ISO 13320:2009
(Main)Particle size analysis — Laser diffraction methods
Particle size analysis — Laser diffraction methods
ISO 13320:2009 provides guidance on instrument qualification and size distribution measurement of particles in many two-phase systems (e.g. powders, sprays, aerosols, suspensions, emulsions and gas bubbles in liquids) through the analysis of their light-scattering properties. It does not address the specific requirements of particle size measurement of specific materials. ISO 13320:2009 is applicable to particle sizes ranging from approximately 0,1 µm to 3 mm. With special instrumentation and conditions, the applicable size range can be extended above 3 mm and below 0,1 µm. For non-spherical particles, a size distribution is reported, where the predicted scattering pattern for the volumetric sum of spherical particles matches the measured scattering pattern. This is because the technique assumes a spherical particle shape in its optical model. The resulting particle size distribution is different from that obtained by methods based on other physical principles (e.g. sedimentation, sieving).
Analyse granulométrique — Méthodes par diffraction laser
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INTERNATIONAL ISO
STANDARD 13320
First edition
2009-10-01
Corrected version
2009-12-01
Particle size analysis — Laser diffraction
methods
Analyse granulométrique — Méthodes par diffraction laser
Reference number
ISO 13320:2009(E)
©
ISO 2009
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ISO 13320:2009(E)
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ii © ISO 2009 – All rights reserved
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ISO 13320:2009(E)
Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Normative references.1
3 Terms, definitions and symbols .1
3.1 Terms and definitions .1
3.2 Symbols.5
4 Principle.6
5 Laser diffraction instrument.6
6 Operational procedures.10
6.1 Requirements.10
6.2 Sample inspection, preparation, dispersion and concentration .10
6.3 Measurement .12
6.4 Precision.14
6.5 Accuracy.15
6.6 Error sources and diagnosis.17
6.7 Resolution and sensitivity.19
7 Reporting of results .20
Annex A (informative) Theoretical background of laser diffraction .22
Annex B (informative) Recommendations for instrument specifications.39
Annex C (informative) Dispersion liquids for the laser diffraction method .42
Annex D (informative) Refractive index, n , for various liquids and solids.43
m
Annex E (informative) Recommendations to reach optimum precision in test methods.48
Bibliography.50
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ISO 13320:2009(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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
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.
ISO 13320 was prepared by Technical Committee ISO/TC 24, Particle characterization including sieving,
Subcommittee SC 4, Particle characterization.
This first edition of ISO 13320 cancels and replaces ISO 13320-1:1999.
This corrected version of ISO 13320:2009 incorporates the following correction:
⎯ in Figure A.2, lower graph, the symbols for datapoints corresponding to “1,39 – 0,0i” and “2,19 – 0,0i”
have been changed to match the plots to which they refer.
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ISO 13320:2009(E)
Introduction
The laser diffraction technique has evolved such that it is now a dominant method for determination of particle
size distributions (PSDs). The success of the technique is based on the fact that it can be applied to various
kinds of particulate systems, is fast and can be automated, and that a variety of commercial instruments is
available. Nevertheless, the proper use of the instrument and the interpretation of the results require the
necessary caution.
Since the publication of ISO 13320-1:1999, the understanding of light scattering by different materials and the
design of instruments have advanced considerably. This is especially marked in the ability to measure very
fine particles. Therefore, this International Standard has been prepared to incorporate the most recent
advances in understanding.
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INTERNATIONAL STANDARD ISO 13320:2009(E)
Particle size analysis — Laser diffraction methods
1 Scope
This International Standard provides guidance on instrument qualification and size distribution measurement
of particles in many two-phase systems (e.g. powders, sprays, aerosols, suspensions, emulsions and gas
bubbles in liquids) through the analysis of their light-scattering properties. It does not address the specific
requirements of particle size measurement of specific materials.
This International Standard is applicable to particle sizes ranging from approximately 0,1 µm to 3 mm. With
special instrumentation and conditions, the applicable size range can be extended above 3 mm and below
0,1 µm.
For non-spherical particles, a size distribution is reported, where the predicted scattering pattern for the
volumetric sum of spherical particles matches the measured scattering pattern. This is because the technique
assumes a spherical particle shape in its optical model. The resulting particle size distribution is different from
that obtained by methods based on other physical principles (e.g. sedimentation, sieving).
2 Normative references
The following referenced documents are indispensable for the application 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 9276-1, Representation of results of particle size analysis — Part 1: Graphical representation
ISO 9276-2, Representation of results of particle size analysis — Part 2: Calculation of average particle
sizes/diameters and moments from particle size distributions
ISO 9276-4, Representation of results of particle size analysis — Part 4: Characterization of a classification
process
ISO 14488, Particulate materials — Sampling and sample splitting for the determination of particulate
properties
ISO 14887, Sample preparation — Dispersing procedures for powders in liquids
3 Terms, definitions and symbols
3.1 Terms and definitions
3.1.1
absorption
reduction of intensity of a light beam not due to scattering
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ISO 13320:2009(E)
3.1.2
coefficient of variation
CV
relative standard deviation (deprecated)
〈positive random variable〉 standard deviation divided by the mean
NOTE 1 The coefficient of variation is commonly reported as a percentage.
