Electron‐density critical points analysis and catastrophe theory to forecast structure instability in periodic solids. Issue 2 (15th February 2018)

• Record Type: Journal Article
• Authors: Merli, Marcello; Pavese, Alessandro
• Is Part Of: Acta crystallographica. Volume 74:Issue 2(2018:Mar.)
• Page Start: 102
• Page End: 111
• Publication Date: 2018-02-15
• Subjects: electron‐density critical points -- catastrophe theory -- phase/state transitions in crystals -- ab initio calculations; Crystallography -- Periodicals; Condensed matter -- Periodicals; 548
• DOI: 10.1107/S2053273317018381
• Languages: English
• ISSNs: 2053-2733

Abstract

Abstract : Electron‐density topology is used to detect instability in periodic solids. 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(x c ) = 0 and λ1, λ2, λ3 ≠ 0 [λ being the eigenvalues of the Hessian of ρ(x ) atx c ], towards degenerate critical points, i.e . ∇ρ(x c ) = 0 and at least one λ equal to zero. The catastrophe theory formalism provides a mathematical tool to model ρ(x ) in the neighbourhood ofx c and 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 Al2 O3 (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.