EUROPEAN PHARMACOPOEIA 6.0 2.9.31.

Particle size analysis by laser light diffraction

the cumulative amount dissolved at each time point divided This chapter provides guidance for the measurement of size
by the surface area exposed. Linear regression is then distributions of particles in different dispersed systems, for
performed on the normalised experimental data relevant example, powders, sprays, aerosols, suspensions, emulsions,
to an appropriate time interval preceding the possible and gas bubbles in liquids, through analysis of their angular
disintegration of the compact. The intrinsic dissolution rate light-scattering patterns. It does not address specific
of the substance tested, expressed in milligrams per minute requirements of particle size measurement of specific
per square centimetre, is determined from the slope of the products.
regression line. The result for intrinsic dissolution rate must
be accompanied by a statement of the precise conditions of PRINCIPLE
compact preparation and test method (dissolution medium,
volume of medium used, stirring rate, temperature etc.). A representative sample, dispersed at an adequate
concentration in a suitable liquid or gas, is passed through
NOTE : when necessary and justified, an apparatus with a a beam of monochromatic light, usually a laser. The light
different configuration may be used, such as a die holder that
scattered by the particles at various angles is measured by a
holds the compact in a fixed vertical position, with agitation
multi-element detector. Numerical values representing the
provided by a paddle positioned at a defined distance from scattering pattern are then recorded for subsequent analysis.
the surface of the compact. These scattering pattern values are then transformed, using
an appropriate optical model and mathematical procedure, to
01/2008:20931
yield the proportion of total volume to a discrete number of
size classes, forming a volumetric particle-size distribution.
2.9.31. PARTICLE SIZE ANALYSIS
BY LASER LIGHT DIFFRACTION APPARATUS
The method is based on the ISO standards 13320-1(1999) An example of a set-up of a laser light diffraction instrument
and 9276-1(1998). is given in Figure 2.9.31.-1. Other equipment may be used.
INTRODUCTION The instrument comprises a laser light source, beam
processing optics, a sample measurement region (or cell), a
The laser light diffraction technique used for the
Fourier lens, and a multi-element detector for measuring the
determination of particle-size distribution is based on the
scattered light pattern. A data system is also required for
analysis of the diffraction pattern produced when particles
deconvolution of the scattering data into a volumetric size
are exposed to a beam of monochromatic light. Historically,
distribution and associated data analysis and reporting.
the early laser diffraction instruments only used scattering
at small angles. However, the technique has since been The particles can enter the laser beam in 2 positions. In
broadened to include laser light scattering in a wider angular the conventional case the particles enter the parallel beam
range and application of the Mie theory, in addition to the before the collecting lens and within its working distance. In
Fraunhofer approximation and anomalous diffraction. so-called reversed Fourier optics the particles enter behind
The technique cannot distinguish between scattering the collecting lens and thus, in a converging beam. The
by single particles and scattering by clusters of primary advantage of the conventional set-up is that a reasonable
particles, i.e. by agglomerates or aggregates. As most path length for the sample is allowed within the working
particulate samples contain agglomerates or aggregates and distance of the lens. The second set-up allows only small path
as the focus of interest is generally on the size distribution lengths but enables measurement of scattered light at larger
of primary particles, the clusters are usually dispersed into angles, which is useful when submicron particles are present.
primary particles before measurement. The interaction of the incident light beam and the ensemble
For non-spherical particles, an equivalent sphere-size of dispersed particles results in a scattering pattern with
distribution is obtained because the technique assumes different light intensities at various angles. The total angular
spherical particles in its optical model. The resulting intensity distribution, consisting of both direct and scattered
particle-size distribution may differ from those obtained light, is then focused onto a multi-element detector by a lens
by methods based on other physical principles (e.g. or a series of lenses. These lenses create a scattering pattern
sedimentation, sieving). that, within limits, does not depend on the location of the

1. Obscuration detector 5. Scattered light not collected by lens (4) 9. Working distance of lens (4)
2. Scattered beam 6. Particle ensemble 10. Multi-element detector
3. Direct beam 7. Light source laser 11. Focal distance of lens (4)
4. Fourier lens 8. Beam processing unit

