Advanced Materials Characterization Workshop of Electron Diffraction Tilting sample to obtain 3-D structure of a crystal Lattice parameter, space group, orientation relationship To

$Page 1: Advanced Materials Characterization Workshop of Electron Diffraction Tilting sample to obtain 3-D structure of a crystal Lattice parameter, space group, orientation relationship To$
Transmission Electron Microscopy

Wacek Swiech, Honghui Zhou, Jim Mabon,

Amish Shah (Intel) and Jian-Guo Wen (ANL)

Frederick Seitz Materials Research Laboratory

University of Illinois at Urbana-Champaign

© 2013 University of Illinois Board of Trustees. All rights reserved.

Advanced Materials Characterization Workshop

June 3rd and 4th, 2013

University of Illinois at Urbana-Champaign | Materials Research Laboratory


Why Use Transmission Electron Microscopy?

AN is 0.95 with air

up to 1.5 with oil

Transmission Electron Microscope

(TEM) Optical Microscope

200 keV electrons l: 0.027 Å

• Sample thickness requirement:

• Thinner than 500 nm

• High quality image: <20 nm

High Resolution TEM

TEM is ideal for

investigating thin foil, thin

edge, and nanoparticles

< 500 nm

Resolution limit: ~200 nm

R = 0.66(Csλ3)1/4

Resolution

Resolution limit: ~0.25 nm

Basic Concepts – Electron-Sample Interaction

magnetic

prism e- x 10^3e- x 10^3

Specimen

Incident high-kV beam

Transmitted

beam

Diffracted

beam

Incoherent

beam

(STEM)

Coherent beam

1. Transmitted electrons (beam)

2. Diffracted electrons (beams) (Elastically scattered)

3. Coherent beams

4. Incoherent beams

5. Inelastically scattered electrons

6. Characteristic X-rays

X-rays

Inelastically

scattered

electrons

TEM can acquire images, diffraction

patterns, spectroscopy and chemically

sensitive images at sub-nanometer to

nanometer resolution.


Structure of a TEM

Gun and

Illumination part Gun: LaB6, FEG

80 – 300keV

Mode selection and

Magnification part View screen

TEM Sample

Objective lens part


How does a TEM Obtain Image and Diffraction?

Conjugate planes

Object Image

Sample

Objective Lens

Back Focal Plane

Incident Electrons

< 500 nm

First Image Plane

Back Focal Plane

View Screen

First Image Plane

u v

u v f _ _ _ 1 1 1

+ =

Structural info

Morphology

Electron Diffraction I

Ewald Sphere

l is small, Ewald sphere (1/l) is almost flat

d

Bragg’s Law

2 d sin q = nl

q Zero-order Laue Zone (ZOLZ)

First-order Laue Zone (FOLZ)

….

High-order Laue Zone (HOLZ)

ZOLZ

FOLZ

SOLZ

X-ray: about 1A

Wavelength

Electrons: 0.037A,

@ 100kV

Electron Diffraction II

50 nm

Polycrystal

Diffraction patterns from single

grain or multiple grains

002

022

Single crystal Amorphous


Selected Area Electron Diffraction (SAED)

Example of SAED

Selected-area aperture

1) Selected-Area Electron Diffraction

2) NanoArea Electron Diffraction

3) Convergent Beam Electron diffraction

Major Diffraction Techniques

SAED

aperture

J.G. Wen, A. Ehiasrian, I. Petrov

Selected Area Electron Diffraction (SAED)

L. Reimer and H. Kohl, Transmission Electron

Microscopy, Physics of Image Formation, 2008.

1. Illuminate a large area of the specimen with a

parallel beam.

2. Insert an aperture in the first image plane to select

an area of the image.

