Atomistic origin of lattice strain on stiffness of nanoparticles

Abstract

Lattice strain plays a crucial role on the properties of nanoparticles. Although the effect of lattice strain on nanoparticles has been widely studied in experimental measurements and calculations, its physical mechanism from the perfective of bond identities is still poorly understood. Herein we put forward an analytical solution of the size effect and external stimuli such as pressure and temperature dependence of lattice strain and bulk modulus of a nanoparticle from the perspective of atomistic origin. A shell-core configuration has been considered for the nanoparticle structure. It has been found that the lattice strain as well as quantum trapping and energy storage exerted by the compressive stress and thermal stress would be responsible for the mechanical behavior of nanoparticles. The theoretical predictions were well consistent with the experimental data and ab initio calculations, implying that the model could be expected to be a general approach to understand mechanical behavior in nanomaterials.

Structure and magnetism of Fe–Co alloy nanoparticles

“…Determination of the Co concentration in our samples on the basis of the comparison of the observed lattice parameters (Table 1) with the above quoted results [1,4,37,38,39] could, however, lead to an overestimation of the Co concentration. Namely, even though the cubic lattice parameter observed for Fe-Co particles with a characteristic size in the order of  100 nm agrees fairly well with that observed for corresponding bulk samples [39], for particles with a size below a few times of 10 nm decreasing particle size is expected to lead to an increase in the magnitude of surface-stress related lattice strain effects and thereby to a reduction of the lattice parameter [40,41]. The peculiar behavior of Fe-Co alloy nanoparticles is furthermore underlined by the recent finding of an increasing {001} crystalplane distance with increasing Co concentration in Fe x Co 1-x nanoparticles with a size in the order of  10 nm [25].…”

First Evidence of Rh Nano-Hydride Formation at Low Pressure

“…Similar exponential increase of the lattice strain with decreasing the size was demonstrated for Ag clusters. 12 This nanoscale effect might induce a comparable behavior to bulk materials under high pressure conditions, as we recently proved for Mg−Ni based nanoparticles. 13 As a consequence, nonabsorbing hydrogen noble elements at nanoscale might start to absorb hydrogen even at ambient temperature and pressure.…”

“…12 Indeed, an exponential increase of the additional pressure and the lattice strain is observed below 4−5 nm. Similar threshold may act as a limit for important change in the physical properties of the present Rh nanoparticles.…”

Surface free energy and surface stress as elastic components of the surface tension of condensed matter

“…These authors deduced the surface stress of small gold parti cles by measuring the reduction of the lattice constant versus the radii of the particles". Nowadays there are hundreds of thousands of experimental and theoretical works considering this effect and dependences of many physico mechanical properties including the complicated connection of the elasticity modulus with the nanoparticle radius, electrolyte composition and the electrode potential, see table, S3 and [34][35][36][37][38][39][40][41][42][43][44][45][46][47]. These works provide a clear proof of the natural con nection between the elastic potential energy (surface energy) and interatomic bonds.…”

“…In high vacuum (as the reference state), there are no external effects and the elastic surface energy is the only and natural energy source leading to surface stress, elastic strain and the lattice contraction (see above), changing the elasticity modulus and to other nano effects [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. Most of these effects have been theoretically explained using the purely elastic lattice respond to both the surface energy and the surface stress.…”