6533b853fe1ef96bd12acc7b
RESEARCH PRODUCT
Electron-density critical points analysis and catastrophe theory to forecast structure instability in periodic solids
Marcello MerliAlessandro Pavesesubject
Hessian matrixElectron densitycatastrophe theory010504 meteorology & atmospheric sciencesCondensed Matter Physic010502 geochemistry & geophysics01 natural sciencesBiochemistryInstabilityInorganic Chemistrysymbols.namesakeStructural BiologyAb initio quantum chemistry methodsGeneral Materials Sciencephase/state transitions in crystalPhysical and Theoretical Chemistryphase/state transitions in crystalsEigenvalues and eigenvectors0105 earth and related environmental sciencesPhysicsab initio calculationelectron-density critical pointCondensed matter physicsab initio calculationsDegenerate energy levelsCondensed Matter PhysicsGibbs free energyelectron-density critical points catastrophe theory phase/state transitions in crystals ab initio calculations.symbolsMaterials Science (all)Catastrophe theoryelectron-density critical pointsdescription
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 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-01-01 |