ISO 13320:2009

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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©
International Organization for Standardization, 2007

ISO/DIS 13320
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ii ISO 2007 – All rights reserved

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

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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.

iv © ISO 2007 – All rights reserved

ISO/CD 13320
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.

ISO/CD 13320
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.

ISO/CD 13320
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
3.1.3
complex refractive index
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
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)

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).
In most applications, the medium is transparent and, thus, its refractive index has no imaginary part.
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ISO/CD 13320
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
ISO/CD 13320
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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ISO/CD 13320
x
particle diameter, μm
x median particle diameter, μm; here used on a volumetric basis, i.e. 50 % by volume of the particles is
smaller than this diameter and 50 % is larger
x particle diameter corresponding to 10 % of the cumulative undersize distribution (here by volume), μm
x particle diameter corresponding to 90 % of the cumulative undersize distribution (here by volume), μm
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
ISO/CD 13320
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.
6 © ISO 2007 – All rights reserved

ISO/CD 13320
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).
ISO/CD 13320
These possibilities are illustrated in Figure 4.

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
8 © ISO 2007 – All rights reserved

ISO/CD 13320
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 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 preparation of liquid dispersions of powders. Annex C provides requirements for 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 hazardous vapour
concentrations. Evaporation of volatile organic liquids may cause sufficient cooling as to induce fluctuating
refractive index values in the liquid medium, which in turn may induce artefacts in the particle size results.
6.1.3 Dispersion gases
For dry dispersion and spray applications a compressed gas can be used. If used, it is essential that it is free
from oil, water and particles. To achieve this, a dryer with a filter is required. In spray applications, it is
essential that evaporation of the liquid does not cause artefacts in the particle size results. Any vacuum unit
should be located well away from the measurement zone, so that the output of the hot air does not disturb the
measuring zone. Draught should be avoided in order to avoid unstable particulate streams.
6.2 Sample inspection, preparation, dispersion and concentration
6.2.1 Sample inspection
Inspect the material to be analysed, visually or with the aid of a microscope, (1) to estimate the size range and
particle shape and (2) to check whether the particles have been dispersed adequately.
The size distribution measured in a sample is only valid for a batch of material if the sample is representative
for that batch and has been dispersed adequately.
6.2.2 Preparation
Prepare a representative sample of suitable volume for the measurement by an adequate sample splitting
technique, for instance a rotating riffler (ISO/FDIS 14488).
ISO/CD 13320
Very small samples can be taken out of a well-mixed paste of particles in liquid. The consistency of the paste
then minimises segregation errors. The pastes are formed by adding dispersant to the sample drop by drop
while mixing it with a spatula. A good consistency for the paste is one like honey or toothpaste. If, by mistake,
the paste becomes too fluid, it shall not be used, and a new preparation shall be initiated.
If the maximum size exceeds the measuring range, remove the material that is too coarse, e.g. by pre-sieving.
In this case determine and report the amount/percentage removed.
Sprays, aerosols and gas bubbles in liquid are usually measured directly, provided that their concentration is
at an adequate level (see 6.2.3 and 6.2.4), since sampling or dilution is generally very difficult without altering
the particle size distribution. If droplets are sprayed into still air, then the small droplets will decelerate faster
than the large ones, leading to a potential velocity bias. Therefore, it is preferable to spray into suitable moving
air stream matched to that of the spray. Consideration should also be given to the prospect of droplet
evaporation, which may cause significant errors, especially for droplets in the (sub-) micrometer range. First,
the fast evaporation of such droplets will reduce their size or even make them disappear. Moreover, artefacts
in the size distribution may appear due to a changing refractive index around the droplets, resulting from the
evolving vapour and the temperature decrease during evaporation.
6.2.3 Dispersion
6.2.3.1 General
Dry powders can be dispersed either in air or in a liquid. The dispersion procedure should be adjusted to the
purpose of the measurement, e.g. it has to be decided whether agglomerates should be detected or dispersed
to primary particles.
The transport conditions for the particles through the measurement zone should also be considered. Adequate
flow should be applied to ensure that particles of all sizes pass the measurement zone at similar velocity in
order to avoid velocity bias in the result. Particles, having a high aspect ratio, have a tendency to show
preferred orientations at the flow conditions existing in the measurement cell. Even at turbulent conditions
their orientation may not be fully random. In Annex A it will be discussed that different orientations of non-
spherical particles will lead to different scattering patterns and, thus, different sizing results.
6.2.3.2 Dispersion in air
For dispersion in air, an adequate dry disperser should be applied. For coarse, free-flowing particles, a free
fall by gravity is usually sufficient for dispersion. For agglomerated particles, compressed air or vacuum is
generally required for dispersion by shear stress with the assistance of mechanical de-agglomeration by
particle-particle or particle-wall collisions (see Figure 5). The complete fractional sample shall be used for the
measurement. All particles should ideally have the same approximate velocity in the measurement zone.
Often, large sample quantities are used for dry dispersion, which can assist the representation of coarse
particles in a wide size distribution. It is necessary to check that comminution of the particles does not occur
and conversely that a good dispersion has been achieved. This is often done by direct comparison of dry
dispersion with a liquid one: ideally, the results should be the same. Another means for checking the degree of
dispersion or comminution is by changing the dispersing energy (e.g. the primary air pressure) and monitoring
the change of the size distribution. Usually upon increasing the dispersing energy the amount of fines is
increased at first, due to improved dispersion. Then, sometimes a point is reached, where the size distribution
is nearly constant with increasing energy. At still higher energies the amount of fines may rise again as a
result of comminution. If such a plateau is reached, its centre defines the optimum dispersing energy. (NOTE:
a plateau is not usually found, e.g. in case of highly aggregated or fragile particles).

