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

Phlogopite-pargasite coexistence in an oxygen reduced spinel-peridotite ambient

The occurrence of phlogopite and amphibole in mantle ultramafic rocks is widely accepted as the modal effect of metasomatism in the upper mantle. However, their simultaneous formation during metasomatic events and the related sub-solidus equilibrium with the peridotite has not been extensively studied. In this work, we discuss the geochemical conditions at which the pargasite-phlogopite assemblage becomes stable, through the investigation of two mantle xenoliths from Mount Leura (Victoria State, Australia) that bear phlogopite and the phlogopite + amphibole (pargasite) pair disseminated in a harzburgite matrix. Combining a mineralogical study and thermodynamic modelling, we predict that the P-T locus of the equilibrium reaction pargasite + forsterite = Na-phlogopite + 2 diopside + spinel, over the range 1.3-3.0 GPa/540-1500 K, yields a negative Clapeyron slope of -0.003 GPa K^-1 (on average). The intersection of the P-T locus of supposed equilibrium with the new mantle geotherm calculated in this work allowed us to state that the Mount Leura xenoliths achieved equilibrium at 2.3 GPa /1190 K, that represents a plausible depth of ~ 70 km. Metasomatic K-Na-OH rich fluids stabilize hydrous phases. This has been modelled by the following equilibrium equation: 2 (K,Na)-phlogopite + forsterite = 7/2 enstatite + spinel + fluid (components: Na₂O,K₂O,H₂O). Using quantum-mechanics, semi-empirical potentials, lattice dynamics and observed thermo-elastic data, we concluded that K-Na-OH rich fluids are not effective metasomatic agents to convey alkali species across the upper mantle, as the fluids are highly reactive with the ultramafic system and favour the rapid formation of phlogopite and amphibole. In addition, oxygen fugacity estimates of the Mount Leura mantle xenoliths [Δ(FMQ) = -1.97 ± 0.35; -1.83 ± 0.36] indicate a more reducing mantle environment than what is expected from the occurrence of phlogopite and amphibole in spinel-bearing peridotites. This is accounted for by our model of full molecular dissociation of the fluid and incorporation of the O-H-K-Na species into (OH)-K-Na-bearing mineral phases (phlogopite and amphibole), that leads to a peridotite metasomatized ambient characterized by reduced oxygen fugacity.

Topological analysis of chemical bonding in the layered FePSe3 upon pressure-induced phase transitions

Two pressure-induced phase transitions have been theoretically studied in the layered iron phosphorus triselenide (FePSe₃ ). Topological analysis of chemical bonding in FePSe₃ has been performed based on the results of first-principles calculations within the periodic linear combination of atomic orbitals (LCAO) method with hybrid Hartree-Fock-DFT B3LYP functional. The first transition at about 6 GPa is accompanied by the symmetry change from R 3 ¯ to C2/m, whereas the semiconductor-to-metal transition (SMT) occurs at about 13 GPa leading to the symmetry change from C2/m to P 3 ¯ 1 m . We found that the collapse of the band gap at about 13 GPa occurs due to changes in the electronic structure of FePSe₃ induced by relative displacements of phosphorus or selenium atoms along the c-axis direction under pressure. The results of the topological analysis of the electron density and its Laplacian demonstrate that the pressure changes not only the interatomic distances but also the bond nature between the intralayer and interlayer phosphorus atoms. The interlayer P-P interactions are absent in two non-metallic FePSe₃ phases while after SMT the intralayer P-P interactions weaken and the interlayer P-P interactions appear.

A Cusp Catastrophe Model for Alluvial Channel Pattern and Stability

The self-adjustment of an alluvial channel is a complicated process with various factors influencing the stability and transformation of channel patterns. A cusp catastrophe model for the alluvial channel regime is established by selecting suitable parameters to quantify the channel pattern and stability. The channel patterns can be identified by such a model in a direct way with a quantified index, which is a 2D projection of the cusp catastrophe surface, and the discriminant function is obtained from the model to distinguish the river state. Predictions based on this model are consistent with the field observations involving about 150 natural rivers of small or medium sizes. This new approach enables us to classify the channel pattern and determine a river stability state, and it paves the way toward a better understanding of the regime of natural rivers to assist decision-making in river management.