This document summarizes a seminar on X-ray crystallography presented by Mounik Rout. The seminar covered the basics of X-ray crystallography including production of X-rays, Bragg's law, instrumentation used, and applications. Different X-ray diffraction methods like powder crystal analysis and rotating crystal method were discussed. The seminar provided an introduction to how X-ray crystallography can be used to determine the 3D structure of crystals and its wide applications in fields like pharmaceuticals and materials science.
X ray, invisible, highly penetrating electromagnetic radiation of much shorter wavelength (higher frequency) than visible light. The wavelength range for X rays is from about 10-8 m to about 10-11 m, the corresponding frequency range is from about 3 × 1016 Hz to about 3 × 1019 Hz.
Production of X rays, Different X ray diffraction methods, Bragg‘s law, Rotating crystal technique, X ray powder technique, Types of crystals and applications of X-ray Diffraction
X ray, invisible, highly penetrating electromagnetic radiation of much shorter wavelength (higher frequency) than visible light. The wavelength range for X rays is from about 10-8 m to about 10-11 m, the corresponding frequency range is from about 3 × 1016 Hz to about 3 × 1019 Hz.
Production of X rays, Different X ray diffraction methods, Bragg‘s law, Rotating crystal technique, X ray powder technique, Types of crystals and applications of X-ray Diffraction
X- Rays were discovered by Wilhelm Roentgen, so x-rays are also called Roentgen rays.
X-ray diffraction in crystals was discovered by Max von Laue. The wavelength range is 10-7 to about 10-15 m.
The penetrating power of x-rays depends on energy-
Hard x-rays: High frequency & More energy
Soft x-rays: Less penetrating & Low energy
X-rays are short-wavelength electromagnetic radiations produced by the deceleration of high energy electrons or by electronic transitions of electrons in the inner orbital of atoms.
X-ray region- 0.1-100 A˚
Analytical purpose- 0.7-2 A˚
Properties: Highly penetrating invisible rays
Liberate minute amounts of heat on passing through matter
Not deflected by electric and magnetic fields
Poly energetic, having widespread energies and wavelengths
Cause ionization (adding or removing electrons in atoms and molecules)
Transmitted by (pass-through) healthy body tissue
Principle: X-ray diffraction is based on constructive interference of monochromatic x-rays and a crystalline sample.
The interaction of incident rays with the sample produces constructive interference when conditions satisfy Bragg’s law.
Production of x rays: X- Rays are generated when the high velocity of electrons impinge on a metal target.
1% of total energy of the electron beam is converted into X –radiation.
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X- Rays were discovered by Wilhelm Roentgen, so x-rays are also called Roentgen rays.
X-ray diffraction in crystals was discovered by Max von Laue. The wavelength range is 10-7 to about 10-15 m.
The penetrating power of x-rays depends on energy-
Hard x-rays: High frequency & More energy
Soft x-rays: Less penetrating & Low energy
X-rays are short-wavelength electromagnetic radiations produced by the deceleration of high energy electrons or by electronic transitions of electrons in the inner orbital of atoms.
X-ray region- 0.1-100 A˚
Analytical purpose- 0.7-2 A˚
Properties: Highly penetrating invisible rays
Liberate minute amounts of heat on passing through matter
Not deflected by electric and magnetic fields
Poly energetic, having widespread energies and wavelengths
Cause ionization (adding or removing electrons in atoms and molecules)
Transmitted by (pass-through) healthy body tissue
Principle: X-ray diffraction is based on constructive interference of monochromatic x-rays and a crystalline sample.
The interaction of incident rays with the sample produces constructive interference when conditions satisfy Bragg’s law.
Production of x rays: X- Rays are generated when the high velocity of electrons impinge on a metal target.
1% of total energy of the electron beam is converted into X –radiation.
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3. INTRODUCTION
X-ray crystallography is a non-destructive technique for determining the molecular
structure of a crystal .
X-ray crystallography uses the principle of X-ray diffraction to analyze the sample .
We can get 3d structure or any sample because it rotates in the sample cell and faces the
X-ray beam in different directions .
This technique helps in analyzing 3d crystal structure of biological materials .
Based on the radiations, X-ray spectroscopy is categorized in 3 type :
1. X-ray diffraction
2. X-ray Absorption
3. X-ray Fluorescence 3
4. .
Diagram of x-ray passing through sample
Diffracted radiation –It is the most accurate method of analysis with high degree of
specificity than any other X-ray spectroscopy method .
X-ray diffraction(XRD) is the diffraction of incident radiation produced by crystalline
sample according to the atom present in it . 4
DIFFRACTED RADIATION
FLUORESCENCE RADIATION
INCIDENT RADIATION
TRANSMITTED(Absorbed) RADIATION
Sample
5. X-ray Absorption :-
When incident beam is passed through the sample then some fraction of X-ray photons
are absorbed .
So the no of photons absorbed by the sample is used to measure the concentration of
the sample .
