xrd basic

Characterization of Nanomaterials
using X-ray Diffraction Technique
Presented by:
Anuradha Verma

Presentation Layout
History
Principle
Instrumentation
Working of XRD
Applications

History
1895- Wilhelm Conrad Röntgen discovered
X-rays.
1901- Honoured by the Noble prize for
physics.
1995- German Post edited a stamp,
dedicated to W.C. Röntgen.

Each material produces a unique X-
ray "fingerprint" of X-ray intensity
versus scattering angle that is
characteristic of it's crystalline
atomic structure.
Qualitative analysis is possible by
comparing the XRD pattern of an
unknown material to a library of
known patterns

 For electromagnetic radiation to be diffracted the
spacing in the grating (~a series of obstacles)
should be of the same order as the wavelength.
 In crystals the typical interatomic spacing ~ 2-3
Å, so the suitable radiation is X-rays.
 Hence, X-rays can be used for the study of
crystal structures.

The rate of flow of energy through unit area perpendicular to
the direction of motion of wave is called the Intensity. And
average value of intensity is proportional to square of
amplitude of wave.
X ray Intensity Measurement:
 Counting no. of photons incident on a detector
 Measuring degree of blackening of photographic film
exposed to x-ray beam.
X-rays
Carrier of Energy
Electromagnetic radiation

X-ray Production
X rays are produced when any electrically charged particle of sufficient Kinetic energy
rapidly decelerate.
X ray tube: -
a) source of electron
b) Two metal electrode [Anode (metal target) maintained at ground potential & cathode
maintained at high negative potential (30kV to 50kV)
c) High acceleration voltage
NB:-
- Chamber is evacuated in order to avoid collisions between air particles and either the
incident electrons or emitted x-rays.
- X-ray leave the tube through windows made of Be.
- Continuous cooling of tube is necessary since anode will soon melt as most K.E of electrons
is converted into heat, <1% is transformed into x rays.

Continuous Spectrum
Radiation are produced due to high voltage maintained across these electrodes that rapidly draws
the electron to the anode with very high velocity. X rays are produced at the point of impact and
radiate in all directions.
K.E = eV = ½ mv2
Analysis of rays coming from target-
Rays are found to consist a mixture of different wavelength and variation of intensity with
wavelength depend on tube voltage.
The radiation represented by such curves is called polychromatic, continuous or
white radiation. Also called as Bremsstrahlung (German- “Braking radiation”
meaning caused by electron deceleration.)

 Some stop in one impact, releasing all energy at once producing photons of
maximum energy and x-rays of minimum wavelength.
eV = h�max
�SWL = 12400/V
 Some electrons are not stopped in one impact but undergoes glancing impact,
partially decrease velocity and fraction of energy is emitted as radiation and
has energy < hvmax and wavelength longer than �SWL.
The totality of wavelengths upward from �SWL constitute CONTINUOUS
SPECTRUM.
Curve become higher and shift to left as applied voltage is increased (no. of
photons produced per sec and av. Energy per photon are both increasing).
Icont. Spectrum = AiZVm
Does every electron decelerates in same way?
NO

Principle of Generation Bremsstrahlung

Characteristic Spectrum
When voltage on an X-ray is raised above certain critical value,
characteristic of the target metal, sharp intensity maxima appear at
certain wavelength.
Since narrow, they are called CHARACTERISTIC LINES.
Several lines are present in K set but only 3 strongest are observed
in normal diffraction work.
Monochromatic x-rays are produced.
The incident electrons have sufficient energy to ionize some of the
Copper 1s (k shell). An electron in outer orbital immediately drops
down to occupy the vacant 1s level and energy released in transition
appear as X-radiation.

Principle of Generation the Characteristic
Radiation

Generation of X-rays
Intensity ratios
Kα : Kα : Kβ = : 5 :

Filters
XRD requires monochromatic radiation but beam not only
contains strong K line but also K line and continuous
spectrum.
The intensity of undesirable component can be decreased
relative to K by passing through beam filter (material
should have Z’< Z-1 of target)
Filter will absorb k component more strongly than K
because of abrupt change in absorption coefficient between
these two wavelengths.

The wavelength of k line is related to
the atomic no. by Moseley‘s law:
٧1/2 = (c/�)1/2 Z
Target k 1 k 2 Av. K Flter
Cr 2.2896 2.2935 2.2909 V
Fe 1.9360 1.9399 1.9373 Mn
Cu 1.5405 1.5443 1.5418 Ni
Mo 0.7093 0.7135 0.7107 Nb
Ag 0.5594 0.5638 0.5608 Pd

Bragg's Law
When x-rays are scattered from a crystal lattice, peaks of scattered
intensity are observed which correspond to the following
Conditions :
1.The angle of incidence = angle of scattering
2.The pathlength difference is equal to an integer number of
wavelengths.
The condition for maximum intensity contained in Bragg's law
above allow us to calculate details about the crystal structure, or if
the crystal structure is known, to determine the wavelength of the
x-rays incident upon the crystal.

