2b Focusing Optics - qub.ac.uk
Transcript of 2b Focusing Optics - qub.ac.uk
Focusing Optics: Additional Background Information
Basic XRD Course (Edition 3) 1
1Basic XRD Course
QUB XRD Course
Focusing Optics
2Basic XRD Course
X-rays: electromagnetic radiation with a wavelength from 0.1 Å to 100 Å (0.01 nm to about 10 nm).
What are X-rays?
3Basic XRD Course
Generation of X-rays
• Electrons are emitted by a hot filament
• High voltage accelerates electrons
• Electrons bombard anode material at high speed
• Kinetic energy of electrons largely transferred into heat and X-ray radiation
Current (mA)
Voltage (kV)
Focusing Optics: Additional Background Information
Basic XRD Course (Edition 3) 2
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Spectrum of X-rays depending on applied voltage and anode material. Characteristic radiation is used for experiments.
Mo-anode
Continuous radiation
Characteristic radiation
Generation of X-rays
X-r
ay In
ten
sity
(rel
ativ
e u
nit
s)
Wavelength (Å)
3
1.0 2.0 3.00
1
2
0
4
5
6
SWL 510
15
20
25kV
Kα
Kβ
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Generation of X-raysContinuous radiation: caused by deceleration of electrons when passing
the positively charged nuclei in the anode or when colliding with electrons of the anode atoms.
KL
M
Radiation (Bremsstrahlung)
Decelerated electron
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KL
M
Knocked-out electron
Decelerated electron
Generation of X-raysCharacteristic radiation: When an atom is bombarded with sufficiently
high energy electrons (E > Ec ) electrons can be knocked out from their shell.
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Characteristic radiation: An electron from a higher shell takes the place of the knocked-out electron. The energy difference between both shells is released in the form of X-ray radiation of a specific wavelength.
KL
M
Characteristic radiation
KαKβ
Generation of X-rays
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Generation of X-rays
L-shell
III
III
Kα2 Kα1
K-shell
Generation of X-rays
Kα1 and Kα2 radiation:
Kα radiation comprises two wavelengths: Kα1 and Kα2.
The wavelengths correspond to the transitions from the L-shell to the K-shell. The L-shell has three energy levels from which level I is empty.
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X-ray Operation Conditions
X-ray Operation Conditions
Intensity of characteristic radiation:
I (λ) = K.mA.(kV – Vc )n
I = intensityK = constantVc = critical voltage for characteristic radiationn = 1.6
In general: kV = 3 to 5 x Vc
Focusing Optics: Additional Background Information
Basic XRD Course (Edition 3) 4
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1 % X-ray
Sample90 %
65 % air scatter
through Be window
to Be window1.5 %
Conclusion on tube efficiency:About 1% x 1.5% x 90% x 65% = 0.0088% of the
tube energy reaches the sample surface as X-rays.
X-ray Operation Conditions
11Basic XRD Course
Element Symbol Kαλ [nm] Application Chromium Cr 0.2291 large unit cells (clays, organic
materials, zeolites), steel (residual stress)
Iron Fe 0.1937 matrix effects of Fe and Cr Cobalt Co 0.1791 ferro materials Copper Cu 0.1542 standard tube Molybdenum Mo 0.0710 single crystal, small unit cells (metals) Silver Ag 0.0561 high absorbing materials Tungsten W 0.0211 Laue camera (continuum needed)
X-ray Operation Conditions
Anode material = choice of wavelength
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tube focus
Soller slit
divergence slit anti-scatter slit
receiving slit
Soller slit
diffracted beam
monochromator
detector
width mask
Classical Powder Diffractometer
Optical components in the X-ray beam path
Focusing Optics: Additional Background Information
Basic XRD Course (Edition 3) 5
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θ θ
Tube focus Receiving Slit
λ = 2 d sin(θ)
d
• Sample surface normal bisects incident and diffracted beams
• Diffracted beams focus at the same distance as the tube focus in receiving slit
• Optimal resolution
Classical Powder Diffractometer
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divergence slit anti-scatter slit
Divergence Slit & Anti-scatter Slit
Divergence slit & anti-scatter slit: determining illuminated and observed length
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• Divergence slit determines the irradiated length on the sample
– major effect on intensities
– minor effect on resolution
• Anti-scatter slit determines observed length on the sample
– used to reduce background
– major effect on the peak-to-background ratio
– ideally the observed area equals the illuminated area
Divergence Slit & Anti-scatter Slit
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Influence of divergence slit
opening
Divergence Slit & Anti-scatter Slit
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• The size of the divergence slit depends on the angular range (starting angle) and on the size of the sample.
