Loading...

PPT – John Spence Overview of electron diffraction' Erice June 9 2004' PowerPoint presentation | free to download - id: 230c03-ZTQ1Z

The Adobe Flash plugin is needed to view this content

John Spence Overview of electron

diffraction. Erice June 9 2004.

1. Pulsed gas diffraction. LEED. RHEED.

Photoelectron diffraction, holography. 2. Spot

(SAD) patterns. Lattice, cell consts. Organics,

inorganics Semi-quantitative

TED HREM. Examples from recent work of Dorset,

Sinkler, Gjonnes, Zou et al. 3. CBED.

Space-group determination, Cell constants,

Strain mapping, Charge-density measurement, HV,

Debye-Waller. Elastic filtering.

Quantitative 4. LACBED. CBIM. Dislocation

Burger's vectors. 5. Coherent Nanodiffraction.

Planar fault vectors. Ronchigrams for aligning

corrected STEMs 6. Diffuse scattering. Phase

transitions, phonons, defect analysis. Isolated

nanostructures ? (Zuo's nanotube) 7. UHV TED

from reconstructed surfaces of thin films.

Quantitative 8. Cryomicroscopy in biology.

(Most successful area of EDImaging).

Solving proteins - organic monolayer

xtals at 0.3nm resolution.

Quantitative 9. Phase identification Combine

CBED (space group), SAD (lattice), EDX ELS

(composition). 10. Advanced topics. HiO

inversion, Precession camera, Dynamical

inversion, Ptychography, in-line STEM

holography, imaging. ELNES QCBED. Serial

Xtallog - protein beam diffn.

- Textbooks and software
- Introductory
- "Electron diffraction in the TEM" by P.

Champness. Royal Micros Soc - ISBN 1859961479 (Google that !). Official Erice

Text ? - (inexpensive paperback, unified presentation)
- Advanced.
- "High Energy Electron Diffraction and

Microscopy" L.-M Peng , - S.L. Dudarev and M.J. Whelan. OUP. 2004.
- 3. Software
- WebEMAPS-Google that !

Specialised or advanced texts by Morniroli,

Reimer, Hirsch et al, Spence and Zuo, Lorreto,

Williams and Carter, Cowley, Spence, Agar,

Kirkland, Fultz and Howe, Dorset, Egerton, De

Graef and much more (eg free software) at

http//www.public.asu.edu/jspence/ElectrnDiffn.ht

ml

Why is electron micro-diffraction a good idea ?

- It provides the strongest continuous signal from

the smallest volume of matter known to science.

Hence good for nanoscience. - Field emission sources are the brightest

continuous particle sources in physics. - The interaction is the strongest of all the

long-lived particles.Hence more signal. - Ratio of elastic to inelastic scattering more

favorable than X-rays (less damage for bio) - TED is uniquely sensitive to ionicity.
- The synthesis of many new nanostructured

materials demands new methods for structure

analysis using nanoprobes.

Diffraction modes in the TEM/STEM.

1. Source conjugate to detector. SAD.

2. Source conjugate to sample. CBED.

S

Angular resolution limited by source

size. Spatial resolution limited by SA aperture

and Cs.

Fine detail in disks comes from outside probe

? Spatial resolution limited by probe size.

1. C2 may be coherently or incoherently

filled. 2. CBED provides maximum info from

smallest volume. 3. For refinement, strain

mapping first - calibrate pattern. 4. We say

that P and P are conjugate points.

V

i

r

t

u

a

l

A

p

e

r

t

u

r

e

S

p

e

c

i

m

e

n

P

P

B

a

c

k

F

o

c

a

l

P

l

a

n

S

A

A

p

e

r

t

u

r

e

a) Selected Area Electron Diffraction

Fig. 1 Three modes of electron diffraction. Both

a) selected area electron diffraction (SAED) and

b) nanoarea electron diffraction (NED, Koehler)

use parallel illumination. SAED limits the sample

volume contributing to electron diffraction by

using an aperture in the image plane of the image

forming lens (objective). NED achieves a very

small probe by imaging the condenser aperture on

the sample using a third condenser lens (eg M

1/20). Convergent beam electron diffraction

(CBED) uses a focused probe.

Elementary electron diffraction and xtallography.

Scattering geometry.

