The elasticity of the ½ a0 <111> and a0 <100> dislocation loop in α-Fe thin foil

Dislocation loops in irradiated ferritic steels have a Burgers vector of the type ½ a₀ <111> or a₀ <100>. When they are located in a thin foil such as the one used in transmission electron microscopy, the presence of the two free surfaces modify the elastic field by the action of the so-called 'image forces' which can in turn influence the loops. In this work, a general analytical method was deployed to calculate the image forces in an anisotropic bcc α-Fe thin foil containing a nanometric dislocation loop. We observe that image forces induce an out of plane displacement that doubles the bulging of the thin foil surfaces induced by the loop. The elastic field and energy induced by the image forces become remarkable when the depth of the dislocation loop is comparable to its size. Moreover, there is large difference in the response to image forces between the ½ a₀ <111> and the a₀ <100> loop, with a stronger one for the ½ a₀ <111> loop, which relates to the anisotropy of the α-Fe.