Analysis of the ASTM Round-Robin

Test on Particle Size Distribution of

Portland Cement: Phase I

Chiara F. Ferraris

Vincent A. Hackley

Ana Ivelisse Avilés

Charles E. Buchanan, Jr.

NISTIR 6883
NISTIR 6883

Analysis of the ASTM Round-Robin

Test on Particle Size Distribution of

Portland Cement: Phase I

Chiara F. Ferraris

Building and Fire Research Laboratory

National Institute of Standard and Technology

Vincent A. Hackley

Materials Science and Engineering Laboratory

National Institute of Standard and Technology

Ana Ivelisse Avilés

Information Technology Laboratory

National Institute of Standard and Technology

Charles E. Buchanan, Jr.

Roan Industries, Inc.

Bakersville, NC, (USA)

May 2002

U.S. Department of Commerce

Donald L. Evans, Secretary

Technology Administration

Phillip J. Bond, Under Secretary for Technology

National Institute of Standards and Technology

Arden L. Bement, Jr., Director
Abstract

Particle size distribution (PSD) is an essential property of cement. The only standard method to

measure the PSD of cement, namely ASTM C115 [1] is limited in scope; this standard describes

a method for determining “fineness” with a lower size detection limit of 7.5 μm. As there is no

standard procedure covering the whole range of cement PSD, the implementation of different

measurement methods varies widely within the industry. In general, the round-robin results

summarized here have demonstrated the high variability between participants using instruments

based on the same physical principles.

ASTM committee C01.25.01 sponsored a round-robin test to measure the PSD of cement. The

aim of the current report is to analyze the data generated during those tests and to summarize the

various approaches available to measure the PSD of cement. The analysis of the data is

conducted in two parts. In the first part, an attempt is made to establish a reference distribution

using a standard cement powder (SRM 114p). This is followed up by a comparison of the roundrobin data in order to initiate discussion on developing a standard test method for cement PSD to

be submitted for ASTM consideration. The report provides all raw data collected during the

round robin tests, and the results of a statistical analysis of the collected data.
Acknowledgements

The authors would like to thank the ASTM Task Group C01.25.01 that provided the data from

the round-robin test. We would like to thank all the participants (listed below in alphabetical

order) of the round-robin for their comments that allowed us to better understand the industry’s

perspective.

Also, we would like to thank Robin Haupt and the staff of Cement and Concrete Reference

Laboratory (CCRL) who were instrumental in providing the samples to the round-robin

participants.

Participants to the Round-Robin:

Ray Braun, Southdown Cement

Gregory Buchanan, Roan Industries, Inc.

Paul Bussee, Southdown

Mario Cesar Cabrera – Cabrera, CENAM

Bob Collins, Blue Circle

Mike Coole, Blue Circle Industries PLC

Fraser Deas, Blue Circle Cement

Jim Kaminski, Malvern

Jennifer Kimball, Dragon

Larry Necessary, Roanoke

Doug Ostrander, Lehigh Cement Co.

Greg Pokrajac, Particle Sizing Systems

Sadananda Sahu, RJ Lee Group, Inc.

Brian Sears, Horiba Instruments Inc.

Nile R. Strohman, W. R. Grace & Co.

Craig Szabo, Lafarge

R.L. Tuttle, Holnam, Inc.

Jesse Uribe, TXI

Ren Xu Coulter
TABLE OF CONTENT

1 INTRODUCTION................................................................................................................. 1

2 DESCRIPTION OF METHODS USED IN THE CEMENT INDUSTRY...................... 3

2.1 LASER Diffraction ............................................................................................................. 3

2.2 Electrical Zone Sensing (Coulter Principle) ....................................................................... 5

2.3 Scanning Electron Microscopy........................................................................................... 6

2.4 Sedimentation ..................................................................................................................... 7

2.5 Sieving ................................................................................................................................ 9

3 ANALYSIS OF DATA FROM THE ROUND-ROBIN................................................... 10

3.1 Reference distribution using SRM 114p........................................................................... 10

3.1.1 Determination of reference distribution using Approach 1: all methods................. 11

3.1.2 Determination of the reference distribution for LASER wet only (Approach 2) ...... 14

3.1.3 Summary ................................................................................................................... 15

3.2 Analysis of the data by method......................................................................................... 19

3.2.1 LASER Diffraction with the specimen dispersed in a liquid (LAS-W)...................... 19

3.2.2 LASER diffraction with the specimen dispersed in air (LAS-D)............................... 19

3.2.3 Electrical Zone Sensing (EZS).................................................................................. 20

3.2.4 SEM and Sedimentation (SED)................................................................................. 20

3.2.5 Summary ................................................................................................................... 21

4 COMPARISON OF THE VARIOUS METHODS USED .............................................. 22

5 CONCLUSIONS ................................................................................................................. 23

6 REFERENCES.................................................................................................................... 24

APPENDICES ...........................................................................................A-25
TABLE OF FIGURES

Figure 1: All data from SRM 114p............................................................................................... 11

Figure 2: Data with the Bootstrap mean after the outliers are eliminated. ................................... 13

Figure 3: Example of correction obtained using the correction factor. The cement used was

CCRL 131. (A) only the outliers R and L were not plotted; (B) the outliers identified by the

bootstrap method are not included........................................................................................ 14

Figure 4: Comparison between the distribution calculated from all the data and the one calculated

from only the LAS-W data. .................................................................................................. 16

Figure 5: Bar graph of the median diameters for all the methods. ............................................... 22

TABLE OF TABLES

Table 1: Particle size measurement methods commonly used in characterizing fine inorganic

powders................................................................................................................................... 2

Table 2: Data from all methods except sets L and R. The results from the Bootstrap calculation

are also shown. Data that lie outside the 95 % confidence limits are shown in bold, and data

that are greater than 5 % outside the 95 % confidence limits are indicated as gray cells..... 12

Table 3: Bootstrap mean and 95 % confidence limits calculated without the outliers................. 13

Table 4: Bootstrap data for the LAS-W without the outliers (B, J, N , U) ................................... 15

Table 5: Data from LAS-W without the sets L and R. The results from the Bootstrap calculation

is also shown. In bold the data that are outside the 95 % confidence limits and in the gray

area the data that are more than 5 % outside the 95 % confidence limits............................. 17

Table 6: Average median diameter from LAS-W method............................................................ 19

Table 7: Average median diameter from LAS-D method. ........................................................... 20

Table 8: Average median diameter from EZS method. ................................................................ 20

Table 9: Median diameters by SEM and Sedimentation .............................................................. 21
1

1 Introduction

Cement can be a problematic material in the application of particle size analysis. First, the size

distribution itself is extremely broad, extending in most cases over two to three orders of

magnitude, from about 100 μm down to below micrometer size. In general, sizing techniques

work best over a limited size range. The optimum range of particle size analysis varies according

to a number of factors, including detector sensitivity and the assumptions associated with the

underlying principle of measurement. Second, cement particles are highly agglomerated in the

dry state, and therefore must be properly dispersed in order to determine the “true” particle size

distribution (PSD). Standard protocols for dispersing cement particles prior to analysis by wet

methods are nonexistent, and the degree of dispersion achieved in dry dispersion (air) methods

will likely vary depending on the method used, the geometry of the dispersing device, the

residence time in the sensing zone and the applied shear force employed to separate physically

agglomerated particles. This introduces a potentially large source of variation at the sample

preparation stage. Third, cement particles are typically irregular in shape and inhomogeneous in

composition. Most commercial methods (see Table 1) are designed specifically for, or work best

with, homogeneous spheres. The degree to which irregularity affects the results vary with

technique, and is generally not well understood or accounted for properly in many methods.

