Gas electron diffraction: Difference between revisions

Revision as of 16:20, 19 December 2018

Revision as of 10:14, 20 December 2018

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{{DEFAULTSORT:Gas Electron Diffraction}}

[[Category:Diffraction]]

'''Theory'''<ref>{{Cite book|title=Stereochemical Applications of Gas‐Phase Electron Diffraction, Part A: The Electron Diffraction Technique|last=Hargittai|first=I.|publisher=VCH Verlagsgesellschaft|year=1988|isbn=3‐527‐26691‐7/0‐89573‐337‐4|___location=Weinheim|pages=}}</ref>

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Scattering occurs at each individual atom (<math> I_a(s)

</math>), but also at pairs (also called molecular scattering) (<math> I_m(s)

</math>), or triples (<math> I_t(s)

</math>), of atoms.


<math> s

</math> is the scattering variable or change of electron momentum and its absolute value defined as

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</math>being the scattering angle

The above mentionend contributions of scattering add up to the total scattering (<math> I_{tot}(s)

</math>):

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</math>, whereby (<math> I_b(s)

</math>is the experimental background intensity, which is needed to describe the experiment completely

The contribution of individual atom scattering is called atomic scattering and easy to calculate.

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</math>is the main contribution and easily obtained if the atomic composition of the gas (sum formula) is known.

The most interesting contribution is the moleculkarmolecular scattering, because it contains information about the distance between all pairs of atoms in a molecule (bonded or non-bonded)

<math> I_m(s) = \frac{K^2}{R^2}I_0\sum_{i=1}^N \sum_{j=1,i\neq j}^N \mid f_i(s)\mid\mid f_j(s)\mid \frac{\sin [s(r_{ij}-\kappa s^2)]}{sr_{ij}}e^{-(1/2 l_{ij} s^2)} \cos [\eta _i (s) -\eta _i (s)]

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</math>is a phase factor which becomes important if a pair of atoms with very different nuclear charge is involved.

The fisrtfirst part is sililarsimlilar to the atomic scattering, but containingcontains two scattering factors of the involved atoms. Summation is performed over all atom pairs.

<math> I_t(s)

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</math>is mostly determined by fitting and subtracting smooth functions to account for the background contribution.

So it is the molecular scatterinscattering intensity that is of interest, and this is obtained by calculation all other contributions and subtracting them from the experimentallylexperimentally measured total scattering function.