Figure 2.9.31.-1. - Example of a set-up of a laser light diffraction instrument

General Notices (1) apply to all monographs and other texts 311
2.9.31. Particle size analysis by laser light diffraction EUROPEAN PHARMACOPOEIA 6.0

particles in the light beam. Hence, the continuous angular Optimisation of the liquid dispersion. Liquids, surfactants,
intensity distribution is converted into a discrete spatial and dispersing aids used to disperse powders must :
intensity distribution on a set of detector elements. — be transparent at the laser wavelength and practically free
It is assumed that the measured scattering pattern of the from air bubbles or particles ;
particle ensemble is identical to the sum of the patterns from — have a refractive index that differs from that of the test
all individual single scattering particles presented in random material ;
relative positions. Note that only a limited angular range — be non-solvent of the test material (pure liquid or
of scattered light is collected by the lens(es) and, therefore, pre-filtered, saturated solution) ;
by the detector.
— not alter the size of the test materials (e.g. by solubility,
DEVELOPMENT OF THE METHOD solubility enhancement, or recrystallisation effects) ;
Traditionally, the measurement of particle size using laser — favour easy formation and stability of the dispersion ;
diffraction has been limited to particles in the range of — be compatible with the materials used in the instrument
approximately 0.1 µm to 3 mm. Because of recent advances (such as O-rings, gaskets, tubing, etc.) ;
in lens and equipment design, newer instruments are capable — possess a suitable viscosity to facilitate recirculation,
of exceeding this range routinely. With the validation report stirring and filtration.
the user demonstrates the applicability of the method for Surfactants and/or dispersing aids are often used to wet
its intended use. the particles and to stabilise the dispersion. For weak acids
Sampling. The sampling technique must be adequate to and weak bases, buffering of the dispersing medium at low
obtain a representative sample of a suitable volume for the or high pH respectively can assist in identifying a suitable
particle-size measurement. dispersant.
Evaluation of the dispersion procedure. The dispersion A preliminary check of the dispersion quality can be
procedure must be adjusted to the purpose of the performed by visual or microscopic inspection. It is also
measurement. The purpose may be such that it is preferable possible to take fractional samples out of a well-mixed stock
to deagglomerate clusters into primary particles as far as dispersion. Such stock dispersions are formed by adding
possible, or it may be desirable to retain clusters as intact as a liquid to the sample while mixing it with, for example, a
possible. In this sense, the particles of interest may be either glass rod, a spatula or a vortex mixer. Care must be taken
primary particles or clusters. to ensure a representative transfer of the sample and that
For the development of a method it is highly advisable to settling of larger particles does not occur.
check that comminution of the particles does not occur, Optimisation of the gas dispersion. For sprays and dry
and conversely, that dispersion of particles or clusters powder dispersions, a compressed gas free from oil, water
is satisfactory. This can usually be done by changing and particles may be used. To remove such materials from
the dispersing energy and monitoring the change of the the compressed gas, a dryer with a filter can be used. Any
particle-size distribution. The measured size distribution vacuum unit should be located away from the measurement
must not change significantly when the sample is well zone, so that its output does not disturb the measurement.
dispersed and the particles are neither fragile nor soluble. In Determination of the concentration range. In order to
addition, the particles of interest can be inspected visually or produce an acceptable signal-to-noise ratio in the detector,
with the aid of a microscope. Moreover, if the manufacturing the particle concentration in the dispersion must exceed a
process (e.g. crystallisation, milling) of the material has minimum level. Likewise, it must be below a maximum level
changed, the applicability of the method must be verified in order to avoid multiple scattering. The concentration
(e.g. by microscopic comparison). range is influenced by the width of the laser beam, the path
Sprays, aerosols and gas bubbles in a liquid should be length of the measurement zone, the optical properties of
measured directly, provided that their concentration is the particles, and the sensitivity of the detector elements.
adequate, because sampling or dilution generally alters the In view of the above, measurements must be performed
particle-size distribution. at different particle concentrations to determine the
In other cases (such as emulsions, pastes and powders), appropriate concentration range for any typical sample
representative samples may be dispersed in suitable of material. (Note : in different instruments, particle
liquids. Dispersing aids (wetting agents, stabilisers) and/or concentrations are usually represented by differently scaled
mechanical forces (e.g. agitation, sonication) are often and differently named numbers, e.g. obscuration, optical
applied for deagglomeration or deaggregation of clusters and concentration, proportional number of total mass).
stabilisation of the dispersion. For these liquid dispersions, Selection of an appropriate optical model. Most instruments
a recirculating system is most commonly used, consisting of use either the Fraunhofer or the Mie theory, though other
an optical measuring cell, a dispersion bath usually equipped approximation theories are sometimes applied for calculation
with stirrer and ultrasonic elements, a pump, and tubing. of the scattering matrix. The choice of the theoretical model
Non-recirculating, stirred cells are useful when only small depends on the intended application and the different
amounts of a sample are available or when special dispersion assumptions (size, absorbance, refractive index, roughness,
liquids are used. crystal orientation, mixture, etc.) made for the test material.
Dry powders can also be converted into aerosols through If the refractive index values (real and imaginary parts
the use of suitable dry powder dispersers, which apply for the used wavelength) are not exactly known, then the
mechanical force for deagglomeration or deaggregation. Fraunhofer approximation or the Mie theory with a realistic
Generally, the dispersers use the energy of compressed estimate of the refractive index can be used. The former has
gas or the differential pressure of a vacuum to disperse the advantages that it is simple, it does not need refractive
the particles to an aerosol, which is blown through the index values and it is extremely useful for analysis of powders
measuring zone, usually into the inlet of a vacuum unit that coarser than about 1-2 µm ; the latter usually provides
collects the particles. However, for free flowing, coarser less-biased particle-size distributions for small particles. In
particles or granules the effect of gravity may be sufficient to order to obtain traceable results, it is essential to document
disperse the particles adequately. the refractive index values used, since small differences in