A universally recognized standard method for characterizing the complete PSD of cement

particles does not currently exist [2]. The only standard test, ASTM C115 [1] (also known as the

Wagner test), is really designed to measure the “fineness” of a cement powder and it is limited to

a minimum particle size of 7.5 μm. As there is no standard procedure covering the whole range

of cement PSD, the implementation of different measurement methods varies widely within the

industry. Therefore, there is the necessity of having a method in which cement is used as a

standard. Other potential sources of variability in sizing methods include adjustable instrument

parameters or material property data required as inputs, and fundamental differences due to the

nature of the technique itself. In the latter case, it must be acknowledged that different methods

may “sense” a different aspect of the size distribution. For instance, a given method may be

sensitive to either particle mass, particle number or projected surface area. As a result, for a

polydisperse system, each method produces a distribution with a slightly different weighting.

Thus the “mean” particle diameter values are expected to differ.

ASTM committee C01.25.01 sponsored a round-robin test to measure the PSD of cement. The

scope of this report is to analyze the data generated during those tests and to summarize various

methodologies available. The analysis of the data is conducted in two parts:

• Attempt to establish a reference distribution using a standard cement (SRM 114p)

• Discussion of the data obtained during round robin tests as an initial step toward

development of a standard tests method for submission to ASTM.
2

Table 1: Particle size measurement methods commonly used in characterizing fine

inorganic powders.

Method1 Abbrev. Underlying Principle

Applicable

Size Range2

(μm)

LASER Diffraction

[Fraunhofer Diffraction, Mie Scattering, LASER Light

Scattering, Elastic Light Scattering]

Dry method (-D)

Wet method (-W)

LAS electromagnetic wave

interaction 0.1 - >100

Quasi-Elastic Light Scattering

[Dynamic Light Scattering, Photon Correlation

Spectroscopy, Optical Beating Spectroscopy]

Heterodyne method

Homodyne method

QELS electromagnetic wave

interaction 0.005-2

Small Angle Neutron Scattering

Ultra-Small Angle Neutron Scattering

SANS

USANS wave interaction 0.001 - 10

Small Angle X-Ray Scattering

Ultra-Small Angle X-Ray Scattering

SAXS

USAXS

electromagnetic wave

interaction 0.001 - 3

LASER Doppler Velocimetry

[LASER Doppler Anemometry] LDV

aerodynamics &

electromagnetic

scattering

0.5 - 10

Electrical Zone Sensing

[Coulter Principle, Coulter Counter] EZS volume displacement 0.4 - >100

Differential Mobility Analysis DMA electrostatic

classification 0.005 - 1

Scanning Electron Microscopy

Field Emission SEM

SEM

FE-SEM imaging 0.02 - 10

Transmission Electron Spectroscopy TEM imaging 0.01 – 0.5

X-Ray Gravitational Sedimentation XGS sedimentation 0.5 - 100

Optical Centrifugal Sedimentation OCS sedimentation 0.01 - >5

X-Ray Centrifugal Sedimentation XCS sedimentation 0.01 - >5

Sedimentation Field Flow Fractionation SdFFF sedimentation

classification 0.03 - >1

Sieving - size exclusion 2 - >100

Gas Adsorption Surface Area Analysis

[Brunauer-Emmet-Teller] BET surface area no limit

Acoustic Attenuation Spectroscopy

[Ultrasonic Attenuation Spectroscopy, Ultrasonic

Spectroscopy]

Coupled phase theory

Scattering theory

Multiple scattering theory

AAS acoustic wave

interaction 0.025 - >100

Electroacoustic Spectroscopy

[Electrokinetic Sonic Amplitude] ESA electroacoustic

response

0.1 - 10

1 Terms in brackets represent other names by which the method is commonly known and/or closely related techniques that have

been grouped together under a single general method. Indented terms represent specific variants, implementations or theoretical

constructs used to analyze measurement results.

2 Size ranges are approximate and provide the extreme limits attainable, given access to all commercially available adaptations of

that method. Actual size ranges may vary significantly between instruments and may depend on the test material.
3

2 Description of methods used in the cement industry1

Based on participation in the round-robin testing, and a general knowledge of the industry, the

most commonly used techniques for characterization of the particle size distribution (PSD) in

cement are as follows:

1. LASER Diffraction

a. with the specimen dispersed in liquid (suspension-based)

b. with the specimen dispersed in air (aerosol-based)

2. Electrical Zone Sensing (Coulter Principle)

3. Sedimentation

4. Sieving

5. Scanning Electron Microscopy

In this section, we present a brief description of each method. We discuss the principles of

operation, the range of application, the key parameters, and the requirements for sample

preparation and their potential impact on the measurement results.

2.1 LASER Diffraction

The LASER diffraction (LAS) method involves the detection and analysis of the angular

distribution of light produced by a LASER beam passing through a dilute dispersion of particles.

Typically, a He-Ne LASER (λ=632.8 nm) in the 5 mW to 10 mW range is employed as the

coherent light source, but more recently solid-state diode LASERs have come into use and

provide a range of available wavelengths in the visible and UV spectrum. Since the focal volume

of the beam senses many particles simultaneously, and thus provides an average value, it is

referred to as an ensemble technique. With the exception of single particle optical scattering

(SPOS), all scattering methods are ensemble techniques, and only ensemble methods will be

considered here. There are a number of different diffraction and scattering phenomena that can

be utilized for particle sizing. Likewise, there are a number of different ways to define and

classify these methods, depending on the underlying principle or its application. We have chosen

here to classify all time-averaged scattering and diffraction phenomena involving LASER optics,

under the general heading of LASER diffraction; however, it should be noted that “LASER

diffraction” is often used in a more narrow way to refer to techniques that utilize only low-angle

scattering. See Table 1 for a list of equivalent or related methods.