[24]
NOTE 2 Adapted from ISO 3534-1:2006 , 2.38.
3.1.3
complex refractive index
n
p
refractive index of a particle, consisting of a real and an imaginary (absorption) part
NOTE The complex refractive index of a particle can be expressed mathematically as
n = n − ik
p p p
where
i is the square root of −1;
k is the positive imaginary (absorption) part of the refractive index of a particle;
p
n is the positive real part of the refractive index of a particle.
p
[27]
In contrast to ISO 80000-7:2008 , item 7-5, this International Standard follows the convention of adding a minus sign to
the imaginary part of the refractive index.
3.1.4
relative refractive index
m
rel
ratio of the complex refractive index of a particle to the real part of the dispersion medium
[26]
NOTE 1 Adapted from ISO 24235:2007 .
NOTE 2 In most applications, the medium is transparent and, thus, its refractive index has a negligible imaginary part.
NOTE 3 The relative refractive index can be expressed mathematically as
m = n /n
rel p m
where
n is the real part of the refractive index of the medium;
m
n is the complex refractive index of a particle.
p
3.1.5
deconvolution
〈particle size analysis〉 mathematical procedure whereby the size distribution of an ensemble of particles is
inferred from measurements of their scattering pattern
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ISO 13320:2009(E)
3.1.6
diffraction
〈particle size analysis〉 scattering of light around the contour of a particle, observed at a substantial distance
(in the ‘far field’)
3.1.7
extinction
〈particle size analysis〉 attenuation of a light beam traversing a medium through absorption and scattering
3.1.8
model matrix
matrix containing vectors of the scattered light signals for unit volumes of different size classes, scaled to the
detector's geometry, as derived from model computation
3.1.9
multiple scattering
consecutive scattering of light by more than one particle, causing a scattering pattern that is no longer the sum
of the patterns from all individual particles
NOTE See single scattering (3.1.20).
3.1.10
obscuration
optical concentration
fraction of incident light that is attenuated due to extinction (scattering and/or absorption) by particles
[25]
NOTE 1 Adapted from ISO 8130-14:2004 , 2.21.
NOTE 2 Obscuration can be expressed as a percentage.
NOTE 3 When expressed as fractions, obscuration plus transmission (3.1.22) equal unity.
3.1.11
optical model
theoretical model used for computing the model matrix for optically homogeneous and isotropic spheres with,
if necessary, a specified complex refractive index
EXAMPLES Fraunhofer diffraction model, Mie scattering model.
3.1.12
reflection
〈particle size analysis〉 change of direction of a light wave at a surface without a change in wavelength or
frequency
3.1.13
refraction
process by which the direction of a radiation is changed as a result of changes in its velocity of propagation in
passing through an optically non-homogeneous medium, or in crossing a surface separating different media
[28]
[IEC 60050-845:1987 ]
NOTE The process occurs in accordance with Snell's law:
n sin θ = n sin θ
m m p p
See 3.2 for symbol definitions.
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ISO 13320:2009(E)
3.1.14
repeatability (instrument)
〈particle size analysis〉 closeness of agreement between multiple measurement results of a given property in
the same dispersed sample aliquot, executed by the same operator in the same instrument under identical
conditions within a short period of time
NOTE This type of repeatability does not include variability due to sampling and dispersion.
3.1.15
repeatability (method)
〈particle size analysis〉 closeness of agreement between multiple measurement results of a given property in
different aliquots of a sample, executed by the same operator in the same instrument under identical
conditions within a short period of time
NOTE This type of repeatability includes variability due to sampling and dispersion.
3.1.16
reproducibility (method)
〈particle size analysis〉 closeness of agreement between multiple measurement results of a given property in
different aliquots of a sample, prepared and executed by different operators in similar instruments according to
the same method
3.1.17
scattering
〈particle size analysis〉 change in propagation of light at the interface of two media having different optical
properties
3.1.18
scattering angle
〈particle size analysis〉 angle between the principal axis of the incident light beam and the scattered light
3.1.19
scattering pattern
angular pattern of light intensity, I(θ ), or spatial pattern of light intensity, I(r), originating from scattering, or the
related energy values taking into account the sensitivity and the geometry of the detector elements
3.1.20
single scattering
scattering whereby the contribution of a single member of a particle population to the total scattering pattern
remains independent of the other members of the population
3.1.21
single shot analysis
analysis, for which the entire content of a sample container is used
3.1.22
transmission
〈particle size analysis〉 fraction of incident light that remains unattenuated by the particles
NOTE 1 Transmission can be expressed as a percentage.
NOTE 2 When expressed as fractions, obscuration (3.1.10) plus transmission equal unity.
