application of two-dimensional x-ray diffraction (xrd ) throughput xrays 1.pdf · x-ray diffraction...

$: Application of Two-Dimensional X-Ray Diffraction (XRD ) Throughput Xrays 1.pdf · X-Ray Diffraction (XRD ) High-throughput Screening with XRD 5 Bruker Confidential 24.06.2008 Phase$
1

24.06.2008Bruker Confidential2

Bob He

Application of Two-Dimensional X-Ray Diffraction (XRD )

High-throughput Screening with XRD


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)

2


Two-dimensional detectors revolutionized the X-ray diffraction

What can you do with XRD ?


Comparison: Area Detector vs. Point Detector

Instant Capture of 2D pattern vs. one intensity value at a time

3


XRD & Single Crystals


XRD & Micro Samples

4


XRD & Textured Materials


XRD & Powders

5


XRD & Strained Materials


Debye Cone

Sample

Incident Beam

XRD Pattern

Discover the γ-information

Open your eyes with XRD

6


XRD2: Comparison with Conventional XRD (1)

The powder diffraction pattern in 3D space (blue) and the conventional diffractometer plane.


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)

7


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


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.

8


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.


XRD2: Geometry Convention (2) - Detector Space

Detector position in the laboratory coordinates is determined by the detector distance D and swing angle α.

9


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


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).

10


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


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:

or:

Ls Ahh =

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

−

−

−

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

−−−

−

−−−−

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

γθ

γθ

θ

ψψωψω

φψφωφψω

φωφψω

φψφωφψω

φωφψω

coscos

sincos

sin

sincoscoscossin

coscossinsincossincos

sincoscossinsin

sincoscossinsinsincos

coscossinsinsin

333231

232221

131211

3

2

1

z

y

x

h

h

h

aaa

aaa

aaa

h

h

h

)sincoscossin(sinsincoscossincoscos)coscossinsin(sinsin1

ωφωψφγθψφγθωφωψφθ

−−++=h

)sinsincossin(cossincoscoscoscoscos)cossinsinsin(cossin2

ωφωψφγθψφγθωφωψφθ

++−−−=h

ψγθωψγθωψθ sincoscoscoscossincossincossin3 −−=h

11


Key Components for XRD2

Patented Hi-Star Area Detector

designed for singleevent detectionquantum efficiency> 80%no intrinsic detectornoiseinstant read-out

Unique Sensitivity &Unique Speed


2-Dimensional MikroGap Detector –VÅNTEC-2000

12


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


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

13


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.


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

14


SUPER SPEED SOLUTIONSTurbo-X-Ray SourceTM (TXS) for PPXRD


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

15


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


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

16


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 ⋅=


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)

17


XRD2 :Defocusing at low incident angle in reflection

Lower resolution when θ2 or (2θ-ω) → 90° ω

ωθθθ

sin)2sin(

sinsin

1

2 −==

bB


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

18


XRD2: Defocusing effect with reflection sample depends on detector and data collection strategy

Defocusing vs. Detectors

0

2

4

6

8

10

12

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Two Theta

Def

ocus

ing

Fact

or

FlatCylinderBB

Defocus effect can be minimized with data collection strategy

Cylinder detector may collect large 2θ range, but with large defocusing effect at high 2θangle


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

19


GADDS - all applications with ONE instrument

D8 DISCOVER with GADDS C2:Rapid Screening System for Many Applications

CatalystsChemistryFine ChemicalsBiochemicalsPetrochemicalsPharmaceuticals… ...

OpticsElectronicsSemiconductorsFuel CellsBatteriesPolymersCoatings… ...


Easy and accurate sample positioning without touching the sample surface

Video image of each material library spot can be automatically stored during data scan

XRD2: Laser/video sample alignment

20


XRD2 for Combinatorial Screening:Cross contamination at low incident angle in reflection

Cross contamination happens when θ1 or ω

sb>

1sinθ

s


Cross contamination at 4° incident angle.

