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MARCELLO MERLI

Electron-density critical points analysis and catastrophe theory to forecast structure instability in periodic solids

  • Autori: Merli, Marcello*; Pavese, Alessandro
  • Anno di pubblicazione: 2018
  • Tipologia: Articolo in rivista (Articolo in rivista)
  • OA Link: http://hdl.handle.net/10447/327971

Abstract

The critical points analysis of electron density, i.e. ρ(x), from ab initio calculations is used in combination with the catastrophe theory to show a correlation between ρ(x) topology and the appearance of instability that may lead to transformations of crystal structures, as a function of pressure/temperature. In particular, this study focuses on the evolution of coalescing non-degenerate critical points, i.e. such that ρ(xc) = 0 and λ1, λ2, λ3≠ 0 [λ being the eigenvalues of the Hessian of ρ(x) at xc], towards degenerate critical points, i.e. ρ(xc) = 0 and at least one λ equal to zero. The catastrophe theory formalism provides a mathematical tool to model ρ(x) in the neighbourhood of xcand allows one to rationalize the occurrence of instability in terms of electron-density topology and Gibbs energy. The phase/state transitions that TiO2(rutile structure), MgO (periclase structure) and Al2O3(corundum structure) undergo because of pressure and/or temperature are here discussed. An agreement of 3-5% is observed between the theoretical model and experimental pressure/temperature of transformation.Electron-density topology is used to detect instability in periodic solids.