Unconventional superconductivity has recently been suggested in the new class of iron-based superconductors in which unusual gap symmetries have been observed together with competing and coexisting superconducting and spin density wave (SDW) ground states. In this proposal, we wish to request beamtime to investigate the exact nature of phase coexistence and related order parameter couplings in isoelectronic systems in which the Ba and substituting elements have significantly different ionic sizes. The proposed (Ba1-xAx)Fe2As2 system (A = K, Na, Li) fulfils this geometrical requirement.