In the name of
Allah
Fundamentals of XRD as
Nanotechnology instruments
Assistance prof. Dr. Luma
Majeed Ahmed
lumamajeed2013@gmail.com,
luma.ahmed@uokerbala.edu.iq
A Brief History of XRD
In 1895, Wilhelm Rontgen discovered Xrays. He won the Nobel Prize in Physics in
1901.(the range is 0.101 – 10 nm)
In 1912, von Laue discovered the
diffraction of X-rays by crystals and won
the Nobel Prize in Physics in 1914.
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(under Max Planck and
Sommerfeld)
From Wikipedia
in 1912 the Braggs, father and son, experimentally discovered the
Bragg law of the X-ray diffraction.
Bragg’s X-ray experiment led to the
discovery of the structure of DNA in
1953.
Reported a book (x-rays and
Sir William H. Bragg
crystal structure) in 1915.
(1862-1942)
Sir William L. Bragg
(1890-1971)
1918: Paul Scherrer uses X-Rays to
determine crystallite size of nanocrystalline gold.
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Paul Scherrer (1890–1969)
Bragg Diffraction Law
Law describing the necessary condition for diffraction
Applicable for photons, electrons and neutrons
Bragg’s law
Condition for efficient specular reflection
(click for java applet)
2d sin   n 
2dhkl sin   n
n: integer
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The Scherrer Equation was published in 1918
K
B 2  
L cos 
Scherrer’s Formula
L = thickness of crystallite
K = constant dependent on crystallite(grain) shape
(0.94) is spherical
(0.90) is tube or rode
(0.89 or 0.85) is wire or any other shape.
 = x-ray wavelength (0.15406 nm
B = FWHM (full width at half max) or integral
breadth
B = Bragg Angle
• Peak width (B) is inversely proportional to crystallite size (L)
• B must transfer from degree to radians by multiply to
when did Scherrer use X-rays to
estimate the crystallite size of
nanophase materials?
𝜋
180
http://prism.mit.edu/xray
Uses of X-ray Powder Diffraction
Data Analysis
Bragg
Example
d = λ / (2 Sin θB)
λ = 1.54 Ǻ, 2θ=38.3
= 1.54 Ǻ / ( 2 * Sin ( 38.3 / 2 ) )
= 2.35 Ǻ
Simple Right!
L
k 
B  cos  B
L = 0.89*λ / (B Cos θB)
Scherrer’s Example
λ = 1.54 Ǻ
= 0.89*1.54 Ǻ / ( 0.00174 * Cos (98.25/ 2 ) )
= 1200 Ǻ
B = (0.100)x π/180 = 0.00174
Simple Right!
Q/calculate the mean crystal size for TiO2 crystal for XRD chart, where
λ= 0.15406 nm, note the crystal is spherical.
𝐾.‫ג‬
L=
𝐵.𝑐𝑜𝑠𝜃
(111)