Microbeam analysis — Analytical electron microscopy — Selected area electron diffraction analysis using a transmission electron microscope

ISO 25498:2018 specifies the method of selected area electron diffraction (SAED) analysis using a transmission electron microscope (TEM) to analyse thin crystalline specimens. This document applies to test areas of micrometres and sub-micrometres in size. The minimum diameter of the selected area in a specimen which can be analysed by this method is restricted by the spherical aberration coefficient of the objective lens of the microscope and approaches several hundred nanometres for a modern TEM. When the size of an analysed specimen area is smaller than that restriction, this document can also be used for the analysis procedure. But, because of the effect of spherical aberration, some of the diffraction information in the pattern can be generated from outside of the area defined by the selected area aperture. In such cases, the use of microdiffraction (nano-beam diffraction) or convergent beam electron diffraction, where available, might be preferred. ISO 25498:2018 is applicable to the acquisition of SAED patterns from crystalline specimens, indexing the patterns and calibration of the diffraction constant.

Analyse par microfaisceaux — Microscopie électronique analytique — Analyse par diffraction par sélection d'aire au moyen d'un microscope électronique en transmission

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6060 - International Standard published
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16-Mar-2018
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INTERNATIONAL ISO
STANDARD 25498
Second edition
2018-03
Microbeam analysis — Analytical
electron microscopy — Selected area
electron diffraction analysis using a
transmission electron microscope
Analyse par microfaisceaux — Microscopie électronique analytique
— Analyse par diffraction par sélection d'aire au moyen d'un
microscope électronique en transmission
Reference number
ISO 25498:2018(E)
ISO 2018
---------------------- Page: 1 ----------------------
ISO 25498:2018(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2018

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

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Email: copyright@iso.org
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Published in Switzerland
ii © ISO 2018 – All rights reserved
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ISO 25498:2018(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ................................................................................................................................................................................................................................vi

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Principle ........................................................................................................................................................................................................................ 3

4.1 General ........................................................................................................................................................................................................... 3

4.2 Spot diffraction pattern ................................................................................................................................................................... 3

4.3 Kikuchi pattern ....................................................................................................................................................................................... 6

4.4 Polycrystalline specimen ................................................................................................................................................................ 7

5 Reference materials .......................................................................................................................................................................................... 7

6 Equipment ................................................................................................................................................................................................................... 8

7 Specimens .................................................................................................................................................................................................................... 8

8 Experimental procedure .............................................................................................................................................................................. 8

8.1 Instrument preparation .................................................................................................................................................................. 8

8.2 Procedure for acquirement of selected area electron diffraction patterns ........................................ 9

8.3 Determination of diffraction constant, Lλ ...................................................................................................................12

9 Measurement and solution of the SAED patterns ..........................................................................................................13

9.1 Selection of the basic parallelogram .................................................................................................................................13

9.2 Indexing diffraction spots ...........................................................................................................................................................15

10 180° ambiguity ....................................................................................................................................................................................................16

11 Uncertainty estimation..............................................................................................................................................................................16

11.1 Factors affecting accuracy ..........................................................................................................................................................16

11.2 Calibration with a reference material .............................................................................................................................17

Annex A (informative) Interplanar spacing ...............................................................................................................................................18

Annex B (informative) Spot diffraction patterns of single crystals for BCC, FCC and HCP

[ ]

structure 7 ..............................................................................................................................................................................................................19

Bibliography .............................................................................................................................................................................................................................38

© ISO 2018 – All rights reserved iii
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ISO 25498:2018(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/ patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation on the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following

URL: www .iso .org/ iso/ foreword .html.

This document was prepared by Technical Committee ISO/TC 202, Microbeam analysis, Subcommittee

SC 3, Analytical electron microscopy.

This second edition cancels and replaces the first edition (ISO 25498:2010), which has been technically

revised.
The main changes to the previous edition are as follows:
— the foreword has been revised;
— the introduction has been revised;
— the scope has been revised;
— the figure of Ewald construction has been deleted;

— the terms and definition of terminological entries 3.1, 3.2, 3.10, 3.11, 3.12, 3.13 and 3.14 have

been added;
— the subclause 4.1 has been added;
— Clause 5 has been revised;

— Clauses 4, 6, 7, and 10 and subclauses 8.1.5, 8.1.6, 8.2.1, 8.2.2, 8.2.4, 8.2.7, 8.2.8, 8.2.11 and 9.1.2 have

been editorially revised;
— the subclause 9.2.5 has been added;
— all formulae have been renumbered;
— Annex A has been revised;
— the subclause B.1 has been revised;
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ISO 25498:2018(E)
— the figures have been modified;
— the bibliography has been updated.
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ISO 25498:2018(E)
Introduction

Electron diffraction techniques are widely used in transmission electron microscopy (TEM) studies.

