1 24.06.2008 Bruker Confidential 2 Bob He Application of Two-Dimensional X-Ray Diffraction (XRD ) High-throughput Screening with XRD 24.06.2008 Bruker Confidential 5 Phase Identification Quantitative Analysis Texture Stress Small Angle X-ray Scattering High-Throughput Screening Micro Diffraction Mapping Forensics and Archaeology Thin Films XRD 2 : Theory, Systems and Applications Geometry Conventions System and Configuration X-ray Diffraction (XRD)
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24.06.2008Bruker Confidential2
Bob He
Application of Two-Dimensional X-Ray Diffraction (XRD )
High-throughput Screening with XRD
24.06.2008Bruker Confidential5
Phase Identification
Quantitative Analysis
Texture
Stress
Small Angle X-ray Scattering
High-Throughput Screening
Micro Diffraction
Mapping
Forensics and Archaeology
Thin Films
XRD2: Theory, Systems and Applications
Geometry Conventions
System and Configuration
X-ray Diffraction (XRD)
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24.06.2008Bruker Confidential17
Two-dimensional detectors revolutionized the X-ray diffraction
What can you do with XRD ?
24.06.2008Bruker Confidential18
Comparison: Area Detector vs. Point Detector
Instant Capture of 2D pattern vs. one intensity value at a time
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XRD & Single Crystals
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XRD & Micro Samples
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XRD & Textured Materials
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XRD & Powders
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XRD & Strained Materials
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Debye Cone
Sample
Incident Beam
XRD Pattern
Discover the γ-information
Open your eyes with XRD
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XRD2: Comparison with Conventional XRD (1)
The powder diffraction pattern in 3D space (blue) and the conventional diffractometer plane.
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scintillation detector
small spot measuredscan necessarylong measuring time
PSD
large 2θ range measured simultaneouslymedium measuring time
GADDS
large 2θ and chi range measured simultaneouslymeasurement of oriented samplesvery short measuring timesintensity versus 2θ by integration of the data
XRD2: Comparison with Conventional XRD (2)
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XRD2: Geometry Convention (1) - Diffraction Space
Diffraction rings (blue) in the laboratory axes (red).⎥
⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−
−
−
=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
γθ
γθ
θ
coscos
sincos
sin
L
z
y
x
h
h
h
h
24.06.2008Bruker Confidential34
XRD2: Ideal Detector for Diffraction Pattern in 3D Space
An ideal detector to measure 3D space diffraction pattern is a sphere with the sample in the center.The direction of a
diffracted beam is defined by γ (longitude) and 2θ (latitude).The incident X-ray
beam points from 2θ=πto 2θ=0.
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XRD2: Diffraction Pattern on 2D Detector
A 2D detector can be treated as a detecting surface intersecting the diffraction cone.The detecting surface
can be a plane or a curved surface, such as sphere or cylinder.The conic section of a
plane may be a circle, ellipse, parabola, or hyperbola depending on the swing angle α.
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XRD2: Geometry Convention (2) - Detector Space
Detector position in the laboratory coordinates is determined by the detector distance D and swing angle α.
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XRD2: Geometry Convention (2) - Detector Space
Conversion of pixel intensity into 2θ and γintensity based on the detector position in the laboratory coordinates: D and α.
)20(,cossincos2222
1 πθααθ <<++
+= −
yxDDx
)(,)sincos(
cossincossincos
22
1 πγπαααα
ααγ ≤<−−+
−−−
= −
Dxyy
DxDx
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XRD2: Geometry Convention (3)- Sample Space
Rotation axes ω, φ, χgand the laboratory axes XLYLZL (red).
Rotation axes ω, φ, χg(ψ) and translation axes XYZ (blue).
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XRD2: Geometry Convention - Transformation Matrix
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
−−−
−
−−−−
ψψωψω
φψφωφψω
φωφψω
φψφωφψω
φωφψω
sincoscoscossin
coscossinsincossincos
sincoscossinsin
sincoscossinsinsincos
coscossinsinsin
The transformation matrix from the laboratory coordinates XLYLZL to the sample coordinates S1S2S3 in Eulerian geometry
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XRD2: Diffraction Vector in Sample Space
The unit vector hS of the diffraction vector Hhkl in the sample coordinates S1S2S3 is given by:In matrix form:
designed for singleevent detectionquantum efficiency> 80%no intrinsic detectornoiseinstant read-out
Unique Sensitivity &Unique Speed
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2-Dimensional MikroGap Detector –VÅNTEC-2000
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Functional Principle of The New VÅNTEC-2000TM – MikroGapTM Technology
MikroGapTM technology with resistive anode:
shortens drift time of ionsfast electrons induce charge on readout strips
Adjusted surface resistance (105
- 107 Ω/ area): high enough to limit dischargeslow enough to support high count rates
US Patent US 6,340,819 B1
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XRD2 : Choice of Detectors: Sensitivity vs. Counting Rate
MiKroGapMWPC
CCD
Image Plate
Detective Quantum Efficiency (DQE):The DQE is a parameter
defined as the square of the ratio of the output and input signal-to-nose ratios (SNR).
