On the Stiffness of Gold at the Nanoscale

Abstract

The density and compressibility of nanoscale gold (both nanospheres and nanorods) and microscale gold (bulk) were simultaneously studied by X-ray diffraction with synchrotron radiation up to 30 GPa. Colloidal stability (aggregation state and nanoparticle shape and size) in both hydrostatic and nonhydrostatic regions was monitored by small-angle X-ray scattering. We demonstrate that nonhydrostatic effects due to solvent solidification had a negligible influence on the stability of the nanoparticles. Conversely, nonhydrostatic effects produced axial stresses on the nanoparticle up to a factor 10× higher than those on the bulk metal. Working under hydrostatic conditions (liquid solution), we determined the equation of state of individual nanoparticles. From the values of the lattice parameter and bulk modulus, we found that gold nanoparticles are slightly denser (0.3%) and stiffer (2%) than bulk gold: V 0 = 67.65(3) Å 3 , K 0 = 170(3)GPa, at zero pressure.

Mechanics under pressure of gold nanoparticle supracrystals: the role of the soft matrix

“…This variation can be estimated using the bulk modulus of the gold core. This bulk modulus has been measured 18,19 but for larger particles: B Gb = 167 GPa, being estimated to 5.72. Recent AFM nanoindentation experiments on small gold nanoparticles 20 have revealed an increase of the gold stiffness for particles smaller than 7 nm.…”

Correlation between Spectroscopic and Mechanical Properties of Gold Nanocrystals under Pressure

“…Given that the nonhydrostatic axial stress component at 31 GPa is known to be σ ≈ 2 GPa from XRD, we conclude that the critical shear stress should be about this value. Note that the fraction of nanospheres undergoing plastic deformation is much smaller than that of broken nanorods at 20 GPa, thus indicating that the nanorods are shear cut along the longitudinal direction of the nanorod.…”

“…The change in particle volume can be well described by a Vinet equation of state with f = ( V / V 0 ) 1/3 . We employed a gold bulk modulus of K 0 = 171 GPa with a value of K 0 ′ = 5.72, as determined by the study of the compressibility of gold nanocrystal colloids by X-ray diffraction with synchrotron radiation in the 0–30 GPa range …”

“…It should be noted that a pressure-induced red shift of the LSPR was observed for the AuNR colloid in the hydrostatic range. The variation of λ LSPR ( P ) can be fairly well described through the Gans model in the hydrostatic regime, considering the calibrated refractive index of the 4:1 MeOH–EtOH solvent , and the equation of state of AuNPs . In the downstroke, the longitudinal resonance blue shifted when the pressure was released.…”

Atomistic Simulations of the Elastic Compression of Platinum Nanoparticles

“…The elastic properties of nanoparticles have been measured experimentally using force-displacement curves from compression tests with atomic force microscopy (AFM) or AFM with in situ transmission electron microscopy (TEM) [12,13], and by measuring lattice distance change with pressure using x-ray diffraction (XRD) in anvil cells [14][15][16]. From AFM and in situ TEM measurements, the elastic modulus is typically calculated using Hertz theory for very small contact forces [17,18].…”