About the reliability of the Maximum Entropy Method in reconstructing electron density: the case of MgO

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

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) at x_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 of x_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 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.

A design of backing seat and gasket assembly in diamond anvil cell for accurate single crystal x-ray diffraction to 5 GPa

We designed a new cell assembly of diamond anvil cells for single crystal x-ray diffraction under pressure and demonstrate the application of the cell to the crystallographic studies for ice VI and ethanol high-pressure (HP) phase at 0.95(5) GPa and 1.95(2) GPa, respectively. The features of the assembly are: (1) the platy anvil and unique-shaped backing seat (called as "Wing seat") allowing the extremely wide opening angle up to ±65°, (2) the PFA-bulk metallic glass composite gasket allowing the easy attenuation correction and less background. Thanks to the designed assembly, the R(int) values after attenuation corrections are fairly good (0.0125 and 0.0460 for ice VI and ethanol HP phase, respectively), and the errors of the refined parameters are satisfactory small even for hydrogen positions, those are comparable to the results which obtained at ambient conditions. The result for ice VI is in excellent agreement with the previous study, and that for ethanol HP phase has remarkable contributions to the revision to its structure; the H12 site, which makes gauche molecules with O1, C2, and C3 sites, may not exist so that only trans conformers are present at least at 1.95(2) GPa. The accurate intensities using the cell assembly allow us to extract the electron density for ethanol HP phase by the maximum entropy method.