ISO 19214:2024

International
Standard
ISO 19214
Second edition
Microbeam analysis — Analytical
2024-10
electron microscopy — Method
of determination for apparent
growth direction of nanocrystals by
transmission electron microscopy
Reference number
© ISO 2024
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ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Specimens. 2
5 Analysis procedure . 2
5.1 Setting the TEM operating condition .2
5.1.1 Preparation of the TEM .2
5.1.2 Accelerating voltage .3
5.1.3 Setting the specimen .3
5.1.4 Calibration of the rotation angle .3
5.2 Data acquisition .3
5.2.1 Select the target crystal .3
5.2.2 Obtaining diffraction patterns .3
5.2.3 Determining the interplanar spacing .4
5.2.4 Index diffraction patterns.4
5.2.5 Non-uniqueness of the indexing result .5
5.3 Determination of the crystalline direction .5
5.3.1 General approach .5
5.3.2 Convert the crystallographic index .7
5.3.3 Result of the multiplicity factor .8
5.3.4 Repetition .8
6 Uncertainty estimation . 8
7 Test report .10
Annex A (informative) Relationships of Miller notation and Miller-Bravais notation for
hexagonal crystals .11
-1
Annex B (informative) Matrix G and G for the crystal systems .12
Annex C (informative) Example test report . 14
Annex D (informative) Example for determination of long-axis direction from Au nanocrystal .15
Bibliography .20

iii
Foreword
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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 19214:2017), which has been technically
revised.
The main changes are as follows:
— the title, introduction and scope have been revised;
— Clause 3 has been revised;
— Figures 1 and 2 have been replaced;
— Annex D has been added;
— editorial revisions have been made.
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
Nanocrystals are a main component in some advanced materials, especially nanomaterials, and also
appear in traditional materials, such as needle-shaped precipitates in steels and alloys. Controlling the
microstructure of these materials during fabrication is very important for quality control considerations.
To control the microstructure and thereby improve the service properties of the relevant materials, the
apparent growth direction, or the longest axis of the nanocrystals is one of the essential parameters. This
direction of nanocrystals is generally determined by transmission electron microscopy (TEM).

v
International Standard ISO 19214:2024(en)
Microbeam analysis — Analytical electron microscopy —
Method of determination for apparent growth direction of
nanocrystals by transmission electron microscopy
1 Scope
This document gives a method for determination of the apparent growth direction of nanocrystals by
transmission electron microscopy. This method is applicable to all kinds of wire-like crystalline materials
synthetized by various methods. This document can also guide in determining an axis direction of the
second-phase particles in steels, alloys, or other materials. The applicable diameter or width of the crystals
to be tested is in the range of tens to one hundred nanometres, depending on the accelerating voltage of
the transmission electron microscope (TEM) and the material itself. Position, which is curved, twisted, and
folded, to determine the apparent growth direction, should not be used.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
the 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 15932, Microbeam analysis — Analytical electron microscopy — Vocabulary
ISO 25498:2018, Microbeam analysis — Analytical electron microscopy — Selected area electron diffraction
analysis using a transmission electron microscope
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 15932 and the following 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
nanocrystal
discrete piece of crystalline material exhibiting a dimensional anisotropy with an axial elongation in one of
the three nanocrystalline lattice direction in the nanoscale
3.2
apparent growth direction
crystalline direction which is parallel to the longest dimension of a single crystal
Note 1 to entry: Apparent growth direction does not involve mechanisms of the phase interface migration.
3.3
Miller notation
indexing system for diffraction patterns, which describes a crystal lattice by three axes coordinate

