Short Intermediate Range Structure at High Pressure and Temperatures
John Parise
SUNY at Stony Brook
The analysis of Bragg scattering and the fitting of models to this scattering is the primary means of validating and determining structure models for condensed matter. The scattering process is well known, and over a century's success in determining small molecule and protein structures, and several Noble prizes, testimony to the power of crystallographic techniques. While comparison of observed and calculated single crystal intensities is the most reliable means of model validation, modern computation methods have greatly expanded the role of powder methods in the analysis materials with long range (> 2 nm) structure.
The atomic structure of nano-phase materials, by definition, can not be analyzed by reference to the sharp Bragg diffraction features alone – there are none. Instead, the short (1 - 5 Å) and intermediate (1 – 2 nm) range order give rise to broadened diffraction features and to an increase in the elastic diffuse scattering under and between Bragg peaks. For 1-D powder diffraction data the Fourier transform of the total elastic scattering (Bragg + diffuse) is the pair distribution function (PDF); the scattering power and number density weighted distribution of interatomic distances in the sample.
In order to be able to integrate over a particular range of distances, to determine coordination numbers for example, the Fourier transform must be carried out on the total elastic scattering, normalized, and taken to sufficiently high Q (=4πsinθ/λ) to minimize Fourier termination ripple. Further, care must be taken to eliminate inelastic scattering. While these requirements are straightforward for samples at ambient conditions, they represent challenges for high pressure data, chiefly because of contributions from the sample environment, pressure cells for example. For large volume high pressure devices the use of tight diffracted beam collimation and point counters, or radial collimation and linear position sensitive detectors are viable options. Uncollimated beams and area detectors with diamond anvil cells will remain the workhorse beamline setup however, and we have been working to make high pressure PDF measurements reliable. Several trial experiments on crystalline, nano, liquid and glassy materials at high pressure demonstrate the power of high energy X-ray scattering, at times combined neutron scattering with isotope substitution as a means to garner valuable extra information, in solving the short and intermediate range structure of "crystallographically challenged" materials at high pressures. Examples include the structural transformations of nano-FeS and glassy GeSe2 to 10 GPa. In some cases these experiments, carried out at 100 keV with a beam focused to 20 µm with Si saw tooth refractive lenses, are at the limit of what it is possible with an APS undulator.
