Size-dependent elasticity of nanocrystalline titania

Abstract

Synchrotron-based high-pressure x-ray diffraction measurements indicate that compressibility, a fundamental materials property, can have a size-specific minimum value. The bulk modulus of nanocrystalline titania has a maximum at particle size of 15 nm. This can be explained by dislocation behavior because very high dislocation contents can be achieved when shear stress induced within nanoparticles counters the repulsion between dislocations. As particle size decreases, compression increasingly generates dislocation networks ͑hardened by overlap of strain fields͒ that shield intervening regions from external pressure. However, when particles become too small to sustain high dislocation concentrations, elastic stiffening declines. The compressibility has a minimum at intermediate sizes.

Mechanical response of nanocrystalline Cu from atomistic simulations

“…This suggests that the proposed scaling of properties might be applicable to a wide range of nanocrystalline solids. Experiments have already measured grain-size dependent elastic moduli [20,21]. We hope that theory and simulations of the kind we present here will assist experimentalists in synthesising new nanomaterials with better properties.…”

Influence of phonon confinement, surface stress, and zirconium doping on the Raman vibrational properties of anatase TiO2 nanoparticles

“…Chen et al [52] recently showed that the bulk modulus (B = 1 K T ) of anatase nanoparticles has a distinct size dependence. It was found that the B increases as the particle diameter L decreases down to 15 nm where it attains a maximum, and then sharply decreases at smaller L. The decreased compressibility K T down to L = 15 nm was explained as due to an increasing amount of strained regions in the nanoparticles such as dislocations which can resist compression since these atoms are already displaced from their neutral positions.…”

“…[53] A positive f indicates that the surface is under tension, which implies lattice contraction. [49] The bulk modulus is reported to be B ≈ 240 GPa, [52] and the mode Grüneisen parameter has previously been reported to be γ i = 4.23. [40] Considering that f × K T = f × 1/B ≈ constant (see discussion in the Models section), i.e.…”

“…It is also qualitatively consistent with the results that Zr doped anatase particles are larger at the anatase-to-rutile phase transformation temperature, thus extending the particle size range where anatase is reported to be the most stable TiO 2 structure. [22] Finally, we comment on the mechanism proposed by Chen [52] for the decreasing K T down to L = 15 nm where dislocations shield the interior from an externally applied pressure. This argument resolves the experimental observations of Hearne [51] and Swamy [40] that the Raman wavenumber of nano-anatase E g (ν 6 ) under external pressure shows a wavenumber drop at 1.5 GPa before the linear bulk-like behavior appears at higher pressures.…”

Friction, wear and mechanical behavior of nano-objects on the nanoscale

“…In the case of reduced properties, this is due to the inverse Hall-Petch effect [52][53][54] where, yield strength and hardness below a critical grain size decreases with grain size. This occurs as the grain is too small to support the pile up of dislocations at grain boundaries and a high enough density of dislocations to resist deformation.…”