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7/30/2019 Lecture+8+Mak Xrd
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PHY 3201 FIZIK KEADAAN PEPEJAL
CHAPTER 2 : Wave Diffraction
and the Reciprocal Lattice
Diffraction of wave by crystals
Scattering wave amplitude
Brillouin Zones
Fourier analysis of the basisBertha Rntgens
Hand 8 Nov, 1895
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PHY 3201 FIZIK KEADAAN PEPEJAL
Learning outcomes :
By the end of this topic, student can able to : Explain Braggs Law.
Explain the diffraction of wave by crystal.
Explain and construct the reciprocal lattice.
Explain the use of x-ray diffraction method
for material characterization.
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X-Rays
X-rays were discovered in
1895 by the German
physicist Wilhelm Conrad
Rntgen and were so namedbecause their nature was
unknown at the time.
He was awarded the Nobelprize for physics in 1901.
Wilhelm Conrad Rntgen
(1845-1923)
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Diffraction of waves by crystal
The wavelength of X-rays is in the range of
few angstroms, which is comparable to theinteratomic spacing in crystals. Thus X-raysare diffracted by the periodically arrangedatoms in a crystal i.e. crystals act as a three-dimensional diffraction grating for X-rays.
Therefore crystal structures can bedetermined by the study of diffraction of X-rays
In 1913, W. L. Bragg presented a simple
explanation of the diffracted beams from acrystal.
Sir Will iam Henry Bragg (1862-1942),
Will iam Lawrenc e Bragg (1890-1971)1915, the father and son were awarded the
Nobel prize for physics "for their services in
the analysis of crystal structure by meansof Xrays".
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Experimental setup
(How do we produce x-rays?)
X-ray production is via Bremstrahlung radiation. The
electrons are produced typically from a tungsten source,
are accelerated towards a metal such as copper, and when
they hit the surface, they slow down. This .brakingradiation. is a broad band of light which is emitted as the
electron slows down (charged particles under acceleration
emit radiation)
(Eg:
Molybdenum)
35 KV
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X-Ray Spectrum of Molybdenum
X-Ray spectrum ofMolybdenum is obtained whenMolybdenum is used as targetmetal.
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 targetmetal are knocked out bybombarding electrons.
Electrons of higher level dropdown by releasing energytoreplace lost electrons
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Consider a monochromatic, parallel beam of X-raysincident on a set of parallel crystals plane of Miller
indices
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Now consider interference between reflections
from successive planes:
Constructive interference
occurs only when
n = AB + BC
AB = BCn = 2AB
Sin = AB/d
AB = d Sin
n = 2 d Sin
= 2 dhkl Sin hkl
Braggs law
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What happens during a diffraction experiment?X-rays of a single wavelength (and therefore, energy) are
incident upon a crystal. The incoming rays are of the
proper wavelength for diffraction (on the order of the
interatomic spacing), and thus we see diffraction peaks
at certain values of , the scattered beam angle. Eachone of these peaks is from a plane of atoms within the
crystal. This is an elastic process.
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10/18PHY 3201 FIZIK KEADAAN PEPEJALDiffraction peaks are observed as a function ofscattered angle
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There are many types of X-ray camera
to sort out reflections from different crystal
planes. We will study only three types of X-
ray photograph that are widely used for the
simple structures.1.Laue photograph
2.Rotating crystal method
3.Powder photograph
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X-Ray Diffraction Method
Laue Rotating Crystal Powder
Orientation
Single Crystal
Polychromatic Beam
Fixed Angle
Lattice constant
Single Crystal
Monochromatic Beam
Variable Angle
Lattice Parameters
Polycrystal (powdered)
Monochromatic Beam
Variable Angle
X-RAY DIFFRACTIONMETHODS
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THE POWDERMETHOD
In powder or polycrystalline diffraction, if possible, we
normally grind the sample down to particles of about
0.002 mm to 0.005 mm cross section. The ideal sample is
homogeneous and the crystallites are randomly
distributed. The sample is pressed into a sample holder.
Ideally we now have a random distribution of all possible
h, k, l planes. If we have a truly random sample, each
possible reflection from a given set of h, k, l planes willhave an equal number of crystallites contributing to it.
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THE POWDERMETHOD
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THE POWDERMETHOD
An x-ray beam diffracted from a lattice plane can be
detected when the x-ray source, the sample and the
detector are correctly oriented to give Bragg
diffraction.A powder or polycrystalline sample contains an
enormous number of small crystallites, which will adopt
all possible orientations randomly
Thus for each possible diffraction angle there arecrystals oriented correctly for Bragg diffraction
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Debye ScherrerCamera
Each set of planes in a
crystal will give rise to a cone
of diffraction. These cones
intersect a strip of
photographic film located inthe cylindrical camera to
produce a characteristic set
of arcs on the film.
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Powder diffractionfilm
When the film is removed from the camera,
flattened and processed, it shows the diffraction
lines and the holes for the incident andtransmitted beams.
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There are a number of various setups for studying crystalstructure using x-ray diffraction.
In most cases, the wavelength of the radiation is fixedand the angle is varied to observed diffraction peakscorresponding to reflections from differentcrystallographic planes.
Using the Bragg law, one can then determine thedistance between the planes.
However, Bragg law is oversimplified, where it
Says nothing about intensity and width of x-raydiffraction peaks
Neglects differences in scattering from different atoms Neglects distribution of charge around atoms.
Hence, to fully understand, we need a deeper analysis todetermine the scattering intensity from the basis of atom.
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