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The primary objective of the present paper is to analyze the influence of interface stress on the elastic field within a nano-scale inclusion. Special attention is focused on the case of non-hydrostatic eigenstrain. From the viewpoint of practicality, it is assumed that the inclusion is spherically shaped and embedded into an infinite solid, within which an axisymmetric eigenstrain is prescribed. Following GoodierÕs work, the elastic fields inside and outside the inclusion are obtained analytically. It is found that the presence of interface stress leads to conclusion that the elastic field in the inclusion is not only dependent on inclusion size but also on non-uniformity. The result is in strong contrast to EshelbyÕs solution based on classical elasticity, and it is helpful in the understanding of relevant physical phenomena in nano-structured solids.

The structural and magnetic properties of LaCoO 3 nanoparticles with the particle size (D) ranging from ∼60 to 450 nm prepared by a sol-gel method are investigated in this paper. It is found that all the nanoparticles have rhombohedral structure as the bulk, while the volume of unit cell monotonically increases with the decrease of the particle size. Magnetic measurements reveal that in all the nanoparticles a weakly ferromagnetic behavior appears below ∼85 K, in agreement with recent studies on single crystals, powders, epitaxially strained thin films, and particles of this compound, and that the magnetic moment increases with reduction in particle size. In particular, both the unit cell volume and ferromagnetic moment show a nearly linear relation with 1/D, which allows us to assign the enhancement of the ferromagnetic moment in the nanoparticles to the lattice expansion. Moreover, from the linear relation, a significant but size-independent ferromagnetic moment can be obtained by extrapolating 1/D to zero, which is very close to the saturated magnetic moment previously reported for the single-crystal samples in the literatures. We propose that the ferromagnetic behavior usually observed in the single crystal and bulk polycrystalline LaCoO 3 at low temperatures may be an intrinsically magnetic property of this material. Additionally, a paramagnetic phase is found to coexist with the ferromagnetic phase at low temperatures for all the nanoparticles and to show a similar dependence on the particle size as the ferromagnetic phase, which suggests that the paramagnetism arises from the higher spin-state Co 3+ ions and may also be an intrinsic property of this material.