Search results for " catastrophe theory"
showing 6 items of 6 documents
Characterization of the pressure induced Ringwoodite toMg-perovskite and Mg-wüstite phase transition by Catastrophe Theory
2010
The pressure-induced ringwoodite to Mg-perovskite and periclase post-spinel phase transition: a Bader’s topological analysis of the ab initio electro…
2011
In order to characterize the pressure-induced decomposition of ringwoodite (c-Mg2SiO4), the topological analysis of the electron density q(r), based upon the theory of atoms in molecules (AIM) developed by Bader in the framework of the catastrophe theory, has been performed. Calculations have been carried out by means of the ab initio CRYSTAL09 code at the HF/DFT level, using Hamiltonians based on the Becke- LYP scheme containing hybrid Hartree– Fock/density functional exchange–correlation terms. The equation of state at 0 K has been constructed for the three phases involved in the post-spinel phase transition (ringwoodite -> Mg-perovskite + periclase) occurring at the transition zone–lower…
Electron-density critical points analysis and catastrophe theory to forecast structure instability in periodic solids
2018
The critical points analysis of electron density,i.e. ρ(x), fromab initiocalculations 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) atxc], 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 ofxcand allo…
Pressure stability field of Mg-perovskite under deep mantle conditions: A topological approach based on Bader's analysis coupled with catastrophe the…
2019
Abstract The pressure stability field of the Mg-perovskite phase was investigated by characterizing the evolution of the electron arrangement in the crystal. Ab initio calculations of the perovskite structures in the range 0–185 GPa were performed at the HF/DFT (Hartree-Fock/Density Functional Theory) exchange–correlation terms level. The electron densities, calculated throughout the ab-initio wave functions, were analysed by means of the Bader's theory, coupled with Thom's catastrophe theory. To the best of our knowledge the approach is used for the first time. The topological results show the occurrence of two topological anomalies at P~20 GPa and P~110 GPa which delineate the pressure ra…
Bader's analysis of the electron density in the Pbca enstatite - Pbcn protoenstatite phase transition
2011
The Bader’s topological analysis of the electron density obtained via ab initio quantum mechanical simulation at Hartree–Fock and DFT level has been performed for experimentally in situ heated structures of enstatite–protoenstatite MgSiO 3 . The measurements have been performed in the temperature range 1200–1400 K. The work was aimed at characterizing both the evolution of the electron arrangement in the crystal and that of the crystal-structure at the enstatite–protoenstatite phase transition in terms of topology of the electron density, with particular care about the Mg–O and the O–O bonds. The observed breaking of some chemical bonds with increasing temperature and/or due to the phase tr…