3.4
Miller-Bravais notation
indexing system for diffraction patterns of hexagonal crystal, which describes the lattice by four axes
coordinate
3.5
reciprocal vector
g
hkl
coordinate vector of hkl lattice point in the reciprocal lattice
Note 1 to entry: Reciprocal vector g is perpendicular to the plane (hkl) of crystal, its length is inversely proportional
hkl
to the interplanar spacing d .
hkl
[SOURCE: ISO 25498:2018, 3.8, modified — Note 1 to entry has been modified. ]
3.6
R vector
R
hkl
coordinate vector from the central spot 000 to the diffraction spot hkl in a diffraction pattern
[SOURCE: ISO 25498:2018, 3.9, modified — Note 1 to entry has been removed.]
3.7
reciprocal space
imaginary space where planes of atoms are represented by reciprocal points and all lengths are the inverse
of their length in real space
4 Specimens
4.1 The sample crystals shall be clean, without contamination or oxidation. They are stable under electron
beam irradiation during TEM analysis.
4.2 Powder or extracted powder specimens of the crystals may be analysed. The sample powder shall be
well dispersed by a suitable technique so that individual crystals can be observed under the TEM.
NOTE One of the techniques in common use is ultrasonic dispersion. In this method, the sample powder is
immersed in ethanol or pure water and dispersed by ultrasonication for about 0,5 h to 1 h, then dropped onto the
supporting film surface of a microgrid. Then, the microgrids are dried at room temperature. The wire-like crystals
are usually parallel to the supporting film plane. Other techniques to prepare individual crystal specimens can also be
[1]
adopted, depending on the physical characteristics of the sample.
4.3 The precipitates or second-phase particles in steels, alloys and the like should be extracted, then
treated as powder specimens; see 4.2.
4.4 Thin-foil specimens of various solid substances prepared by suitable methods (focused ion beam, ion
[2]
beam thinning, etc.) are applicable. The specimen shall be thin enough to transmit the electron beam.
5 Analysis procedure
5.1 Setting the TEM operating condition
5.1.1 Preparation of the TEM
The TEM working condition shall comply with ISO 25498:2018, 8.1.

