Synchrotron X-Ray Laue Micro/Nanodiffractiontpsbl.nsrrc.org.tw/userdata/upload/21A/2017 XMAS...

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Synchrotron X-Ray Laue

Micro/NanodiffractionNobumichi Tamura

Advanced Light Source

Lawrence Berkeley National Laboratory

Fiber-textured Gold film

Garnet Laue pattern

Cu kossel lines

Si blisters

Outline

What is X-Ray Laue Microdiffraction?

- X-ray Laue (polychromatic) diffraction

with a small x-ray (~micron size) beam

What do you need to do X-Ray Laue

Microdiffraction? (Synchrotron radiation, X-Ray

Focusing Optics, Beamline, X-Ray Detector,

supercomputer…)

What information can you get from Laue

patterns?

- Crystal orientation

- Strain/stress

- Plasticity

Going 3D

A century old technique

Max von Laue (1879-1960)

Nobel prize in 1914

MEMS

Spatial resolution from microbeam allows for

mapping crystalline and mechanical properties of

small devices…

What X-Ray Laue Microdiffraction could

do for you (in a nutshell) ?

What type of problems can be investigated with x-ray microdiffraction?

Mechanical properties of materials at the inter and intra-granular

level

Ex: deformation processes in bulk materials, failure analysis

Mechanical properties of small devices (microelectronics,

MEMS & NEMS, etc.)

Ex: reliability issues in microelectronics

Spatially resolved characterization of heterogeneous materials

Ex: distribution of phases in soils, minerals, composites or

alloys

Applications in a wide range of fields, including materials science, microelectronics, geology,

earth science, biomaterials, archaeology, and nanotechnology.

Ferromanganese

concretions in a

soil sample

(Courtesy: A.

Manceau)

TWA800 crash

was due to fuel

tank fatigue

failure (Source

CNN)

Multilevel Cu

interconnect

structure

An overview of Scientific projects at the ALS Microdiffraction

beamline• Mechanical properties of materials

• Size effect studies: Nanopillar compression, Nanowires

deformation

• stress in Ni-based superalloys

• stress in Cu-Nb multilayers

• residual stress in dental crown

• tin whisker growth

• electromigration in Pb-free solder

• Environmental and Earth Science

• Precipitates in acid mine drainage

• Stress in shocked quartz

• Uranium speciation on contaminated sites

• Materials characterizations

• strongly correlated materials: VO2

• Novel materials: High pressure metal carbides and

nitrides, Zeolite structures

• Batteries: Lithium batteries, solid oxide fuel cells

• Archeological artifacts: Roman Terra Sigillata poteries

• Solid hydrogen polymorphs

• Characterization of biomaterials

Mechanics of Nitinol Endovascular Stents

A. Mehta et al. UCB, Advanced

Materials (2007) 19, 1183–1186

Gradual Ordering in Red Abalone Nacre

P.U.P.A. Gilbert et al. , JACS, 130(51) (2008)

17519-17527.

VO2 Stress-Temperature

Phase Diagram

Jinbo Cao et al., UCB , Nano

Letters, 10 (7) (2010) pp 2667–

2673

Novel Rhenium Nitrides

Alexandra Friedrich,et al.,

Physical Review Letters

105, 085504.

Strain-induced M1-M2 phase

transition in VO2 nanowires

Hua Guo,et al., Nanoletters,

11 (8), pp 3207–3213.

Structure and Mechanical Properties

of a Pteropod Shell

Taiji Zhang et al. , 2011. Angewandte

Chemie. 50(44):10361-5.

Mechanical properties of

indium nanopillars

Lee G. et al., Acta

Materialia, 58 (4) (2010)

1361-1368.

Laue X- Ray Diffraction

X-ray diffraction with polychromatic (white) x-ray beam

Zirconium, deformed 5%Some mineral in fly ash

X-ray (l)

X-ray

Detector

X-Ray diffraction basics:

measurement

Crystal“Bragg condition” is rarely

satisfied!

l

Note: X-ray Detectors of choice

today are area detectors !

Ewald

construction

2dhkl sin(q) = n l

X-Ray Crystallography

needs a usable set of

reflections… how to

achieve this?

2q

hkl

X-ray (l)

X-ray

Detector

Single

Crystal

“Conventional” Single Crystal X-

Ray crystallography

Debye-Scherrer rings

X-ray (l)

X-ray

Detector

Polycrystals

(“powder”)

X-Ray diffraction: measurement with monochromatic beam

“Powder” diffraction

l

l

Diffraction

cones

h1k1l1h2k2l2

X-Ray diffraction: measurement with polychromatic beam

Polychromatic

X-ray (Dl)

X-ray

Detector

Single

Crystal

l1l2

li

Laue diffraction

Bragg’s condition is

satisfied simultaneously for

many reflections => no

need to rotate the sample to

get a usable set of

reflections

Data collection is fast!

