Modeling and measuring the strain state of decahedral nanoparticles

OPHUS, C.; CORTHEY, G.; ERCIUS, P. A.; LINCK, M.; RADMILOVIC, V.; SALVAREZZA, R. C.; DAHMEN, U.

Manchester

Congreso; The 15th European Microscopy Congress; 2012

Many researchers are currently fabricating, characterizing and testing nanoparticles for many different applications due to the extremely large parameter space available in particle structure, size, chemistry and shape [1]. The strain state of a nanoparticle can affect photoluminescent [2], electromagnetic [3] and catalytic [4] material properties. Therefore it is important to measure the strain state of nanoparticles, and use models to predict the strain state for new materials. One common nanoparticle structure for fcc materials is the five-fold twinned decahedral structure. An ideal regular decahedral particle is constructed from five tetrahedral domains rotated around a shared central axis, and contains a disclination of power -7.4°. Exact analytic solutions exist for a homogenous, isotropic sphere and cylinder with arbitrary disclination power [5]. However all real materials exhibit some degree of anisotropy and real decahedral particles are not simple geometric shapes [6]. In this study we use molecular statics to model the strain state in anisotropic gold decahedral nanoparticles of many different geometries. We then use high-resolution transmission electron microscopy (HRTEM) to map the projected strain state of different composition and size nanoparticles and compare the experimental strain distributions to that of our models with structures energy-minimized using molecular statics. A nanoparticle with very small dimensions will tend to shrink due to the positive surface tension of all facets. However, this reduction in size will not be uniform if elastic properties of the particle material are anisotropic or the particle boundary conditions (free surfaces at facets) are not uniform. Therefore, atomic columns will be curved in the low-index zone axis direction used in HRTEM studies. We analyze the effects of this column curvature in HRTEM experiments using multislice simulation. The results of one such simulation are plotted in Figure 1. Figure 1C shows the difference in measured peak positions between the projected potential plotted in Figure 1A and a simulated exit wave shown in Figure 1B. When an atomic column bends away from the center of a particle, the peak of the projected potential is further away from the particle center than the measured peak position in a micrograph. This is caused by the channelling effect, where the propagating electron beam is focused down atomic . We examine this phenomenon in detail. To test the strains predicted by our molecular statics models, we have performed HRTEM studies on decahedral nanoparticles with a variety of sizes and compositions, including Au, AuAg and RhPd. One such measurement is presented in Figure 2A. By fitting a lattice to all atomic column peaks, we can map the strain of each segment of the particle which is shown in Figure 2B. Despite the fact that the particle has 5 segments of almost identical size, large differences are observed between segments. The segments on the left and on the bottom contain large defects including dislocations. The remaining three segments all show a similar strain field, which appears to depend directly on the inner segment angle. A rotationally symmetric simulated particle is shown in Figure 2C. The angular dependence of the simulated strain fields agrees very well with our experimental measurements. The difference between a segment inner angle and the ideal fcc lattice angle is the disclination power of that segment. We have modelled the elastic response of decahedral segments as function of the disclination power and compared the models to additional experimental measurements [7]. 120-124 [7] We are thankful to Velimir Radmilovic for useful discussions. CO wishes to acknowledge financial support from the National Sciences and Engineering Research Council of Canada. Figure 1. Decahedral Au nanoparticle structure simulated with molecular statics: (A) projected potential, (B) simulated micrograph intensity and (C) difference in measured peak positions between (A) and (B), with displacements enhanced by a factor of eight.