Powder X-Ray Diffraction (PXRD)

PXRD is a technique frequently used for phase identification of a sample and to give information on crystal structure. Although SEM, TEM, SAED and EDX can give important information on the local microstructure of materials, PXRD is helpful when it is necessary to

29

study the bulk powder (for example, to determine if the material is made up of multiple phases). In this research, PXRD patterns were obtained by using a PANalytical Empyrean diffractometer, where the Cu Kα x-ray source (with a wavelength of 0.15418 nm) was produced by bombarding copper metal with high-energy electrons. The patterns produced were analysed using the Highscore Plus software. PXRD has been used in this research to identify the phases present in each of the materials studied and to support crystallinity data that had been obtained through SAED (14).

Figure 2.8. Illustration of the formation of PXRD patterns in reflection mode. The patterns were obtained by rotating the angle between the sample and detector across a range of θ values (15).

In order to prepare specimens for PXRD analysis, the powder samples were finely ground to ensure homogeneity and then carefully deposited onto a low background silicon wafer, which had been coasted with a thin layer of petroleum jelly. This wafer was then placed inside a specialised PXRD holder. Data was collected in reflective mode where the incident high energy X-rays penetrate the sample a number of microns beneath the surface before being deflected towards a detector (Figure 2.8). The alternative method to this is to collect the data in transmission mode where the high energy X-rays travel through the sample and are collected by the detector on the other side. Due to the randomly oriented nature of the crystalline domains in a powdered sample, either mode should produce the same data. In both

30

cases, a monochromator (an optical device that only transmits a selective wavelength of light) is used to allow only Cu Kα radiation to reach the detector and to filter out any unwanted X- rays such as Cu Kβ radiation. In reflection mode, the monochromator is positioned over the detector, whereas in transmission mode the X-rays pass through the monochromator before reaching the sample.

To enable us to observe all possible peaks, the detector will be rotated through a range of θ values (see Figure .8) and the number of counts at each angle will be recorded, allowing the computer to generate the XRD pattern. The range of angles should be selected based on where peaks should appear for the phases present in the sample. For example, in this project the range of θ values used was 5° to 80° for the ZnO samples and 10° to 80° for the CaCO3 samples as there were no expected peaks below 10° for CaCO3. The scanning speed can also be altered by the user in order to regulate the time it takes to acquire the spectrum and to adjust the signal-to-noise ratio for the diffraction peaks. As every peak in the PXRD pattern corresponds to a different d-spacing, and as every crystalline material has unique d- spacings, the PXRD patterns can be compared to standard reference diffraction patterns from databases such as the Inorganic Crystal Structure Database (ICSD) in order to determine which materials/phases are present (16).

In PXRD the 3D arrangement of atoms within a crystalline sample acts as a diffraction grating to the incident X-ray beam. The atoms are arranged into planes of various orientations with an interplanar distance, d. When the X-rays reach these planes they interact with the electrons in the atoms and are diffracted at a range of angles. The mix of constructive and destructive interference of the diffracted beams then generates the diffraction pattern. Sharp, crystalline peaks are observed in the patterns when Bragg’s Law, Equation . , is obeyed where n is an integer number, λ is the wavelength of the incident X- rays, d is the distance between planes in the atomic lattice and θ is the angle between the incident X-ray and the atomic plane (known as the Bragg angle).

nλ = dsinθ (2.2)

The parameters for Bragg’s Law are illustrated in Figure .9 where it can be seen that an incident X-ray interacting with an inner plane of atoms (labelled b) must travel further

31

than an X-ray which interacts with an outer plane (labelled a). The extra length travelled by beam b is equal to 2dsinθ. Bragg’s Law is satisfied, and therefore constructive interference

occurs, only when this distance is equal to an integer number of multiples of the wavelength of the incident radiation.

Figure 2.9. Illustration of the parameters used to derive Bragg’s Law.

The broadening of the peaks in PXRD patterns can be used to determine the average size of ordered, crystalline domains, τ, using the Scherrer equation (Equation 2.3) where K is the shape factor, λ is the wavelength of the incident X-rays, β is the line broadening of a peak at half the maximum intensity in radians (also referred to as the full width at half maximum, FWHM) and θ is the Bragg angle. The shape factor, K, is dimensionless with a value close to unity, it varies with the actual shape of the crystallite so in the current work when the Scherrer equation is used, calculations are based on K = 0.92 as this is the typical value for a spherical crystallite (17).

32