1/dhkl sqrt(h2 k2 l2)/a q/l g for

cubic system, cell const a. Bragg's Law for HEED

(small angle approx) q 2qB l /dhkl

where q is the scattering angle. Electron

de-Broglie wavelength is l 1.22643 / (V

0.97845E-6 V2)1/2 with V the accelerating

voltage, and l in nm.

dhkl

q

qB

Ewald sphere construction ensures conservation of

energy, xtal momentum. (But ! Apply uncertainty

principle in beam dirn. for "elastic" scattering

. Dt.DKz 1, where Dt thickness t. DKz

DSg 1/t Hence expect strong Bragg beams

for a small range of incident beam directions

within excitation error DSg.)

1/l

Sg

g

Phase identification of unknown structures by

CBED and SAD.

- Find space-group by CBED.
- 2 Use EDX and ELS to determine atoms present and

approximate stoichiometery. (Can Nb2O5 be - distinguished from NbO2 by EDX ? Probably.
- 3. Find Bravais lattice from spot patterns with

HOLZ ring. Use dlL/R, L camera length, R spot

radius.

uH

- Find relative position of FOLZ projected onto
- HOLZ. This gives centering. (eg I, body centered

in recip space, fcc in real) - From FOLZ ring we get c axis dimension. Sg 1/c

lU2H/2 - From spot measurements get approx cell consts.
- More accurate Bravais lattice and cell consts
- can be obtained by method of Zuo Ultramic 52,

459 "A new method of - Bravais Lattice determination" using HOLZ lines

in central CBED disk.

FOLZ

4. Use the indexed patterns given in Spence

and Zuo book ?. (HOLZ points indicated on ZOLZ).

ORSimulate any pattern (WebEMAPS-Google

that !) with random atom posns in known space

group. 5 Use Electron Diffraction data base

http//www.nist.gov/srd/nist15.htm and/or Powder

Diffraction File.

NIST Standard Reference Database

15 NIST/Sandia/ICDD Electron Diffraction

Database Designed for phase characterization

obtained by electron diffraction methods, this

database and associated software permit highly

selective identification procedures for

microscopic and macroscopic crystalline

materials. The database contains chemical,

physical, and crystallographic information on a

wide variety of materials (over 81,534) including

minerals, metals, intermetallics, and general

inorganic compounds. The Electron Diffraction

Database has been designed to include all the

data required to identify materials using

computerized d-spacing/formula matching

techniques. The data for each entry include

the conventional cell reduced cell

lattice type space group calculated or

observed d-spacings chemical name chemical

and empirical formula material class

indicators references. . . This database and

search software are available in magnetic tape

format and in CD-ROM format.

Can one Google a set of d spacings ? (Try it now

for Si on wireless web)

Ewald sphere in more detail We can associate

an excitation error (in Ang-1) with every

Bragg beam in a TED pattern.

The Bragg condition corresponds to Sg 0. In

the zone-axis (symmetric) orientation, the

excitation error is Sg l g2 / 2

t

FT

WebEMAPS-Google that ! Kirkland's book has source

code for ms

Approximations for diffracted amplitudes.

Kinematic. F01 (single

scattering)

Two beam F01 - Fg

Thick phase grating

Multislice

Bloch-waves.

Spence and Zuo, "Electron Microdiffraction" Plenum

1992 gives Fortran listings and

full documentation of multislice and Bloch wave.

(No Transcript)

Comparison of N-beam, PGA, kinematic approx. for

NbO

PGAFT exp(if(R)t)

KinVg t sin(pSgt)/(pSgt)

Phase

Exact (N-beam)

Note kin intensity goes as t2 Dyn intens is

"sinusiodal". kin phase is linear. X-ray

amplitudes dont involve t at all !

PGA

Lynch, Moodie, O'Keeffe Acta A31, 300

Kinematic

Amplitude, not intensity.

Conclude Need t lt 8 nm Inorg t lt 20 nm

Org Layer structures help (projection)

kin

Thickness

Failure of kinematic approx.

111

000

At x1 (b), central beam is strong Image consists

mainly of interference between central beam and

each beam, producing a faithful image.

Increasing thickness

Kinematic t2

000

Thickness (A)

At x5 (c), central beam is weak. Image consists

mainly of interference between beams, producing

an image of half-spacings, and rotated.