3.1.23
width of size distribution
the width of the particle size distribution (PSD), expressed as the x /x ratio
90 10
NOTE For normal (Gaussian) size distributions, often the standard deviation (absolute value), σ, or the coefficient of
variation (CV) is used. Then, about 95 % of the population of particles falls within ± 2σ from the mean value and about
99,7 % within ± 3σ from the mean value. The difference x − x corresponds to 2,6σ.
90 10
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ISO 13320:2009(E)
3.2 Symbols
A
extinction efficiency of size class i
i
C particulate concentration, volume fraction
CV coefficient of variation
f
focal length of lens
i square root of −1
i
photocurrent of detector element, n
n
I(θ) angular intensity distribution of light scattered by particles (scattering pattern)
I
intensity of horizontally polarized light at a given angle
h
spatial intensity distribution of light scattered by particles on the detector elements (measured
I(r)
scattering pattern by detector)
I
intensity of vertically polarized light at a given angle
v
J
first order Bessel Function
i
wavenumber in medium: 2πn /λ
k
m
k
imaginary (absorption) part of the refractive index of a particle
p
l
distance from scattering object to detector
a
l
illuminated pathlength containing particles
b
L vector of photocurrents (i , i . i )
n 1 2 n
m
relative, complex refractive index of particle to medium
rel
M model matrix, containing calculated detector signals per unit volume of particles in all size classes
n
real part of refractive index of medium
m
n
real part of refractive index of particle
p
n
complex refractive index of particle
p
O obscuration (1 − transmission); only true for single scattering
r radial distance from focal point in focal plane
vector of volume content in size classes (V , V … V )
V
1 2 i
V
volume content of size class i
i
v velocity of particles in dry disperser
x particle diameter
x
geometric mean particle size of size class i
i
median particle diameter; here used on a volumetric basis, i.e. 50 % by volume of the particles are
x
50
smaller than this diameter and 50 % are larger
x
particle diameter corresponding to 10 % of the cumulative undersize distribution (here by volume)
10
x
particle diameter corresponding to 90 % of the cumulative undersize distribution (here by volume)
90
dimensionless size parameter: πxn /λ
α
m
∆Q
volume fraction within size class i
3,i
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ISO 13320:2009(E)
scattering angle with respect to forward direction
θ
angle with respect to perpendicular at boundary for a light beam in medium (as used in Snell's law;
θ
m
see 3.1.13, Note)
angle with respect to perpendicular at boundary for a light beam in particle (as used in Snell's law;
θ
p
see 3.1.13, Note)
λ wavelength of illuminating light source in vacuum
standard deviation
σ
angular frequency
ω
4 Principle
A sample, dispersed at an adequate concentration in a suitable liquid or gas, is passed through the beam of a
monochromatic light source, usually a laser. The light scattered by the particles, at various angles, is
measured by multi-element detectors, and numerical values relating to the scattering pattern are recorded for
subsequent analysis. These numerical scattering values are then transformed, using an appropriate optical
model and mathematical procedure, to yield the proportion of the total volume of particles to a discrete
number of size classes forming a volumetric particle size distribution (PSD).
The laser diffraction technique for the determination of PSDs is based on the phenomenon that particles
scatter light in all directions with an intensity pattern that is dependent on particle size. Figure 1 illustrates this
dependency in the scattering patterns for two sizes of spherical particles. In addition to particle size, particle
shape and the optical properties of the particulate material influence the scattering pattern.
a) b)
Figure 1 — Scattering pattern for two spherical particles: the particle generating pattern a) is twice as
large as the one generating pattern b) (simulated images for clarity)
5 Laser diffraction instrument
A set-up for a laser diffraction instrument is given in Figure 2.
In this Fourier set-up, a light source (typically a laser or other narrow-wavelength source) is used to generate
a monochromatic, coherent, parallel beam. This is followed by a beam processing unit, usually a beam
expander with integrated filter, producing an extended and nearly ideal beam to illuminate the dispersed
particles.
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ISO 13320:2009(E)
Key
1 obscuration/optical concentration detector
2 scattered beam
3 direct beam
4 fourier lens
5 scattered light not collected by lens 4
6 ensemble of dispersed particles
7 light source (e.g. laser)
8 beam processing unit
9 working distance of lens 4
10 multi-element detector
11 focal distance of lens 4
NOTE For explanations of symbols, see 3.2.
Figure 2 ⎯ Fourier set-up of a laser diffraction instrument
A sample of particles, dispersed at an adequate concentration, is passed through the light beam in a
measuring zone by a transporting medium (gas or liquid). This measuring zone should be within the working
distance of the lens used. Sometimes, the particle stream in a process passes directly through the laser beam
for measurement. This is the case in the measurement of sprays and aerosols. In other cases (e.g. when
measuring emulsions, pastes and powders), samples can be dispersed in fluids and caused to flow through
the measurement zone. Often dispersants (wetting agents; stabilizers) and/or mechanical forces (agitation;
sonication) are applied for deagglomeration of particles and for stabilization of the dispersion. For these liquid
dispersions, a recirculation system is most commonly used, consisting of an optical measuring cell, a
dispersion bath usually equipped with stirrer and ultrasonic elements, a pump and tubing.
