Experimental determination of core electron deformation in diamond

Abstract

Synchrotron powder X-ray diffraction data are used to determine the core electron deformation of diamond. Core shell contraction inherently linked to covalent bond formation is observed in close correspondence with theoretical predictions. Accordingly, a precise and physically sound reconstruction of the electron density in diamond necessitates the use of an extended multipolar model, which abandons the assumption of an inert core. The present investigation is facilitated by negligible model bias in the extraction of structure factors, which is accomplished by simultaneous multipolar and Rietveld refinement accurately determining an atomic displacement parameter (ADP) of 0.00181 (1) Å(2). The deconvolution of thermal motion is a critical step in experimental core electron polarization studies, and for diamond it is imperative to exploit the monatomic crystal structure by implementing Wilson plots in determination of the ADP. This empowers the electron-density analysis to precisely administer both the deconvolution of thermal motion and the employment of the extended multipolar model on an experimental basis.

Spatial distribution of electrons near the Fermi level in the metallic LaB6 through accurate X-ray charge density study

“…The technique successfully determined the detailed charge density features which were quantitatively comparable to those determined theoretically17202122232425. Recently, the charge density studies from ultra-high resolution synchrotron radiation powder diffractions have been reported using an all-in-vacuum diffractometer installed at PETRA-III26. Core electron deformations of diamond26, silicon27 and cubic boron nitride28, and anharmonic thermal vibration of copper29 have been observed from powder diffraction data.…”

“…Recently, the charge density studies from ultra-high resolution synchrotron radiation powder diffractions have been reported using an all-in-vacuum diffractometer installed at PETRA-III26. Core electron deformations of diamond26, silicon27 and cubic boron nitride28, and anharmonic thermal vibration of copper29 have been observed from powder diffraction data. Several analytical procedures such as Wilson plot26272829, and uncertainty estimation using particle statics27 were used in the studies.…”

“…Core electron deformations of diamond26, silicon27 and cubic boron nitride28, and anharmonic thermal vibration of copper29 have been observed from powder diffraction data. Several analytical procedures such as Wilson plot26272829, and uncertainty estimation using particle statics27 were used in the studies. These techniques are under development since it still depends on materials262728.…”

Raman spectroscopic features of the neutral vacancy in diamond from ab initio quantum-mechanical calculations

“…The atomic thermal ellipsoids of pure diamond are perfectly spherical and the corresponding ADP has a value which is commonly reported in the range (16.1-22.3) Â 10 À4 Å 2 , with a recent accurate determination of 18.1 Â 10 À4 Å 2 . 59 The ab initio evaluation of ADPs requires lattice dynamical calculations to be performed by accounting for phonon dispersion. Within the direct space (frozen phonon) approach adopted here, increasing the size of the SC in the lattice dynamical calculation corresponds to increasing the sampling of the phonon dispersion within the first Brillouin zone in reciprocal space.…”

Bonding Nature of LiCoO₂ by Topological Analysis of Electron Density from X-ray Diffraction

“…In addition, stable third-generation SR X-ray sources enable us to measure the high quality diffraction data. 8,9 We have developed a method for determining accurate charge densities using multiple overlaid SR powder data sets. 8,[10][11][12] The error of the structure factors determined by the method is less than 1.0%, which is comparable to that of the very accurate Pendellösung method 13 which needs a large perfect crystal of well-defined wedge shape and target materials have been extremely limited such as silicon.…”