Strictly speaking, one can differentiate between light waves that are scattered, diffracted or

absorbed by the dispersed particles. The scattered light consists of reflected and refracted waves,

and depends on the form, size, and composition of the particles. The diffracted light arises from

edge phenomena, and is dependent only on the geometric shadow created by each particle in the

ballistic light beam: diffraction is therefore independent of the composition of the particles. In

the case of absorption, light waves are removed from the incident beam and converted to heat or

 

1

 Commercial equipment, instruments, and materials mentioned in this report are identified to foster understanding.

Such identification does not imply recommendation or endorsement by the National Institute of Standards and

Technology (NIST), nor does it imply that the materials or equipment identified are necessarily the best available for

the purpose.
4

electrical energy by interaction with the particles; absorption depends on both size and

composition.

The influence of composition is revealed through the complex refractive index, m = n − ik , where

i = −1 . For nonabsorbing (i.e., transparent) particles, k = 0, where k, the imaginary component

of the refractive index, is related to the absorption coefficient of the material. Both the real part

of the refractive index, n, and the imaginary part, k, are wavelength-dependent. Scattering arises

due to differences in the refractive index of the particle and the surrounding medium (or internal

variations in heterogeneous particles). Therefore, in order to use a scattering model to calculate

the PSD that produced a specific scattering pattern, one must first know the complex refractive

index of both the particles and the medium (typically, the latter is selected such that k = 0).

Values of n have been published for many bulk materials [3], but in the case of cement, n is

routinely estimated based on a mass average of the refractive indices for the individual material

components [4]. The imaginary refractive component is more difficult to determine and/or find

in the published literature [5, 6], and this often represents a significant challenge to the use of

scattering methods for fine particle size measurements [7].

The influence of absorption becomes more important as the particle size decreases, and is

therefore more likely to impact the range below the micron of the cement PSD. As a general rule

of thumb, the darker or more colored a specimen appears, the higher the imaginary component.

For white powders, such as high-purity alumina, k=0. Cement, on the other hand, is generally

gray to off-white in color, and therefore one can anticipate a finite, but relatively low value for

the imaginary component (k = 0.1 is often reported for cement, although this value is unverified

and will likely vary for different formulations).

Mie theory, which describes scattering by homogeneous spheres of arbitrary size, is the most

rigorous scattering model available, and is used in many commercial instruments. For nonspherical particles like cement, Mie theory provides a volume-weighted equivalent spherical

diameter. Mie theory has been applied with mixed success to the analysis of fine powders with

diameters from several 100s of micrometers down to several tenths of micrometers. An accurate

representation of the “true” size distribution by Mie scattering is dependent on a knowledge of

the complex refractive index, and will be impacted by the degree of asymmetry present in the

particles and the dispersion procedure used to prepare the test sample. The Mie approach does

not work well for extremely fine particulates in the range below 100 nm, possibly because of

increased sensitivity to changes in the refractive index that occur with these materials.

For very large particles (relative to the wavelength of light), the diffraction effect can be

exploited without reference to Mie theory or the complex index of refraction. Diffracted light is

concentrated in the forward direction, forming the so-called Fraunhofer diffraction rings. The

intensity and distribution of diffracted light around the central beam can be related to particle

size, again assuming spherical geometry. The range of validity for this method is limited on the

low end to particle diameters a few times greater than the wavelength of the incident light for

particles that are opaque or have a large refractive index contrast with the medium [8]. For

somewhat more transparent particles, or particle with a moderate refraction contrast, the lower

limit is increased to about 40 times the wavelength of light. For a He-Ne LASER, this

corresponds to about 25 μm. The benefit of using Fraunhofer diffraction is that the interpretation
5

is not dependent on the absorptive or refractive properties of the material. A totally absorbing

black powder, a translucent glass powder, and a highly reflective white powder, having the same

particle size and shape, will produce identical Fraunhofer patterns within the valid size range. On

the other hand, inappropriate use of the Fraunhofer approximation outside of the valid range can

lead to large systematic errors in the calculated PSD [4,9]. These errors are especially prevalent

in the range below the micron size, where errors exceeding 100 % are possible. Partial

transparency can lead to the appearance of “ghost” particles. These are virtual particles,

generally in the range below the micron size, produced as an artifact of refractive dispersion of

light within the transparent particles. The refracted light is registered at large scattering angles as

anomalous diffraction, and is therefore interpreted by the Fraunhofer analysis as being produced

by very small particles.

In general, the LAS method requires that the particles be in a dispersed state, either in liquid

(suspension) or in air (aerosol). The former is commonly referred to as the “wet” method (LASW) while the latter is termed the “dry” method (LAS-D). In Fraunhofer diffraction, the pattern

does not depend on the refractive index, so there is no theoretical difference between using a

liquid or a gas as a dispersing medium. For Mie scattering, the higher refractive index contrast in

air, compared with most liquids, may somewhat impact the scattering pattern, but should not

alter the results in any way.

Differences between LAS-D and LAS-W methods arise primarily from the different ways in

which the particles are dispersed in each case. In liquid, it is possible to modify solution

conditions, by changing pH or adding chemical dispersing agents for example, or to break up

aggregates using mechanical or ultrasonic energy. Thus, in general, a better state of dispersion

can be achieved in an appropriately selected liquid medium. For silicates and most metal oxides,

water is an excellent dispersing medium. However, due to the reactive nature of cement in water,

alcohols, such as isopropanol, methanol, and ethanol, are commonly used in its place. In the

LAS-D method, a stream of compressed air (or a vacuum) is used to both disperse the particles

and to transport them to the sensing zone. This method of dispersion works well for large, noncolloidal-phase spheroids, where the interfacial contact area is small and the physical bonds

holding the individual particles together are relatively weak. For the particles smaller than a

micron and highly asymmetric, the higher surface-to-volume ratio results in more intimate and

numerous contact points and, as a consequence, a greater driving force is needed to separate

aggregated particles.

2.2 Electrical Zone Sensing (Coulter Principle)

The electrical zone sensing (EZS) technique is based on the Coulter principle. In this method, the

powder is dispersed at a very low concentration in an electrolytic (i.e., conducting) solution,

which is then drawn through a small orifice in an insulating wall on either side of which

electrodes are placed. As each particle enters the orifice, or sensing zone, the volume of solution

displaced by the particle causes a transient change in the measured electrical impedance across

the opening. The amplitude of this impedance pulse is proportional to the particle’s volume. By

accumulating pulses over time, a PSD is constructed. EZS is a particle counting method capable

of producing a number-weighted or mass-weighted distribution of particle sizes.
6

In order to relate the registered pulse amplitude to a specific particle size or volume, the

instrument must be calibrated using particles having a narrow size distribution (i.e.,

monodisperse). Alternatively, the instrument can be calibrated using the test powder itself, if the

entire size range of the powder is covered in the measurement. If particles are present that are too

small to register a pulse, then the fraction of undetected particles can be determined by

comparing calibration results from both methods.

