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Sedimentology (1997) 44, 523-535

Comparison of laser grain size analysis with pipette and sieve analysis: a solution for the underestimation of the clay fraction MARTIN KONERT and JEF VANDENBERGHE Faculty of Earth Sciences, Vrije Universiteit, De Boelelaan 1085, 1081 HV Amsterdam, The Netherlands

ABSTRACT

Classically, the grain size of soil and sediment samples is determined by the sieve method for the coarse fractions and by the pipette method, based on the ‘Stokes’ sedimentation rates, for the fine fractions. Results from the two methods are compared with results from laser diffraction size analysis, which is based on the forward scattering of monochromatic coherent light. From a point of view of laboratory efficiency, the laser sizing technique is far superior. Accuracy and reproducibility are shown by measurements on certified materials. It appears that laser grain size measurements of certified materials correspond very well with the certificated measurements. Tests were also done on a set of randomly selected sediments of fluvial, aeolian and lacustrine origin. Except for the (<2 pm) clay fraction, there is a coarsening of the mean diameter of one to two size classes (0.25 q ) , caused by the non-sphericity of the particles. The platy form of the clay particles induces considerable differences (eight size classes) between pipette and laser measurements: the <2 pm grain size, defined by the pipette method corresponds with a grain size of 8 pm defined by the Laser Particle Sizer for the studied sediments. Using a higher grain size level for the clay fraction, when laser analysis is applied, enables workers in the geological and environmental field to compare classical pipette analysis with a laser sizing technique.

INTRODUCTION

This article presents the results of a study which compares laser analysis with pipette and sieve analysis. The clay fractions (<Z pm, <16 pm) are classically analysed with the standard pipette procedure NEN 5753l (1990). These are the fractions of the mineral parts of carbonate and humus-free sediments or soils. The standard procedure NEN 5753 is prescribed for environmental work and is recommended for research work. The sand fractions (63-2000 pm) are classically analysed with a set of sieves. Size classes of 0-25 9 are usual. Other methods used are particle counters, for instance the electrical sensing method of ‘Coulter Counter’ or instrumental sedimentation devices like the ‘Sedigraph’, and the ‘Laser Particle Sizer’ based on forward light scattering.

DUTCH NORM: Soil: determination of particle size distribution by sieve and pipette.

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The latter method is now widely used but with several different designs and based on different hardware and software principles.

Each technique defines the size of a particle in a different way and thus measures different properties of the same material. The pipette method defines a particle diameter as equivalent to that of a sphere settling in the same liquid with the same speed as the unknown sized particle, the so-called ‘Stokes-diameter’, The sphere is usually assigned to the density of quartz.

The sieve defines a particle diameter as the length of the side of a square hole through which the particle can just pass. A particle diameter found by a ‘Laser Diffraction Spectrophotometer’ is equivalent to a sphere that gives the same diffraction as the particle does. A ‘Laser Diffrac- tion spectrophotometer’ sees the particle as a two-dimensional object and gives its grain size as a function of the cross-sectional area of that

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particle. Mostly, clay minerals are platy and their density varies between 2 and 3 g cm ~ “, depending on their hydration properties. In addition, fine quartz particles in the < 2 pm fraction can reach about 20%”. Accordingly it is very difficult to measure the density of <2pm suspended particles.

The use of the pipette method is based on the following assumptions: a sedimentation speed is constant and not too fast. The particle Reynolds number must be smaller than one (Re, <l). b particles are spheres, solid and smooth. c densities of the particles are equal to quartz, 2.65 g cm ~ ‘3.

d no interactions occur between the particles or between the particles and the wall of the sedimentation vessel. e particles do not affect the viscosity of the liquid.

The results of sieve analysis are affected by the following factors: the method of calibration of the sieves, the shape of the particles, chemical and mechanical stability and uniformity in density and porosity.

When using a ‘Laser Particle Sizer’ the following assumptions are made: a the transformation of diffraction patterns to grain sizes is based on matrices, which are calculated for spheres. Thus the diffraction along the cross-sectional area of the particle (the dynamic ‘projected area’) is assigned to diffraction of spheres. b orientation is assumed to be random, but often, measurements take place in a continuous flow of particles in which the particle may be orientated, with respect to its shape. c the Fraunhofer-theory for transformation of the diffraction pattern to grain size distribution (e.g. Born & Wolf, 1975) is applied also for the particles <15 pm, instead of the Mie-theory (e.g. Grehan & Gousebet, 1979; Wiscombe, 1980). Matrices based on Fraunhofer are calculated from diffraction by the particles and differences in absorption and refraction indices have no effect on the calculated grain size distribution. Accord- ing to our experience, Fraunhofer-theory is well suited for non-spherical clay particles. When we compare computations of measurements between the two theories in these low size ranges, the amount of material in the fine tail is relatively suppressed when Mie-theory is used. Hence the measured percentages depend upon the method of measurement, the theoretical basis for inversion, the actual inversion procedure

M. Konert and J. Vandenberghe

(Agrawal et al., 1991), and upon the properties of the particles.

