ISO 13320:2009

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 2009
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ii © ISO 2009 – All rights reserved

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

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.
iv © ISO 2009 – All rights reserved

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.
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
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
2 © ISO 2009 – All rights reserved

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.
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
4 © ISO 2009 – All rights reserved

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
smaller than this diameter and 50 % are larger
x
particle diameter corresponding to 10 % of the cumulative undersize distribution (here by volume)
x
particle diameter corresponding to 90 % of the cumulative undersize distribution (here by volume)
dimensionless size parameter: πxn /λ
α
m
∆Q
volume fraction within size class i
3,i
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.
6 © ISO 2009 – All rights reserved

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)
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.
8 © ISO 2009 – All rights reserved

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.
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 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, in order to: a) estimate the size
range and particle shape; and b) 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 using an adequate sample
splitting technique, e.g. a rotating riffler (ISO 14488).
Very small samples can be taken out of a well-mixed paste of particles in liquid. The consistency of the paste
then minimizes 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.
10 © ISO 2009 – All rights reserved

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 PSD. If droplets are sprayed into still air, then the small droplets decelerate faster than the large ones,
leading to a potential velocity bias. Therefore, it is preferable to spray into a 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. Firstly, the fast evaporation
of such droplets reduces their size or even makes 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. Annex A discusses the fact that different orientations of non-
spherical particles lead to different scattering patterns and, thus, different sizing results.
6.2.3.2 Dispersion in gas
For dispersion in gas, an adequate dry disperser should be applied. For coarse, free-flowing particles, free fall
by gravity is usually sufficient for dispersion. For agglomerated particles, compressed gas or vacuum is
generally required for dispersion by shear stress with the assistance of mechanical deagglomeration 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. 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 a dry with a liquid
dispersion: 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.

a)  Velocity gradients caused b)  Particle-to-particle collisions c)  Particle-to-wall collisions
by shear stress
NOTE For explanations of symbols, see 3.2.
Figure 5 — Processes involved in dry dispersion of powders
6.2.3.3 Dispersion in liquid media
For the preparation of liquid dispersions, refer 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.
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 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 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 for a precision of 3 % for the x . This requires 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 cannot be given, as it is a function of particle
size, PSD width, laser beam width and pathlength 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 pathlength — 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 to 30 % may not
cause multiple scattering. To ensure appropriate obscuration limits, perform particle size measurements at
different concentration levels for the material of interest, and monitor shifts in the distribution. Clause A.9
provides some information on the relation between particulate concentration, particle size and obscuration.
6.3 Measurement
6.3.1 Procedure
6.3.1.1 General
A typical measurement of a PSD by laser diffraction comprises the following steps:
6.3.1.2 Setting up instrument and blank measurement
After selection of the appropriate particle size range and proper optical alignment, perform a blank
measurement 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.
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6.3.1.3 Sample preparation
Prepare and disperse a sample according to 6.2. Ensure that the sample is 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 deagglomeration without
comminution and to a sufficiently low concentration to ensure single scattering.
6.3.1.4 Data collection of the scattering pattern
Allow a measuring time for data collection sufficient for 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 co-ordinates (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.
6.3.1.5 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 the 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, values of the imaginary part of the
refractive index (about 0,01i to 0,03i) are required to accommodate surface roughness of particles, where
some light is randomly scattered.
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
PSD. This bias often manifests itself as inappropriate quantities of material being ascribed 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.
6.3.1.6 Conversion of scattering pattern into PSD
This deconvolution step is the inverse of the calculation of a scattering pattern for a given PSD. Several
mathematical algorithms have been developed for this purpose (References [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 (Reference [6]) uses the observed
fluctuations of the detector signals to introduce proper weighting of these data and to calculate confidence
intervals for the PSD.
6.3.2 Precautions
6.3.2.1 Before starting, and during any measurement, follow the instructions given in the instrument
manual. Take the precautions in 6.3.2.2 to 6.3.2.10.
6.3.2.2 Before switching on the power to the instrument, make sure that all components of the system are
properly earthed (grounded). All the particle dispersing and transporting devices, such as the ultrasonic bath,
the dry disperser, the vacuum inlets and vacuum hoses, shall be earthed to prevent ignition of organic
solvents or dust explosions caused by electrostatic discharges.
6.3.2.3 After switching the power on, allow sufficient time for the instrument to stabilize. Gas lasers such
as the He-Ne laser require adequate warm-up time (usually more than 30 min).
6.3.2.4 Check the instrument status and, if necessary, set up the requi
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