Bob He, Bruker AXS

Denver X-ray Conference, August 6-10, 2012

Two-dimensional X-ray Diffraction – Recent Advances and Applications

Diffraction Patterns vs. Atomic Arrangement

XRD2: Two-dimensional X-ray Diffraction

XRD2 : Innovation and Development

The most dramatic development in XRD2 happens in X-ray source, detector and data evaluation algorithms:

Source: highest flux for fast data collection, even on sample of micro-volume, micro-area and weak diffraction.

Detector: collect 2D pattern with large solid angle, high sensitivity, high count rate, high resolution and low noise.

Applications and data evaluation algorithm: data collection strategy and data evaluation. (Diffraction Vector Approach).

XRD2: X-ray source and image?

Liouville’s theorem.

16.08.2012 5 Bruker Confidential

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.

ab

f1f2

S1

A1

S2

A2

source

optics

image

x

y

QF

ba 21 SS FQ 21 AA

Sources

8/16/2012 6

Characteristic X-ray generation

• All present day monochromatic home laboratory sources are based on characteristic radiation from a material anode

• The efficiency of this process is very low

• Approximately 99% of the incident electron power is converted to heat, not X-rays

• Dissipation of this waste heat fundamentally limits the brightness of the source

8/16/2012 7

How can one make a source brighter?

• Source performance is ultimately limited by anode melting

• There are three ways to improve performance

• Make the focus on the anode smaller

• Allows higher heat extraction efficiency

• Microfocus sources

• Rotate the anode faster

• Spreads the heat more efficiently

• Improved rotating anode

• Use a liquid metal anode

• Can’t melt (it is already molten!)

• Metal jet sources

8/16/2012 8

How to make brighter source I: Microfocus sources

Large spot

Quasi-one dimensional heat flow limits power loading

Small spot

Two dimensional heat flow (more efficient cooling)

Relative performance improved by 10 times

)2ln(

2 0max

r

TTp m

Brightness (B) is proportional to power loading (p) Power loading is higher for smaller spot focus

8/16/2012 9

ImS microfocus source

• Intensity 3x1010 X-rays/mm2-sec (Cu Ka)

• 8 times higher than conventional 5.4 kW rotating anode

• Typical lifetime >5 years

• High reliability

• 3 year warranty

• >300 installed

• Air-cooled

• Available in Cr, Cu, Mo, Ag

8/16/2012 10

ImS & VÅNTEC-2000 vs. Classic Set-up Corundum Comparison

Sealed Tube with Göbel Mirror

45kV, 40mA, (1800 W)

0.3mm collimator

total counts: 78K

Microsource (ImS)TM

45kV, 0.650mA, (30 W)

0.3mm collimator

total counts: 1235K

Intensity: 15.8x; Efficiency: 948x !

How to make a brighter source II: Rotating anode sources

• Power loading can be increased by over an order of magnitude by rotating the anode surface to spread out the heat load

• Power load is also (modestly) increased by smaller spot

• In latest generation rotating anodes angular velocity is 10,000 rpm

• This improves performance by 50 times

w

vTTp m 0max

w=beam width v=anode velocity

8/16/2012 12

TXS HB High brilliance rotating anode

• Highest intensity rotating anode

• 2x1011 X-rays/mm2-sec Cu Ka

• 50 times the intensity of a 5.4 kW

classic RAG with multilayer optics

• Cu, Mo, Ag anodes

• Low maintenance

• Easy to align, highly stable mount

• No alignment base

• Precrystallized, prealigned filaments

• No realignment required after

filament changes (2X per year)

• Precision aligned anode

• No realignment required after anode

exchange (1X per year)

8/16/2012 13

What are the limits of rotating anode performance?