The incident beam will be scattered at all scattering centres,
which lay on lattice planes.
The beam scattered at different lattice planes must be scattered
coherent, to give an maximum in intensity.
The angle between incident beam and the lattice planes is
called θ.
The angle between incident and scattered beam is 2θ .
The angle 2θ of maximum intensity is called the Bragg angle.
Bragg’s Description

Lattice Plane
Lattice plane is a plane which intersects atoms of a unit cell across
the whole 3D lattice.
There are many ways of constructing lattice planes through a lattice.
The perpendicular separation between each plane is called the
d-spacing.

Miller Indices
Miller indices are used to specify directions
and planes.
These directions and planes could be in
lattices or in crystals.
The number of indices will match with the
dimension of the lattice or the crystal.
e.g. in 1D there will be 1 index and 2D there will
be two indices etc.

• (h,k,l) represents a point – note the exclusive use of commas
•Negative numbers/directions are denoted with a bar on top of the
number
• [hkl] represents a direction
• <hkl> represents a family of directions
• (hkl) represents a plane
• {hkl} represents a family of planes

The index represents a set of all such parallel vectors

Miller Indices for Planes: Procedure
1.Identify the plane intercepts on the x, y and z-axes.
2.Specify intercepts in fractional coordinates.
3.Take the reciprocals of the fractional intercepts.

The plane intersects the x-axis at point a. It runs
parallel along y and z axes.
•Thus, this plane can be designated as (1,∞,∞)

Pink Face
= (1/1, 1/∞, 1/∞) = (100)
Green Face
= (1/∞, 1/∞, 1/1) = (001)
Yellow Face
= (1/∞, 1/1, 1/∞) = (010)

Reflection Planes in a Cubic Lattice

A scintillation counter may be used as detector
instead of film to yield exact intensity data.
Using automated goniometers step by step
scattered intensity may be measured and stored
digitally.

Parallel-Beam Geometry with Göbel Mirror

“Grazing Incidence X-ray Diffraction”
Grazing Incidence Diffraction” with
Göbel Mirror

Grazing Incidence Diffraction for Thin Film
Phase Analysis
X-ray radiation - large penetration depth into any matter
Grazing Incidence Diffraction (GID) is the technique to overcome
this restriction.
 GID measurements are performed at very low incident angles to
maximize the signal from the thin layers.
 This allows phase analysis on very thin layers
 Surface sensitivity down to nm scale
 Depth profiling of the phase composition of layered samples
 Göbel Mirrors for incident and diffracted beam with enhanced
sensitivity and shorter measurement times
not surface sensitive

 For the GID, the incident and diffracted beams
are made nearly parallel by means of a narrow
slit or Göbel Mirrors on the incident beam and
along Soller slit on the detector side.
 The stationary incident beam makes a very
small angle with the sample surface (typically
0.3°to 3°), which increases the path length of
the X-ray beam through the film.
 This helps to increase the diffracted intensity,
while at the same time, reduces the diffracted
intensity from the substrate.
 Overall, there is a dramatic increase in the film
signal-to background ratio.

d-spacings of lattice planes –
Depend on the size of the elementary cell and determine the
position of the peaks.
Each peak measures a d-spacing that represents a family of
lattice planes .
Intensity of each peak-
Caused by the crystallographic structure, the position of the
atoms within the elementary cell and their thermal
vibration.
Line width and shape of the peaks-
Derived from conditions of measuring and properties - like
particle size - of the sample material.
Relative positions of the diffraction peaks
Depends on size and shape of the unit cells and provide
information about the location of lattice planes in the crystal
structure

Each peak also has an intensity which differs from other peaks in
the pattern and reflects the relative strength of the diffraction.
In a diffraction pattern, the strongest peak is, by convention,
assigned an intensity value of 100, and other peaks are scaled
relative to that value.

Information content of an idealized
diffraction pattern

Determination
of
atomic
arrangement

Single Crystal:- Unit of lattice in which atoms
are arranged in specific position (same
orientation)
Grain:- Bunch of crystals which are arranged
in same direction.
Particles:- Contains many grains.
Crystallite:-An individual perfect crystal or
region of regular crystalline structure in the
substance of a material.
Crystallites are arranged in random fashion in
the sense of different lattice planes.

Debye Scherrer’s formula
(To calculate average crystallite size)
Use FWHM of most intense peak
X =
Xradian = x*3.14/180
Xradian =
� - X-ray wavelength and
- full width at half maxima (FWHM)
� - Bragg’s diffraction angle.

Dislocation density, Number of crystallites per unit
surface area and strain of the films
Dislocation density ( ):
Number of crystallites per unit surface area (N):
d -film thickness (obtained from cross-sectional SEM
image
Strain of the films ( ):

Determination of
crystalline phases
and orientation
(using JCPDS
card)

Conclusions
Non-destructive, fast, easy sample prep
High-accuracy for d-spacing
calculations
Can be done in-situ
Crystalline powder samples and thin
film samples can be studied.
Standards are available for thousands
of
material systems

xrd basic

More Related Content

What's hot (20)

Viewers also liked (20)

Similar to xrd basic (20)

More from Anuradha Verma (16)

Recently uploaded (20)

xrd basic