How do we know these multiple-scattering

calcns are accurate ? Because they precisely

fit experimental data, as here. (Zuo J. Elec Mic

47, 121)

Conclusion Accurate quantification of ED data is

only possible if multiple scattering is included

in calculations But. for light-element

inorganic nanostuctures, kinematic theory is

accurate enough to solve structures especially if

good data can be obtained in 3D !

MgO (111) systematics CBED fitted at 120 kV

using elastic imaging energy filter. (Zuo 97)

- Conditions for quantifiable TED.
- Data must be collected under known conditions.

Experimental parameters (thickness, - wavelength, etc) must be accurately known if not

kinematic.(All beams t2. Normalise) - Xtalline samples must have no defects, uniform

thickness, no bending. - Scattering must be known to be weak if kinematic

theory used. - 4. Phase problem may need to be solved.

Three-dimensional data may be needed.

- How these conditions are fulfilled for the 3

quantitative methods. - For cryo-em of proteins Sample in C,N,O,H. All

light atoms in ice. Thickness lt 20nm. 3D data.

Not atomic resolution. Xtal quality problem.

Thickness known because one monolayer ! - For QCBED. Probe is so small that xtal is

perfect. Multiple scattering theory used. - UHV TED of Surfaces. Scattering from monolayer

is weak. Ignore bulk interaction. "Thickness"

known. - For HREM TED.
- Use observation of forbidden reflections (screw,

glide, away from Bragg condition) as test for

single scattering. (Find space-group by CBED to

indicate which are forbidden ?). At Bragg,

forbiddens remain forbidden (black cross) even if

dynamical.

- Tests for kinematic scattering.
- Use Friedel's law. If a crystal is known to be

acentric, but I(g) I(-g), there is no

multiple - scattering. (for acentrics, Vg V-g, but

V(r) is real). This works for unknown structures. - Blank discs. If the intensity variation across

CBED discs is constant, this suggests weak

scattering. (Wu, Spence Acta A58, 580.

"Kinematic and dynamical CBED for solving thin

organic films at helium temperature. Tests with

anthracene"). - Study organic monolayers. Thickness equals known

molecular size. Problem - make self-supporting

sample ! (eg use ice). Poor sample quality. LB

films- mols lie on side. - Use wedge-shaped sample. Match image against

thickness. Similar for CBED. - Inclined, planar-fault on known plane can be

used to give thickness on wedge. - Accurate fitting to CBED pattern with multiple

scattering program will calibrate thickness

within lt 4 A - Find space-group by CBED to locate true

forbiddens (use primitive cell),index pattern.

Then forbidden reflections in SAD from thin, bent

areas suggest no multiple scattering. - Credibility requires the same structure to be

determined from the same sample by XRD and TED !

Are the TED intensities consistent and

reproducible ? Can you record the same set of TED

diffracted intensities twice, from different

areas of the same sample ? - Remember- modern XRD software always gives some

answer ! (R factor ?Potl vs Rho).

(screw, glide)

Elementary Xtallography.

centering was used to give orthogonal coords.

- Xtal Bravais lattice molecule.
- There are only 14 possible Bravais lattices, s.t.

the surroundings of every point are identical. - Seven primitive cells exist (seven xtal systems

cubic, hexagonal, triclinic ,monoclinic,

orthorom, tetragonal, trigonal ) - Get 7 more from centering, P, I, F, C.

(primitive, body-centered, centered on every

face, centered on two) - The xtal system is defined by the symmetry of the

xtal. (eg any xtal with four 3-folds is cubic). - From the cell constants a,b,c, a,b,g the

reciprocal lattice is generated by FT. eg a

b X c /W. - The point group is based on mirror, inversion,

and rotation symetries alone. There are 32. (eg

for mols). - Translational symmetry adds the possibility of

screw and glide symmetries. There are 230 space

groups. - There are 2 types of truly forbidden reflections

- Space group (screw,glide axes). Non-spherical

atoms. - Third type "forbidden" due to centering is

historical artifact, due to method of indexing.

Use primitive cell ! - The f'bdns generated by a centered cell were

never there ! Physically, electrons diffract from

the primitive cell.