• Faster rotation (w) allows higher power loading

• However, faster rotation also increases mechanical stress

• State-of-the-art rotating anodes are operated close to mechanical failure limits

• Little room for further improvement

2232

h Rt2

R

t

PRw

w

wRp wmax

8/16/2012 14

NEW: Liquid metal sources

• High-speed liquid-metal-jet anode

• Anode is regenerative

• No longer limited by melting

• >500 kW/mm2 e-beam power density

• Rotating anode limited to maximum 50 kW/mm2

8/16/2012 15

E-beam

Interaction

point

Metal jet

Spot Size

20 µm 10 µm 5 µm

5 mm

8/16/2012 16

Spot size

[µm, FWHM]

Voltage

[kV]

Power

[W]

Ga Kα Brightness

[Photons/(s×mm2×mrad2×line]

5 60 50 1.5×1011

10 60 100 7.6×1010

20 60 200 3.8×1010

• X-ray photon energy: Ga Ka 9.25 keV (=1.34 Å)

• Suitable replacement for Cu Ka 8.06 keV (=1.54 Å)

So, is it possible to put a synchrotron beamline on a table top?

• Yes, at least the equivalent of a typical present generation bending magnet beamline

8/16/2012 17

Detector

8/16/2012 18

XRD2: Choice of Detectors Sensitivity vs. Count Rate

MiKroGap

MWPC

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

NS

NSDQE

Detector geometry:

Be-window opening 140 mm in dia.

Frame size: 2048 x 2048 pixels 1024 x 1024 pixels 512 x 512 pixels

Pixel size: 68 mm x 68 µm 136 mm x 136 µm 272 mm x 272 µm

Detector working distance: 5~30 cm in D8 DISCOVER enclosure

2θ range in a single frame: 5 cm 83 10 cm 56 15 cm 42 20 cm 33 25 cm 27 30 cm 23

VÅNTEC-500 – Outperforms all previous gaseous detectors.

Cu (220) (200) (111)

Si (311)

Cu (311) (220) (200) (111)

Si (311)

VÅNTEC-500 Upgrade: Comparison to Hi-Star Detector

Large active area and smooth background

Applications & XRD2 Algorithm

8/16/2012 23

XRD2 & Single Crystals

l

k

h

)(

)(

)(

0

0

0

ssc

ssb

ssaLaue equation

S0

S

XRD2 & Powders

Bragg law

sin2dn

Debye Cone

Sample

Incident Beam

XRD2: Diffraction pattern with both g and 2 information

g

g

cos2sin

sin2sin

12cos10ss

H

Diffraction vector with g: Expressed in sample space:

z

y

x

h

h

h

aaa

aaa

aaa

h

h

h

333231

232221

131211

3

2

1

XRD2: Sample Space & Unit Diffraction Vector

The components of the unit

vector hS in the sample

coordinates S1S2S3 is then

given by

Or in expanded

form:

z

y

x

h

h

h

aaa

aaa

aaa

h

h

h

333231

232221

131211

3

2

1

)sincoscossin(sinsincos

cossincoscos)coscossinsin(sinsin1

wwg

gww

h

)sinsincossin(cossincos

coscoscoscos)cossinsinsin(cossin2

wwg

gww

h

h3 sin cos sin cos sin cos cos cos cos sin w g w g

XRD2: Phase ID Measurement Geometry

XRD2: Single Frame Covering All

2 coverage: 70 at 8 cm detector distance

In-situ measurement for chemical reaction, phase transformation or other real-time physical changes.

Sample with strong texture and large grain

XRD2: Frame Merge and Integration

4 frames at 20 cm

Merged frames 2 coverage: 100

Integrated profile for phase ID search/match

XRD2: Fundamental Equation for Stress Measurement

As a second order

tensor, the

relationship between

the measured strains

and the strain tensor

is given by:

the fundamental

equation for stress measurement in XRD2:

jiij

hkl hh wg}{

),,,(

sin

sinln)222

()(

0322331132112

2

333

2

222

2

111221

3322111

hhhhhh

hhhSS

The D8 DISCOVER with DAVINCI VÅNTEC-500 for stress measurement

Almen strip (spring

steel)