This is similar to any other absorption method like UV-Visible / IR spectroscopy by
giving the information about the absorbing material in the sample .
X-ray Fluorescence :-
When incident beam is passed through the sample then the electrons of the atoms of
sample gets excited by absorbing some energy , when those electrons come to ground
state from exited state they emitt some radiation which have longer wavelength than
incident beam .
By measuring the wavelength and intensity of the generated radiation analyst can
perform qualitative as well as quantitative analysis .
5
7. Production of X-ray
When high velocity of electrons will strike on metal target then X-ray will produce .
It can explain by Bohr’s atomic model .
Bohr’s atomic model
Energy of the outer shell is higher than inner shell .
7
e¯
e¯
e¯
K SHELL
L SHELL
M SHELL
N SHELL
8. Principle :-
If one high velocity electron will strike the atom then it knock one electron completely
from that atom and get out from that by producing a void space .
An electron from higher shell falls on the void space .
It will release energy in the form of X-ray because of coming from higher orbit to lower
orbit .
The energy of released X-ray will be equal to the difference in the energy between 2
shells .
Ex-ray = EL – EK (if e¯ falls from L shell)
=EM – EK(if e¯ falls from M shell)
=EN – EK(if e¯ falls from N shell) 8
9. Theory of production of X-ray:-
The high velocity eˉ will strike the anode material in a discharge tube , which leads to
production of X-ray .
The striking eˉ interact with the strong electric field of the atomic nuclei constituting
the anode material , which results deacceleration of the striking eˉ and release of energy
due to loosing of kinetic energy and radiation of photons which are responsible for
production of X-rays .
9
eˉ
X-rays
Atomic nuclei
11. The process by which photons are emitted by an eˉ is known as ‘Bremsstrahlung’ which
means deacceleration of radiation .
Initial energy of striking eˉ = Ei
Energy for X-rays(Photons) =Ex-rays
Final energy of eˉ after deacceleration = Ef
Ef = Ei - Ex-rays
Ei = Ef + Ex-rays
If all initial kinetic energy (Ei) will convert into X-rays ,then velocity of the eˉ become 0 .
So Ef = 0 ,and Ei = Ex-ray
This is the condition which will give the X-rays of highest energy and low wavelength .
11
12. Bragg’s law
X-ray diffraction based on Bragg’s law:-
When the X-ray is incident onto a crystal surface, its angle of incidence θ, will reflect
with the same angle of scattering, θ. And, when the path difference, d is equal to a whole
number, n, of wavelength, constructive interference will occur.
Bragg’s equation = n λ = 2dsin θ , where n is order of diffraction 12
β
α
d
A
B
C
D
θ θ
θ
θ
θ
θ
O
Y
X Z Parallel planes of crystal surface
d= Inter planner distance
Θ= Glancing angle
C , D = Diffracted X-rays
A ,B = Incident X-rays
13. Derivation of the equation :-
As per the fig. when X-ray falls on the crystal at angle θ then some rays will reflect from
upper plane at same angle θ .
After extrapolating the reflection line then found that there are 2 angle :-
<XOY=θ , <ZOY =θ
And AO=BX , CO=DZ so the path difference
will be XY+YZ ----- 1
Path diff. is defined as an integral multiple of
wavelength =n λ----- 2
So that n λ=XY+YZ---- 3
Taking Sin θ =
So in ∆XOY , Sin θ=
XY=OY×SIN θ
=>XY= d × SIN θ----- 4
13
L
H
L= Length of perpendicular
H= Hypotenuse
XY
OY
14. In ∆ZOY , SIN θ=
ZY=OY×SIN θ
ZY= d×SIN θ---- 5
Putting equ.5 in equ.3
n λ= d×SIN θ + d×SIN θ
n λ= 2d×SIN θ ----- 6------ Bragg’s equation
where n = Order of diffraction
λ = wavelength ,
d = interplanar distance
Bragg’s equation gives the relationship between:-
1.wavelength of X-rays
2. Interplanar distance in crystal planes
3.Angle of reflection
14
ZY
OY
θ =Glancing angle
SIN θ values = 0 30 45 60 90
0 ½ 1/√2 √3/2 1
17. Working & Instruments :-
High voltage electric current supplied to heat the tungsten filament to emitt electron
from cathode .
Electrons from cathode striking on anode forms X-ray which will go through Beryllium
window towards the sample through a Collimator reducing undesirable radiation .
Then it passes to Monochromator which gives required X-ray beam to the sample .
Sample have the crystal surface which diffract the X-ray beam to detector made up of
photographic type or counter types .
Detector detects the beam intensity and proceed the signal to amplifier .
Amplifier amplifies the given signal and then the signal proceeds to the recorder screen .
17
18. X-ray tube :- It is a large vaccum tube containing a heated cathode of Tungsten filament &
a Cu or Mo(Molybdenum) operated at higher voltage up to 60kv .
Collimator :- It passes narrow beam of X-ray by arrangement of 2 closely packed metal
plates separated by a small gap .
