3
`
`Particle size analysis by image analysis
`
`3.1 Introduction
`
`A microscope examination should always be carried out whenever a sample
`is prepared for particle size analysis. Such an examination allows an
`estimate of the particle size range of the powder under test and its degree of
`dispersion. If the dispersion is incomplete it can be determined whether
`this is due to the presence of agglomerates or aggregates and, if
`agglomeration is present, may
`indicate the need for an alternative
`dispersing procedure.
`Microscopy is often used as an absolute method of particle size analysis
`since it is the only method in which the individual particles are observed
`It is particularly useful in aerosol science where
`and measured [1-3].
`particles are often collected in a fonn suitable for subsequent optical
`examination. It is useful not only for particle size measurement but also for
`particle shape and texture evaluation, collectively called morphology, with
`sensitivity far greater than other techniques. Reports have also been
`presented of the use of microscopy to relate particle size to processing
`characteristics of valuable mineral ores [4,5]. Particle shape may be defined
`either qualitatively or quantitatively. The fonner includes the use of such
`tenns as acicularity, roundness and so on. The latter, more definitively,
`compares perpendicularly oriented diameters, for example, to obtain shape
`factors. The introduction of automatic image analyzers al lows for the
`factors which were previously
`detennination of complex shape
`unobtainable. These factors are of great value in defining crystal
`morpho logy and relating this to operating (attrition during conveying,
`compaction and so on) and end-use properties.
`A size analysis by number is simpkr to perform than an analysis by
`mass since, in the former, the statistical reliability depends solely on the
`number of particles measured. For a mass analysis the omission of a single
`I 0 µm particle leads to the same error as the omission of a thousand I µm
`
`

`

`Image analysis
`
`143
`
`particles since they both have the same volume. For a particle size analysis
`by mass, 25 particles in the largest size category have to be counted, in
`order to obtain an estimated standard error of less than 2%.
`If all the
`particles in this area were counted the final count would run into millions.
`It is obvious therefore that the area to be examined must decrease with
`decreasing particle size and the results obtained must be presented as
`particles per unit area.
`The problem may be likened to determining the size distribution of a
`number of differently sized homogeneous balls in a container. If the balls
`are of size 2, 2'12, 4, 4'12·· · ·· ··64, 64'12, in line with the size ratios often
`adopted in optical microscopy, and the relative frequency of the top size
`category is found to be 8 in 1000 particles this can be readily converted to a
`mass frequency when the number of balls in the other size categories is
`known. If the estimated mass of the 25 particles is 10% of the sample then
`If, on
`the forecasted percentage standard error is ( 10/'125) i.e. 2%.
`completing the analysis, the mass percentage of the coarsest fraction is
`greater than 10% then it is necessary to count more coarse particles in order
`to maintain this level of accuracy.
`The errors in converting from a number to a volume (mass) distribution
`are greatest when the size range is wide. For a narrowly classified powder,
`ranging in size from say I 0 to 30 µm, it is necessary to use an arithmetic
`grading of sizes, probably a 2 µm interval in this case, but the same rules
`still apply and the direct conversion of a number distribution to a weight
`distribution can still give rise to considerable error at the coarse end of the
`size distribution. Using closer size intervals adds little to analytical
`accuracy but can greatly increase the computation time.
`The images may be viewed directly or by projection. Binocular
`eyepieces are preferred for particle examination but monoculars for
`carrying out a particle size analysis since, by using a single eyepiece, the
`tube length can be varied to give stepwise magnification. Most
`experienced operators prefer direct viewing but projection viewing, less
`tiring to the eye, is often used for prolonged counting. Projection may be
`front or back. With the former the operation is carried out in a darkened
`room due to the poor contrast attainable. Back projection gives better
`illumination but image definition is poor; this can be rectified by using a
`system whereby two ground-glass screens are placed with their faces in
`contactt and one is moved slowly relative to the other [6].
`Some automatic counting and sizing devices work from photographic
`negatives or positives. The principle objection that can be leveled against
`photographic methods is that only particles in focus can be measured
`accurately and this can lead to serious bias. Although photographic
`
`