It can be argued that neither of the methods show ‘true’ results, but the methods are just measuring different properties of the same material. Considering the preceding remarks, tremendous differences between results of the methods may occur. Several authors (McCave et al., 1986; van Dongen, 1989; STOWA-report, 1992; Loizeau et al., 1994) argue that laser diffraction underestimates the amount of clay particles by 20-70% with respect to the clay content determined from pipette analysis. As discussed above, the particle shape is likely to be most significant in measuring the grain size. More particularly, the deviation from spheres has to be considered. As examples, some ‘clay’ particles have been examined by SEM-analysis. Figure 1A shows a SEM-photograph of a clay fraction of 1-2pm precipitated after ‘Stokes’. It shows platy particles with a diameter up to 10 microns. Also, the density of the particles should be considered. As an example, Fig. 1B shows an untreated lacustrine sample from the fill of the Bandung Basin in Java, Indonesia. Here we are not looking at mineral particles but at diatoms with unusual shapes and a density much lower than the supposed 2.65 g cm ~ ’.

PREVIOUS WORK

It is not our intention to give a complete overview of literature on the comparison of methods in grain size determinations. We mention work which is relevant only for the present study.

Van Dongen (1989) made a comprehensive comparison between the pipette method according to NEN 5753 and the laser diffraction method with the Malvern Master Sizer. Mie-theory was applied. Before measuring the samples with the Master Sizer, the samples were sieved over a 63 pm screen, making an extra step necessary to calculate the entire grain size distribution. For both methods the pre-treatment was equal and done after NEN 5753. Van Dongen found a correlation coefficient for sediment samples of 1-=0,85 (n = 68) for the relation:

Y= 0.1 8 5 OX+ 0-66 19

where X is the weight percentage clay (<2 pm) from the pipette method and Y is the volume percentage ( < Z pm) of the Malvern Master Sizer. Van Dongen did not look for correlations with

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Comparison of laser grain size with pipette and sieve analysis 525

other values of the grain size distributions found by the laser.

In a similar study, comparing laser and pipette, McCave et al. (1986) did not pre-treat the samples in the way van Dongen did (removal of chalk and organic matter and with washing steps). Instead, 5 min of ultrasonic treatment with Calgon was applied. McCave et al. also reported poor comparisons between the Malvern 3600E and the Coulter Counter. The size range measured depends upon the focal length of the focusing Fourier lens of the laser. McCave et al. used a 63mm lens (size range 1.2-118pm) and a 100 mm lens (size range 1.9-188 pm) for the laser measurements. The detection limit is 0-5 pm. Besides mathematical problems with particles out of the detection range, the limitation of the detection limit makes comparison with the pipette method difficult. Between the two lenses of the instrument, McCave et al., found a correlation coefficient of r= 0.61 5 (n= 55) for the relation:

Y=0.744X+ 0.030

where X is the percentage of clay 0.5-1.9pm obtained with the 63 mm lens and Y is the percentage obtained with the 100 mm lens. Compar- ing the 100mm lens with the pipette analysis, they found r=@75 (n=50) for the relation:

Y= 0.161X+ 0.207

where Y is as before and X is the percentage <2 Km measured by pipette, and using the 63 mm lens, they found r=0.75 (n=71) for the relation:

Y=0-217X+ 1.125.

According to these results, correlation of the grain size determinations obtained by the two lenses of this instrument is very poor. Moreover, the percentages d - 9 pm measured by this laser equipment are very different from the pipette results. Agrawal et al. (1991) concluded that inconsistent results observed by different lenses imply algorithmic problems. To avoid such problems, it is better to use only deconvolution methods, which consider the complete forward scattering pattern as completely as possible.

Austin and Shaw (1983) developed a method for the conversion of the results from laser analysis to equivalent sieve size distributions. The use of another conversion model between laser results and dry-sieving results was recommended by Shillabeer et al. (1992). The latter authors found

that differences between the two methods are too large, masking possible changes in particle size distributions when the results have to be compared. Shillabeer et al. (1992) present 32 conversion factors for eight sediment types. For mathematical reasons their comparisons between the two methods are limited to four divisions of the Wentworth scale <500 pm.

The influence of particle shape on grain size analysis is often hypothetical. Jonasz (1991) argues that the projected area of a non-spherical particle averaged over the particle orientation is larger than that of a sphere with equal volume. If this is true, it will lead to coarser results by applying the laser method instead of sieves. Syvitski et al. (1991) conclude that particle size instruments should no longer have their results compared with those of the classical methods of sieving and pipetting, because digital systems are far superior.

