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
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
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 .
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 .
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
The energy of released X-ray will be equal to the difference in the energy between 2
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 .
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 .
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
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= d × SIN θ----- 4
L= Length of perpendicular
14. In ∆ZOY , 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
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 .
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
4.Solid-state semi-conductor Detector
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
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
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
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
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 .
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 .
Spot formation on film
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 .
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 .
30. 1. REFERENCES
2. Critchley, Liam. (2020, October 16). The Applications & Principles of
3. AZoM. Retrieved on March 10, 2022 from
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:
8. Modern analytical techniques in failure analysis of aerospace,
chemical, and oil and gas industries, ISBN 9780081001172