Applications include phase identification, determination of the crystallographic lattice type and

lattice parameters, crystal orientation and the orientation relationship between two phases, phase

transformations, habit planes and defects, twins and interfaces, as well as studies of preferred crystal

orientations (texture). While several complementary techniques have been developed, for example

microdiffraction, convergent beam diffraction and reflected diffraction, the selected area electron

diffraction (SAED) technique is the most frequently employed.

This technique allows direct analysis of small areas on thin specimens from a variety of crystalline

substances. It is routinely performed on most of TEM in the world. The SAED is also a supplementary

technique for acquisition of high resolution images, microdiffraction or convergent beam diffraction

studies. The information generated is widely applied in the studies for the development of new

materials, improving structure and/or properties of various materials as well as for inspection and

quality control purpose.

The basic principle of the SAED method is described in this document. The experimental procedure

for the acquirement of SAED patterns, indexing of the diffraction patterns and determination of the

diffraction constant are specified. ISO 25498 is intended for use or reference as technical regulation for

transmission electron microscopy.
vi © ISO 2018 – All rights reserved
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INTERNATIONAL STANDARD ISO 25498:2018(E)
Microbeam analysis — Analytical electron microscopy
— Selected area electron diffraction analysis using a
transmission electron microscope
1 Scope

This document specifies the method of selected area electron diffraction (SAED) analysis using a

transmission electron microscope (TEM) to analyse thin crystalline specimens. This document applies

to test areas of micrometres and sub-micrometres in size. The minimum diameter of the selected area

in a specimen which can be analysed by this method is restricted by the spherical aberration coefficient

of the objective lens of the microscope and approaches several hundred nanometres for a modern TEM.

When the size of an analysed specimen area is smaller than that restriction, this document can also

be used for the analysis procedure. But, because of the effect of spherical aberration, some of the

diffraction information in the pattern can be generated from outside of the area defined by the selected

area aperture. In such cases, the use of microdiffraction (nano-beam diffraction) or convergent beam

electron diffraction, where available, might be preferred.

This document is applicable to the acquisition of SAED patterns from crystalline specimens, indexing

the patterns and calibration of the diffraction constant.
2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements of this document. For dated references, only the edition cited applies. For

undated references, the latest edition of the referenced document (including any amendments) applies.

ISO/IEC 17025, General requirements for the competence of testing and calibration laboratories

3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1
Miller index

notation system for crystallographic planes and directions in crystals, in which a set of lattice planes or

directions is described by three axes coordinate
3.2
Miller-Bravais index

notation system for crystallographic planes and directions in hexagonal crystals, in which a set of

lattice planes or directions is described by four axes coordinate
3.3
(h k l)
Miller indices (3.1) of a specific set of crystallographic planes
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ISO 25498:2018(E)
3.4
{hkl}
Miller indices (3.1) which denote a family of crystallographic planes
3.5
[uvw]
Miller indices (3.1) of a specific crystallographic direction or a zone axis
3.6
interplanar spacing
hkl

perpendicular distance between consecutive planes of the crystallographic plane set (h k l) (3.3)

3.7
(uvw)*
notation for a set of planes in the reciprocal lattice

Note 1 to entry: The normal of the reciprocal plane (uvw)* is parallel to the crystallographic zone axis [uvw] (3.5).

