Accurate structure analysis with synchrotron radiation. An application to borazone, cubic BN

A re-interpretation of the structure of the silver borate, Ag16B4O10, in the light of the extended Zintl-Klemm concept

The borate Ag₁₆B₄O₁₀ was synthesized at high temperature and at elevated oxygen pressures [Kovalevskiy et al. (2020). Chem. Sci. 11, 962-969]. Its structure consists of [B₄O₁₀]^8- polyanions (isostructural to P₄O₁₀) embedded in an Ag matrix. According to the standard valences Ag⁺, B³⁺ and O^2-, the formula has an excess of eight e^- which the above authors proposed were located, pairwise, in four Ag₄ tetrahedra within the silver substructure. That conclusion was based on the semiconducting and diamagnetic properties, as well as the very small `attractors' of the Electron Localization Function (ELF) found at the centre of these Ag₄ tetrahedra. However, a large overlap of the projected density of states (DOS) of silver and oxygen indicated possible dispersion interactions between both atomic species. In this article, an alternative description is proposed based on the extended Zintl-Klemm concept. The anion [B₄O₁₀]^8- can be formulated as Ψ-[N₄O₁₀] P₄O₁₀, if it is assumed that the eight e^- are transferred to the four B atoms, so converting them into Ψ-N, this then makes sense of its similarity with P₄O₁₀, [N₄(CH₂)₆], adamantane and tetraisopropyladamantane. When the Ag atoms connect to the O atoms, they arrange as the H atoms do in hexamethylenetetramine (HMTA). If the two lone pairs of each of the bridging O atoms in Ψ-[N₄O₁₀] are equated to the C-H bonds in HMTA, then, this same equivalence exists between the C-H bonds and the O-Ag bonds in the compound Ag₁₆B₄O₁₀. The 24 Ag atoms surrounding each [B₄O₁₀]^8- group prolong the sphalerite structure of the borate anion by means of Ag-O bonds which also fit the sphalerite structure formed of AgO. The eight excess electrons might then be distributed between the Ag and the O atoms, so making sense of the mixing of the Ag and O states. The Ag atoms bonded to the O atoms of the [B₄O₁₀]^8- groups form a coat that interconnects the borate anions through Ag-O bonds. To establish the validity of this new proposal, the study needs to be extended to the compound Ag₃B₅O₉.

Continuity of phonon dispersion curves in layered ionic materials

The coupling of lattice vibrations with macroscopic electric fields in ionic crystals is examined from first principles based on density functional theory and density functional perturbation theory. Our analyses show that the coupled optical phonon-photon modes are well represented by using the pure phonon modes evaluated at [Formula: see text] as a basis. In addition, we find that apparent 'discontinuities' and mode 'disappearances' in the phonon dispersion curves of ionic materials for [Formula: see text] in hexagonal and other anisotropic materials are caused by the directional dependence of the Born effective charge tensor which is responsible for this coupling. The full dispersion curves, including the phonon-photon transverse modes are shown to be continuous functions of wavevector. Our work in this report provides a promising tool for first principles evaluation of phonon polaritons that may be accessible to experiment. Explicit examples are explored for cubic and hexagonal BN; the calculated results are in good agreement with previous computational values and available experimental measurements.

Misfit accommodation mechanism at the heterointerface between diamond and cubic boron nitride

Diamond and cubic boron nitride (c-BN) are the top two hardest materials on the Earth. Clarifying how the two seemingly incompressible materials can actually join represents one of the most challenging issues in materials science. Here we apply the temperature gradient method to grow the c-BN single crystals on diamond and report a successful epitaxial growth. By transmission electron microscopy, we reveal a novel misfit accommodation mechanism for a {111} diamond/c-BN heterointerface, that is, lattice misfit can be accommodated by continuous stacking fault networks, which are connected by periodically arranged hexagonal dislocation loops. The loops are found to comprise six 60° Shockley partial dislocations. Atomically, the carbon in diamond bonds directly to boron in c-BN at the interface, which electronically induces a two-dimensional electron gas and a quasi-1D electrical conductivity. Our findings point to the existence of a novel misfit accommodation mechanism associated with the superhard materials.

Interfaces between two materials often show interesting properties. Here, the authors demonstrate that diamond and cubic boron nitride, the hardest materials known, can be grown on top of each other through a novel misfit accommodation mechanism, forming a two-dimensional electron gas at the interface.

How good can our beamlines be?

The accuracy of X-ray diffraction data depends on the properties of the crystalline sample and on the performance of the data-collection facility (synchrotron beamline elements, goniostat, detector etc.). However, it is difficult to evaluate the level of performance of the experimental setup from the quality of data sets collected in rotation mode, as various crystal properties such as mosaicity, non-uniformity and radiation damage affect the measured intensities. A multiple-image experiment, in which several analogous diffraction frames are recorded consecutively at the same crystal orientation, allows minimization of the influence of the sample properties. A series of 100 diffraction images of a thaumatin crystal were measured on the SBC beamline 19BM at the APS (Argonne National Laboratory). The obtained data were analyzed in the context of the performance of the data-collection facility. An objective way to estimate the uncertainties of individual reflections was achieved by analyzing the behavior of reflection intensities in the series of analogous diffraction images. The multiple-image experiment is found to be a simple and adequate method to decompose the random errors from the systematic errors in the data, which helps in judging the performance of a data-collection facility. In particular, displaying the intensity as a function of the frame number allows evaluation of the stability of the beam, the beamline elements and the detector with minimal influence of the crystal properties. Such an experiment permits evaluation of the highest possible data quality potentially achievable at the particular beamline.

Twinning model for a new pseudo-hexagonal BN

A model for a twin consisting of two domains is proposed for a new pseudo-hexagonal modification of high-density boron nitride. A structure refinement based on high resolution diffraction data taken with 0.5 Å synchrotron radiation resulted in R factors below 0.015 for each domain. The refinement against detwinned and composite data converged to R = 0.053, with domain ratio 0.462(2):0.538.

Phase measurement for accurate mapping of chemical bonds in acentric space groups

Although the electron density is fundamental to the study of chemical bonding and density-functional theory, it cannot be accurately mapped experimentally for the important class of crystals lacking inversion symmetry, since structure factor phase information is normally inaccessible. We report the combination of x-ray and electron diffraction experiments for the determination of the electron density in acentric AlN, using multiple-scattering effects in convergent-beam electron diffraction to obtain sensitivity to structure factor phases, and describe a new error metric and weighting scheme for multipole refinement using combined measurements of structure factor magnitudes and phases.

X-ray determination of ‘isoelectronic’ element distribution: A discussion on two-λ versus single-wavelength measurements

Partially or fully ordered distributions of two elements on two crystallographically different positions play an increasingly important role in material and earth sciences. As a consequence of the simple principle ‘what can be studied in reciprocal space (or appropriately selected parts of it), does not deserve Fourier mapping in direct space’, we discuss:

1. For determining distributions of elements with similar atomic numbers, a single-wavelength measurement suffices and gives better results than the combination of data measured at two wavelengths providing different anomalous scattering.

2. The least-squares technique or other procedures employing carefully selected reflections are superior to electron counting from Fourier maps. In particular, a two-λ-difference Fourier, being well suited for obtaining qualitative information about element distributions, cannot be recommended for the derivation of quantitative results.

The conclusions are valid under the assumption that the crystal structure is sufficiently well known, except an ‘order parameter’ describing the preference of one of the two elements for one of the two sites.