Stress in titania nanoparticles: an atomistic study.

Stress engineering is becoming an increasingly important method for controlling electronic, optical, and magnetic properties of nanostructures, although the concept of stress is poorly defined at the nanoscale. We outline a procedure for computing bulk and surface stress in nanoparticles using atomistic simulation. The method is applicable to ionic and non-ionic materials alike and may be extended to other nanostructures. We apply it to spherical anatase nanoparticles ranging from 2 to 6 nm in diameter and obtain a surface stress of 0.89 N m(-1), in agreement with experimental measurements. Based on the extent that stress inhomogeneities at the surface are transmitted into the bulk, two characteristic length-scales are identified: below 3 nm bulk and surface regions cannot be defined and the available analytic theories for stress are not applicable, and above about 5 nm the stress becomes well-described by the theoretical Young-Laplace equation. The effect of a net surface charge on the bulk stress is also investigated. It is found that moderate surface charges can induce significant bulk stresses, on the order of 100 MPa, in nanoparticles within this size range.