Average and local strain fields in nanocrystals

Abstract

This article presents a rigorous and self-consistent comparison of lattice distortion and deformation fields existing in energy-optimized pseudo-spherical gold nanoparticles obtained from real-space and powder diffraction strain analysis techniques. The changes in atomic positions resulting from energy optimization (relaxation) of ideally perfect gold nanoparticles were obtained using molecular dynamics modeling. The relaxed atomic coordinates were then used to compute the displacement, rotation and strain components in all unit cells within the energy-optimized (relaxed) particles. It was seen that all of these terms were distributed heterogeneously along the radial and tangential directions within the nanospheroids. The heterogeneity was largest in the first few atomic shells adjacent to the nanoparticle surface, where the continuity of crystal lattice vectors originating from the interior layers was broken because of local lattice rotations. These layers also exhibited maximum shear and normal strains. These (real-space) strain values were then compared with the average lattice strains obtained by refining the computed diffraction patterns of such particles. The results show that (i) relying solely on full-pattern refinement techniques for lattice strain analysis might lead to erroneous conclusions about the dimensionality and symmetry of deformation within relaxed nanoparticles; (ii) the lattice strains within such relaxed particles should be considered 'eigenstrains' ('inherent strains') as defined by Mura [Micromechanics of Defects in Solids, (1991), 2nd ed., Springer]; and (iii) the stress/strain state within relaxed nanoparticles cannot be analyzed rigorously using the constitutive equations of linear elasticity.

Computational diffraction reveals long-range strains, distortions and disorder in molecular dynamics simulations of irradiated single crystals

“…7(d), red curve]. As can be observed, this measurement largely overestimates the microstrain in the whole investigated range, consistently with other studies (Stukowski et al, 2009;Xiong et al, 2019). The reason for this discrepancy is that peak broadening is sensitive to correlated displacements, via the term hexpfiQ Á ½uðr j Þ À uðr k Þgi in equation ( 3).…”

“…Moreover, these methods inherently neglect long-range correlations in the atomic displacements, i.e. the displacement field around an atom in a given coordination shell is assumed to be independent of the displacement field around the nextnearest neighbor, so that the strain averaged over the whole MD cell generally differs from the result that would have been obtained from a diffraction experiment (Xiong et al, 2019).…”

“…Over the past three decades, a large number of studies have been dedicated to the determination of strain from atomicscale simulations (Zimmerman et al, 2009;Mott et al, 1992;Gullett et al, 2008;Stukowski & Arsenlis, 2012;Stukowski et al, 2009;Zhang et al, 2015;Xiong et al, 2019;Leonardi et al, 2012). In these studies, the local deformation tensor is obtained from the evolution of the coordinates of the atoms constituting a coordination shell between any two time steps of an MD trajectory ('kinematical' approach).…”

Temperature reversible synergistic formation of cerium oxyhydride and Au hydride: a combined XAS and XPDF study

“…Here it is determined that V 0 is equal to 66.6 Å 3 , or a lattice parameter of 4.05 Å which is contracted as compared to bulk Au (4.078 Å). Elsewhere it has been noted that there is a large contraction in the lattice volume in the surface of fcc nanocrystals 78,79 and as such this would indicate that the Au is present in nanocrystalline form in this sample.…”

Comment on the article The nanodiffraction problem

“…article, and this exchange in Journal of Applied Crystallography, will stimulate the development of a rigorous theoretical framework for the analysis of nanocrystalline diffraction patterns. Until such a framework is in place, diffraction analysis results from such systems should be treated with caution given, also, that significant details of the distribution of unit-cell parameters within nanoparticles are eliminated during diffraction averaging (Xiong et al, 2019).…”