X-ray diffraction

This section describes the basics of (angle dispersive) XRD and show how it can be used to determine the atomic structure of materials. This section also provides details of the synchrotron X-ray source and equipment used to measure the results that are presented in this thesis.

The basics of XRD

XRD is a characterisation technique based on the constructive interference of monochro- matic X-rays and is used to identify crystal structures and atomic spacings. In this technique a collimated beam of monochromatic X-rays is incident towards a sample, where some of the X-rays will interact with electrons present in the sample and they will be scattered, or diffracted, at a specific angle θ towards a detector, as shown in Fig. 3.15(a). This angle θ directly relates to both the energy (or wavelength) of the

incoming X-ray and the distance between atomic planes within the sample, referred to as dhkl. This distance, dhkl, can be determined using Bragg’s law

Figure 3.15: (a) A diffraction schematic explaining Bragg’s law. Image taken from ref [178]. (b) A schematic showing a diffracted X-ray beam projected onto a detector. Image adapted from ref [179].

nλ= 2dhklsin(θ) (3.2)

where n is a positive integer, λ is the wavelength of the incident X-rays, and θ is dependent on where the specific diffracted X-rays hit the detector. For Bragg’s law to be satisfied, a non-zero component of the diffracted plane must lie parallel to the incident beam.

A schematic drawing is shown in Fig. 3.15(b) of X-rays being diffracted from an isotropic polycrystalline material. For a specific dhkl within the sample the X-

rays diffract at an angle of 2θ relative to the incident beam which is measured on the detector. Now that θ and λ are known, a value for dhkl can be calculated. All

materials will have several characteristic dhkl spacings that relate to their crystal

structure and atomic composition.

For the example shown in Fig. 3.15(b), a diffraction ring is produced (not a spot). This is because the specific planes in the individual crystals are oriented

randomly relative to the incoming beam, as would be the case for a highly disordered or amorphous material which is relevant to this thesis. It is also important to note that the interaction cross-section of an X-ray with an atom is purely related to the number of electrons per atom, which generally increases with the atomic number, Z [180]. This is unfortunate for the experiments conducted in this thesis, as all materials exposed to X-rays for diffraction experiments are highly disordered and made from carbon.

X-ray diffraction facility and equipment

All XRD data presented in this thesis were measured at the Advanced Photon Source (APS). The APS is a 7 GeV third generation synchrotron hard X-ray radiation source located at Argonne National Laboratory near Chicago, USA. An aerial image of the APS is shown in Fig.3.16(a).

Figure 3.16: (a) An aerial image of the Advanced Photon Source at Argonne National Laboratory. Image adapted from ref [181]. (b) A schematic drawing of sector 16’s detector hutches. Image taken from ref [182].

The source of this synchrotron is a hot cathode electron gun which emits pulses of electrons. These electron pulses are initially accelerated to 250 MeV and are directed towards a tungsten target, where they collide and are converted into positrons and

further accelerated using a linear accelerator to 450 MeV. Once at 450 MeV they enter a booster (or injector) ring where they are accelerated further to 7 GeV [183]. Once they reach 7 GeV they are then injected into the main storage ring as shown in Fig. 3.16(a).

Around the main storage ring there are 40 straight sections. One of these straight sections is set aside for positron injection from the booster ring, four sections are used to replenish energy lost traveling around the ring, and the remaining 35 sections are utilised for experiments and are referred to as sectors.

All of the XRD measurements presented in this thesis were performed at sector 16, which is commonly referred to as the High Pressure Collaborative Access Team (HPCAT). HPCAT’s location on the main storage ring is shown in Fig. 3.16(a). This sector is comprised of several experimental “hutches”, as shown in Fig. 3.16(b). All measurements in this thesis were taken using the insertion device undulator beamline 16-ID-B.

Figure 3.17: (a) A schematic drawing of the HPCAT ID-B experimental table. Image taken from ref [182]. (b) A photo of the HPCAT ID-B experimental table.

X-ray source from the main storage ring and focus it toward the ID beamlines at HPCAT [182]. This white beam passes through a branching diamond double crystal monochromator (BDCM) which directs it down the ID-B beam path. The BDCM can be adjusted to provide a high flux beam with a monochromatic energy selected in the range 18-60 KeV. The beam then enters the ID-B experimental hutch, as shown in Fig. 3.17(a), where it passes through a set of Kirkpatrick-Baez (KB) mirrors designed to focus it down to a spot size with a FWHM of 3×6µm and a flux of ∼1012 _photons

per second [184].

An electrically controlled high precision stage is used to align the sample relative to the beam. A narrow tube with an inner diameter of 25-50 µm, referred to as a pinhole, is inserted between the KB mirror assembly and sample to limit air scattering. After interacting with the sample the diffracted beam is recorded on a 1M-Pilatus detector, as shown in Fig. 3.17(b). The sample/detector setup is calibrated using a well-characterised CeO2 powder diffraction sample. The software associated with this

experimental setup is called DIOPTAS [185] which is used to integrate and remove background from raw diffraction spectra.