Different size apertures can be used depending on the size range of interest; multiple orifices can

be employed for powders having a very broad distribution of sizes, like cement. In the latter

case, the orifice detection ranges should overlap. A range of orifice sizes are normally available,

from 10 μm up to 2000 μm. The applicable range of particle sizes that can be measured using

any given orifice is from about 2 % to 40 % of the orifice diameter [11]. Therefore, the

maximum applicable size range is from 0.2 μm to 800 μm, although a lower limit of 0.6 μm is

probably more realistic for normal operating conditions [10]. The lower detection limit arises due

to electrical and thermal interference. For particles with a density similar to the liquid, there is no

theoretical upper limit. For denser particles, the ability to keep the larger particles suspended is a

limiting factor. The use of higher viscosity liquids can help in this case.

Coincident passage of two or more particles through the sensing zone is a potential source of

error in EZS measurements. Coincidence can cause the instrument to count the combined pulse

height of multiple small particles as a single large particle, thereby skewing the size distribution

towards the high end. A pulse discrimination system can be adjusted to correct for this effect by

rejecting distorted pulses. Another potential problem is particle asymmetry. Asymmetric (flaky)

particles, commonly found in cement, rotate as they pass through the orifice. Since it is the

volume swept out by the particle that is measured, this can also lead to oversizing. Porous

particles (e.g., fly ash) are generally unsuitable for EZS measurements, because their effective

densities are not known.

2.3 Scanning Electron Microscopy

In this method, a focused electron beam (5 kV to 50 kV) is scanned over the sample in parallel

lines. The particles are fixed onto a planar substrate, and are normally coated with a thin

conductive layer, often an amalgam of gold and palladium. The electrons interact with the

sample, producing an array of secondary effects, such as back-scattering, that can be detected

and converted into an image. The image can then be digitized and presented to an image

analyzer, which uses complex algorithms to identify individual particles and record detailed

information about their morphology. In this manner, size and shape can be accurately assessed,

but only for a relatively small population of particles (a few hundred at best). By comparison,

most ensemble techniques (e.g., LAS) sample thousands or tens of thousands of particles

simultaneously. Scanning electron microscopy (SEM) is therefore a particle counting technique

and produces a number-weighted size distribution. In actuality, SEM measures the projected

surface area diameter or length.

Limitations and errors in the SEM method generally arise from two sources: sample preparation

and image distortions or irregularities. Probably the single largest source of error is sample

preparation. In order for the analyzer to avoid confusing single particles that are touching
7

(coincident) with larger particles or agglomerates, the primary particles must be well dispersed in

a monolayer on the substrate surface, and must be clearly separated from each other. Specimens

formed by drying of a dilute suspension onto a SEM support often contain agglomerates that

form during the drying process. Specimens formed from a dry powder always exhibit

agglomerative artifacts, and are not suitable for size assessment. In addition, the particles in the

test specimen must be homogeneously distributed over the measurement field, so that the

analysis accurately reflects the true distribution. Segregation of particles during sample

preparation can lead to heterogeneous deposition, which can cause large systematic errors. An

additional source of uncertainty comes from the poor statistical sampling that results from the

relatively low number of particles counted by SEM analysis, compared with ensemble methods

like LAS or other single particle counting techniques like EZS.

A practical resolution of 15 nm to 20 nm can be expected for SEM, establishing a lower limit for

accurate particle size analysis of about 0.2 μm in secondary electron mode. An order of

magnitude improvement can be obtained using the newer field emission SEM (FESEM), which

has a practical resolution of about 1 nm. The FESEM uses lower electron voltages and generally

does not require a conductive coating. The upper limit for imaging techniques like SEM is

statistically-limited, since fewer large particles will be present in the same imaging field, and

thus as the particle size increases it will require a prohibitively large number of separate

specimens to obtain a statistically acceptable number of particles. This counting issue will be

especially important at the upper size range for cement, where particles approach 100 μm in

diameter. The image analyzer can be calibrated using a standardized graticule.

The primary benefit of SEM analysis is that it provides highly detailed information about not

only particle size, but also particle shape, surface texture and chemical composition, and at

resolutions not approachable by other techniques. Transmission electron microscopy (TEM),

which measures the transmitted electron beam after it passes through the sample, is applicable

for particle sizing in the extreme lower size limit, below 0.2 μm, although much of the three

dimensional information is lost in this case. Drawbacks of using electron microscopy as a routine

sizing method are time, high cost and the high level of operator expertise and training necessary.

2.4 Sedimentation

Sedimentation methods are based on the application of Stokes' Law, which describes the

terminal velocity for an isolated sphere settling in a viscous fluid under the influence of a

gravitational field (i.e., free falling). For low Reynolds numbers (i.e., laminar flow conditions),

the terminal velocity depends on the density contrast between the particle and medium, the

viscosity, and the particle size.

Applications of sedimentation can be grouped into cumulative and incremental techniques [11].

In the cumulative method, the rate at which the particles settle is determined, typically by

weighing the mass of settled particles at a certain depth over time. In the incremental method, the

change in concentration or density of the material with time is measured at known depths,

typically using optical or X-ray sensing. Because of the faster analysis time and better suitability

for automation, incremental methods have found greater commercial application. In particular,

the X-ray sedimentation (XGS) method is well established in several industries. In XGS, the

absorption of a thin horizontally collimated X-ray beam is determined at a known depth and
8

time, and referenced to the absorption of the pure solvent. The absorption caused by the presence

of the particles at a specified depth at a given time is proportional to the concentration (by mass)

of particles at that depth having a diameter smaller than dS, where dS is the calculated Stokes

diameter. By measuring the particle density at different depths and times, a cumulative massaveraged distribution is generated.

Stokes’ Law is valid only if the Reynolds number (Re) does not exceed about 0.25 (in order for

the error in the Stokes’ diameter not to exceed about 3 %) [12]. Since Re is a function of particle

size, this permits calculation of a well-defined upper size limit for sedimentation methods.

Portland cement is commonly assigned a density of 3.2 g/cm3. This value does not consider that

different particles will have different density values depending on their composition, it simply

applies a single mean density value for the powder. It also does not consider that variations in

cement formulations will undoubtedly impact the average density. For purposes of estimating the

upper limit, we will use a value of 3.2 g/cm3. The largest (spherical) particle diameter that can be

sized accurately using XGS is therefore about 95 μm in isopropyl alcohol at 25 °C. Particles

larger than this value will settle more slowly than the velocity predicted by Stokes’ Law. The

upper size limit can be increased by using a suspending fluid with a higher viscosity. Irregularly

shaped particles should settle according to their equivalent spherical volume at very low Re

values. At higher Re values, the drag force is greater for asymmetric particles compared to

spherical particles of an equivalent volume, and so the settling rate will decrease relative to

Stokes’ Law. For fine particles, the effect of Brownian motion exerts a significant influence on

settling at diameters below about 1 μm in water and about 0.7 μm in isopropyl alcohol.

