  A phase diagram of superconducting Sr(Fe$_{1-x}$Co$_x$)$_2$As$_2$ as a
function of doping (x) is determined by a series of thermodynamic and transport
measurements on single crystals. On comparison with a similar phase diagram for
Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ (Co-doped Ba122), we find that the increased
dimensionality of Co-doped Sr122 results in a single first-order-like
transition where the magnetic and structural transitions coincide, unlike the
case of Co-doped Ba122 that exhibits split quasicontinuous magnetic and
structural transitions. We relate this dimensionally-tuned splitting in the
magnetic and structural transitions to the relative size of superconducting
temperatures in these materials.