METHODS

In this study the FRITSCH ‘Laser Particle Sizer’ A22’ is used. The manufacturers claim a working range of 0.16-1250 pm. All particles give diffraction in all directions. Thus, light scattered by particles outside the measured range affects the results over that measured range. Therefore, laser analyses are only valid when the whole particle distribution is considered in the matrix solution. The A22 therefore combines the range of 0.16- 1250pm out of two measurements with focal lengths of 9 and 474mm, respectively, in the same suspension. The suspension is pumped through a sample cell placed in the convergent laser beam and the forward scattered light falls on the 31 photosensitive sensor rings. The particle size distributions from the diffraction patterns measured by the laser are calculated using the Chahine inversion scheme (Chahine, 1970; Santer & Herman, 1983). For the calculations of narrowly distributed populations, like sieve fractions or mono-sized samples, a special version is used with disabling of the noise filter. Just like Loizeau et al. (1994) we used degassed water (deionized). In our experience unstable backgrounds and pre- cipitation of air bubbles on the particles were noticed if degassed water was not used.

For characterizing the ‘Laser Particle Sizer’ certified reference material, recommended by a

A22: A(na1ysette)ZZ is a trade mark of Fritsch GmbH, Idar Oberstein, Germany.

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526 M. Konert and J. Vandenberghe

Fig. 1. A, B.

Fig. 1. (A) SEM-photograph of the clay fraction 1-2 pm of sample 25822; precipitates with the pipette method. The platy particle in the centre has a maximum diameter of about 10 pm. (B) SEM-photograph of an untreated lacustrine sample from the Bandung Basin in West Java, Indonesia, core 11, depth 18 m (Dam, 1994). Determinations of the clay content (12 pm) yields 72.9% from the pipette method and 21.7% from the laser method. (C) SEM-photograph of BCR 66, fraction < 2 pm; precipitates with the pipette method. (D) SEM-photograph of BCR 70, fraction < 2 pm; precipitates with the pipette method. (E) SEM-photograph of sample GR1720, prepared as sample 25822 (see A). At the lower left corner a platy particle occurs with a maximum diameter of the flat side of about 6.2 pni. At the middle of this picture, two particles are orientated on their side, the left one has a thickness of about 0.39 pm. (F) SEM-photograph of sample GR1720. The platy particle at the right side shows a thickness of about 0.36 pm.

commission of the European Communities, was used. The material, BCR samples (BCR- information, 1980; 1985), consists of ground quartz powder and natural quartz sand originat- ing from a quarry in Germany. The two methods used for certification are the pipette gravitational sedimentation method and sieving. They are fully described in the BCR information reports (1980; 1985). This makes these samples very appropriate

for this study. Quartz particles are not platy (see Fig. lC,D) and the density is known. Therefore, a better similarity for the clay fraction between the pipette method and the laser method may be expected. To test the instrument for the fine range, BCR 66 and BCR 70 samples were measured. For the coarse range the test samples BCR 68 and BCR 130 were used. From each BCR sample 10 independently taken subsamples

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Fig. 1. C, D.

(+lOOmg of BCR’s 66, 70 and & 5 g of BCR’s 68,130) were boiled in 100 mL deionized water with 0.3 gram Na,P,O,~lOH,O. The background was measured each time before sample input to ensure independence.

A randomly selected set of field samples was used to consider the correlation between the pipette fraction of <2 pm with the ‘Laser Particle Sizer’. The samples are from different parts of The Netherlands (Limburg, Brabant and Twente) and taken from cores and from exposures. The fine sediments are of fluvial and lacustrine origin, while the sandy samples are mostly of aeolian origin. Finally 158 samples were selected with their clay content <2 pm, measured by the pipette method. The selection was made over the whole analytical range from 0 to 80% clay in the whole sample. For each class of clay (5% range), 10 samples were chosen with the restriction of not

more than two samples from the same site anci origin in the same class. To illustrate that the problem of underestimation of the clay fraction may be caused by the platy particles of the clay minerals, the pipette fraction of <16 pm was also considered. Both fractions (<2 pm and <16 pm) were measured twice to get duplicates.

To understand the deviations between the sieve method and the laser method several experiments were carried out. First, the sieve fractions of a broadly distributed sample were compared with the sieve fractions of glass spheres. These glass spheres were sieved through the same set of sieves. Secondly, from the same 158 samples, as used above, 42 sandy samples were sieved in classes of 0-25 p from 53 to 2000 pm. These 42 samples were used to compare the mean diameter, the mean square deviation (MSD) and the skewness over that particular range. Thirdly, six

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Fig. 1. E, F.

closely related samples, in terms of origin and grain size, were measured by the two methods. These samples were from an aeolian sand deposit covering a Berlling peat from the Mariahout section in the southern Netherlands described by Bohncke (1993).

