ISO 25498:2025

International
Standard
ISO 25498
Third edition
Microbeam analysis — Analytical
2025-05
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 2025
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Published in Switzerland
ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms, definitions and abbreviations . 1
3.1 Terms and definitions .1
3.2 Abbreviated terms and symbols.3
4 Principle . 3
4.1 General .3
4.2 Spot diffraction pattern.4
4.3 Kikuchi pattern .6
4.4 Diffraction pattern of polycrystalline specimen .7
5 Reference materials . 8
6 Apparatus . 8
6.1 Transmission electron microscope (TEM) .8
6.2 Recording of SAED patterns and images .8
7 Preparation of specimens . 9
8 Procedure . 9
8.1 Instrument preparation .9
8.2 Procedure for acquiring SAED patterns from a single crystal .10
8.3 Determination of diffraction constant, Lλ . 12
9 Measurement and solution of the SAED patterns . 14
9.1 Selection of the basic parallelogram .14
9.2 Indexing diffraction spots . 15
10 180° ambiguity .16
11 Uncertainty estimation . 16
11.1 General .16
11.2 Uncertainty in camera constant .17
11.3 Calibration with a reference material .17
11.4 Uncertainty in d-spacing values . .18
Annex A (informative) Interplanar spacings of references .20
Annex B (informative) Spot diffraction patterns of single crystals for BCC, FCC and HCP
[7]
structure .21
Bibliography .42

iii
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
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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 document 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).
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This document was prepared by Technical Committee ISO/TC 202, Microbeam analysis, Subcommittee SC 3,
Analytical electron microscopy.
This third edition cancels and replaces the second edition (ISO 25498:2018), which has been technically
revised.
The main changes are as follows:
— Scope has been revised;
— ISO/IEC 17025 has been moved from normative references to bibliography;
— Figure 1 has been replaced;
— Subclause 6.3 has been deleted;
— Subclause 8.3.6 has been deleted, the content of 8.3.6 has been moved to 8.3.2;
— Subclause 9.2.5 has been added and the following subclause has been renumbered;
— Clause 11 has been revised, 11.1,11.2,11.3 and 11.4 have been added;
— Subclauses B.4.1 and B.4.2 have been added;
— Bibliography has been updated and ISO/IEC Guide 98-3 (GUM:1995) has been added.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

iv
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, nano-
diffraction, 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 TEMs 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 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.
v
International Standard ISO 25498:2025(en)
Microbeam analysis — Analytical electron microscopy
— Selected area electron diffraction analysis using a
transmission electron microscope
1 Scope
This document specifies the method for 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 hundreds of nanometres for a modern TEM.
When the size of an analysed specimen area is smaller than the spherical aberration coefficient restriction,
this document can also be used for the analysis procedure. However, because of the effect of spherical
aberration and deviation of the specimen height position, 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 diffraction, where available, can be preferred.
This document is applicable to the acquisition of SAED patterns from crystalline specimens, indexing the
patterns and calibration of the camera constant.
2 Normative references
There are no normative references in this document.
3 Terms, definitions and abbreviations
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1 Terms and definitions
3.1.1
Miller notation
indexing system for crystallographic planes and directions in crystals, in which a set of lattice planes or
directions is described by three axes coordinate
3.1.2
Miller-Bravais notation
indexing system for crystallographic planes and directions in hexagonal crystals, in which a set of lattice
planes or directions is described by four axes coordinate
3.1.3
interplanar spacing
d
hkl
perpendicular distance between consecutive planes of the crystallographic plane set (hkl)

3.1.4
reciprocal vector
g
hkl
vector in the reciprocal lattice
Note 1 to entry: The reciprocal vector, g , is normal to the crystallographic plane (h k l) with its magnitude inversely
hkl
proportional to interplanar spacing d (3.1.3).
hkl
3.1.5
R vector
R
hkl
coordinate vector from the direct beam, 000, to a diffraction spot, hkl, in a zone diffraction pattern
Note 1 to entry: See Figure 1.
3.1.6
camera length
L
effective distance from the specimen to the screen or recording device in a transmission electron microscope
in diffraction mode
3.1.7
camera constant
diffraction constant
Lλ
product of the wavelength of the incident electron wave and camera length (3.1.6)
[SOURCE: ISO 15932:2013, 3.7.1]
3.1.8
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 15932:2013, 5.5]
3.1.9
dark field image
image formed by a diffracted beam only by using the objective aperture for selection or by collecting the
diffracted beams with an annular dark-field detector
[SOURCE: ISO 15932:2013, 5.6]
3.1.10
energy-dispersive X-ray spectrometry
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 15932:2013, 6.6]
3.1.11
eucentric position
specimen position at which the image exhibits minimal lateral motion resulting from specimen tilting
3.1.12
selected area (selector) aperture
moveable diaphragm that is used to select only radiation scattered from a specific area of the specimen to
contribute to the formation of a diffraction pattern
[SOURCE: ISO 15932:2013, 3.2.3.5]

