Gas electron diffraction (GED) is one of the applications of
electron diffraction
Electron diffraction refers to the bending of electron beams around atomic structures. This behaviour, typical for waves, is applicable to electrons due to the wave–particle duality stating that electrons behave as both particles and waves. Si ...
techniques.
The target of this method is the determination of the structure of
gaseous molecules, i.e., the
geometrical arrangement of the atoms from which a molecule is built up. GED is one of two experimental methods (besides microwave spectroscopy) to determine the structure of free molecules, undistorted by intermolecular forces, which are omnipresent in the solid and liquid state. The determination of accurate molecular structures by GED studies is fundamental for an understanding of
structural chemistry
Structural chemistry is a part of chemistry and deals with spatial structures of molecules (in the gaseous, liquid or solid state) and solids (with extended structures that cannot be subdivided into molecules).
The main tasks are:
* The formulat ...
.
Introduction
Diffraction occurs because the
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
of electrons accelerated by a potential of a few thousand volts is of the same order of magnitude as internuclear distances in molecules. The principle is the same as that of other electron diffraction methods such as
LEED
Leadership in Energy and Environmental Design (LEED) is a
green building certification program used worldwide. Developed by the non-profit U.S. Green Building Council (USGBC), it includes a set of rating systems for the design, construction ...
and
RHEED, but the obtainable diffraction pattern is considerably weaker than those of LEED and RHEED because the density of the target is about one thousand times smaller. Since the orientation of the target molecules relative to the electron beams is random, the internuclear distance information obtained is one-dimensional. Thus only relatively simple molecules can be completely structurally characterized by electron diffraction in the gas phase. It is possible to combine information obtained from other sources, such as
rotational spectra,
NMR spectroscopy
Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy or magnetic resonance spectroscopy (MRS), is a spectroscopic technique to observe local magnetic fields around atomic nuclei. The sample is placed in a magnetic fiel ...
or high-quality quantum-mechanical calculations with electron diffraction data, if the latter are not sufficient to determine the molecule's structure completely.
The total scattering intensity in GED is given as a
function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-oriente ...
of the
momentum
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
transfer, which is defined as the difference between the
wave vector
In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), ...
of the incident
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
beam and that of the scattered electron beam and has the
reciprocal dimension of
length
Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Interna ...
.
The total scattering intensity is composed of two parts: the atomic scattering intensity and the molecular scattering intensity. The former decreases monotonically and contains no information about the molecular structure. The latter has
sinusoidal
A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the '' sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in m ...
modulations as a result of the
interference
Interference is the act of interfering, invading, or poaching. Interference may also refer to:
Communications
* Interference (communication), anything which alters, modifies, or disrupts a message
* Adjacent-channel interference, caused by extr ...
of the scattering
spherical waves generated by the scattering from the atoms included in the target molecule. The interferences reflect the distributions of the atoms composing the molecules, so the molecular structure is determined from this part.
Experiment
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
electron beam
Cathode rays or electron beam (e-beam) are streams of electrons observed in discharge tubes. If an evacuated glass tube is equipped with two electrodes and a voltage is applied, glass behind the positive electrode is observed to glow, due to ele ...
is generated in an electron gun, enters a diffraction chamber typically at a vacuum of 10
−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
Liquid nitrogen—LN2—is nitrogen in a liquid state at low temperature. Liquid nitrogen has a boiling point of about . It is produced industrially by fractional distillation of liquid air. It is a colorless, low viscosity liquid that is wide ...
). The scattered electrons are detected on the surface of a suitable detector in a well-defined distance to the point of scattering.
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
Photographic plates preceded photographic film as a capture medium in photography, and were still used in some communities up until the late 20th century. The light-sensitive emulsion of silver salts was coated on a glass plate, typically thinn ...
, an electron imaging plate (usual technique today) or other position sensitive devices such as
hybrid pixel detector Hybrid pixel detectors are a type of ionizing radiation detector consisting of an array of diodes based on semiconductor technology and their associated electronics. The term “hybrid” stems from the fact that the two main elements from which th ...
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
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
).