A list of absent refln indices due to centering,

screw, glide, and many indexed patterns

(including HOLZ) is given in Spence and Zuo,

Electron Microdiffraction, 1992 . Plenum. Use Int

Tables for Crystallography.

Solutions to the phase problem.

If diffraction patterns can be collected under

kinematic conditions, we must solve phase

problem. (Phases can be obtained from FT

of HREM image if wpo approx holds. /- if

centric).

Modern PX used MAD. (Heavy atom, abs. Most

proteins dont diffract to atomic

resolution) Modern inorganic xtallog uses Direct

Methods, requires atomic resolution data, lt1000

(?) atoms. Then the powerful atomicity

constraint can be used. Recently, the simple

"charge flipping" algorithm has been developed. (

Oszlanyi and Suto, Acta A60, p.134 (2004) )

Recently the phase problem for continuous

scattering from non-periodic objects has been

solved experimentally with electrons and X-rays

by new iterative methods. ("lensless

imaging") see - Weierstall et al Ultramic 90,

171 and Zuo et al Science 300, p. 1419 for

electrons and Marchesini et al Phys

Rev B68 (140101) (2003) for soft X-rays. These

iterative algorithms are developed from work by

Fienup, Gerchberg, Saxton and others.

If you use XRD software for TED data, be aware of

two important differences between XRD and TED

data 1. For XRD, all reflections are collected

at the Bragg condition. Not so for zone-axis

TED. 2. For XRD, reflections are

angle-integrated. Not so for TED or, usually,

CBED.

A new algorithm for xtal phase problem "Charge

flipping" Oszlányi Acta A60 134, '04.

- Start with measured Fhkl, random phases.
- Transform.
- 3 Set Im(r)0. Find x20 of largest positive

r, keep them. (Support estimate) - 4 Reverse sign (flipping) of all other r(r)

below threshold x. - 5. Go to 2.

r

1

R factor

C6Br6 exptl data

Unlike direct methods does not need known scatt

factors ! flipping finds support ! Converges

to same structure indep of initial phases.

x was reduced here

Iteration number

Solve structure of C6Br6 by flipping, using

experimental X-ray data. (Wu, O'Keeffe,

Spence, Groy. Acta A In press 04. Use fractional

a, since F0 unknown)

010 400th iteration, R 0.029

24 peaks with the highest density

- How do we know if a peak is an atom ? If

stoichiometery, space group known, choose n

largest. - If not, repeat with different starting random

phases. Add results. Noise peaks decrease, atoms

dont. - Dioxane (SnBr4) also solved. Atomic numbers

given by height of peaks (if normalised). - Gives correct atomic coords.
- Needs atomic resolution data. If not, see heavy

atoms. Works for non-periodics to find support,

like shrinkwrap. - Wont work in 2D for xtals (not enough

zero-density). Does work with oversampled 2D

non-periodic (more zero density)

Imaging theory - needed because collection of 3D

diffraction data is difficult Flipping doesnt

work in 2D (and requires atomic resolution data).

Oops ! Double diffraction

Electron beam

(Lens phase shift)

1. For a perfect lens, image is magnified copy of

exit face wave-function. 2. This is a faithful

representation of the projected potential only if

kinematic, and flat Ewald sphere.(wpo) 3. FT of

such an exit face wave wave gives "structure

factors" Vg. propn to diff. pattern spot

intensities. 4. If multiple scattering inside

sample, FT of exit face wave still gives d.p. But

spots are not stucture factors.

Electron/specimen interaction refraction with

locally varying index

Incident wave. Plane of constant phase is flat.

electrons go faster along atoms, with higher

kinetic energy, shorter wavelength, more wiggles.

sample

Exit wave Phase front has wobble

-i

kin

Representation on argand diagram Wave has a

range of phase values In kinematic theory,

phase is 90o wrt (000)

(000)

1

The dynamical exit-face wave.

Kinematic scattering

FT

plane wave

Thin !

Image (copy of exit face wavefunction)

Diffraction pattern (Structure factors)

Exit face wavefunction (Faithful projection)

FT

Multiple (dynamic) scattering

plane wave

Thick !

Image

Diffraction pattern (Not structure factors !)

Exit face wavefunction (Not faithful projection.

Correct period)

Note FT relationship between exit face and

diffraction pattern is preserved with multiple

scattering

HREM imaging theory for weak phase objects.