3. Focus the first imaging lens on the back focal plane

Al

matrix

Al-Cu

matrix

Selected Area Electron Diffraction

1. Can observe a large area of

specimen with a bright beam

2. Since the image plane is

magnified, can easily select an

area with an aperture A 50

mm aperture can select a 2 mm

area

3. Useful to study thick films, bulk

samples, and in-situ phase

transformations

1. Cannot select an area less

than ~1 mm due to spherical

aberrations and precision in

aperture position

2. Difficult to record diffraction

from individual nanoparticles

or thin films

Advantages

Disadvantages

Spherical Aberrations

Selected

Area

Aperture


Nanoarea Electron Diffraction (NAED)

1. Very weak beam – difficult to see

and tilt the sample

2. More complex alignment than

conventional TEM

3. High resolution images are difficult

to obtain Need to switch

between NAED and TEM modes)

Disadvantages

1. Focus the beam on the front

focal plane of the objective

lens and use a small

condenser aperture to limit

beam size

2. A parallel beam without

selection errors A 10 mm

aperture can form a ~ 50 nm

probe size

3. Useful to investigate individual

nanocrystals and superlattices

Technique

55 nm nanoprobe

Diffraction from a single Au rod

A. B. Shah, S. Sivapalan, and C. Murphy


Nanoarea Electron Diffraction

M. Gao, J.M. Zuo, R.D. Twesten, I. Petrov, L.A. Nagahara & R. Zhang,

Appl. Phys. Lett. 82, 2703 (2003)

J.M. Zuo, I. Vartanyants, M. Gao, R. Zhang and L.A. Nagahara,

Science, 300, 1419 (2003)

5 mm condenser aperture 30 nm

This technique was developed by CMM


Aperture-Beam Nanoarea Electron Diffraction

20 mm condenser aperture 20 nm probe size

Conjugate planes

Condenser

Aperture Sample

5 n m5 n m

SrTiO3

CeO2

a) b)

5 n m5 n m

2 nm

020S 011S

002S

002C 220C 111C

u v

This technique was developed by CMM

Applications of Electron Diffraction

Tilting sample to obtain 3-D structure of a crystal

Lattice parameter, space group, orientation relationship

To identify new phases, TEM has advantages:

1) Small amount of materials

2) No need to be single phases

3) Determining composition by EDS or EELS

Disadvantage: needs experience

1, 2, 3, 4, 6-fold symmetry

No 5-fold for a crystal

5-fold symmetry

More advanced electron diffraction techniques

New materials discovered by TEM

Quasi-crystal Carbon Nanotube

Helical graphene

sheet


Convergent Beam Electron Diffraction (CBED)

Back Focal Plane

Parallel beam

Sample

Convergent-beam

Sample

1. Point and space group

2. Lattice parameter (3-D) strain field

Large-angle bright-field CBED

Bright-disk Dark-disk Whole-pattern

3. Thickness

4. Defects

CBED SAED


Major Imaging Techniques

1) Imaging techniques in TEM mode

a) Bright-Field TEM (Diff. contrast)

b) Dark-Field TEM (Diff. contrast)

c) Weak-beam imaging

hollow-cone dark-field imaging

d) Lattice image (Phase)

e) High-resolution Electron Microscopy

(Phase)

Simulation and interpretation

2) Imaging techniques in scanning

transmission electron microscope

(STEM) mode

1) Z-contrast imaging (Dark-Field)

2) Bright-Field STEM imaging

3) High-resolution Z-contrast imaging

(Bright- & Dark-Field)

3) Spectrum imaging

1) Energy-Filtered TEM (TEM mode)

2) EELS mapping (STEM mode)

3) EDS mapping (STEM mode)

Major Imaging Contrast Mechanisms:

1. Mass-thickness contrast

2. Diffraction contrast

3. Phase contrast

4. Z-contrast

Mass-thickness contrast


TEM Imaging Techniques

I. Diffraction Contrast Image:

Contrast related to crystal

orientation

Kikuchi Map [111]

[110]

[112]

[001]

Application:

Morphology, defects, grain boundary, strain field, precipitates

Two-beam condition

[001]

Transmitted beam

Diffracted beam

Phase Contrast Image



Objective Lens

Aperture Back Focal Plane

Diffraction Pattern

Bright-field Image

First Image Plane

Dark-field Image

Sample Sample

T D

II. Diffraction Contrast Image: Bright-field & Dark-field Imaging

Two-beam condition

Bright-field Dark-field



Dislocations & Stacking Faults

Bright Field Image

At edge dislocation, strain from extra half

plane of atoms causes atomic planes to

bend. The angle between the incident beam

and a few atomic planes becomes equal to

the Bragg Angle ΘB.

II. Diffraction Contrast Imaging

R. F. Egerton, Physical

Principles of Electron

Microscopy, 2007.

