X – RAY DIFFRACTIONPRESENTED BY

Iswar Hazarika

Ist yr. M. PHARM.DEPT. OF PHARMACOLOGY

The Oxford College of Pharmacy,

CONTENTS1. Introduction2. Production of X-Ray3. Elementary Crystallography4. Miller indices5. Bragg’s law6. Instrumentation7. X-Ray diffraction method8. Application of X-ray diffraction

1. Introduction: X-Ray Definition:X-Rays are short wavelength

electromagnetic radiation between UV & gamma ray, which consist of wavelength in the region about 0.1Å to 100Å

For analytical purpose, the range of 0.7-2.0 Ao is the most useful region.

A German professor Rontgen in 1895 discovered X-ray while working with a discharge tube

Barium platinocyanide screen placed near discharge tube began to glow. The glow continued even when a wooden screen was placed between them

These x-rays could pass through bodies, which are opaque to ordinary light

http://en.wikipedia.org/wiki/Image:EM_Spectrum3-new.jpg

2. X-Ray generation

For analytical purposes, X-rays are obtained in three ways:

1. by bombardment of a metal with a beam of high-energy electrons,

2. by exposure of a substance to a primary beam of X-rays in order to generate a secondary beam of X-ray fluorescence,

3. by use of a radioactive source whose decay process results in X-ray emission,

How does X-ray generate:?Process of producing X-Rays may be

visualised in terms of Bhor’s theory of atomic Structure

When a fast moving electron impinges on an atom, it may knock out an electron completely from one of the inner shell of the atom

Following that, one of the electron from outer layer will fall into the vacated orbital with simultaneous emission of X-Ray proton

The X-rays are named according to the shell from which the electron is knocked out, eg. K X-ray, L X-ray etc.

K X-ray is again divided into Kα & kβ depending on whether electron falls from the closest shell or the next nearest shell

Kα is again named Kα1 & Kα2 according to the energy levels of the different electrons in L-shell & kβ1, kβ2 for kβ rays.

The energy of these waves is given by the equation

hν = E(outer shell)- E(inner shell)

3. Elementary CrystallographyCrystallography: Science of study of crystal

forms.Crystal: A homogenous solid formed by repeating

3dimensional pattern of atoms, ions or molecules & having smooth external surface

The aspects of crystallography most important to the effective interpretation of XRD data are:I. conventions of lattice description, II. unit cells, III. lattice planes, IV. d-spacing and Miller indices,V. crystal structure and symmetry elements

Unit cell

The smallest group of particles within a crystal that retains the geometric shape of the crystal is known as a unit cell

A crystal lattice is a repeating array of any one of fourteen kinds of unit cells.

There are four types of unit cells that can be associated with each crystal system.

b

a

c

α

β

γ

A UNIT CELL

Examine the 14 Bravais Lattices in Detail

The Bravais lattices

When the crystal systems are combined with the various possible lattice centerings, we arrive at the Bravais lattices.

They describe the geometric arrangement of the lattice points, and thereby the translational symmetry of the crystal.

In three dimensions, there are 14 unique Bravais lattices which are distinct from one another in the translational symmetry they contain. All crystalline materials recognized until now (not including quasicrystals) fit in one of these arrangements.

The Bravais lattices are sometimes referred to as space lattices.

Lattice ◦Lattice: A lattice is a repeating array of any one

of fourteen kinds of unit cells ◦If in an actual crystal, we replace all the atoms or

group of atoms or ions which are called structural units, by points we get a three dimensional network or arrangement of points designated as the lattice.

Lattice Notation:Lattice points are specified without brackets –100,

101, 102, etc.Lattice planes: are defined in terms of the Miller

indices

4. MILLER INDICES: Miller Indices are the reciprocals of the fractional

intercepts (with fractions cleared) which the plane makes with the crystallographic x,y,z axes of the three nonparallel edges of the cubic unit cell.

Spacing between planes in a cubic crystal    where dhkl = interplanar spacing between planes with Miller indices h,k,and l.a = lattice constant (edge of the cube)h, k, and l = Miller indices of cubic planes being considered.  

l + k + h

a = d

222hkl

Example: The plane shown intercepts a at100, b at

010 and c at 002. The Miller index of the plane is thus

calculated as 1/1(a), 1/1(b), 1/2(c), and reduced to integers as 2a,2b,1c.

