  Systematic measurements of the resistivity, heat capacity, susceptibility and
Hall coefficient are presented for single crystal samples of the electron-doped
superconductor Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$. These data delineate an $x-T$
phase diagram in which the single magnetic/structural phase transition that is
observed for undoped BaFe$_2$As$_2$ at 134 K apparently splits into two
distinct phase transitions, both of which are rapidly suppressed with
increasing Co concentration. Superconductivity emerges for Co concentrations
above $x \sim 0.025$, and appears to coexist with the broken symmetry state for
an appreciable range of doping, up to $x \sim 0.06$. The optimal
superconducting transition temperature appears to coincide with the Co
concentration at which the magnetic/structural phase transitions are totally
suppressed, at least within the resolution provided by the finite step size
between crystals prepared with different doping levels. Superconductivity is
observed for a further range of Co concentrations, before being completely
suppressed for $x \sim 0.018$ and above. The form of this $x-T$ phase diagram
is suggestive of an association between superconductivity and a quantum
critical point arising from suppression of the magnetic and/or structural phase
transitions.