Different pre-treatment of samples has been reported in publications, or pre-treatment has not been mentioned [Shillabeer et ~ l . , 1992). We are convinced that an inadequate pre-treatment will affect grain size measurements enormously. Moreover, to compare the results of the two methods used here, the organic matter and car- bonates were removed as described in NEN 5 7 3 5 . The weight of carbonate- and organic matter-free sediment was determined before analysis. A brief description of the pre-treatment is given in Appendix A and a description of the sieve and

pipette analysis is given in Appendix B. The pre-treatment for the laser analysis (Appendix C) is basically the same as that for pipette analysis, but with some steps simplified. The amount of material needed for laser analysis depends on the grain size characteristics, typically 100-200 mg for fine samples and 5-10 g for sandy samples.

RESULTS

Laser measurements of certified BCR samples The grain size distributions of the BCR samples obtained by our laser measurements are compared with the certified values in Fig. 2 and Table 1. The mean diameter of BCR 66, 68 and 130 shows a slightly coarser distribution, while the mean diameter of BCR 70 shows a slightly finer

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samples result in a difference for the mean diameter (d i f fmean) and in a difference for the MSD ( diff MSD) :

- Certified data --- Laser measurements

Fig. 2. Cumulative curves of the certified data and the measured laser curves of the BCR samples 66, 68, 70 and 130. The average of 10 measurements is given.

distribution by laser analysis. BCR 66 shows an underestimation of the percentage <2 pm in comparison with the certified values, while BCR 70 shows an overestimation. The MSD is always slightly higher in the laser measurements in comparison with the certified data (Table 1).

The calibrations of the sieves used for the BCR samples, 68 and 130, were performed using the countinglweighing procedure described in Appen- dix 1 of the certification report (BCR-information, 1980). Briefly, this involved the counting and weighing of about 10 mg of particles just passing the sieve. Then an equivalent volume diameter of the sieve is calculated. Because of the imperfect sphericity of the particles, the diameters derived in this way are larger than the original diameter of the sieve. This explains the small deviations of the mean diameter between the laser measurements and the certified data of the two BCR samples.

Sieve and laser measurements

Laser and sieve analysis of the test series of 42 sand samples chosen from the set of 158 field

diff mean= - 0 . 2 7 ~ f 0.10 (n=42) dif lMSD= +0.14p If 0.08 (n=42).

It means that the laser measurements are some- what coarser and more broadly divided than the sieve analyses. Because our stack of sieves was not calibrated, the diff mean of the 42 sand samples is larger then the values obtained with the BCR samples.

The differences between laser and sieve measurements have a methodological origin. As outlined in the introduction, different properties are measured in both methods. More particularly, the shape or sphericity of the particles is of prime importance. To evaluate the importance of these factors, the following test was done. Through a set of sieves, with intervals of 0.25 q~ from 63 pm to 1000 ,urn, one poorly sorted field sand sample was sieved. The sand grains of this sample are not spherical or well rounded. The collected fractions were measured by the Laser Particle Sizer. Through the same stack of sieves a population of randomly sized glass spheres was sieved and measured in the same way. The laser measurements of three sieved fractions of sand grains and glass spheres are given as an example in Fig. 3. The MSDs and the differences for the mean diameter between the theoretical middle of the sieve fractions and measurements of the two series are presented in Fig. 4. The sieving results show clearly that the sand appears coarser than the glass spheres. The mean diameters of the glass sphere fractions measured by the laser remain inside the boundaries of the sieve sizes ( - 0.125 v, and +0.125 9). Also, all the MSDs of the sand fractions show larger values than those of the glass spheres. The differences between the laser and the sieve analyses are interpreted as being

Table 1. The statistical results of the BCR data, derived from the certificate of measurement and the laser measurements.

BCR 66 9.67 0.75 0.05 87.1 & 3.9 (n=43) 9.51 i O . 0 2 0.83 *0.01 0.195 0.05 77.6 i 1.1 (n=l0) - 0.16 +0.08 BCR 70 8.22 0.95 - 0.36 27.4h2.6 (n=20) 8.43k0.01 1 .091042 - 0.01f0.04 36.4&0.5 (n=10) +0.21 +0.14 BCR 130 2.98 0.67 0.37 (n=36) 2.87 f 0.02 0.77 & 0.01 0.47 !C 0.04 (n=lo) - 0.11 BCR 68 1.43 0.51 0.13 (n=20) 1.39 f 0.02 0.63 +@02 0.55 i 0.05 (n=10) - 0-04 +@12

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530 M. Konert and J . Vandenberghe

lo00 500 250 125 63 ~rm

Sieve fractions (phi)

Fig. 3. Laser measurements of three sieve fractions (63-75, 180-212, and 600-850pm) of a natural sand compared with glass spheres in the same ranges.

