Some notes on the selection of structural chirality by CBED

Johnson, Andrew; Preston, A. R.

doi:10.1016/0304-3991(94)90071-x

Cited by 9 publications

(19 citation statements)

References 9 publications

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“…where P is the periodicity in the z direction and k z = n 2π P , n ∈ N. Because of the periodicity, the latter is quantized, which results in a quantized transferred forward momentum k 0 − k z in Eq. (4). In what follows we consider consider only elastically scattered electrons for which the energy and the magnitude of the wavenumber are conserved during the scattering process.…”

Section: Theoretical Formulationmentioning

confidence: 99%

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Orbital angular momentum in electron diffraction and its use to determine chiral crystal symmetries

Juchtmans

Verbeeck

2015

Phys. Rev. B

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In this work we present an alternative way to look at electron diffraction in a transmission electron microscope. Instead of writing the scattering amplitude in Fourier space as a set of plane waves, we use the cylindrical Fourier transform to describe the scattering amplitude in a basis of orbital angular momentum (OAM) eigenstates. We show how working in this framework can be very convenient when investigating, e.g., rotation and screw-axis symmetries. For the latter we find selection rules on the OAM coefficients that unambiguously reveal the handedness of the screw-axis. Detecting the OAM coefficients of the scattering amplitude thus offers the possibility to detect the handedness of crystals without the need for dynamical simulations, the thickness of the sample nor the exact crystal structure. We propose an experimental setup to measure the OAM components where an image of the crystal is taken after inserting a spiral phase plate in the diffraction plane and perform multislice simulations on α-quartz to demonstrate how the method indeed reveals the chirality. The experimental feasibility of the technique is discussed together with its main advantages with respect to chirality determination of screw axes. The method shows how the use of a spiral phase plate can be extended from a simple phase imaging technique to a tool to measure the local OAM decomposition of an electron wave, widening the field of interest well beyond chiral space group determination.

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Section: Theoretical Formulationmentioning

confidence: 99%

“…Therefore, dynamical scattering is needed where, again, simulations have to be compared with the experiment. An additional difficulty is that not all HOLZ diffraction spots are sensitive to the chirality of the crystal and one has to identify these in order use them to determine the chirality [4,5].…”

Section: Introductionmentioning

confidence: 99%

Orbital angular momentum in electron diffraction and its use to determine chiral crystal symmetries

Juchtmans

Verbeeck

2015

Phys. Rev. B

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“…In the case of low quartz, multiple scattering within the ZOLZ is essential for the identification of mirror planes and hence the indexing (Goodman & Secomb, 1977), and it will be seen later that a modification of the analytical method to be described may possibly be applied to such cases. The present paper is an extension of work on a simple experimental method of hand determination from a single CBED pattern reported by Johnson & Preston (1994). In that paper, the interpretation was made using either full n-beam or three-beam calculations.…”

Section: Introductionmentioning

confidence: 98%

“…It has been known for a few decades that the hand of chiral structures can be determined from convergent-beam electron diffraction (CBED) experiments (Goodman & Secomb, 1977;Goodman & Johnson, 1977;Tanaka et al, 1985;Johnson & Preston, 1994). This ability is due to multiple scattering within the crystal leading to an exit wave on which the relative phases (as well as the amplitudes) of the Fourier coefficients of the crystal potential have a significant influence.…”

Section: Introductionmentioning

confidence: 99%

Chiral determination: direct interpretation of convergent-beam electron diffraction patterns using the series expansion of Cowley and Moodie

Johnson

2007

Acta Crystallogr Sect B

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Given a small number of structure factors of a known chiral structure of unknown hand, it is shown that the hand can be determined from the sign of the contrast difference of two reflections in a suitably oriented convergent-beam electron diffraction (CBED) pattern. A simple formula for this difference, which takes into account all the significant second-order scattering, is derived using the series expansion of Cowley and Moodie for n-beam diffraction. The reason for the success of a three-beam interpretation is investigated. The method is applied to patterns from thin crystals in which a mirror projection symmetry can be found and its validity is demonstrated by agreement with experiment using samples of known hand. The advantages of recording patterns near major zone axes are discussed as well as some other experimental aspects of chiral determination using CBED.

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“…All methods developed so far thus require dynamical simulations and depend in a sensitive way on sample thickness. An additional difficulty appears as not all HOLZ diffraction spots are sensitive to the handedness of the crystal and one has to identify them to be able to determine the chirality 4,5 . In this work, we propose the use of electron vortex beams to break the symmetry imposed by Friedel's law as an alternative way to distinguish SGs in one of the enantiomorphic SG pairs from table (I) without having to rely on dynamical scattering.…”

Section: Introductionmentioning

confidence: 99%

Using electron vortex beams to determine chirality of crystals in transmission electron microscopy

et al. 2015

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We investigate electron vortex beams elastically scattered on chiral crystals. After deriving a general expression for the scattering amplitude of a vortex electron, we study its diffraction on point scatterers arranged on a helix. We derive a relation between the handedness of the helix and the topological charge of the electron vortex on one hand, and the symmetry of the Higher Order Laue Zones in the diffraction pattern on the other for kinematically and dynamically scattered electrons. We then extend this to atoms arranged on a helix as found in crystals which belong to chiral space groups and propose a new method to determine the handedness of such crystals by looking at the symmetry of the diffraction pattern. Contrary to alternative methods, our technique does not require multiple scattering which makes it possible to also investigate extremely thin samples in which multiple scattering is suppressed. In order to verify the model, elastic scattering simulations are performed and an experimental demonstration on Mn2Sb2O7 is given where we find the sample to belong to the right handed variant of its enantiomorphic pair. This demonstrates the usefulness of electron vortex beams to reveal the chirality of crystals in a transmission electron microscope and provides the required theoretical basis for further developments in this field.

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Some notes on the selection of structural chirality by CBED

Cited by 9 publications

References 9 publications

Orbital angular momentum in electron diffraction and its use to determine chiral crystal symmetries

Orbital angular momentum in electron diffraction and its use to determine chiral crystal symmetries

Chiral determination: direct interpretation of convergent-beam electron diffraction patterns using the series expansion of Cowley and Moodie

Using electron vortex beams to determine chirality of crystals in transmission electron microscopy

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