Introduction
After the discovery of X-rays, scientist started working on the wave nature of these rays. To test the nature, X-rays have to produce interference and diffraction patterns. For diffraction to occur, the wavelength should be in the order of its slit width. But we know that X-ray have shorter wavelength and it is quite impossible to make such a slit / grating of smaller dimension. So the wave nature was studied in atomic level. Scientist by name Laue suggested that crystal can act like a space grating to observe diffraction. This experiment was later supported by Bragg’s equation.
Consider a plane lattice crystal with inter planar distance d. Suppose a beam of X-rays of wavelength λ is incident on the crystal at an angle θ , the beam will be reflected in all possible atomic planes. The path difference between any two reflected waves is equal to the integral multiple of wavelength. The ray P gets reflected from the surface while the ray Q has to under go some path difference. The extra distance traveled by the ray Q from the figure is
(BC +CD). From the diagram either BC or CD is equal to d sin theta. So the path difference is
d sin θ + d sin θ = n λ
2 d sin θ = n λ
Here n is the order = 1,2, 3 …… .This is Braggs law
The crystal which is considered as the slit is placed in the Bragg spectrometer for investigation. X-rays are incident on the crystal at different angles and its corresponding ionization current is noted. The below is the plot of ionization current and incident angle
At a certain values of the angle of incidence, the ionization current is increases abruptly or at peak value. Basing on the angle at maximum current, the planar distance can be calculated using Bragg’s law.
After the discovery of X-rays, scientist started working on the wave nature of these rays. To test the nature, X-rays have to produce interference and diffraction patterns. For diffraction to occur, the wavelength should be in the order of its slit width. But we know that X-ray have shorter wavelength and it is quite impossible to make such a slit / grating of smaller dimension. So the wave nature was studied in atomic level. Scientist by name Laue suggested that crystal can act like a space grating to observe diffraction. This experiment was later supported by Bragg’s equation.
X Ray diffraction Analysis : Bragg’s law
Consider a plane lattice crystal with inter planar distance d. Suppose a beam of X-rays of wavelength λ is incident on the crystal at an angle θ , the beam will be reflected in all possible atomic planes. The path difference between any two reflected waves is equal to the integral multiple of wavelength. The ray P gets reflected from the surface while the ray Q has to under go some path difference. The extra distance traveled by the ray Q from the figure is
(BC +CD). From the diagram either BC or CD is equal to d sin theta. So the path difference is
d sin θ + d sin θ = n λ
2 d sin θ = n λ
Here n is the order = 1,2, 3 …… .This is Braggs law
X Ray diffraction : Analysis of the Pattern
The crystal which is considered as the slit is placed in the Bragg spectrometer for investigation. X-rays are incident on the crystal at different angles and its corresponding ionization current is noted. The below is the plot of ionization current and incident angle
At a certain values of the angle of incidence, the ionization current is increases abruptly or at peak value. Basing on the angle at maximum current, the planar distance can be calculated using Bragg’s law.
When the angle increases i.e. order of the spectrum, the intensity of the X- rays decreases
Ionization current will never fall to zero.
Thus we can say the diffraction analysis of X-rays helped us to study the crystal structure.
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