Direct observation of elastic displacement modes by grazing-incidence X-ray diffraction

The Ground State of Epitaxial Germanene on Ag(111)

Two-dimensional (2D) honeycomb lattices beyond graphene, such as germanene, appear very promising due to their outstanding electronic properties, such as the quantum spin Hall effects. While there have been many claims of germanene monolayers up to now, no experimental evidence of a honeycomb structure has been provided up to now for these grown monolayers. Using scanning tunneling microscopy (STM), surface X-ray diffraction (SXRD), and density functional theory, we have elucidated the Ge-induced ( 109 × 109 ) R ± 24.5 ° reconstruction on Ag(111). We demonstrate that a powerful algorithm combining SXRD with STM allows us to solve a giant surface reconstruction with more than a hundred atoms per unit cell. Its extensive unit cell indeed consists of 98 2-fold or 3-fold coordinated Ge atoms, forming a periodic arrangement of pentagons, hexagons, and heptagons, with the inclusion of six dispersed Ag atoms. By analogy, we show that the ( 7 7 × 7 7 ) R ± 19.1 ° reconstruction obtained by segregation of Ge through an epitaxial Ag/Ge(111) film possesses a similar structure, i.e., Ge pentagons/hexagons/heptagons with a few Ag atoms. Such an organization is more stable than that of pure Ge monolayers and can be assigned to the ground state of epitaxial germanene.

Influence of the elastic deformations on the form factor of polyhedral nanocrystals: the illustrative example of the pseudomorphic inclusion

Using an analytically tractable example, the pseudomorphic inclusion, this article examines the influence of elastic deformations on the form factor of polyhedral nanocrystals. A control parameter, the total amplitude of the variation of the complex density phase, is identified and it is shown that for low enough deformations the characteristic asymptotic behaviours as a function of the scattering vector associated with the polyhedral crystal shape are preserved, leading to a strong contrast in the dependence of the form factor on orientation. Using the sections method, it is explained why these results can be generalized to more realistic elastic situations.

Epitaxial growth and structure of cobalt ferrite thin films with large inversion parameter on Ag(001)

Cobalt ferrite ultrathin films with the inverse spinel structure are among the best candidates for spin filtering at room temperature. High-quality epitaxial CoFe₂O₄ films about 4 nm thick have been fabricated on Ag(001) following a three-step method: an ultrathin metallic CoFe₂ alloy was first grown in coherent epitaxy on the substrate and then treated twice with O₂, first at room temperature and then during annealing. The epitaxial orientation and the surface, interface and film structure were resolved using a combination of low-energy electron diffraction, scanning tunnelling microscopy, Auger electron spectroscopy and in situ grazing-incidence X-ray diffraction. A slight tetragonal distortion was observed, which should drive the easy magnetization axis in-plane due to the large magneto-elastic coupling of such a material. The so-called inversion parameter, i.e. the Co fraction occupying octahedral sites in the ferrite spinel structure, is a key element for its spin-dependent electronic gap. It was obtained through in situ resonant X-ray diffraction measurements collected at both the Co and Fe K edges. The data analysis was performed using FDMNES, an ab initio program already extensively used to simulate X-ray absorption spectroscopy, and shows that the Co ions are predominantly located on octahedral sites with an inversion parameter of 0.88 (5). Ex situ X-ray photoelectron spectroscopy gives an estimation in accordance with the values obtained through diffraction analysis.

Modeling elastic anisotropy in strained heteroepitaxy

Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the [Formula: see text] [Formula: see text] on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to [Formula: see text] facets on the surface.