`

`144 Powder sampling and particle size determination
`
`methods are often convenient and provide a permanent record, the
`processing time may well offset any advantage obtained. This is
`particularly true when a weight count is required since, from statistical
`considerations, a large number of fields of view are required for accurate
`results.
`Light microscopy is best suited for the size range 0.8 to 150 µm, with a
`resolution of around 0.2 µm depending on the wavelength of the light
`source. Scanning ele-ctron microscopy (SEM) operates in the size range
`from 0.1 µm to I 000 µm with a resolution of I 0 nm and transmission
`electron microscopy (TEM) from 0.0 l µm to I 0 µm with a resolution of
`5 nm. Back scattered electrons and x-rays contain information on the
`chemistry and average atomic number of the material under the beam.
`Groen et. al. [7] determined the optimum procedure for automatic
`focusing of a microscope. Kenny [8] examined the errors associated with
`detecting the edge of the particle image and outlined a technique, suitable
`for automatic image analysis for minimizing this error.
`The shape and texture of construction aggregates are important
`parameters that have a direct bearing on the strength and durability of their
`asphalt and concrete end products. Typically, a batch of material is
`rejected if more than a specific fraction of particles have elongation and
`flatness ratio that exceed some limit.
`Jn the ASTM procedure [9] the
`measurements are carried out on l 00 particles using specially designed
`calipers. More recently this has been replaced by image analysis which
`reduces the measurement time to less than 10 minutes [IO]. In addition,
`is capable of conducting other useful particle
`this procedure
`characterization measurements without the need for additional image
`processing time. One such measurement incorporated into the design is
`roughness defined as '"surface irregularity" and 'jaggedness".
`Examples of determining both a number and a mass distribution are
`given below. Although the examples relate to manual counting, the
`conditions also govern size analyses by automatic image analyzers.
`
`3.2 Standards
`
`Relevant national standards are available covering particle size analysis by
`microscopy. BS 3406 Part 4 [11] is the British Standard guide to optical
`microscopy. The American standard ASTM E20 was discontinued in 1994
`[12). ASTM 175-82 [13]
`is a standard defining terminology for
`microscope related applications. ASTM E766-98 [14] is a standard
`practice for calibrating the magnification of an SEM. NF X 11-661 [ 15] is
`the French standard for optical microscopy. NF XI 1-696 [16] covers
`
`

`

`Image analysis
`
`145
`
`ISO/CD 13322 [I 7] is a draft
`general image analysis techniques.
`international standard on image analysis methods.
`
`3.3 Optical microscopy
`
`Optical microscopy is most often used for the examination of particles from
`about 3 µm to 150 µm in size, although a lower limit of 0.8 µm is often
`quoted. Above 150 µm a simple magnifying glass is suitable.
`The most severe limitation of optical transmission microscopy is its
`small depth of focus, which is about 10 µmat a magnification of lOOx and
`about S µm at I OOOx. This means that, for a sample having a wide range of
`sizes, only a few particles are in focus in any field of view. Further, in
`optical transmission microscopy, the edges of the particles are blurred due
`to diffraction effects. This is not a problem with particles larger than about
`5 µm s ince they can be studied by reflected light, but only transmission
`microscopy, with which silhouettes are seen, can be used for smaller
`particles.
`A two dimensional array of latex spheres is often used for measuring
`more or less uniformly sized lattices. Hartman [18-20] investigated the
`errors
`in
`this method which comprise focusing,
`image distortion,
`misreading of photomicrographs, distortions in the photographic material,
`anisotropy, other array defects, non-uniformity of particle size, coating of
`solutes on the lattices and contact deformation. Hartman introduced a new
`method, the center finding technique in which the latex spheres acts as
`lenses enabling the center-to-center distance to be determined with high
`accuracy (10 ± 0.4) µm for 10 µm particles. The National Physical
`Laboratory [21] introduced an NPL certified stage graticule [22] to test
`linearity over the complete image field.
`
`3.3.1 Upper size limit for optical microscopy
`
`The method is preferably limited to sub-200 mesh sieve size (75 µm) but
`larger particles may be counted and sized provided their fractional weight
`is less than 10% of the total weight of the powder. When the fractional
`oversize weight exceeds I 0%, these particles should be removed and a
`sieve and microscope analyses merged. Alternatively such large particles
`can be sized using a simple magnifying glass.
`
`