10 © ISO 2007 – All rights reserved

ISO/CD 13320
a) Velocity gradients caused by b) Particle to particle collisions c) Particle to wall collisions
shear stress
Figure 5  Processes involved for dry dispersion of powders
6.2.3.3 Dispersion in liquid media
For the preparation of liquid dispersions reference is made to ISO 14887. A variety of liquids is available.
Annex C contains guidelines on the selection of an appropriate liquid for wet dispersion. Generally, pasting,
stirring and sonication can be used to facilitate proper dispersion of particles in the liquid. A preliminary check
on the dispersion quality can be made by visual/microscopic inspection of the suspension. Also, it is possible
to perform some measurements of the suspension in the laser diffraction instrument, with intermediate
sonication: the measured size distribution should not change significantly if the sample is well dispersed and
the particles are neither fragile nor soluble.
NOTE The minimum volume of sample, required for repeatable measurement, increases as the width of the size
distribution becomes greater in order to allow a sufficient number of large particles to be present (see ISO/FDIS
14488). The volume of the dispersion fluid required to suspend these samples increases accordingly if the limits of
optical concentration are to be observed.
For example, ISO/FDIS 14488 demands for a powder containing particles in the broad size range of 2 μm to
200 μm, a true sample volume of at least 0,3 ml is required for a precision of 3% for the x . This will require at
least 500 ml of suspension fluid to ensure single scattering. The measurement time (or the number of detector
readings that are averaged for a measurement) should be sufficient to ensure that an adequate representation
of all particle sizes is reached. Appropriate conditions should be established experimentally, in relation to the
desired precision.
6.2.4 Concentration
The particle concentration in the measurement zone should be high enough to produce an adequate signal (or
in other words to reach an acceptable signal-to-noise ratio with respect to precision), yet low enough to ensure
multiple scattering to be insignificant to the particle size result.
The effect of multiple scattering is generally to increase the angle of scattering and, thus, to shift the size
distribution results to lower sizes. An exact concentration range can not be given, as it is a function of particle
size, particle size distribution (PSD) width, laser beam width and path length of the dispersed particles in the
measurement zone. As an indication it can be said that the typical volumetric concentration for analysis of 1
μm particles is about 0,002 % – for measurement in a cell with 2 mm path length – whereas the concentration
for 100 μm particles could be about 0,2 %. Check the instrument documentation for additional information.
Some guidance can be taken from the measured obscuration or transmission value, which is for the above
examples about 5 % and 25 %, respectively. In general, the proportion of small particles in a size distribution
dominates in the upper concentration limit. If all the particles are larger than 100 μm, then an obscuration of
up till 30 % may not cause multiple scattering. To ensure appropriate obscuration limits one should perform
particle size measurements at different concentration levels for the material of interest and monitor shifts in
the distribution. Annex A.9 provides some information on the relation between particulate concentration,
particle size and obscuration.
ISO/CD 13320
6.3 Measurement
6.3.1 Procedure
A typical measurement of a particle size distribution by laser diffraction comprises the following steps:
a) Setting up instrument and blank measurement
After selection of the appropriate particle size range and proper optical alignment, a blank measurement
is performed immediately prior to the sample measurement in which a particle-free dispersion medium is
used under the same instrument conditions to be employed for the sample measurement. These
background signals are used (1) to check the proper functioning of the instrument and (2) to be
subtracted later from the detector signals coming from the measurement of the material of interest.
