EN ISO 21363:2022

SLOVENSKI STANDARD
01-marec-2022
Nanotehnologije - Meritve porazdelitve velikosti in oblike delcev s transmisijsko
elektronsko mikroskopijo (ISO 21363:2020)
Nanotechnologies - Measurements of particle size and shape distributions by
transmission electron microscopy (ISO 21363:2020)
Nanotechnologien - Messungen von Partikelgrößen- und Partikelformverteilungen mittels
Transmissionselektronenmikroskopie (ISO 21363:2020)
Nanotechnologies - Détermination de la distribution de taille et de forme des particules
par microscopie électronique à transmission (ISO 21363:2020)
Ta slovenski standard je istoveten z: EN ISO 21363:2022
ICS:
07.120 Nanotehnologije Nanotechnologies
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 21363
EUROPEAN STANDARD
NORME EUROPÉENNE
January 2022
EUROPÄISCHE NORM
ICS 07.120
English Version
Nanotechnologies - Measurements of particle size and
shape distributions by transmission electron microscopy
(ISO 21363:2020)
Nanotechnologies - Détermination de la distribution de Nanotechnologien - Messungen von Partikelgrößen-
taille et de forme des particules par microscopie und Partikelformverteilungen mittels
électronique à transmission (ISO 21363:2020) Transmissionselektronenmikroskopie (ISO
21363:2020)
This European Standard was approved by CEN on 26 December 2021.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2022 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 21363:2022 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
The text of ISO 21363:2020 has been prepared by Technical Committee ISO/TC 229 "Nanotechnologies”
of the International Organization for Standardization (ISO) and has been taken over as
is held by AFNOR.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by July 2022, and conflicting national standards shall be
withdrawn at the latest by July 2022.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
Any feedback and questions on this document should be directed to the users’ national standards body.
A complete listing of these bodies can be found on the CEN website.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the
United Kingdom.
Endorsement notice
The text of ISO 21363:2020 has been approved by CEN as EN ISO 21363:2022 without any modification.

INTERNATIONAL ISO
STANDARD 21363
First edition
2020-06
Nanotechnologies — Measurements of
particle size and shape distributions
by transmission electron microscopy
Nanotechnologies — Détermination de la distribution de taille et de
forme des particules par microscopie électronique à transmission
Reference number
ISO 21363:2020(E)
©
ISO 2020
ISO 21363:2020(E)
© ISO 2020
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting
on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address
below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2020 – All rights reserved

ISO 21363:2020(E)
Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms, definitions and symbols . 1
3.1 Core terms — Particles . 1
3.2 Core terms — Image capture and analysis . 4
3.3 Core terms — Statistical symbols and definitions . 5
3.4 Core terms — Measurands . 7
3.5 Core terms — Metrology .10
3.6 Core terms — Transmission electron microscopy .13
3.7 Statistical symbols, measurands and descriptors .14
3.7.1 Statistical symbols .14
3.7.2 Measurands and descriptors .14
4 Stakeholder needs for TEM measurement procedures .15
5 Sample preparation .16
5.1 General .16
5.2 Sample sources .17
5.3 Use a representative sample .17
5.3.1 General.17
5.3.2 Powder samples .17
5.3.3 Nanoparticle dispersions in liquids .17
5.4 Minimize particle agglomeration in the sample dispersion .18
5.5 Selection of the mounting support .18
6 Instrument factors .18
6.1 Instrument set-up.18
6.2 Calibration .19
6.2.1 General.19
6.2.2 Calibration standards .19
6.2.3 General calibration procedure .19
6.3 Setting TEM operating conditions for calibration .21
7 Image capture .22
7.1 General .22
7.2 Setting a suitable operating magnification .22
7.3 Minimum particle area .23
7.4 Number of particles to count for particle size and shape distributions .23
7.5 Uniform background .24
7.6 Measurement procedure .24
7.6.1 General.24
7.6.2 Developing a test sample .25
7.6.3 Effects of magnification .25
7.6.4 Frames (micrographs) .25
7.7 Revision of image capture protocols .25
8 Particle analysis .25
8.1 General .25
8.2 Individual particle analysis .25
8.3 Automated particle analysis .26
8.4 Example — Automated particle analysis procedure .26
9 Data analysis .27
9.1 General .27
ISO 21363:2020(E)
9.2 Raw data triage — Detecting touching particles, unselected particles, artefacts and
contaminants .27
9.3 Data quality assessment — Repeatability, intermediate precision and reproducibility .28
9.4 Fitting distributions to data .30
9.5 Assessing measur ement uncertainty for samples under repeatability, intermediate
precision or reproducibility conditions.31
9.5.1 Grand statistics for fitted parameters — Three or more datasets .31
9.5.2 Measurement uncertainty of fitted parameters .31
9.5.3 Example — Measurement uncertainty for a size descriptor .32
9.6 Bivariate analysis .32
10 Reporting .33
Annex A (informative) Case studies overview .36
Annex B (informative) Discrete spheroidal nanoparticles .38
Annex C (informative) Size mixture .41
Annex D (informative) Shape mixture .53
Annex E (informative) Amorphous aggregates .58
Annex F (informative) Nanocrystalline aggregates .62
Annex G (informative) Nanofibres with irregular cross-sections .66
Annex H (informative) Nanoparticles with specific crystal habits .73
Bibliography .80
iv © ISO 2020 – All rights reserved

ISO 21363:2020(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 of 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 www .iso .org/
iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 229, Nanotechnologies.
