X – Ray Diffraction

X Ray Diffraction

5/27/20161Department of Life Sciences , University of Mumbai

X Ray DiffractionStudy of Crystal Structure.5/27/20162By,Assistant Professor RINKESH KURKUREHead Department of Physics,Bharat college, Badlapur(w)Department of Life Sciences , University of Mumbai

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OVERVIEWCrystal structures and atoms position in cubic cell with plane.Electromagnetic Spectrum and X- rayProduction of X-rays.Interaction of X-rays with matter.What can we analyzed by X- rayBraggs LawScherrers FormulaData analysis of XRD.

5/27/20163Department of Life Sciences, University of Mumbai

Crystal structures and atoms position in cubic cell with planesa Crystal Structure is a unique arrangement of atoms, ions or molecules5/27/20164Department of Life Sciences, University of Mumbai

SPACE LATTICE AND UNIT CELL.Atoms, arranged in repetitive 3-Dimensional pattern, in long range order (LRO) give rise to crystal structure.Properties of solids depends upon crystal structure and bonding force.An imaginary network of lines, with atoms at intersection of lines, representing the arrangement of atoms is called space lattice.Unit cell is that block of atoms which repeats itself to form space lattice.Materials arranged in short range order are called amorphous materials.

Unit CellSpace Lattice


BRAVIAS LATTICECubic Unit Cell a = b = c = = = 900

Simple CubicBody CenteredFace centeredSimpleBody Centered

Tetragonal a =b c = = = 9005/27/20166Department of Life Sciences, University of Mumbai

BRAVIAS LATTICE.Orthorhombic a b c = = = 900

SimpleBase CenteredFace CenteredBody Centered

SimpleRhombohedral a = b = c = = 9005/27/20167Department of Life Sciences, University of Mumbai

BRAVIAS LATTICEHexagonal a = b c = =900 = 1200

HexagonalMonoclinicTriclinicBase CenteredMonoclinicMonoclinic a b c = = 900 900Triclinic a b c 900


Atom Positions in Cubic Unit CellsAtom positions are located using unit distances along the axes.In cubic crystals, Direction Indices are vector components of directions resolved along each axes, resolved to smallest integers.Direction indices are position coordinates of unit cell where the direction vector emerges from cell surface, converted to integers. 5/27/20169Department of Life Sciences, University of Mumbai

Atom Positions in Cubic Unit CellsCartesian coordinate system is use to locate atoms. In a cubic unit cell Y axis is the direction to the right.X axis is the direction coming out of the paper.Z axis is the direction towards top.Negative directions are to the opposite of positive directions.


ELECTROMAGNETIC SPECTRAThe electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object has a different meaning, and is instead the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object.5/27/201611Department of Life Sciences, University of Mumbai

ELECTROMAGNETIC SPECTRA

5/27/201612Department of Life Sciences , University of Mumbai

X-RAYS

Dr. Wilhelm Conrad Rntgen5/27/201613Department of Life Sciences, University of Mumbai

X-RAYS PRODUCTIONInformation about crystal structure are obtained using X-Rays. The X-rays used are about the same wavelength (0.05-0.25 nm) as distance between crystal lattice planes.


CHARACTERISTIC X-RAYSX-Ray spectrum of Molybdenum is obtained when Molybdenum is used as target metal. K and K are characteristic of an element. For Molybdenum K occurs at wave length of about 0.07nm. Electrons of n=1 shell of target metal are knocked out by bombarding electrons. Electrons of higher level drop down by releasing energy to replace lost electrons


INTERACTION OF X-RAYS WITH MATTER


INTERACTION OF X-RAYS WITH MATTER5/27/201617Department of Life Sciences, University of Mumbai

ANALYSIS BY X-RAY


What can we analyzed by X- ray5/27/201619Department of Life Sciences, University of Mumbai

BRAGGS &SCHERRER LAW5/27/201620Department of Life Sciences, University of Mumbai

BRAGGS LAWFor rays reflected from different planes to be in phase, the extra distance traveled by a ray should be a integral multiple of wave length .

n = MP + PN(n = 1,2)n is order of diffractionIf dhkl is interplanar distance,Then MP = PN = dhkl.Sin Therefore, = 2 dhkl.Sin 5/27/201621Department of Life Sciences, University of Mumbai

SinceSubstituting for d,Therefore


Now for two planes A and B we have

Dividing each other, we get


X-Ray Diffraction


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Smaller Crystals Produce Broader XRD Peaks


t = thickness of crystalliteK = constant dependent on crystallite shape (0.89)l = x-ray wavelengthB = FWHM (full width at half max) or integral breadthqB = Bragg Angle

Scherrers Formula


What is B?

B = (2 High) (2 Low)

B is the difference in angles at half max

2 highNoise2 lowPeak5/27/201627Scherrers FormulaDepartment of Life Sciences, University of Mumbai

When to Use Scherrers FormulaCrystallite size

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X – Ray Diffraction