1/lmin

1/lmax

Ewald

Advantages of Laue X-Ray diffraction:

- No sample rotation required

- Data collection is very fast (sample mapping, time resolved experiments),

- No sphere of confusion problem for “small beams”

- Very small crystals

- Probed region is fixed

X-ray

Sample

X-ray

Sample

Single crystal

(macro)

Polycrystal (meso-

micro)

Polycrystal (micro-

nano)

YES YES NO

Laue X-Ray diffraction Caveats:

- Intensity interpretation is difficult => not routine for

structure solution

- Length of scattering vectors qhkl (wavelength) not a priori

known (absolute lattice parameters, hydrostatic strain)

- Crystal size has to be large enough (or X-ray beam small

enough) so that beam sees a “single crystal”!

The beamline and end-station

… Light, camera, action !!

Outside view from the ALS (photo: M. Kunz) Inside view of the ALS

The many advantages of using synchrotron radiation vs

a lab source…

- Orders of magnitude brighter x-ray

source

- Continuous wavelength spectrum

(Energy tunability) => x-ray

spectroscopy

- Highly collimated => spatial

resolution

- X-ray polarization => magnetic

material studies

- Time structure => time-resolved

studies

Lab source: 60 s

exposure

Synchrotron: 1 s

exposure

Data collected on a

same crystal at lab

source and

synchrotron

Faster data collection

Better angular resolution

Higher spatial resolution (x-ray focusing)

The many advantages of using synchrotron radiation vs

a lab source…

The Advanced Light Source at LBNL

3rd generation synchrotron source

construction started in 1987, runs since 1993

Synchrotron: beamlines at the ALS

source

M1 toroid mirror

shield wall

lead hutch

roll slits,

primary focus

virtual object

Si(111) 4 bounce

monochromator

JJ X-ray slits

aperture slits

KB mirrorssample

24.8 m24.665 m

24.53 m24 m22.4 m

13 m

ELEVATION

PLAN

source

M1 toroid mirror

Si(111) 4 bounce

monochromator

roll slits,

primary focus

virtual object

JJ X-ray slits

aperture slits

KB mirrors

sample

BL12.3.2: a dedicated Laue (polychromatic) X-Ray microdiffraction at the ALS

Detectors

Beam size on sample: 1 x 1 um2

Photon energy range: 5-24 keV (monochromatic or white beam)

• DECTRIS Pilatus 1M area detector

• Vortex-EM (SII Nanotech.) single element Si-drift fluorescence detector, 50 mm2 active area

• Sample mounted on a XYZ stage and a PI piezo stage

• c cradle for changing X-ray incidence angle

• Heating/Cooling stage

• Flexible positioning of sample and detector allow for both reflection and transmission geometries

Instrumentation: Sample stage, x-ray detectors

PI XY piezo stage

XY Nanomotion

stages

Huber χ cradle

Huber Z and φ

stages

• Laser triangulation sample positioning system (Keyence)

a) Fresnel zone plate, b) Multilayer Laue Lenses c) Bragg-Fresnel lens, d) Compound

Refractive Lenses, e) Waveguide, f) Kinoform lenses, g) multi-bounce capillary, h) single

bounce capillary, i) Kirkpatrick-Baez total external reflection mirrors, j) Multilayer mirrors in

KB configuration

X-Ray focusing optics

What X-Ray focusing optics to use for Laue X-Ray

microdiffraction?

Flux Density

Gain

Resolution

(nm)

Chromatic

aberration

Radiation at exit Scan in

Energy

Fresnel Zone

Plate (FZP)

~ 300 000 60-5000 (4-15

keV)

~ 1/l Monochromatic Possible

Bragg-

Fresnel Lens

(BFL)

~ 1000 100-5000 No Monochromatic Difficult

Compound

Refractive

Lenses

(CRL)

~ 500 ( l

dependant)

40-5000 ~ 1/l2 Monochromatic Difficult

Tapered

Capillary

~ 100 100-5000 No White or

Monochromatic

Yes

Kirkpatrick-

Baez Mirrors

~ 300 000 60-5000 No White or

Monochromatic

Yes

X-Ray

Waveguide

~ 500 ( l

dependant)

35-200 ~ 1/l2 Monochromatic Difficult

Flux Density Gain = Beam Compression Ratio x Efficiency

Reflective Focusing Optics

Kirkpatrick-Baez Elliptical

Mirrors

• Use total external reflection on two

orthogonal ultrasmooth elliptically

shaped mirrors

• Obtained by

• Bending of a flat mirror

• Differential coating of a spherical

mirror

• Further figure errors correction

by ion-beam sputtering, …

• Characteristics:

• Achromatic

• High efficiencyKB mirror system developed at the ALS

(bending of flat mirrors)

