624
DOI: 10.1002/jpln.201000255
J. Plant Nutr. Soil Sci. 2011, 174, 624–633
Methodological aspects of determining soil particle-size distribution using
the laser diffraction method
Magdalena Ryżak1* and Andrzej Bieganowski1
1
Institute of Agrophysics, Polish Academy of Sciences, Doświadczalna 4, 20–290 Lublin 27, Poland
Abstract
This paper presents the influence of selected methodological aspects on the results of particlesize distribution (PSD) as measured by the laser diffraction method (LDM). The investigations
were carried out using the Mastersizer 2000 with Hydro MU attachment (Malvern Ltd., UK). It
was found that for the investigated soils: (1) optimal speed of pump and stirrer was 2500 rpm,
(2) optimal measurement time was ≈ 1 min, (3) there are two, practically equivalent methods for
soil-sample dispersion: chemical (with the use of a solution of sodium hexametaphosphate) or
physical (by means of ultrasound application for 4 min at a maximum power of 35W), (4) one
must not use the chemical and physical dispersing methods simultaneously, because this can
lead to aggregation (not dispersion) of soil particles, (5) the Fraunhofer theory (physical models)
can be used to convert scattered-light data to PSD. In the case of the Mie theory, the best results
were obtained for a refractive index (RI) in the range of 1.5–1.6 and an absorption index (AI) of
1.0. It was also found that most of the discussed parameters depend on design of the measuring
device and on the type and volume of the investigated suspensions. It is necessary, therefore, to
explain how the data was obtained every time and to specify the details in the methodological
part of the paper.
Key words: particle-size distribution (PSD) / laser diffraction method (LDM) / soil / dispersion of soil
Accepted November 28, 2010
1 Introduction
Particle-size distribution (PSD) is one of the most important
soil characteristics. PSD influences soil properties such as
pore distribution, water retention, water conductivity (Hajnos
et al., 2006; Sławiński et al., 2006), and thermal and sorption
properties. It also indirectly influences soil nitrification (Włodarczyk et al., 2008) and many other soil properties (Czyż
and Dexter, 2009; Balashov et al., 2010; Ke˛sik et al., 2010).
Sedimentation methods are currently used to measure PSD.
There is an international standard describing the pipette
method, which is one of the sedimentation methods (ISO
11277, 1998). A new method called the laser diffraction
method (LDM) for measuring PSD, however, is becoming
more and more popular. Whenever a new method appears,
research is conducted to determine the applicability of the
method by comparing the new method with other methods
used so far. Comparisons of the LDM with sedimentation
methods have been carried out (Arriaga et al., 2006; Goossens, 2008; Taubner et al., 2009; Ryżak and Bieganowski,
2010) but so have investigations simply using the new laser
diffraction method (Hayton et al., 2001; Murray, 2002; Campbell, 2003; Sperazza et al., 2004; Blott and Pye, 2006;
McCave et al., 2006). As with every new method, the laser
diffraction method has many proponents and opponents.
Literature review has led to the conclusion that the comparison of published results needs to be treated qualitatively
rather than quantitatively. There are two main types of causes
of uncertainty associated with quantitative comparison of
published results. The first is objective causes. There are
many different types of laser diffraction devices, from different
generations and from various manufacturers. The development of these devices and the hardware and software innovations applied to them introduces a serious source of uncertainty in such comparisons. The second type of causes making comparison of result difficult is subjective causes—
resulting from human error (error caused by researcher). The
various measuring procedures (at different stages of measurement) are the main reason. Study of available papers
shows that not only is there a lack of a standard method of
measurement, but also a lack of information about measurement details in the methodological part of the paper. For
instance, there was no information about which mathematical
model (Fraunhofer or Mie theory) was used in the calculations in some of the papers published after the year 2000.
When the Mie theory was used, there was often no information about the optical parameters of the continuous and dispersion phases (absorption and refractive indexes).
The laser diffraction method is based on measuring the scattered laser beam on measured soil particles. The scattered
laser light is registered on detectors. The angle at which the
beam is scattered is inversely proportional to the soil particle
size. The software provided by the manufacturer recalculates
the information from the detectors into volumetric PSD.
