Gas electron diffraction: Difference between revisions

Revision as of 13:01, 14 February 2022

Revision as of 19:54, 14 February 2022

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[[File:GED scheme 1.jpg|left|thumb|440x440px|Scheme 1: Schematic drawing of an electron diffraction apparatus]]

[[File:Data reduction.jpg|left|thumb|440x440px|Scheme 2: Data reduction process from the concentric scattering pattern to the molecular scattering intensity curve]]

Figure 1 shows a drawing and a photograph of an electron diffraction apparatus. Scheme 1 shows the schematic procedure of an electron diffraction experiment. A fast [[Cathode ray|electron beam]] is generated in an electron gun, enters a diffraction chamber typically at a vacuum of 10^-7−7 mbar. The electron beam hits a perpendicular stream of a gaseous sample effusing from a nozzle of a small diameter (typically 0.2  mm). At this point, the electrons are scattered. Most of the sample is immediately condensed and frozen onto the surface of a cold trap held at -196 °C ([[liquid nitrogen]]). The scattered electrons are detected on the surface of a suitable detector in a well-defined distance to the point of scattering.

[[File:GED Apparatus.jpg|center|thumb|500x500px|Figure 1: Gas-diffraction apparatus at the University of Bielefeld, Germany]]

[[File:Rotating sector.jpg|alt=Figure 3: Scheme of a rotating sector, placement of the rotating sector within a GED apparatus and two examples of diffraction pattrens recorded with and without rotating sector.|thumb|440x440px|Figure 3: Scheme of a rotating sector, placement of the rotating sector within a GED apparatus and two examples of diffraction pattrens recorded with and without rotating sector.]]

The scattering pattern consists of diffuse concentric rings (see Figure 2). The steep decent of intensity can be compensated for by passing the electrons through a fast rotation sector (Figure 3). This is cut in a way, that electrons with small scattering angles are more shadowed than those at wider scattering angles. The detector can be a [[photographic plate]], an electron imaging plate (usual technique today) or other position sensitive devices such as [[Hybridhybrid pixel detector|hybrid pixel detectors]]s (future technique).

The intensities generated from reading out the plates or processing intensity data from other detectors are then corrected for the sector effect. They are initially a function of distance between primary beam position and intensity, and then converted into a function of scattering angle. The so called atomic intensity and the experimental background are subtracted to give the final experimental molecular scattering intensities as a function of ''s'' (the change of [[momentum]]).

These data are then processed by suitable fitting software like [http://unexprog.org/ UNEX] for refining a suitable model for the compound and to yield precise structural information in terms of bond lengths, angles and torsional angles.

== Theory ==

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== Results ==

[[File:Examples P4 P3As.jpg|thumb|440x440px|Figure 5: Examples of molecular intensity curves (lefte) and their Fourier tranformed, the radial districution curves of P4 and P3As. ]]

Figure 5 shows two typical examples of results. The molecular scattering intensity curves are used to refine a structural model by means of a [[Least-squares function approximation|least squares]] fitting [http://unexprog.org/ program]. This yield precise structural information. The [[Fourier transformation]] of the molecular scattering intensity curves gives the radial distribution curves (RDC). These represent the probability to find a certain distance between two nuclei of a molecule. The curves below the RDC represent the diffrerence between the experiment and the model, i.e. the quality of fit.

The very simple example in Figure 5 shows the results for evaporated white [[phosphorus]], P₄. It is a perfectly tetrahedral molecule and has thus only one P-P distance. This makes the molecular scattering intensity curve a very simple one; a sine curve which is damped due to molecular vibration. The radial distribution curve (RDC) shows a maximum at 2.1994 Å with a least-squares error of 0.0003 Å, represented as 2.1994(3) Å. The width of the peak represents the molecular vibration and is the result of [[Fourier transform|Fourier transformation]]ation of the damping part. This peak width means that the P-P distance varies by this vibration within a certain range given as a vibrational amplitude ''u'', in this example ''u''_T(P‒P) = 0.0560(5) Å.

The slightly more complicated molecule P₃As has two different distances P-P and P-As. Because their contributions overlap in the RDC, the peak is broader (also seen in a more rapid damping in the molecular scattering). The determination of these two independent parameters is more difficult and results in less precise parameter values than for P₄.

Some selected other examples of important contributions to the [[structural chemistry]] of molecules are provided here:

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== Links ==

* http://molwiki.org/wiki/Main_Page -- AMain_Page—A free encyclopaedia, mainly focused on molecular structure and dynamics.

* The story of gas-phase electron diffraction (GED) in [https://www.researchgate.net/publication/332484908_The_story_of_gas-phase_electron_diffraction_GED_in_Norway Norway] <ref>{{Cite journal|last=Kveseth|first=Kari|date=August 2019-08|title=The story of gas-phase electron diffraction (GED) in Norway|url=http://link.springer.com/10.1007/s11224-019-01309-w|journal=Structural Chemistry|language=en|volume=30|issue=4|pages=1505–1516|doi=10.1007/s11224-019-01309-w|issn=1040-0400}}</ref>

==References==