Total neutron diffraction: the correct way to determine the true structure of crystalline materials?

Abstract

Crystallography, using conventional Bragg diffraction, and the study of atomic correlation functions, using total diffraction, have historically been carried out separately. There exist two different scientific communities, which in the case of neutron diffraction normally use different instruments. However, modern time-of-flight neutron diffractometers allow data to be collected to high maximum momentum transfer, Qmax, and with good reciprocal-space resolution, d/d. The high Qmax yields correlation functions with good real-space resolution, whilst the good reciprocal-space resolution yields data well suited to conventional crystallographic analysis. We show how the Liquids and Amorphous Diffractometer, LAD, at the ISIS spallation neutron source at the Rutherford Appleton Laboratory has been used to obtain new information on a number of disordered crystalline molybdates, Li2MoO3, LiMoO2 and D2MoO3. The average crystal structures are determined using Rietveld refinement of the Bragg diffraction data, whilst the local structures are determined by modelling the correlation functions, T(r), obtained from total neutron diffraction data. Reconciling the information from the two techniques provides a deeper understanding of structures than is possible using either technique in isolation. Finally, we discuss how the next generation of instruments will allow the development of this technique with specific reference to the new General Materials Diffractometer, GEM, at ISIS.

Local structure and disorder in crystalline Pb9Al8O21

“…The correlation function approach to the analysis of total diffraction data was originally developed mostly for structural studies of non-crystalline materials [5,6]. However, recently correlation function methods are increasingly being applied to the study of the structure of disordered crystalline materials [7][8][9]. The correlation function provides a measurement of the instantaneous interatomic distances which occur in a sample, and the advantage of using the correlation function method is that it provides a direct measurement of these distances which is model-independent and does not depend on assumptions about the LRO or crystallographic symmetry.…”

“…For the lone-pair Pb 2+ ion, a low coordination number (in the range 2-5) involves a highly asymmetric coordination shell in which the bonds to its neighbours are directed throughout only part of the encompassing globe, with an identifiable void in the distribution of bonds [44]. For high coordination numbers (9,10) the coordination shell of Pb 2+ is symmetric in nature, with the bonds distributed much more evenly in direction, whilst for intermediate coordination numbers (6)(7)(8) either type of bond distribution may be found. As shown in Fig.…”

The structure of a bioactive calcia–silica sol–gel glass

“…Conventional powder diffraction experiments typically focus on the observed Bragg peaks (in Q-space), and the analogous studies of amorphous materials focus on the diffuse pair correlation function (in real-, r-, space). Here, a total diffraction strategy is adopted 26 in which Bragg analysis in Q-space and Fourier analysis of the r-space pair distribution, to provide both crystallographic and local order information, are combined. The experimentally determined interference functions, i(Q), for the unreacted and reacted samples are shown in Fig.…”

Aperiodicity, structure, and dynamics inNi(CN)2

“…1͑a͔͒. Neutron total-scattering methods have enabled realspace modeling of the local structure via the experimental pair distribution function, 7,17,18 and very good agreement in real space was obtained for a model in which the square-grid layers are stacked in a perpendicular direction at intervals of 3.20 Å. 7 The same model also accounted for the sharp diffraction features in reciprocal space but was unable to reproduce the diffuse scattering or to predict the correct reflection conditions ͓Fig.…”