Peculiarities of simulation of diffraction patterns of nanostructured materials

S. Cherepanova, S. Tsybulya

Boreskov Institute of Catalysis, Lavrentieva 5, Novosibirsk, 630090 Russia

E-mail: svch@catalysis.nsk.su

Nanostructured materials are specific objects of structural analysis. Peculiarities of their diffraction patterns arise from presence of defects such as grain boundaries and planar defects (PDs), which are elements of nanostructure. High concentration of PDs gives rise to diffuse scattering both in vicinity of Bragg maxima (peak broadening or peak broadening with its shift) and/or in background region (appearance of diffuse peaks or halo). Software developed [1] makes it possible to calculate diffuse scattering in the terms of 1D disordered crystal model.

In the oxide systems PDs such as antiphase boundaries (APBs) shifting cation layers and keeping anion ones have different influence on diffraction lines arising from one plane system. We observed such diffraction effect on the diffraction patterns of α-Fe₂O₃ and some low temperature oxides of aluminium. For example, 100 diffraction line is broader than 300 one on the X-ray diffraction pattern of α-Fe₂O₃ received from hematite and 220 diffraction line is broader than 440 one on the X-ray diffraction patterns of γ-, η-, χ-Al₂O₃, received from boehmite, bayerite and gibbsite correspondingly. These diffraction phenomenon couldn’t be explained by size or strain effects. Simulation of diffraction patterns shows, that presence of APBs along (001) planes in corundum type structures doesn’t influence on diffraction lines for whichdivisible by 3. At the same time other diffraction lines become broader with increasing density of APBs. For spinel type structures, simulation of diffraction patterns shows that APBs along (110) planes don’t affect 440 diffraction line but 220 one becomes broader.

Another diffraction effect is splitting of diffraction lines on broadened and non-broadened components. Such effect can appear when PDs introduce additional anisotropy in crystal. For example, for cubic crystals, which have four equivalent directions, 111 peak consists of 8 components. Presence of PDs in one of these directions leads to broadening of six peak components whereas two components are kept without changes. Such splitting effect is given on the Fig.1, where diffraction pattern calculated for the model containing 20% PDs and experimental one for η-Al₂O₃ are shown in the range of 111 peak.

High concentration of PDs randomly distributed in particle can cause appearance of asymmetric hk diffuse peaks in the positions of hk0 reflections. Such peaks appear as a result of loss of periodicity in one direction. Turbostratic carbon, which structure is characterised by random shift of graphite layers, can be considered as structure with high concentration (100%) of PDs. Simulation of X-ray scattering for turbostratic structures shows that only 00l and asymmetric hk reflections presents on the XRD patterns [1].

Figure1. Splitting of 111 peak.

Another example is γ-Al₂O₃, which also characterised by high concentration of PDs, which are well-defined translations because of dislocation splitting. High concentration (20%) of PDs in the (100) plane for spinel type structures also leads to appearance of diffuse peaks in the hk positions whereas reduced hkl reflections are still present on the simulated diffraction pattern. In some cases appearance of hk diffuse peaks near diffraction lines can cause shift of gravity centre of these lines. In particular, this is observed on the γ-Al₂O₃ diffraction patterns where 311 peak is shifted to smaller angles due to appearance of 31 diffuse peak.

PDs non-randomly distributed (or correlated) can lead to appearance of diffuse peaks in the positions characterising hypothetical or really existing polytypes. We use models with correlated PDs for fcc (3C-polytype) metals containing thin (less than 2 nm) twins or coherent hcp (2H-polytype) microdomains. In the first case diffuse peaks appear in the positions of 6H-polytype ABCACB. In the second case additional diffuse peaks appear in the positions of 2H-polytype. We observed the second effect on the diffraction pattern of metallic Co used as catalyst in the reaction of CO disproportionation [1].

To sum up: most of nanostructured materials have high concentration of PDs producing diffusion scattering, which can be analysed with use of simulation of XRD patterns for 1D disordered crystal models.

Acknowledgements

This study was supported by the Russian Foundation of Basic Research, grant No. 04-03-32346.

We would like to express our thanks to Dr. G. Kryukova for HREM experiments.

[1] S.V. Cherepanova, S.V. Tsybulya, Proceedings of the EPDIC 8, Y.Andersson, E.J.Mittemeijer, U.Welzel eds. (2002) Uppsala (Sweden).