X-ray Diffraction

Presented by:

Mohd. Nasir

Mahendra Baingne

Outline

• Introduction• X-ray diffraction• Experimental Method• Applications• Conclusion

X-rays

• X-rays were discovered by the German physicist Roentgen in 1895.

• It were so named because their nature was unknown at the time.

• X-ray region lies before the UV region of the electromagnetic spectrum.

• It covers wavelengths from about 0.1 Å to

100 Å.

The spectrum of electromagnetic radiation.

X-raysSource: NCERT textbook/Class-11/chemistry-1/page-36

Energy

Wavelength

Production of X-rays

• X-rays are produced whenever high speed electrons collide with a metal target.

a). A source of electrons.

b). A high accelerating voltage.

c). A metal target.

X-rays tube

Crystal Structure

• A crystal may be defined as a solid composed of atoms arranged in a periodic pattern in three dimensions.

Lattice

Lattice may be regarded as sort of framework or skeleton on which the actual crystal is built up.

Source: Elements of X-ray diffraction by B.D . Cullity

Unit Cell

a,b, c and α, β γ are the lattice parameter.

The fourteen Bravais lattices

Source: Elements of X-ray diffraction by B.D . Cullity

Source: Elements of X-ray diffraction by B.D . Cullity

X-ray Diffraction

• When X-rays interact with a solid material the scattered beams can add together in a few directions and reinforce each other to yield diffraction, this is called X-rays diffraction.

• This is a tool for the investigation of the fine structure of matter.

• Constructive interference is the result of synchronized light waves that add together to increase the light intensity.

• Destructive İnterference results when two out-of-phase light waves cancel each other out, resulting in darkness.

Constructive & Destructive Waves

X-ray diffraction: Bragg’s Law

θ

θ θ

θ

d

12 1 2

A C

B

O

Rays 1 and 2 interfere constructively if Total Path Difference is integral multiple of the wavelength, λ Total p.d. = AB + BC

∆OAB and ∆OCB are equivalent.AB=BC=d*sinθ

Diffraction condition is:2 d sinθ = n λ

• Bragg’s reflection can only occur for wavelength (λ<2d).For most of the crystal planes d is of order of 3 Aº or less, which means

λ can not exceed about 6 Aº.

Methods of X-ray diffraction

X-Ray Diffraction Method

Laue

OrientationSingle Crystal

Polychromatic BeamFixed Angle

Rotating Crystal

Lattice constantSingle Crystal

Monochromatic BeamVariable Angle

Powder

Lattice ParametersPolycrystal (powdered)Monochromatic Beam

Variable Angle

2 d sinθ = λ

Methods of powder diffraction

a) Debye Scherrer’s method

b) Focusing method

c) Pinhole methodOrientation of diffracted beamIn these method narrow strip of film is used.Recorded diffraction line consist of short line

formed by intersection of cone of radiation and film

16

Fundamental of Powder diffraction method

Purpose:- Phase identification and information on unit cell of crystalline

material, avg. bulk composition.

Crystalline structure acts as 3D diffraction grating for x rays.

XRD is based on constructive interference of X ray and crystalline

sample.

Monochromatic radiation : strong k characteristic component of general

radiation.

To expose various planes in the crystal, rather than a rotating a single

crystal, powder sample is use. This exposes various crystal planes

simultaneously to the X-rays. 17

Component of camera

18

Powder diffraction method

19Bruker D8 Analytical X-ray Systems(source: institute instrumentation centre IIT Roorkee)

• If a monochromatic x-ray beam is directed at a single crystal, then only one or two diffracted beams may result.

20

If the sample consists of some tens of randomly orientated single crystals, the diffracted beams are seen to lie on the surface of several cones. The cones may emerge in all directions, forwards and backwards.

A sample of some hundreds of crystals (i.e. a powdered sample) show that the diffracted beams form continuous cones. A circle of film is used to record the diffraction pattern as shown. Each cone intersects the film giving diffraction lines. The lines are seen as arcs on the film.

