Presentation on theme: "X-RAY DIFFRACTION TECHNIQUE"— Presentation transcript:
1X-RAY DIFFRACTION TECHNIQUE Dr. Pramod Kumar SinghSchool of Basic Sciences & ResearchSchool of Engineering and TechnologySharda University, Greater Noida, INDIAE mail:
2X-ray Diffraction The most important X-ray diffraction There are number of physical methods for investigating the structures of solids.Each technique has its own merit and weaknesses.The most important X-ray diffraction*Fingerprint characterization of crystalline materials*Determination of their crystal structures.
10X-ray Diffraction Optical grating and diffraction of light Diffraction of light by an optical grating.An optical grating may consist of a piece of glass on which have been ruled a large number of accurately parallel and closely spaced lines.The separation of lines should be a little larger than the wavelength of light, say 10,000 Å.
11Consider what happens to a beam of light which hits the grating perpendicular to the plane. A piece of glass without the lines would simply transmit the light
12*In the grating lines act as a secondary point sources of light and radiate light in all the directions.Interference then occurs between the waves originating from each lines source.
13In certain directions, adjacent beams are in phase with each other and constructive interference occurs to give a resultant diffracted beam in the direction.When the beams are out of phase, they cancel each other and the net intensity becomes zero
14Production of X-raysX-rays are produced when high speed electrons are suddenly stopped by a solid object.Of the total energy supplied, only a fraction (about 1%) is converted to X-rays.Most of the energy is transferred into heat.To prevent the target from melting, it is cooled from behind by running water.Thus the target material must be made of a high melting material which has good thermal conductivity.For the production of high intensity X-rays a target element should have a high atomic number.Pure transition metals such as Mo, Cu, Cr etc. are typical target materials.
15Imagine an atom consisting of a nucleus surrounded by a system of electrons contained in shells called K, L, M etc. as shown in Figure.The electrons in K, L and M shells are the electrons with principal quantum number 1, 2 and 3 respectively.
16An electron bombarding the target may have sufficient energy to completely displace a K electron from the target atom.This produces an unstable ion, and 10-4 sec. later an electron from an outer shell drops into the vacant position.
17This transition is accompanied by the emission of a characteristics X-ray If the vacancy is filled by an M electron then the photon produced is called a Kb1 X-ray.If the vacancy is filled by an L electron the a Ka1 or a Ka2 X-ray is produced, depending on the sub shell of the electron.
19Diffraction of X-rays from crystals By 1912 the nature of X-rays – whether they were particles or waves was unresolved.This was eventually achieved by von Laue using a crystal of copper sulphate as the diffraction grating.X-ray diffraction by a crystal of beryl using the Laue method.
20X-ray diffraction by a crystal of beryl using the Laue method. Diffraction of X-rays from crystalsCrystalline solids consist of regular arrays of atoms, ions or molecules with inter atomic spacing of the order of 100 pm.For diffraction to take place, the wavelength of the incident light has to be of the same order of magnitude as the spacing of the grating.Because of the periodic nature of the internal structure, it is possible for crystals to act as a three dimensional diffraction grating to light of a suitable wavelength: a Laue photograph is shown in the figureX-ray diffraction by a crystal of beryl using the Laue method.