500 250 125 63 pm

E -0 1 - - - - - - - - .. .... ... .... ...... .... ~~ ~~. ...... . .-

-0.2 I 1 I

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Sieve classes, Wentworth scale

--tf diff mean f diff mean t MSD + MSD sand spheres sand spheres

Fig. 4. Laser measurements of sand and glass spheres fractions. Both sieved through the same stack of sieves (63-1000pm). On the X-axis the sieve classes are plotted. On the Y-axis (left side) the diffmean from the theoretical class mean is plotted and on the secondary Y-axis (right side) the Mean Square Deviations are plotted.

caused by different sphericity or shape. This effect is exemplified by the aeolian section at Mariahout, which has been sampled in detail to identify possible variations in grain size. The differences between the mean diameters and the MSDs from laser and sieve analyses are comparable (Table 2). A t the top of the section (80-100 cm) the deviations are larger than those at the bottom (140-160cm). This holds both for the mean diameter and the mean square deviation.

According to the test described above the ‘finer’ sieve analyses are due to the deviation from

spherical grain form. To test this relationship for the Mariahout section, c. 300 particles of each sediment sample were measured by the IBAS image analysis system3. Measurements were made in a two-dimensional view for the fraction 125-212pm (3-2.25 y ) of the three top samples and for the fraction 90-150 pm (3.5-2.75 y ) of the three samples at the bottom of the section. Two parameters, FSHAPE and FCIRCLE (IBAS User’s Manual, 1991) were considered (Table 3). The first parameter, the FSHAPE, is the aspect ratio of the particle, defined as

DMIN FSHAPE = ___

DMAX

where DMAX is the longest diameter of a particle obtained by selecting the largest diameter from 32 different directions while DMIN is defined simi- larly as the shortest diameter (i.e. at an angular resolution of 5.7 degrees). The second parameter, FCIRCLE is the circularity shape factor of the particle, defined as

4.II.AREA FCiR CLE =

PERIM’

where AREA is the area of the two-dimensional orientated particle and PERiM is the particle perimeter. The values of FCIRCLE range between close to 0 , for very elongated or rough objects, and 1 for circular objects. From Table 3 it follows that, in the Mariahout section the parameter FCIRCLE at the top of the section differs significantly (t-test) from that at the bottom. It follows that the upper part is not only coarser but also contains more elongated particles than the lower part. This corresponds with a larger difference between the laser and sieve mean diameter (diffmean) and a larger diff MSD. But, the F S H A P E outcomes show no significant differences. It means that the mag- nitude of the difference of the mean grain sizes between the two methods is related to the shape or sphericity of the sediment grains and may be used as such.

Pipette and laser measurements

For 158 sediment samples, the pipette fractions percentage < 2 pm and percentage <16 pm were determined in duplicate. The standard deviation

IBAS analysis system is a trade mark of Kontron Elektronik GmbH, Germany.

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Table 2. Sieve and laser results from six aeolian sediment samples from the section Mariahout. The correlation between sieve and laser analysis is r=0.998 (n=6).

Mean Mean diff MSD MSD diff Skewn Skewn Sediment Depth sieve laser Mean sieve laser MSD sieve laser sample (cm) (PI (PI (PI (vl (10) (PI (PI (PI

3122 80 2.67 2.39 - 0.28 0.48 0.64 0.16 ~ 0.46 - 0.51 3123 90 2.58 2.32 - 0.26 0.45 0.59 0.14 - 0.16 - 0.41 3124 100 2.54 2.22 - 0.32 0.47 0.63 0.16 - 0.21 - 0.43 3128 140 3.12 2.96 - 0.16 0.42 0.53 0.11 - 0.31 - 0.20 3129 150 3.01 2.87 ~ 0.14 0.43 0.54 0.11 - 0.35 - 0.15 3130 160 3.10 2.95 - 0.15 0.43 0.54 0.11 - 0.39 - 0.20

Table 3. The outcomes of ESHAPE and FCIRCLE on the six aeolian sediment samples from the section Mariahout.

Sediment Depth sample (cm)

~ _ _ _ _

3122 80 3123 90 3124 100 3128 140 3129 150 3130 160

FSHAPE

0.718 f 0.096 0.727 f 0.098 0,725 f 0.102 0.730 f 0.101 0.721 f 0.107 0.723 f 0.097

FCIRCLE

0.822 f 0.094 0.829 f 0.090 0.820 f 0.088 0.882 f 0.065 0.872 f 0.071 0.850 f 0.072

n __

2 94 300 297 300 300 295

s of series of duplicate analyses with equal spread is derived by

(3)

where d is the difference between the duplicates and k is the number of samples with k degrees of freedom. The standard deviation of the <2 pm fraction is: s=1.2 (n=158), while the standard deviation of the <16 pm fraction is: s=1.5 (n = 158).

Because the general relationship between the pipette and laser data is sought, a regression analysis was applied, although the Reduced Major Axis Method (RMA) could be used also. The variables examined are the laser cumulative percentages Y and the pipette percentage X . The equation of the regression lines is

Y=aX+b (4)

To estimate the degree of interrelation between the pipette and the laser analysis the correlation coefficient r is used. Ideally, a correlation coefficient r >0.95 should be obtained with a

slope (a) of one and an intercept (b) of zero for the relation between X and Y. Figure 5A shows the correlation between the <2 pm clay fractions resulting from the two methods.