XRD2 for Combinatorial Screening:Cross contamination at low incident angle in reflection

21


XRD2 for Combinatorial Screening:Reflection System (CS)


Lin

(Cps

)

0

1

2

2-Theta - Scale9 10 20 30 40

XRD2: Data Collection:Acetaminophen powder

5 second data collection 30 second data collection

22


XRD2: reflection vs. transmission

Reflection mode frame from corundum at 5°incident angle.

Transmission mode frame with perpendicular incident beam.


Lin

(Cps

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

2-Theta - Scale3 10 20 30

Reflection and Transmission Data Collection:Ibuprofen powder

10 second overall data collection

R

TT

23


D8 DISCOVER with GADDS CST :Combinatorial Screening Transmission (CST)

Reduce background from sample holderImprove resolution at

low incident angleEliminate cross-cell

data contaminationReduce primary

beam air scatteringUS Patent #6,859,520


Reflection Transmission convertible Geometry

US Patent #7,242,745

D8 DISCOVER with GADDS HTS :Combinatorial Screening Reflection & Transmission

24


Beam-down Transmission

D8 DISCOVER with GADDS HTS:Combinatorial Screening Reflection & Transmission


SUPER SPEED SOLUTIONS:Turbo-X-ray Source for PXRD (θ-2θ)

VÅNTEC-2000TXS

XYZ stage with ω

rotation

25


X-ray Source for XRD2:IµSTM for PPXRD θ-θ Reflection


Operations: Import1)Corundum06192007_newsource - File: Corundum06192007_newT_01.raw - Type: 2Th alone - Start: 22.000 ° - End: 55.200 ° - Step: 0.020 ° - Step time: 100. s - Temp.: Operations: Import1)corundum6282007 - File: corundum6282007_05.raw - Type: 2Th alone - Start: 22.000 ° - End: 55.200 ° - Step: 0.020 ° - Step time: 100. s - Temp.: 25 °C (Room) - Time S

Corundum06192007_newsource - Obs. Max: 35.150 ° - Max Int.: 21.1 Cps - FWHM: 0.187 °

corundum6282007 - Obs. Max: 35.144 ° - Max Int.: 1.25 Cps - FWHM: 0.189 °

Lin

(Cps

)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

2-Theta - Scale22 30 40 50

Black: sealed tube

Red: IµS & VÅNTEC-2000

Comparison after Data Integration

Observation- (104) reflection

Black: Max Int: 1.25cps

FWHM : 0.189

Red: Max Int: 21.1cps

FWHM: 0.187

26


Comparison: IbuprofenIµS & VÅNTEC-2000 vs. Clasical set-up

IµS – XRD2 – foc

2mmX2mm on sample, and 200um spot focused on detector

small slice for integration to obtain better resolution

15 sec collection time

Sealed Tube

• 0.3 mm collimator

• Sample-Detector distance 29 cm

120 sec collection time


Combined System with XRD and RamanD8 SCREENLAB

US Patent #7269245

27


X-ray collimator

Alignment laser

Microscope w/ zoom X-ray

detector

Unilab probe

Light shield

Sample plate

Combined System with XRD and RamanD8 SCREENLAB


Carbamazepine

Lin

(Cou

nts)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

13000

14000

15000

16000

17000

18000

2-Theta - Scale4 10 20

0

5000

10000

15000

20000

25000

30000

250 500 750 1000 1250 1500 1750 2000 2250

Carbamazepine

Cou

nts

Raman Shift

XRD&Raman Examples

XRD Image

RAMAN

28


PolySNAP for Combined Analysis:Correlation among XRD, Raman and Other Probes

Cell display

Dendrogram

3D plots


XRD2 Screening: Conclusions

Two-dimensional XRD has many advantages in combinatorial screening, including high speed and improved statistics.XRD screening can be done in either

reflection or transmission depending on the sample and plate design.The new instrument allows the XRD

screening at either reflection or transmission modes with automated conversion.

application of two-dimensional x-ray diffraction (xrd ) throughput xrays 1.pdf · x-ray diffraction...

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