`

`146 Powder sampling and particle size determination
`
`3.3.2 Lower size limit/or optical microscopy
`
`The theoretical limit of resolution of an optical microscope is expressed by
`the fundamental formula:
`
`d _JA.
`l - NA
`
`(3.1)
`
`where dl is the limit ofresolution, i.e. particles in closer proximity than this
`appear as a single particle, A, is the wavelength of the illuminant, the
`numeriical aperture of the objective NA = µsin(} whereµ is the refractive
`index of the immersion medium, 0 is the angular aperture of the objective
`and f is a factor of about 0.6 to allow for the inefficiency of the system.
`For A,= 0.6 µm the resolving power is a maximum with NA = 0.95 (dry)
`and NA= 1.40 (wet) giving lower size limits, dmin = 0.38 µm and 0.26 µm
`respectively. The images of particles having a separation of less than these
`limits merge to form a single image.
`The resolution of the human eye is around 0.3 mm, therefore the
`maximum effective magnification with white light is:
`
`30mm~ 1000
`28µm
`
`Particles smaller than the limit of resolution appear as diffuse circles;
`image broadening occurs, even for particles larger than dmin.> and this
`results in oversizing. Some operators routinely size down to this level but
`the British Standard BS 3406 Part 4 [l l] is probably correct in stipulating a
`minimum size of 0.8 µm and limited accuracy from 0.8 to 2.3 µm.
`Powders containing material smaller than this are usually imaged by
`transmission or scanning electron microscopy and the resulting negatives or
`prints examined.
`Charmain (23) in an investigation into the accuracy of sizing by
`transmission optical microscopy, showed
`that for
`two-dimensional
`silhouettes greater than I µm in diameter, the estimated size under ideal
`conditions was about 0.13 µm too high; a 0.5 µm silhouettes gave a visual
`estimate of 0.68 µm and all silhouettes smaller than 0.2 µm appeared to
`have a diameter of 0.5 µm (Figure 3. I). The measurements were made
`with the circular discs immersed in oil. Due to less precise focusing with
`three-dimensional particles, real particles are subject to greater errors.
`
`

`

`Image analysis
`
`147
`
`Rowe [24] showed that wide differences m particle sizing can occur
`between operators because of this effect.
`
`3.4 Sample preparation
`
`Great care has to be taken in slide or grid preparation since the
`measurement sample is so small that it is difficult to make it representative
`of the bulk. Many particulate systems contain agglomerates and aggregates
`and, if it is necessary that they retain their integrity, the dispersing
`procedure needs to be very gentle. Further, since it is usually impossible to
`measure every particle in the measurement sample it is necessary that it be
`dispersed uniformly. Small regions selected at random or according to
`some predetermined plan must therefore be representative of the w hole.
`The ana lysis is suspect if the regions in o ne area of the measurement
`sample give a very different size distribution to those in another area.
`The simplest procedure
`is
`to extract samples from an agitated
`suspension; for less robust materials a procedure detailed in reference [3]
`may be used in which an air j et circulates the suspension through a
`sampling tube that can be closed and withdrawn to provide samples for
`analysis.
`S lides may be of three main types: dry, temporary and
`permanent. For very easily dispersed materia l, the particles may be
`
`3.0
`Visual
`estimate
`(µm)
`
`2.0
`
`1.0
`
`, , ,
`
`0.0
`
`0
`
`0.5
`
`1.5
`2
`1
`True disc diameter (µm)
`
`2.5
`
`3
`
`Fig. 3.1 Oversizing of small discs by optical m icroscopy [23)
`
`