The aim of this paper was to perform an analysis of the influence of different methodological aspects of LDM on the PSD
results. All aspects discussed in the paper are universal for
all apparatus using LDM, although some of the parameters
(for instance the speed of the particles moving through the
laser beam) can be controlled in different ways.
* Correspondence: Dr. M. Ryżak; e-mail: [email protected]
 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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J. Plant Nutr. Soil Sci. 2011, 174, 624–633
2 Materials and methods
Methodological aspects of laser PSD 625
meters), 23 soil samples were measured and analyzed.
Twenty-two samples were collected from the arable layer and
one sample (Tab. 1, profile 10) was collected from the parent
rock.
2.1 Materials
The soil samples chosen for the measurements were derived
from 23 soil profiles which are quantitatively and qualitatively
representative for SE Poland. The samples were dried at
105°C, gently crushed, and dry-sieved at 2 mm mesh size.
Descriptions of selected properties of the investigated
mineral soil samples are given in Tab. 1. PSD obtained from
the sedimentation method according to ISO 11277 (1998) is
presented in Tab. 1.
The first stage of investigation consisted in selection of the
pump and stirrer speed and of the measuring time. The problem of rapid sedimentation of large particles under the influence of the force of gravity during mixing is especially evident
in soils in which the biggest fraction (sand fraction) is found.
Taking this into consideration, the sample which has one of
the biggest content of sand fraction from all of the samples—
the Eutric Cambisols (Tab. 1, sample from profile 6)—was
selected for measuring the influence of pump and stirrer
speed on sedimentation and selection of measuring time. For
the realization of the second stage of the measurements (procedure of soil-sample preparation), the representatives of different types of mineral soils were selected: Haplic Phaeozem, Mollic Gleysol, Calcaric Cambisol, and Orthic Luvisol
(Tab. 1, samples profiles: 10, 11, 18, and 23). For the realization of the third stage of the measurements (selection of theory and in the case of Mie theory, selection of optical para-
2.2 Apparatus
Laser analyzer Mastersizer 2000 (Malvern Instruments) with
Hydro MU adapter was used to determine the PSD of soil
samples. The measurement range of the apparatus is
0.02–2000 lm.
The Hydro MU adapter is equipped with:
– a stirrer; to prevent sedimentation of particles in the beaker, by circulating the sample in the measuring system and
facilitating flow through the measuring cell. The speed of
rotation of the stirrer ranges from 0 to 4000 rpm and can
be regulated in increments of 50 rpm.
– an ultrasonic probe; with a maximum power of 35 W and a
frequency of 40 kHz. The amplitude ranges from 2 to 20
lm and can be regulated in increments of 0.5 lm (defined
by the manufacturer as 2–20 units in increments of 0.5
units).
For the determination of PSD, the Mastersizer apparatus
uses two sources of light: red (wavelength 633 nm) and blue
(wavelength 466 nm).
Table 1: Selected properties of soils.
Soil profile Soil
number
Corg
/%
Particle-size distribution
/ % (∅ / mm)
sand
2–0.05
silt
0.05–0.002
clay
< 0.002
Eutric Cambisols
50
58
71
62
70
95
96
94
40
31
25
27
27
4
3
5
10
11
4
11
3
1
1
1
0.82
0.94
0.65
0.73
0.79
2.28
0.99
0.77
9
10
Orthic Luvisols
88
84
11
6
1
10
1.01
0.15
11
12
13
14
15
16
Haplic Phaeozems
59
60
86
63
60
60
30
34
13
32
34
29
11
6
1
5
6
11
1.24
1.48
2.10
2.07
1.11
1.62
17
Eutric Fluvisol
86
12
2
1.14
18
19
20
21
22
Calcaric Cambisol
61
85
49
78
91
21
13
35
17
8
18
2
16
5
1
0.61
1.62
0.77
1.21
0.98
23
Mollic Gleysol
53
34
13
3.08
1
2
3
4
5
6
7
8
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626
Ryżak, Bieganowski
The quantity of soil sample that is added into the measuring
system is determined by a parameter called “obscuration”,
which is measured by the apparatus every time a sample is
added, as it is being added. Obscuration is the degree to
which the light from the laser beam is obscured by the particles being measured. The manufacturer recommends that
the value of obscuration should be between 10% and 20%.