The correlation coefficients (r) and the slopes (a) for the relation between the pipette fraction <2 pm and the laser fractions from <1.0 to <31.3 pm (from <10 to <5 y ) , in steps of 0.25 q are shown in Fig. 5B. Inspection of Fig. 5B shows that the value of the laser measurements at 7 y (8 pm) gives the best slope (nearest to 1) with a correlation coefficient of 0.939. The correlation diagram between the laser fraction <8 pm and the pipette fraction < 2 pm is given in Fig. 5C.

A similar relation is sought for the <16 pm pipette fraction The diagrams are given in Figs 6A,B,C which show the regression equations. The nearest slope to 1 is at 5.5 y , 22 pm (laser) related to <16 pm (pipette) (Fig. 6C). In summary the pipette fraction < 2 pm compares the best with laser analysis at <8 pm. This is a shift of 2 y , The pipette fraction <16 pm compares best at <22 pm by laser, a shift of 0.5 y.

DISCUSSION AND CONCLUSIONS

Two prerequisites have to be fulfilled for any grain size analysis by laser diffraction. (1) The whole grain size range has to be considered in order to avoid any distortion from smaller and larger particles. (2) The sediment must not floccu- late. In this study carbonate and humus were removed.

The comparison between laser and sieve size measurements of glass spheres gives information about the precision of the laser method in relation to sieves and is very good. The measurements on the four BCR quartz samples demonstrate a very good and reproducible agreement between the laser and classical methods.

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r=0.957 (n=158) ........................................................................

........ .................................................................... h

k?

L i 3 c;l

2

1

'0 10 20 30 40 50 60 70 80

. . . . . . . . . . . . . . . .

........................

.....................................

..................................................

Pipette <2 pm (%) Pipette 4 6 p m (%)

+ Slope --t Correlation eoef.

C 80

7 0 e0.939 (n=158)

..............

.x---- .............................................

Pipette <2 pm (%)

Fig. 5. (A) Correlation diagram of the laser analysis <2 pm and the pipette analysis <2 pn with regression equation. (B) Y-axis (left side) slopes of the relations between 2 1 cumulative size classes of the Laser Particle Sizer (5-10 q) and the pipette fraction <2pm. Y-axis (right side) gives the associated correlation coefficients. (C) Correlation diagram of the laser analysis <8 pm and the pipette analysis <2 pm with regression equation.

0.4$ , y0.89 4 4.5 5 5.5 6 6.5 7 7.5 8

Phi + Slope --t Correlation coef.

......................

..................................

...............................................

K.. ...........................................................

"0 10 20 30 40 50 60 70 80 90 100 Pipette 4 6 pm (%)

Fig. 6. (A) Correlation diagram of the laser analysis <16 pm and the pipette analysis <16 pm with regression equation. (B) Y-axis (left side) slopes of the relations between 1 7 cumulative size classes of the Laser Particle Sizer (4-8 rp) and the pipette fraction <16 pm. Y-axis (right side) gives the associated correlation coefficients. (C) Correlation diagram of the laser analysis <22 pm and the pipette analysis <16 pm with regression equation.

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Generally, laser analysis on sediments >63 pm (sands) gives slightly coarser results of 0.25-0.5 v, as compared to sieve analysis. The difference is caused by the non-spherical form of natural sand particles. The laser analysis gives a 'mean diarn- eter' of the particles, while the sieve analysis provides a measure of the width of the particle (b-axis). Thus, variations in deviation between laser and sieve analysis depend on particle form and, inversely, have the potential to give an estimate of the sphericity of the particles.

For the two fine BCR-samples the laser and pipette method show fairly corresponding results in the clay range. This is caused by the fact that the <2 pm fraction of the BCR-samples consists of blocky, and certainly not platy quartz particles. On the contrary, clay minerals give strikingly different results depending on the kind of technique applied. This is mainly due to the form of the clay minerals. Clay particles with a 'Stokes' diameter of about 2 pm can have a length (diameter) of 10 pm with a thickness of about 0.4pm, measured by the Scanning Electron Microscope (Fig. lA,E,F). The volume equivalent sphere has a diameter of about 3.9 pm. To avoid confusion, caused by the effect of grain shape in relation to the instrumental analysis, it is recommended to read the clay fraction not at 2 prn when Laser Particle Sizers are used. Ideally for each group of sediments the exact correlation between the <2 prn of the pipette analysis and the laser analysis should be established as in Fig. 5A,B. For a large set of Quaternary fluvial and aeolian samples in the Netherlands, the 8 pm of the laser is a good average corresponding with the 2 pm of the classical pipette analysis (as measured by the Fritsch A22 Laser Particle Sizer, applying Fraunhofer theory). In addition to the particle form, the mineral densities also affect pipette size determinations. The <16 pm fraction shows a much smaller shift to larger diameters, because in the size classes around 16 pm, typically platy clay minerals are practically absent.