Synchrotron X-Ray Microdiffraction: other technical

developments

• Large area fast X-Ray 2D detectors:

capture in a single frame a large portion

of the reciprocal space

• Increase in resolution (smaller pixels),

efficiency, readout speed

• Diffraction scans in a reasonable time

Deformed Ta crystal diffraction

pattern

Dectris Pilatus 1 M

hybrid pixel detector

(1 M pixels, 179x168

mm active area)

MAR 165 CCD detector (2M pixels,

165 mm diameter active area)

Laue X-Ray Microdiffraction data

analysis

How to interrogate a diffraction pattern …

San Andreas Fault quartz Barium Titanite STARDUST

Laue patterns provide information on crystal structure, grain orientation, plastic and elastic strain.

What can we learn from a Laue (white beam) pattern ?

Laue X-Ray Microdiffraction:

methodology

The sample is scanned under a white X-ray

microbeam. At each step a diffraction (Laue)

pattern is collected with the area detector. A

preliminary X-ray fluorescence scan can be

used to precisely locate the region of interest

SEM image of an

encapsulated Al(Cu)

interconnect (4 mm

wide x 30 mm long)

Ti fluorescence mapWhite beam (Laue) diffraction

pattern of an Al(Cu)

interconnect. The brighter

spots are from Si wafer.

The indexation of the Laue patterns provide

the crystal orientation matrix of the area

illuminated by the X-ray microbeam. The

analysis of the entire scan gives the grain

orientation map of the sample.

Al grain orientation

map

Si spots from the wafer have

been digitally removed. The

remaining Al spots are

indexed.


methodology

Measuring strain/stress with Laue X-Ray microdiffraction

Measuring “shifts” of the Laue reflection positions from their “unstrained” ones provide the deviatoric strain tensor.

Homogeneity property:

Transformation matrix:

Detector Detector

X-ray

Before compression After compression

Deviatoric strain:

Stress map


methodology

Deviations of the Laue peaks positions from their “unstrained” positions provide the distortional strain tensor.

–Stress tensor: sij = Cijkl ekl

Plasticity effect on Laue peaks: GND and GNBs

Excess dislocations of the same sign (Geometrically Necessary Dislocations or GNDs) cause lattice curvatures that can be measured by Laue…

1) If GND are randomly distributed, the resulting deformation is equivalent to a pure bending

L

bθtan

Rb

1

Cahn-Nye Relation

2) Subgrains boundaries (GNBs) are the result of redistribution of dislocations in dislocation walls

1.- (1,1,1) [-1,1,0] [1,1,-2]

2.- (1,1,1) [-1,0,1] [1,-2,1]

3.- (1,1,1) [0,-1,1] [-2,1,1]

4.- (-1,-1,1) [-1,1,0] [1,1,2]

5.- (-1,-1,1) [-1,0,-1] [-1,2,1]

6.- (-1,-1,1) [0,-1,-1] [2,-1,1]

7.- (-11,-1) [1,1,0] [-1,1,2]

8.- (-11,-1) [-1,0,1] [1,2,1]

9.- (-11,-1) [0,-1,-1] [-2,-1,1]

10.- (-11,1) [1,10] [1,-1,2]

11.- (-11,1) [-1,0,-1] [-1,-2,1]

12.- (-11,1) [0,-1,1] [2,1,1]

Plasticity effect on Laue peaks: Active slip systems

Electromigration induced plastic deformation in Al interconnects

Accelerated test at 280 °C

g, b, t

Streak directions of the Laue spots provide information on the dislocation slip system

Shape of the reflections can be fitted to simulated reflections

Peak shapes provides information on plastic deformation

and dislocation distribution in the diffracted volume.

Cahn-Nye Relation

Pure bending

Subgrain boundary

Exp. Simul.Burgers vector and

dislocation line directions

can be derived from the

shape of the Laue

reflections (Barabash et al.,

2002 and 2003)

Dislocation density map


methodology

Rb

1

L

bθtan

Grain orientation

Strain tensor

components

Dislocation density

Microstructure images generated from ~30,000 diffraction patterns

Scanning X-Ray Microdiffraction as a quantitative microstructure

imaging tool

X-Ray Microfluorescence/ X-Ray Microdiffraction combo

Fe Cu

Quartz Pyrite Chalcopyrite

Scanning X-Ray Microdiffraction

as a quantitative microstructure

imaging tool

Analyzing 1000s of

Laue patterns is

computationally

intensive

Bl12.3.2 uses NERSC supercomputing

facility to analyze Laue data

Shocked quartz (32,500 patterns analyzed

in 88 minutes on a 48 nodes cluster)

(Mis-) Orientation

Peak width

24 dual node

UNIX cluster

Going 3D

How to get depth resolution?