Exit face wavefield

Weak scattering

Diffracted amplitude

Add lens, aperture

4

Image amplitude

Image intensity

Notes dark atoms predicted on bright background

at Scherzer focus, where - 90 degree lens

phase-shift adds to - 90 degree scattering phase

(i exp i p/2). Then replace P(u,v) exp() in 4

by -i to give image I(x,y) 1 - 2 s fp(-x,-y)

for ideal lens without aperture.

Intensity in image

1

A

B

Position

WPO

Not WPO

Contrast A/B must be small for WPO.

High contrast - not a weak phase object !

"Multiple scattering is the usual condition in

electron diffraction"

Kisielowski et al NCEM LBL Ultram 2001.

(No Transcript)

Diffractograms for wpo. Finding structure factor

phases from HREM images.

The complex Fourier transform of the WPO image

intensity can be obtained in a computer as

where

2

where D, C are constants. Hence if c is known,

the phase of the fourier coefficients of the

projected potential can be found. These phases

are 0 or 180 degrees (wrt some origin) for

centric projections

From "HREM" by JCHS, 3rd Edn 2003. OUP

- Solving structures from point electron

diffraction patterns alone. - Examples. 1. Inorganic.
- Weirich et al. Acta A56, p.29 (2000). Ti2Se

Octahedra. Short b axis along beam. - Direct Methods.SIR97 SAD patterns from areas

thin enough to show no forbidden - reflections. Symmetry related merging. Assume

FhklIhkl for "extinction" model. - (Cowley 1992). Unlike XRD, peak heights in

potential map are not proportional - to atomic number. Note xtal thickness neither

known nor enters analysis. No - corrections for Ewald sphere curvature. EDX used

for stoichiometry. R24. - Film, CCD. Five other fine-grained structures

solved. Atom position error 0.2 Ang.

Solving structures from point electron

diffraction patterns alone. Examples. 2.

Organics (Proteins are another story

!) Dorset. Acta A54, p. 750 (1998).

Linear chain polymers require view

normal to chain - difficult ! Caprolactane was

xtallized in two orientations. Direct

methods. Solved.

Example 3. The precession camera. (Vincent and

Midgely 1994, Marks 03 JMCFest., Gjonnes

et al 1998). AlmFe intermetallic. Patterson and

Direct Methods. 3D. No short axis.

Precession data is "more kinematic" since

angle-integrated.(Direct beam precesses around

ZOLZ). Blackman, 1939 gives

angle-integrated 2-beam soln. Ig Ug2

t for small t, but remarkably Ig Ug

for large t. Structure solved with 3 Fe

and 12 Al atoms.

Definition of R factor

Solving xtal structures by combining HREM images

and TED patterns. Example Inorganic. Zou et

al. Acta A59, p.526 (2003).

AlCrFe. 3D "quasixtal". a4nm !. 13 different

TED Zones. 124 atoms found. Film WPO assumed, and

HREM images corrected for defocus, Cs. Phases

obtained from these. Magnitudes from TED

patterns. Some projections are centro. Xtal is

not. Symmetry merging. CRISP used. No correction

for Ewald sphere curvature. (Same method as

proteins). No thickness

- Space-group determination by CBED.
- Find point group hence crystal system (cubic,

hexagonal, trigonal, tetragonal, orthorhombic,

monoclinic, triclinic). - Find Bravais lattice and centering. Index.
- Find screw and glide elements. Find space group

by adding these translational symmetries to the

point group laid down at every point of Bravais

lattice.

BeO (wurtzite) CBED down c. 100kV . Elastic

imaging filter. Sixfold axis. Projection

diffraction group 6mm1R

(No Transcript)

c

Bragg condition is along line B

Dynamically forbidden reflections in BeO

(hexagonal, wurtzite) shows 21 (contained in 63 )

screw axis along c and/or c glide axis.

from Zuo and Spence, Microdiffraction, Plenum, 92

Electrons, X-rays and Neutrons

Electrons

X-ray

Neutrons

Mn

Mn3

Mn3

- Compared to X-rays and Neutrons, Electrons
- Interact strongly with matter
- Have bright source
- Are very sensitive to charge states at small

scattering angles - Are scattered predominantly by nuclei at high

scattering angles - Have the smallest probe 1 Å

Jim Zuo/MATSE

(cf Tanaka, Tsuda, Saunders, Bird, Nufer, Mayer,

Fox) .