3.8
reciprocal vector
hkl
vector in the reciprocal lattice

Note 1 to entry: The reciprocal vector, g is normal to the crystallographic plane (h k l) (3.3) with its magnitude

hkl,
inversely proportional to interplanar spacing d (3.6).
hkl
3.9
R vector
hkl

vector from centre, 000 (the origin), to the diffraction spot, hkl, in a diffraction pattern

Note 1 to entry: See Figure 1.
3.10
camera length

effective distance between the specimen and the plane where diffraction pattern is formed

[SOURCE: ISO 15932:2010, 3.7]
3.11
camera constant
product of the wavelength of the incident electron wave and camera length (3.10)

Note 1 to entry: Because of the small Bragg angle, the Bragg condition can be given in the first-order

approximation, Rd⋅≅Lλ , where d is the interplanar spacing of plane, (hkl), (3.3) and R (3.9) is the

hkl
hklhkl hkl
distance of the diffraction spot, hkl, from the incident beam.
[SOURCE: ISO 15932:2010, 3.8, modified]
3.12
bright field image

image formed using only the non-scattered beam, selected by observation of the back focal plane of the

objective lens and using the objective aperture to cut out all diffracted beams
[SOURCE: ISO 15932:2010, 5.6]
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ISO 25498:2018(E)
3.13
dark field image

image formed by a diffracted beam only by using the objective aperture for selection or by collecting

the diffracted beam with an annular dark-field detector
[SOURCE: ISO 15932:2010, 5.6]
3.14
energy-dispersive X-ray spectroscopy
EDS

analytical technique which enables the elemental analysis or chemical characterization of a specimen

by analysing characteristic X-ray emitted by the matter in response to electron irradiation

[SOURCE: ISO 15932:2010, 6.6]
3.15
eucentric position

specimen position at which the image exhibits minimal lateral motion resulting from specimen tilting

4 Principle
4.1 General

When an energetic electron beam is incident upon a thin crystallographic specimen in a transmission

electron microscope, a diffraction pattern will be produced in the back focal plane of the objective lens.

This pattern is magnified by the intermediate and projector lenses, then displayed on a viewing screen

and recorded (see Reference [3]). This pattern can also be displayed on a monitor if the TEM is equipped

with a digital camera system.
4.2 Spot diffraction pattern

The diffraction pattern of a single crystal appears as an array of “spots”, the basic unit of which is

characterized by a parallelogram. A schematic illustration of a spot diffraction pattern is shown in

Figure 1. Each spot corresponds to diffraction from a specific set of crystal lattice planes in the

specimen, denoted by Miller indices (hkl). The vector, R , is defined by the position of the diffracted

hkl

spot, hkl, relative to position on the pattern corresponding to the transmitted beam, i.e. the centre-

spot, 000, of the pattern. It is parallel to the normal of the reflecting plane, (hkl). The magnitude of R

hkl

is inversely proportional to the interplanar spacing, d , of the diffracting plane, (hkl) (see References [4]

hkl
to [9]). In the context of this document, vectors R , R , RR− and
hk l hk l hk lh kl
11 1 22 2 22 21 11
RR+ are simplified as R , R , R and R , respectively. The included angle between
() 1 2 2−1 1+2
hk lh kl
22 21 11

vectors, R and R , is denoted by γ*. The basic parallelogram is defined by R and R , where they are the

1 2 1 2

shortest and next shortest in the pattern respectively and not along a common line. The spot, h k l , is

2 2 2
positioned anticlockwise around the centre spot relative to spot, h k l .
1 1 1

Because the centre-spot is often very bright, it is often difficult to determine the exact centre of the

pattern. Therefore, a practical procedure is to establish the magnitude of R by measuring the

hkl

distance between the spots, hkl and hkl on the diffraction pattern and dividing by two,

i.e. RR=+ R . Figure 2 shows an example of the SAED pattern where the magnitude of R ,

hklh( kl )
hkl
1 1 1
R and R is obtained from RR+ , RR+ and RR+ respectively.
2 2−1 () () ()
11 22 21−−21
2 2 2
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ISO 25498:2018(E)
Key

R vector from 000 to spot, h k l , the shortest vector in the diffraction pattern

1 1 1 1
R vector from 000 to spot, h k l , the next shortest vector
2 2 2 2

NOTE The basic parallelogram is constituted by diffraction spots, h k l , h k l , (h +h , k +k , l +l ), and

1 1 1 2 2 2 1 2 1 2 1 2
central spot, 000.
Figure 1 — Schematic spot diffraction pattern from a single crystal
Key

R vector from 000 to spot, h k l , the shortest vector in the diffraction pattern

1 1 1 1
R vector from 000 to spot, h k l , the next shortest vector
2 2 2 2
NOTE The basic parallelogram is constituted by R and R .
1 2
Figure 2 — Example of SAED spot pattern
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ISO 25498:2018(E)

The relationship between the interplanar spacing, d , and the magnitude, R for a reflecting plane,

hkl hkl,

(hkl), can be approximately expressed as shown in Formula (1) (see References [7] and [8]):