Near dislocations,

electrons are strongly

diffracted outside the

objective aperture

Specimen

Principal

Plane

Objective

Aperture

Transmitted

Beam

Diffracted

Beam


Weak-beam Dark Field Imaging

High-resolution dark-field imaging

1g 2g 3g

Planes do not satisfy

Bragg diffraction

Possible planes satisfy

Bragg diffraction

Dislocations can be imaged

as 1.5 nm narrow lines Bright-field Weak-beam

C.H. Lei

g g

S

Weak-beam means

Large excitation error

Exact Bragg condition Taken by I. Petrov

“Near Bragg Condition”

Experimental weak-beam



Dislocation loop

Diffraction contrast images of typical defects

Phase = 2 p g • R

Dislocations Stacking faults

df0 pi

dz xg

= fgexp{2pi(sz+g.R)}

Howie-Whelan equation

g 1 2 3

2 3 -p Each stacking fault changes phase

Two-beam condition for defects Use g.b = 0 to determine Burgers vector b

Sample

Dislocations

Stacking faults

II. Diffraction Contrast Image


Lattice Beam Imaging

Two-beam condition Many-beam condition

C.H. Lei M. Marshall

[001]


Lattice Imaging

From a LaB6 Gun Field-Emission Gun

Delocalization effect from a Schottky-emission gun (S-FEG)

Lattice image of film on substrates


High Resolution Transmission Electron Microscopy (HRTEM)

Dfsch = - 1.2 (Csl)2

1

Scherzer defocus

Resolution limit

rsch = 0.66 Cs l

1

4

3

4

1 Scherzer Defocus:

Positive phase contrast “black atoms”

2 Scherzer Defocus: ("2nd Passband" defocus).

Contrast Transfer Function is positive

Negative phase contrast ("white atoms")

1 Dfsch 2 Dfsch

f(x,y) = exp(isVt(x,y))

~1 + i s Vt(x,y)

Vt(x,y): projected potential

Simulation of images Software: Web-EMAPS (UIUC)

MacTempas

J.G. Wen Contrast transfer function

Scanning Transmission Electron Microscopy

magnetic

prism e- x 10^3e- x 10^3

Inelastically scattered electrons

Focused e-beam

STEM

Probe size

0.2 – 0.5 nm

Thickness

<100 nm

“Coherent” Scattering

(i.e. Interference)

“Incoherent”Scattering

i.e. Rutherford

Dark-field

Bright-field

x-rays 1. Raster a converged probe across

and collect the integrated signal

on an annular detector (dark field)

or a circular detector (bright field).

2. An incoherent image is chemically

sensitive (Z-contrast) under

certain collection angles

3. Annular dark field (ADF) STEM is

directly interpretable and does not

have contrast reversals or

delocalization effects like HRTEM

4. STEM resolution is determined by

the probe size, which is typically

0.2 to 0.5 nm for a modern FEG

STEM.

5. Since STEM images are collected

serially, the resolution is typically

limited by vibrations and stray

fields

Technique

SEM vs STEM

magnetic

prism e- x 10^3e- x 10^3

Inelastically scattered electrons

Primary e-beam

0.5-30 keV backscattered electrons

secondary electrons <50 eV

Auger electrons

x-rays

1 mm

Primary e-beam

60-300 keV x-rays

STEM

Probe size

0.1 – 0.5 nm

Thickness

<100 nm

“Coherent” Scattering

(i.e. Interference)

“Incoherent”Scattering

i.e. Rutherford

Dark-field

Bright-field

SEM

STEM technique is similar to SEM, except the

specimen is much thinner and we collect the

transmitted electrons rather than the reflected

electrons

TEM vs ADF-STEM

5 nm

5 nm

TEM

ADF-STEM

Ir nanoparticles

10nm

Z-contrast image

Ge quantum dots on Si substrate

1. STEM imaging gives better

contrast

2. STEM images show Z-

contrast

q

I Z2

L. Long J.G. Wen

Annular dark-field (ADF) detector

Z-contrast imaging

Z

ADF STEM Applications

A. B. Shah et al., 2008

Superlattice of LaMnO3-SrMnO3-SrTiO3 Dopant atoms in Si

P. M. Voyles et al., 2002


Bright Field STEM vs ADF STEM

40kX 1Mx 15Mx

40kX 1Mx 15Mx

Si GexSi1-x

Si GexSi1-x

Si – Ge Superlattice

Spherical Aberration

1.3

mm

± 1

0 n

m

2.4 m

Since 1936, Scherzer proved that spherical and chromatic

aberrations would ultimately limit the resolution of the electron

microscope. The method to correct aberrations was well known, but

experimental aberration correctors were not successful until ~1998

due to complexities in alignment and lack of computing power.


