Constrained refinement techniques applied to the structure of ammonium hydrogen sulphate above the ferroelectric transition

The structure of ammonium hydrogen sulphate (AHS) in its room-temperature, non-ferroelectric phase - as determined from X-ray and neutron data - has been published [Nelmes, R. J. (1971). Acta Cryst. B27, 272]. The asymmetric unit contains two sulphate groups, S1 and S2. The thermal parameters as published showed unusually high values for oxygen atoms in just one of these groups - namely S1. The closely similar results subsequently obtained for the isomorphous salt rubidium hydrogen sulphate [Ashmore, P. (1970). Private communication] suggested the appearance of these high values to be significant. The techniques of constrained least-squares refinement and significance testing have now been applied to the analysis of this and other features of the AHS structure. The advantages and remaining limitations of these techniques and the methods of applying them are explained and illustrated. The principal conclusion reached is that S1 is disordered equally between two sites. It is also shown that the inclusion of the HSO₄^- hydrogen atoms is significant; that the sulphate groups SO₃.O(H)^2- are distorted from a regular trigonal shape, principally by displacement of the O(H) atom - the oxygen to which the hydrogen is closer in the sulphate-linking O-H . . . O bonds; and that in thermal motion the sulphate groups can be treated as rigid bodies. The disorder of S1 is of considerable interest with regard to the transition to a ferroelectric phase at -3 °C.