 3 2
LRλ = ×−dR1 /LR= ×−d 1 Δ (1)
() ()
hklhkl hklhkl hkl
 
 
where
Δ is equal to RL/ ;
hkl
L is the diffraction camera length and equal to f × M × M ;
o i p
where
f is the focal length, in millimetres, of the objective lens in the microscope;
M is the magnification of the intermediate lens;
M is the magnification of the projector lenses;

Lλ is the camera constant (or diffraction constant) of the transmission electron microscope

operating under the particular set of conditions. This parameter can be determined from the

diffraction pattern of a crystalline specimen of known lattice parameters (see 8.3);

λ is the wavelength, in nanometres, of the incident electron beam which is dependent upon the

accelerating voltage and can be given by Formula (2) (see Reference [4]):
1,226
λ nm = (2)
VV10+ ,97881× 0

where V is the accelerating voltage, in volts, of the TEM; the factor in parenthesis is the relativistic

correction.

For most work using a TEM, the value of Δ in Formula (1) is usually smaller than 0,1 % and, hence, a

more simplified Formula (3) may be used, namely
Rd⋅≅Lλ (3)
hklhkl

For the derivation of the above equation, refer to the textbooks (see References [4] to [9]).

The use of Formula (3) requires measuring the length of R . Since, as mentioned earlier, the location of

hkl

the pattern centre may not be easily determined; it is recommended that the distance measurement

taken, 2R , be from the h k l diffracted spot to the hk l spot on the pattern. This is equivalent

1 1 1
hk l 11 1
11 1

to a diameter measurement on the ring pattern from a polycrystalline specimen. To obtain the

interplanar information, the measured distance, 2R ,is halved and Formula (3) applied.

hk l
11 1

If the camera constant is known, the interplanar spacing, d , of plane, (hkl), can be calculated.

hkl

The included angle between any two vectors, R and R , can also be measured on the

hk l hk l
11 1 22 2

diffraction pattern. This is equal to the angle between the corresponding crystallographic planes,

hk l and hk l .
() ()
11 1 22 2

Since diffraction data from a single pattern will provide information on a limited number of the possible

diffracting planes in a specimen area, it is necessary to acquire additional diffraction patterns from the

same area (or from different grains/particles of the same phase). This requires either the tilting of the

specimen or the availability of differently oriented grains or particles of the same phase.

Acquire a second diffraction pattern from another zone axis from the same area by tilting (or tilting and

rotating) the specimen so that the two patterns contain a common spot row (see 8.2.10 and Figure 5).

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ISO 25498:2018(E)

Index the diffracted spots, and then select three non-planar spots in the two patterns to constitute

a reciprocal lattice, which, if the spots correspond to low values of Miller indices, may define the

primitive unit cell of the crystal lattice. Therefore, crystal lattice parameters can be determined and

the orientation of the grain or particle in the thin specimen can also be calculated.

4.3 Kikuchi pattern

When a specimen area is nearly perfect but not thin enough, Kikuchi lines may occur. They arise from

electrons scattered inelastically through a small angle and suffering only a very small energy loss being

scattered again, this time elastically. This process leads to local variations of the background intensity

in the diffraction pattern and the appearance of Kikuchi lines.

The Kikuchi patterns consist of pairs of parallel bright and dark lines, which are parallel to the

projection of the corresponding reflecting plane, (hkl). The bright (excess) line and dark (defect) line in

the Kikuchi pattern are denoted by K and K , respectively. Therefore, the line pair, K

Bh− kl Dh− kl Bh− kl

and K , will be perpendicular to the vector, R from the corresponding crystallographic plane

Dh− kl hkl

(hkl). Namely they are perpendicular to the reciprocal vector, g , of the plane, (hkl).

hkl

An example of a Kikuchi pattern is given in Figure 3, where the bright line, K , and dark line,

Bh− kl

K , pair is superimposed on the spot pattern. The perpendicular distance, D , between the

Dh− kl Kh− kl

line pair, K and K , is related to the interplanar spacing, d , and camera constant, Lλ, by

Bh− kl Dh− kl hkl
Formula (4).
Dd⋅≅Lλ (4)
Kh− kl hkl
Key
K bright line of Kikuchi pair
B−hkl
K dark line of Kikuchi pair
D−hkl
D distance between the line pair K and K
Kh− kl Bh− kl Dh− kl
+ centre of the direct beam
Figure 3 — Kikuchi pattern from a steel specimen

The distance between the two Kikuchi lines equals to the distance between the diffraction spot, hkl,

and the central spot, 000. The angles between intersecting Kikuchi pairs are the same as the angles

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ISO 25498:2018(E)

between their corresponding diffraction spots, and can be measured accurately. These angles are also

equal to the angles between the relevant crystallographic planes.

