Diffraction peak profiles of surface relaxed spherical nanocrystals

Abstract

A model is proposed for surface relaxation of spherical nanocrystals. Besides reproducing the primary effect of changing the average unit cell parameter, the model accounts for the inhomogeneous atomic displacement caused by surface relaxation and its effect on the diffraction line profiles. Based on three parameters with clear physical meanings - extension of the sub-coordination effect, maximum radial displacement due to sub-coordination, and effective hydrostatic pressure - the model also considers elastic anisotropy and provides parametric expressions of the diffraction line profiles directly applicable in data analysis. The model was tested on spherical nanocrystals of several fcc metals, matching atomic positions with those provided by Molecular Dynamics (MD) simulations based on embedded atom potentials. Agreement was also verified between powder diffraction patterns generated by the Debye scattering equation, using atomic positions from MD and the proposed model.

Keywords:

• Nanocrystalline materials
• surface relaxation
• diffraction line profiles
• line profile analysis
• atomistic modelling
• powder diffraction

Acknowledgements

Authors would like to thank Luca Gelisio and Alberto Flor for MD calculations, C.L. Azanza Ricardo for simplification of some analytical expressions, and finally to D. Paz-Linares and prof. E. Estevez-Rams for useful discussions.

Notes

No potential conflict of interest was reported by the authors.

1 For a sphere of diameter D. Expressions for other shapes are available, as well as for a distribution of sizes [76].