  Single crystals of intermediate valent EuPd$_2$Si$_2$ were grown from an
Eu-rich melt by the Bridgman as well as the Czochralski technique. The chemical
and structural characterization of an extracted single crystalline
Czochralski-grown specimen yielded a slight variation of the Si-Pd ratio along
the growth direction and confirms the existence of a finite
Eu(Pd$_{1-m}$Si$_m$)$_2$ homogeneity range. The thorough physical
characterization carried out on the same crystal showed that this tiny
variation in the composition strongly affects the temperature T$_v$ at which
the valence transition occurs. These experiments demonstrate a strong coupling
between structural and physical properties in the prototypical
valence-fluctuating system EuPd$_2$Si$_2$ and explain the different reported
values of T$_v$.
