XRD Analysis (X-Ray Diffraction)

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 X-Ray Diffraction (XRD)



      To understand the XRD we need to learn about the history of crystals.


Question 1:- Why Do Crystals Have Regular External Shapes?

 

 # There is a famous postulate by Robert Hooke


“Because they have a regular arrangement of ‘building blocks’(atoms in the modern language)”


{Robert Hooke father of ‘Microscopy’, wrote the first book on the microscopy study of material}


               X-rays were discovered in 1895 by Wilhelm Conrad Roentgen (1845-1923) who was a Professor at Würzburg University in Germany. In his laboratory he was working with a cathode-ray tube in his laboratory, crystals on a table near his tube were started glowing like a fluorescent glow. The tube on which Roentgen was working was filled with positive and negative electrodes encapsulated in a glass envelope (bulb). When a high voltage has applied the air in the tube was evacuated and there is the fluorescent glow. Roentgen shielded the tube with heavy black paper and discovered a green-coloured fluorescent light. This light was generated by a material located a few meters away from the tube.

     


Question 2:- Are X-rays waves or Particles?

  Laue’s Predictions:-

  • If crystals are periodic arrangements of the Atom.

  • If X-Rays are Waves.

                            Then

Crystals should act as a 3D diffraction grating for the X-Rays.


                  Two great results are proved from a single experiment. This experiment is considered to be one of the greatest scientific discoveries of the Twentieth Century. For his discovery of the diffraction of X-rays by crystal he won the Nobel Prize in 1914.



Bragg’s Law

Bragg’s First Law:-

                          There exists a set of crystal lattice planes, for every diffracted beam, such that the diffraction beam appears to be specularly reflected from this set of planes. 


Braggs’ recipe for the Nobel Prize?


Calling the diffraction a reflection!!!




“The Important thing in science is not so much to obtain new facts as to discover new ways of thinking about them.”


W.L.Bragg



The Important thing in science is not so much to obtain new facts as to discover new ways of thinking about them


William Lawrence Bragg (left) and William Henry Bragg. Credit: Smithsonian Institution Archives. Image # SIA2007-0340.


                                   Father and Son shared the Nobel Prize in 1915


Bragg’s Second Law:-


                        The direction of diffracted beams can be treated as the X-Rays that are reflected like mirror reflections from the parallel atomic planes of the crystal.


 

                      n λ = 2dsinØ


  • n = order of diffraction

  • λ = wavelength

  • d = interatomic distance

  • Ø = angle of incidence of X-rays

 

                There are only certain directions Ø in which the given wavelength λ from all parallel planes add up in the phase strong diffraction beam. Moreover, since Ø<1 and wavelength λ<2d are necessary conditions for the occurrence of the Bragg diffraction. There are mainly three experimental methods of X-ray diffraction for the analysis of the material.


  1. Laue Method

  2. Single Crystal Method

  3. Power Method


Experimental Diffraction Settings:-


Method

Wavelength

Angle of Incidence

Laue Method

Variable λ

Fixed Ø 

Single Crystal Method

Fixed λ

Variable Ø 

Powder Method

Fixed λ

Variable Ø 



Important Question:-


# Why do we use only the Crystal Form of specimen for XRD Analysis?

                     Crystal form simply means cooling and condensing that compound going to be used for XRD analysis. Normally all molecules or macro-compounds that are going for XRD analysis are not stagnant; they are present in different orientations and get modified from time to time. To get a particular shape of the particular structure and compound the only way is to freeze them. Now they are stagnant and stop rotating so we get accurate research.  


# Basic Idea of XRD

                  A crystal consists of a periodic arrangement of the unit cell into a lattice. The unit cell can contain a single atom or atoms in a fixed arrangement. Crystals consist of planes of atoms that are spaced a distance ‘d’ apart but can be resolved into many atomic planes, each with a different ‘d’ spacing. a, b and c (length) and a, b and g angles between a, b and c are lattice constants or parameters which can be determined by XRD. 


                       For Specimen preparation the powder should be range from 0.1 micrometres (Peak broadening) to 40 micrometres (less diffraction occurring).


                      Basic Idea of XRD analysis we are bombarding X-Ray on a particular specimen of Crystal and X-ray diffracted from the specimen. X-ray diffraction is unique for each and every molecule if X-ray diffraction is simple then the structure of the molecule is simple and if diffraction is more complex then the structure of the molecule is complex.

       

# Most Important application of the XRD:-

  1. Obtain XRD pattern

  2. Measure d-spacing 

  3. Obtain integrated intensities 

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