Dry powders can also be converted into aerosols through application of dry powder dispersers, which apply
mechanical forces for deagglomeration. Here, a dosing device feeds the disperser with, ideally, a
near-constant mass flow of sample. The disperser uses the energy of a compressed gas or the differential
pressure to a vacuum to disperse the particles. It outputs an aerosol that is blown through the measuring zone,
usually into the inlet of a vacuum pipe that collects the particles. Coarse, non-agglomerated powders can be
transported through the measurement zone by gravity.
There are two positions in which the particles can enter the laser beam. In the Fourier optics case, the
particles enter the parallel beam before and within the working distance of the collecting lens [see Figure 3a)].
This allows for the measurement of spatially extended particle systems. In the reverse Fourier optics case, the
particles enter behind the lens and, thus, in a converging beam [see Figure 3b)].
The advantage of the Fourier set-up is that a reasonable pathlength for the sample is allowed within the
working distance of the lens. The reverse Fourier set-up demands small pathlengths but provides one solution
that enables the measurement of scattered light at larger angles.
The interaction of the incident light beam and the ensemble of dispersed particles results in a scattering
pattern with different light intensities scattered at various angles (see Annex A for the theoretical background
of laser diffraction). The total angular intensity distribution I(θ ), consisting of both direct and scattered light, is
then focused by a positive lens or an ensemble of lenses onto a multi-element detector. The lens(es)
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ISO 13320:2009(E)
provide(s) for a scattering pattern which, within limits, is not dependent upon the location of the particles in the
light beam. The continuous angular intensity distribution I(θ ) is converted into a discrete spatial intensity
distribution I(r) on a set of detector elements.
Key Key
1 detector 1 detector
2 fourier lens 2 flow through cuvette for dispersed
particles
3 ensemble of dispersed particles
3 particle
4 working distance
5 focal distance
NOTE For explanations of symbols, see 3.2.
a) Fourier set-up: particles are in parallel beam before b) Reverse Fourier set-up: particles are in converging
and within working distance of lens beam between lens and detector
Figure 3 — Illustrations of optical arrangements used in laser diffraction instruments
Some instruments contain extra features to improve particle size analysis:
a) an extra light source at the same optical axis having a different wavelength;
b) one or more off-axis light sources, either at less or at more than 90° with respect to the optical axis;
c) polarization filters for light source and detectors;
d) scattered light detectors at angles smaller than 90° but larger than the conventional angular range
(forward scattering);
e) scattered light detectors at around 90° for measurement of intensities in different polarization directions;
f) scattered light detectors at angles larger than 90° (backscattering).
These possibilities are illustrated in Figure 4.
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ISO 13320:2009(E)
Key
1 light source assembly including beam expansion 8 low angle detector(s), either bespoke design or pixel
and/or collimation array
2 light source wavelength 1 9 transmission or obscuration detector
3 light source wavelength 2 10 high angle detector array
4 beam switching arrangement 11 horizontally polarized light detector
5 reverse Fourier lens(es) position 12 vertically polarized light detector
6 measurement cell or general measurement zone 13 alternative entry point for light source
7 Fourier lens(es) position 14 alternative entry point for light source
Figure 4 ⎯ Possibilities for optical arrangements in laser diffraction instrument
It is assumed that the recorded scattering pattern of the particle ensemble is identical to the sum of the
patterns from all individual particles (single scattering). Furthermore, the scattering pattern is assumed to
come from spherical particles.
Detection of the scattering pattern is done by a number of silicon detectors or photodiodes and/or a pixel array
detector. These detectors convert the spatial intensity distribution I(r) into a series of photocurrents, i .
n
Subsequent electronics then convert and digitize the photocurrents into a set of energies, L , representing the
n
scattering pattern. A central element measures the intensity of the scattered and non-scattered light and, thus,
with a calculation, provides a measure of optical concentration or obscuration. Some instruments provide
special geometries of the central element in order to automatically re-centre or re-focus the detector by
moving the detector or the lens. It is desirable that the detector elements are positioned so as to prevent the
light reflected from internal surfaces from re-traversing the optical system.
A computer controls the measurement and is used for storage and manipulation of the detected signals, for
storage and/or calculation of a proper form of the optical model (usually as a model matrix containing
light-scattering vectors per unit of volume per size class, scaled to the detector's geometry and sensitivity) and
for calculation of the PSD (see Annex A for the theoretical background of laser diffraction). Also, it may
provide automated instrument operation.
Significant differences exist, both in hardware and software, not only between instruments from different
manufacturers but also between different types from one company. The instrument specifications should give
adequate information for proper judgement of these differences. Annex B contains recommendations for the
specifications of laser diffraction instruments.