21The array of black points (section through a crystal) Figure illustrates the Bragg condition for the reflection of X-ray by a crystal.The array of black points (section through a crystal)Lines joining the dots mark a set of parallel planes with Miller indices hkl and interplanar spacing dhkl.Path difference EF+FGEF + FG = 2d SinThe intensity of the diffracted beam will be maximum if the path difference is an integral multiple of wavelength2d Sin = n This is Braggs equation
22For the reflected beams the Figure illustrates the Bragg condition for the reflection of X-ray by a crystal.The ray A is scattered by the atom at B and the ray D is scattered by the atom at F.For the reflected beams thePath difference EF+FGEF + FG = 2d Sin2d Sin = n This is Braggs equationThe intensity of the diffracted beam will be maximum if the path difference is an integral multiple of wavelength
23Linear (1D) Diffraction Scans have better resolution and less noise
24Applications of X-ray-diffraction The methods of X-ray diffraction has been used for more than 100 years to identify and characterize crystalline phases in solid materialsXRD technique is a powerful tool to distinguish between crystalline and amorphous materialsIt is used for qualitative and quantitative analysis of crystalline materials
25Applications of X-ray-diffraction X-ray diffraction from single crystals are used for crystal structure determinationsPowder X-ray diffraction is used for lattice parameter determination of crystal latticePowder X-ray diffraction is used for study of solid state reactions
26Qualitative analysis For qualitative analysis powder X-ray diffraction technique is used. Modern instruments have computer programme for qualitative analysis The pattern of each phase depends on its crystal structure and chemical compositionThe pattern is treated simply as a set of peaks , each with a position and intensity
27Qualitative analysisThe pattern for a mixture of phases is a simple combination of patterns of individual phasesQualitative XRD analysis compares the pattern to a library of patterns of known materialsThe most commonly used library is the Powder Diffraction File (PDF) or JCPDS-ICDD dataJoint Committee on Powder Diffraction Standards-International Center for Diffraction Data
28Databases such as the Powder Diffraction File (PDF) contain d, I lists for thousands of crystalline phases.The PDF contains over 200,000 diffraction patterns.Modern computer programs can help you determine what phases are present in your sample by quickly comparing your diffraction data to all of the patterns in the database.The PDF card for an entry contains a lot of useful information, including literature references.
29Quantitative analysis Some suitable internal standard is usedThe ratio of intensity of one phase of the material to the intensity of the internal standard is calculated and a calibration curve is plottedFrom the calibration curve the quantity of the particular material is determined
31Uses: different structures NaClKClEven if two structures are the same (and they are chemically similar) differences can be observed:Peak positions (unit cell changes) and relative intensities (atoms)NaClKCl
32Uses: different structures BUT, sometimes you can’t really see any changes on visual inspection…Zeolite AZeolite AThis often happens in “open” structures where there is space for change of light atoms
33Uses: polymorphsDifferent polymorphs will have different powder patternse.g. Zn S
34Peak Broadening In an X-ray diffraction pattern, peak width depends on the instrumentradiation not pure monochromaticHeisenberg uncertainty principlefocussing geometrythe sample…- a crystalline substance gives rise to sharp lines, whereas a truly amorphous material gives a broad “hump”.What happens between the two?
36Peak Broadening Scherrer’s Formula 0 B= Bragg Angle t = thickness of crystalliteK = constant dependent on crystallite shape (0.89)= x-ray wavelengthB = FWHM (full width at half max) or integral breadth0 B= Bragg AngleB is the line broadening, by reference to a standard (Bs), and BM is that of materials, so that
37When to Use Scherrer’s Formula Crystallite size <1000 ÅPeak broadening by other factorsCauses of broadeningSizeStrainInstrumentIf breadth consistent for each peak then assured broadening due to crystallite sizeK depends on definition of t and BWithin 20%-30% accuracy at best
38Uses: particle size determination Here we see particle size increasing with temperature30oC1050oC
39Particle size determination: Example Peak at 28.2° 2 with FWHM of 0.36° 2Standard material has FWHM of 0.16° 2 = CuK = Å0.36 ° = 0.36 x /180 = rad0.16 ° = 0.16 x /180 = radB = radt = 255 Å = m
40Uses: more advanced Structure refinement – the Rietveld method A refinement technique, not determinationWhole-pattern fitting - not just the Bragg reflectionsNeeds a MODEL - pattern calculated from model, compared point-by-point with observed pattern.Originally developed (1967,1969) for use with neutron data- good reproducible peak shapesfirst report of application to X-ray dataHugo Rietveld, b1932
41Uses: Rietveld Refinement xyzCa/Ce0.33330.6667(18)Ce0.2337(4)0.25Si0.403(3)0.380(3)O10.316(4)0.467(4)O20.597(5)O30.340(2)0.252(3)0.071(3)O4Here there was a similarity between the powder pattern of this phase and an existing one – also chemical composition similar.
42Uses: more advanced Quantitative phase analysis (how much of each) Naïve approach - relative intensity of peak maxima?- Consider mixture of Ba,Si,O- Ba component would scatter more than Si component (e.g. Ba2SiO4 c.f. SiO2)Thus uses Rietveld method and takes into account relative scattering from each crystalline phase