x ray diffraction 1

8/3/2019 X Ray Diffraction 1

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X-Ray Diffraction

AUTONOMOUS

X-rays

crystal

Photographic plate

X-Ray Pattern

slits


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Diffraction of X-rays:

In 1912 German Physicist Laue suggested that a

crystal which consists of of a 3-D array ofregularly spaced atoms can the serve the purposeof a grating.

Laue ,and his associates Friedrich and Knippingsucceeded in diffracting X-rays by passingthrough a thin crystal


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NaCl

S

1

X-rays

Screen

P

O


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A simple interpretation of the diffractionpattern

was given by W.L.Bragg ,the spots areproduced due to the reflection of some ofincident X-rays from the various sets ofparallel crystal which contain the large

number of atoms.


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Diffraction of x-rays by crystal

planes X-rays are the EM radiation.

The wavelengths of x-rays lies between

0.1A and 100A The dimensions of atoms and inter atomic

spacing is about 1A to 2A

The crystals produce the diffraction of x-rays when wavelength matches with thevalues 1A to 2A


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Introduction:Introduction:

XX--ray diffraction techniques are very useful for crystal structure analysis andray diffraction techniques are very useful for crystal structure analysis andidentification of different types of crystals.identification of different types of crystals.

Experimental study of crystalline materials became possible only after the discoveryExperimental study of crystalline materials became possible only after the discoveryof xof x--rays.rays.

Diffraction occurs when waves traveling through an object whose dimensions areDiffraction occurs when waves traveling through an object whose dimensions areorder of wavelength.order of wavelength.

Typical inter atomic spacing in crystals is 2Typical inter atomic spacing in crystals is 2--33A.A.

The xThe x--rays have wavelengths (0.02rays have wavelengths (0.02A to 100A to 100A) in this range . Hence xA) in this range . Hence x--ray diffractionray diffractionis utilized to study the crystal structures.is utilized to study the crystal structures.


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Braggs lawBraggs law

Braggs law states that, the path differenceBraggs law states that, the path difference

between the two reflected rays by the crystalbetween the two reflected rays by the crystal

planes should be an integral multiple ofplanes should be an integral multiple of

wavelength of incident xwavelength of incident x--rays for producingrays for producing

maxima or constructive interference.maxima or constructive interference.

The crystal act as a series of parallel reflectingThe crystal act as a series of parallel reflectingplanes.planes.


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Consider a ray PA reflected at a atom A, inConsider a ray PA reflected at a atom A, in

the directionthe direction ARAR from plane 1 andfrom plane 1 and

another ray QB reflected at another atom Banother ray QB reflected at another atom Bin the direction BS.in the direction BS.


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Plane 1

Plane 2

Plane 3

A

B

C D

PQ

R S

d90

90


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The path difference between these twoThe path difference between these two

rays is CB+BDrays is CB+BD

The two rays will reinforceeach other andThe two rays will reinforceeach other and

produce an intense spot , when pathproduce an intense spot , when path

difference is an integral multiple of wavedifference is an integral multiple of wave

length.length.


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CB+BD=nCB+BD=n

CB=BD=d sinCB=BD=d sin

2d sin2d sin= n= n

Where n = 1,2,3,..first , second order etc.Where n = 1,2,3,..first , second order etc.

For 1st order sinFor 1st order sin1 =1 = /2d./2d.

For2nd order sinFor2nd order sin2 = 22 = 2 / 2d./ 2d.

For 3rd order sinFor 3rd order sin3 = 33 = 3 / 2d./ 2d. wherewhere 1,1, 2 and2 and 3 are the glancing angles for n=1,2 and3 are the glancing angles for n=1,2 and

3 respectively.3 respectively.


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Importance of Braggs law

For cubic:

For BCC

For FCC


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X-ray Diffraction Techniques:

There are three main experimental XThere are three main experimental X--rayray

diffraction methods by which the crystaldiffraction methods by which the crystalstructure can be analyzed.structure can be analyzed.

1.Laue method.1.Laue method.

2.Powder method.2.Powder method.

3.Rotating crystal method.3.Rotating crystal method.


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Laue method:

Consider heterogeneous beam of xConsider heterogeneous beam of x--rays in the wavelengthrays in the wavelengthof 0.2of 0.2A to 2A to 2A originating from a suitable source.A originating from a suitable source.

In this technique, the crystal stationary in a heterogeneousIn this technique, the crystal stationary in a heterogeneousbeam of xbeam of x--rays.rays.

The diffraction pattern consists of a bright central spotThe diffraction pattern consists of a bright central spotand a set of spots arranged in a definite pattern about theand a set of spots arranged in a definite pattern about thecentral spot.central spot.

The symmetrical pattern caused by diffraction of xThe symmetrical pattern caused by diffraction of x--raysraysby crystal planes is called the Laue pattern.by crystal planes is called the Laue pattern.


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crystal

Photographic plate

Laue pattern

X-rays

slits


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Photographic film

P

o

White x-radiation

crystal

2

D


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The crystal is fixed, for an incident angle , the

diffracted angle becomes 2.

Consider, D is the distance between the crystal

and photographic film and OP = R.


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From COP,

Tan2 = OP/OC

OP = OC tan2

R = D tan2

By the interpretation of the reflection spots inthe photographic film, the crystal structure of

thegiven specimen can be determined. This method is used to study the orientation ofThis method is used to study the orientation of

the crystal and verify crystal symmetry.the crystal and verify crystal symmetry.


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Powder method (Debye scherrer

method): Powder crystal method is a standard technique to study the structure of microPowder crystal method is a standard technique to study the structure of micro

crystals.crystals.

This method gives the information regarding the size ofThis method gives the information regarding the size of crystals, presencecrystals, presence ofofimpurities,distortion,etcimpurities,distortion,etc

It is used for accurate determination of lattice parameters in crystalsIt is used for accurate determination of lattice parameters in crystals

The powdered specimen is kept inside a small capillary tubeThe powdered specimen is kept inside a small capillary tube

If a monochromatic XIf a monochromatic X--ray beam is directed on to a singleray beam is directed on to a single crystal, thencrystal, then only one oronly one ortwo diffracted beams may result.two diffracted beams may result.


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y If the sample consists of few tens of

randomly oriented single crystal ,thediffraction beams are seen to lie on the

surface of several cones. The cones may

emerge in all direction ,forward andbackward

y

20


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A sample of few hundred of crystals(i.e

Powdered sample) show that the diffracted

beams form continuous cones .

21


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w1

w2

r

2

2

Incident x-ray beam

S

Crystal powder


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The distance s on the film between two diffractionThe distance s on the film between two diffractionlines corresponding to a particular plane is related to thelines corresponding to a particular plane is related to theBraggs angle by the equation.Braggs angle by the equation.

Where r is the specimen to film distance.Where r is the specimen to film distance.

r

s

r

s

4

4

!

!

U

U


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1. Laue diffraction method is most used for mounting the single crystalsin a precisely known orientation.It is very much useful for study ofcrystal symmetry.

2. X-ray powder diffraction has large number of applications.

Study of d-spacing.

Study of mixtures.

Study of alloys.

Stress determination in metals.

Determination of particle size.

3. Rotating crystal method is generally used to align the crystals andmeasure lattice parameters and determine the crystal structure.

Applications ofX-ray

Diffraction

x ray diffraction 1

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