Symmetry, topology and crystal deformations: a phase-field crystal approach

by Vidar Skogvoll (University of Oslo)

Tuesday 2 May 2023, 11:00 → 12:00 Europe/Stockholm

Albano 3: 6228 - Mega (22 seats) (Albano Building 3)

zoom link : https://stockholmuniversity.zoom.us/j/622224375

 

Topology protects your iPhone photos! Beyond linear elasticity, the response of single crystals under stress is given primarily by the motion of dislocations. The mobility, interactions, and entanglement of which determine the structural integrity and partly the electronic properties of materials, which becomes especially important for smaller systems, such as the microscopic chips in your phone containing those beautiful pictures of yours from the French Riviera. Dislocations are topological defects in the crystal structure. In this talk, I will explain how crystal structure is described by density functional theory and introduce a simple such (Ginsburg-Laundau type) model, the phase-field crystal (PFC), to derive an explicit expression for the dislocation velocity. I will show how dislocations are topological defects of an order parameter on the 3-torus and how the decomposition of the 3-torus into its product topologies S1×S1×S1 is used to reconstruct the dislocation density tensor from the PFC. The result is valid beyond this model, and the general framework can be used to study topological defects in other systems exhibiting spontaneous symmetry breaking.