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.
ISO 21363:2020(E)
Introduction
Characterization procedures for nanoparticles often include, but are not limited to, size, shape, surface
structure (or texture), and surface chemistry. These measurements, combined with phase information,
such as crystalline phase, constitute the morphology of the material. This document focuses on two
attributes of morphology, size and shape distributions, for discrete, agglomerated and aggregated nano-
objects (materials with at least one dimension in the nanoscale, 1 nm < a length dimension < 100 nm).
Transmission electron microscopy, a standard tool for measurements on the nanoscale, provides
two-dimensional images of particle projections. This generic workflow for measuring and evaluating
particle size and shape distributions on the nanoscale includes sample preparation, instrument factors,
image capture, particle analysis, data analysis, and reporting. Seven case studies have been included to
illustrate how the generic protocol can be applied to different particle morphologies and sample types.
Three discrete particle test samples are reported: spheroidal (gold nanospheres), a bimodal mixture of
particle sizes (colloidal silicas), and a mixture of particle shapes (gold nanorods and gold nanocubes).
Two aggregate test samples are reported: amorphous aciniform aggregates (carbon black) and
aggregates of primary crystallites (titania). Measurements methods are also presented for low aspect
ratio samples and nanoparticles with specific crystal habits. Several of the case studies are supported
by interlaboratory collaborations conducted under the guidelines of the Versailles Project on Advanced
[42]
Materials and Standards (VAMAS) for interlaboratory comparisons (ILCs) .
Three types of size and shape descriptors are considered. Size descriptors include those determined by
linear or areal measurements. Shape descriptors include elongational descriptors, such as ratios of two
length descriptors, and ruggedness descriptors, which represent surface irregularities.
The protocol emphasizes qualitative and quantitative analysis of data quality by the user. Qualitative
comparisons of datasets include determining the similarity or differences between single descriptor
means or multivariate means. Quantitative comparisons of datasets are based on difference or
similarities between the parameters of reference models fitted to descriptor distributions. At least two
parameters (mean and spread) and their uncertainties are needed to define a descriptor distribution.
In some cases, these two quantitative parameters and their uncertainties may not be sufficient for
characterization of particle size and shape distributions. Data visualization techniques, such as residual
deviation and quantile plots, and data correlations, such as pairs of size and shape descriptors or
fractal analysis, can provide additional ways to evaluate and differentiate test samples. Taken together,
qualitative and quantitative quality metrics plus visualization and correlation tools permit users to
tailor the protocol to their qualitative and quantitative quality targets.
vi © ISO 2020 – All rights reserved

INTERNATIONAL STANDARD ISO 21363:2020(E)
Nanotechnologies — Measurements of particle size and
shape distributions by transmission electron microscopy
1 Scope
This document specifies how to capture, measure and analyse transmission electron microscopy
images to obtain particle size and shape distributions in the nanoscale.
This document broadly is applicable to nano-objects as well as to particles with sizes larger than
100 nm. The exact working range of the method depends on the required uncertainty and on the
performance of the transmission electron microscope. These elements can be evaluated according to
the requirements described in this document.