`

`148 Powder sampling and particle size determination
`
`shaken from a fine brush or the end of a spatula on to a slide. Humphries
`[25) describes a microsample splitter that assists the fre.e flow of grains in
`order to provide the very small samples needed for microscopy: A diagram
`of the device is reproduced in a book by Hawkins [26]. Hawkins also
`describes a moving pavement version of the spinning riffler designed for
`preparation of representative samples of free flowing particles on
`microscope slides [27). A novel method of mounting particles on regularly
`spaced adhesive circles has also been developed. This method of mounting
`results in an ordered array rather than the random chaos of usual methods
`and greatly faci litates particle analysis [28,29].
`Some acceptable procedures for easily dispersed powders are described
`by Green [30] and Dunn [31]. For a temporary slide the powder can be
`incorporated into a viscous liquid, such as glycerin or oil, in which it is
`known to disperse completely. Some operators work the powder into the
`liquid with a flexible spatula; others roll it in with a glass rod. Either of
`these procedures can cause particle fracture and a preferable alternative is
`to use a small camelhair brush. A drop of this liquid can then be
`transferred to a microscope slide and a cover slip gently lowered over it.
`Rapid pressing of the cover slip must be avoided as it causes preferential
`transfer of the larger particles to the edge of the cover slip. It is undesirable
`for liquid to spread outside the limits of the cover slip; improved spreading
`is best effected with highly viscous liquids by pre-warming the microscope
`slide. Sealing the cover slip with amyl acetate (nail varnish is a good
`substitute) makes the slide semi-permanent.
`If low viscosity liquids are
`used it is necessary to have a well, or depression, on the slide to contain the
`dispersion.
`The method of Orr and Dallevalle [32) for the production of permanent
`slides is to place a small representative sample of the powder to be
`analyzed in a I 0 ml beaker, add 2 to 3 ml of a solution containing about 2%
`colloidon in butyl acetate, stir vigorously and place a drop of suspension on
`the still surface of distilled water in a large beaker. Prior to adding the
`suspension the surface is cleaned by allowing a drop of butyl acetate to fall
`on it. As the resulting film expands, it sweeps any particles on the surface
`to the walls of the beaker. As the drop of suspension spreads, the volatile
`liquid evaporates and the resulting film may be picked up on a clean
`microscope slide and completely dried. A dispersing agent may be added
`to prevent flocculation.
`Pennanent slides may also be produced by using the alternative
`combinations of Canada balsam or polystyrene in xylol, dammar in
`turpentine, gum arabic in glycerin, styrex in xylene, rubber in xylene and
`gelatin in water [33). With a l % solution this may be formed by dropping
`
`

`

`Image analysis
`
`149
`
`it on to the cleaned surface of distilled water; with a 0.5% solution it may
`be cast directly on to a microscope slide; spreading is accelerated if the
`slide is first washed in a detergent.
`Dullien and Mehta [34] use Cargill's series H compound, having a
`refractive index of 2.0, as a mounting medium for salt particles. This gives
`a transparent yellow background for the particles and, since it has a higher
`refractive index than salt, the particles appear as dark spots. A range of
`systems is necessary in order to select one where the difference in
`refractive index gives an easily detectable image.
`MiHipore recommend filtering a dilute suspension through a 0.2 µm
`PTFE membrane filter that is then placed on a dry microscope slide. The
`slide is then inverted over a watch glass half filled with acetone, the vapors
`of which render the filter transparent after two to three minutes.
`Harwood [35) describes two methods for dispersing difficult powders.
`One involves the use of electrical charges to repel the particles then fixing
`the aqueous solution with a gelatin-coated slide to overcome Brownian
`motion. The other, for magnetic materials, involves heating the sample to a
`temperature above the Curie point then dispersing it and fixing it on a slide
`to cool.
`Allen [36] mounted the powder directly into clear cement, dispersing it
`by using sweeping strokes of a needle and spreading the film on a
`microscope slide to dry. Lenz [37] embedded particles in solid medium
`and examined slices of the medium.
`Particles may also be suspended in a filtered agar solution that is poured
`on to a microscope slide where it sets in seconds [38]. Variations in
`analyses between these procedures may occur due to particles settling on
`the slide with preferred orientations. Ellison showed that if particles were
`allowed to fall out of suspension on to a microscope slide they would do so
`with a preferred orientation. Also, if the dispersing is not complete, the
`presence of floes will give the appearance of coarseness [39]. Pidgeon and
`Dodd [ 40], who were interested in measuring particle surface area using a
`microscope, developed methods for preparing slides of particles in random
`orientation. For sieve size particles, a thin film of Canada balsam was
`spread on the slide and heated until the liquid was sufficiently viscid,
`determined by scratching with fine wire until there was no tendency for the
`troughs to fill in. Particles sprinkled on the slide at this stage were held in
`random orientation. After a suitable hardening time, a cover glass coated
`with glycerol or wann glycerol jelly, was placed carefully on the slide.
`Sub-sieve powders were dispersed in a small amount of melted glycerol
`jelly. When the mixture started to gel a small amount was spread on a dry
`slide. After the mount had set, it was protected by a cover slip coated with
`
`

