Elastic interactions between ’’voids’’ induced by solute segregation

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Abstract
Expressions are derived for the elastic interaction energy between void‐solute shell composites. These composites consist of spherical void cores surrounded by spherically symmetric solute shells containing a uniform concentration of irradiation segregated solute. The solutes are assumed ’’misfitting’’ and as such represent sources of internal stress. The elastic interaction energy between composites arises because of the so‐called inhomogeneity interaction and has minimum values at certain composite separations and solute shell thickness. The existence of these minima obtains largely because the misfit of the composites increases as the composite separation R increases. For a constant misfit, the interaction energy would decrease monotonically approximately as R−6. The surface stress of voids is taken to be zero in the calculations so that the only source of interaction between composites is the stress induced by solute segregation. The calculations are performed for both two‐composite and N‐composite interactions, and we show that, primarily, only nearest‐neighbor interactions are significant. The calculations are compared with experimental investigations of void ordering in an Ni ion‐irradiated Nb‐1Zr alloy containing 0.0038 atom fraction of oxygen as an impurity. Given experimentally determined void sizes and auxiliary data, the correct void lattice parameter is predicted when the solute shell thickness is ∼30% of the composite radius. In pure Nb, it is found the O, C, or N impurities are necessary for void ordering, which supports the main thesis of the present paper, viz., solutes/impurities are a primary cause of void ordering.