Transcript Slide 1
X-ray Diffraction
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Electromagnetic Spectrum
1024
1021
1018
Gamma Rays
UV
10-12
10-9
109
106
IR
X-rays
10-15
1012
1015
Frequency (Hz)
Long Radio Waves
Micro
10-6
103
10-3
TV FM
1.0
AM
103
106
Wavelength (m)
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What are X-rays?
X-Rays (Roentgen rays) were dicovered by Roentgen in 1895. They
are a kind of electromagnetic radiation of very short wavelength and
very high energy produced when high-speed electrons strike a solid
target. The wavelength range lyes between 0.0001 and 10 nm i.e.,
the range between ‘gamma rays’ and ‘ultraviolet rays’
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History of X-ray and XRD
Wilhelm Conrad Röntgen discovered
X-Rays in 1895.
1901 Nobel prize in Physics
Wilhelm Conrad Röntgen (1845-1923)
Bertha Röntgen’s Hand 8 Nov, 1895
A modern radiograph of a hand
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Risks
X-Rays penetrat matter but not all
of them come out. Some get lost. The
missing X-rays having very high
energy get absorbed in the body and
the X-ray's energy is released. This
energy is transferred to an electron,
which does a lot of damage in a small
area.
X-Rays affect the DNA of cells.
For the levels of radiation one gets
at the dentist and the doctor, the body
is able to repair most all of the
damage done.
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Origin of X-Rays
• A vacuum tube consists of a cathode, an anode, an a
heating filament.
• The heated cathode emits electrons (e-).
• A field of ~50kV accelerates the electrons onto the anode.
• The elctrons bump on atoms and slow down, emitting
radiation of a continuous distribution of wavelengths
(``Bremsstrahlung'').
• Some electrons cause sharp atomic transitions, resulting
in X-rays with definite wavelengths (0.1~50A).
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The X-ray generator
X-rays
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The X-ray generator
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Wavelengths for X-Radiation are Sometimes Updated
Copper
Anodes
Bearden
(1967)
Holzer et al.
(1997)
Cobalt
Anodes
Bearden
(1967)
Cu Ka1
1.54056Å
1.540598 Å
Co Ka1
1.788965Å 1.789010 Å
Cu Ka2
1.54439Å
1.544426 Å
Co Ka2
1.792850Å 1.792900 Å
Cu Kb
1.39220Å
1.392250 Å
Co Kb
1.62079Å
1.620830 Å
Cr Ka1
2.28970Å
2.289760 Å
Molybdenum
Anodes
Holzer et al.
(1997)
Chromium
Anodes
Mo Ka1
0.709300Å
Mo Ka2
0.713590Å 0.713609 Å
Cr Ka2
2.293606Å 2.293663 Å
Mo Kb
0.632288Å 0.632305 Å
Cr Kb
2.08487Å
2.084920 Å
Often quoted values from Cullity (1956) and Bearden, Rev. Mod. Phys. 39 (1967)
are incorrect.
0.709319 Å
Values from Bearden (1967) are reprinted in international Tables for X-Ray Crystallography
and most XRD textbooks.
Most recent values are from Hölzer et al. Phys. Rev. A 56 (1997)
Has your XRD analysis software been updated?
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What are the atomic processes
that can produce X-rays?
(1) White radiation
electrons from an external source are deflected around
the nucleus of a target atom and X-rays of multiple
wavelengths are emitted, depending on the kinetic energy
lost by the electron on deflection
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What are the atomic processes
that can produce X-rays?
(2) Characteristic emission
An incident e- bumps onto an inner level
e-. Both electrons fly out and energy is
emitted as an electromagnetic wave
(white). The “hole” is filled with a higher
level electron and this is accompanied
by
X-ray emission (characteristic). These
peaks are labeled Ka, Kb, La, Lb, etc,
depending on the specific energy levels
involved.
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X-Ray interactions with an object
X-Ray elastic scattering is the basis for
crystallographic analysis WXRD and SAXS
X-Ray inelastic scattering is the basis for
analytical methods such as XPS (X-ray
Photoelectron Spectroscopy), XRF, AES
(Auger Electron Spectroscopy)and EDAX
(Energy Dispersive Analysis by x-ray)
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History of X-ray and XRD
The first kind of scatter process to be
recognised was discovered by Max von Laue
who was awarded the Nobel prize for physics
in 1914 "for his discovery of the diffraction of
X-rays by crystals". His collaborators Walter
Friedrich and Paul Knipping took the picture
on the bottom left in 1912. It shows how a
beam of X-rays is scattered into a
characteristic pattern by a crystal. In this
case it is copper sulphate.
The X-ray diffraction pattern of a pure
substance is like a fingerprint of the
substance. The powder diffraction method is
thus ideally suited for characterization and
identification of polycrystalline phases.
Max von Laue (1897-1960)
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Bragg’s Law
Sir William Henry
Bragg (1862-1942)
William Lawrence
Bragg (1890-1971)
The father and son team of Sir
William Henry and William Lawrence
Bragg were awarded the Nobel prize
for physics "for their services in the
analysis of crystal structure by
means of Xrays“ in 1915.
Bragg's law was an extremely
important discovery and formed the
basis for the whole of what is now
known as crystallography. This
technique is one of the most widely
used structural analysis techniques
and plays a major role in fields as
diverse as structural biology and
materials science.
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Bragg’s Law
• Correlates X-ray wave length,
l, interplanar spacing, d, and
reflection angle, q.
• Scattering atoms (circled in red)
behave like slits in Young’s
experiment.
2d hkl sin q n nl
d hkl
sin q
2
a
h2 k 2 l 2
l
4a
2
h
2
a
N
k2 l2
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Crystal planes and Miller’s indices
• Each plane in a crystal is defined by Miller’s indices
z
z=1
h a / x
k a / y
l a / z
crystal plane normal n (h, k,l)
y
y=1
x
x=1
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Since a crystal has an ordered 3-D periodic arrangement of atoms (ions
or molecules) the atomic planes in any crystal can be related to the unit
cell.
One can label each set of planes uniquely by considering their
(fractional) intersection with the unit cell axes a,b,c and converting
these to INTEGERS h, k, and l.
e.g. the planes that intersect the b-axis at ½ and are parallel to a and
c. ( a/ , b/2, c/) are defined by the MILLER INDiCES (0 2 0)
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A reminder: finding Miller Indices of a plane
Extend the plane to make it cut the crystal axis system
at points (a1, b1, c1)
Note the reciprocals of the intercepts, i.e.:
Multiply or divide by the highest common factor to
obtain the smallest integer numbers.
Replace negative integers with bar over the number,
i.e. we replace -h by
Note:
If the plane is parallel to an axis, we say it cuts at
and
If the plane passes through the origin, we translate
the unit cell in a suitable direction.
We use round brackets ( ) to describe a single plane
and curly brackets { } to describe a family of planes.
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Can be found for each set of planes provided we know the
unit cell parameters.
e.g. for a CUBIC unit cell:
d(100) = a
d(010) = b
(= a)
d(030) = ( 13 )a
d(110) = (
1
2
)a
For unit cells with a = b = = 90º
Which for a CUBIC unit cell simplifies to
1 h2 k 2 l 2
2 2 2
2
d
a
b
c
1
h2 k 2 l 2
2
d
a2
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d = λ / (2 Sin θB)
λ = 1.54 Ǻ
= 1.54 Ǻ / ( 2 * Sin ( 38.3 / 2 ) )
= 2.35 Ǻ
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Bravis Lattices
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