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ISO 13320:2009(E)
6 Operational procedures
6.1 Requirements
6.1.1 Instrument location
The instrument should be located in a clean environment that is free from excessive electrical noise,
mechanical vibration and temperature fluctuations, and out of direct sunlight and airflows. The operating area
should conform to local health and safety requirements. The instrument should either contain a rigid internal
optical bench or be installed on a rigid table or bench to avoid realignment of the optical system at frequent
intervals.
WARNING ⎯ The radiation of instruments equipped with a laser can cause permanent eye damage.
Never look into the direct path of the laser beam or its reflections. Avoid blocking the laser beam with
reflecting surfaces. Observe relevant local laser radiation safety regulations.
6.1.2 Dispersion liquids
Any suitable, optically transparent liquid of known refractive index may be used. Thus, a variety of liquids is
available for the preparation of liquid dispersions of powders. Annex C provides information on the dispersion
liquids.
Observe local health and safety regulations if an organic liquid is used for dispersion. Use a cover for the
ultrasonic bath when using liquids with a high vapour pressure to prevent the formation of hazardou
...
DRAFT INTERNATIONAL STANDARD ISO/DIS 13320
ISO/TC 24/SC 4 Secretariat: ANSI
Voting begins on: Voting terminates on:
2007-07-06 2007-12-06
INTERNATIONAL ORGANIZATION FOR STANDARDIZATION • МЕЖДУНАРОДНАЯ ОРГАНИЗАЦИЯ ПО СТАНДАРТИЗАЦИИ • ORGANISATION INTERNATIONALE DE NORMALISATION
Particle size analysis — Laser diffraction methods
Analyse granulométrique — Méthodes par diffraction laser
(Revision of ISO 13320-1:1999)
ICS 19.120
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Conformément aux dispositions de la Résolution du Conseil 15/1993, ce document est distribué
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©
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ISO/DIS 13320
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but shall
not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In the
unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
Copyright notice
This ISO document is a Draft International Standard and is copyright-protected by ISO. Except as permitted
under the applicable laws of the user's country, neither this ISO draft nor any extract from it may be
reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, photocopying,
recording or otherwise, without prior written permission being secured.
Requests for permission to reproduce should be addressed to either ISO at the address below or ISO's
member body in the country of the requester.
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Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
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©
ii ISO 2007 – All rights reserved
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ISO/CD 13320
Contents Page
1 Scope .1
2 Normative references .1
3 Terms, definitions and symbols.2
3.1 Terms and definitions .2
3.2 Symbols.4
4 Principle.5
5 Laser diffraction instrument.5
6 Operational procedures .9
6.1 Requirements.9
6.2 Sample inspection, preparation, dispersion and concentration .9
6.3 Measurement.11
6.4 Precision.14
6.5 Accuracy.14
6.6 Error sources; diagnosis .16
6.7 Resolution; sensitivity .18
7 Reporting of results.19
Annex A (informative) Theoretical background of laser diffraction.21
Annex B (informative) Recommendations for instrument specifications .35
Annex C (informative) Dispersion liquids for the laser diffraction method .38
Annex D (informative) Refractive index for various liquids and solids .39
Annex E (informative) Recommendations to reach optimum precision in test methods.44
Bibliography.46
© ISO 2006
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from the publisher.
International Organization for Standardization
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Printed in Switzerland
© ISO 2007 – All rights reserved iii
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ISO/CD 13320
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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
ISO 13320 was prepared by Technical Committee ISO/TC 24, Sieves, sieving and other sizing methods,
Subcommittee SC 4, Sizing by methods other than sieving.
Annexes A to E of this part of ISO 13320 are for information only.
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Introduction
The laser diffraction technique has evolved such that it is now a dominant method for determination of particle
size distributions. The success of the technique is based on the fact that it can be applied to various kinds of
particulate systems, is fast and can be automated and that a variety of commercial instruments is available.
Nevertheless, the proper use of the instrument and the interpretation of the results require the necessary
caution.
Since the first version of this ISO Standard 13320-1 was published in 1999, the understanding of light
scattering by different materials and the design of instruments has advanced considerably. This is especially
marked in the ability for the measurement of very fine particles. Therefore, it is necessary to revise this
International Standard to capture the most recent advances in understanding.
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Particle size analysis — Laser diffraction methods
1 Scope
This ISO standard provides guidance on instrument qualification and size distribution measurement of
particles in many two-phase systems (e.g. powders, sprays, aerosols, suspensions, emulsions and gas
bubbles in liquids) through the analysis of their light scattering properties. It does not address the specific
requirements of particle size measurement of specific materials. ISO 13320 is applicable to particle sizes
ranging from approximately 0,1 μm to 3 mm. With special instrumentation and conditions the applicable size
range can be extended above 3 mm. Some advance is also noted for particles smaller than 0,1 μm.
For non-spherical particles a size distribution is reported, where the predicted scattering pattern for the
volumetric sum of spherical particles matches the measured scattering pattern. This is because the technique
assumes a spherical particle shape in its optical model. The resulting particle size distribution will be different
from those obtained by methods based on other physical principles (e.g. sedimentation, sieving).
