X – RAY DIFFRACTIONPRESENTED BYIswar HazarikaIst yr. M. PHARM.DEPT. OF PHARMACOLOGYThe 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 wavelengthelectromagnetic radiation between UV & gamma ray,which consist of wavelength in the region about 0.1Å to100Å For analytical purpose, the range of 0.7-2.0 Ao is themost useful region. A German professor Rontgen in 1895 discovered X-raywhile working with a discharge tube Barium platinocyanide screen placed near dischargetube began to glow. The glow continued even when awooden screen was placed between them These x-rays could pass through bodies, which are opaqueto ordinary light
2. X-Ray generationFor analytical purposes, X-rays are obtained in threeways: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-rayfluorescence,3. by use of a radioactive source whose decay processresults in X-ray emission,
How does X-ray generate:? Process of producing X-Rays may bevisualised in terms of Bhor’s theory ofatomic Structure When a fast moving electron impinges onan atom, it may knock out an electroncompletely from one of the inner shell ofthe atom Following that, one of the electron fromouter layer will fall into the vacated orbitalwith simultaneous emission of X-Rayproton
The X-rays are named according to theshell from which the electron is knockedout, eg. K X-ray, L X-ray etc. K X-ray is again divided into Kα & kβdepending on whether electron falls fromthe closest shell or the next nearest shell Kα is again named Kα1 & Kα2 accordingto the energy levels of the differentelectrons in L-shell & kβ1, kβ2 for kβ rays. The energy of these waves is given by theequationhν = E(outer shell)- E(inner shell)
3. Elementary CrystallographyCrystallography: Science of study of crystalforms.Crystal: A homogenous solid formed by repeating3dimensional pattern of atoms, ions or molecules& having smooth external surface The aspects of crystallography most important tothe 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 cellThe smallest group of particles within acrystal that retains the geometric shape ofthe crystal is known as a unit cellA crystal lattice is a repeating array of anyone of fourteen kinds of unit cells.There are four types of unit cells that canbe associated with each crystal system.
The Bravais lattices When the crystal systems are combined with thevarious possible lattice centerings, we arrive at theBravais lattices. They describe the geometric arrangement of thelattice points, and thereby the translationalsymmetry of the crystal. In three dimensions, there are 14 unique Bravaislattices which are distinct from one another in thetranslational symmetry they contain. All crystallinematerials recognized until now (not includingquasicrystals) fit in one of these arrangements. The Bravais lattices are sometimes referred to asspace lattices.
Lattice◦ Lattice: A lattice is a repeating array of any oneof fourteen kinds of unit cells◦ If in an actual crystal, we replace all the atomsor group of atoms or ions which are calledstructural units, by points we get a threedimensional network or arrangement of pointsdesignated as the lattice.Lattice Notation: Lattice points are specified without brackets –100,101, 102, etc. Lattice planes: are defined in terms of the Millerindices
4. MILLER INDICES: Miller Indices are the reciprocals of the fractionalintercepts (with fractions cleared) which the plane makeswith the crystallographic x,y,z axes of the threenonparallel edges of the cubic unit cell. Spacing between planes in a cubic crystalwhere dhkl = interplanar spacing between planes withMiller indices h,k,and l.a = lattice constant (edge of the cube)h, k, and l = Miller indices of cubic planes beingconsidered.l+k+ha=d 222hkl
Example:The plane shown intercepts a at100, b at010 and c at 002.The Miller index of the plane is thuscalculated as 1/1(a), 1/1(b), 1/2(c), andreduced to integers as 2a,2b,1c.Miller indices are by convention given inparentheses, i.e., (221).
