  We report a high resolution neutron diffraction investigation of the coupling
of structural and magnetic transitions in Ba1xKxFe2As2. The
tetragonal-orthorhombic and antiferromagnetic transitions are suppressed with
potassium-doping, falling to zero at x <~ 0.3. However, unlike Ba(Fe1xCox)2As2,
the two transitions are first-order and coincident over the entire phase
diagram, with a biquadratic coupling of the two order parameters. The phase
diagram is refined showing that the onset of superconductivity is at x = 0.133
with all three phases coexisting until x >~ 0.24.