3.1.13
Bragg angle
θ
B
angle between the incident beam and the atomic planes, at which diffraction takes place
3.2 Abbreviated terms and symbols
BCC body-centred cubic structure
FCC face-centred cubic structure
HCP hexagonal close-packed structure
SAED selected area electron diffraction
TEM transmission electron microscope
(hkl) Miller indices of a specific set of crystallographic planes
{hkl} Miller indices which denote a family of crystallographic planes
[uvw] Miller indices of a specific crystallographic direction or a zone axis
(uvw)* Notation for a set of planes in the reciprocal lattice
NOTE The normal of the reciprocal plane (uvw)* is parallel to the crystallographic zone axis [uvw]
4 Principle
4.1 General
When an energetic electron beam is incident upon a thin crystal 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], [4], [5]). This pattern can also be displayed on a monitor if the TEM is equipped with a digital
camera system.
The geometric relationship of the parameters for selected area electron diffraction (SAED) technique can be
understood through the Ewald sphere construction, which is illustrated in Figure 1.

Key
1 incident beam
2 specimen
3 direct beam
4 diffracted beam
5 Ewald sphere
reciprocal vector g
hkl
7 diffraction pattern
R vector
hkl
L is the diffraction camera length;
θ is Bragg angle;
B
λ is the wavelength of the incident electron beam.
Figure 1 — Ewald sphere construction illustrating the diffraction geometry in TEM
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. An example of the spot diffraction pattern is shown in Figure 2. 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 spot, hkl, relative to position on the
hkl
pattern corresponding to the direct 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 is inversely proportional to the interplanar spacing,
hkl
d , of the diffracting plane, (hkl) (see References [4] to [9]). In the context of this document, vectors
hkl
R , R , RR − and RR + are simplified as R , R , R and R
() ()
hk l hk l hk lh kl hk lh kl 1 2 21− 12+
11 1 22 2 22 21 11 11 12 22
respectively. The included angle between vectors, R and R , is denoted by γ*. The basic parallelogram is
1 2
defined by R and R , where they are the shortest and next shortest in the pattern respectively and not along
1 2
a common line. The spot, h k l , is positioned anticlockwise around the centre spot relative to spot, hk l .
2 2 2 11 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 distance between
hkl
the spots, hkl and hkl on the diffraction pattern and dividing by two, i.e.
RR=+ R . On the example pattern shown in Figure 2, the magnitude of R , R and R is
()
hklhkl 1 2 21−
hkl
1 1 1
obtained from RR+ , RR+ and RR+ respectively.
() () ()
11 22 21−−21
2 2 2
Key
R is the vector from 000 to spot, h k l , the shortest vector in the diffraction pattern
1 1 1 1
R is the 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 the spot diffraction pattern from a single crystal
The relationship between the interplanar spacing, d , and the magnitude of R for a reflecting plane,
hkl hkl
(hkl), can be approximately expressed as shown in Formula (1) (see References [7] and [8]):
 2
LRλ =×dR1− ()/LR=×d ()1−Δ (1)
hklhkl hklhkl hkl
 
