Density functional theory calculation and thermodynamic analysis of the bridgmanite surface structure

Bridgmanite, a high temperature and pressure form of $MgSiO_3$, is believed to be Earth's most abundant mineral and responsible for the observed seismic anisotropy in the mantle. Little is known about surfaces of bridgmanite but knowledge of the most stable surface terminations is important for understanding various geochemical processes as well as likely slip planes. A density functional theory based thermodynamic approach is used here to establish the range of stability of bridgmanite as well as possible termination structures of the (001), (010), (100) and (011) surfaces as a function of the chemical potential of oxygen and magnesium. The results presented provide a basis for further theoretical studies of the chemical processes on bridgmanite surfaces in the Earth's mantle and slip plane analysis.Comment: 4 Pages,4 figure

Fast and Robust Algorithm for the Energy Minimization of Spin Systems Applied in an Analysis of High Temperature Spin Configurations in Terms of Skyrmion Density

An algorithm for the minimization of the energy of magnetic systems is presented and applied to the analysis of thermal configurations of a ferromagnet to identify inherent structures, i.e. the nearest local energy minima, as a function of temperature. Over a rather narrow temperature interval, skyrmions appear and reach a high temperature limit for the skyrmion density. In addition, the performance of the algorithm is further demonstrated in a self-consistent field calculation of a skyrmion in an itinerant magnet. The algorithm is based on a geometric approach in which the curvature of the spherical domain is taken into account and as a result the length of the magnetic moments is preserved in every iteration. In the limit of infinitesimal rotations, the minimization path coincides with that obtained using damped spin dynamics while the use of limited-memory quasi-newton minimization algorithms, such as the limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm, significantly accelerates the convergence

Site preference of Fe atoms in the olivine (FexMg2−x)SiO4(Fe_xMg_{2-x})SiO_4 and its surface

Olivine is involved in many natural reactions and industrial reactions as a catalyst. The catalytic ability is highly possible rely on the $Fe^{2+}$ in olivine. We use density functional theory calculation and thermodynamics to investigate the site preference of Fe atom in olivine which composition from iron-rich to iron-poor and its surfaces. The $Fe^{2+}$ always shows its high spin (quintet) state which has larger ion radius than $Mg^{2+}$ in olivine crystal and surfaces. The $Fe^{2+}$ inside the surface slab prefers the smaller M1 site than M2 site by enlarge the metal-oxygen octahedra when occupied the metal site as in the bulk system. Energy contribution of entropies accumulation caused temperature raise stops this preference at the temperature where a cation order-disorder distribution energy crossover happen in olivine. Surface exposed site provide $Fe^{2+}$ large space due its unsaturated nature. This lead a higher level of preference of $Fe^{2+}$ to the surface site than any metal site inside the crystal no matter M1 or M2 site is exposed. This indicate the $Fe^{2+}$ in the bulk system can diffuse to a metal site exposed on the surface driven by the energy difference. Many reactions can use the on surface $Fe^{2+}$ as a catalyst because of the active chemical behavior of Fe. Meanwhile this energetics preference should be considered in the future model to explain the natural observed zoning olivine have a high Fe edge and low Fe center. These microscopic understanding can be essential to many olivine related geochemical and astrochemical reactions.Comment: 8 figure

Long-timescale simulations of H2_2O admolecule diffusion on Ice Ih(0001) surfaces

Long-timescale simulations of the diffusion of a H$_2$O admolecule on the (0001) basal plane of ice Ih were carried out over a temperature range of 100 to 200 K using the adaptive kinetic Monte Carlo method and TIP4P/2005f interaction potential function. The arrangement of dangling H atoms was varied from the proton-disordered surface to the perfectly ordered Fletcher surface. A large variety of sites was found leading to a broad distribution in adsorption energy at both types of surfaces. Up to 4 % of the sites on the proton-disordered surface have an adsorption energy exceeding the cohesive energy of ice Ih. The mean squared displacement of a simulated trajectory at 175 K for the proton-disordered surface gave a diffusion constant of 6$\cdot$10$^{-10}$ cm$^2$/s, consistent with an upper bound previously reported from experimental measurements. During the simulation, dangling H atoms were found to rearrange so as to reduce clustering, thereby approaching a linear Fletcher type arrangement. Diffusion on the perfectly ordered Fletcher surface was estimated to be significantly faster, especially in the direction along the rows of dangling hydrogen atoms. From simulations over the range in temperature, an effective activation energy of diffusion was estimated to be 0.16 eV and 0.22 eV for diffusion parallel and perpendicular to the rows, respectively. Even a slight disruption of the rows of the Fletcher surface made the diffusion isotropic.Comment: 24 pages, 8 figures, 1 tabl