Miller indices are by convention given in parentheses, i.e., (221).

Interference A source of light gives out energy which is

uniformly distributed in the surrounding medium. If two or more light waves superimpose ,then the

distribution of energy is not uniform. If crest of one wave falls on the crest of the other

and trough of one wave falls on the trough of other, the amplitude of the resultant wave increases.

On the other hand ,if the crest of one wave falls on the trough of the other the resultant amplitude decreases

Therefore the light intensity decreases. The modification in the distribution of light

energy due to superposition of two or more waves is called interference

5. BRAGG’s EQUATION

dhkl

dhkl Sin

The path difference between ray 1 and ray 2 = 2dhkl Sin

For constructive interference: n = 2dhkl Sin

Ray 1

Ray 2

Deviation = 2

Condition for Bragg’s lawTwo beams with identical wavelength and phase

approach a crystalline solid and are scattered off two different atoms within it.

The lower beam traverses an extra length of 2dsinθ Constructive interference occurs when this length

is equal to an integer multiple of the wavelength of the radiation

A diffraction pattern is obtained by measuring the intensity of scattered waves as a function of scattering angle

Very strong intensities known as Bragg peaks are obtained in the diffraction pattern when scattered waves satisfy the Bragg condition

6. INSTRUMENTATION

I. Production of x-rays

II. Collimator

III. Monochromators

IV. Detectors

I) Production of x raysX-rays are generated when high velocity

electron impinge on a metal targetFilament of tungsten is a cathode which is

heated by a battery to emit electron (cathode rays)

The electron on striking the target (which is a +ve voltage in the form of anode) will transfer their energy to its metallic surface and it gives of X-ray radiation

Choice of target metal depends upon the sample to be examined

2) Collimator X-rays produced by the target are

randomly directedThey form a hemisphere with a target at

the centerIn order to get a narrow beam of x-rays,

collimator are usedIt consist of two sets of closely packed

metal plates separated by a small gapIt absorbs all the X-ray except the narrow

beam that passes between the gap

2) Collimator

3) Monochromator

a) Filter

b) Crystal monochromator

i) Flat crystal monochromatorii) Curved crystal monochromator

a) Filter Filter is a window of material that absorbs

undesirable radiation but allows the radiation of required wavelength to pass

This method makes use of large difference in the mass absorption coefficient

Example: When Zirconium filter is used for molybdenum

radiationZirconium absorbs strongly the radiation of

molybdenum at short wavelength but weakly absorb the Kα lines of molybdenum

Thus it allow Kβ lines to pass hence zirconium is a β-filter

b) Crystal Monochromator It is made up of suitable crystalline

material positioned in the X-ray beam so that the angle of reflecting planes satisfy Braggs equation for required wavelength

It splits the beam into the component wavelength in the same way as the prism

Such a crystalline substance is called an analysing crystal

Its of two type:◦Flat crystal monochromator◦Curved crystal monochromator

Detectors

a) Photographic Methods

b) Counter Methodsi) Geiger-muller tube counter

ii) Proportional counter iii) Scintillation detector iv) Solid-state-semi-conductor detector v) Semi-conductor detector

Photographic Methods A plane or cylindrical film is

used to record the position & intensity of the x-ray beam

Film after exposing to x-ray is developed

The blackening of developed film is expressed in terms of density units D given by

I0 & I refer to incident & transmitted intensities of x-rays

D is related to total x-ray energy that causes the

blackening of photographic film Value of D is measured by

densitometer

Counter Methods a) Geiger-muller tube counter:- Geiger tube is filled with inert gas like argon The central wire anode is maintained at a positive

potential of 800-2500V When x-ray enters the Geiger tube, it undergoes

collision with the filling gas resulting in the production of ion pairs

The electron produced moves towards the central anode and the +ve ion moves towards the outer electrode

The electron is accelerated by the potential gradient and causes the ionisation of large number of argon atoms resulting in production of avalanche of electrons that are travelling towards the central anode

Geiger-muller tube counter:- 800-2500V , OUTPUT PULSE- 1-10V

b) Proportional CounterIts construction is same as that of Geiger tube counter.

