Maximum-entropy analysis of the cubic phases of KOH and KOD, NaOH and NaOD

Abstract

The maximum-entropy method (MEM) for structure determination is applied on the plastically crystalline phases of KOH and KOD characterized by delocalized H + or D + ions in a simple rock salt structure. The structure factors measured by neutron diffraction already give a consistent picture of the hydrogen distribution by conventional Fourier and modelling methods, which helps to understand the merit of the MEM. Owing to the negative sign of the scattering length of hydrogen, the MEM can, in a limited sense 'model free', separate off the hydrogen density distribution. It is found, however, that the MEM cannot be applied naively for these compounds and reasons are given why the uniform density as a priori information has to be given up in the present case. The a priori information procedure to be used is discussed. In addition, and perhaps unexpectedly, the deuterium density is also obtained.

Giant Haven Ratio for Proton Transport in Sodium Hydroxide

“…Calculating from this a chemical potential we obtain " H3!¹ S3#R¹ ln(N*/N). [14] H3 and S3 are the standard molar reaction enthalpy and entropy for the process under consideration (see Eq. [13]).…”

IFO: a Program for Image-Reconstruction-Type Calculation of Atomic Distribution Functions for Disordered Materials

“…Practice has shown that such tasks can be quite successfully tackled by employing image-reconstructiontype techniques such as the maximum-entropy (MEM) method (Linden, 1995). In fact, MEM, or its modifications, is nowadays widely employed in applied crystallography (Mtiller & Hansen, 1994;Schotte et al, 1995;Lin & Tsao, 1996;Schleger et al, 1997) and some MEM applications to structure data of disordered materials are also known (Wei, 1986, Mufioz et al, 1988Jal et al, 1991;Allen & Howe, 1992). However, no thoroughly tested, generally applicable and easy-to-use procedure for image-reconstruction-type processing of S(q) and RDF data has been developed until now.…”

Reorientational disorder of anions in the hydrogen sulfides of sodium and potassium (NaDS and KDS) investigated by neutron diffraction between T=4 K and T=470 K

“…This may be caused by a rotational-translational coupling between anions and cations similar to the observations for the cubic phases of NaOH and KOH. 2,5,43 TABLE V. Crystallographic parameters and coefficients of the cubic harmonics ͑HTM͒ as obtained by analysis of the extracted structure factors with cubic harmonics. The structure factors were determined by Rietveld refinement of the diffraction patterns of NaDS (Tϭ400 K) and KDS (T ϭ470 K), space group Fm3 m. …”

“…A similar effect was observed in NaOD/OH and KOD/OH. 2,5,43 A model with rotational-translational coupling between the cations and the dipoles was suggested by the authors. Many properties of the title compounds and NaOD/OH and KOD/OH are comparable: charge asymmetric anions, coordination sphere of the anions, and time scale (10 Ϫ12 s) of the reorientational motion of the anions.…”