Convection currents in the settling suspension may further limit the lower size range. Although

instrument manufacturers frequently claim a lower limit of 0.2 μm, XGS results for particles

smaller than a micrometer must be viewed with a critical eye.

The only parameters required for XGS are the density of the solid and liquid phases, and the

viscosity of the pure liquid. Particle concentrations required for XGS analysis depend on the Xray absorption properties of the solid, but for ceramics are typically around 1 % to 3 % in terms

of volume fraction. The correct sample concentration will reduce the X-ray beam intensity by

roughly 20 % to 30 % [13]. The particles must remain stable against agglomeration during

settling. An unstable suspension will exhibit a distribution skewed toward larger sizes.

Dispersing agents, coupled with pH adjustment, are commonly utilized to increase stability in

aqueous systems.

Gravitational sedimentation has limited practical value for particles under a few micrometers in

diameter due to the prohibitively long settling times. It is not uncommon for a single size

distribution analysis to require six hours or more, depending on the finest size fraction present.

By replacing the gravity field with a centrifugal field, smaller particle sizes can be analyzed in

much shorter periods of time. The underlying principles for centrifugal sedimentation are largely

the same as in the gravitational case, but the calculations and measurement geometry are more

complex because the particle velocity increases with distance from the center of rotation. Since

most commercial instruments based on the centrifugal method are designed principally for the

analysis of very fine particulates, the upper size range tends to be rather low (typically between

2 μm and 10 μm). On the low size end, the analysis range can extend down to about 0.01 μm,

depending on the speed of the centrifuge and the sensitivity of the detection system. Centrifugal
9

systems use either light or X-ray detection to determine particle concentration as a function of

distance.

2.5 Sieving

Sieving is a simple and widely used method of classifying powders according to their physical

size alone, independent of other physical or chemical properties, by using a series of woven wire

or punch plate sieves arranged in decreasing order of aperture size [14]. The sieve method covers

a wide particle size range, from roughly 37 μm to 125 mm using woven wire sieves [15].

Micromesh sieves extend the lower size range to about 5 μm, but as the aperture decreases in

size, the time required to sieve an equivalent mass of powder increases. Sieves are identified

according to their ASTM mesh size, where a 400 mesh sieve corresponds to a minimum square

aperture of 37 μm. A variety of sieve aperture ranges are available. Sieving can be performed

either dry or wet, with manual or machine agitation, and for a set time or until a sufficiently low

and constant powder flow rate is observed through the sieves. Key variables that influence

sieving results include particle shape, presence of very fine particles, initial sieve loading, time

and method of agitation, and cohesiveness of the powder (in dry sieving only). Repeatability can

be high, although reproducibility is often poor due to the many variables that provide sources for

user error [11].

Because of size limitations at the lower end, sieving, by itself, is not a suitable method for

characterizing the complete PSD of cement powders. In conjunction with other methods,

however, it can serve as a means for pre-classification of powders. Overall, sieving is better

suited for analyzing the large size fraction contained in cement powders, i.e., larger than 50 μm.
10

3 Analysis of data from the Round-robin

ASTM committee C01.25.01 sponsored a round-robin test to measure the PSD of cement. The

participants were asked to use the PSD technique that they routinely use. The data requested

from the participants included only the measurement method and the cumulative PSD. No

detailed description of the procedure was required. Twenty-one organizations participated and

the first four methods described in Section 2 were used. The identity of participant organizations

remains confidential, therefore a letter is used to distinguish between participants.

Four portland cements provided by the Cement and Concrete Reference Laboratory (CCRL) to

all participants were included in the tests: 131, 132, 135 and 136 (the numbers were assigned by

CCRL). The characteristics of these cements, as measured in the CCRL proficiency program, are

given in Appendix A. The standard cement, SRM 114p, was also used to establish a reference

PSD for cement.

Appendix B summarizes in a tabular format all PSD data received from the participants of the

round-robin. In the remainder of this section, the data is analyzed first to establish the reference

distribution using SRM 114p and then to provide a detailed examination of the data with results

for the four portland cements arranged according to measurement method. Unfortunately, in

some cases (e.g., SEM, sieving), only a single set of results is available to represent each method.

Therefore, it is not possible to analyze reproducibility between laboratories in those cases. Later

in this report (Section 4), we provide a direct comparison of methods.

3.1 Reference distribution using SRM 114p

The round-robin results for SRM 114p were analyzed separately from the other cements with the

objective of producing a reference material that instrument operators could use to "calibrate"

their systems or at least validate their methodology. In other words, the reference distribution of

SRM 114p could be used to check that the PSD results obtained by a particular instrument fall

within a defined margin of error, or it could be used to offset the measured values by a sizerange-dependent factor in order to bring them within the acceptable margin of error. To achieve

this goal, two approaches were considered:

1. Establish a single calibration curve that represents an average distribution for all methods

inclusive.

2. Establish a single calibration curve for each method, e.g., LAS-W or EZS.

Both approaches have advantages and disadvantages. In the first case (Approach 1), the

calibration curve would be less precise (greater margin of error) due to variations in the precision

of different methods being averaged. On the other hand, the first approach is simpler and more

convenient because everyone would use the same calibration curve. In the second case

(Approach 2), the distribution could be more precise, because variations resulting from

differences in measurement principle or precision would be eliminated. As a disadvantage,

several calibration curves would have to be established: one for each method.

From the data in Appendix B, there were 15 participants using the LASER diffraction method

with the specimen dispersed in a liquid (LAS-W), while no more than two participants used any
11

other method. Thus, following Approach 2 leads to the determination only of the calibration

curve for LAS-W. Obviously, all 21 sets could be used if Approach 1 is followed.

Another key issue is to eliminate outliers from the calculation of the reference distribution curve.

A criteria for determining outliers was needed. By examining the data in Appendix B for SRM

114p, it is clear that some sets of data are so different from the others that they can be considered

as outliers (Figure 1). It is obvious that sets R and L should not be considered. To determine the

outliers from the rest of the data, a more sophisticated method called bootstrapping was used. A

description of this method and its use is presented in Appendix C. Full discussion of how to

select the outliers and determine the mean distribution will be discussed in Sections 3.1.1 and

3.1.2.

A A A

A

A

A

A

A

A

A A

A A A

0

20

40

60

80

100

1 10 100

Particles size [μm]

Cumulative [%]

A A

B

C

D

F

G

H

I

J

K

L

N

O

Q

R

S

T

U

V

W

X

Figure 1: All data from SRM 114p.