 
where
R
Δ hkl
is equal to ;
()
L
is the diffraction camera length and equal to fM×× M ;
L
oi p
where
f
is the focal length, in millimetres, of the objective lens in the microscope;
o
M
is the magnification of the intermediate lens;
i
M
is the magnification of the projector lenses;
p
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 pat-
tern 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 accel-
erating voltage and can be given by Formula (2) (see Reference [4]):
1,226
λ()nm = (2)
−6
VV(,10+×978810 )
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:
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 the
hkl
pattern centre may not be easily determined; it is recommended that the distance measurement taken,
2R , be from the hk l diffracted spot to the hk l spot on the pattern. This is equivalent to a diameter
hk l 11 1 11 1
11 1
measurement on the ring pattern from a polycrystalline specimen (Section 4.4 and Figure 4). 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. The included
hkl
angle between any two vectors, R and R , can also be measured on the diffraction pattern. This is
hk l hk l
11 1 22 2
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 8.2.11 and Figure 5). Index
the diffracted spots, and then select three non-coplanar 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 and K , will be
Bh− kl Dh− kl Bh− kl Dh− kl
perpendicular to the vector, R , from the corresponding crystallographic plane (hkl). Namely they are
hkl
perpendicular to the reciprocal vector, g , of the plane, (hkl).
hkl
An example of the Kikuchi patterns is given in Figure 3, where the bright line, K , and dark line, K ,
Bh− kl Dh− kl
pairs are superimposed on the spot pattern. The perpendicular distance, D , between the line pair,
Kh− kl
11 1
K and K , is related to the interplanar spacing, d , and camera constant, Lλ, by
Bh− kl Dh− kl hk l
11 1 11 1 11 1
Formula (4).
Dd ×λ ≅L (4)
Kh− kl hkl
Key
bright line of Kikuchi pair
K
Bh− kl
dark line of Kikuchi pair
K
Dh− kl
D distance between the line pair K and K
Kh− kl Bh− kl Dh− kl
11 1 11 1 11 1
+ 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 between the
R vectors of their corresponding diffraction spots, and can be measured accurately. These angles are
hkl
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 position change is hard to distinguish. 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 [4] 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 Diffraction pattern of 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
hkl
calculated using Formula (3). Indices of the diffraction rings can be ascribed and 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]).

NOTE Au possesses a face-centred cubic (FCC) structure with lattice parameter a = 0,407 8 nm
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 can 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).
Reference materials in common use are polycrystalline specimens made from pure gold (Au) [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 Apparatus
6.1 Transmission electron microscope (TEM)
The TEM shall be equipped 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.

7 Preparation of specimens
7.1 Most specimens are prepared as thin foils (see References [2], [10] and [11]). 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 or sub-micrometre. The area is always
defined by selected area (selector) 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 contamination.
7.4 For those materials that are stable under energetic particle beam bombardment, contamination on the
specimen surface can be avoided or removed by ion beam sputtering or other techniques, such as plasma
cleaners, before the TEM observation.
7.5 Prepared specimens should be labelled and placed in a special specimen box and preserved in a
desiccator or evacuated container.
8 Procedure
8.1 Instrument preparation
8.1.1 The general working condition of the TEM laboratory should comply with ISO/IEC 17025 (see
Reference [1]).
8.1.2 It is recommended to use the cold trap of TEM before conditioning in order to minimize specimen
contamination.
8.1.3 When the vacuum of the transmission electron microscope is suitable for operation, switch on and
select an appropriate accelerating voltage so that the incident electron beam can penetrate through the
specimen.
8.1.4 Carry out the axis alignment for the electron optical system.
8.1.5 The success of the selected area electron diffraction method relies on the validity of indexing the
diffraction patterns arising, irrespective of which axis in the specimen lies parallel to the incident electron
beam. Such analysis is therefore aided by specimen tilt and rotation facilities.
Place the specimen to be tested and the reference firmly in the double-tilting or tilting-rotation or double-
tilting rotation specimen holder, and insert the holder into the specimen chamber.
A specimen coated with an evaporated layer of reference material can be directly placed in the specimen
holder and inserted into the chamber.
8.1.6 When the SAED patterns need to be related to features observed in the corresponding micrograph,
the angle of rotation between the two may need to be determined and compensated for.
The method in common use is to take a diffraction pattern and a micrograph of a molybdenum trioxide
crystal specimen. The rotation angle of the image is then measured on the photographic plates or digital