312 See the information section on general monographs (cover pages)

the values assumed for the real and imaginary part of the and calculated scattering patterns (e.g. least squares), some
complex refractive index may cause significant differences in constraints (e.g. non-negativity for amounts of particles),
the measured particle-size distributions. Small values of the and/or some smoothing of the size distribution curve.
imaginary part of the refractive index (about 0.01 - 0.1 i) are The algorithms used are specific to each make and model
often applied to allow the correction of the absorbance for of equipment, and are proprietary. The differences in the
the surface roughness of the particles. algorithms between different instruments may give rise to
Repeatability. The attainable repeatability of the differences in the calculated particle size statistics.
method mainly depends on the characteristics of the Replicates. It is recommended that the number of replicate
material (milled/not milled, robust/fragile, width of its size measurements (with individual sample preparations) to be
distribution, etc.), whereas the required repeatability depends performed per sample is defined, in a substance-specific
on the purpose of the measurement. Mandatory limits method.
cannot be specified in this monograph, as repeatabilities
(different sample preparations) may vary appreciably from REPORTING OF RESULTS
one substance to another. However, it is good practice to aim The particle size analysis data are usually reported as
at acceptance criteria for repeatability such as srel ≤ 10 per cumulative undersize distribution and/or as density
cent [n = 6] for any central value of the distribution (e.g. distribution by volume. The symbol x is used to denote the
for x50). Values at the sides of the distribution (e.g. x10 and particle size, which in turn is defined as the diameter of a
x90) are oriented towards less stringent acceptance criteria volume-equivalent sphere. Q3(x) denotes the volume fraction
such as srel ≤ 15 per cent [n = 6]. Below 10 µm, these values undersize at the particle size x. In a graphical representation,
must be doubled. x is plotted on the abscissa and the dependent variable Q3
on the ordinate. Most common characteristic values are
MEASUREMENT calculated from the particle size distribution by interpolation.
Precautions. The instructions given in the apparatus manual The particle sizes at the undersize values of 10 per cent,
are followed : 50 per cent, and 90 per cent (denoted as x10, x50, and x90
— never look into the direct path of the laser beam or its respectively) are frequently used. x50 is also known as the
reflections ; median particle size. It is recognised that the symbol d is
also widely used to designate the particle size, thus the
— earth all apparatus components to prevent ignition of symbol x may be replaced by d.
solvents or dust explosions ;
Moreover, sufficient information must be documented
— check the apparatus set-up (e.g. warm-up, required about the sample, the sample preparation, the dispersion
measuring range and lens, appropriate working distance, conditions, and the cell type. As the results depend on the
position of the detector, no direct bright daylight) ; particular instrument, data analysis program, and optical
— in the case of wet dispersions, avoid air bubbles, model used, these details must also be documented.
evaporation of liquid, schlieren or other inhomogeneities
in the dispersion ; similarly, avoid improper mass-flow CONTROL OF THE APPARATUS PERFORMANCE
from the disperser or turbulent air-flow in the case of dry Use the apparatus according to the manufacturer’s
dispersions ; such effects can cause erroneous particle-size instructions and carry out the prescribed verifications at an
distributions. appropriate frequency, according to the use of the apparatus
Measurement of the light scattering of dispersed sample(s). and substances to be tested.
After proper alignment of the optical part of the instrument, Calibration. Laser diffraction systems, although assuming
a blank measurement of the particle-free dispersion medium idealised properties of the particles, are based on first
must be performed. The background signal must be below principles of laser light scattering. Thus, calibration in the
an appropriate threshold. strict sense is not required. However, it is still necessary
Generally, the time for measurement permits a large number to confirm that the instrument is operating correctly. This
of detector scans or sweeps at short time intervals. For each can be undertaken using any certified or standard reference
detector element, an average signal is calculated, sometimes material that is acceptable in industrial practice. The entire
together with its standard deviation. The magnitude of measurement procedure is examined, including sample
the signal from each detector element depends upon collection, sample dispersion, sample transport through
the detection area, the light intensity and the quantum the measuring zone, measurement, and the deconvolution
efficiency. The co-ordinates (size and position) of the procedure. It is essential that the total operational procedure
detector elements together with the focal distance of the is fully described.
lens determine the range of scattering angles for each The preferred certified or standard reference materials
element. Most instruments also measure the intensity consist of spherical particles of a known distribution
of the central (unscattered) laser beam. The ratio of the ranging over one decade of size. They must be certified
intensity of a dispersed sample to that in its absence (a blank as to the mass-percentage size distribution by an absolute
measurement) indicates the proportion of scattered light and technique, if available, and used in conjunction with an
hence the particle concentration. agreed, detailed operation procedure. It is essential that the
Conversion of scattering pattern into particle-size real and imaginary parts of the complex refractive index
distribution. This deconvolution step is the inverse of the of the material are indicated if the Mie theory is applied
calculation of a scattering pattern for a given particle-size in data analysis. The representation of the particle-size
distribution. The assumption of spherical particle shape distribution by volume will equal that of the distribution by
is particularly important as most algorithms use the mass, provided that the density of the particles is the same
mathematical solution for scattering from spherical particles. for all size fractions.
Furthermore, the measured data always contain some The response of a laser diffraction instrument is considered
random and systematic errors, which may vitiate the size to meet the requirements if the mean value of x50 from at least
distributions. Several mathematical procedures have been 3 independent measurements does not deviate by more than
developed for use in the available instruments. They 3 per cent from the certified range of values of the certified
contain some weighting of deviations between measured or standard reference material, i.e. the mean value together