Below 10%, the number of particles is too small to obtain reliable results. Above 20%, the laser beam can be subject to
secondary refraction because the number of particles is too
large, and this may falsify the resultant PSD (Malvern Worcs,
1999). The volume of distilled water to which the soil samples
were added at the dispersion phase was ≈ 800 mL (in a
1000 mL beaker). This volume was experimentally selected
and allowed for good mixing of the suspension without simultaneously sucking air bubbles into the measuring system and
without splashing any of the suspension out of the beaker.
The measurement of PSD using the LDM consists of recording the beam which is diffracted off of the particles in suspension and returned to the detectors. Because the Mastersizer
2000 apparatus records the source signal from the detectors,
it is possible to calculate the results by selecting one of the
algorithms which are supplied by the manufacturer. It is necessary to select an appropriate theory (Mie or Fraunhofer) as
well as an appropriate algorithm to use in the calculations.
These selections depend on the properties of the particles
being measured. The manufacturer provides three groups of
algorithms: general purpose analysis (GPA), multiple narrow
modes (MNP), and single mode (SM). Within each algorithm
group, there are two more algorithms: irregular-shape ratio
(ISR) and spherical-shape ratio (SSR). The GPA algorithm is
a calculation procedure recommended by the manufacturer
for particles with unknown properties or for samples containing a large number of various fractions. The MNP algorithm is
a calculation procedure for mixtures that are known to contain
particles of two (or more) monodispersive fractions, i.e., distributions of the individual fractions are narrow and best when
they are also discrete. The SM algorithm is a calculation procedure used for estimating the grain-size distribution of monodispersive individual fractions with narrow grain-size distribution. The ISR algorithm is related to the shape of the measured
particles. Although one of the assumptions of this method is
that the particles are perfect spheres, the manufacturer has
provided a module permitting greater accuracy of results
when the particles under study are not perfect spheres. The
SSR algorithm is a calculation procedure for spherical particles. Based on the specific properties of the soil samples, the
following algorithms were chosen GPA and ISR.
2.3 Selection of pump and stirrer speed
Proper selection of pump and stirrer speed should guarantee
consistency of measurements throughout the measuring time
and also eliminate the difficulties associated with too much
intensive stirring and, thus, either sucking air bubbles in
(which can be treated as soil particles by the measuring system) or splashing of the suspension out of the beaker. The
apparatus Mastersizer 2000 with Hydro MU attachment is
equipped with a pump which is integrated with the stirrer. Taking into account previous experience, for this investigation
 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
J. Plant Nutr. Soil Sci. 2011, 174, 624–633
this parameter was modified to cover a pump speed range
from 1200 to 3000 rpm, regulated in increments of 200 rpm.
2.4 Selection of measuring time
The measurements consist of a number of “snap shots” (i.e.,
a number of records of the intensity of the detectors) during
the measuring time. The greater the number of shots, the
lower the uncertainty of the measurement, because statistically the representation of the sample being measured in the
measuring cell is increased. For a better explanation of the
above statement, one can consider a situation where there
are a very large number of identical particles of a definite size
and one much larger particle suspended in the suspension.
The probability that the large particle will be found in the
measuring cell (and in effect be taken into account in the
averaged final result) will increase as the number of individual
measurements increases. From the point of view of representative results, extending the measuring time reduces the
uncertainty. On the other hand, any laboratory which carries
out thousands of analyses per month tends to cut down on
the measuring time. It is therefore necessary to determine
the minimum measuring time which will guarantee satisfactory reproducibility of results. In the Mastersizer 2000, the
measuring time can be regulated from 1 to 131 s (half of the
time is designed for red light and the other half for blue light).
A previously prepared sample was placed in the measuring
system, and 10 measurements of PSD were conducted. The
measuring time for each measurement was 5 s. Next, without
removing the sample from the measuring system, another 10
measurements were conducted for a measuring time
extended by 5 s. PSD measurements of 10 were conducted,
each time extending the measuring time by 5 s, up to a measurement time of 40 s. For each measuring time, the changes
of diameter d(0.9) (decile 0.9, i.e., particle size below which
90% of all particles are contained) were monitored, to check
whether all of the large particles get to the measuring cell during the measurement.
