X-Ray Diffraction Methods

Dr. Saloni Sharma

PG Department of Physics

X-Ray Diffraction

• The phenomenon of X-Ray Diffraction is useful for the determination of the structure of solids as well as for the study of the X-Ray spectroscopy.
• Bragg’s law is widely used for these applications.
• Bragg’s law for crystal structure determination, requires matching of λ and θ

• Bragg’s law for crystal structure determination, requires matching of λ and θ
• For this either a continuous range of wavelength λ or θ is provided, so that the value of λ is arbitrarily chosen for a given value of the orientation θ.
• Three commonly used methods for the study of crystal structure:
• a) Laue Method
• b) rotating crystal method
• c) Powder Method

Laue Method

• It is one of the most important and most commonly used method for the determination of crystal structure

Laue Method

Laue Method

Laue’s Method

• The diffraction pattern obtained on the photographic plate consists of a symmetrical arrangement of spots depending upon the symmetry properties of the crystal lattice.
• The Laue’s method is generally used to determine the crystal symmetry.
• For example, for a crystal with four fold symmetry and axis parallel to the beam of X-rays, four-fold rotation of crystal would produce identical Laue patterns.

Limitation of Laue’s Method

• Laue’s method cannot be used for the determination of crystal structure, because out of the continuous range of wavelengths, a number of wavelength may be reflected in different orders from a single plane producing an overlapping of certain reflections at a single spot. Thus a number of reflections may be missing in the Laue pattern.

Rotating Crystal Method

Rotating Crystal Method

• For obtaining the diffraction pattern, a photographic plate is attached inside the cylinderical holder alongwith its surface. Generally, the vertical axis are taken as the rotation axis as shown in figure.

Rotating Crystal Method

• During the course of rotation of the crystal, X-rays will be diffracted whenever the orientation of the crystal plane with respect to X-rays is such that the Bragg’s condition is satisfied.
• All those planes of the crystal which are parallel to the axis of the rotating spindle diffract the incident rays into a horizontal plane perpendicular to the axis whereas, there will be no diffraction from the planes which contain the incident beam of X-rays.

Rotating Crystal Method

• However, all those planes which are inclined at certain angle to the axis of rotation will produce reflections above and below the horizontal plane, thereby producing lines or layers above and below the plane depending upon the inclination of the planes.
• These lines are called the layer lines and are produced due to the diffraction spots aligned along a line.

Powder Crystal Method

• The Bragg’s method and the rotating crystal method require the precise mounting of a single crystal on a certain crystal axis which is a tedious task to do. To overcome this difficulty, powder crystal method is used.
• This method was developed by Debye, Scherrer and Hull. In this method, the crystalline material is ground to powder form so that the crystallites assume random orientations.

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Powder Crystal Method

Powder Crystal Method

• The reflections will occur from the family of parallel planes which are inclined to the X-ray beam at different angles.
• Also the higher orders of reflection apart from the first order, second order reflections will also be produced.
• Since for the given value of angle θ, a large number of orientations of a given family of planes is possible, the X-rays diffracted corresponding to a particular value of d and θ will lie on the surface of a cone whose axis lie along the direction of the incident beam and apex is at the sample with semi-vertical angle 2θ.

Powder Crystal Method

Powder Crystal Method

The experimental setup of the powder crystal method is as shown in figure.

X-rays are made monochromatic by passing them through a filter.

These monochromatic rays are collimated into a fine beam by passing them through two lead slits.

This collimated beam is now made to fall on the powder specimen taken in capillary tube made of non diffracting material and suspended along the axis of a cylinderical camera having a photo film attached round its inner surface.

Powder Crystal Method

• This camera is called Debye-Scherrer camera and surrounds the crystal powder completely on all directions upto an angle of 180⁰ with the direction of incident X-rays.
• Since the width of the photo film is small, only small parts of the circular rings are formed on it.
• When the film is developed and laid flat on a table, the shape of the rings obtained are as shown in figure

Powder Crystal Method

Powder Crystal Method

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