Determination of the electrostatic potential and electron density of silicon using convergent-beam electron diffraction

Abstract

A structure-analysis method using convergent-beam electron diffraction (CBED) developed by Tsuda et al. [Tsuda & Tanaka (1999), Acta Cryst. A55, 939-954; Tsuda, Ogata, Takagi, Hashimoto & Tanaka (2002), Acta Cryst. A58, 514-525] has been applied to the determination of the electrostatic potential and electron density of crystalline silicon. CBED patterns recorded at nine different incidences are simultaneously used to improve the accuracy of the refinement. The Debye-Waller factor and low-order structure factors of silicon have been successfully refined only using CBED data. The electrostatic potential and electron-density distribution have been reconstructed from the refined parameters. The latter clearly shows the bonding electrons between the nearest neighbor atoms. The obtained results are compared with the results of other CBED and recent X-ray diffraction experiments. The influence of the number of refined low-order structure factors on the electron density is discussed. The effect of the reduction of experimental data points on the accuracy of the refined parameters is also examined.

Developing orbital-free quantum crystallography: the local potentials and associated partial charge densities

“…This work exploits the data of the accurate X-ray diffraction experiment. It is important that the electrostatic and exchange potentials in solids may be also directly measured by scanning transmission electron microscopy at subatomic spatial resolution and electron holography (Spence, 1993;Avilov et al, 1999;Ogata et al, 2008;Winkler et al, 2020). Therefore, static PAEM potential may be expressed via quantities, accessible for different experimental methods.…”

Direct observation of rotation of polarization at 90-degree domain walls in BaTiO3

“…A Bloch-wave dynamical diffraction simulation code MBFIT was used to calculate intensity distributions of CBED patterns. 41,[52][53][54][55][56]…”

Improvement of precision in refinements of structure factors using convergent-beam electron diffraction patterns taken at Bragg-excited conditions

“…The determination of low-order structure factors using CBED has been reported by many researchers (Zuo et al, 1988(Zuo et al, , 1997(Zuo et al, , 1999(Zuo et al, , 2000Spence & Zuo, 1992;Spence, 1993;Deininger et al, 1994;Saunders et al, 1995Saunders et al, , 1996Tsuda & Tanaka, 1999;Streltsov et al, 2001Streltsov et al, , 2003Tsuda et al, 2002Tsuda et al, , 2010Zuo, 2004;Wu et al, 2004;Zheng et al, 2005;Friis et al, 2003Friis et al, , 2004Friis et al, , 2005Jiang et al, 2003Jiang et al, , 2004Ogata et al, 2004Ogata et al, , 2008Sang et al, 2010Sang et al, , 2011Sang et al, , 2013Saeterli et al, 2011;Nakashima et al, 2011;Nakashima, 2017). Ogata et al (2008) and Nakashima et al (2011) considered that the refinement of loworder structure factors using CBED patterns taken at slightly tilted incidences satisfying Bragg conditions of the reflections increases the sensitivity to the corresponding structure factors. However, the comparison between structure factors determined from the zone-axis (ZA) and Bragg-excited CBED patterns, which is pivotal for discussing their precision and sensitivities in the study of chemical bonding, has not been reported.…”