The antiferromagnetic Cr(V) peroxychromates, M3Cr(O-2)(4), M = K, Rb, and Cs, become ferroelectric when mixed with NH4+, but the underlying mechanism is not understood. Our dielectric relaxation, Raman scattering, and high-frequency EPR measurements on the M3-x(NH4)(x)Cr(O-2)(4) family clarify this mechanism. At 295 K, (NH4)(3)Cr(O-2)(4) is tetragonal (I (4) over bar 2m), with the NH4+ ions occupying two distinctly different sites, N1 and N2. A ferroelectric transition at T-cl = 250 K is revealed by lambda-type anomalies in C-p and dielectric constant, and lowering of symmetry to Cmc2(1). Below T-cl, the N1 sites lose their tetrahedral symmetry and thus polarization develops. Raman detection of translational modes involving the NH4+ ions around 193 cm(-1) supports this model. EPR around T-cl revealed that the [Cr(O-2)(4)](3-) ions reorient by about 10 degrees. A minor peak at T-c2 approximate to 207 K is attributed to a short-range ordering that culminates in a long-range, structural order at T-c3 approximate to 137 K. At T-c3, the symmetry is lowered to PI with significant changes in the cell parameters. Rb+ and Cs+ substitutions that block the N1 and N2 sites selectively show that T-cl is related to the torsional motion of the N1 site, while T-c2 and T-c3 are governed by the motional slowing down of the N2 site. These data show that the multiferroic behavior of this family is governed by the rotational and translational dynamics of the NH4+ ions and is tunable by their controlled substitutions. Relevance to other classes of possible multiferroics is pointed out.