It may be stated that laser particle size determination will always differ from sieve and pipette analysis when particle forms deviate from the sphere form and particle density is hetero- geneous. However, knowledge of the properties of the measurement technique and the physical properties of the material allow comparison and use of data from different methods.

Our conclusions are supported by the theory of Stokes settling velocities. Lerman et al. (1974) have tabulated the expressions for settling velocity of particles of varied shape in the Stokes

(viscous) range. For spheres, in terms of particle radius, the settling velocity Us is

(5)

where r, is the radius of the sphere, g is the acceleration due to gravity, y, is the particle density, p is the density of the medium, and 11 is viscosity. For a disc of radius a and thickness h, settling broadside, the settling velocity U, is

where re is the radius of the volume equivalent sphere. In terms of a sphere volume equal to the disc volume, the radii a and re are related through

4a > ' a = re( ih) (7)

Substituting of (7) into (6) and rearranging yields

11

Equating Us and U, yields

(91 2

9 r2 = 0.1965 ha

Putting h/a=R, the thickness ratio, into (9) yields

For a clay plate falling edgewise the constant in Eq. (6) is 0.357 which yields

r - = 1.15& a

If we consider Fig. lA,E,F, the platy particle of 10 pm length (diameter) with a thickness of 0.36 pm yields a thickness ratio R of 0.072. The r/a ratio, calculated from ( lo) , is 0.252. That is to say a 2 pm diameter sphere (r=1 pm) is equivalent to a 7.9 pm diameter (2a) clay plate 0.29 pm thick (h), when falling broadside. For the same clay plate falling edgewise the 2 pm diameter sphere is equivalent to a 6.5 pm diameter clay plate 0.23 pm

Q 1997 International Association of Sedimentologists, Sedimentology, 44, 523-535

534

thick. These calculations correspond very well with the experimental results which show a correspondence of the 2 pm pipette analysis with the 8 pm diameter in the laser analysis.

M. Konert and I . Vandenberghe

ACKNOWLEDGMENTS

The authors sincerely thank Drs A. Bikker and Drs C. J. Hemker for their interest and support and for the many substantial discussions with respect to the laser method and its mathematics. It was very fruitful and essential for the introduction of the laser method at our laboratory. Roe1 van Elsas and Marjan Boone from the Laboratory for Sediment Analyses are acknowledged for the many pipette and sieve analyses. Also, thanks to Saskia Kars for making the SEM photographs and to Drs M. Reinders for his assistance on the BIAS image analysis system. We thank Dr I. N. McCave for the helpful review.

REFERENCES

Agrawal, Y.C., McCave, I.N. and Riley, J.B. (1991) Laser diffraction size analysis. In: Principles, methods and applications of particle size analysis (Ed. by J. P. M. Syvitski), pp. 119-128. Cambridge University Press, New York.

Austin, L.G. and Shaw, I. (1983) A method for inter- conversion of Microtrac and sieve size distributions. Powder Technology, 35, 271-278.

BCR information (1980) Certification report on reference materials of defined particle size. Quartz BCR no. 66, 67, 68, 69, 70. Report EUR 6825 en. Com- mission of the European Communities, Luxembourg.

BCR information (1985) Reference materials of defined particle size. Quartz BCR no. 130, 131. Report EUR 9769 en. Commission of the European Communities, Luxembourg.

Bohncke, S. J.P. (1993) Lateglacial environmental changes in the Netherlands: spatial and temporal patterns. Quat. Sci. Rev., 12, 707-717.

Born, M.A. and Wolf, E. (1975) Principles of optics. Pergamon Press, Oxford.

Chahine, M.T. (1970) Inverse Problems in Radiative Transfer: Determination of Atmospheric Parameters. J. Atmos. Sci., 27, 960-967.

Dam, M.A.C. (1994) The Late Quaternary evolution of the Bandung Basin, West-Java, Indonesia. PhD thesis, Vrije Universiteit, Amsterdam.

Grehan, G. and Gousebet, G. (1979) Mie theory: new progress, with emphasis on particle sizing. Applied Optics, 18, 3489-3493.

IBAS User’s manual (1991) Volume 2. Kontron Elektronik GmbH, Germany.

Jonasz, M. (1991) Size, shape, composition and structure of microparticles from light scattering. In: Principles, methods and applications of particle size analysis (Ed. by J. P. M. Syvitski), pp. 143-162. Cambridge University Press, New York.

Lerman, A., Lal, D. and Dacey, M.F. (1974) Stokes’ settling and chemical reactivity of suspended particles in natural waters. In: Suspended solids in water (Ed. by R. J, Gibbs), pp. 17-47. Plenium Press, New York.

