Article pubs.acs.org/JPCC
Powder X‑ray Diffraction Electron Density of Cubic Boron Nitride Nanna Wahlberg,† Niels Bindzus,† Lasse Bjerg,† Jacob Becker,† Sebastian Christensen,† Ann-Christin Dippel,‡ Mads R. V. Jørgensen,† and Bo B. Iversen*,† †
Center for Materials Crystallography, Department of Chemistry and iNANO, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark ‡ DESY Photon Science, Notkestrasse 85, D-22607 Hamburg, Germany S Supporting Information *
ABSTRACT: Conventionally, the core electron density (ED) of atoms in molecules is considered to be virtually unperturbed by chemical bonding effects. Here we report a combined experimental and theoretical investigation of the ED of cubic boron nitride including a detailed modeling of the core ED. By modeling structure factors obtained from very-high-resolution synchrotron powder X-ray diffraction data, it is possible to model not only the valence ED but also the response of the core ED to the effects of chemical bonding. The biggest challenge when studying the core ED is the deconvolution of the thermal motion from the experimental structure factors, since the thermal motion is strongly correlated to core ED deformation. However, atomic displacement parameters could be estimated from a full pattern Rietveld-multipolar refinement, and they are shown to be in good correspondence with ab initio lattice dynamics calculations. The corresponding extended multipole model including both core and valence ED refinement suggests that 2.0 electrons are transferred from the boron atomic basin to the nitrogen atomic basin. The core density was found to deplete upon bonding, which is in line with a significant charge transfer.
1. INTRODUCTION
Cubic boron nitride (cBN, Figure 1) resembles diamond in many aspects: they are isostructural, isoelectronic, and among the hardest materials known to man.8 Though diamond is the
The electron density (ED) is arguably the most informationrich characteristic observable in natural science, and, remarkably, it is available from relatively simple X-ray diffraction experiments.1 Conventionally, X-ray ED analysis is based on modeling of structure factors obtained from accurate singlecrystal X-ray diffraction experiments using atom-centered multipole models.2−4 The multipole model has been used in numerous studies to determine the ED in a great variety of crystals spanning from simple organic molecules to extended inorganic structures and even proteins.5 With the everincreasing accuracy of X-ray diffraction data, more and more complex systems have been addressed, and complemented by a fast moving development of sophisticated methods to analyze the physical and chemical properties of molecules and crystals based on the ED.6 For simple, high-symmetry crystal structures with minimal peak overlap it can be advantageous to use synchrotron powder X-ray diffraction (PXRD) due to negligible extinction and absorption effects and the fact that measurements are done on a single scale. This was demonstrated for diamond based on benchmark PXRD data collected to a sin(θ)/λ resolution of 2.07 Å−1.7 The analysis extended beyond a standard description of the covalent bonding in diamond, and it revealed a contraction of the core−shell. Indeed, within the past few years, the study of core polarization has emerged as a new frontier in chemical bonding studies. © 2015 American Chemical Society
Figure 1. Unit cell of cBN. Black spheres represent boron, gray spheres represent nitrogen. The (110) plane is depicted. Received: December 1, 2014 Revised: February 3, 2015 Published: February 19, 2015 6164
DOI: 10.1021/jp511985d J. Phys. Chem. C 2015, 119, 6164−6173
The Journal of Physical Chemistry C
Article
into account, a more sophisticated model must be applied. One of the most used models is the Hansen−Coppens (HC) multipole model,5 which allows a detailed modeling of the bonding ED. In this model the pseudoatom is divided into an inert core and a deformable valence density. The valence density may be modified by varying the number of electrons, the radial behavior, and by introducing aspherical features:
hardest material, cBN is chemically inert in conditions where diamond reacts.9 In addition to the exceptional hardness, recent theoretical results have suggested thin films of cBN to be conducting.10 The physical properties are related to the bonding between the atoms, and thus the ED. By investigating the ED of cBN we may obtain a deeper insight into the physical origin of these phenomena. To study ED features in the core region it is essential to measure data to very high resolution in reciprocal space. The benchmark diamond data were collected on a recently commissioned vacuum powder diffractometer, which greatly suppresses the background signal stemming from Compton scattering of air.7,11 The availability of accurate structure factors to very high order makes it possible to model the ED in far greater detail than what is done in the standard multipolar refinement. Besides revealing the ED of the inner atom, the accurate high-order structure factors also provide access to a more accurate estimation of the thermal motion of the atoms. The extreme hardness, or more correctly the stiffness, of cBN reduces the thermal diffuse scattering (TDS), which not only contributes to the background, but also to the Bragg peak intensity. The TDS contribution increases with the scattering angle and, consequently, the high-order reflections will be most affected.12 Thus, not only is the high-order Bragg scattering weaker at higher temperature, but the TDS contribution is also larger. If a model is constructed based on the structure factors with significant uncorrected TDS contribution, the main effect will be a decrease in thermal motion. However, uncorrected TDS intensity may also affect the very subtle features in the ED. In the present case of boron nitride the TDS contribution is negligible and it is estimated to be of the same size as for diamond (