2 Normative references
The following normative documents contain provisions that, through reference in this text, constitute
provisions of ISO 13320. For dated references, subsequent amendments to, or revisions of, any of these
publications do not apply. However, parties to agreements based on ISO 13320 are encouraged to investigate
the possibility of applying the most recent edition of the normative document indicated below. For undated
references, the latest edition of the normative document referred to applies. Members of ISO and lEC maintain
registers of currently valid International Standards.
ISO 9276-1, Representation of results of particle size analysis — Part 1: Graphical representation
ISO 9276-2, Representation of results of particle size analysis — Part 2: Calculation of average particle
sizes/diameters and moments from particle size distributions
ISO 9276-4, Representation of results of particle size analysis —Part 4: Characterisation of a classification
process
ISO 14887, Sample preparation — Dispersing procedures for powders in liquids
ISO/FDIS 14488:2007, Particulate materials — Sampling and sample splitting for the determination of
particulate properties
NOTE ISO/FDIS 14488 is under development.
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3 Terms, definitions and symbols
3.1 Terms and definitions
3.1.1
absorption
reduction of intensity of a light beam traversing a medium; the energy is lost as heat or may be re-radiated as
fluorescence and/or phosphorescence
3.1.2
coefficient of variation (also known as relative standard deviation)
relative measure (%) for precision: standard deviation divided by mean value of population and multiplied by
100
3.1.3
complex refractive index
1
N refractive index of a particle, consisting of a real and an imaginary (absorption) part
p
N = n – ki
p p
3.1.4
relative refractive index
2
m complex refractive index of a particle, relative to that of the medium
3.1.5
deconvolution
mathematical procedure whereby the size distribution of an ensemble of particles is inferred from
measurements of their scattering pattern
3.1.6
diffraction
scattering of light around the contour of a particle, observed at a substantial distance (in the ‘far field’)
3.1.7
extinction
attenuation of a light beam traversing a medium through absorption and scattering
3.1.8
model matrix
matrix containing light scattering vectors for unit volumes of different size classes, scaled to the detector's
geometry, as derived from model computation
3.1.9
multiple scattering
subsequent scattering of light by more than one particle, causing a scattering pattern that is no longer the sum
of the patterns from all individual particles (in contrast to single scattering)
1
This document follows the convention of adding a minus sign to the imaginary part of the refractive index. Both n and k
are positive numbers; i stands for √(-1).
2
In most applications, the medium is transparent and, thus, its refractive index has no imaginary part.
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3.1.10
obscuration
optical concentration
percentage or fraction of incident light that is attenuated due to extinction (scattering and/or absorption) by the
particles (obscuration = 1 – transmission, when expressed as a fraction.)
3.1.11
optical model
theoretical model used for computing the model matrix for optically homogeneous spheres with, if necessary,
a specified complex refractive index, e.g. calculation by Fraunhofer diffraction or Mie scattering
3.1.12
reflection
change of direction of a light wave at a surface without a change in wavelength or frequency
3.1.13
refraction
change of the direction of propagation of light determined by change in the velocity of propagation in passing
from one medium to another; in accordance with Snell's law
3.1.14
repeatability (instrument)
closeness of agreement between multiple measurement results of a given property in the same dispersed
sample aliquot, executed by the same operator in the same instrument under identical conditions within a
short period of time (NOTE: this type of repeatability does not include variability due to sampling and
dispersion)
3.1.15
repeatability (method)
closeness of agreement between multiple measurement results of a given property in different aliquots of a
sample, executed by the same operator in the same instrument under identical conditions within a short period
of time (NOTE: this type of repeatability includes variability due to sampling and dispersion)
3.1.16
reproducibility (method)
closeness of agreement between multiple measurement results of a given property in different aliquots of a
sample, prepared and executed by different operators in similar instruments according to the same method
3.1.17
scattering
general term describing the change in propagation of light at the interface of two media having different optical
properties
3.1.18
scattering angle
angle between the principal axis of the transmitted light beam and the scattered light
3.1.19
scattering pattern
angular or spatial pattern of light intensities [/(θ) and /(r) respectively] originating from scattering, or the related
energy values taking into account the sensitivity and the geometry of the detector elements
3.1.20
single scattering
scattering whereby the contribution of a single member of a particle population to the total scattering pattern
remains independent of the other members of the population
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3.1.21
single shot analysis
analysis, for which the entire content of a sample container is used
3.1.22
transmission
percentage or fraction of incident light that remains un-attenuated by the particles (transmission = 1 –
obscuration, when expressed as fraction)
3.1.23
width of size distribution
the width of the particle size distribution (PSD), expressed as the x /x ratio
90 10
NOTE For normal (Gaussian) size distributions, often the standard deviation (absolute value) or the coefficient of
variation (relative percentage) is used. Then, about 95 % of the population of particles falls within ± 2 standard deviations
from the mean value and about 99,7 % within ± 3 standard deviations from the mean value. The difference x – x
90 10
corresponds to 2,6 σ.