Interference A source of light gives out energy which isuniformly distributed in the surroundingmedium. If two or more light waves superimpose ,then thedistribution of energy is not uniform. If crest of one wave falls on the crest of the otherand trough of one wave falls on the trough ofother, the amplitude of the resultant waveincreases. On the other hand ,if the crest of one wave fallson the trough of the other the resultantamplitude decreases Therefore the light intensity decreases. The modification in the distribution of lightenergy due to superposition of two or morewaves is called interference
5. BRAGG’s EQUATIONdhkl The path difference between ray 1 and ray 2 = 2dhkl Sin For constructive interference: n = 2dhkl SinRay 1Ray 2Deviation = 2
Condition for Bragg’s law Two beams with identical wavelength and phaseapproach a crystalline solid and are scattered offtwo different atoms within it. The lower beam traverses an extra length of2dsinθ Constructive interference occurs when this lengthis equal to an integer multiple of the wavelengthof the radiation A diffraction pattern is obtained by measuringthe intensity of scattered waves as a function ofscattering angle Very strong intensities known as Bragg peaks areobtained in the diffraction pattern whenscattered waves satisfy the Bragg condition
6. INSTRUMENTATIONI. Production of x-raysII. CollimatorIII. MonochromatorsIV. Detectors
I) Production of x rays X-rays are generated when high velocityelectron impinge on a metal target Filament of tungsten is a cathode which isheated by a battery to emit electron(cathode rays) The electron on striking the target (whichis a +ve voltage in the form of anode) willtransfer their energy to its metallicsurface and it gives of X-ray radiation Choice of target metal depends upon thesample to be examined
2) Collimator X-rays produced by the target arerandomly directed They form a hemisphere with a target atthe center In order to get a narrow beam of x-rays,collimator are used It consist of two sets of closely packedmetal plates separated by a small gap It absorbs all the X-ray except the narrowbeam that passes between the gap
a) Filter Filter is a window of material that absorbsundesirable radiation but allows the radiationof required wavelength to pass This method makes use of large difference inthe mass absorption coefficientExample: When Zirconium filter is used formolybdenum radiation Zirconium absorbs strongly the radiation ofmolybdenum at short wavelength but weaklyabsorb 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 crystallinematerial positioned in the X-ray beam sothat the angle of reflecting planes satisfyBraggs equation for required wavelength It splits the beam into the componentwavelength in the same way as the prism Such a crystalline substance is called ananalysing crystalIts of two type:◦ Flat crystal monochromator◦ Curved crystal monochromator
Photographic Methods A plane or cylindrical film isused to record the position& intensity of the x-raybeam Film after exposing to x-rayis developed The blackening of developedfilm is expressed in terms ofdensity units D given byI0 & I refer to incident &transmitted intensities of x-raysD is related to total x-rayenergy that causes theblackening of photographic filmValue of D is measured bydensitometer
Counter Methodsa) Geiger-muller tube counter:- Geiger tube is filled with inert gas like argon The central wire anode is maintained at apositive potential of 800-2500V When x-ray enters the Geiger tube, itundergoes collision with the filling gas resultingin the production of ion pairs The electron produced moves towards thecentral anode and the +ve ion moves towardsthe outer electrode The electron is accelerated by the potentialgradient and causes the ionisation of largenumber of argon atoms resulting in productionof avalanche of electrons that are travellingtowards the central anode
b) Proportional CounterIts construction is same as that of Geiger tube counter.Gas used - Xenon & Krypton(heavy gas is used) ?Because it is easily ionisedThe voltage applied is less than that of Geiger plateauDead time – (~0.2 µs)Sensitivity & efficiency – is comparable with Geigertube counter
c) Scintillation Detector In Scintillation detector, there is a large NaIcrystal activated with a small amount of thallium When X-ray is incident upon the crystal, thepulses of visible light are emitted Visible light so obtained can be detected by aphotomultiplier tube Crystals used – sodium iodide, anthracene,naphthalene, & p-terphenol inxylene. Dead time - very short and this allows forcounting of high rates
d) Solid state semi-conductor detector In this type of detector, the electrons produced by X-raybeam are promoted to conduction band The current which flows is directly proportional to theincident x-ray energy. Main disadvantage – we have to use this detector at lowtemperature to minimise the noise & prevent deteriorationin characteristics
e) Semi-conductor Detectors Si(Li) and Ge(Li) Principle of Semi-conductor detector issame as proportional counter, except thematerials used are in a solid state When x-ray falls on a semiconductor or asilicon lithium-drifted detector, itgenerates an electron (-e) and a hole(+e).
X-Ray Diffraction MethodsUsed for investigating internal structures.The following methods are used:-1. Laue Photographic methoda) Transmission Methodb) Back-Reflection method2. Bragg X-ray spectrometer3. Rotating crystal Method4. Powder Diffraction Method
Laue Photographic MethodThe Laue method is mainly used todetermine the orientation of large singlecrystals White radiation is reflected from, ortransmitted through, a fixed crystalTwo Types:-a. Transmission Method: In the transmission Lauemethod, the film is placed behind the crystal torecord beams which are transmitted through thecrystal.b. Back Reflection Method: In the back-reflectionmethod, the film is placed between the x-raysource and the crystal. The beams which arediffracted in a backward direction are recorded.
Transmission methodMain featuresi) A is source of x-ray (Whiteradiation) which is obtained froma tungsten target at about60,000Vii) B is a pinhole collimator. WhenX-ray pass through this pinholecollimator, a fine pencil of x-raysis obtained. The small is thediameter the sharper is theinterferenceiii) C is a crystal whose internalstructure is to investigated. Thecrystal is set on a holder to adjustits orientationiv) D is a film arranged on a rigidbase. This film is provided withbeam stop to prevent direct beamfrom causing excessive fogging ofthe film
The position of crystalis held stationary in abeam of X-ray The X-ray after passingthrough the crystal arediffracted and arerecorded on aphotographic plate Crystal orientation isdetermined from theposition of the spots Each spot can beindexed, i.e. attributedto a particular plane,using special charts The Leonhardt chart isused for transmissionpatterns.