Seeing Bonds

TED of diffuse scattering from phonon modes in

silicon - beyond the Einstein model.

I(q,w) e.g q-2 w-2 for these transverse

acoustic modes phonones, where e (along

-1,1,0,1,1,0) is phonon polarization, q

(along 110,-1,1,0) is phonon

wavevector and w phonon freq. Recorded

in Koehler mode at 105K on Fuji Image Plates

Hoier, Kim, Zuo, Spence Shindo, MSA 95

The atomic mechanism of metal-insulator phase

transition in Magnetite

a

b

(400)

(000)

(220)

Diffuse scattering in Magnetite at

metal-insulator Verwey transition (about

120K). a) 130K b)326 K. Inset (800) left (880)

right. Elastically filtered scattering recorded

using Image Plates. (Leo Omega 912). Zuo,

Pacaud, Hoier, Spence. Micron, 31, p. 527 (2000).

v

p

154 K

129 K

386 K

184 K

Temperature dependence of diffuse around (800)

Bragg spots compared with theory for polaron

(Yamada).

The monoclinic cell of our low temperature charge

ordering model (model 2, B-sites only). The

yellow tetrahedrons (molecular polarons) form a

linked chain with alternating opposite dipoles

(red arrows). The chains are separated by

molecular polarons of different orientations

(blue). The left shows the schematic arrangement

of the spiral chains (shown as bars) above and

below Verwey transition.

First atomic-resolution diffractive image

reconstruction.

Double-walled Nanotube

SAD TEM

Image reconstructed from electron-diffraction

pattern by HiO

J.M.Zuo et al Science 300, 1420 (2003).

First atomic- resolution image of a DWNT by any

method ?. Obtained by HiO. Aberration-free. Give

s ID, OD, Chiral vectors. Zuo et al 2003. What

limits resolution ?

The challenge of electron crystallography.

In the age of nanoscience, there is an urgent

need for a method of rapidly solving new ,

inorganic nanostructured materials. Many are

fine-grained, light element, crystallites which

cannot be solved by XRD. The unsolved challenge

of 50 years is..

To collect three-dimensional diffraction data

under kinematic conditions. Then not restricted

to short c axis. Note centers of each CBED disc

in a small-probe pattern provide a point pattern

! Blank disks suggest single-scattering

conditions. To solve the same unknown

structure first by TED and then by XRD, get same

result.

- The difficulties are
- Goniometers. Loss of area during tilt.
- Contamination
- Automation of tilt and data collection.
- Radiation damage.

GO TO http//www.public.asu.edu/jspence/ElectrnDi

ffn.html For free software ! Useful books,

papers, group web pages , conferences etc !!!!!

OR Google IUCr

(No Transcript)

(0 2 0)

(4 0 0)

(0 0 0)

Convergent Beam Electron Diffraction displays a

rocking curve simultaneously in every diffracted

order. The rocking curve is the change in

intensity of a particular diffracted beam with

variation of the incident beam direction. Each

point in the (000) central disc represents a

different incident beam direction. One such point

is coupled to conjugate points in all the other

discs differing by reciprocal lattice vectors.

Dynamically forbidden reflections.

Screw axis along c, k. Alternate reflections

along c extinguished kinematically.

Scattering paths arranged in pairs which cancel

on black lines, cross, for all thickness and

voltage ! Black cross appears on disk at Bragg

condition. Black lines on other kinematically

forbiddens

Gjonnes and Moodie, Acta A19, p. 65 (1965).

Reciprocity.

S

B

A

Formally, in systematics orientation, F(h,g)

F(h, -g2h) where g is at Bragg. Here let h1,

g2 in A, then expect F(1,2) F(1, 0),

and in B.

Multislice testgold,(111) systematics, 200 kV.

-2

-1

0

1

2

g

0.00086

0.0423

Amplitude of Bragg beams.

0.423

0.913

0.000869

Orientation A

0.0423

0.0215

Orientation B

0.0000131

0.0102

0.924

In these two different orientations, one from

each family of diffracted beams has identical

complex amplitude This holds for all thicknesses

! Every beam has different intensity in the two

orientations, except 1 !