General Notices (1) apply to all monographs and other texts 313
2.9.33. Characterisation of crystalline solids by XRPD EUROPEAN PHARMACOPOEIA 6.0

with its standard deviation. The mean values for x10 and x90 particle orientation within the sample) ; and diffraction line
must not deviate by more than 5 per cent from the certified profiles (depending on instrumental resolution, crystallite
range of values. Below 10 µm, these values must be doubled. size, strain and specimen thickness).
Although the use of materials consisting of spherical Experiments giving angular positions and intensities of
particles is preferable, non-spherical particles may also be lines can be used for applications such as qualitative phase
employed. Preferably, these particles have certified or typical analysis (for example, identification of crystalline phases)
values from laser diffraction analyses performed according and quantitative phase analysis of crystalline materials. An
to an agreed, detailed operating procedure. The use of estimate of the amorphous and crystalline fractions(6) can
reference values from methods other than laser diffraction also be made.
may cause a significant bias. The reason for this bias is that In addition, analysis of line-profile broadening can also
the different principles inherent in the various methods may allow the determination of crystallite size (size of coherently
lead to different sphere-equivalent diameters for the same scattering domains) and micro-strain.
non-spherical particle.
The X-ray powder diffraction (XRPD) method provides an
In addition to the certified reference materials mentioned
advantage over other means of analysis in that it is usually
above, product samples of typical composition and
non-destructive in nature (specimen preparation is usually
particle-size distribution for a specified class of products
limited to grinding to ensure a randomly oriented sample).
can also be used, provided their particle-size distribution
XRPD investigations can also be carried out under in situ
has proven to be stable over time. The results must comply
conditions on specimens exposed to non-ambient conditions,
with previously determined data, with the same precision
such as low or high temperature and humidity.
and bias as for the certified reference material.
Verification of the system. In addition to the calibration, PRINCIPLE
the performance of the apparatus must be verified at regular
time intervals or as frequently as appropriate. This can be X-ray diffraction results from the interaction between
undertaken using any suitable material as mentioned in the X-rays and electron clouds of atoms. Depending on the
previous paragraph. atomic arrangement, interferences arise from the scattered
X-rays. These interferences are constructive when the path
The verification of the system is based on the concept that the difference between 2 diffracted X-ray waves differs by an
equipment, electronics, software and analytical operations integral number of wavelengths. This selective condition
constitute an integral system, which can be evaluated is described by the Bragg equation, also called Bragg’s law
as an entity. Thus the entire measurement procedure is (see Figure 2.9.33.-1) :
examined, including sample collection, sample dispersion,
sample transport through the measuring zone, and the
measurement and deconvolution procedure. It is essential
that the total operational procedure is fully described. The wavelength λ of the X-rays is of the same order of
In general, unless otherwise specified in the individual magnitude as the distance between successive crystal lattice
monograph, the response of a laser diffraction instrument is planes, or dhkl (also called ‘d-spacings’). θhkl is the angle