b. Back Reflection Method Crystal orientation isdetermined from theposition of the spots Each spot can beindexed, i.e.attributed to aparticular plane,using special charts The Greninger chartis used for back-reflection patterns
Bragg’s X-Ray Spectrometer Method X-ray from the anticathode Qare allowed to pass throughadjustable slit A & allowed tofall on Crystal C The position of the crystal canbe adjusted by the vernieralong the circular scale The reflected rays passesthrough slit D and enters theionization chamber throughnarrow aluminum window The ionization chamber ismounted on an arm & itsposition is determined by asecond vernier Each plate of two is connectedto +ve and –ve of battery tomeasure the strength ofionization current
Working: The crystal is mounted in such a position thatθ=0o & ionization chamber adjusted toreceive the X-rays The crystal and ionization chamber are madeto move in small steps so that the anglethrough which the chamber is moved is twicethe angle through which the crystal is rotated The ionization at first falls but for certainvalue of θ it rises sharply & this correspondsto the direction of x-ray spectrum
Measurement of λ The wavelength of X-ray can bedetermined by employing the followingequation2dsinθ = nλ The value of θ for various spectraproduced by reflection from a crystal ismeasured & the mean value of λ/d isdetermined The value of λ/d is known as latticeconstantLattice constant = λ/d Knowing d, the wavelength λ can becalculated
Measurement of d The lattice spacing d is connected to celledge by the following relationd = a(√2)/2 for simple latticed = a/2 for fcc crystal latticed = a(√3)/2 for bcc crystal lattice Where a can be calculated asa=[(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’slaw: The X-rays are allowed to fall on the crystalsurface Then crystal is rotated to reflect from variouslattice planes Then various ratio of lattice spacing for variousgroup of spacing is obtained This ratio has been found to be different fordifferent crystals The experimentally observed ratios are comparedwith the calculated ratios(i) d100:d110:d111 = 1:1/√2:1/√3 for simple cubiclattice(ii) d100:d110:d111 = 1:1/√2:1/√3 for fcc crystal(iii) d100:d110:d111 = 1:1/√2:1/√3 for bcc crystal
X-rays are generated in the x-ray tube The beams are made monochromatic byfilter Monochromatic rays then passes throughcollimating system Xrays then falls on crystal mounted on ashaft which can be rotated at a uniformuniform angular ratee by a small motor When the shaft rotates it satisfies bragg’srelation which produces spot onphotographic plate
Powder crystal Method Main featuresi) A is source of x-ray.ii) X-ray beam falls on thepowder P through slits S1 & S2function of this slits is to getnarrow pencil of x-ray.iii) Fine powder P struck on a hairby means of gum is suspendedvertically in the axis ofcylindrical camera. Thisenables sharp lines to beobtained on the photographicfilm which is surrounded bypowder crystal in form ofcircular arc.iv) The x-rays after falling on thepowder passes out of thecamera through a cut in thefilm so as to minimise thefogging produced by beam.v) On the flat photographic platethe observed pattern consist oftraces.
Powder crystal Method THEORYWhen a monochromatic beam of x-ray is allowed tofall on the powder of a crystal, then the following possibilitiesmay happen…i) There will be some particles out of the random orientation ofsmall crystals in fine powder, which lie within a given set oflattice planes for reflection to occurii) While another fraction of a grains will have another set ofplanes in the correct position for the reflections to occur andso on.iii) Reflections are also possible in the different order of each set.
All the like orientations of the grains dueto the reflection for each set of planes &for each order will constitute a diffractioncone Crystal structure can be obtained from thearrangement of the traces & their relativetraces If angle of incidence is θ, the angle ofreflection will be 2θ If the film radius is r, the circumference2πr corresponds to a scattering angle of360o
Then we can write l/2πr = 2θ/360 θ = 360l/πr The value of θ can be calculated from theequation substituting this value in Bragg’s equationthe value of d can be calculatedApplication: The method is useful for cubic crystals Methods is used for determining the complexstructure of metals This method is useful to make distinctionbetween the allotropic modification of thesame substance
Applications of X-Rays Structure of crystals Polymer characterization Soil classification based on crystallinity Analysis of industrial dusts Corrosion products can be studied Tooth enamel and dentine have beenexamined Degree of crystallinity of a polymer andsludge Elucidating the structure of RNA and DNA Determination of cis and trans isomers Particle size determination Crystalline compounds (gall stones) in thebody can be detected
REFERENCES1. Chatwal GR, Anand SK. Instrumental Methodsof Chemical analysis. 5th edition. HimalayaPublishing house. 2.303-2.3392. Connolly JR. introduction to X-Ray PowderDiffrection. Elementary Crystallography for X-ray, Spring 20123. http://en.wikipedia.org/wiki/X-ray_crystallography4. http://en.wikipedia.org/wiki/Bragg%27s_law5. http://www.matter.org.uk/diffraction/x-ray/laue_method.htm6. http://www.xtal.iqfr.csic.es/Cristalografia/parte_06-en.html7. Gauglitz G, Vo-dinh T. Handbook ofspectroscopy. Wiley-Vch GmbH & Co. publisherpage.360