When the specimen is tilted, the diffraction spots only gradually change the brightness, faint or increase

the intensity, but their positions are almost at the same place. Instead, Kikuchi lines are sensitive to

the tilting. Their movement is significant on the viewing screen. Hence, specimen tilting can be guided

by Kikuchi map from one zone axes to another one. The Kikuchi patterns present the real crystal

symmetry of the specimen. They can also be used in establishing crystal orientation with a very high

accuracy (see References [5] and [9]).

The problem is that Kikuchi patterns cannot always be observed in all of the specimens. In most cases,

the SAED studies rely mainly on the spot patterns, though they are not as accurate as Kikuchi patterns.

4.4 Polycrystalline specimen

For randomly oriented aggregates of polycrystals, the diffraction pattern is comprised of a series of

concentric rings centred on the spot, 000, of the direct beam. An example of the pattern from

polycrystalline gold (Au) specimen is given in Figure 4. Each diffracted ring arises from the diffraction

beams from differently oriented crystallographic planes of the form, {hkl}; each of these having an

identical interplanar spacing. From the diameter of each diffraction ring, the corresponding interplanar

spacing, d , can be calculated using Formula (3). Indices of the diffraction rings can be ascribed and

hkl

then the lattice parameters can also be determined. For the method of indexing ring patterns, refer to

that used in X-ray powder diffraction (see Reference [9]).

Figure 4 — Diffraction ring pattern with indices from a polycrystalline Au specimen

5 Reference materials

A reference specimen is required for determining the diffraction constant, Lλ, of the microscope in

electron diffraction studies. In principle, any thin crystalline foil or powder could be considered as

the reference specimen, provided its crystalline structure and lattice parameters have been acquired

accurately and they are certified and stable under irradiation of the electron beam. It should be

ensured that the reference material, which is as thin as electrons can penetrate through it, has the same

crystallographic properties as the bulk material. In addition, a number of sharp diffraction rings or

spots with known indices can be observed. The thickness of the crystal foil or powder grain size should

be consistent with the beam energy and the quality of the diffraction pattern so that clear diffraction

patterns can be observed (when it is too thick, the pattern will lack sharpness).

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ISO 25498:2018(E)

Reference materials in common use are polycrystalline specimens made from pure gold [which has a

face-centred cubic (FCC) lattice with parameter, a = 0,407 8 nm] or pure aluminium (Al) (FCC structure

with lattice parameter a = 0,404 9 nm). The mass fraction of Au or Al in the reference materials shall be

not less than 99,9 %. The reference specimen shall be prepared by evaporating a small piece of Au or Al

on a grid with a supporting film.

It is also feasible to evaporate a layer of the reference material onto a local surface area of the specimen,

which is to be analysed.
6 Equipment

6.1 Transmission electron microscope (TEM) shall be with double tilt or tilt rotation or double-tilt

rotate specimen holder.
6.2 Recording of SAED patterns and images.

The SAED patterns and images obtained on the transmission electron microscope shall be recorded on

the photographic films or imaging plates or an image sensor built in the digital camera.

When films are used, a darkroom with a negative developing and fixing outfit is required.

6.3 Facilities for specimen preparation.
7 Specimens

7.1 Most specimens are prepared as thin foils (see References [2] and [10]). Such specimens can be

obtained in the form of thin sections from a variety of crystalline substances including metallic and non-

metallic materials. The shape and external size of the specimen should match that of the TEM specimen

holder or, alternatively, it can be held by a support grid.

Fine powders and/or extraction replicas can also be used. These specimens shall be prepared on the

grid with supporting films.

7.2 An applicable area to be tested is in the sizes of micrometre and sub-micrometre. The area is

always defined by selected aperture. The selected area shall be thin enough for the electron beam to pass

through it and diffraction patterns can be observed on the viewing screen.

7.3 The surface of the specimen shall be clean, dry and flat without an oxidizing layer or any

...

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