Radiation sources for diffraction

2.2.4.1. X-ray sources

X-rays are electromagnetic radiation of wavelength ~ 1Å[27]. They can be generated either by laboratory or synchrotron sources through different processes, but in both cases resulting in monochromatic X-rays required for XRD[129]. In XRD experiments, the intensity of the diffracted beam is measured as a function of 2θ, which is the angle between the diffracted and undiffracted beams.

In laboratory based powder X-ray diffractometers[27, 129], electrons are produced by heating a metal filament, usually tungsten, and then accelerated through a voltage of 40 kV to bombard a metal target, usually made of copper, cobalt or molybdenum. The instrument used in this thesis had a cobalt target. The bombardment of high energy electrons causes ionisation of the core K- shell (n=1) electrons of the target anode. Electrons from outer orbitals fill the holes created in the core shell by the ionisation of ions; by this X-rays are emitted with energy corresponding to the energy gap between the two electronic states and hence have different wavelength than the radiation for diffraction. Electrons originating from the L shell (n = 2) give rise to Kα radiation, and electrons from the M shell (n = 3) give rise to Kβ radiation; both comprise of two components: Kα1 and Kα2, and Kβ1 and Kβ2, respectively, because the transition has a slightly different energy for the two possible spin states of an electron. The Kα radiation is more intense than Kβ, as it occurs more often, and it is the one used in diffraction experiments. Since a monochromatic X-ray beam is desired for the XRD experiments, the Kβ radiation has to be removed; Kβ1 is absorbed by appropriate filters depending on the target material (Fe filter for Co target) and Kβ2 can be removed with the use of an appropriate monochromator.

In a synchrotron[19, 130], the electrons are produced in an electron gun where the cathode is under high voltage and heated in a vacuum. The electrons are accelerated to near light-speed by a sequence of particle accelerators and finely tuned bending magnets, producing an extremely intense synchrotron radiation in large storage rings. The synchrotron radiation consists of wavelengths from infra-red to X-rays; a specific X-ray wavelength can be selected by using appropriate monochromators.

Page | 50 2.2.4.2. Neutron sources

Accelerated particles, such as neutrons, possess wave-like characteristics as described by the de Broglie relationship (Equation 2.9). The neutrons that are used for diffraction have wavelengths of the order 0.5 to 3 Å[27, 131]

.

Equation 2.9

where p is momentum and h the Planck constant

The generation of neutrons for diffraction is expensive and hazardous, and is therefore carried out at specialised facilities. There are two types of neutron sources: reactor sources and spallation sources[131]. The reactor source at the Institut Laue-Langevin (ILL) facilities in Grenoble, France, produces neutrons by nuclear fission of 235U. The ND data presented in this thesis were collected at ISIS facility (Rutherford Appleton Laboratory in Oxfordshire, UK) which is a spallation neutron source. The production of neutron by spallation is based on the collision of a high energy proton beam into the nuclei of a heavy-metal target (in ISIS, it is a tungsten target). This results in the destruction of a metal nucleus into two or three smaller nuclei and several neutrons. The spallation process yields about 30 neutrons per proton.

In ISIS, the beam of protons is produced by an 800 MeV proton accelerator, consisting of an injector and a synchrotron, producing intense pulses of protons 50 times a second[132]. This generates high energy neutrons, which are slowed down by moderators to useful speeds for research and directed to the neutron beamlines were experiments are carried out. The detectors are at fixed 2θ scattering angles and the diffracted radiation is recorded as a function of neutron time of flight (t.o.f), which is defined as the time that a neutron needs to reach the detector, and wavelength. Neutron wavelength ( ) is related to its velocity (v) by the de Broglie relationship (Equation 2.9), by expressing the momentum (p) as the multiplication product of velocity and mass of nucleus:

Equation 2.10

Page | 51 By considering a fixed path length (distance, L) of the neutron from moderator to detector and the time of flight (t) taken for a neutron to reach the detector, the relationship gives:

Equation 2.11

Combining this expression with Bragg’s law (Equation 2.1), it is possible to relate the neutron time of flight (t) to d-spacing.

Equation 2.12

Hence, by using detectors at fixed 2θ positions and a fixed path length L, the values of interplanar spacing d, defined by the Miller indices, can be determined by using neutron time- of-flight (t.o.f.) as the variable.

The resolution of ND diffraction data[133], as expressed by the uncertainty in d-spacing (Δd), is affected by the uncertainties in timing ( ), angle ( ) and path length ( ), as given in Equation 2.13.

Equation 2.13

The uncertainty in timing ( ) is mainly influenced by the moderation time of the neutron, during the moderation process. The error in path length ( ) originates from the thickness of the moderators and the widths of sample and detectors. As can be deduced from Equation 2.13 the resolution increases when using a long flight path (L) between the moderator and the detector, which also increases the time of flight (t), for a given detector angle (Δθ=0). Maximum resolution can be reached when the detector angle are approximately at 2θ= 180ο or θ=90 ο and the cot2θ factor in Equation 2.13 becomes zero.

Page | 52 2.2.4.3. Electron sources

Electrons[27, 123, 124] have wave characteristics, usually λ= 0.0087-0.037Å, which allow them to be used for diffraction experiments. As aforementioned ED is usually combined with electron microscopes which operate either in transmission or reflection mode[27]. The principles of electron microscopes are further discussed in Section 2.3. In electron microscopes, electron beam is produced by electron guns and are accelerated through a high voltage (usually 50 to 300keV). The electron guns provoke electron emission in two different ways: either heating of a W or LaB6 filament (thermionic gun) or by applying an extraction voltage (field emission gun). The wavelength (λ) of the electron beam is related to the accelerating voltage (V):

Equation 2.14

where m and e- are the mass and charge of the electron and h the Planck constant. This relation is derived from combination of the de Broglie relation (λ= h/p= h/m , Equation 2.10, Section 2.2.4.2, page 50) where the velocity is related to the kinetic energy of the electrons (Ekin= ½ m 2), which is equal to the energy provided (E= eV).

At the high acceleration voltages reached in electron microscopes, the velocity of electrons reaches the speed of light (c= 2.998 x 108 m/s) and relativistic effects have to be taken into account for accurate determination of the wavelength (λ) of the electron beam (Equation 2.15).

Equation 2.15

Page | 53