`

`I 50 Powder sampling and particle size determination
`
`glycerol jelly. With this technique, it is necessary to refocus for each
`particle since they do not lie in the same plane. Several of these techniques
`were examined by Rosinski et. al. [41) in order to find out which gave the
`best reproducibility.
`The siz ing of fibrous particles by microscopy presents serious problems
`including overlapping. In order to minimize this it is necessary to work
`with only a few particles in the field of view at any one time. Timbrell
`[ 42,43] showed that certain fibers showed preferred orientations in a
`magnetic field, e.g. carbon and amphibole asbestos. He dispersed the fibers
`in a 0. 5% solution of colloidon in amyl acetate and applied a drop to a
`microscope slide, keeping the slide in a magnetic field until the film had
`dried. For SEM examination an aqueous film may be drained through a
`membrane filter held in a magnetic field. In order to reduce overlapping to
`an acceptable level it is necessary to use a far more dilute suspension than
`for more compact particles.
`Various means of particle identification are possible with optical
`identification of
`microscopy. These include dispersion staining for
`asbestos particles [ 44] and the use of various mounting media [ 45]. Proctor
`et. al. (46,47) dispersed particles in a solidifying medium of Perspex
`monomer and hardener. This was poured into a plastic mold that was
`slowly rotaled to ensure good mixing. Microscope analyses were carried
`out on thick sections; a lower size limit of 5 µm was due to contamination.
`Zeiss [48] describes a method for measuring sections of milled ferrite
`powder. The powder was mixed in 40:60 volume ratios wirth epoxy resin
`using a homogenizing head rotating at 25,000 rpm. The mixture was then
`poured into a 0.5 in diameter mold and cured al 60°C and 1000 psi to
`eliminate a ir bubbles. The casting was then polished in a vibratory polisher
`using 0.3 and 0.5 µm a lumina in water. A photomicrograph of the polished
`section was used for s11Jbsequent analysis.
`Automatic and quantitative microscopes tend to give erroneous results
`for transparent particles. To overcome this problem Amor and Block [49) a
`silver staining technique to make the particles opaque. The particles are
`dry-mounted on to a thin fi lm of tacky colloido n on a microscope slide.
`Si lver is then deposited from solution using the silver mirror reaction.
`Preliminary sensitizing the crystalline surface ensures that much more
`silver is deposited on the particles than on the colloidon. A method of
`sta ining particles in aqueous solution prior to deposition on a membrane
`fi lter for analysis is also given.
`Hamilton and Phelps [50] adapted the metal shadowing technique for
`the preparation of transparent profiles of dust particles. The process
`consisted of evaporating in vacuo a thin metal film in a direction normal to
`
`

