Characterization: XCharacterization: X
--
rayray
Characterization:
XCharacterization:
X
rayray
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X-ray Characterization: Scattering Techniques and Diffraction in Material Science, Study notes of Physics
An overview of x-ray characterization techniques, focusing on scattering methods and diffraction principles. Topics include x-ray generation, line spectrum and characteristic x-rays, absorption and filtering, bragg's law, and allowed diffractions. It also covers diffraction intensity, peak width, and common xrd techniques.
Typology: Study notes
Pre 2010
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Characterization: XCharacterization: X
- -rayray
Characterization: XCharacterization: X ray
ray
Scattering TechniquesScattering Techniques
Liu, UCD 250-2, 2009, NanoFab
2
Line SpectrumLine Spectrum
Characteristic x
-ray:
Characteristic x ray:
unique to element X-ray
Liu, UCD 250-2, 2009, NanoFab
4
Cu LinesCu Lines
Liu, UCD 250-2, 2009, NanoFab
5
Absorption/FilteringAbsorption/Filtering^ x
eI
I
^
)/ ( ^
(^33)
/^
Z k^ ^
M^
b^
ti^
ffi i
t
o x^
eI
I^
^
(^33)
/^
Z k^ ^
^
Mass absorption coefficient
x : thickness
– Absorption coefficient (cm
-1)
1/^
- One absorption length
Liu, UCD 250-2, 2009, NanoFab
7
DiffractionDiffraction
Scalar description:
Bragg’s Law:
2dsin
=n
Vector description:
Laue conditions:
k
= k
- ko = G - necessary
Liu, UCD 250-2, 2009, NanoFab
8
o^
y
q-value: |
k
^4^
sin
/^
Polycrystalline NaClPolycrystalline NaCl Why no (210), (211)…?
Liu, UCD 250-2, 2009, NanoFab
10
Structure FactorStructure Factor
)
( 2
n n n^
lw kv hui
N
n
hkl^
ef
F^
1
electron one by
scattered wave the of
amplitude
cell unita in atoms the all by
scattered wave the of
amplitude | |^
F e.g.: fcc lattice, 4 sam e atom s at (0, 0, 0), ( ½ , ½ , 0), (½ , 0, ½ ) and (0, ½ , ½ ).
]
(^1) [^
)( )( ) (^
kli lki khi
f F^
^
0 if
h^ k^ l^
ll^ dd^
electronll one by
scattered wave the of
amplitude
]
(^1) [^
)( )( ) (^
kli lki khi
hkl^
e e e f F^
^
^
(^0) if^ h
, k, l
are all odd or all even
Allowed diffraction:Allowed diffraction:
fcc:
all odd or all even bcc:
h+k+l=even
Liu, UCD 250-2, 2009, NanoFab
11
Diffraction IntensityDiffraction Intensity
M e A^
2
2
2
2
cos sin
2 cos 1 p| F|
^
Structure factor FMultiplicity factor pMultiplicity factor pLorentz factor Absorption factor A(
Debye-Waller (temperature) factor
Liu, UCD 250-2, 2009, NanoFab
13
Peak WidthPeak Width
Scherrer formulaFWHM
(^
di^
88
. 0
FWHM=
(radian) cos D
Sources for broadening
SizeSizeInstrument widthStress Liu, UCD 250-2, 2009, NanoFab
14
Phase IdentificationPhase Identification
Account for all peaks:
positionl ti
i t
it
Liu, UCD 250-2, 2009, NanoFab
16
relative intensitypeak width