Standard Schlenk techniques, using argon as the purge gas, were utilised in the synthesis of ionic liquids due to their hygroscopic nature. The argon gas was passed through anhydrous calcium sulphate before use in order to ensure a dry environment. All glassware was oven-dried and purged three times with argon prior to use.
3.3: X-ray Diffraction
3.3.1: Introduction and X-ray Generation
X-ray diffraction data is traditionally of importance to chemists as a tool for crystal structure determination. The information obtained relates to the crystal lattice of the material, and can be used to help characterise the crystalline phases present. X-rays are diffracted by electrons and the information from an X-ray diffraction study concerns the electron density distribution.
X-rays are short-wavelength electromagnetic radiation with a wavelength, λ, in the
range of 0.1 to 100 Å. X-rays are typically generated in the laboratory by bombarding a metal with high-energy electrons produced by heating a metal filament until it becomes white hot, emitting photo-electrons. The electrons rapidly decelerate as they enter the metal and collide with the metal atoms, generating radiation with a continuous range of wavelengths called Bremsstrahlung. Superimposed on this are a few high-intensity, sharp peaks (Figure 3.2) which are characteristic of the target material.
Intensity
Wavelength
Figure 3.2: Bremsstrahlung background with high-intensity sharp transition peaks superimposed on it.
The high-intensity sharp peaks arise from the interaction of the incoming electrons with the electrons in the inner shells of the target material atoms as illustrated in Figure 3.3. This works by an incoming electron colliding with an electron in the inner shell K (i.e. a shell where n=1) transferring enough energy to eject it. Another electron from the higher energy shell (e.g. L shell, i.e. n=2) falls into the vacancy and emits the excess energy as an X-ray photon. The emitted X-ray photon has the energy that is equal to the difference between the upper and lower energy levels of the electron that filled the core hole. X-ray Energy Ejected electron Ionization Electron beam L K
3.3.2: Crystallographic Space Groups
In order to solve a crystal structure it is first necessary to assign a unit cell. This is the smallest repeating unit which shows the full symmetry of the crystal structure. There are seven unique crystal systems possible in three-dimensional crystal structures (Figure 3.4). a a a a a c a b c a b c β a b c a β γ α a a c 60° 120° a a a α α α
cubic tetragonal orthorhombic monoclinic
triclinic hexagonal trigonal
Figure 3.4: The seven crystal systems and their unit cell shapes
The unit cell of the crystal is repeated on a regular three-dimensional space lattice to form the complete crystal. This gives one lattice point per unit cell, resulting in a so- called primitive lattice, P. However sometimes it is more convenient to have more than one lattice point per cell, resulting in centred lattices (face centred, F; side centred, C or body centred, I). There are 14 different Bravais lattices which arise from all the possible centrings in each crystal system.
Each crystal system is governed by the presence or absence of symmetry. A symmetry element is a physically identifiable point, line, or plane in a molecule about which symmetry operations are applied. A symmetry operation is a reflection in a plane, a rotation about a line or an inversion through a point which leaves the molecule afterwards with an identical appearance. All symmetry operations can be classified as proper rotations (rotations by a certain fraction of 360 º about a rotation axis), or improper rotations (the combination of a rotation and a simultaneous reflection in a plane perpendicular to the axis and passing through the centre of the molecule). In three-dimensional crystals, a rotation or reflection can be combined with translation to give, respectively, screw axes and glide planes.
The total collection of all the symmetry operations for a molecule is called a point group, and each group has its own characteristic properties and a conventional symbol. These symmetry operations can be combined in 32 different ways giving 32 crystallographic point groups which are compatible with the periodic nature of crystals. The combined configuration of a crystallographic point group repeated on a Bravais lattice is a space group. A space group describes the symmetry of the atomic structure of the crystal. The total number of possible space groups is 230.
3.3.3: Diffraction of X-rays by Crystals
A crystal is made up of a three-dimensional regular arrangement of atoms with a repeating pattern. This leads to an internal periodicity that acts as a diffraction grating for the X-rays. The observed pattern is the result of the constructive and destructive
interference of the X-rays scattered by all the regularly arranged atoms (Figure 3.6).4
a)
b)
Figure 3.6: a) Constructive interference (waves exactly in phase), b) Destructive interference (waves exactly out of phase)
To observe any diffraction intensity, there must be constructive interference between all the waves diffracted by the electrons in the crystal lattice (Figure 3.7). For constructive
interference, the path length difference (2dsinθ) between scatterings from successive
planes must be an integer number of wavelengths (nλ). θ is the incident angle and
constructive interference is observed when the incident angle satisfies Bragg’s law :
nλ = 2dsinθ