In many cases the scientific value of neutron-scattering data can be increased considerably by using atomistic or molecular modelling methods as an aid to understanding the experimental data
We give examples of how modelling helps to choose between ambiguous analyses, provide starting models for analytical methods and give understanding of how the structure and dynamics of a material relate to its function.
Experimental data collected at major facilities such as ANSTO are raw material that is used to build scientific understanding. The bridge between the data and understanding may be simply a case of fitting the various pieces of information together, but modern materials are complex and, in the same way that the picture helps solve a jig-saw puzzle, modelling can help enormously in putting the pieces together correctly.
Therefore scientists and computers link the output of neutron-scattering experiments to real models that allow “where atoms are and how they move” to be visualised. Computing clusters with robust software offer the opportunity to not only treat the data, but also to calculate the atomistic model of the structure (or dynamics) and compare it with the experimental data.
For neutron scattering, the critical part is linking these atomistic-modelling packages with the calculation of the corresponding neutron-scattering signal.
Over the past couple of years we have been developing the expertise and resources that are needed to analyse experimental neutronscattering data by use of atomistic modelling.
Comparison of experimental data with results from modelling can now be a required part of the analysis. A significant part of neutron-scattering data collected at OPAL has been and continues to be analysed using our modelling facilities.
A complete list of modelling capability is given at the end of this report and some recent examples showing modelling of “where atoms are and how they move” are given below.
Modelling for neutron diffraction - “where atoms are”
For example, fast-ion conductors that are used in fuel cells require that atoms are in a regular grid, but with spaces, or vacancies that allow the atoms to move. This is analogous to the game where letters are moved around in a square grid to make words – which would be impossible if there were no space.
The problem in more complex systems is to find where the spaces are so that we can understand the conduction process. Clearly, there is a huge number of possibilities but which is right? Our measured data can give us some important clues in this, but it’s like the jig-saw without the picture – too hard to solve when it gets beyond a certain complexity.
Modelling helps here because the real answer is the arrangement with the lowest energy (mountains crumble to the sea). We can calculate the energy of all possible arrangements, but in a complex system there may be many arrangements with similar energy.
Think of these arrangements as the pictures and the best answer is obviously where the picture that makes sense with the pieces so that the jigsaw puzzle can be solved.
A good example of an essential role atomistic modelling can play in understanding structure and behaviour of materials is a study of Ba4Nb2O9 which we recently carried out using OPAL, ISIS (UK), FRM-II (Germany) facilities and the ANSTO computing cluster. The composition with such a deceptively simple chemical formula was first prepared in the early 1970s.
However, its crystal structure and hence the physical properties were never fully understood despite a substantial effort of several groups over the years. We initially used a variety of experimental techniques to study the material (X-ray and neutron powder and single crystal diffraction, thermal analysis, ionic conductivity measurements) gradually helped us realise that the material contains significant amount of hydrogen and is in fact a hydrate better described by a formula Ba6Nb3O13.5*nH2O.
While the basic blocks of the crystal structure (Nb2O9 dimers) were quickly revealed from the diffraction data the details of arrangement of extra oxygen atoms and protons were still difficult to determine, as the material proved to be both oxygen and proton conducting having highly disordered and mobile oxygen/proton sublattices.
Semi-empirical modelling of the crystal structure using force-fields did not produce any meaningful results as the structure apparently contains both covalent and ionic bonds that is a difficult task for the classical force-field approach. Finally, structure optimisation using DFT (densityfunctional theory) framework (Vienna Ab-Initio Simulation Package, VASP code at ANSTO) revealed that protons exist in the structure as hydroxyl OH groups (Fig. 1).
Furthermore, the following ab initio molecular dynamics study suggested the mechanism of proton conductivity when proton is transferred by hopping between pairs of cooperatively rotating tetrahedra [1].
Modelling for neutron spectroscopy “how atoms move”
We also use modelling to understand why a material performs well or badly in its desired application so that we can improve it. This usually involves understanding not only where the atoms are, but also how they move due to the effects of temperature. The way in which neutrons are scattered by atomic nuclei is extremely well characterised, which makes it straightforward to calculate the expected neutron spectrum for any dynamical model, providing a very convenient link between atomistic models and experimental neutron-scattering data.
Other articles in this report [2-5] show how this modelling (VASP) allows the observed spectral peaks to be assigned to particular atomic motions which then allow us to understand the origin of properties such as negative thermal expansion [2] and super-ionic conductivity [3]. Molecular dynamics of organic photovoltaic materials have an important effect on charge transport and have previously been studied by neutron scattering [4].
In these systems light excites one of the molecules as shown in Figure 2 which allows an electron to be separated from the molecules, passed along the column and then extracted at an electrode to provide electrical energy. One of the difficulties is that thermal motion causes themolecules (discs) to move around which hinders passing the electron up the column.
Neutron experiments and modelling have characterised the motions of the disks [4] and we are now working with the Technical University of Delft, The Netherlands, and the Institute Laue-Langevin, France, to understand how these motions affect the transfer of charge.
The disc-like molecules must have radial-branches, or tails attached to them which were always thought to play a purely structural role, causing the discs to stick together in columns. Modelling has recently shown not only the importance of disc-dynamics, but also that a significant part of the charge is actually passed via the tails [5].
Current modelling capability for neutron scattering analysis and physical property prediction.
The following is a fairly complete list of the modelling expertise that we now have available for neutron scattering analysis:
1. Verifying crystal structures again firstprinciples energy calculations.
2. Deriving and energetically reasonable starting models for structure refinement.
3. Choosing between different disordered structures.
4. Structure of glasses and amorphous systems.
5. Spin-density distributions.
6. Electron density distribution.
7. Lattice dynamics for temperature factors and inelastic scattering.
8. Molecular dynamics for temperature factors, thermal expansion and inelastic scattering.
9. Band structure and density of states.
10. Elastic, dielectric and piezoelectric constants.
11. Optical properties (UV spectra, polarisability, reflectivity and refractive index).
Acknowledgement
The work presented here has been done in close collaboration with colleagues from the University of Sydney, University of Aveiro (Portugal), Institut Laue Langevin (France) and the Technical University of Delft (The Netherlands)
Authors
Gordon J Kearley and Maxim Avdeev
ANSTO
References
- C. D Ling, M. Avdeev, R. Kutteh, V.V. Kharton, A.A. Yaremchenko, S. Fialkova, N. Sharma, R.B. Macquart, M. Hoelzel and M. Gutmann, Chemistry of Materials 21, 3853-3864 (2009).
- V. K. Peterson, G. J. Kearley, Y. Wu, C. J. Kepert, A. J. Ramirez-Cuesta and E. Kemner, Angew. Chem. Int. Ed. 49 (3), 585-588 (2010).
- S. A. Danilkin, M. Yethiraj and G. J. Kearley, J. Phys. Soc. Japan, 79 (Supplement A), 25-28. (2010).
- Mulder, F. M.; Stride, J.; Picken, S. J.; Kouwer, P. H. J.; de Haas, M. P.; Siebbeles, L. D. A.; Kearley, G.J., J Am. Chem. Soc., 2003; 125(13) 3860.