• A smaller divergence slit gives a smaller illumination on the sample and less diffracted intensity.
Divergence Slit & Anti-scatter Slit
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Divergence and irradiated length
40
5
10
15
25
30
35
20
0 10 20 30 40 500
2θ
irra
dia
ted
len
gth
(m
m)
1/321/16
1/8
¼
½
1
2
R = 240 mm
Divergence Slit & Anti-scatter Slit
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If You Want to Gain Intensity….
• Make sure that you never over-irradiate the sample at low 2Theta angles…
… it will give a very high background!
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Divergence Slit Size and Peak Intensities
0
2000
4000
Counts
Position [°2Theta]10 20 30
¼ deg divergence1 deg divergence
factor 3.75
factor 1.47!
20 mmlength
Hint:you can observethe irradiated length on the status bar of the X’Pert Data Collector!
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receiving slit
Receiving Slit
Tube focus and receiving slit: determining instrument resolution
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Tube Focus and Receiving Slit
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Soller slit Soller slit
Soller Slits
Soller slits: limiting axial divergence
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Soller Slits
• Soller slits consist of large numbers of parallel plates in the plane of diffraction.
• Soller slits limit the spread of the incident and diffracted X-ray beam out of the plane of diffraction: 0.01, 0.02, 0.04 and 0.08 rad.
– large effect on intensities
– moderate effect on resolution (low/high 2θ)
• It is good practice to place similar Soller slits in the incident and diffracted beam.
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Instrument geometry influence - Sollers
8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.02Theta (°)
0
20000
40000
60000
80000
100000
120000
Inte
nsi
ty (
cou
nts
)
0.04 rad, 15 minutes0.02 rad, 45 minutes0.01 rad, 110 minutes
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β-filter & Monochromator
diffracted beam
monochromator
Possible places β-filter
β-filter & Monochromator
β-filter and/or monochromator: removing
unwanted radiation
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β-filter & Monochromator
• The β-filter and the diffracted beam monochromator remove unwanted wavelengths like the Kβ-line and continuous radiation.
• The β-filter selectively absorbs radiation.
• Monochromators select radiation by means of diffraction.
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Sup
pre
ssio
n
Wavelength
Cu
Kα
W L
αC
u K
β
Ni filter
β-filter & Monochromator
Use filter material with absorption edgein between Kα and Kβline.
For example:Cu-radiation
Ni filter• Intensity Cu Kα : 50 %• Intensity Cu Kβ : 1%
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receiving slit
Curved graphite diffractedbeam monochromator
detector entrance slit
λ > λCu
λ < λCu
β-filter & Monochromator
Only X-ray waves with correct wavelength pass the entrance slit of the detector.
Others do not focus in the entrance slit of the detector.
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Diffracted Beam Monochromator
Anti scatter slit
Detector
Curved crystalmonochromator(Graphite)
Receiving slit
Polycrystalline sample
Soller slits
X-ray tube(line focus)
Divergence slit
Soller slits
Beam mask
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line focus X-ray tube
Curved Ge(111) incidentbeam monochromator
divergence slit
Kα1
Kα2
β-filter & Monochromator
The symmetrically cut curved Ge(111) monochromator in combination with the divergence slit filters out the Kα2component leaving a beam with Kα1 radiation only.