2.5 Procedure of soil-sample preparation—
selection of soil-sample dispersion
Natural aggregations of soil particles require breaking down
before PSD can be determined; otherwise the aggregates will
break down during the measurement and cause instability
and a lack of result reproducibility (Pini and Guidi, 1989). The
efficiency of the soil-sample-preparation method (dispersing
soil aggregates) can be determined by analyzing change (or
lack of change) in the value of diameter d(0.5) (also known as
the median) during consecutive measurements.
Measurements concerned with the methodology of soil-sample preparation were conducted for the following methods of
dispersion:
– application of ultrasound (by ultrasonic probe built-in to the
Hydro MU adapter with minimum and maximum power) to
the soil samples placed in the measuring system in dry
form;
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J. Plant Nutr. Soil Sci. 2011, 174, 624–633
– application of ultrasound with tip displacement of 20 lm
(maximum power) to soil samples which were soaked in
water for 6 and 24 h;
– application of a solution of Na-hexametaphosphate and
anhydrous CaCO3 (35.7 g Na-hexametaphosphate and
7.94g anhydrous CaCO3 topped up with distilled water to
1000 mL [Polish Standard PN-R-04032, 1998]), sometimes
known as calgon;
– application of ultrasound with a tip displacement of 20 lm
(maximum power) to soil samples which were prepared
with calgon (for 40 g of soil sample: 50 mL of calgon was
added to samples containing carbonate—samples from
Calcaric Cambisols, profiles 18–22; and 25 mL of calgon
was added to soil samples not containing carbonate).
At this stage of the experiment, all measurements were conducted within 1 h from the moment the sample was placed in
the measuring system. In the case of ultrasound application,
the ultrasonic probe operated during the measurement. The
results were registered at 60 s intervals.
2.6 Procedure of soil-sample preparation—other
stages of this work
Regardless the results of the selection of the sample dispersion for all other stages of this work the chemical procedure
of soil dispersion was chosen. The argument was to be compatible with ISO 11277 (1998) standard. It was experimentally
verified that the median of dispersed soil did not change during the measurement—verifying that all aggregates were broken up and that the sample remained stable throughout the
measurement.
2.7 Selection of theory and—in the case of the Mie
theory—selection of optical parameters
The next stage of the research consisted of evaluating the
impact of the selection of a theory (Mie or Fraunhofer) applied
Methodological aspects of laser PSD 627
to convert the diffraction data to PSD. In the case of the Mie
theory being chosen, the impact of selection of optical properties was also determined. Selection of the Mie theory entails
the necessity of defining the optical parameters: the refractive
index for the dispersing medium, and the refractive and
absorption indexes for the medium being dispersed. The
refractive indexes for the two mediums should differ considerably from each other.
Since soil is a heterogeneous mixture containing different
minerals (with different optical properties), it is necessary to
assume approximate values for the optical properties of the
investigated suspensions. On the basis of literature, in this
work it was assumed that the smallest value of refractive
index was 1.43 (for opal) and the biggest was 3.22 (for hematite) (Sperazza et al., 2004). The parameters defined by the
manufacturer for materials similar to soil were taken into
account (the set of parameters called China Clay (lo), China
Clay (av), China Clay (hi) and default parameters for samples
with unknown properties) (Malvern Worcs, 1999). Because
there is a broad gap between the value of refractive index
which is recommended by the manufacturer and the maximum value for hematite, a value for refractive index equal to
2.00 was taken as an intermediate value. The absorption
indexes were selected so as to take into account materials
which were completely transparent (absorption index equal to
0) and completely absorbing (absorption index equal to 1)
(Sperazza et al., 2004). Intermediate values of 0.01 and 0.1
were also chosen. Table 2 presents a compilation of investigated theories and values of optical parameters.
As a measure of selection of the theory, and in the case of
the Mie theory—the selection of optical parameters, a parameter called “residual weighted” was used. Residual
weighted returns a number that is the % residual in the comparison of the fitted and corrected data when the weighting of
the detector set is factored into the calculation (Malvern
Worcs, 1999). According to the recommendation of the manufacturer, the result is correct if the residual weighted is <
Table 2: Values of optical parameters assumed for calculation. Setup no. 1 corresponds to the Fraunhofer theory; optical parameters are not
defined. Setup no. 10—“Default”—was predefined by manufacturer for materials with unknown parameters. Setup no. 8, 13, and 17 were
predefined by the manufacturer for materials similar to soil and were called respectively “China Clay (lo)”, “China Clay (av)”, and “China Clay
(hi)”.
