[SY-B3] Elastic fields and interaction between self-interstitial atom defects in bcc metals.
Strongly anisotropic self-interstitial defect configurations form spontaneously in body-centred cubic metals, like sodium or tungsten, if an extra atom is inserted in the crystal lattice and the resulting structure is relaxed into the lowest energy configuration. The equilibrium structure and modes of Brownian motion of individual SIA defects in body-centred transition metals are now well established. Yet, there is still no regular approach to modelling evolution of ensembles of such defects that would include the treatment of elastic interaction between them. The difficulty appears fundamental, illustrating the lack of a suitable mathematical formalism, linking the discrete atomistic representation of nano-scale defects with continuum elasticity. We derive an analytical expression for the dipole tensor of a dislocation loop, valid in the isotropic and anisotropic elasticity approximations, and explore it in the limit of infinitely small loop size. We discover that the prediction for the dipole tensor of a point defect that does not agree with numerical calculations even for defects in tungsten, a material that is well described by isotropic elasticity theory. We then derive an analytical formula for the dipole tensor of a defect using a two-parameter tensor form, which shows that in addition to a pure prismatic dislocation loop character, the elastic field of a SIA defect contains a significant dilatation component. We evaluate the energy of interaction between SIA defects, and between a SIA defect and a dilatation centre, e.g. a vacancy cluster. To illustrate applications of the new formalism, we compute the energy of interaction between SIA defects ordered as a periodic simple cubic super-lattice, encountered in a DFT calculation. Surprisingly, we find that the energy minimum of such a periodic configuration corresponds to the orientation of the directional unit vector of the defect collinear with a 111 direction.
This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreements No 633053 and No 755039. Also, it has been part-funded by the RCUK Energy Programme (Grant Number EP/P012450/1).
This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreements No 633053 and No 755039. Also, it has been part-funded by the RCUK Energy Programme (Grant Number EP/P012450/1).