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 9276-3, Representation of results of particle size analysis — Part 3: Adjustment of an experimental
curve to a reference model
ISO 9276-6:2008, Representation of results of particle size analysis — Part 6: Descriptive and quantitative
representation of particle shape and morphology
ISO 29301, Microbeam analysis — Analytical electron microscopy — Methods for calibrating image
magnification by using reference materials with periodic structures
3 Terms, definitions and symbols
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 Core terms — Particles
3.1.1
nano-object
discrete piece of material with one, two or three external dimensions in the nanoscale (3.1.2)
[SOURCE: ISO/TS 80004-2:2015, 2.2]
3.1.2
nanoscale
length range approximately from 1 nm to 100 nm
[SOURCE: ISO/TS 80004-1:2015, 2.1, modified — Note 1 to entry has been deleted.]
ISO 21363:2020(E)
3.1.3
particle
minute piece of matter with defined physical boundaries
[SOURCE: ISO 26824:2013, 1.1, modified — Notes 1, 2 and 3 to entry have been deleted.]
3.1.4
constituent particle
identifiable, integral component of a larger particle (3.1.3)
[SOURCE: ISO/TS 80004-2:2015, 3.3, modified — Note 1 to entry has been deleted.]
3.1.5
agglomerate
collection of weakly or medium strongly bound particles (3.1.3) where the resulting external surface
area is similar to the sum of the surface areas of the individual components
Note 1 to entry: The forces holding an agglomerate together are weak forces, for example van der Waals forces or
simple physical entanglement.
Note 2 to entry: Agglomerates are also termed secondary particles and the original source particles are termed
primary particles.
[SOURCE: ISO/TS 80004-2:2015, 3.4]
3.1.6
aggregate
particle (3.1.3) comprising strongly bonded or fused particles where the resulting external surface area
may be significantly smaller than the sum of calculated surface areas of the individual components
Note 1 to entry: The forces holding an aggregate together are strong forces (for example, covalent bonds) or
those resulting from sintering or complex physical entanglement.
Note 2 to entry: Aggregates are also termed secondary particles and the original source particles are termed
primary particles.
Note 3 to entry: Entries 3.1.6 to 3.1.10 define elements of agglomerates and aggregates, some of which are
illustrated in Figure 1. Constituent particles in an aggregate are tightly fused into a discrete entity (the
aggregate), while the constituent particles in an agglomerate are weakly bound and generally easily dispersed
under shear or mechanical stress.
2 © ISO 2020 – All rights reserved

ISO 21363:2020(E)
a)  Primary particles in an b)  Primary particles in an c)  Agglomerate of aggregates
agglomerate aggregate
d) Nano-object (if less than 100 nm) e)  Agglomerate of both primary
or particle particles and aggregates
Figure 1 — Schematic showing elements of agglomerates and aggregates
[SOURCE: ISO/TS 80004-2:2015, 3.5, modified — In the definition, “may be significantly smaller” has
replaced “is significantly smaller” and “calculated” has been added before “surface areas”. In Note 1
to entry, “ionic bonds” in the example and the final phrase “or otherwise combined former primary
particles” have been deleted. Note 3 to entry and Figure 1 have been added.]
3.1.7
nanoparticle
nano-object (3.1.1) with all three external dimensions in the nanoscale (3.1.2) where the lengths of the
longest and shortest axes of the nano-object do not differ significantly
[SOURCE: ISO/TS 80004-2:2015, 4.4, modified — “three” has been added and Note 1 to entry has been
deleted.]
3.1.8
nanorod
solid nanofibre (3.1.9)
[SOURCE: ISO/TS 80004-2:2015, 4.7]
ISO 21363:2020(E)
3.1.9
nanofibre
nano-object (3.1.1) with two similar external dimensions in the nanoscale (3.1.2) and the third
dimension significantly larger
[SOURCE: ISO/TS 80004-2:2015, 4.5, modified — “similar” has been added and Notes 1, 2 and 3 to entry
have been deleted.]
3.1.10
nanophase
physically or chemically distinct region or collective term for physically distinct regions of the same
kind in a material with the discrete regions having one, two or three dimensions in the nanoscale (3.1.2)
Note 1 to entry: Nano-objects (3.1.1) embedded in another phase constitute a nanophase.
3.1.11
nanodispersion
material in which nano-objects (3.1.1) or a nanophase (3.1.10) are dispersed in a continuous phase of a
different composition
[SOURCE: ISO/TS 80004-4:2011, 2.14]
3.1.12
particle size
x
dimension of a particle (3.1.3) determined by a specified measurement method and under specified
measurement conditions
Note 1 to entry: Different methods of analysis are based on the measurement of different physical properties.
Independent of the particle property actually measured, the particle size can be reported as a linear dimension,
an area or a volume.