Number
of setup
Refractive
index (RI)
Absorption
index (AI)
Number
of setup
Refractive
index (RI)
Absorption
index (AI)
14
1.555
1
1
Fraunhofer theory
2
3
4
5
1.43
0
0.01
0.1
1
15
16
17
18
1.577
0
0.01
0.1
1
6
7
8
9
1.533
0
0.01
0.1
1
19
20
21
22
2
0
0.01
0.1
1
10
1.52
0.1
3.22
11
12
13
1.555
0
0.01
0.1
23
24
25
26
0
0.01
0.1
1
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628
Ryżak, Bieganowski
1%. For the optical parameters: the lower the values of the
residual weighted, the better suited the optical parameter that
was selected (information from the apparatus manual). The
value of the residual weighted parameter was determined for
all 23 soil samples and for all 26 sets of optical parameters.
Then for each set of optical parameters the values of residual
weighted for all 23 soils were summed up. The lowest value
of sum for any specific set of parameters indicated a wellchosen set of optical parameters.
2.8 Procedure of reducing obscurance in the
course of measurement
In the course of measurements of soil particle distribution,
conducted in water with the use of the Mastersizer 2000
apparatus, there was a methodological problem that had to
be solved. For some soils, because of soil aggregate dispersion, the obscurance increased above the maximum level of
20% recommended by the manufacturer. To eliminate that
phenomenon, detrimental to the credibility of the measurements, a procedure was developed for the removal of excess
particles during the course of the measurement, thus reducing the obscurance. In brief, when obscurance exceeded a
level of 20% during the course of the measurement, the
recording of laser-beam diffraction on the detectors was
stopped without stopping the stirring and flow of the suspension through the measurement cell. While the pump continued to run, the drain hose (provided for draining the suspension from the measurement cell to the beaker) was disconnected. This permitted a part of the suspension to be drained
into a vessel prepared in advance and removed from the
measuring system, thus reducing the obscurance. Then the
volume was supplemented with distilled water up to 800 cm3.
This operation was repeated until an obscurance of 10% was
obtained. After this procedure was completed, the drain hose
was reconnected to the measuring system and the measurement was resumed. This procedure is described in detail by
Bieganowski et al. (2010).
J. Plant Nutr. Soil Sci. 2011, 174, 624–633
3 Results and discussion
3.1 Selection of pump and stirrer speed
The measure of stability of results is taken to be the variation
coefficient calculated for decile 0.9—d(0.9). This decile is
selected because it describes the limit between the biggest
particles in suspension and all others. The relationship between the variation coefficient for decile 0.9 and changes of
pump and stirrer speed in the measuring system is presented
in Fig. 1.
Based on Fig. 1 it can be stated that the results obtained for
speeds < 2000 rpm are burdened with a big uncertainty. This
uncertainty is caused by the segregation of the soil sample
by sedimentation. The energy provided by the stirrer is too
low to assure a good representation of the soil sample and
the heaviest particles are “visible” in the measuring cell. It is
worth adding that at a pump and stirrer speed equal to
1200 rpm, the soil particles are not totally moved from the
beaker to the measuring cell. At a speed of 3000 rpm, splashing out of the suspension was observed (in spite of the fact
that the beaker was filled by water to ≈ 4/5 of its volume)
which caused a change in the properties of the measured
particles during the measurement. Taking into account the
results obtained in this part of the experiment, a pump and
stirrer speed equal to 2500 rpm was assumed for further
work. The optimal pump and stirrer speed which was determined and accepted for further experiments should not be
treated as a universal value. For example, a pump and stirrer
speed equal to 1800 rpm, proposed by Sperazza (Sperazza
et al., 2004), was found to be too low in our experiments (see
Fig. 1). It is probable that in the case of sediment samples
< 50 lm, a speed of 1800 rpm would be sufficient.
In the event that the suspension being measured has a more
homogeneous composition with regard to mass particles, a
lower speed of pump and stirrer is sufficient. In general, the
determination of the parameter of pump and stirrer speed
depends on the properties of the sample being measured,
and information about this should be put in the methodological part of the paper.
Figure 1: Relationship between the variation coefficient for the value of decile d(0.9) and the changes of
pump and stirrer speed in the measuring system of
an Eutric Cambisol.