considered to meet the requirements if the x50 value does not between the incident ray and the family of lattice planes,
deviate by more than 10 per cent from the range of values of and sinθhkl is inversely proportional to the distance between
the reference material, i.e. the mean value together with its successive crystal planes or d-spacings.
standard deviation. If optionally the values at the sides of the The direction and spacing of the planes with reference to
distribution are evaluated (e.g. x10 and x90), then these values the unit cell axes are defined by the Miller indices {hkl}.
must not deviate by more than 15 per cent from the certified These indices are the reciprocals, reduced to the next-lower
range of values. Below 10 µm, these values must be doubled. integer, of the intercepts that a plane makes with the unit
cell axes. The unit cell dimensions are given by the spacings
a, b and c and the angles between them, α, β, and γ.
The interplanar spacing for a specified set of parallel hkl
01/2008:20933 planes is denoted by dhkl. Each such family of planes may
show higher orders of diffraction where the d values for the
2.9.33. CHARACTERISATION OF related families of planes nh, nk, nl are diminished by the
factor 1/n (n being an integer : 2,3,4, etc.).
CRYSTALLINE AND PARTIALLY Every set of planes throughout a crystal has a corresponding
CRYSTALLINE SOLIDS BY X-RAY Bragg diffraction angle, θhkl, associated with it (for a specific
POWDER DIFFRACTION (XRPD) wavelength λ).
A powder specimen is assumed to be polycrystalline so that
Every crystalline phase of a given substance produces a at any angle θhkl there are always crystallites in an orientation
characteristic X-ray diffraction pattern. allowing diffraction according to Bragg’s law(7). For a given
Diffraction patterns can be obtained from a randomly X-ray wavelength, the positions of the diffraction peaks (also
oriented crystalline powder composed of crystallites or referred to as ‘lines’, ‘reflections’ or ‘Bragg reflections’)
crystal fragments of finite size. Essentially 3 types of are characteristic of the crystal lattice (d-spacings), their
information can be derived from a powder diffraction theoretical intensities depend on the crystallographic unit
pattern : angular position of diffraction lines (depending on cell content (nature and positions of atoms), and the line
geometry and size of the unit cell) ; intensities of diffraction profiles on the perfection and extent of the crystal lattice.
lines (depending mainly on atom type and arrangement, and Under these conditions the diffraction peak has a finite
(6) There are many other applications of the X-ray powder diffraction technique that can be applied to crystalline pharmaceutical substances such as : determination of crystal structures,
refinement of crystal structures, determination of crystallographic purity of crystalline phases, characterisation of crystallographic texture, etc. These applications are not described in this chapter.
(7) An ‘ideal’ powder for diffraction experiments consists of a large number of small, randomly oriented spherical crystallites (coherently diffracting crystalline domains). If this number is
sufficiently large, there are always enough crystallites in any diffracting orientation to give reproducible diffraction patterns. To obtain a precise measurement of the intensity of diffracted X-rays,
it is recommended that the crystallite size be small, i.e. typically 10 µm or less, depending on the characteristics of the specimen (X-ray absorption, shape, etc.) and the diffraction geometry.

314 See the information section on general monographs (cover pages)