Note 2 to entry: The symbol x is used denote linear particle size. However, it is recognized that the symbol d is
also widely used. Therefore, the symbol x may be replaced by d.
[SOURCE: ISO 9276-1:1998, 4.2, modified — Converted into a term and definition entry.]
3.1.13
particle size distribution
distribution of particles (3.1.3) as a function of particle size (3.1.12)
[SOURCE: ISO/TS 80004-6:2013, 3.1.2, modified — Note 1 to entry has been deleted.]
3.1.14
particle shape
external geometric form of a particle (3.1.3)
Note 1 to entry: Shape description requires two scalar descriptors, i.e. length and spread.
[SOURCE: ISO/TS 80004-6:2013, 3.1.3, modified — Note 1 to entry has been added.]
3.1.15
particle shape distribution
distribution of a specific particle shape (3.1.14) descriptor for a sample population
3.2 Core terms — Image capture and analysis
3.2.1
field of view
field that is viewed by the viewing device
[SOURCE: ISO 13322-1:2014, 3.1.6, modified — Note 1 to entry has been deleted.]
4 © ISO 2020 – All rights reserved

ISO 21363:2020(E)
3.2.2
measurement frame
selected area from the field of view (3.2.1) in which particles (3.1.3) are sized and counted for image
analysis
[SOURCE: ISO 13322-1:2014, 3.1.10]
3.2.3
binary image
digitized image consisting of an array of pixels (3.2.4), each of which has a value of 0 or 1, whose
values are normally represented by dark and bright regions on the display screen or by the use of two
distinct colours
[SOURCE: ISO 13322-1:2014, 3.1.2]
3.2.4
pixel
smallest element of an image that can be uniquely processed, and is defined by its spatial coordinates
and encoded with colour values
[SOURCE: ISO 12640-2:2004, 3.6, modified — Note 1 to entry has been deleted.]
3.2.5
pixel-resolution
number of imaging pixels (3.2.4) per unit distance of the detector
[SOURCE: ISO 29301:2017, 3.24, modified — Note 1 to entry has been deleted.]
3.2.6
pixel count
total number of pixels (3.2.4) per file, length, or area depending on the unit used
[SOURCE: ISO 19262:2015, 3.191]
3.2.7
micrograph
record of an image formed by a microscope
[SOURCE: ISO 10934-1:2002, 2.94]
3.2.8
artefact
artifact
unwanted distortion or added feature in measured data arising from lack of idealness of equipment
[SOURCE: ISO 18115-2: 2013, 5.6]
3.3 Core terms — Statistical symbols and definitions
3.3.1
coefficient of variation
C
v
ratio of the standard deviation to the arithmetic mean
Note 1 to entry: It is commonly reported as a percentage.
Note 2 to entry: For example, the coefficient of variation for a sample mean may be represented by:
s⋅100
c =
v
x
ISO 21363:2020(E)
where x is the descriptor’s mean and s is the descriptor’s standard deviation for several datasets. These “grand
statistics” are used to evaluate descriptor data for interlaboratory comparisons.
[SOURCE: ISO 27448:2009, 3.11, modified — Notes 1 and 2 to entry have been added.]
3.3.2
standard error of estimation
σ
est
measure of dispersion of the dependent variable (output) about the least-squares line obtained by curve
fitting or regression analysis
Note 1 to entry: The standard error of estimation may be determined by:
n
yy−
()
∑ i
i=1
σ =
est
nk−
where
n is the number of data points;
k is the number of coefficients in the equation.
Note 2 to entry: The standard error of the mean may be determined by:
s
σ =
est,x
n
Note 3 to entry: The standard error is the standard deviation of the sampling distribution of a statistic. The
example is for a sample mean. Standard error of the mean is an estimate of how close the sample mean is to the
population mean. This value decreases as the sample size increases.
[SOURCE: ISO 772:2011, 7.31, modified — The admitted term “residual standard deviation” has been
deleted. Notes 1, 2 and 3 to entry have replaced the original Notes 1 and 2 to entry.]
3.3.3
relative standard error
RSE
standard error divided by its statistic
Note 1 to entry: It is expressed as a percentage.
Note 2 to entry: For example, the relative standard error of the mean is:
100⋅σ
est,x
RSE =
x
x
3.3.4
measurement bias
estimate of a systematic measurement error
Note 1 to entry: Bias is present when a statistic is systematically different than the population parameter it is
estimating.