`

`Image analysis
`
`151
`
`a slide containing particles. The particles are then removed by a jet of air
`or water, leaving sharp transparent profiles.
`
`3.5 Measurement of plane sections through packed beds
`
`When the size distribution of particles embedded in a continuous solid
`phase is required, the general approach is to deduce the distribution from
`the size of particle cross-section in a plane cut through the particle bed.
`The problem has occupied the attention of workers in diverse fields of
`science, who have tended to work in isolation and this has led to much
`duplication of effort. The historical development of this technique has been
`reviewed by Eckhoff and Enstad [51] and the relevant theory of Schei I by
`Dullien et. al. [52]. A theoretical analysis [53] has been criticized on
`several grounds [54].
`Dullien et. al. [55-57] examined salt particles embedded in a matrix of
`Wood's metal using the principles of quantitative stereology. They then
`leached out the salt particles and examined the matrix using mercury
`porisimetry. Poor agreement was obtained and this they attribute to the
`mercury porosimetry being controlled by neck diameter. Nicholson
`[58]considered the circular intersections of a Poisson distribution of
`spherical particles to estimate the particle size distribution. Saltzman et. al.
`[59] generated a computer based i.maging system for slices through a
`packed bed and found good experimental agreement.
`
`3.6 Particle size
`
`The images seen in a microscope are projected areas whose dimensions
`dependl on the particles' orientation on the slide. Particles in stable
`orientation tend to present their maximum area to the microscopist, that is
`the smaller dimensions of the particles are neglected, hence the sizes
`measured by microscopy tend to be greater t han those measured by other
`methods. Any one particle has an infinite number of linear dimensions
`hence, if a chord length is measured at random, the length wm depend upon
`the particle orientation on the slide.
`These orientation dependent
`measurements are known as statistical diameters, acceptable only when
`determined in such numbers as to typify a distribution. They are measured
`parallel to some fixed direction and are acceptable only when orientation is
`random; i.e. the distribution of diameters measured parallel to some other
`direction must give the same size distribution. They are representative of
`the two largest particle dimensions, since the smallest is perpendicular to
`the viewing plane if the particles are in stable orientation.
`
`

`

`152 Powder sampling and particle size determination
`
`Acceptable statistical diameters are:
`
`•
`
`•
`
`•
`
`•
`
`•
`
`Martin's diameter (dM) is the length of the line which bisects the area
`of the particle's projected area. The line may be in any direction,
`which must be maintained constant throughout the analysis [ 60,61].
`Feret's diameter (dF) is the distance between two tangents on
`opposite sides of the particle parallel to some fixed direction [62].
`Longest dimension. A measured diameter equal to the maximum
`value of Feret's diameter.
`Perimeter diameter (de) is the diameter of a circle having the same
`circumference as the particle.
`Projected area diameter (d0
`) takes into account both dimensions of
`the particle in the measurement plane, being the diameter of a circle
`having the same projected area as the particle.
`It is necessary to
`differentiate between this diameter and the projected area diameter
`for a particle in random orientation (dp) since, in this case, the third
`and smallest dimension of the particle 1s also included.
`
`The easiest diameter to measure is the Feret diameter but this is
`significantly larger than the other two diameters for most powders. It is
`probably best to reserve this diameter for comparison purposes and for
`rounded particles. Of the other two diameters, the projected area diameter
`is preferred since two dimensions are included in one measurement and the
`projected area is easier to estimate using globe and circle graticules than the
`length of the chord that bisects the image.
`It has been shown {63,64] that the relationship between specific surface
`and Martin's diameter is:
`
`s =~
`v d
`M
`
`(3.2)
`
`Since the surface-volume diameter is inversely proportional to Sv, the
`constant of proportionality being a minimum of six for spherical particles,
`Martin's diameter is systematically d ifferent to the surface-volume
`diameter. Experiments confirm that, on the whole, dM<da<dF. The ratios
`of these three diameters remains fairly constant for a given material and
`may be expressed as. a shape function. For example dpldM = 1.2 for
`Portland cement and 1.3 for ground glass [65].
`Heywood measured crushed sandstone which had passed through a
`I J/8 in. square aperture sieve and been retained on a 1 in. square aperture
`
`