Loizeau, J.L., Arbouille, D., Santiago, S. and Vernet, J.P. (1994) Evaluation of a wide range laser diffraction grain size analyzer for use with sediments. Sedimen-

McCave, I.N., Bryant, R. J., Cook, H.F. and Coughanowr, C.A. (1986) Evaluation of a laser diffraction size analyzer for use with natural sediments. J. Sedim. Petrol., 56, 561-564.

NEN 5753 (1990) Bepaling van de korrelgrootteverdeling met behulp van zeef en pipet. Nederlands Normalisatie-instituut, Delft.

Santer, R. and Herman, M. (1983) Particle size distributions from forward scattered light using the Chahine inversion scheme. Applied Optics, 22,

Shillabeer, N., Hart, B. and Riddle, A.M. (1992) The use of a mathematical model to compare particle size data derived by dry sieving and laser analysis. Estuarine, Coastal and Shelf Sci., 35, 105-111.

STOWA-report (1992) Bepaling van de lutumfractie in waterbodems (Ed. by J. F. Noorthoorn van der Kruijff). Stichting Toegepast Onderzoek Water- beheer, Den Haag.

Syvitski, J.P.M., Leblanc, K.W.G. and Asprey, K.W. (1991) Interlaboratory instrument calibration exper- iment. In: Principles, methods and applications of particle size analysis (Ed. by J. P. M. Syvitski), pp. 174-193. Cambridge University Press, New York.

Van Dongen, W. (1989) Bepaling korrelgrootteverdeling van waterbodems en zwevende stof. IJking van de laserbuigingsmethode met de zeef- en pipet methode volgens NEN 5753. Afstudeerverslag HLO-chemie, RijkswaterstaatLRIZA, Lelystad.

Wiscombe, W.J. (1979) Improved Mie scattering algor- ithms. Applied Optics, 19, 1505-1509.

tology, 41, 353-361.

2294-2301.

Manuscript received 29 April 1996; revision accepted 10 September 1996.

APPENDIX A

A description of the pre-treatment for pipette and sieve analysis: 0 Weigh 19-2Og into weighed beakers of

800mL. For coarse samples the weight is 39-41 gram. Oxidize with aliquots of 15 mL H,O, 30% until organic matter is removed. Destroy the excess peroxide by boiling.

0

R> 1997 International Association of Sedimentologists, Sedimentology, 44, 523-535


Add as much 1.ON HC1 as necessary to dis- solve CaCO, (4mL per percentage CaCO,) with an excess of 25 mL 1.ON HC1. Fill to 400mL and heat until boiling-point. (NEN 5735 advises 15 min of boiling). If the carbonate content is not known, one has to analyse this precisely. In this study it was done following the Scheibler method. Rinse the walls of the beakers carefully to avoid loss of material during the next operations. Remove dissolved elements by filling with deionized water after removal of supernatant water; stand overnight and decant the clear liquid. Repeat one more time. Dry 48 h at 50-60°C. Weigh the beakers. Disperse the samples by adding 50 mL, 0.120 M Na,P,07-10H,0, fill to 400 mL with deionized water and boil for 5 min. Decant the samples quantitatively into cylinders of one litre with a diameter of 6 cm. Cool to 20°C.

APPENDIX B

A brief description of measuring the pipette and sieve fractions: 0 Stir the suspension intensively. After exactly

15 min of settling a sample of 20 mL from a depth of 20.8 cm is taken with a clay-pipette designed after Kohn. This is the fraction <16ym. For the fraction < 2 ym the settling time is 16 h at 20.8 cm. Dry and weigh the fractions. Correct the weight for the

Na,P,O,~lOH,O addition before calculating the percentages.

0 After analysing the pipette fractions ( < 2 , <16 pm and normally also the <22, <32, and <44 pm fractions) the remaining suspension is wet sieved over a 53 pm screen and the fraction >53 ym is dried at 105°C.

0 For further analysis use a set of sieves between 63 and 2000 pm, divided into ranges O f 0.25 p.

APPENDIX C

A description of the pre-treatment for laser analysis: 0 Oxidation is carried out with aliquots of

10 mL of 30% H,O,. 0 Boiling with 10% HC1 is normally done with

5 mL in a 100mL suspension. If there is a violent reaction, more acid must be added. Normally 1-2 aliquots were needed for the samples used in this study.

0 Rinse the walls of the beakers carefully to avoid loss of material during the next operations.

0 One decantation of the dissolved salts is enough for a sufficient dilution of the dissolved cations. Also the amount of Na,P,O7~10Hz0 need not be precise because the correction for weight is not necessary. A standard spatula is used to add about 0.3 g of the dispersant. After cooling, the samples can be measured by a Laser Particle Sizer. Single measurements were made in this study.

0

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