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.

X-ray Tube (cross section)

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

Derivation of Bragg’s Law

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)

Intercepts: (1,1, ∞)- (110)

Intercepts: (1,1, 1)- (111)

Intercepts: (1/2,1, 0)- (210)

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

Working of XRD

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