images, on which the micrograph and superimposed diffraction pattern has been recorded. For details of
the calibration procedure, refer to the appropriate text books (see References [4], [5] and [9]).
When the rotation angle of the TEM has been compensated by the manufacturer, the procedure in 8.1.6 may
be ignored.
8.1.7 When a digital camera is equipped and to be employed for the study, set the camera in operating
condition by following the user’s guide of the manufacturer.
To avoid damaging the camera, reduce incident beam intensity and use beam stop to block the central spot
when acquiring SAED diffraction patterns.
For detail procedure of the operation and calibration, refer to instruction from the manufacturer.
8.2 Procedure for acquiring SAED patterns from a single crystal
8.2.1 Obtain a magnified bright field image of the specimen on the viewing screen of the transmission
electron microscope. Adjust the specimen height to focus the image so that the image movement is minimized
during the tilting of the specimen. Namely, set the eucentric position of the specimen. The procedure for
establishing the eucentric position of the specimen may be obtained by consulting the manufacturer's
operating manual.
NOTE If the TEM is not equipped with a specimen height control function, this procedure can be omitted.
8.2.2 Adjust the magnification of the specimen image until details in the specimen can be observed clearly.
A suitable magnification for SAED analysis is usually from several thousands to tens of thousands times.
Focus the image and correct the astigmatism.
8.2.3 Insert the selected area (selector) aperture and focus the image of this aperture. Then, focus the
specimen image again. This makes the selected area (selector) aperture plane conjugate with the image
plane of the objective lens.
8.2.4 Switch the microscope from image mode to the SAED mode, focus the image of the objective lens
aperture; that is, make this objective lens aperture coincide with the back focal plane of the objective lens.
Return to the bright field image mode and focus the image again.
8.2.5 Insert the reference (i.e. the calibration standard) and locate it at the eucentric position. Choose a
camera length, L, consistent with the capabilities of the subsequent measuring equipment and then obtain a
diffraction pattern from it. Focus the diffraction pattern and correct any astigmatism carefully to make the
diffraction pattern sharp. Record the diffraction pattern of the reference.
8.2.6 If the reference and test specimen are not in the same specimen holder, withdraw the reference
and insert the test specimen again, without changing the operating conditions and without switching the
microscope off. Again, locate it at the eucentric height.
8.2.7 Obtain a focused bright field image of the specimen again with an appropriate magnification. Select
a region of interest (ROI) on the specimen image using the selected area (selector) aperture. Record the
image of this ROI in the specimen. The phase boundaries and/or grain boundaries in the specimen should be
kept away from the selected ROI when a single crystal grain is analysed.
8.2.8 Switch the TEM to the SAED diffraction mode again, withdraw the objective lens aperture and obtain
a diffraction pattern on the viewing screen. Where possible, tilt the specimen slightly so that the brightness

of the spots in the diffraction pattern is evenly distributed, or where Kikuchi lines appear; the Kikuchi line
pairs are symmetrical about the pattern centre.
This pattern will then derive from a low index direction in the crystal approximately; the direction is
antiparallel to the incident electron beam. This crystal direction will be the zone axis, []uv w , which is
11 1
*
the normal of the reciprocal plane, ()uv w , i.e. the diffraction pattern (see References [4] to [7]).
11 1
NOTE The beam direction is defined as antiparallel to the incident electron beam.
Adjust (defocus) the second condenser lens current (the brightness knob) to sharpen the diffraction spots,
making them as sharp as possible.
8.2.9 Record the pattern or/and save the original uncompressed pattern in the computer system. Take
note of the reading on the X and Y axis of the specimen tilting device as X and Y , respectively. Using dark
1 1
field conditions either by beam tilt or shifting the objective lens aperture, identify the source of the pattern.
8.2.10 Insert the reference specimen and obtain a second diffraction pattern from the reference. Record
this diffraction pattern (see also 8.3), making sure that the same experimental conditions are used (i.e.
accelerating voltage, lens settings and, especially, the specimen height and camera length, L).
NOTE Polycrystalline reference or specimens need not be tilted to achieve a specific zone axis orientation.
8.2.11 Obtain sufficient data for each phase of interest by either of the following procedures.
a) Specimen tilting procedure: obtain the second pattern by tilting the specimen.
Choose a row of close-spaced diffraction spots collinear with the central transmitted spot on the
*
diffraction pattern, which is denoted by indices of reciprocal plane, uv w . Keep this row of the
()
11 1
spots visible on the viewing screen, while tilting the specimen until the second diffraction pattern,
*
()uv w appears. Make sure the brightness of the spots in the second pattern is evenly distributed.
22 2
The reciprocal space geometry of the two patterns is schematically illustrated in Figure 5. The angle
* *
between the diffraction patterns, ()uv w and ()uv w , is ψ , which equals to the angle between
11 1 22 2
the two zone axes, []uv w and []uv w . This angle can be determined from the tilt angle of the
11 1 22 2
specimen holder.
If Kikuchi patterns are visible, the specimen tilting can be guided by the Kikuchi map. The second
diffraction pattern (or more patterns) may be obtained directly.
With a rotate-tilt specimen holder or a double-tilting rotate holder, a chosen row of the spots can be
aligned with a tilt axis; the second diffraction pattern (or more patterns) may be obtained directly.
Repeat the procedure described in 8.2.8, recording the pattern and/or saving it on the computer system.
Take note of the reading on the X and Y axis of the specimen-tilting device as X and Y , respectively.
2 2
b) Multi grains procedure: obtain the patterns from several areas, i.e. different particles or grains of the
same phase. This procedure is recommended for any of the following situations:
1) the maximum tilting angle of the specimen holder is not large enough, so that the second diffraction
pattern cannot be reached by tilting;
2) the particles to be analysed in the specimen are too small;
3) the specimen is sensitive to the electron beam illumination, e.g. the selective area is contaminated
or decomposes following a short irradiation by the electron beam.
When this procedure is employed, the source of each diffraction pattern is necessary to confirm. Choose
appropriate diffraction spots to form a dark field image to check it. Further confirmation can be achieved
through simultaneous use of EDS (energy dispersive X-ray spectrometry) facility, when available.

