Total Scattering Analysis

Introduction

Total scattering or pair distribution function (PDF) analysis utilises not only Bragg scattering from a material but also the diffuse scattering in order to look beyond the average structure to examine the local, or short-range structure.

The information below aims to assist users in:
a) Planning a total scattering experiment;
b) Writing proposals for beamtime; and
c) Finding additional information on this technique.

Preparing for a Total Scattering Experiment

Although PDF analysis is widely applicable its validity is strongly influenced by the quality and nature of the data collected.
In determining an appropriate instrument for data collection one should consider:

  1. The maximum momentum transfer, Qmax, required by the study.
  2. Instruments which allow:
    • High Q-resolution.
    • Good counting statistics at high Q.
    • Low and stable instrument background.
  3. Corrections required, such as: absorption, Compton scattering, scattering length (neutron diffraction experiments), multiple scattering, etc

When conducting the experiment is important to ensure:

  • Repeatability
    • Ensure that background measurements are repeatable; for example, do NOT move the beam stop during the experiment period.
    • Measure background before and after data measurement for each sample, to verify stability.
  • Samples are mounted in borosilicate glass or kapton capillaries.
  • The best possible angular resolution is achieved (i.e. use the smallest possible capillary).
  • Sample/capillary stays in beam; wobble must be minimised.
  • The packing density is measured upon packing the capillary.
  • Data are separately acquired with:
    • no sample or container in the beam (to get the instrumental background);
    • the sample container (capillary) only; and
    • the sample + sample container.
  • Data are normalised to incident beam intensity, I0.

Other considerations include:

  • The use of variable/multi-temperature data. As non-ambient temperature measurements provide information on whether certain observed effects are related to thermal motion it may be prudent to obtain data at 2, or more, temperatures.
  • A compromise between Q-resolution and beam intensity is often required, thus:
    • If Qmax<15 Å-1 then the measurement has little value, and if the intensity at high energies is very low then counting time becomes prohibitive.
    • Variable count time is advisable to improve statistics at higher angle.

Writing a PDF Proposal

Proposals for beamtime at the Australian Synchrotron or for travel funding to an overseas synchrotron are ranked on their merit.  Insufficient experiment detail is often the cause for a poor ranking.  For overseas travel funding it must be shown, through a detailed proposal, that the experiment is infeasible at the Australian Synchrotron.

In addition to the proposal recommendations listed at Beamtime on this beamline applicants for total scattering experiments will need to demonstrate that they have modelled the structure of interest and experiment conditions to be used. Structures and data may be modelled using PDFgui, which is useful for ascertaining the effect of altering Qmax on the data quality.

When assessing the suitability of the Australian Synchrotron powder diffraction instrument the following must be considered and commented upon in the beamtime/funding proposal:

  1. The maximum momentum transfer, Qmax, that can be achieved at the Australian Synchrotron powder diffraction beamline is ca. 21 Å-1.
  2. Fluorescence from elements 37Rb to 43Tc and 81Tl to 91Pa in the energy range 15-21 keV prohibits examination of samples containing these elements, using the Mythen detector. E.g.
    fluorescence
  3. X-ray absorption by the sample. Calculate the linear absorption coefficient, μ (in cm-1), of the sample at the wavelength at which data will be acquired. Note, to minimise absorption correction μ*r should be <1, where r = radius of capillary (in cm) and μ must take into account the packing density (generally 40-60%).

References and Software for Further Assistance

R. G. Haverkamp & K. S. Wallwork, X-ray pair distribution function analysis of nanostructured materials using a Mythen detector, J. Synchrotron Rad. 16, 849-856 (2009).

T. Egami and S. J. L. Billinge, Underneath the Bragg Peaks: Structural Analysis of Complex Materials. Oxford: Pergamon (2003).

R. B. Neder and Th. Proffen, Diffuse Scattering and Defect Structure Simulations: A cook book using the program DISCUS, Oxford : Oxford University Press (2008).

Total scattering information and notes: http://totalscattering.lanl.gov

PDGgui (http://www.diffpy.org/index.shtml) C. L. Farrow, P. Juhás, J. W. Liu, D. Bryndin, E. S. Božin, J. Bloch, Th. Proffen and S. J. L. Billinge, PDFfit2 and PDFgui: computer programs for studying nanostructure in crystals, J. Phys.: Condens. Matter 19, 335219 (2007).

PDFgetX2 (http://www.pa.msu.edu/cmp/billinge-group/programs/PDFgetX2/ - this requires the IDL Virtual Machine) X. Qiu, J. W. Thompson, and S. J. L. Billinge, PDFgetX2: A GUI driven program to obtain the pair distribution function from X-ray powder diffraction data, J. Appl. Cryst. 37, 678-678 (2004).

PDFgetN (http://pdfgetn.sourceforge.net/) P. F. Peterson, M. Gutmann, Th. Proffen and S. J. L. Billinge, PDFgetN: A user-friendly program to extract the total scattering structure function and the pair distribution function from neutron powder diffraction data, J. Appl. Cryst. 33, 1192 (2000).

DISCUS (http://discus.sourceforge.net/)

Acknowledgements

Thank you to Thomas Proffen for his advice and assistance.