, in accordance with what has been recently shown for vapor
bubbles in equilibrium with the liquid. Then, within the Seeding framework, we
use Classical Nucleation Theory to obtain both the interfacial free energy
{\gamma} and the nucleation rate. The latter is in very good agreement with
independent estimates using techniques that do not rely on Classical Nucleation
Theory when the mislabeling criterion is used to identify the molecules of the
solid cluster. We therefore argue that the radius obtained from the mislabeling
criterion provides a good approximation for the radius of tension, Rs. We
obtain an estimate of the Tolman length by extrapolating the difference between
Re (the Gibbs dividing surface) and Rs to infinite radius. We show that such
definition of the Tolman length coincides with that obtained by fitting
{\gamma} versus 1/Rs to a straight line as recently applied to hard spheres
[Montero de Hijes et al., J. Chem. Phys. 151, 155401, 2019]
