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Everything you wnat to know about X-Ray Diffraction

Component parts of an X-ray Diffractometer

Schematic arrangement of XRD Diffractometer components

X-ray studies are mainly carried out in two basic configurations, namely, Single crystal and Powder XRD. However, the component parts of the x-ray spectrometer are in general common and comprise of:

  • Source of x-rays
  • Sample stage
  • Detector

The article will provide basic details on the component parts of the x-ray diffractometer.

Source of x-rays

Schematic diagram of X-ray tube
Schematic diagram of X-ray tube

X-ray tube is a common source of x-rays. It comprises of an evacuated tube which contains a copper block anode bearing a metal target made of any of the metals such as molybdenum, tungsten, copper, rhodium, silver or cobalt .The cathode is a tungsten filament .On passage of electric current through the filament electrons are generated which move towards the anode under the highly accelerated voltage typically 30 – 150 kV. The accelerating electrons on striking the metal surface knock out electrons from the inner shells and the vacancies created are filled by electrons from the outer shells. In the process metal atoms emit x-rays. However, this involves heating of the metal block and x-rays constitute only a small fraction of the total energy liberated. The emitted x-rays exit the tube through  a berylium window. The copper block needs to be cooled with a supply of water to dissipate the excessive heat generated. The Be window helps transmit a monochromatic beam of x-rays. Further monochromatization can be achieved by making use of a zirconium filter when using molybdenum as metal target. It absorbs the unwanted emissions while allowing the desired wavelengths to transmit.

Sample stage

Sample stage is also known as sample holder or a goniometer. Single crystal diffractometers make  use  of 4 circle  goniometers. These circles help position the crystal planes for optimum  x-ray diffraction settings. The sample stage can be a simple needle that holds the crystal in place or glass plate or fiber on which the crystal is mounted using an epoxy resin. Only sufficient quantity of epoxy resin is used so that the crystal is clearly mounted and not embedded in the resin. The fiber is mounted on a brass mounting pin and then inserted into the goniometer head. The sample is then centred with an optical arrangement such as a microscope or video camera and making adjustments along X, Y and Z directions to achieve optimum centering under the crosshairs of the viewer.

Detectors

In earlier days photographic films were used for recording the absorption pattern of diffracted beams. With the advances in detection technology more sensitive detector options were incorporated in advanced instruments. Such detectors include gas filled transducers, scintillation counters and semiconductor transducers. Solid state detectors offer highest levels of sensitivity and speed of analysis.

 Subsequent articles will cover the operating principles and benefits of single crystal and powder systems.

 

Crystal Geometries – Lattices and Miller Indices

Seven Crystal System Shapes
Seven Crystal System Shapes

Crystals are three-dimensional symmetric arrangements of atoms, molecules or ions. Such arrangements repeat themselves at regular intervals keeping the same relative orientation to one another. This is a unique property of crystalline materials which are specific to different crystalline compounds irrespective of the source of origin be it natural or synthetic.

If you consider each atom, molecule or ion as a point then such an arrangement is in translational symmetry and the outline of such arrangement is called a crystal lattice .A unit cell comprising of single type of atoms is monoatomic whereas one comprising of more than one type of atoms is called polyatomic cell.

Crystals can be considered as planes joining groups of atoms with fixed distances and angles .These dimensional constants are characteristic features of different crystalline materials.

Crystal Geometries
Crystal Geometries

Crystal Systems

A crystal system is a group of crystal structures used to describe the axial arrangement of crystals. There are seven basic crystal shapes

Cubic

This arrangement consists of three axis perpendicular to each other with all sides equal in length. The cubic system has a lattice point at each of its eight corners and has six faces.

Hexagonal

The hexagonal arrangement has four axes. Three of these are horizontal at 120° to each other and the fourth axes is perpendicular to the three horizontal axes. It comprises of eight faces

Tetragonal

A tetragonal system has a square base and top like in cubic arrangement but has an extended vertical height. It has three axes at 90° to each other and a total of six faces

Rhombohedral

The rhombohedral is similar in shape to a cube but is inclined in one direction.Its three axes are perpendicular to each other with two horizontal and one vertical. It has six faces.