Monochromator:- It has 2 type :
1.Filter type – X-ray beam will partially monochromatize passing required radiation by
absorbing undesirable radiation .
2.Crystal type – It is made up of suitable crystalline materials like-NaCl , Quartz , etc.
Detector :- 1. Photographic method – A film is exposed and developed in X-rays passed
through the sample .
2. Counter Method – 1.Geiger Muller counter
2.Propertional Counter
3.Scintillation Detector
4.Solid-state semi-conductor Detector
5.Semi-conductor Detector
18
20. Bragg’s X-ray spectrometer method
Bragg designed a spectrometer to measure the intensity of x-ray beam following Bragg's
equation i.e. n λ = 2dsin θ
20
G
θ
θ
Crystal(sample
)
Pb slit
Ionization chamber
CH3Br
21. Working:-
High voltage current is applied on the tungsten filament generating heat which helps the
cathode to emitt electron .
Later the electron strikes on the anode surface producing X-rays which passes through
Beryllium window to the sample.
Collimator placed right after Be window absorbs undesirable radiation and passes
required X-ray beam towards monochromator .
Monochromator converts polychromatic beam to monochromatic beam and then passes
it to sample surface.
The crystalline sample reflect the beam at glancing angle to ionization chamber through
lead slits .
The reflected X-rays ionizes Ch3Br gas to allow current flow in the chamber by
electrodes .
Galvanometer present outside to measure the ionization current, which is require to
form a peak in respective to the intensity of X-ray reflected by the crystal .
The ionization current is measured for different values of glancing angle . A graph is
drawn between the glancing angle and ionization current. 21
24. Working
X-ray is generated in the X-ray tube and X-ray beam is made Monochromatic .
Monochromatic radiation will fall on the crystal Mounted on a shaft which can be
rotated at uniform angular rate .
Shaft will rotate the crystal at slow rate so that planes of crystal surface coming
successfully onto their reflecting positions .
The incident X-ray beam will diffract in many angle and fall on photographic film and
some rays will be transmitted .
In case of any rotated angle of the crystal plane the diffraction of X-ray occurs and
directed it into photographic film and no change in case when plane is parallel to the
incident X-ray . 24
Parallel to plane In a rotated angle
25. Each diffracted radiation produces a spot inside the photographic film present in camera .
Photographic film will be fixed perpendicular to the incident ray beam inside the
cylindrical camera .
There is 2 type of photography :- 1.Complete rotation
2.Oscillation method
Complete rotation :- series of complete revolution will takes place .
-Each plane in the crystal diffracts 4 times during rotation of 360º .
Oscillation Method :- Crystal is oscillated through an angle of 15º to 20º .
- The photographic plate is also moved accordingly .
- This method can be use to determine the size of unit cell in crystal .
25
27. POWDER CRYSTAL OR DEBYE METHOD
This technique is a rapid analytical technique used for identification of a crystalline
material by converting it into fine powdered particles .
27
Unwrapped film
Spot formation on film
Cylindrical camera
28. Working :-
Powdered sample is taken in a Capillary tube inside the axis of the camera .
The transmitted beam will pass through a hole to minimize the fogging due to direct beam.
On the photographic film diffraction and reflection pattern will be recorded .
Powder particles having different orientation of plane and they will show different pattern
of cone shape whose interaction with photographic film takes place .
From the shape and distance from 2 similar pattern the identification can be done .
And the equation to get this is l= 2πr × or θ =
Here θ = Incident angle , Reflection/diffraction =2 θ(∵ of taking 2 angle in that cone)
r = radius of the film , circumference= 2πr .
Corresponds to the scattering angle = 360º
l = Length of arc of a circle or length of any 2 similar pattern .
28
Θ
360º
360l
4πr
29. APPLICATION
Used for the identification of unknown crystalline materials .
For characterization of crystalline materials .
Polymer characterization can be done .
Used to identify impurity .
Determine the unit cell dimensions .
Measurement of sample purity .
Used to carried out drug excipient incompatibility study .
Uses to analyze 3d crystal structure of biological materials .
The powder method is used to determine the value of the lattice parameters accurately .
Now a days often used to probe specific ways in how the structure of a material , drug
will interact in certain environments .
29
30. 1. REFERENCES
2. Critchley, Liam. (2020, October 16). The Applications & Principles of
X-Ray Crystallography.
3. AZoM. Retrieved on March 10, 2022 from
https://www.azom.com/article.aspx?ArticleID=18684.
4. https://youtu.be/HjKI4Kh1RgU
5. Critchley, Liam. 2020. The Applications & Principles of X-Ray
Crystallography. AZoM, viewed 10
6. March 2022, https://www.azom.com/article.aspx?ArticleID=18684.
7. Instrumental methods of analysis –Willards, 7th ed . ISBN:
9788123909431
8. Modern analytical techniques in failure analysis of aerospace,
chemical, and oil and gas industries, ISBN 9780081001172
30