These data are then processed by suitable fitting software lik
UNEXfor refining a suitable model for the compound and to yield precise structural information in terms of bond lengths, angles and torsional angles.
Theory
GED can be described by scattering theory. The outcome if applied to gases with randomly oriented molecules is provided here in short:
Scattering occurs at each individual atom (
), but also at pairs (also called molecular scattering) (
), or triples (
), of atoms.
is the scattering variable or change of electron
momentum
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
, and its absolute value is defined as
:
with
being the electron
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
defined above, and
being the scattering angle.
The above-mentioned contributions of scattering add up to the total scattering
:
where
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:
:
with
,
being the distance between the point of scattering and the detector,
being the intensity of the primary electron beam, and
being the scattering amplitude of the ''i''-th atom. In essence, this is a summation over the scattering contributions of all atoms independent of the molecular structure.
is the main contribution and easily obtained if the atomic composition of the gas (sum formula) is known.
The most interesting contribution is the molecular scattering, because it contains information about the distance between all pairs of atoms in a molecule (bonded or non-bonded):
:
with
being the parameter of main interest: the atomic distance between two atoms,
being the mean square amplitude of vibration between the two atoms,
the anharmonicity constant (correcting the vibration description for deviations from a purely harmonic model), and
is a phase factor, which becomes important if a pair of atoms with very different nuclear charge is involved.
The first part is similar to the atomic scattering, but contains two scattering factors of the involved atoms. Summation is performed over all atom pairs.
is negligible in most cases and not described here in more detail.
is mostly determined by fitting and subtracting smooth functions to account for the background contribution.
So it is the molecular scattering intensity that is of interest, and this is obtained by calculation all other contributions and subtracting them from the experimentally measured total scattering function.
Results
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
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...
fittin
program This yield precise structural information. The
Fourier transformation
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
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
Phosphorus is a chemical element with the symbol P and atomic number 15. Elemental phosphorus exists in two major forms, white phosphorus and red phosphorus, but because it is highly reactive, phosphorus is never found as a free element on Ear ...
, P
4. 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
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
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 P
3As 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 P
4.
Some selected other examples of important contributions to the
structural chemistry
Structural chemistry is a part of chemistry and deals with spatial structures of molecules (in the gaseous, liquid or solid state) and solids (with extended structures that cannot be subdivided into molecules).
The main tasks are:
* The formulat ...
of molecules are provided here:
* Structure of
diborane
Diborane(6), generally known as diborane, is the chemical compound with the formula B2H6. It is a toxic, colorless, and pyrophoric gas with a repulsively sweet odor. Diborane is a key boron compound with a variety of applications. It has attracte ...
B
2H
6
* Structure of the planar trisilylamine
* Determinations of the structures of gaseous elemental
phosphorus
Phosphorus is a chemical element with the symbol P and atomic number 15. Elemental phosphorus exists in two major forms, white phosphorus and red phosphorus, but because it is highly reactive, phosphorus is never found as a free element on Ear ...
P
4 and of the binary P
3As
* Determination of the structure of
C60 and C
70
* Structure of
tetranitromethane
Tetranitromethane or TNM is an organic oxidizer with chemical formula . Its chemical structure consists of four nitro groups attached to one carbon atom. In 1857 it was first synthesised by the reaction of sodium cyanoacetamide with nitric acid.
...
* Absence of local C
3 symmetry in the simplest
phosphonium ylide H
2C=PMe
3 and in
amino-phosphanes like P(NMe
2)3 and
ylide An ylide or ylid () is a neutral dipolar molecule containing a formally negatively charged atom (usually a carbanion) directly attached to a heteroatom with a formal positive charge (usually nitrogen, phosphorus or sulfur), and in which both atoms ...
s H
2C=P(NMe
2)
3
* Determination of intramolecular
London dispersion interaction effects on gas-phase and solid-state structures of diamondoid dimers
Links
* http://molwiki.org/wiki/Main_Page—A free encyclopaedia, mainly focused on molecular structure and dynamics.
* The story of gas-phase electron diffraction (GED) i
Norway
References
{{DEFAULTSORT:Gas Electron Diffraction
Diffraction