`

`Image analysis
`
`153
`
`sieve. He determined the projected area with a planimeter and calculated
`the mean projected diameter; he next estimated the diameter using both the
`opaque and transparent circles on a globe and circle graticule and also
`determined Feret and Martin diameters. His conclusion, based on an
`examination of 142 particles, was that the Feret diameter was greatly
`different to the other diameters for elongated particles, but that the Martin
`and projected area diameters are sufficiently in agreement for all practical
`purposes. This was disputed by Walton [66] who showed that the Feret
`diameter, averaged over all particle orientations, was equal to the other
`diameters. Herdan [67] examined Heywood's data more rigorously and
`found that:
`
`(a) The Feret diameter was significantly different from the other four
`diameters.
`(b) The Martin diameter showed significant difference from that
`obtained using the globe and circle graticule if the planimeter data
`were accepted as standard.
`
`He concluded that there was no definite advantage to be gained by
`laboriously measuring profiles. As one might expect, the projected area
`diameters gave the best estimate of the true cross-sectional areas of the
`particles. This does not rule out the use of the other diameters if they are
`conveniently measured, since the cross sectional-area diameter of a particle
`is not necessarily its optimum dimension.
`
`3. 7 Calibration
`
`It is necessary to use a calibrated eyepiece scale when carrying out a
`microscope analysis. The simplest form consists of a glass disc that is
`fitted on to the field stop of the ocular. Engraved upon the disc is a scale
`that is calibrated against a stage micrometer placed in the object plane;
`typically this is a microscope slide on which is engraved a linear scale. The
`image of the scale is brought into coincidence with the ocular scale by
`focusing. With a single tube microscope the magnification be varied
`somewhat by racking the tube in or out. The stage graticule is then
`replaced by the microscope slide containing the sample. The microscope
`slide is made to traverse the eyepiece scale and particles are sized as the
`cross tlhe reference line. Linear eyepiece graticules labeled 0 to I 00 may be
`used to scan the sample so that the linear dimensions yields a size
`distribution as a function of the Martin or Feret diameter. Special
`graticules are also available containing globes (opaque images) and circles
`
`

`

`I 54 Powder sampling and particle size determination
`
`(transparent images). The former are designed for the sizing of opaque
`images and the latter for transparent images.
`
`3. 7.1 Linear eyepiece graticules
`
`These are linear scales, typically 10 mm, divided into I 00 divisions of
`100 µm, or 2 mm divided into I 00 divisions of 20 µm each. They are
`placed in the focus of the microscope eyepiece so that they are coincident
`with the image of the microscope slide on the microscope stage.
`Calibration is effected using a stage graticule, 10 mm (100 x 100 µm),
`I mm (JOO x 10 µm) or 100 µm (50 x 2 µm), which is placed in the object
`plane.
`Kohler illumination should be used [ 11] to give uniform illumination of
`the viewing plane. Using an oil immersion objective, it is possible to
`resolve down to about 1 µm, although a 15% oversizing is to be expected at
`this level due to diffraction effects.
`Ocular graticules having a
`linear scale are satisfactory for the
`measurement of linear dimensions of particles. Particle sizes obtained with
`a linear eyepiece graticule are best classified arithmetically hence it is most
`suited to particles having a narrow size range.
`
`3. 7.2 Globe and circle graticules
`
`Linear eyepiece graticules have been criticized on the grounds that the
`dimensions measured are greater than those determined by other methods.
`To overcome this objection, grids inscribed with opaque and transparent
`circles have been developed. For best results, opaque images are measured
`using the (opaque) globes while transparent images are best measured using
`the (transparent) circles. This permits direct comparisons between the
`projected areas of the particles and the areas of the circles. According to
`Cauchy the projected area is a quarter of the surface area for a random
`dispersion of convex particles (68] hence this measurement is fundamental
`to the properties of the powder.
`The earliest of these graticules by Patterson and Cawood has 10 globes
`and circles ranging in diameter from 0.6 to 2.5 µm when used with a
`+2 mm I OOx objective-eyepiece combination and is suitable for thermal
`precipitator work [69].
`Fairs [70] designed graticules covering a size range of 128: 1 using
`reference circles with a root two progression in diameter except for the
`smaller sizes. He considered this system to be superior to the Patterson-
`
`

`

`Image analysis
`
`155
`
`Cawood where the series is much closer. He also described a graticule,
`having nine circles in a '12 progression of sizes, for use with the projection
`microscope [71]. This was incorporated in a projection screen instead of
`being
`in the eyepiece and was adopted by the British Standards
`Organization [ 1 l].
`Watson [72] developed a graticule designed specifically to measure
`particles in the 0.5 to 5 µm (respirable dust) size range.
`May's graticule, [73] covers 0.25 to 32 µm in a root two progression of
`sizes (the lower limit is highly suspect).
`
`7
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`4 •
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`3 •
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`1
`•
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`I
`I
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`I
`I
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`4
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`3
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`0
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