Neutron powder diffraction experiments of (ND4)(2)SeCl6, (ND4)(2)PtCl6 and (ND4)(2)PtBr6 were performed to investigate the mechanism of the strong deuterium substitution effect on the phase transitions of the (NH4)(2)MX6 family, The isotope effect is strong in the first and second compounds and weak in the third, The data were collected in the d-spacing range 0.5-4.3 Angstrom by using a time-of-flight powder diffractometer VEGA installed at the pulsed cold neutron source in KEK. The intensity data of high-temperature phases (HTP) were measured at the temperatures corresponding to 1.3T(c) (T-c: transition temperature), and the low-temperature phases (LTP) at 4 K. The HTPs of the three compounds have an antifluorite type cubic structure (a approximate to 9.8 Angstrom and Z=4) as previously reported while the LTPs of (ND4)(2)PtCl6 and (ND4)(2)PtBr6 are tetragonal with a tentative space group P4(2)/n and unit cell dimensions similar to those of the HTPs. The LTP of (ND4)(2)SeCl6 may have an orthorhombic structure with a larger unit cell. The Rietveld refinement and Fourier analysis for the HTPs revealed that the D atoms in (ND4)(2)SeCl6 and (ND4)(2)PtCl6 are broadly distributed around the crystallographic threefold rotation axis with three weak overlapping maxima, while that of (ND4)(2)PtBr6 is more strongly localized at three positions away from the threefold rotation axis. These results indicate that the transitions are due to orientational ordering of the ND; ions and that the strong isotope effects may be quantum effects associated with the ND4+ motion in a shallow rotational potential. (C) 1997 American Institute of Physics.