(211) & (200) rings

Ring distortion when

sample rotates with

and

Parameter setting

Results reporting: 11= -1068 18 MPa 22= -1085 18 MPa

XRD2: Stress Measurement –Example

Evaluate the data quality

Principal stress and stress ellipse –equibiaxial

XRD2: Fundamental Equation for Texture Analysis

The pole figure angles

(a,b) can be calculated

from the unit vector

components by the pole

mapping equations:

2

2

2

1

1

3

1 cossin hhh a

00

00cos

2

2

2

2

2

1

11

hif

hif

hh

h

b

bb

The D8 DISCOVER with DAVINCI VÅNTEC-500 for texture measurement

Steel can

(200) & (110) rings

Intensity variation during

scan

XRD2: Quantitative phase analysis: Retained Austenite

by Jon Giencke

16.08.2012

XRD2: Crystal Size by g profile analysis:

Organic glass for food & drugs

*Courtesy of Prof. Lian Yu, U. of Wisconsin - Madison 38

16.08.2012 39 Bruker Confidential

XRD2: Data Collection:

Acetaminophen powder

The spotty diffraction ring is due to the large crystallites compared to the sampling volume (beam size).

The number of spots on the ring is determined by crystallite size, instrumental window (g-range), multiplicity of the crystal plane, and effective diffraction volume.

The size of jelly beans and candy bin determines how many you can fill.

16.08.2012 40 Bruker Confidential

XRD2: Particle size measurement by g profile analysis:

For XRD2, the instrumental window is given by

so

s s- o

b

b

Dg

b1

b2

s

)]2/sin(arcsin[cos221 gbbb D

XRD2: Particle Size Analysis

1 nm 10 nm 100 nm 1 mm 10 mm 100 mm 1 mm

2 profile analysis g profile analysis

particle size range in pharmaceutical systems

2 profile analysis, suitable for <100 nm. Scherrer equation:

where B is FWHM corrected

for instrument broadening,

C is 0.9~1 (crystal shape).

g profile analysis is suitable for particle size from sub-micrometer to a few millimeters.

cosB

Ct

Gold nano-particle

3D Display

8/16/2012 44

Texture Measurement Using VANTEC-500: Magnetron sputter-deposited Cu films

Cu (311) (220) (200) (111)

Si (311)

Four diffraction rings are observed at 10 cm detector distance.

Four pole figures can be measured simultaneously.

Diffraction spots from Si wafer appear on some frames.

Texture Measurement Using VANTEC-500: Magnetron sputter-deposited Cu films

3D display for frames collected at Dx=20 cm

Cu(111) and Cu(200)

Si (220) with Si wafer of (100) cut.

H

3D Display – Fibre Diffraction

Jim Britten, Bruker-NYU XRD Workshop June 2011

47

Extruded, distorted polypropylene. Elnagmi / Jain

C∞ -axis in diffraction pattern

Example 1 – Random Orientation GaAs NW on Carbon nanotube ‘fabric’

Jim Britten, Bruker-NYU XRD Workshop June 2011 48

Why bother with XRD3? Sometimes there are surprises!

Example 2 – Multiple (8) Orientation GaAs NW’s on Si Substrate

Jim Britten, Bruker-NYU XRD Workshop June 2011 49

2D scan sequence

Full scan in MAX3D

More About XRD2

1. Introduction. 2. Geometry Conventions. 3. X-Ray Source and Optics. 4. X-Ray Detectors. 5. Goniometer and Sample Stages. 6. Data Treatment. 7. Phase Identification. 8. Texture Analysis. 9. Stress Measurement. 10. Small-Angle X-Ray Scattering. 11. Combinatorial Screening. 12. Quantitative Analysis. 13. Innovation and Future Development.

December 8, 2010 51 16. August 2012 51 © Copyright Bruker Corporation. All rights reserved