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Incident Beam Monochromator
X-ray tube(line focus)
Incident beam monochromator
Irradiation slit
Programmabledivergence slit
Soller slits
Detector
Polycrystalline sample
Anti scatter slit
Receiving slit
Soller slits
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s
R
Sample Stages
Displacement error:
Sample stage and/or sample above or below diffraction plane: peaks are displaced from original position by
Rcoss2
2θθ =Δ
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QUB XRD Course
X’Celerator Optics
Getting the best out of yourX’Celerator detector
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What is RTMS Technology? (1)
Receiving slit + detector
Polycrystalline sample
Line focus
Divergence slit
Scan directionScan direction
Classical geometry (Bragg-Brentano)
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What is RTMS Technology? (2)
Polycrystalline sample
X’Celerator
Line focus
Divergence slit
Scan directionScan direction
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What is RTMS Technology? (3)
Polycrystalline sample
X’Celerator
Line focus
Divergence slit
Scan directionScan direction
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What is RTMS Technology? (4)
Polycrystalline sample
X’Celerator
Line focus
Divergence slit
Scan directionScan direction
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The Incident Beam Anti-scatter Slit
Diverg
ence
slit
Polycrystalline sample
X’Celerator
Line focus
Scan direction
Scatter at edges of
divergence slit
Anti-sc
atte
r slit
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The Incident Beam Anti-scatter Slit
• So: 1º divergence slit 2º inc. beam anti-scatter slit
Divergence slit size1/32º1/16º1/8º¼º½º1º2º4º
Anti-scatter slit size1/16º1/8º¼º½º1º2º4º-
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The Diffracted Beam Anti-scatter Slit
Polycrystalline sample
X’Celerator
Line focus
Diverg
ence
slit
Scan direction
Anti-sc
atte
r slit
Anti-scatter slit
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The Programmable Anti-scatter Slit
• Two modes of operation:– constant observed length
– constant observed angle
• Can be changed at will
• Actual opening is also a function of the active length of the X’Celerator: important when working at low angles!
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Constant Length and Associated Divergence
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 40 80 120 160Angle (deg 2Theta)
Div
erg
ence
(d
egre
es)
20 mm
10 mm
5 mm
Maximum 1 deg divergence: so 2 deg
anti-scatter slit Maximum angle: 50 deg 2Theta
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Example: NIST SRM 1976 Al2O3
Position [°2Theta]20 30 40 50 60 70 80 90 100 110 120 130
0
10000
20000
30000
40000 NIST SRM 1976, Al2O3
Counts
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Example: NIST SRM 1976 Al2O3
Position [°2Theta]25 30 35 40
Counts
0
10000
40000 NIST SRM 1976, Al2O3
Al2O3 Kα1 + Kα2
Mullite (Al6Si2O13)
Al2O3 Kβ
Ni absorption edge
Al2O3 Kα3
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Sample Fluorescence
• X-rays excite the atoms in the sample
• As a result of this, characteristic X-radiation is emitted
• If this emitted radiation is close to the Cu Kα, it is detected!
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Sample Fluorescence - An Example
0
10000
20000
30000
40000
Counts
Position [°2Theta]20 30 40 50 60 70 80 90
NiCo2O3 Cu Kα1 radiation
¼º divergence slit
Higher backgrounddue to the presence of Co in the sample
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Sample Fluorescence (1)
8 keV
7 keV ‘halo’Sealed X-ray
tube
Powder sample containing Co
?
8 keV
Diffraction peak from 8 keV photon
Constant backgroundfrom samplefluorescence
inte
nsi
ty
2θ angle
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• Crystal which acts as band pass filter
The Monochromator
Wavelength
Ni filterMonochromator
Inte
nsi
ty
Ni filter
Cu
Kα
W L
αC
u K
β
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Rules of Thumb - Monochromators
• Monochromators help to reduce the range of problematic elements
Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As
Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As
Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As
Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As
Cu, inc. beam mono
Cu, dif. beam mono
Co, inc. beam mono
Co, dif. beam mono
low high
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Rules of Thumb - Beta Filters
• β-filters: more background, but least reduction of Kα
• For best results, the β-filter should be placed in the diffracted beam
– exceptions: Ni with Cu radiation, Fe with Co(!)
• For not-too-complex patterns, Mo radiation is a valuable alternative
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Rules of Thumb - Continued
• When going from Cu to Co radiation…– the peak intensities drop with a factor of about 3…
– exception: Fe and Co samples: there the intensity rises with a factor of 3!
• Effect of varying penetration depth when absorption edges of elements in the sample are close to the characteristic radiation