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J. Plant Nutr. Soil Sci. 2011, 174, 624–633
Methodological aspects of laser PSD 629
Figure 2: Relationship between variation
coefficient for decile d(0.9) and changes in
the duration of measurement of an Eutric
Cambisol.
3.2 Selection of measuring time
To select the duration of measurement, similarly as for the
selection of pump and stirrer speed, the decile d(0.9) was
assumed as a measure of result correctness. The relationship between variation of decile d(0.9) and duration of measuring time is presented in Fig. 2. Based on analysis of the
relationship presented in Fig. 2 one can observe that the
value of the variation coefficient stabilizes after a measurement time of ≈ 20–25 s. The total measuring time is linearly
correlated to the number of individual measurements (in 1 s,
the apparatus realized 1000 sample measurement “snap
shots”). Therefore the graph presented in Fig. 2 can be interpreted as follows: during a shorter measuring time the probability that all particles will appear in the measuring cell in the
same proportions as in the sample is small. Hence, the big
differences between results—the number of particular measurements (snap shots) is too small to obtain representative
results. Not until the measuring time is long enough do the
results stabilize, because the number of “snap shots” is
enough to obtain a representative distribution.
For our investigations, a measuring time of 30 s was
assumed, which in practice came down to reading the result
once per minute (30 s for measurement in red light and 30 s
for measurement in blue light). In literature, information about
the duration of measurement appears only occasionally.
From a methodological point of view, this makes it difficult to
evaluate the uncertainty of results presented in publications.
As in the case of selection of pump and stirrer speed, there is
no universal measuring time fit for all samples. For example,
in the work quoted above, Sperazza et al. (2004) assumed
12 s as the measuring time. It is possible that for measuring
fine particles (< 50 lm) a measuring time of 12 s might be
sufficient.
3.3 Procedure of soil-sample preparation
(dispersion)
The procedure of dispersing soil aggregates is, from the point
of view of determining particle-size distribution, one of the
 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
most important factors affecting the reliability of the results.
Insufficiently broken up soil aggregates disintegrate during
the measurement and change the properties of the sample
during the measurement. In literature, one can find many
methods of dispersing soil samples. Nowadays, the most frequently used methods are: chemical dispersion (using a solution of Na-hexametaphosphate, sometimes with anhydrous
CaCO3) and physical dispersion (using ultrasounds). Chemical dispersion has been repeatedly verified as an effective
method, resulting in the inclusion of this method in international standards (ISO 11277, 1998). In this work, the chemical
dispersion method of sample preparation was treated as a
reference method. The application of ultrasound is a faster
method of soil dispersion than the application of a solution of
Na-hexametaphosphate, hence its attractiveness and wider
usage (Gee and Bauder, 1987; Konert and Vandenberghe,
1997; Goossens, 2008; Singer et al., 1988; Pye and Blott,
2004). This is evidenced by the fact that nowadays ultrasound probes are built-in to apparatus used for the determination of PSD by laser diffraction. In literature, one can find
the combination of these two methods of soil dispersion, i.e.,
chemical dispersion combined with ultrasound dispersion
(McCave et al., 1986; Pini and Guidi, 1989; Buurman et al.,
1997; Zobeck, 2004; Arriaga et al., 2006).
As a measure of the effectiveness of soil dispersion, the variation of median (so-called diameter d(0.5)) for PSD was
assumed. The lack of change in d(0.5) in successive measurements shows that in a given dispersion method it is impossible to break down more soil aggregates after d(0.5) stabilizes. Sample graphs of median variation during successive
measurements in the soil sample from Mollic Gleysol are presented in Fig. 3. To sum up the data presented in Fig. 3 and
the results of the experiments, it should be stated that—as
expected—the chemical method of dispersion was entirely
sufficient (in Fig. 3, the variation of median in time is practically invisible). Equally sufficient was the application of the
ultrasound probe with the maximum power for Mastersizer
2000 – 35 W (20 units). Stabilization of the median in this
case occurred after 3–4 min. After ≈ 10 min, the value of the
median reached the same value as in dispersion with the use
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Ryżak, Bieganowski
J. Plant Nutr. Soil Sci. 2011, 174, 624–633
Figure 3: Relationship between median
d(0.5) and measuring time for different
methods of soil-sample dispergation for
Mollic Gleysol.
of the Na-hexametaphosphate solution. Using the ultrasound
probe with the minimum power (2 units) did not give satisfactory results because even after 60 min the value of the median was greater than in the case of chemical dispersion.