8.2.12 When the diffraction patterns are recorded on negative films, develop, fix and dry the films in the
darkroom. Keep the negative films one by one in individual protective bags with labels.
8.2.13 When the diffraction patterns are recorded by digital camera or imaging plates, save the original
uncompressed diffraction patterns in the computer system as individual files with labels. All parameters of
the acquisition of this file shall be documented and reported.
8.2.14 Each pattern, either recorded on negative film or by digital camera as well as by imaging plate,
shall be numbered and labelled with the following information: specimen designation and serial number,
accelerating voltage, nominal camera length, L, tilting angles, operator, date, etc. All processing operations
on the diffraction patterns and images shall be reported
Key
* *
ψ
is the angle between the diffraction pattern ()uv w and ()uv w
11 1 22 2
RR′ =
Figure 5 — Reciprocal space geometry of the spot diffraction patterns
8.3 Determination of diffraction constant, Lλ
8.3.1 The procedure for the determination of the diffraction constant, Lλ, uses a reference specimen
such as polycrystalline pure gold or pure aluminium (see Clause 5). Figure 4 shows an example of the ring
patterns from a polycrystalline gold specimen. Record the diffraction pattern (see 8.2).
8.3.2 When diffraction patterns are recorded on photographic films, place the negative film on which the
diffraction pattern of the reference specimen was recorded, emulsion side up on the film viewer. Measure
the diameters of the diffraction rings on the film of the reference specimen when a polycrystalline reference
is used. Note the diameter of these rings from inner to outer as D , D , D , D , … (mm), etc., respectively.
1 2 3 4
When the diffraction patterns are recorded by the digital camera, the above measurement is carried out on
the computer system.
8.3.3 Indices, hkl, of the diffraction rings for a reference specimen with FCC structure are 111, 200, 220,
311, 222, 400, 331, 420, 422, … respectively from the inner to outer rings (see Figure 4). The corresponding
interplanar spacings, d , are given for both Au and Al in Annex A or calculated by the crystallographic
hkl
formulae (see References [4] to [9]).
8.3.4 According to Formula (3), calculate the diffraction constants as follows:
(mm·nm)
Dd·
1 111
L λ=
(mm⋅nm)
Dd·
2 200
L λ =
(mm⋅nm) …, etc.
Dd·
3 220
L λ =
where
d , d and d is the interplanar spacing of the crystallographic plane {111} , {200} and {220} of
111 200 220
the specimen respectively;
D , D and D is the diameter of diffracted ring {111}, {200} and {220} of the specimen respectively,
1 2 3
on the ring pattern of the specimen.

Key
D/2 is one- half diameter of a diffracted ring, expressed in mm
Lλ is the diffraction constant, expressed in mm·nm
Figure 6 — LDλ∼ /2 curve from a polycrystalline Au specimen
8.3.5 Plot the LDλ∼ /2 curve using the data in 8.3.2 and 8.3.4 (an example of the LDλ∼ /2 plot is shown
in Figure 6). This graph can be used for all reflections (spots) from the specimen being analysed under
completely identical conditions. Since the diffraction constant, Lλ, actually varies slightly with the diffraction
ring diameter, it is recommended to either:
a) use the LDλ∼ /2 c
...