Powder diffraction method

Preparation of sample and mounting

Monochromatic X ray production

Film loading

Intensity measurement

Intensity is measured by electric counter.Electric counter convert x ray into pulse of

electronic current in circuit connected to counter.No of pulse is proportional to no of entering

electron In diffraction camera intensity is related to

amount of blackening produced on photo graphic plate.

Amount of blackening is converted in x ray intensity by micro-photometer.

21

Determination of Crystal Structure

Step1:Shape and of unit cell are deduced from angular position of diffracted lines.

Step2: Number of atoms per unit cell is then computed from shape and of the unit cell, the Chemical composition of the specimen, and its measured density.

Step3: finally the position of atoms with in the unit are deduced from the relative intensities of diffracted beams.

23

Analysis of X-ray film

2θ = 0° 2θ = 180°

θ1θ1θ1 θ1θ2 θ2θ3 θ2θ2 θ3θ3 θ3

d3d3d3d3 d2d2 d2 d2d1d1 d1 d1

R

D

4θ3(rad) = D / R 4θ3(degree) = 57.296 D / R or

D

24

Calculating Lattice Constant

If radius of the camera R = 57.296 mm then,

θ (degree) = D (mm) / 4

4θ (degree) = 57.296 D / R

For first order diffraction, d can be calculated by :

d =λ

2 sin θ

However, (hkl) assignment is not possible here. Hence…

25

Lattice Constant Calculation Contd…

d 2hkl = a 2 / N

where N = h 2 + k 2 + l 2

√h 2 + k 2 + l 2

adhkl = Now,

2 d sin θ = λ 4 d 2 sin2 θ = λ2

4 a2

Nsin2 θ = λ2

sin2 θ

N=

λ2

4 a2= Constant

Possible values of N can be 1,2,3,4,5,6…

26

Prepare a Table

θ sin θ sin2 θ1 2 3

10.83° 0.1879 0.03530.035

30.0177

0.0118

15.39° 0.2654 0.07040.070

40.035

20.0235

18.99° 0.3254 0.10590.105

90.052

90.0353

sin2 θ / N

sin2 θ

N=

λ2

4 a2= 0.0353 For λ = 1.5404 A,

a = 4.10 A

X-Ray Tube Sample

Detector

X-Ray Diffraction

Schematic of difference between the diffraction pattern of various phases

DIFFRACTION PATTERN FOR SINGLE PHASE

Inte

nsi

ty

Source: http://www.spec2000.net/09-xrd.htm

DIFFRACTION PATTERN FOR TWO PHASE

Inte

nsi

ty

Source: http://www.spec2000.net/09-xrd.htm

Chemical Analysis

• Qualitative Analysis diffraction pattern

• Quantitative Analysis Intensities

Pattern of unknown

Source: Elements of X-ray diffraction by B.D . Cullity

Pattern of unknown

Source: Elements of X-ray diffraction by B.D . Cullity

Pattern of copper

Source: Elements of X-ray diffraction by B.D . Cullity

Pattern of copper

Source: Elements of X-ray diffraction by B.D . Cullity

Source: Elements of X-ray diffraction by B.D . Cullity

Why special?

• Determines actual compound• For example

AxBy & AxB2y

• Other methods – only A & B• This method- all the chemical compounds in

their present states of existence.• Plain carbon steel.

• Different allotropesCrystalline modifications in Solid silica .

1 amorphous

6 different crystals • Ores, clays, refractories, alloys, corrosion

products, wear products, industrial dusts, etc.

Some More Advantages

• Much faster.• Requires very small sample.• Nondestructive.• Minimal or no sample preparation

requirements.• Ambient conditions for all analysis.

Safety Aspects

• Electric shock ----high voltage across electrodes

• Radiation Injury---- tolerance dose.

• Heat effect

• Invisible & burns may not be felt immediately.

• First noticeable effect ---- lowering of WBC.

Conclusion

• X-ray diffraction is a tool for the investigation of the fine structure of matter.

• The relation by which diffraction occurs is known as the Bragg’s law or equation.

• Because each crystalline material has a characteristic atomic structure, it will diffract X-rays in a unique characteristic pattern.

THANK YOU