x-ray crystallography is a technique for qualitative and quantitative analysis of elements which is done with the help of X-ray. there are different methods under this technique . This presentation will give you an idea about how x-rays are produced , law upon which it works & different methods under this.

1. X-ray Crystallography
Production of x-rays, Bragg's law & Diff. x-ray method
Vinit Gohel
2061615005
M.Pharma (Pharmaceutical Analysis)

2. X-ray spectrometry is a technique for qualitative and quantitative
analysis of elements which is done with the help of X-ray. there are
different methods under this technique . This presentation will give you
an idea about how x-rays are produced , law upon which it works &
different methods under this.
Abstract

3. Atomic Structure
Atomic structure of an element
• Atomic structure contains different shells
• Each shell contain certain number of electrons
• Number of electron is calculated by formula i.e., 2n². Where n= sequence
of shell number (1,2,3,and so on)
ex- number of e¯ in K shell will be 2*1²= 2
number of e¯ in L shell will be 2*2²= 8
• energy of outer shell will be greater than inner shells

4. Production of X-rays
When a e¯ with high velocity strikes atom then, an e¯ from the shell gets knock out & high velocity e¯ itself
gets out from the atom
e¯ e¯
e¯
• When an electron from shell gets knock out, there a
vacant space is created, which is filled by electron
from outer shell/higher energy shell
• Electron from higher energy shell comes to lower
energy shell & energy is released in the form of x-
rays
• Suppose in the diagram , electron from K shell is
knocked out then electron from L,M or N will fill
the vacant space
• The released x-ray energy will be equal to the
difference between energy of 2 shells
Energy of x-ray = Energy of higher shell - Energy of lower
shell

5. • E x-ray = EL – EK (if electron falls from L shell)
• E x-ray = EM – EK (if electron falls from M shell)
• E x-ray = EN – EK (if electron falls from N shell)
Frequency of emitted x-ray can be determined by the formula
μ ={E(higher shell)-E(lower shell)} / h(plank’s constant)
Example:-
μ = (EL-EK)/h (when electron of K shell is replaced from L shell ) or,
μ = (EM-EK)/h (when electron of K shell is replaced from M shell )

6. Production of X-ray by Bremsstrahlung
B r e m = d e c e l e r a t i o n & S t r a h l u n g = r a d i a t i o n
e¯ e¯
X-ray
• When high velocity electron strike the anode in discharge
tube then x-ray is produced.
• The striking e- strikes the strong + field of atom which
reduces the velocity of e-. Due to this there is a change/loss
in kinetic energy and this in turn radiate x-ray.
• This process of emission of x-ray from e- is known as
Bremsstrahlung.

7. let,
Initial energy of striking e- = Ei
Energy of x-rays = Ex-ray
Final energy of e- after deceleration = Ef
So,
Ef = Ei - Ex-ray
Due to heavy mass of nucleus as compared to e- , it will absorb negligible amount of energy
If all initial energy of e- will convert into x-ray then velocity/final energy of e- will become 0,
Ef = 0
Therefore,
Ei = Ex-ray
We could say that, in this condition we will get x-ray of highest energy or least wavelength
Theory related to bremsstrahlung

8. Bragg’s law
Inter
planner
distance
Incident ray Diffracted ray
• Assume that a beam of ray(A) falls at point (B) on
the upper surface (α) of crystal at angle (θ)
• The beam of ray will reflect with same angle (θ)
• Some ray will also incident in successive layer of
crystal (here, β at point B’ with same angle θ and
reflect with same angle θ )
• By exponentially extending the line AB & CB we get
to points i.e. Y and X respectively
• Angle XBB’ and YBB’ will also be θ Distance AB =
A’X & CB=C’Y
• Path difference between A&A’ will be
=XB’+B’Y………..(i)
• Path diff. is integral multiple of wavelength & is
represented by n* λ …….(ii)
• Therefore , n* λ = XB’+B’Y……(iii)
X Y
α
β

9. In the △ XBB’
Sinθ = XB’/BB’ or
XB’ = Sinθ * BB’
XB’ = Sin θ * d….(iv)
Putting the value of (iv) & (v) in equation (i) we get
n*λ = Sinθ *d + Sinθ * d
Or,
n*λ =2 d Sin θ which is Bragg’s Equation
Where ,
n=order of diffraction
λ =wavelength
d = interplanar distance
θ = glancing angle
Bragg’s eq gives the relationship between wavelength of X-ray,
interplanar distance & angle of reflection
In the △ YBB’
Sinθ = YB’/BB’ ,or
YB’= Sinθ * BB’
YB’= Sinθ * d….(v)

10. What happens when x-ray strikes sample ?
Incident rays
Sample’s
Atom
With certain
crystalline
structure
Transmitted rad.
Fluorescence rad.

11. X-ray Diffraction Method
• Based upon scattering of x-rays by crystal
• arrangement and the spacing of atoms in crystalline materials has been determined directly from diffraction
studies
• determines the structures of such complex natural products as steroids, vitamins, and antibiotics.
• X-ray diffraction also provides a convenient and practical means for the qualitative identification of
crystalline compounds.

12. X-ray Absorption Method
Fig: X-ray ab. Spectra for lead & silver
• In this when an x-ray strikes innermost electron of an atom
some part of the energy gets absorbed and that electron
goes into exited state.
• The highest probability for absorption occurs when the
energy of the x-ray is exactly equal to the energy required to
remove the electron.
• Beer's law is as applicable to the absorption of X-ray
radiation. Convenient form of Beer’s law is
x = sample thickness in centimeters
P0 = power of incident beams
P = powers of the transmitted
ρ = is the density of the sample
μM =mass absorption coefficient, a quantity that is independent
of the physical and chemical state of the element

13. X-ray Fluorescence Method
• In this method the sample are irradiated with x-ray. The
elements in the sample are excited by absorption of the
primary beam and emit their own characteristic fluorescence
when comes back to normal state.
• Process is also known as x-ray emission method
• Quantitative determination of lightest element can be done
• Qualitative identification of elements having atomic numbers
greater that of oxygen (>8) are done also.
• Advantage of XRF is that it is nondestructive.

14. • Principles of Instrumental Analysis (6th Edition) by Douglas A. Skoog.
Reference