Spherical Aberration Correction

Before correction After correction

Cs + (–Cs) = 0


Spherical Aberration Corrector for TEM & STEM

Harold Rose

Univ. of Tech. Darmstadt

Max Haider

CEOS, Germany N

Cs< 0

N

Hexapole 1

Hexapole 2

Round Lens 1

Round Lens 2

Optical

Axis

e-Beam

Uli Dahmen

NCEM

Hexapole Cs Corrector


Spherical Aberration Corrector for STEM

Ondrej Krivanek

Nion Company

Quadrupole-Octupole C3-C5 corrector

First sub-Å image resolved in a STEM

P. E. Batson et

al., Nature, 2002.


JEOL JEM2200FS with Probe Corrector @ UIUC

Diffuser

Multilayer wall

The STEM can obtain

1 Å spatial resolution

Only if the instabilities

of the room are

controlled

Piezo

Stage


Spherical Aberration Correction

JEOL 2010F

Cs = 1 mm

Probe size

0.3 nm

JEOL 2200FS

with probe corrector

Probe size

0.1 nm

Image corrector Probe corrector


Improved Resolution and Contrast with Cs Corrector

63 pm

Aberration correction combined with a high stability environment and high

quality specimens allow for atomic resolution imaging over a large area.

4k x 4k image shown.


Sub-Å test using GaN film along [211] zone axis

Annular dark field STEM image

of hexagonal GaN [211]

Fourier transform of the image;

image Fourier components

extend to below 50 pm.

63 pm

TEAM Microscope at LBNL

New Applications Possible Only with Aberration Correction

1. Better Contrast for STEM Imaging

with smaller probe

2. Reduced delocalization for HRTEM

imaging

3. Sub-2Å resolution imaging at low

voltage (60 – 100 kV) for TEM and

STEM

4. 10-20 X more probe current in the

STEM for EELS and EDS

spectroscopy

Ronchigram

43

Specimen

Analytical (Scanning) Transmission Electron Microscopy

Incident

High-kV Beam

Bremsstrahlung

X-rays

Auger

Electrons

Secondary

electrons (SE)

Characteristic

X-rays

X-ray Energy Dispersive

Spectroscopy

Back scattered

electrons (BSE)

Forward

Scattered

electrons

Inelastically

scattered

electrons

Electron Energy Loss Spectroscopy

Elastically

scattered

electrons

EDS and EELS in STEM Mode 44

Spatially Resolved Analysis Sub nanometer in aberration-corrected STEM !

Further refined probe

• Down to ~ 0.1 – 0.2 nm

• Carries more current

~ 1-10 nm

Aberration-corrected


Some relevant transition events explored in EELS and EDS

• EELS: named by the initial state, e.g., L3: 2p3/2 → [3S1/2, 3d3/2, 3d5/2]

• EDS: named by the initial core-hole state, e.g., Kα: 2p → 1s

David Muller 2006: http://www.ccmr.cornell.edu/igert/modular/docs/4_Chemical_Identification_at_Nanoscale.pdf

Energy Loss

X-ray


X-ray Energy Dispersive Spectroscopy in STEM

• High spatial resolution (~ nm compared with ~ μm in SEM) — refined incident probe — significantly reduced interaction volume (directly related to the specimen thickness)

Masashi Watanabe: X-ray Energy-Dispersive Spectrometry in Scanning Transmission Electron Microscopes

in Scanning Transmission Electron Microscopy Imaging and Analysis

reproduced from Williams and Carter: Transmission electron microscopy (2009)

• Degraded analytical sensitivity — significantly reduced interaction volume (directly related to the specimen thickness)

— collection limited by microscope column detector configuration (0.3 sr out of 4 π sr)