3.2 Symbols
A
extinction coefficient of size class i
i
a distance from scattering object to detector
b
illuminated path length containing particles, mm
C particulate concentration, volume fraction
CV coefficient of variation, %
f focal length of lens, mm
angular intensity distribution of light scattered by particles (scattering pattern)
I(θ)
I
Intensity of horizontally polarised light at a given angle
h
I(r) spatial intensity distribution of light scattered by particles on the detector elements (measured
scattering pattern by detector)
I Intensity of vertically polarised light at a given angle
v
i
square root of (-1)
i photocurrent of detector element n, μA
n
k
wave number: 2π/λ
k
imaginary (absorption) part of particle's refractive index
p
L vector of photocurrents (i , i ,. i )
1 2 n
M
model matrix, containing calculated detector signals per unit volume of particles in all size classes
m relative, complex refractive index of particle to medium
n
real part of refractive index of medium
m
n real part of refractive index of particle
p
N complex refractive index of particle
p
O obscuration (1 – transmission)
r radial distance from focal point in focal plane, μm
V vector of volume concentrations in size classes (V , V , … V )
1 2 i
V volume concentration of size class i
i
v velocity of particles in dry disperser
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x
particle diameter, μm
x median particle diameter, μm; here used on a volumetric basis, i.e. 50 % by volume of the particles is
50
smaller than this diameter and 50 % is larger
x particle diameter corresponding to 10 % of the cumulative undersize distribution (here by volume), μm
10
x particle diameter corresponding to 90 % of the cumulative undersize distribution (here by volume), μm
90
α dimensionless size parameter: π x/λ
scattering angle with respect to forward direction
θ
θ angle with respect to perpendicular at boundary for a light beam in medium (as used in Snell's law;
m
see refraction)
θ angle with respect to perpendicular at boundary for a light beam in particle (as used in Snell's law;
p
see refraction)
wavelength of illuminating light source in vacuum, nm
λ
σ standard deviation
4 Principle
A representative sample, dispersed at an adequate concentration in a suitable liquid or gas, is passed through
the beam of a monochromatic light source, usually a laser. The light scattered by the particles, at various
angles, is measured by multi-element detectors and numerical values relating to the scattering pattern are
recorded for subsequent analysis. These numerical scattering values are then transformed, using an
appropriate optical model and mathematical procedure, to yield the proportion of the total volume of particles
to a discrete number of size classes forming a volumetric particle size distribution.
The laser diffraction technique for determination of particle size distributions is based on the phenomenon that
particles scatter light in all directions with an intensity pattern that is dependent on particle size. Figure 1
illustrates this dependency in the scattering patterns for two sizes of spherical particles. In addition to particle
size, particle shape and the optical properties of the particulate material influence the scattering pattern.
a) b)
Figure 1— Scattering pattern for two spherical particles: the particle generating pattern a) is twice as
large as the one generating pattern b) (simulated images for clarity)
5 Laser diffraction instrument
A set-up for a laser diffraction instrument is given in Figure 2.
In this Fourier set-up, a light source (typically a laser or other narrow-wavelength source) is used to generate
a monochromatic, coherent, parallel beam. This is followed by a beam processing unit, usually a beam
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expander with integrated filter, producing an extended and nearly ideal beam to illuminate the dispersed
particles.
Key
1 Obscuration/optical concentration detector 7 Light source (e.g. laser)
2 Scattered beam 8 Beam processing unit
3 Direct beam 9 Working distance of lens 4
4 Fourier lens 10 Multi-element detector
5 Scattered light not collected by lens 4 11 Focal distance of lens 4
6 Ensemble of dispersed particles
Figure 2 Fourier set-up of a laser diffraction instrument
A representative sample of particles, dispersed at an adequate concentration, is passed through the light
beam in a measuring zone by a transporting medium (gas or liquid). This measuring zone should be within the
working distance of the lens used. Sometimes, the particle stream in a process passes directly through the
laser beam for measurement. This is the case in measurement of sprays and aerosols. In other cases (such
as emulsions, pastes and powders), representative samples can be dispersed in fluids and caused to flow
through the measurement zone. Often dispersants (wetting agents; stabilisers) and/or mechanical forces
(agitation; sonication) are applied for de-agglomeration of particles and for stabilisation of the dispersion. For
these liquid dispersions a recirculation system is most commonly used, consisting of an optical measuring cell,
a dispersion bath usually equipped with stirrer and ultrasonic elements, a pump and tubing.
Dry powders can also be converted into aerosols through application of dry powder dispersers, which apply
mechanical forces for de-agglomeration. Here a dosing device feeds the disperser with ideally a near-constant
mass flow of sample. The disperser uses the energy of a compressed gas or the differential pressure to a
vacuum to disperse the particles. It outputs an aerosol that is blown through the measuring zone, usually into
the inlet of a vacuum pipe that collects the particles. Coarse, non-agglomerated powders can be transported
through the measurement zone by gravity.
