Nanopowder Diffraction

TL;DR

This paper reviews nanopowder diffraction phenomena in small nanocrystals, emphasizing atomistic simulations, surface effects, and the limitations of traditional analysis methods like Rietveld, with a focus on metal nanocrystals and twinning effects.

Contribution

It introduces new atomistic modeling approaches for interpreting diffraction patterns of nanocrystals, highlighting surface relaxation and twinning effects, and critiques the applicability of Rietveld analysis for defective nanoparticles.

Findings

Peak shifts are influenced by atomic scattering and Lorentz factors.

Surface relaxation contributes to additional peak shifts in real nanocrystals.

Multiple twinning significantly affects diffraction peak positions and intensities.

Abstract

As in the available literature there are still misconceptions about powder diffraction phenomena observed for small nanocrystals ($D<10$ nm), we propose here a systematic and concise review of the involved issues that can be approached by atomistic simulations. Most of phenomenological tools of powder diffraction can be now verified constructing realistic atomistic models, following their thermodynamics and impact on the diffraction pattern. The models concern small cuts of the perfect lattice as well as relaxed nanocrystals also with typical strain and faults, proven by experiments to approximate the real nanocrystals. The discussed examples concern metal nanocrystals. We describe the origin of peak shifts that for cuts of the perfect lattice are mostly due to multiplying of broad profiles by steep slope factors -- atomic scattering and Lorentz. The Lorentz factor embedded in the Debye summation is discussed in more detail. For models relaxed with realistic force fields and for the real nanocrystals the peak shift additionally includes contribution from surface relaxation which enables development of an experimental {\it{in situ }} method sensitive to the state of the surface. Such results are briefly reviewed. For small fcc nanocrystals we discuss the importance and effect of multiple (111) cross twinning on the peak shift and height. The strain and size effects for the perfect multitwinned clusters -- decahedra and icosahedra, are explained and visualised. The manuscript proposes new methods to interpret powder diffraction patterns of real, defected (twinned) fcc nanoparticles and points to unsuitability of the Rietveld method in this case.