Surface stresses are the source of the size-dependent elastic behavior of nanoparticles. In addition, they are known to affect the electrochemical properties of materials as well as the stability and formation of phases. Surface stresses induce bulk stresses in solid bodies which, in turn, modify the energy barriers for formation and migration of defects. Previous studies on spherical particles with uniform surface stress, e.g. by Müller and Albe (Acta Mater. 55:3237, 2007) and by Glinchuk et al. (phys. stat. sol. (b) 244:578, 2007) have shown increasing defect formation barriers and decreasing defect migration barriers with decreasing particle size. In non-spherical particles, however, surface stresses lead to an inhomogeneous bulk stress distribution. Consequently, this should cause a heterogeneous impact on defect formation and migration, an issue which has been investigated so far.
This study is concerned with the influence of anisotropic surface stresses on the formation and migration of point defects in a faceted nanoparticle of lithium cobalt oxide. Elastic parameters and anisotropic surface stress components are computed by electronic Density Functional Theory calculations and are incorporated into a continuum model implemented by the Finite Element method. The particle geometry is derived from a Wulff construction. Using the defect dipole tensor, we determine the changes in the energy barriers for point defect formation and migration.
Within the considered nanoparticle, the surface stresses result in a highly heterogeneous bulk stress distribution with a vortex-like transition region between the tensile particle core and its non-uniformly stressed boundaries. Both the center and the exterior of the particle show enhanced energy barriers for both the formation and the migration of a Li vacancy. These barriers experience a reduction in the transition region in the particle, culminating in a peak increase in diffusivity and ionic conductivity by 41% respectively 45%.
Overall, this yields a net increase in ionic conductivity by circa 5% for a particle at a length-scale of 10nm. This surface stress-enhanced conductivity decays rapidly with increasing particle size.