X-Ray Diffraction (XRD)

The application of X-rays to establish the crystal properties of a material was not realised until the early part of the 20^* century. XRD is a tool for investigating the fine structure of matter, however an introduction of the lattice and crystalline structure is presented first to allow for a better understanding of the principles of this technique.

A crystal is usually composed of atoms, ions or molecules that are termed asymmetric units. The location of these units forms a pattern which is repeated to form the structure. This pattern of particles is termed unit cell. The length of the sides and the angles between them constitute the parameters used to define the unit cell known as the lattice constants. Lengths are given as a, b and c while angles are a, (3 and y. According to their arrangement, unit cells

unit cells in three dimensions is known as Bravais lattices. Miller indices are another important feature in the description of the unit cells and are defined as

the reciprocals of the fractional intercepts which the plane makes with the

crystallographic axes (Cullity 1978) and are usually referred to as (h, k, I)

planes. The separation of planes is denoted by d-spacing known as the interplanar spacing dhki, which describes the distance between similar atomic planes in a mineral (the interatomic spacing) and measured in angstroms,

A

(Shriver ef a/. 1995).

Although X-rays were discovered in 1895 by Roentgen, this was without any precise understanding of the radiation. In 1912 Max von Laue established the exact nature of X-rays and suggested that they are diffracted as they pass through a crystal in a manner similar to the reflection of light off a mirror. He also suggested that there was a relationship between the wavelengths of the X- rays and the d-spacings of the planes in the crystal (Cullity 1978).

X-rays are electromagnetic radiation of exactly the same nature as light but with shorter wavelengths and can be produced through the acceleration of electrons from a hot tungsten filament across a high voltage towards the anode housing the metal target (usually copper in XRD systems) at high velocity, resulting in X-ray production at the point of impact and radiation in all directions. The International System of Units 81 unit for measuring X-ray wavelengths is nanometre, nm (1 nm = 10

A).

X-rays that are made up of many wavelengths are white radiation also known as continuous or Bremsstrahlung. If the voltage in the X-ray tube is increased, sharp intensity maxima appear at certain wavelengths superimposed on the continuous spectrum. These narrow wavelengths are characteristic of the metal target thus known as characteristic

lines K, L, M. etc. X-ray diffraction uses the K lines only as the other lines are easily absorbed.

It is now established that diffraction occurs when X-rays interact with a regular structure whose repeat distance is about the same as the wavelength. X-rays have wavelengths on the order of a few Angstroms, the same as typical interatomic distances in crystalline solids. A beam of incoming X-rays may be reflected in a constructive interference when the crystal is oriented at a calculated angle based on the model of lattice planes. It is thus, a plane at a given angle that is responsible for the reflection of X-rays in such a constructive interference. Yet most beams do not interfere constructively and are out of phase. Only during constructive interference is the path length difference an integral number of wavelengths. This relation is summarised in Braggs law:

/l= 2dsin0

Equation 2.1 where

X = wavelength in A

0 = the diffraction angle in degree d = the interatomic spacing in A

The diffracted beam makes an angle 0 of reflection equal to the angle 0 of incidence (Van Grieken et al. 2002). 0 of incidence is measured between the incident beam and the particular crystal plane under consideration (Figure 2.5)

Figure 2.5 Bragg m odel o f lattice planes.

It is worth noting that the diffracted beam is stronger than all reflected beams but is much weaker than the incident beam. Unlike reflection of visible light from a thin surface layer, the diffracted beam consists of a number of rays scattered by all the atoms of the crystal which lie in the path of the incident beam. Diffraction takes place only at angles of incidence satisfying Bragg’s law and requires monochromated K line X-rays while reflection of visible light occurs at any angle of incidence. Finally the reflection of light off a good mirror is 100% whereas the intensity of the diffracted beam is much weaker.

A diffractometer uses X-rays to record diffraction patterns from any crystalline solid. With a diffraction pattern, an unknown mineral can be identified or the atomic-scale structure of an already identified mineral can be characterized. A flat plate is used for mounting the samples, and the intensities of the reflections and the diffraction patterns are collected and interpreted electronically. Systematic X-ray diffraction data for thousands of mineral species are available for comparison purposes, most of which is collected and published by the JCPDS-lnternational Centre for Diffraction Data, which uses chronological or random order in listing substances. Alternatively the American Society for Testing and Materials (ASTM) cards and files can be referred to, as they characterise each substance by d values of the three strongest lines di, 62

and d3.

The X-ray tube consists of an electron source, high acceleration voltage and a metal target. Due to the high voltage difference between the tungsten filament and copper target, electrons from the filament are accelerated and hit the copper target with enough energy to produce the characteristic X-rays of copper. As heat is generated during the production of X-rays a cooler is normally required to cool the X-ray tube.

In summary, XRD is based on the scattering phenomenon, where the scattered rays have definite phase relations between them due to the periodic arrangement of the atoms in the crystal. Although the majority of the reflected rays interfere in a destructive manner, a few constructive interferences take place forming the diffracted beam. Characteristic diffraction patterns can be assigned to a given substance whether that substance is present in the pure state or as part of a mixture of substances, thus enabling qualitative chemical analysis through diffraction which provides information about the chemical combination of the elements involved and the particular phases they are in. Quantitative analysis is possible by measuring the proportion of a phase in a mixture by the intensity of the diffraction lines (Cullity 1978, Van Grieken et al.

2002)

In document Ion Implantation As A Route To Enhancing Osseointegration On Modified Titanium Surfaces (Page 60-64)