  We present a combined high-resolution x-ray diffraction and x-ray resonant
magnetic scattering (XRMS) study of as-grown BaFe2As2. The structural/magnetic
transitions must be described as a two-step process. At T_S = 134.5 K we
observe the onset of a second-order structural transition from the
high-temperature paramagnetic tetragonal structure to a paramagnetic
orthorhombic phase, followed by a discontinuous step in the structural order
parameter that is coincident with a first-order antiferromagnetic (AFM)
transition at T_N = 133.75 K. These data, together with detailed
high-resolution x-ray studies of the structural transition in lightly doped
Ba(Fe{1-x}Co{x})2As2 and Ba(Fe{1-x}Rh{x})2As2 compounds, show that the
structural and AFM transitions do, in fact, occur at slightly different
temperatures in the parent BaFe2As2 compound, and evolve towards split
secondorder transitions as the doping concentration is increased. We estimate
the composition for the tricritical point for Co-doping and employ a mean-field
approach to show that our measurements can be explained by the inclusion of an
anharmonic term in the elastic free energy and magneto-elastic coupling in the
form of an emergent Ising-nematic degree of freedom.
