We study continuum limits of discrete models for (possibly heterogeneous) nanowires. The lattice energy includes at least nearest and next-to-nearest neighbour interactions: the latter have the role of penalising changes of orientation. In the heterogeneous case, we obtain an estimate on the minimal energy spent to match different equilibria. This gives insight into the nucleation of dislocations in epitaxially grown heterostructured nanowires.
Citation: Roberto Alicandro, Giuliano Lazzaroni, Mariapia Palombaro. 2018: Derivation of a rod theory from lattice systems with interactions beyond nearest neighbours, Networks and Heterogeneous Media, 13(1): 1-26. doi: 10.3934/nhm.2018001
We study continuum limits of discrete models for (possibly heterogeneous) nanowires. The lattice energy includes at least nearest and next-to-nearest neighbour interactions: the latter have the role of penalising changes of orientation. In the heterogeneous case, we obtain an estimate on the minimal energy spent to match different equilibria. This gives insight into the nucleation of dislocations in epitaxially grown heterostructured nanowires.
The six tetrahedra in the Kuhn decomposition of a three-dimensional cube
Two possible recovery sequences for the profile at the centre of the figure. Here we picture only a part of the wire containing just one species of atoms, therefore the transition at the interface is not represented. A kink in the profile may be reconstructed by folding the strip, i.e., mixing rotations and rotoreflections (left); or by a gradual transition involving only rotations or only rotoreflections (right). In the limit, the former recovery sequence gives a positive cost, while the latter gives no contribution. If the stronger topology is chosen, the appropriate recovery sequence will depend on the value of the internal variable, which defines the orientation of the wire
Lattices with dislocations: choice of the interfacial nearest neighbours in