SEM STEM

• TEM mode spot, area

• STEM mode spot, line-scan and 2-D mapping

Ti0.85Nb0.15 metal ion etch

Spatial resolution ~ 1 nm

Line scan

A. Ehiasrian, I. Petrov

X-ray Energy Dispersive Spectroscopy Applications

Area Mapping

Al

Mo

Si

Au

Ti

Mo

Ga

Ti

Au HAADF

voids

2-D mapping

L. Wang

A B

A B

Fe

Cr

Nb

Al

Ti


Electron Energy Loss Spectroscopy – Electron Spectrometer

Post-column In-column

Gatan Imaging Filter (GIF)

JEOL Omega-type Energy filter

Gatan Imaging Filter (GIF)

e- x 10^3e- x 10^3

http://img17.imageshack.us/img17/1686/spectprism.jpg

Analogy: Optical prism

Electron Energy Loss Spectrum

ZLP Low-loss

• Zero-loss (ZLP)

• Low-loss spectrum (< 50 eV)

due to interactions with weakly bound outer-shell electrons

— Plasmon peak (excitation of oscillations of weakly bound electrons)

— Inter- and Intra-Band transitions

• Core-loss spectrum (> 50 eV)

due to interactions with tightly bound inner-shell electrons

— Inner shell ionization

Ti-L

O-K

Mn-L

La-M

x100

Core-loss

~ 50 eV

Energy Loss (eV)

Energy (KeV)

Spectrum Comparison between EELS and EDS

x 1

0^3

eV

-10

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

x 1

0^3

450 500 550 600 650 700 750 800 850 900

eV

Fe2O3

x 1

0^3

eV

-30

-20

-10

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

x 1

0^3

450 500 550 600 650 700 750 800 850 900

eV

bkgd

Spectrum

Bkgd

Edge

Fe2O3

Energy Loss (eV)

Fe-L3,2 Fe-L3,2 O-K O-K

Fe-L

Energy Loss (eV)

Correlations of Core-loss EELS Features With Electronic Structures

Empty States Conduction/valence bands Core-shell energy levels

Neighboring atoms

O-K

Ni-L3,2 Ni-M3,2

Gatan: Review of EELS Fundamentals

O-1s O-2p

Ni-2p

Ni-3d


Electron Energy Loss Spectrum Applications

Gatan: Review of EELS Fundamentals

• Elemental composition: the core-level binding energy is unique

• Near edge fine structure (ELNES): transition is only possible to local unoccupied states

— information about electronic structures

• Extended fine structures (EXELFS): atom-specific radical distribution of near neighbors

• Measuring the collective excitations, e.g., the combined response of the valence electrons and the electron magnetic field.

• Specimen thickness

• Optical and electronic properties

— Polarization response (complex dielectric function)

— Band structure, e.g., band gap

Thickness measurement

EELS Near Edge Structure (ELNES) — Chemical Bonding

V J Keast, J. Microscopy, 203, 135 (2001)

C-C Sp3 bonding

C-C Sp3 bonding

C-C Sp2 bonding

C-C Sp2 bonding

π* - Sp2 bonded

C-H bonding

C-H bonding

C-H* bonding

• Chemical Shift of L3 and L2 peak

• L3/L2 ratio (white line ratio)

• O-K edge near edge fine structure (ELNES)

EELS Near Edge Structure (ELNES) — Oxidation State of Transition Metal Oxide

M. Varela, et.al., PHYSICAL REVIEW B 79, 085117 (2009) H. Zhou

Energy Loss (eV)

Spectr

um

Image

Counts

eV

0

2000

4000

6000

8000

Counts

500 600 700 800 900

eVC

ounts

eV

0

1000

2000

3000

4000

5000C

ounts

500 600 700 800 900

eV

Counts

eV

0

2000

4000

6000

8000

Counts

500 600 700 800 900

eV

Survey Image Spectrum Image Extracted Spectrum V-L mapping Ni-L mapping

NiO

VO1+x

VO2 V-L3,2

Ni-L3,2

STEM EELS Spectrum Imaging

H. Zhou

V-L3,2

Each image pixel carries one EELS spectrum — spatial and spectroscopy information are stored together

Atomic-column resolution Spectrum Imaging

Ti-L O-K Mn-L La-M

Sca

n D

irectio

n

DE Electron Energy Loss

Ti L

O K Mn L

La M

Substrate Side

LaMnO3 SrTiO3

Atomic-column Resolution Spectrum Imaging


Atomic-column Resolution Spectrum Imaging

D. A. Muller et al., Science, 2008.

La Ti

Mn RGB Image

La0.7Sr0.3MnO3 – SrTiO3 Superlattice

Mapping of the interface chemistry and bonding States

A. B. Shah et al., Phys. Rev. B, 2010

10 x 5 LaMnO3 – SrMnO3 Superlattice

Extra states are found at sharp interfaces.

