A continuum approach is used to model a twin lamella as a flat section embedded in an elastically isotropic medium under applied stresses. The twin formation energy as the sum of self energy of the disclination dipole, and the elastic interaction between the disclination dipole and the applied strain, associated with the twin-matrix interfacial energy was calculated. The minimization of the formation energy with respect to the dimensions of the lamella is related to the twin nucleation, which gives the condition for when twin nucleation is energetically favorable. Based on the assumption that the nucleation of twin is a thermally activated process, the critical stress dependent on the sample diameter was obtained, that is the smaller the sample size, the larger the apparent stre...[ Read more ]

A continuum approach is used to model a twin lamella as a flat section embedded in an elastically isotropic medium under applied stresses. The twin formation energy as the sum of self energy of the disclination dipole, and the elastic interaction between the disclination dipole and the applied strain, associated with the twin-matrix interfacial energy was calculated. The minimization of the formation energy with respect to the dimensions of the lamella is related to the twin nucleation, which gives the condition for when twin nucleation is energetically favorable. Based on the assumption that the nucleation of twin is a thermally activated process, the critical stress dependent on the sample diameter was obtained, that is the smaller the sample size, the larger the apparent strength. Compared to the conventional infinite model related to twinning, the effect of surface or boundary was studied.

Theoretical analysis and molecular dynamics simulations are conducted to study systematically surface eigen-displacement and surface Poisson’s ratios of solids, which play essential roles in surface energy, surface strain and surface stress. Face-centered cubic (001) Au thin films were taken as typical examples to illustrate the physical picture. The surface eigen-displacement is a critical surface strain at the equilibrium state after normal relaxation and thus an intrinsic surface property. Surface Poisson’s ratios are also intrinsic surface properties. Combining surface eigen-displacement and surface Poisson’s ratios with surface eigen-stress and surface tangential elastic constants lays foundations of surface elasticity of solids.

Taking advantages from both Gibbs and McLean adsorption isotherms, we develop a Gibbs-approach based adsorption isotherm for grain boundary (GB) segregation in nanograined (ng) polycrystals. An excess GB thickness is introduced to describe the excess of GB atomic volume in comparison with the atomic volume in lattice. The GB bulk modulus is determined with the excess GB thickness and a universal function. The newly developed adsorption isotherm is able to analyze simultaneously stresses, concentrations and their coupling behaviors in grains and GBs. Numerical calculations and plots are conducted to illustrate the theoretical analysis. The results show that the apparent solute concentration could be greatly enhanced in ng materials, due to a large grain boundary volume fraction and a considerable increase in the lattice concentration that is, in turn, boosted by the concentration-induced stresses.

The Gibbs-approach based adsorption isotherm for nanograined polycrystals is applied to the H-Pd solid solutions. Using the published experimental data of lattice strain and sample strain of the nanograined Pd, with an averaged grain size of 10 nm and in thermodynamic equilibrium with a H₂ partial pressure, we determined H concentrations and stresses, as a function of the H₂ partial pressure, in both grains and grain boundaries. More importantly, we determined the intrinsic properties of grain boundaries, such as the grain boundary bulk modulus, the grain boundary excess thickness, the difference in chemical potential between grains and grain boundaries, etc. With the determined intrinsic properties, the Gibbs-approach based adsorption isotherm predicted the H segregation in grain boundaries of nanograined Pd with an averaged grain size of 5 nm. The predication was verified by other reported experimental data.

Using the Gibbs-approach based adsorption isotherm and the experimental data of nominal H concentration in Pd nanoparticles with a mean diameter of 3.6 nm versus H₂ partial pressure, we determined the H-trap depth of Pd surface, the H concentrations and stresses in both core and surface shell of the nanoparticles. The results indicate that in addition to the surface segregation of H atoms, the tensile hydrostatic stress induced by the difference in concentration between the core and the surface shell greatly enhances the H concentration in the crystalline core in comparison with that in the bulk Pd counterpart under the same H₂ partial pressure.