b) Sample preparation
A sample is prepared and dispersed according to Section 6.2. The sample should be representative for
the batch of product within a stated confidence interval. The amount of test sample should correspond to
at least the minimum required for precision. The dispersion conditions should lead to complete de-
agglomeration without comminution and to a sufficiently low concentration to ensure single scattering.
c) Data collection of the scattering pattern
The measuring time for data collection should be sufficient to allow a statistically adequate representation
of the sample. Check therefore the effect of the elapsed measurement duration on the sizing result. For
each detector element an average signal is calculated, sometimes together with its standard deviation.
Net signals may be calculated by subtraction of the background signals. The magnitude of the signal from
each detector element depends upon the detection area, the light intensity and the quantum efficiency.
The coordinates (size and position) of the detector elements together with the focal distance of the lens
determine the region of scattering angles for each element. Generally all these factors are factory
determined and stored in the computer.
Most instruments also measure the power of the central laser beam. The fractional difference between a
dispersed sample and a blank experiment is given as a value of obscuration or transmission, which is
indicative of the total amount of scattered light and the particle concentration.
d) Selection of an appropriate optical model
Most often either the Mie theory or the Fraunhofer approximation is used for calculation of a scattering
matrix, which represents the signal at each detector element per unit volume of particles in given size
classes. The choice depends upon the size range of the particles to be measured, their optical properties
and the application (see Annex A). Other light scattering theories may be applied for calculation of this
scattering matrix; however, such occurrences are uncommon.
When using the Mie theory, the refractive indices of particulate and medium, or their ratio, should be
established and entered into the instrument in order to allow calculation of the model matrix (see Annex D for
refractive index values of liquids and solids). For practical reasons, small values of the imaginary part of the
refractive index (about 0,01 – 0,03 i) are required to accommodate surface roughness of particles, where
some light is randomly scattered.

NOTE Good understanding of the influence of the complex refractive index in the light scattering from particles is
strongly advised in order to apply the Mie theory or the Fraunhofer approximation correctly. Inappropriate choice of
the optical model or of the values of the refractive index may result in significant bias of the resulting particle size
distribution. This bias often manifests itself as inappropriate quantities of material being subscribed to the size
classes at the lower end of the size distribution.
To obtain traceable results it is essential that the refractive index values are used as reported.
12 © ISO 2007 – All rights reserved

ISO/CD 13320
e) Conversion of scattering pattern into particle size distribution
This deconvolution step is the inverse of the calculation of a scattering pattern for a given particle size
distribution. Several mathematical algorithms have been developed for this purpose [5, 7, 8, 11, 14, 17].
They contain some weighting of deviations between measured and calculated scattering patterns (e.g.
least squares) and some constraints of the size distribution curve. These constraints restrict the final
particle size result to values for the quantity in each size class that are either positive or zero and limit the
differences between the quantities in subsequent size classes. A procedure [6] uses the observed
fluctuations of the detector signals to introduce proper weighting of these data and to calculate
confidence intervals for the particle size distribution.
6.3.2 Precautions
Before starting, and during any measurement, the instructions given in the instrument manual should
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