Mn-L3 O-K

LMO

SMO

LMO

SMO

Sharp

Rough


Comparison of EELS and EDS

EELS EDS

• Atomic composition • Chemical bonding • Electronic properties • Surface properties ….

• Atomic composition only

Spatial resolution: 0.1 - 1 nm Spatial resolution: 1 nm – 10 nm

Energy resolution: ~ 1 eV Energy resolution: ~ 130 eV (Mn Kα)

Relatively difficult to use The interpretation sometimes involves theoretical calculation

Easy to use The interpretation is straightforward

High collection efficiency (close to 100 %)

Low collection efficiency (1-3%)

Sensitive to lighter elements Signal weak in high loss region

Sensitive to heavier elements Low yield for light elements


Energy Filtered Transmission Electron Microscopy

Gatan: Review of EFTEM Fundamentals

Forming images with electrons of selected energy loss

1. Unfiltered image or diffraction pattern (DP) is formed

2. Image or DP is transformed into the spectrum

3. Part of the spectrum is selected by energy-selecting slit

4. Selected part of spectrum is transformed back into an energy-filtered image or DP

Spectrum imaging

• ZLP imaging

• Plasmon imaging

• Edge imaging

ZLP

Low-loss

Ti

O

Mn

La

Edges

Image at DE1

Image at DE2

Image at DE3

Image at DEn

e- x 10^3e- x 10^3

DE

x

y

Spectrum imaging

Energy Filtered Transmission Electron Microscopy

EFTEM Spectrum Imaging: • Energy filtered broad beam technique • Fills data cube taking one image at each energy at a time • Less time STEM Spectrum Imaging • Focused probe method • Fills data cube by taking one spectrum at each location at a

time • Less does

• Elastic electrons only

“Inelastic fog” removed

• Contrast enhanced

(Good for medium

thick samples)

• For Z < 12, the

inelastic cross-section

is larger than elastic

cross-section

ZLP

Spectrum imaging EFTEM – Zero-loss Peak imaging

Images from Gatan Review of EFTEM Fundamentals

Low-loss

Unstained/osmicated cebellar cortex

CBED Pattern

A B

EFTEM – Plasmon Peak imaging

A B

W Al

Spectrum imaging

Spectrum image (20 images) Al mapping image W mapping image

J.G. Wen

30 nm

EFTEM – Plasmon Peak imaging


EFTEM – Edge Peak imaging

Ti

Si

J.G. Wen

Image

Ti EELS spectrum

Three-window method

Jump ratio Three Window Mapping

Jump Ratio Imaging

Pre-edge image Post-edge image


List of TEMs and Functions at UIUC

2010 LaB6 2100 Cryo

2010F 2200FS

Thank you !

• Heating stage (up to 1000°C)

• Cooling stage (with liquid N2 )

1. JEOL JEM 2010 LaB6 TEM

• TEM, low dose, NBD, HRTEM, in-situ

experiments

2. JEOL JEM 2100 LaB6 (Cryo-TEM)

• TEM, Low dose, special cryo-shielding

3. JEOL JEM 2010F Analytical (S)TEM

• TEM, BF, DF, NAED, CBED, EDS,

STEM, EELS, EFTEM

4. JEOL JEM 2200 FS Cs corrected (S)TEM

• Ultra high resolution Z-contrast STEM,

BF STEM, NBD, CBED, EDS, EELS,

EFTEM

5. Hitachi H-9500 TEM (expected 09/2013)

• In-situ heating and gas reaction,

HREM, NAED, 300 kV, LaB6 electron

source, Gatan K2 camera for fast

recording at 400 frames per second or

1000 frames per second using partial

fame.


Acknowledgments

66

Documents

Advanced Materials Characterization Workshop of Electron Diffraction Tilting sample to obtain 3-D structure of a crystal Lattice parameter, space group, orientation relationship To