X-Ray Powder Diffraction

Celina GwizdalaChem 393Dr Kumar

Spectroscopy• Large group of analytical methods that deal with the

interactions of various types of radiation with matter• Molecular Spectroscopy

– UV/Vis– Luminescence– IR & Raman– NMR– MS

• Atomic Spectroscopy– Atomic Absorption & Fluorescence– Atomic Emission– Atomic MS– X-Ray

X-ray Spectroscopy

measurements of :- emission- absorption- scattering- fluorescence- diffraction:

- single crystal- powder

Wave diffraction and interference

• parallel beams are bent asthey pass by sharp edges

• constructive and destructiveinterference

• bands that are perpendicularto the direction of wave’spropagation

• interference pattern dependson the wavelength of the lightand the distance betweenthe slits

X-ray Diffraction

• X-rays are diffracted by a pair of atoms• Interatomic distances fall around 10-10 m• X-rays have appropriate wave length to

experience diffraction by the atoms incrystalline substances (10-12 to 10-9 m)

• distances between the atoms can bemeasured with monochromatic X-rays

Background and History

• discovery made by Max van Laue 1912:diffraction of X-rays by CuSO4

• Two research teams (USA & Germany)discovered that a fine grained crystal aggregatesalso diffracted X-rays

• Two separate methods of structure elucidation insolids developed:

- Diffraction by a single large crystal- Diffraction by an aggregate of fine crystals

Crystal X-ray diffraction• Electrons from all atoms at that

surface interact with the electricfield of radiation and causescattering

• A beam that strikes that surface atangle _ will be scattered by thesurface by the same angle _

• If the atoms in the crystal form twodimensional arrays that areequally spaced and the distancebetween those arrays is roughlythe same as the wavelength of theradiation, then constructive anddestructive interference amongthe scattered rays will take place.

Crystal X-ray diffractionBragg’s Law• If O, P and R are atoms that

scatter individual beams, then thepath distance

AP + PC = n_• scattered radiation will be in phase

at OCD andAP = PC = d sin_

• the condition of scattering inphase is

n_ = 2d sin_sin_ = n_ / 2d

• diffracted radiation at angle otherthan _ experiences a destructiveinterference

The Instrument

• X-ray tube- tungsten filamentcathode- anode coated with atarget metal

• filters ormonochromators

• sample• detector

Powder camera

Undiffracted radiation coming out of thecollimator passes out of a cylindrical camera andupon reaching the sample gets diffracted andrecorded on a strip of photographic film set onthe inner wall

Powder camera

• Radiation that is successfully reflected assumes a shapeof a cone with a half opening angle of 2_ and uponreaching the film it is recorded as a ring

• For radius of every circle there is a specific angle ofreflection _ that can be easily determined from thegeometry of the camera

Photographic film• Each circle on the film

represents one solution ofthe Bragg equation

• The film strip is wrappedon a cylindrical formcoaxial with the sample

• The distance between thearcs (S) corresponds to4_ and Bragg angle

_ = S/4R

Applications of the X-ray powderdiffraction

• qualitative and quantitative phase analysis• determination of unit cell parameters• solid solution lattice parameters• crystal structure determination• particle size measurement• short range order in non-crystalline solids• crystal defects and disorder• degree of crystallinity

Degree of crystallinity in anamorphous sucrose

• X-ray patterns ofsucrose(a) amorphous(b) partially crystalline(c) and crystalline

• Darker shadesrepresent higherintensity and innerrings represent lower2_ values

Reference:

Nunes, C.; Mahendrasingam, A.; Suryanarayanan, R. PharmaceuticalResearch 2005, 22(11), 1942

Azároff, L. V.; Buerger, M. J. The Powder Method in X-ray Crstallography;McGraw-Hill Book Co.: New York, 1958

Skoog, D. A.; Holler, F. J.; Niemen, T. A. Principles Of Instrumental Analysis;Thomson Learning: Toronto,1998

Drago, R. S. Physical Methods for Chemist; Surfside Scientific Publishers:Gainesville, 1992