  1% $^{119}$Sn-doped La$_{0.5}$Ca$_{0.5}$MnO$_3$ was studied by M\"ossbauer
spectroscopy, magnetic moment and resistivity measurements. The M\"ossbauer
spectra below the charge-ordering temperature are explained with ferromagnetic
(FM), antiferromagnetic (AF), and ferromagnetic spin cluster (CL) components.
The magnetic and thermal hystereses of the relative intensities of the
components observed in the M\"ossbauer spectra, and of the bulk properties such
as magnetic moment and electrical resistivity, in the temperature range 125-185
K, are characteristic of phase equilibrium in a first-order transition, i.e. of
phase separation in the system below the charge-ordering (CO) transition. The
cluster component displays a significant hyperfine field up to $\sim 125$ K.
Above this temperature it exhibits superparamagnetism, becoming the dominant
component above the charge-ordering transition. These results are discussed in
the framework of recent investigations of the manganite system with other
techniques which also show phase separation.