Δ=mc −c : the absolute difference between the mean measured value and the certified value. Bias of the
mcrm
normal mean of this study would be the average of the individual absolute differences between a measured mean
and the certified reference material mean.
6 © ISO 2020 – All rights reserved

ISO 21363:2020(E)
n
Δ
∑ mi,
i=1
bias=
n
[SOURCE: ISO/IEC Guide 99:2007, 2.18, modified — Notes 1 and 2 to entry have been added.]
3.3.5
residual
difference between the observed value of the response variable and the estimated value of the response
variable
3.3.6
residual standard deviation
description of the scatter of the information values about the calculated regression line
Note 1 to entry: It is a figure of merit, describing the precision (3.5.5) of the calibration.
[SOURCE: ISO 8466-1:1990, 2.5]
3.3.7
quantile plot
graphical method of comparing two distributions where the quantiles of the empirical (data)
distribution are plotted on the y-axis while the quantiles of the theoretical (reference) distribution with
the same mean and variance as the empirical distribution are plotted on the x-axis
3.4 Core terms — Measurands
3.4.1
measurand
quantity intended to be measured
[SOURCE: ISO/IEC Guide 99:2007, 2.3, modified — The notes have been deleted.]
3.4.2
image descriptor
descriptor extracted from one image
[SOURCE: ISO/IEC 15938-13:2015, 2.1]
3.4.3
Feret diameter
distance between two parallel tangents on opposite sides of the image of a particle (3.1.3)
Note 1 to entry: The maximum Feret diameter (3.4.4) is used in this document.
[SOURCE: ISO 13322-1:2014, 3.1.5, modified — Note 1 to entry has been added.]
3.4.4
maximum Feret diameter
maximum length of an object whatever its orientation
[SOURCE: ISO/TR 945-2:2011, 2.1, modified — Note 1 to entry has been deleted.]
3.4.5
minimum Feret diameter
minimum length of an object whatever its orientation
3.4.6
perimeter
total length of the object contour
[SOURCE: ISO/TR 945-2:2011, 2.3]
ISO 21363:2020(E)
3.4.7
equivalent circular diameter
diameter of a circle having the same area as the projected image of the particle (3.1.3)
EXAMPLE The ecd is:
4⋅ A
ecd=
π
where A is the area of the particle.
[SOURCE: ISO 13322-1:2014, 3.1.1, modified — Note 1 to entry has been deleted and the example has
been added.]
3.4.8
equivalent perimeter diameter
d
epd
diameter of a circle having the same perimeter (3.4.6) as the projected image of the particle (3.1.3)
Note 1 to entry: It may be calculated as follows:
P
d =
epd
π
where P is the length of the perimeter.
3.4.9
convex hull
smallest convex set containing a given geometric object
[SOURCE: ISO 19123:2005, 4.1.2]
3.4.10
aspect ratio
ratio of the minimum (3.4.5) to the maximum Feret diameter (3.4.4)
Note 1 to entry: It may be calculated, for example, as follows:
x
Fmin
aspect ratio=
x
Fmax
where
x is the minimum Feret diameter;
Fmin
x is the maximum Feret diameter.
Fmax
[SOURCE: ISO 26824:2013, 4.5, modified — Note 1 to entry has replaced the original Notes 1 and 2
to entry.]
3.4.11
ellipse ratio
ratio of the lengths of the axes of the Legendre ellipse of inertia
Note 1 to entry: For example, the ellipse ratio can be the ratio of the minor and major axes of the Legendre ellipse
fitted to the particle (3.1.3); elliptical shape factor, thus:
x
Lmin
ellipseratio=
x
Lmax
where
8 © ISO 2020 – All rights reserved

ISO 21363:2020(E)
x is the length of the minor axis of Legendre ellipse of inertia;
Lmin
x is the length of the major axis of Legendre ellipse of inertia.
Lmax
[SOURCE: ISO 26824:2013, 4.4, modified — Note 1 to entry has been replaced.]
3.4.12
extent
bulkiness
ratio of particle area to the product of the Feret (3.4.3) and the minimum Feret diameters (3.4.6)
Note 1 to entry: For example, the extent may be calculated as:
A
extent=
xx⋅
Fmin Fmax
where
x is the minimum Feret diameter;
Fmin
x is the maximum Feret diameter.
Fmax
[SOURCE: ISO 9276-6:2008, 8.1.3, modified — Converted into a term and definition entry. The definition
has been added.]