3.1.1 Determination of reference distribution using Approach 1: all methods

Table 2 shows the results obtained from all SRM 114p data without sets R and L. It also shows

the mean and the two-sided 95 % confidence limits as calculated using the bootstrap method

(detailed on this method in Appendix C). The next step is to determine any outliers. The

bootstrap method does not give the criterion needed to determine the outlier. Therefore, we

arbitrarily selected the following criterion: if an organization's set of data contained more than

four data points that are more than 5 % absolute value outside the confidence limits of all data

sets, then it is considered an outlier. The absolute value 5 % is defined as the difference between

the measured value and the confidence limits, high or low.
12

Table 2: Data from all methods except sets L and R. The results from the Bootstrap calculation are also shown. Data that lieoutside the 95 % confidence limits are shown in bold, and data that are greater than 5 % outside the 95 % confidence limits

are indicated as gray cells.

Data from all devices Bootstrap results Size

[μm] A B C D F G H I J K N O Q S T U V W X Mean Low High

1 0.5 17.2 10.7 6.9 15.1 6.8 7.1 15.7 5.2 0.0 1.3 8.3 14.4 13.6 3.9 2.2 4.5 7.9 5.4 10.51

1.5 2.0 22.2 14.3 10.3 18.2 11.7 12.6 18.3 0.1 8.3 0.1 3.6 14.2 19.9 18.6 7.4 3.9 6.4 10.7 7.2 14.06

2 4.4 25.2 17.0 12.9 20.6 15.2 16.1 20.7 2.2 11.1 3.9 6.3 18.5 9.0 23.3 22.4 10.2 6.7 8.3 13.4 10.1 16.583 10.3 29.1 21.4 17.6 23.7 20.5 20.8 25.2 8.8 16.2 23.0 11.5 25.6 13.6 27.8 27.4 15.1 8.8 12.3 18.9 16.2 21.754 16.5 32.1 25.2 21.5 27.6 24.8 24.4 29.3 12.9 20.6 32.0 16.3 29.1 18.1 31.2 31.2 19.5 12.3 16.4 23.2 20.5 26.176 27.6 37.7 31.9 28.2 35.0 31.8 30.6 36.3 18.9 28.0 38.1 24.2 36.2 26.1 37.2 38.5 27.0 15.4 23.9 30.2 27.4 32.988 38.2 43.4 37.5 34.0 40.8 37.6 36.5 42.1 24.1 34.1 46.7 30.5 42.3 33.1 43.1 45.4 33.1 21.3 30.4 36.6 33.2 39.41

12 54.8 55.6 47.3 44.1 47.6 47.3 48.0 51.7 34.7 44.1 63.4 41.0 52.4 45.2 53.8 59.2 42.8 27.4 41.5 47.5 43.7 51.2116 68.2 67.2 55.6 53.0 55.3 55.4 58.6 59.9 45.8 52.5 78.7 50.0 60.8 55.2 62.7 71.1 50.9 41.1 51.0 57.4 53.8 61.3724 78.8 84.1 69.0 68.7 69.1 69.2 76.6 73.2 63.5 66.1 93.8 65.0 74.3 70.0 76.1 86.4 64.3 56.0 66.6 72.1 68.5 76.2632 84.1 92.8 79.3 78.9 79.4 79.8 88.4 82.9 75.9 76.2 98.0 76.6 83.9 80.3 85.2 93.8 74.9 79.7 78.3 82.6 79.9 85.6348 92.7 98.6 91.4 91.8 89.0 92.5 97.8 93.7 90.2 88.2 99.8 90.3 94.7 93.6 94.7 98.7 88.3 91.4 91.7 93.1 91.6 94.6264 96.3 99.9 96.3 96.7 95.4 97.8 99.6 98.0 95.5 93.7 100.0 96.3 98.7 97.6 98.0 99.7 94.5 99.2 97.3 97.4 96.6 98.1896 99.4 100.0 98.9 99.2 99.2 99.6 100.0 100.0 98.5 97.4 100.0 99.4 100.0 99.3 99.7 100.0 98.7 100.0 100.0 99.4 99.11 99.72

128 99.9 100.0 99.5 99.7 99.5 99.8 100.0 100.0 99.3 98.1 100.0 99.6 100.0 99.8 100.0 100.0 99.7 100.0 100.0 99.73 99.49 99.89
13

In Table 2, all data points that are outside the confidence limits are in bold and data points of

more than absolute value 5% outside the confidence limits are in gray cells. So, if any column

contains more than 4 data in a gray cell, than that data set is an outlier. Using this criterion, the

sets A, B, J, N, T, U and W were considered outliers.

The next step is to recalculate mean distribution of SRM 114p and its 95 % confidence limits

without the outliers. The reason of this recalculation is to have a better-defined distribution. This

was done again using the bootstrap method and the results are shown in Table 3. Figure 2 shows

the data with the bootstrap mean and 95 % confidence limits, after the outliers were eliminated.

It is clear that the distribution obtained is narrower than shown in Figure 1. The data in Table 3

could be used to correct the data obtained by all methods as shown in Appendix D-1.

0

20

40

60

80

100

1 10 100

Size [μm]

cumulative [%]

C

D

F

G

H

I

K

O

Q

S

V

X

Mean

Low

High

Figure 2: Data with the Bootstrap mean after the outliers are eliminated.

Table 3: Bootstrap mean and 95 % confidence limits calculated without the outliers.

Size

[μm]

1 1.5 2 3 4 6 8 12 16 24 32 48 64 96 128

Mean 7.8 11.4 13.8 18.6 22.8 29.9 36.0 46.1 54.8 69.4 79.9 91.9 96.8 99.3 99.6

Low 5.5 8.7 11.1 16.0 20.2 27.5 33.7 44.2 53.0 67.4 78.0 90.5 95.9 98.8 99.3

High 10.4 14.1 16.4 21.2 25.3 32.1 38.3 48.1 56.6 71.6 82.2 93.5 97.8 99.7 99.9

Therefore, the methodology that uses the mean curve to correct the data measured by various

instruments would be:

• Calculate the correction factor for each size, defined as the ratio between the measured value

and the mean value as shown in Table 3. It should be noted that in this round-robin test the

particle sizes shown in Table 3 were arbitrarily pre-selected.

• Multiply all measured data by this correction factor.
14

This procedure was applied to the four cements used in this study using all the data sets available

with the exception of sets R and L because they were clear outliers. Appendix D-1 shows graphs

of all data.