Gas used - Xenon & Krypton (heavy gas is used) ?Because it is easily ionised

The voltage applied is less than that of Geiger plateau

Dead time – (~0.2 µs)

Sensitivity & efficiency – is comparable with Geiger tube counter

c) Scintillation Detector

In Scintillation detector, there is a large NaI crystal activated with a small amount of thallium

When X-ray is incident upon the crystal, the pulses of visible light are emitted

Visible light so obtained can be detected by a photomultiplier tube

Crystals used – sodium iodide, anthracene, naphthalene, & p-terphenol in xylene.

Dead time - very short and this allows for counting of high rates

d) Solid state semi-conductor detector

In this type of detector, the electrons produced by X-ray beam are promoted to conduction band

The current which flows is directly proportional to the incident x-ray energy.

Main disadvantage – we have to use this detector at low temperature to minimise the noise & prevent deterioration in characteristics

e) Semi-conductor Detectors

Si(Li) and Ge(Li)Principle of Semi-conductor detector is

same as proportional counter, except the materials used are in a solid state

When x-ray falls on a semiconductor or a silicon lithium-drifted detector, it generates an electron (-e) and a hole (+e).

Semi-conductor Detectors

X-Ray Diffraction Methods

Used for investigating internal structures. The following methods are used:-1. Laue Photographic method

a) Transmission Methodb) Back-Reflection method

2. Bragg X-ray spectrometer3. Rotating crystal Method4. Powder Diffraction Method

Laue Photographic Method

The Laue method is mainly used to determine the orientation of large single crystals White radiation is reflected from, or transmitted through, a fixed crystalTwo Types:-a. Transmission Method: In the transmission Laue

method, the film is placed behind the crystal to record beams which are transmitted through the crystal.

b. Back Reflection Method: In the back-reflection method, the film is placed between the x-ray source and the crystal. The beams which are diffracted in a backward direction are recorded.

Transmission methodMain featuresi) A is source of x-ray (White

radiation) which is obtained from a tungsten target at about 60,000V

ii) B is a pinhole collimator. When X-ray pass through this pinhole collimator, a fine pencil of x-rays is obtained. The small is the diameter the sharper is the interference

iii) C is a crystal whose internal structure is to investigated. The crystal is set on a holder to adjust its orientation

iv) D is a film arranged on a rigid base. This film is provided with beam stop to prevent direct beam from causing excessive fogging of the film

The position of crystal is held stationary in a beam of X-ray

The X-ray after passing through the crystal are diffracted and are recorded on a photographic plate

Crystal orientation is determined from the position of the spots

Each spot can be indexed, i.e. attributed to a particular plane, using special charts

The Leonhardt chart is used for transmission patterns.

b. Back Reflection Method

Crystal orientation is determined from the position of the spots

Each spot can be indexed, i.e. attributed to a particular plane, using special charts

The Greninger chart is used for back-reflection patterns

Bragg’s X-Ray Spectrometer Method X-ray from the anticathode Q are

allowed to pass through adjustable slit A & allowed to fall on Crystal C

The position of the crystal can be adjusted by the vernier along the circular scale

The reflected rays passes through slit D and enters the ionization chamber through narrow aluminum window

The ionization chamber is mounted on an arm & its position is determined by a second vernier

Each plate of two is connected to +ve and –ve of battery to measure the strength of ionization current

Working:The crystal is mounted in such a position

that θ=0o & ionization chamber adjusted to receive the X-rays

The crystal and ionization chamber are made to move in small steps so that the angle through which the chamber is moved is twice the angle through which the crystal is rotated

The ionization at first falls but for certain value of θ it rises sharply & this corresponds to the direction of x-ray spectrum

Measurement of λThe wavelength of X-ray can be determined

by employing the following equation 2dsinθ = nλ

The value of θ for various spectra produced by reflection from a crystal is measured & the mean value of λ/d is determined