3.4.13
compactness
degree to which the projection area A of the particle (3.1.3) is similar to a circle, considering the overall
form of the particle (3.1.3) with the maximum Feret diameter (3.4.4)
Note 1 to entry: For example, the compactness may be calculated as:
4⋅A
π
compactness=
X
Fmax
where
A is the area of the particle;
x is the maximum Feret diameter.
Fmax
[SOURCE: ISO 9276-6:2008, 8.1.3, modified — Converted into a term and definition entry. In the
definition, “projection area A of the particle” has replaced “particle (or its projection area)” and “with
the maximum Feret diameter” has been added.]
3.4.14
convexity
ratio of the perimeter (3.4.6) of the convex hull (3.4.9) envelope bounding the particle (3.1.3) to its
perimeter
Note 1 to entry: For example, the convexity may be calculated as:
P
C
convexity=
P
where
ISO 21363:2020(E)
P is the length of the perimeter of the convex hull (envelope) bounding the particle;
c
P is the length of the perimeter.
[SOURCE: ISO 9276-6:2008, 8.2, modified — Converted into a term and definition entry. The definition
has been added.]
3.4.15
circularity
C
degree to which the projected area of the particle (3.1.3) is similar to a circle, based on its perimeter (3.4.6)
Note 1 to entry: For example, the circularity may be calculated as:
x
4⋅⋅π A
a
C==
x
P
p
where
x is the area-equivalent diameter of a particle;
a
x is the perimeter-equivalent diameter of particle;
p
A is the area of the particle;
P is the length of the perimeter.
[SOURCE: ISO 26824:2013, 4.12, modified — “projected area of the particle” has replaced “projection
area of the particle A”, “based on its perimeter” has replaced “considering the smoothness of its
perimeter P”. The formula and Note 1 to entry have been replaced.]
3.4.16
roundness
square of the compactness (3.4.13)
3.4.17
solidity
ratio of the projected area A to the area of the convex hull (3.4.9) A (envelope)
C
Note 1 to entry: For example, the solidity may be calculated as:
A
solidity=
A
C
[SOURCE: ISO 26824:2013, 4.13, modified — Note 1 to entry has been added.]
3.5 Core terms — Metrology
3.5.1
repeatability condition of measurement
condition of measurement, out of a set of conditions that includes the same measurement procedure,
same operators, same measuring system, same operating conditions and same location, and replicate
measurements on the same or similar objects over a short period of time
[SOURCE: ISO/IEC Guide 99:2007, 2.20, modified — The admitted term “repeatability condition” and
the notes have been deleted.]
10 © ISO 2020 – All rights reserved

ISO 21363:2020(E)
3.5.2
intermediate precision condition of measurement
condition of measurement, out of a set of conditions that includes the same measurement procedure,
same location, and replicate measurements on the same or similar objects over an extended period of
time, but may include other conditions involving changes
[SOURCE: ISO/IEC Guide 99:2007, 2.22, modified — The admitted term “intermediate precision
condition” and the notes have been deleted.]
3.5.3
reproducibility condition of measurement
condition of measurement, out of a set of conditions that includes different locations, operators,
measuring systems, and replicate measurements on the same or similar objects
Note 1 to entry: The different measuring systems may use different measurement procedures.
Note 2 to entry: A specification should give the conditions changed and unchanged, to the extent practical.
[SOURCE: ISO/IEC Guide 99:2007, 2.24, modified — The admitted term “reproducibility condition” has
been deleted.]
3.5.4
measurement accuracy
closeness of agreement between a measured quantity value and a true quantity value of a measurand
(3.4.1)
Note 1 to entry: The concept “measurement accuracy” is not a quantity and is not given a numerical quantity
value. A measurement is said to be more accurate when it offers a smaller measurement uncertainty.
Note 2 to entry: The term “measurement accuracy” should not be used for measurement trueness and the term
“measurement precision” should not be used for “measurement accuracy”, which, however, is related to both
these concepts.
Note 3 to entry: “Measurement accuracy” is sometimes understood as closeness of agreement between measured
quantity values that are being attributed to the measurand.
[SOURCE: ISO/IEC Guide 99:2007, 2.13, modified — The admitted terms “accuracy of measurement”
and “accuracy” have been deleted. In Note 1 to entry, “measurement uncertainty” has replaced
measurement error”.]
3.5.5
precision
measurement precision
closeness of agreement between indications or measured quantity values obtained by replicate
measurements on the same or similar objects under specified conditions
Note 1 to entry: Measurement precision is usually expressed num
...