This method could then be used to correct data obtained with any method and could be

considered as a calibration of the instrument. Unfortunately, it is not that simple. If the results

obtained would have being considered outliers, (i.e., sets of data that are more than 5 % absolute

value outside the confidence limits obtained with the Bootstrap method), the correction is not

enough. This can be seen in Figure 3A where sets W, J or N are still clearly outside the

confidence limits. On the other hand if the data set is within the confidence limits, the correction

factor will reduce the spread of the data (Figure 3B). Therefore, the reference SRM 114p could

be used in two ways:

• To check that the measurements are within acceptable range of the reference. This will allow

the operator to determine if experimental errors or malfunctioning of the instrument should

be considered

• To calibrate the instrument by correcting the results obtained using the reference cement

W ithout R and L

0

10

20

30

40

50

60

70

80

90

100

1 10 100

Size [μ m ]

Cumulative [%]

A

B

C

D

F

G

H

I

J

K

N

O

Q

S

T

U

V

W

X

A

W ithout A, B,J,L,N,R,T,U,W

0

10

20

30

40

50

60

70

80

90

100

1 10 100

Size [μ m ]

Cumulative [%]

C

D

F

G

H

I

K

O

Q

S

V

X

B

Figure 3: Example of correction obtained using the correction factor. The cement used was

CCRL 131. (A) only the outliers R and L were not plotted; (B) the outliers identified by the

bootstrap method are not included

3.1.2 Determination of the reference distribution for LASER wet only (Approach

2)

If the same procedure is followed but this time using only the data obtained by Laser wet (LASW), new Bootstrap mean and 95 % confidence limits can be calculated (Table 5). Using the same

criteria as in Approach 1 (Section 3.1.1) the outliers are the set B, J, N and U. The outliers are

the same as in the first case with the exception of set T. It is not quite clear why set T is an

outlier in this case. The Bootstrap mean can then be calculated without using the outliers and this

is shown in Table 4. These data could be used to calculate the correction factor as shown above

(Section 3.1.1). The resulting size distributions are shown in Appendix D-2.
15

Table 4: Bootstrap data for the LAS-W without the outliers (B, J, N , U)

Size

[μm]

1 1.5 2 3 4 6 8 12 16 24 32 48 64 96 128

Mean 8.7 12.6 15.5 20.2 24.2 32.2 37.2 47.2 55.9 70.3 80.8 92.4 97.0 99.4 99.7

Low 6.3 9.4 12.2 17.1 21.5 28.6 34.7 44.6 53.8 68.1 78.9 90.8 96.1 98.9 99.3

High 11.3 15.4 18.3 23.1 27.0 33.7 39.8 49.7 58.4 72.7 83.2 94.0 97.9 99.8 99.9

3.1.3 Summary

Two approaches to determine the reference distribution for cement were examined. In Approach

1 all data available with no consideration of the measurement method were used. On Approach 2

only the data generated with the LAS-W method were used. In both cases, a mean distribution

was generated. Figure 4 shows the two distributions generated. It can be noticed that the two

curves are not very different, but somewhat higher values are calculated, especially in the fines,

when only the LAS-W data are used.

In the second step, the cements were corrected using a correction factor. The correction factor is

the ratio between the measured data and the reference distribution. The results of this correction

are shown in Appendix D-1 and D-2.

The calculated mean distribution curve could be used as a reference to calibrate any instrument

to be used for measuring the PSD of cement. Eventually, this method for generating the

reference distribution could be standardized and be attached to the specifications of the

SRM 114p or any other future SRM cement.
16

0

10

20

30

40

50

60

70

80

90

100

1 10 100

Particle size [μm]

cumulative [%]

all data

LAS-W only

Figure 4: Comparison between the distribution calculated from all the data and the one

calculated from only the LAS-W data.
17

Table 5: Data from LAS-W without the sets L and R. The results from the Bootstrap calculation is also shown. In bold thedata that are outside the 95 % confidence limits and in the gray area the data that are more than 5 % outside the 95 %confidence limits.

Data from LASER Wet Bootstrap results Size

[μm] B C D FGH I J KNOQTUX Mean Low High

1 17.2 10.7 6.9 15.1 6.8 7.1 15.7 - 5.2 0.0 1.3 8.3 14.4 13.6 4.5 8.9 6.4 12.1

1.5 22.2 14.3 10.3 18.2 11.7 12.6 18.3 0.10 8.3 0.05 3.6 14.2 19.9 18.6 6.4 11.8 8.5 15.2

2 25.2 17.0 12.9 20.6 15.2 16.1 20.7 2.2 11.1 3.9 6.3 18.5 23.3 22.4 8.3 14.9 10.9 17.93 29.1 21.4 17.6 23.7 20.5 20.8 25.2 8.8 16.2 23.0 11.5 25.6 27.8 27.4 12.3 20.8 17.2 23.54 32.1 25.2 21.5 27.6 24.8 24.4 29.3 2.9 20.6 32.0 16.3 29.1 31.2 31.2 16.4 24.9 21.1 27.66 37.7 31.9 28.2 35.0 31.8 30.6 36.3 18.9 28.0 38.1 24.2 36.2 37.2 38.5 23.9 31.7 29.0 34.48 43.4 37.5 34.0 40.8 37.6 36.5 42.1 24.1 34.1 46.7 30.5 42.3 43.1 45.4 30.4 37.8 34.7 40.8

12 55.6 47.3 44.1 47.6 47.3 48.0 51.7 34.7 44.1 63.4 41.0 52.4 53.8 59.2 41.5 48.7 45.2 52.516 67.2 55.6 53.0 55.3 55.4 58.6 59.9 45.9 52.5 78.7 50.0 60.8 62.7 71.1 51.0 58.4 55.0 63.124 84.1 69.0 68.7 69.1 69.2 76.6 73.2 63.5 66.1 93.8 65.0 74.3 76.1 86.4 66.6 73.5 69.7 78.932 92.8 79.3 78.9 79.4 79.8 88.4 82.9 75.9 76.2 98.0 76.6 83.9 85.2 93.8 78.3 83.3 80.1 87.248 98.6 91.4 91.8 89.0 92.5 97.8 93.7 90.2 88.2 99.8 90.3 94.7 94.7 98.7 91.7 93.5 91.9 95.664 99.9 96.3 96.7 95.4 97.8 99.6 98.0 95.5 93.7 100.0 96.3 98.7 98.0 99.7 97.3 97.5 96.6 98.596 100.0 98.9 99.2 99.2 99.6 100.0 100.0 98.5 97.4 100.0 99.4 100.0 99.7 100.0 100.0 99.5 98.9 99.7

128 100.0 99.5 99.7 99.5 99.8 100.0 100.0 99.34 98.1 100.0 99.6 100.0 100.0 100.0 100.0 99.7 99.3 99.9

19

3.2 Analysis of the data by method

3.2.1 LASER Diffraction with the specimen dispersed in a liquid (LAS-W)

The plot of all data using the LAS-W technique is shown in Appendix E. Clearly, there is

significant, although not large, scatter in this data. As shown in Table 6 (columns labeled “all

data”), this scatter is reflected in the calculated median (50 % of mass less than) diameters. As

discussed on Section 3.1.2, the sets B, J, N, and U were found to be outliers and it was shown

that the correction factors are not enough to correct them. Therefore, the median was recalculated

without these sets. Table 6 shows how the median diameters and their standard deviations

change with the elimination of the outliers. The standard deviation is reduced but not for all

cements. For instance CCRL 131 median size did not change. By looking at the graphs in

Appendix E, it is clear that different outliers could be picked if instead of cement 114p another of

the other cements was taken as the reference. As no details are known from these measurements,

it is hard at this time to determine why.