The initial dispersion of samples by soaking in water for 6 and
24 h before the measurement and then using the ultrasound
probe did not change the situation, i.e., in the case of ultrasound with maximum power it did not speed up the stabilization of the value of the median, and in the case of ultrasound
with minimum power it did not cause a decrease in the value
of the median to a level which would correspond to the value
obtained for chemical dispersion. Very similar relationships
were obtained for the other investigated soils. Obviously, in
each case the variation in the median value was different (the
smallest for Orthic Luvisol and the largest for Calcaric Cambisol) depending on the soil aggregate stability (Bieganowski
et al., 2010). In general, chemical dispersion using hexametaphosphate solution and physical dispersion using ultrasound (with a maximum power for 4 min) are equivalent
methods for soil-sample dispersion. It should be kept in mind
that the power of the ultrasound and the duration of ultrasonic
probe operation determined in this work are connected with
the measuring system, i.e., the maximum power is defined by
the apparatus and the volume of suspension in the beaker.
The volume of suspension in this research was 800 mL in a
1000 mL beaker. Changing this parameter requires additional
validation. It is worth noting that using the ultrasound probe
reduced the measuring time significantly. In the case of using
the hexametaphosphate solution, the results were stable
almost from the very beginning, but it should be kept in mind
that the procedure of sample preparation using hexametaphosphate solution is long and tedious. In this context, a time
of 4–5 min for the ultrasound method meant cutting down the
measuring time significantly. An additional advantage of
using laser diffractometry is the possibility of monitoring the
effectiveness of soil aggregate dispersion. Recording the
median of distribution (or any other decile) is easy and does
not require any additional work.
In discussing the problems with sample dispersion, it is worth
mentioning another problem that is sometimes raised in literature. Some authors suggest that an elongated time of
 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ultrasound application can cause not only the break-down of
soil aggregates but also grinding of the “elementary” soil particles (Chappell, 1998; Pye and Blott, 2004; Sperazza et al.,
2004). Results obtained in this work seem to negate this suggestion because the value of the median (during ultrasound
dispersion) stabilized at a specific level and stayed at this
level even after 1 h. The same was true for chemical dispersion. In the case of the grinding phenomenon occurring, the
value of the median should continually decrease and reach a
value below that which was obtained for chemical dispersion.
Based on the results obtained in this investigation, it should
be stated that these two methods cannot be combined. In
Fig. 4, the variation of the median (for soil samples prepared
before the measurement with hexametaphosphate solution)
during ultrasound dispersion is presented. In all cases, increases of the median were observed, with the exception of
Orthic Luvisol. This verified that aggregation of small particles
into bigger ones occurred. This phenomenon has been observed before by other scientists (Chappell, 1998; McCave
et al., 1986).
3.4 Selection of the theory and in case of Mie
theory selection of optical parameters
Sum of the values of the residual parameter are presented in
Fig. 5. The lower the value of the residual parameter the better the distribution matches the data obtained from the measurement. That is why the selection of the theory (and in the
case of the Mie theory the selection of the set of optical parameters) was adopted as the criterion for the minimum of sum
calculated for all the soils. The lowest value of this sum was
obtained for the Fraunhofer theory. Therefore, it is the Fraunhofer theory that should be selected in the measurement of
soil samples.
In literature, one can find contradictory information concerning the use of a defined theory for data conversion. Some
authors choose the Fraunhofer theory (Beuselinck et al.,
1998; Pye and Blott, 2004; Loizeau et al., 1994), while others
prefer using the Mie theory (Buurman et al., 1997, 2001;
Eshel et al., 2004; Zobeck, 2004; Arriaga et al., 2006; Sperazza et al., 2004). The international standard ISO 13320
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J. Plant Nutr. Soil Sci. 2011, 174, 624–633
Methodological aspects of laser PSD 631
Figure 4: Relationship between the median
d(0.5) and the time of measurement by
simultaneous application of chemical dispersion (hexametaphosphate solution) and
physical dispersion (ultrasound with the
maximum power of 35W) for all investigated
soil types.