The DQE of a real detector is less than 100% because not every incident x-ray photon is detected, and because there is always some detector noise.
MiKroGap™ has the best overall performance.
2
)/()/(
⎟⎟⎠
⎞⎜⎜⎝
⎛=
in
out
NSNSDQE
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XRD2:X-ray intensity. What X-ray intensity?
Four parameters are often used to describe x-ray intensity within a bandwidth ∆λ :Flux is defined as the total x-ray photons passing a plane crossing the x-ray beam
per unit time. The typical unit for flux is photons/second or pps. The flux is sometimes also referred to as the integrated intensity of the x-ray beam.
Fluence is defined as the number of x-ray photons passing a unit area of the beam crossing a plane per unit time. The typical unit is photons/second⋅mm2 or pps/mm2.An alternative terminology for fluence is flux density. Fluence is an appropriate parameter for measuring the local counting rate of area detectors.
Brightness is defined as photons passing through a surface defined by unit solid angle. The typical unit is photons/second⋅milliradian2 or pps/mrad2. Since no linear dimension is defined in brightness, it is more appropriate to be used for measuring emission strength of a point source.
Brilliance is defined as photons passing through a unit area of surface within unit solid angle. The typical unit is photons/second⋅mm2⋅milliradian2 or pps/mm2⋅mrad2. It is more appropriate to compare two sources of different focal spot size.
photons-per-second (pps) = count-per-second (cps) if measurement counts are calibrated.
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XRD2: X-ray intensity and beam divergence. Liouville’s theorem?
Liouville's theorem describes the nature of the x-ray source and optics:
or
The brilliance of an x-ray source can not be increased by the optics.
The product of divergence or image size can be equal or great than the product of capture angle and source size.
A source size lager than the effective size only increases the power consumption.
The optics should be located as close as possible to the source.
α β
f1 f2
S1
A1
S2
A2
source
optics
image
x
y
ΘΦ
βα 21 SS ≤ Φ≤Θ 21 AA
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SUPER SPEED SOLUTIONSTurbo-X-Ray SourceTM (TXS) for PPXRD
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Lin
(Cps
)
0
1
2
3
4
5
6
7
8
9
2-Theta - Scale23 30 40 50
SUPER SPEED SOLUTIONSTXS vs. Sealed Tube with Corundum Plate
Gain factor > 6
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Bright sealed tube for ultimateconvenience
Incoatec Microfocus Source – IµS
The source - tube
• High brilliance
• Low energy: 30 W
• Low maintenance
• Tube change as easy as forconventional sealed-tubes
• Air-cooled
• Spot size < 100 µm
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IµS & VÅNTEC-2000 vs. Sealed TubeCorundum Comparison
Single 40mm Göbel Mirror,
45kV, 40mA,
0.3mm collimator
total counts: 78K
IµS & VÅNTEC-2000
45kV, 0.650mA,
0.3mm snout
total counts: 1235K
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1D/2D: Point Spread Function and Resolution
Consider a very small diffraction spot (blue line-delta function)An adjacent spot – red lineRMS (root-mean-square) is another parameter for PSF:
A perfect detector - dashed blue line. A real detector - intensity in a spread distribution.Can be measured if the separation is larger than FWHM.
RMS2.3548FWHM ⋅=
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2D detector resolution: Kα1-Kα2 split at 35° 2θ with NIST1976 (measured with VÅNTEC-2000)
∆λ (Kα2-Kα1) →∆2θ=0.06º→ 210 µm on the detector (20 cm)
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XRD2 :Defocusing at low incident angle in reflection
Lower resolution when θ2 or (2θ-ω) → 90° ω
ωθθθ
sin)2sin(
sinsin
1
2 −==
bB
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Cylinder detector with 5° incident angle for 5°~80° 2θ
Flat detector with several (5°,15°,25°,35°) incident angles for 5°~80° 2θ
XRD2: Defocusing effect with reflection sample depends on detector and data collection strategy
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XRD2: Defocusing effect with reflection sample depends on detector and data collection strategy
Defocus effect can be minimized with data collection strategy
Cylinder detector may collect large 2θ range, but with large defocusing effect at high 2θangle
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XRD2: Phase ID: γ-integration with merged frames
Software with automatic data collection strategy to minimize defocusing effect, and merge and integrate diffraction frame into diffraction profile for phase ID.
γγ
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GADDS - all applications with ONE instrument
D8 DISCOVER with GADDS C2:Rapid Screening System for Many Applications