There are two positions in which the particles can enter the laser beam. In the Fourier optics case the particles
enter the parallel beam before and within the working distance of the collecting lens (see Figure 3a). This
allows for the measurement of spatially extended particle systems. In the Reverse Fourier optics case the
particles enter behind the lens and, thus, in a converging beam (see Figure 3b).
The advantage of the Fourier set-up is that a reasonable path length for the sample is allowed within the
working distance of the lens. The Reverse Fourier set-up demands small path lengths but provides one
solution that enables the measurement of scattered light at larger angles.
The interaction of the incident light beam and the ensemble of dispersed particles results in a scattering
pattern with different light intensities scattered at various angles (see Annex A for theoretical background of
laser diffraction). The total angular intensity distribution I(θ), consisting of both direct and scattered light, is
then focused by a positive lens or an ensemble of lenses onto a multi-element detector. The lens(es)
provide(s) for a scattering pattern which, within limits, is not dependent upon the location of the particles in the
light beam. The continuous angular intensity distribution I(θ) is converted into a discrete spatial intensity
distribution I(r) on a set of detector elements.
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Key
1 Detector 4 Working distance
2 Fourier lens 5 Focal distance
3 Ensemble of dispersed particles
a) Fourier set-up: particles are in parallel beam before and within working distance of lens
Key
1 Detector
2 Flow through cuvette for dispersed particles
3 Particle
b) Reverse Fourier set-up: particles are in converging beam between lens and detector
Figure 3 Illustrations of optical arrangements used in laser diffraction instruments
Some instruments contain extra features to improve particle size analysis:
• An extra light source at the same optical axis having a different wavelength.
• One or more off-axis light sources, either at less or at more than 90 degrees with respect to the optical
axis.
• Polarisation filters for light source and detectors.
• Scattered light detectors at angles smaller than 90 degrees but larger than the conventional angular
range (forward scattering).
• Scattered light detectors at around 90 degrees for measurement of intensities in different polarisation
directions.
• Scattered light detectors at angles larger than 90 degrees (backscattering).
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These possibilities are illustrated in Figure 4.
11
9
8
10
7
14
6
1
5
12
2
4
13
3
Key
1 Light source assembly including beam 8 Low angle detector(s), either bespoke
expansion and/ or collimation design or pixel array
2 Light source wavelength 1 9 Transmission or obscuration detector
3 Light source wavelength 2 10 High angle detector array
4 Beam switching arrangement 11 Horizontally polarised light detector
5 Reverse Fourier lens(es) position 12 Vertically polarised light detector
6 Measurement cell or general measurement zone 13 Alternative entry point for light source
7 Fourier lens(e s) position 14 Alternative entry point for light source
Figure 4 Possibilities for optical arrangements in laser diffraction instrument
It is assumed that the recorded scattering pattern of the particle ensemble is identical to the sum of the
patterns from all individual particles (single scattering). Furthermore, the scattering pattern is assumed to
come from spherical particles.
Detection of the scattering pattern is done by a number of silicon detectors or photodiodes and/or a pixel array
detector. These detectors convert the spatial intensity distribution I(r) into a series of photocurrents i .
n
Subsequent electronics then convert and digitize the photocurrents into a set of energies L , representing the
n
scattering pattern. A central element measures the intensity of the scattered and non-scattered light and, thus
with a calculation, provides a measure of optical concentration or obscuration. Some instruments provide
special geometries of the central element in order to automatically re-centre or re-focus the detector by
moving the detector or the lens. It is desirable that the detector elements are positioned so as to prevent the
light reflected from internal surfaces from re-traversing the optical system.
A computer controls the measurement and is used for storage and manipulation of the detected signals, for
storage and/or calculation of a proper form of the optical model (usually as a model matrix containing light
scattering vectors per unit of volume per size class, scaled to the detector's geometry and sensitivity) and for
calculation of the particle size distribution (see Annex A for theoretical background of laser diffraction). Also it
may provide automated instrument operation.
Significant differences exist, both in hardware and software, not only between instruments from different
manufacturers but also between different types from one company. The instrument specifications should give
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adequate information for proper judgement of these differences. Annex B contains recommendations for the
specifications of laser diffraction instruments.
6 Operational procedures
6.1 Requirements
6.1.1 Instrument location
The instrument should be located in a clean environment that is free from excessive electrical noise,
mechanical vibration and temperature fluctuations and is out of direct sunlight and airflows. The operating
area should conform to local health and safety requirements. The instrument should either contain a rigid
internal optical bench or be installed on a rigid table or bench to avoid realignment of the optical system at
frequent intervals.
WARNING The radiation of instruments equipped with a laser can cause permanent eye damage.
Never look into the direct path of the laser beam or its reflections. Avoid blocking the laser beam with
reflecting surface
...
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