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

Electron‐density critical points analysis and catastrophe theory to forecast structure... 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 xc 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 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A Foundations of Crystallography Wiley

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

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References (65)

Publisher
Wiley
Copyright
Copyright © 2018 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/S2053273317018381
pmid
29493539
Publisher site
See Article on Publisher Site

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 xc 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 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.

Journal

Acta Crystallographica Section A Foundations of CrystallographyWiley

Published: Mar 1, 2018

Keywords: ; ; ;

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