BiFeO3 attracts considerable attention because of its multiferroic and ferroelectric properties. Nd-substitutions in antiferromagnetic BiFeO3 induce a significant ferromagnetic response. (Bi1-xNdx)FeO3 solid solutions feature both displacive and magnetic phase transitions. The nature of the structural transition depends on the Nd-content but in all cases is accompanied by an unusually large (nearly 2 %) volume change. Variable-temperature magnetic measurements confirmed a strong coupling between the displacive transition and magnetic response. The goal of the proposed experiments is to obtain systematic total neutron scattering data across the structural transition to understand the relations between the large volume change and local- and average-structure characteristics in BiFeO3-based magnetoelectrics.