5.1.2 Accelerating voltage
The applicable accelerating voltage of the TEM for the analysis mainly depends upon the thickness of the
specimen to be studied. Stability of the crystals under electron beam irradiation is also important for the
accelerating voltage setting. As long as the structure and/or morphology of the specimen is not altered during
the analysis, clear images and sharp diffraction patterns can be obtained on the TEM. The corresponding
accelerating voltage or higher may be suitable for the work.
5.1.3 Setting the specimen
Place the specimen to be tested firmly in the double-tilting or tilting-rotation specimen holder, then insert the
holder into the specimen chamber. It is recommended to use the cold finger of the TEM before conditioning.
5.1.4 Calibration of the rotation angle
As specified in ISO 25498:2018, 8.1.6, to be able to successfully correlate the axis of interest in an image with
the corresponding diffraction pattern, the rotation angle between the micrograph and its corresponding
diffraction pattern may need to be calibrated. A molybdenum trioxide crystal specimen may be used as a
reference for the rotation angle calibration. The analyst may refer to textbooks such as References [3] and
[4] for the experimental procedure for this calibration.
NOTE For some transmission electron microscopes, the rotation angle has been compensated by the manufacturer.
In this case, step 5.1.4 can be ignored.
5.2 Data acquisition
5.2.1 Select the target crystal
On the viewing screen, TV monitor, or computer screen of the TEM, get an overview image of the specimen in
low magnification mode. Select an individual crystal which is clean and free from damage or distortion as the
target. Under bright-field imaging mode, adjust the magnification to get a clear magnified image of the target
crystal. Adjust the specimen height (Z axis) to the eucentric position. Adjust the focal length of the images.
5.2.2 Obtaining diffraction patterns
5.2.2.1 General
Various electron diffraction techniques may be applicable for the determination of the crystal axis direction.
The selected area electron diffraction (SAED) and microbeam diffraction techniques are in common use;
however, for the present purpose, the spot diffraction patterns or the patterns formed by the incident beam
through a small angle aperture are preferred.
5.2.2.2 Procedure
The procedure for taking diffraction patterns and micrographs of the target crystal is as follows.
a) Select a suitable position of the target crystal in the specimen and select a diffraction mode (SAED,
microbeam diffraction, or other suitable mode). Switch to the diffraction mode to get a spot diffraction
pattern. Tilt the specimen slightly so that the brightness distribution on the diffraction pattern is
symmetrical and a zero-order Laue zone pattern is displayed. Therefore, the zone axis, Z (with index
[u v w ]), of this diffraction pattern is nearly reverse parallel to the incident beam direction, B . Record
1 1 1 1
this diffraction pattern, Z and take note of the reading on the X and Y tilting angle of the double tilting
1,
specimen stage as X and Y respectively.
1 1,
NOTE Refer to the instruction manual provided by the microscope manufacturer for the operation procedure
for each diffraction mode.
b) Switch back to the imaging mode without changing the specimen orientation to get a correlative
bright field image, M , of the target crystal. Check the focus of this image and take a photo or save
it in the computer system. This image, M is formed under the incident beam direction, B , which is
1, 1
approximately reversely parallel to the zone axis, Z .
c) Return to the diffraction mode and tilt the specimen to produce a second diffraction pattern with zone
axis Z . Record this diffraction pattern, Z , and take note of the reading on the X and Y tilt angle of the
2 2
specimen holder as X and Y , respectively.
2 2
d) Repeat step b) to form the second bright field image, M , of the target crystal. This image, M , is formed
2 2
under the incident beam direction, B , which is nearly reversely parallel to the zone axis, Z , of the
2 2
specimen.
e) The angle, ψ, between the two specimen holder positions (that is, the angle ψ* between the zone axis,
Z , with index [u v w ] and Z , with index [u v w ]) can be obtained from the differences between the
1 1 1 1 2 2 2 2
readings on the X and Y tilting angles at each position (see ISO 25498:2018, 8.2).
5.2.3 Determining the interplanar spacing
To determine the interplanar spacing, d , of the plane (hkl) in crystals, the simplified Bragg law, as shown
hkl
in Formula (1), shall be followed.
Lλ=R × d (1)
hkl hkl
where
L is the camera length;
λ is the wavelength of the incident electron beam;
R is the distance between the central spot and the diffracted spot of a crystalline plane (hkl) in the
hkl
diffraction pattern;
d is the interplanar spacing of the crystalline plane (hkl).
hkl
Lλ is the camera constant. Transmitted spot should be coincident with the optic axis. It is necessary that the
central spot is the transmitted spot of used diffraction pattern.
When the camera constant Lλ is known, the interplanar spacing d can be found, in principle, using
hkl
Formula (1) by measuring the distance R . However, in practice, 2R (the distance between the spots hkl
hkl hkl
and hk l ) shall be measured, then divided by two to calculate the distance R .
hkl
In most cases, the camera constant, Lλ, shall be calibrated for the present work. The practical procedure for
camera constant calibration is specified in ISO 25498:2018, 8.3.
Camera constant, Lλ, calibration is usually performed by using a reference specimen such as polycrystalline
pure gold or pure aluminium. At a given accelerating voltage, record the ring diffraction pattern of the
reference specimen. Index the diffraction rings and measure the diameters 2R of the corresponding
hkl
ring (hkl), respectively. Find the interplanar spacing d for a plane (hkl) of the reference specimen by the
hkl
crystallographic formulae. The camera constant, Lλ, can then be calculated using Formula (1). In practice,
either the Lλ ∼ D/2 plot or an average value of the camera constant may be used.
When the crystalline structure and the confident lattice parameters of the specimen are already known, the
diffraction constant, Lλ, may be calculated from its diffraction pattern directly. The approximate value of Lλ
can be found on a console readout display of a modern TEM.
5.2.4 Index diffraction patterns
For specimens comprised of crystals in the nanometre size regime, most of the time, only spot diffraction
patterns can be observed. Kikuchi patterns seldom appear owing to their small thickness. Therefore, only
the procedure for indexing spot diffraction patterns is specified in this document.

The practical procedure for indexing diffraction patterns may refer to ISO 25498:2018, Clause 9. For the
[3][4][5][6]
convenience of applying this document, the indexing process is briefly summarized as follows:
a) Select two diffracted spots, hk l and hk l , from the diffraction pattern such that these spots are
11 1 22 2
nearest and next-nearest to the central spot, 000, respectively. Measure the length of correlative vectors
R and R which are defined as the vector from the origin, 000, to the diffraction spot hk l
hk l hk l , 11 1
11 1 22 2
and the spot hk l , respectively, in the diffraction pattern. Calculate the corresponding inter-planar
22 2
spacing d and d Then, assign tentative index values for each spot.
hk lhk l .
11 1 22 2
b) Measure the included angle between the vectors R and R as well as the angle between
hk l hk l
11 1 22 2
R and R respectively, where R is defined as the R vector of the
hk l hh−−,,kk ll− hh−−,,kk ll−
22 2 21 21 21 21 21 21
diffraction spot with index h -h , k -k , l -l . Adjust the indices for each spot such that the angle is
2 1 2 1 2 1
coincident with the calculated angle by the crystallographic formulation. When the experimental value
is consistent with the known value within error, the diffraction spots can be indexed.
c) Calculate the zone axis, Z, of the diffraction pattern [u v w] by
...