recommends using the Fraunhofer theory when measuring
particles > 50 lm and the Mie theory when measuring particles that are < 50 lm (ISO 13320, 1999). In the case of soil it
is difficult, because in soil samples particles of various sizes
occur. The reason for which the Fraunhofer theory gives better results for soil samples might be heterogeneity of samples, especially optical heterogeneity. There are different
mineral and organic particles in soil. Only among mineral particles there might be such as posses small and big values of
the refractive index (see Tab. 2 where refractive index varies
from 1.43 for opal to 3.22 for hematite). That is why arbitrary
assumption of one set of optical parameters might be the
source of uncertainty of final results. Using the Fraunhofer
theory eliminates the necessity of defining the optical properties and, consequently, reduces the uncertainty. However, if it
was necessary to choose the Mie theory then comparably
small values of the sum of the residual parameter were obtained for sets of optical parameters number 5 (RI = 1.43;
AI = 1), 9 (RI = 1.533; AI = 1), 14 (RI = 1.555; AI = 1), and 18
(RI = 1.577; AI = 1). It is worth to notice that for all these sets
of parameters the value of absorption index was equal 1. On
the base of this, one can conclude that from those two optical
parameters, in the case of determining PSD, the absorption
index is the most important. The value determined in our
experiments is different from that proposed by the producer.
As far as the value of the refractive index is concerned, one
of the three values given by the producer in the software
might be assumed.
Relating to data from literature, it is necessary to quote
repeatedly the mentioned work by Sperazza et al. (2004) who
obtained a final conclusion similar with presented in this
work. The authors evaluated fitting of the distribution obtained with the LDM to the distribution obtained for properly
prepared samples by mixing known proportions of given fractions. They concluded that as absorption reached a value of
1, the values for sediment concentration calculated by the
software were the closest to our measured sediment concentration. At absorption settings ≥ 0.9 for mixed mineral compositions the difference from varying RI values was negligible.
Estimated grain-size distributions were highly dependent on
values of absorption setting for analyses of natural sediments.
4 Conclusions
(1) The pump and stirrer speed selected for specific analysis
will be dependent on the design of the apparatus and on the
extent of heterogeneity of measured samples (with respect to
PSD). For homogeneous samples, this speed may be lower.
Figure 5: Sum of the values of the residual
parameter for investigated soil samples. Numbers
determine the assumed parameters corresponding
to the numbers of sets determined in Tab. 2.
 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
www.plant-soil.com
632
Ryżak, Bieganowski
Thus it is indispensable to evaluate this parameter every time
before measurements are conducted on a new material. The
assumed parameters must be presented in the methodological part of the work.
In this work the optimal speed of pump and stirrer was determined to be 2500 rpm.
(2) The selection of the measuring time depends on the heterogeneity of the measured sample (with respect to PSD).
Thus it is also important to present the choice of this parameter in the experiment in the methodological part of the
work.
In this work the measuring time was assumed as equal to
1 min (30 s for red light and 30 s for blue light).
(3) The dispersion of soil samples for PSD measurement
may be carried out in two practically equivalent methods:
chemically (using hexametaphosphate solution) or physically
(by ultrasound). In the case of using ultrasound, the power
and the duration of ultrasound operation should be experimentally chosen because these are dependent on the design
of the ultrasound probe and on the type and volume of substance measured. The analysis of variation (or lack of variation) and the value of the distribution median is a good parameter which permits evaluation of the efficiency of dispersion.
The value adopted should be described in the methodological
part of the work.
For the soil samples measured in this work, the power of
ultrasound probe was 35 W and the duration was equal to
4 min—this dispersion was practically equivalent to the chemical dispersion.
(4) One must not simultaneously use the chemical dispersion
(using hexametaphosphate solution) and the physical dispersion (using ultrasound) because this may cause an opposite
effect, i.e., secondary aggregation instead of dispersion.
(5) Since the soil is a mixture of small particles (∅ < 50 lm)
and big particles (∅ > 50 lm) with different optical properties
(refractive index and absorption index), the Fraunhofer theory
should be used for the conversion of the intensity of scattered
light into PSD. In the case of using the Mie theory, the best
results were obtained for a refractive index between 1.5 and
1.6 and for absorption index equal to 1.0.
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