Vincent Favre-Nicolin

A better FOX: using flexible modelling and maximum likelihood to improve direct-space ab initio structure determination from powder diffraction

Abstract Ab initio structure determination using direct-space methods, although relying on an essentially brute-force approach, can be greatly improved through smarter algorithms. The most basic improvement involves the use of prior information to reduce the number of configurations evaluated to find the structure solution. It is however vitally important that the parametrization used to incorporate this prior information does not reduce the efficiency with which the configuration space is explored. We will show that this can be achieved by defining molecules and polyhedra through a set of restraints associated to dedicated random changes, allowing to solve structures up to three times as fast as with the ‘standard’ approach where atomic positions are parametrized directly from bond lengths, bond angles and dihedral angles. To further enhance the efficiency of the algorithm, it is also possible to ‘tune’ the convergence criterion used to compare the structural model to the observed diffraction data (usually χ2 or Rwp). By using Maximum Likelihood principles, it is shown that incorporating the fact that the model is approximate in the χ2 evaluation can improve the algorithm convergence towards the structure solution.

Direct space methods of structure determination from powder diffraction: principles, guidelines and perspectives

In the last twenty five years structure determination from powder diffraction has evolved from a complex, time-consuming method to one easily usable. While the use of direct methods is restricted to samples well crystallized (sharp peaks, high resolution diffraction), structure solution using global optimization in direct space have become extremely popular, using either publicly or commercially available software. In this article we present a short history of direct space methods of structure determination from powder diffraction, and a list of available software. We then give an overview of frequent issues when solving structures in direct space, as well as how algorithms are currently evolving to solve more complex structures.

Analysis of strain and stacking faults in single nanowires using Bragg coherent diffraction imaging

Coherent diffraction imaging (CDI) on Bragg reflections is a promising technique for the study of three-dimensional (3D) composition and strain fields in nanostructures, which can be recovered directly from the coherent diffraction data recorded on single objects. In this paper, we report results obtained for single homogeneous and heterogeneous nanowires with a diameter smaller than 100 nm, for which we used CDI to retrieve information about deformation and faults existing in these wires. We also discuss the influence of stacking faults, which can create artefacts during the reconstruction of the nanowire shape and deformation.

Coherent x-ray wavefront reconstruction of a partially illuminated Fresnel zone plate

A detailed characterization of the coherent x-ray wavefront produced by a partially illuminated Fresnel zone plate is presented. We show, by numerical and experimental approaches, how the beam size and the focal depth are strongly influenced by the illumination conditions, while the phase of the focal spot remains constant. These results confirm that the partial illumination can be used for coherent diffraction experiments. Finally, we demonstrate the possibility of reconstructing the complex-valued illumination function by simple measurement of the far field intensity in the specific case of partial illumination.

FOX : A friendly tool to solve nonmolecular structures from powder diffraction

Structural characterization from powder diffraction of compounds not containing isolated molecules but three-dimensional infinite structure _alloys, intermetallics, framework compounds, extended solids_ by direct space methods has been largely improved in the last 15 years. The success of the method depends very much on a proper modeling of the structure from building blocks. The modeling from larger building blocks improves the convergence of the global optimization algorithm by a factor of up to 10. However, care must be taken about the correctness of the building block, like its rigidity, deformation, bonding distances, and ligand identity. Dynamical occupancy correction implemented in the direct space program FOX has shown to be useful when merging excess atoms, and even larger building blocks like coordination polyhedra. It also allows joining smaller blocks into larger ones in the case when the connectivity was not a priori evident from the structural model. We will show in several examples of nonmolecular structures the effect of the modeling by correct structural units

Coherent-diffraction imaging of single nanowires of diameter 95 nanometers

Photonic or electronic confinement effects in nanostructures become significant when one of their dimension is in the 5-300 nm range. Improving their development requires the ability to study their structure shape, strain field, interdiffusion maps using novel techniques. We have used coherent diffraction imaging to record the 3-dimensionnal scattered intensity of single silicon nanowires with a lateral size smaller than 100 nm. We show that this intensity can be used to recover the hexagonal shape of the nanowire with a 28 nm resolution. The article also discusses limits of the method in terms of radiation damage.

Elastic strain relaxation in GaN/AlN nanowire superlattice

The molecular-beam epitaxy growth of AlN/GaN nanowire superlattices has been studied by using a combination of in situ x-ray diffraction experiments, high-resolution electron-microscopy analysis and theoretical calculations performed in a valence force field approach. It is found that the nanowire superlattices are in elastic equilibrium, in contrast with the two-dimensional case but in line with the predicted increase in the critical thickness in the nanowire geometry.

In situ resonant x-ray study of vertical correlation and capping effects during GaN∕AlN quantum dot growth

Grazing incidence anomalous x-ray scattering was used to monitor in situ the molecular beam epitaxy growth of GaN∕AlN quantum dots (QDs). The strain state was studied by means of grazing incidence multiwavelength anomalous diffraction (MAD) in both the QDs and the AlN during the progressive coverage of QDs by AlN monolayers. Vertical correlation in the position of the GaN QDs was also studied by both grazing incidence MAD and anomalous grazing incidence small angle scattering as a function of the number of GaN planes and of the AlN spacer thickness. In a regime where the GaN QDs and the AlN capping are mutually strain influenced, a vertical correlation in the position of QDs is found with as a side effect an average increase in the QD width.

In situ investigation of the island nucleation of Ge on Si(001) using x-ray scattering methods

The growth of Ge on Si(001) is investigated in situ at 500 and 600°C, combining grazing incidence diffraction, multiple wavelength anomalous diffraction, and small angle scattering. This allows probing simultaneously the island shape, strain state, composition, and the transition from wetting layer to island growth. At 500°C no intermixing occurs. The wetting layer is found to decrease by one atomic layer at the onset of island nucleation. At 600°C interdiffusion plays an important role in strain relaxation leading to a more stable wetting layer. Small angle scattering yields the island morphology and shows the transition from pyramids to multifacetted domes.

Interface-driven phase separation in multifunctional materials: the case of GeMn ferromagnetic semiconductor

We use extensive first principle simulations to show the major role played by interfaces in the mechanism of phase separation observed in semiconductor multifunctional materials. We make an analogy with the precipitation sequence observed in over-saturated AlCu alloys, and replace the Guinier-Preston zones in this new context. A new class of materials, the