Pair distribution function of nanopowders

J. Dolinár, S . Daniš

Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic

jan.dolinar@matfyz.cz

PDF is method developed almost 80 years ago, but until recently it was applied almost exclusively on amorphous materials and liquids. Nowadays, when high quality data from synchrotrons a neutron sources are available, it is becoming a popular method also for research of crystalline materials. Usually only high energy radiation sources are used, because wide Q-space interval measurement is needed in order to produce good resolution in the real space PDF. Despite this, some authors (see [1,2]) admit that it may be possible in some applications to obtain useful data using regular laboratory X-ray sources. In case of nanoparticles this would be especially helpful as it would allow very convenient way of studying some of their properties that are not accessible from reciprocal space experiments.

Our aim is to prove this possibility and to develop necessary tools and methods. Our equipment consists of HZG4 theta-2theta goniometer, molybdenum X-ray tube as a radiation source and simple scintillation detector. The process of converting measured intensities I(q) into real space pair distribution function g(r) is in our case rather simple and straightforward. The combination of low energy beam and nanopowder sample, allows to neglect many of the corrections that usually have to be carried out in ordinary PDF experiments. At the present moment our calculations account only for background correction, K_α2 separation and various scaling and normalization adjustments. Polarization correction is planned in very near future. In spite of this simplicity, very satisfactorily results were obtained.

To confirm the quality of calculated PDF various simulations were made and compared to data obtained from measurement. One of such comparisons carried out for TiO₂ nanoparticles in anatase phase is presented in Fig. 1. Note that although most of the features in simulated PDF are at same positions as in measured data, only the shape of the peaks is different. This disagreement is not due to errors in PDF calculation, but rather a flaw of nanoparticle model used in simulation. To support this statement we attach the very same comparison performed on LaB₆ crystalline powder in Fig 2. In this case, model of bulk material was used in simulation, as is appropriate for μm-sized crystallites.

Further goals are to develop better apparatus for theoretical simulations, fine-tune the calculation of PDF and also adapt our hardware to allow faster, easier and more precise data collection. After the method is ready and reliable, we plan to study nanoparticle specific defects, like surface deformations.

References

1. T. Egami, S.J.L. Billinge, Underneath the Bragg peaks: structural analysis of complex materials. New York: Elsevier. 2003.

2. Th. Proffen, S. J. L. Billinge, T. Egami and D. Louca, Z. Kristallogr., 218, (2003), 132-143.

Figure 1. Comparison of PDF calculated from measurement of TiO₂ nanoparticles with simulated PDF. Note the incorrect shape of peaks in simulated line caused by inaccurate model.

Figure 2. Comparison of PDF calculated from measurement of crystalline LaB₆ with simulated PDF.