Orthogonal

Orthogonal crystals consist of three axes perpendicular to each but of different lengths.It has six faces.

Monoclinic

Monoclinic crystal has three unequal axes. The front face axes are oblique to each other and the third axes is perpendicular to the other two. The system has six faces

Triclinic

The structure has three unequal crystallographic axes which   intersect one another obliquely. It has six faces.

Bravais in 1848 postulated that seven crystal systems can exist in 14 distinct types of configurations. The unit cells of Bravais lattice are

Cubic – 3(simple cubic, body centred cubic, face centred cubic)

Tetragonal – 2(simple, body centred )

Orthorhombic – 4 (simple, body centred, base centred, face centred)

Hexagonal-1 (simple)

Rhombohedral – 1(simple)

Monoclinic – 2(simple, base centred)

Triclinic – 1 (simple)

Miller indices

 The atomic orientations in crystals are responsible for their shapes. It often becomes necessary to define different planes within a lattice mathematically. Physical properties of materials such as electrical conductivity, thermal conductivity, deformation under loads,etc are dependent on orientations in some crystals. Such behaviour is referred to as anisotropy.

To understand Miller induces it is important to understand the commonly used expressions

x, y, z are axes passing through origin

a,b,c are unit cell lengths along the three axes

Miller induces express planes as (hkl) where h, k and l are integers.

Gen Convention for assigning Miller indices:

  • Determine the intersection of the plane along the three axes-a,b and c.
  • Suppose a plane intersects x axis at a/2, y axis at the end and c axis at c/3. These are expressed as 1/2,1and 1/3.
  • The reciprocals of these become 2,1, 3.
  • The Miller indice of this plane is expressed as (213), ie, in brackets and without commas.

In a cubic system planes having same indices regardless of order and sign are equivalent but the same will not be true for other geometries.

 

Role of Bragg’s law in X-Ray Diffraction studies

X-ray Crystal diffraction
X-ray Crystal diffraction

Bragg’s law is the foundation stone on which the edifice of x-ray diffraction stands. It holds same significance in crystal structure determinations as the Beer- Lambert law(link) holds in light absorbance measurements. The law was established by Sir W.H Bragg and his son Sir W.L Bragg in 1913 to explain the diffraction of x-rays from atomic planes of crystals of sodium chloride, zinc sulphide and diamond.The Nobel prize for Physics was awarded to the Bragg duo in 1915 for their contribution in the field of crystallography.

A beam of x-rays incident to a crystal face gets partially scattered by the atoms of the crystal. The fraction that is not scattered reaches the next atomic layer where another part is scattered and remainder passes across to the next layer and so on. As a result the diffraction pattern is generated from the constructive and destructive interference of X-rays diffracted from each plane. The diffracted beams interact constructively if the beams are in phase or destructively if they are out of phase. A basic requirement for x-rays to diffract is that the sample exhibit crystallinity and the spacing between the atomic layers must lie in the wavelength range of x-ray radiation.

Diffraction pattern on film
Diffraction pattern on film

The Bragg’s law can be expressed mathematically as

nλ = 2d Sinθ

where,

 λ is the wavelength of x-ray beam

θ the angle of incidence

d  the spacing between the atomic planes

n is an integer

Diffracted beam from several randomly oriented crystals in the sample progresses in a conical shape from the crystal face and the diffraction pattern can be displayed on a photographic film as a series of concentric rings.

Based on XRD measurements you can record the distance between the atomic layers of the crystal lattice, estimate bond lengths and angles, and confirm the identity of the unknown materials by correlating their crystal lattice structure with standard reference materials.

The law though developed to  observe scattering of X-rays by  crystals is applicable to determine the structure using different beams such as electrons, ions, neutrons or protons with wavelengths in the range of distances between the atoms or molecules in the crystal.

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