Crystal structure determination by direct inversion of dynamical microdiffraction patterns

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The intensity at points where coherent convergent-beam transmission diffraction discs overlap is shown to be described by interference between elements of the same row but different columns of the dynamical scattering matrix for an axial orientation. These intensities are used as the basis for an exact, nonperturbative inversion of the multiple electron scattering problem, allowing crystal structure factors to be obtained directly from the intensities of multiply scattered Bragg beams. Eigenvectors of the structure matrix are obtained using coherent CBED patterns from many crystal orientations. Unique eigenvalues are obtained from these patterns recorded at two accelerating voltages. The inevitable variation in electron probe position at different crystal tilts is considered. The analysis applies to centrosymmetric crystals with anomalous absorption, to centrosymmetric projections of acentric crystals and to acentric crystals if the mean absorption potential only is included. The method would allow the direct synthesis of charge-density maps of unknown crystal structures at high resolution from multiple scattering data, using a scanning transmission electron microscope (STEM). The resolution of this map may be much higher than the first-order d-spacing; however, the STEM need only be capable of resolving this first-order spacing. Such a charge-density map provides fractional atomic coordinates and the identification of atomic species (as in X-ray crystallography) from microcrystalline samples and other multiphase inorganic materials for which large single crystals cannot be obtained or X- ray powder patterns obtained or analysed. In summary, we solve the inversion problem of quantum mechanics for the case of electron scattering from a periodic potential, described by the nonrelativistic Schrodinger equation, in which the scattering is given as a function of some parameter, and the potential sought.

Original languageEnglish (US)
Pages (from-to)214-221
Number of pages8
JournalJournal of Microscopy
Volume190
Issue number1-2
DOIs
StatePublished - 1998

Fingerprint

Crystal structure
Electrons
inversions
Crystals
crystal structure
Electron scattering
Multiple scattering
Charge density
crystals
Electron microscopes
Scattering
Schrodinger equation
Scanning
electron scattering
electron microscopes
spacing
Quantum theory
X ray crystallography
Eigenvalues and eigenfunctions
Crystal orientation

Keywords

  • Crystal structure
  • Dynamical scattering

ASJC Scopus subject areas

  • Instrumentation

Cite this

Crystal structure determination by direct inversion of dynamical microdiffraction patterns. / Spence, John.

In: Journal of Microscopy, Vol. 190, No. 1-2, 1998, p. 214-221.

Research output: Contribution to journalArticle

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