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.
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