Al-sapphire composite (Bale et al., 2008)

-Broader energy bandpass

toward high energy allows for 3D

X-ray microdiffraction techniques

(depth resolution)

- 4 possible techniques:

- depth fitting

- triangulation

- wire scan (DAXM)

- diffraction tomography

Depth fitting: depth as a fitting parameter

X-rays

•Another white beam technique

•Given a certain geometry and

assuming certain angles between

reflections, depth can be included

as a “fitting” parameter

•The depth can be fitted

independently or with other

parameters (geometrical, grain

orientation, strain) using a least-

square approach.

N. Tamura, W.J. Choi and K.N. Tu, ALS/UCLA


Tilt angles of

CCD with respect to

incident beam

(2 par.)

Center channel

of CCD (2 par.)

Distance CCD-sample

(1 par.)

X-ray

CCD Camera

Sample

•Other parameters include:

•calibration parameters (5 parameters)

•strain (5 parameters)

•grain orientation (3 parameters)

•Parameters are refined

sequentially. Some are

determined using a

calibration sample

•Procedure requires

Laue patterns with large

number of spots

Whisker grain indexation =>

crystallographic orientation matrix

Z position (depth) fits => Angle between

whisker and sample surface

=> whisker growth direction (c-axis)

Application: what is the growth direction of a tin whisker ?

-0.51 -0.52 -0.53 -0.54 -0.55-0.74

-0.73

-0.72

-0.71

-0.70

-0.69

-0.5000

-0.4950

-0.4900

-0.4850

-0.4800

-0.4750

-0.4700

-0.4650

-0.4600

-0.4550

-0.4500

-0.4450

-0.4400

-0.4350

-0.4300

-0.4250

-0.4200

-0.4150

-0.4100

-0.4050

-0.4000

Y (mm)X

(m

m)

-0.74 -0.73 -0.72 -0.71 -0.70 -0.69 -0.68

-0.52

-0.50

-0.48

-0.46

-0.44

-0.42

-0.40

Z (

mm

)

X (mm)

surface

whisker


Data collection: fast (x 1)

Depth resolution: ~ 20-25 um

The Triangulation technique

H. A. Bale, J. C. Hanan, N. Tamura

Mechanical & Aerospace Engineering, Oklahoma State University,

Stillwater, OK

XZ

Y

XZ

Y

XZ

Y

Sample: 140 mm diameter

sapphire fiber in Al matrix.

Principle: white beam Laue

patterns at several detector

distances

40 mmThe triangulation

technique


technique

•Triangulation consists in ray-tracing back

the reflections back to the sample.

•If several reflections from a grain are

known, all the reflections belonging to this

grain should converge to the point of origin

of the scattering rays.

•Algorithm:

•Reflections positions are fitted using

a 2D shape function

•Reflections are sorted out by grains

using multigrain indexation

•Diffraction patterns taken at several

distances are scaled and stacked

together (here 10 images/point)

•Point of origin (depth) of diffraction

for each grain (grain position) are

ray-traced backed.

•Strain is computed at correct depth

The triangulation technique

•Slices: cross section of

grains at certain depth

(show grain orientation,

strain)

•Depth +/- 25 mm accuracy

(depends on the number

of reflections, number of

image distances, …)


Depth resolution by

pattern correlation

between images

from different

distances

Sn sample

Data collection: moderate (x 5-10)

Depth resolution: ~ 5 um


The 3D Structural Microscope or DAXM (Differential

Aperture X-Ray Microscope)

Analytical procedure:

•Wire position with respect to the area

detector and beam position need to be

carefully calibrated

•Ray trace of outgoing beam is given by

position of wire when it extinguishes the

reflection and position of reflection on the

area detector. Depth from which the

intensity comes can be computed

•In order to have the right accuracy, b<<a

•Pixel intensities are sorted by depth. Laue

diffraction pattern from each depth is

reconstructed and can be analyzed

(orientation, strain, …)

Area Detector

Wire

a

b

X-ray

Developed at the APS (Larson, Ice et al., 2000)

Scanning wire used to sort detector pixel intensities

by depth



Use of a gold wire mounted on two scan

stages as a depth profiler

Example: Ni sample



Ni polycrystal

Data collection: slow (x 300-600)

Depth resolution: ~ 1 um

(-4,2,4)

Time to conclude …

Laue X-Ray Microdiffraction

- Laue X-ray diffraction

- X-Ray focusing optics (KBs)

- Synchrotron radiation

- 2D X-ray detector

Outputs:

- Crystal orientation, strain/stress, dislocation densities

Applications:

Non destructive (non-invasive) 2D (and 3D) mapping of materials

mechanical and microstructural properties.

Phase identification, ? Structure solution

More info:

[email protected]

https://sites.google.com/a/lbl.gov/bl12-3-2/

mailto:[email protected]

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