The value of λ/d is known as lattice constant

Lattice constant = λ/d Knowing d, the wavelength λ can be

calculated

Measurement of dThe lattice spacing d is connected to cell

edge by the following relationd = a(√2)/2 for simple latticed = a/2 for fcc crystal latticed = a(√3)/2 for bcc crystal latticeWhere a can be calculated as

a=[(M*n)/(N*ρ)]1/3

◦M= Molecular Weight◦n= No. of atoms in unit cell◦N= Avogadro’s number◦Ρ= Density

Determination of crystal structure by bragg’s law:

The X-rays are allowed to fall on the crystal surface

Then crystal is rotated to reflect from various lattice planes

Then various ratio of lattice spacing for various group of spacing is obtained

This ratio has been found to be different for different crystals

The experimentally observed ratios are compared with the calculated ratios(i) d100:d110:d111 = 1:1/√2:1/√3 for simple cubic lattice(ii) d100:d110:d111 = 1:1/√2:1/√3 for fcc crystal(iii) d100:d110:d111 = 1:1/√2:1/√3 for bcc crystal

Rotating Crystal Method

X-rays are generated in the x-ray tubeThe beams are made monochromatic by

filterMonochromatic rays then passes through

collimating systemXrays then falls on crystal mounted on a

shaft which can be rotated at a uniform uniform angular ratee by a small motor

When the shaft rotates it satisfies bragg’s relation which produces spot on photographic plate

Powder crystal Method Main featuresi) A is source of x-ray. ii) X-ray beam falls on the powder

P through slits S1 & S2 function of this slits is to get narrow pencil of x-ray.

iii) Fine powder P struck on a hair by means of gum is suspended vertically in the axis of cylindrical camera. This enables sharp lines to be obtained on the photographic film which is surrounded by powder crystal in form of circular arc.

iv) The x-rays after falling on the powder passes out of the camera through a cut in the film so as to minimise the fogging produced by beam.

v) On the flat photographic plate the observed pattern consist of traces.

Powder crystal Method THEORY

When a monochromatic beam of x-ray is allowed to fall on the powder of a crystal, then the following possibilities may happen…

i) There will be some particles out of the random orientation of small crystals in fine powder, which lie within a given set of lattice planes for reflection to occur

ii) While another fraction of a grains will have another set of planes in the correct position for the reflections to occur and so on.

iii) Reflections are also possible in the different order of each set.

All the like orientations of the grains due to the reflection for each set of planes & for each order will constitute a diffraction cone

Crystal structure can be obtained from the arrangement of the traces & their relative traces

If angle of incidence is θ, the angle of reflection will be 2θ

If the film radius is r, the circumference 2πr corresponds to a scattering angle of 360o

Then we can writel/2πr = 2θ/360 θ = 360l/πrThe value of θ can be calculated from the

equation substituting this value in Bragg’s equation

the value of d can be calculated Application:The method is useful for cubic crystalsMethods is used for determining the complex

structure of metalsThis method is useful to make distinction

between the allotropic modification of the same substance

Applications of X-RaysStructure of crystalsPolymer characterizationSoil classification based on crystallinityAnalysis of industrial dustsCorrosion products can be studiedTooth enamel and dentine have been examinedDegree of crystallinity of a polymer and sludgeElucidating the structure of RNA and DNADetermination of cis and trans isomersParticle size determinationCrystalline compounds (gall stones) in the body

can be detected

REFERENCES1. Chatwal GR, Anand SK. Instrumental

Methods of Chemical analysis. 5th edition. Himalaya Publishing house. 2.303-2.339

2. Connolly JR. introduction to X-Ray Powder Diffrection. Elementary Crystallography for X-ray, Spring 2012

3. http://en.wikipedia.org/wiki/X-ray_crystallography

4. http://en.wikipedia.org/wiki/Bragg%27s_law5. http://www.matter.org.uk/diffraction/x-ray/la

ue_method.htm6. http://www.xtal.iqfr.csic.es/Cristalografia/pa

rte_06-en.html7. Gauglitz G, Vo-dinh T. Handbook of

spectroscopy. Wiley-Vch GmbH & Co. publisher page.360

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