Table 6: Average median diameter from LAS-W method.

All data no B J N U

Cement Median

Diameter

[μm]

Standard

Deviation

[μm]

Median

Diameter

[μm]

Standard

Deviation

[μm]

114P 12.9 2.6 13.3 1.8

131 10.3 2.4 10.2 2.4

132 8.0 2.4 7.3 1.1

135 12.2 1.7 12.1 1.4

136 12.9 2.0 12.7 1.6

3.2.2 LASER diffraction with the specimen dispersed in air (LAS-D)

The plot of the measurements is shown in Appendix E. As we have only two PSDs to consider,

and no indication of the methods used to disperse the material for analysis, it is not possible to

determine the specific reasons for the observed variations. It is also impossible to determine the

outlier, other than by comparing with the other methods distribution. In that case the set L is an

outlier. Table 7 shows the median for the two sets with the standard deviation and the median

for the set V (the set supposedly correct). The median values of V are higher than the ones of the

average of sets L and V.
20

Table 7: Average median diameter from LAS-D method.

Cement

Median

Diameter

[μm]

Standard

Deviation

[μm]

Median

diameter

only V

[μm]

114P 10.2 7.5 15.6

131 7.4 4.7 10.7

132 6.0 2.5 7.8

135 8.9 6.9 13.8

136 10.8 7.6 16.2

3.2.3 Electrical Zone Sensing (EZS)

The plot of the measurements is shown in Appendix E. As we have only two PSDs to average,

and no indication of the methods used to disperse the material for analysis, it is not possible to

determine the specific reasons for the observed variations. It is also impossible to determine the

outlier, other than by comparing with the other methods distribution. In that case the set R is an

outlier. Table 8 shows the median for the two sets with the standard deviation and the median

for the set W (the set supposedly correct). The median values of W are lower than the average of

the R and W. On the other hand, the set W was also considered an outlier when SRM 114p was

analyzed (see Section 3.1.1). As we have no other data, there is no possibility of determining a

better value for this method.

Table 8: Average median diameter from EZS method.

Cement

Median

Diameter

[μm]

Standard

Deviation

[μm]

Median

diameter

only W

[μm]

114P 59.9 55.4 20.8

131 14.7 7.2 9.6

132 45.0 53.9 6.8

135 48.2 57.1 7.8

136 50.0 54.2 11.7

3.2.4 SEM and Sedimentation (SED)

The other two measurements methods, SEM and Sedimentation (SED), did not have replicates.

Therefore, we cannot perform a similar analysis as done with the other three methods examined

here. Nevertheless, Table 9 shows the median diameters calculated for the two methods.
21

Table 9: Median diameters by SEM and Sedimentation

Median Diameter

Cement [μm]

SEM Sed.

114P 10.8 13.9

131 9.0 10.1

132 10.1 7.7

135 10.8 12.2

136 10.4 13.1

3.2.5 Summary

The following findings are observed:

 The measurement by LAS-W exhibited some scatter, but elimination of outliers reduced the

scatter considerably.

 The measurements by LAS-D or by EZS show a very large scatter. Because of the small data

set size (2 PSDs per measurement method), it is not possible to determine the source of this

scatter nor to determine which, if either, of the PSDs is an outlier, unless the data are

compared to all the other sets.

The possible reasons that could explain some of the scatter observed in the data from all these

tests are:

 The parameters used to determine the distribution from the measurement assume certain

values for material properties, such as the index of refraction of the cement and of the

medium or the density of the particles. Since these parameters are not standardized, and were

not reported by the participants, different laboratories may have used different or incorrect

values.

 The experimental conditions, such as the dispersion medium, the preparation of the specimen

(dispersion method), as well as the instrument used to measure the PSD, may have varied

between laboratories.

These observations point to the difficulties in determining the correct method and value for a

cement PSD. In future round-robin testing, care should be taken to ensure that the same sample

preparation method is used for each technique and that the parameter values used by the

operators are also the same or determined using the same method. We recommend that the

ASTM committee address the issue of determining the correct experimental set-up and sample

preparation protocol for each measurement method.
22

4 Comparison of the various methods used

To compare all the particle size distributions measured with the various sets, an average

distribution could be calculated for each measurement method. The recommended procedure to

calculate this representative curve should be to use the Bootstrap method to calculate the mean

and the two sided 95 % confidence limits, given the data for each measurement method. But as

only the LAS-W has enough data to justify such a procedure, the average median diameters will

be used as a comparison. Also, the calculation of median values from only two sets and in some

cases one set should be used with caution. In an ideal situation, all the median diameters should

be identical regardless of the method used. It is clear that is not the case in Figure 5.



















































































































































 0

5

10

15

20

25

114P 131 132 135 136

Cement type

Median Diameter [

μm]

 LAS-W

 LAS-D

 EZS

 SEM

Siev-Sed

average

Figure 5: Bar graph of the median diameters for all the methods.

The following observations can be made:

• If only the LAS-D data from set V is considered, then the data corresponds very closely

with the LAS-W method. As this similarity between the two methods is based on only one

data set for LAS-D, more testing is needed to verify this similarity.

• The EZS does not compare with the other methods. However, it should be kept in mind that

the only value that we considered was set W, which was considered an outlier for SRM

114p. The other set available was R, which was also considered an outlier for SRM 114p.

• Depending on the cement used, the SEM method median value is either higher or lower than

the average value. Only once for cement CCRL 131, the SEM value is similar to the others.

But again this is the result from only one set, therefore, there is not enough evidence for

indication of variability. It should be also noted that the SEM seems to "see" fewer small

particles and more larger one, as shown by the graphs in Appendix E. This is probably due

to agglomeration of the small particles.
23

• The sedimentation method seems to follow the average of all methods. It should be noted

that measurements below 3 μm in size were reported. As we do not have more details, it is

impossible if this is a limitation due to the method or the reporting.

These are very preliminary findings because of the limited sample size (i.e., number of data) for

most of the measurement methods and the lack of knowledge about the parameters used to

interpret the measurements.

5 Conclusions

From this round-robin test, the most frequently used PSD measurement technique by the industry

is LASER diffraction with dispersion of cement in a liquid. The SEM method, as applied in the

current test, is relatively new and was used by only one participant in the round robin. Similarly,

the sedimentation method was used by only one participant and it did not report data below 3

μm; it should be determined if this represents the complete PSD or if it is a reporting issue. There

were two sets using EZS, but both were determined to be outliers based on measurements of the

reference material SRM 114p. Because the scope of the ASTM committee is to determine the

best method or methods to measure PSD of cement, the methods to be standardized should be

carefully selected. In other words, the committee should concentrate its initial efforts on the most

widely used and most promising measurement methods (e.g., wider range of size and better

reproducibility).

In this first round-robin test, there was not enough information collected to be able to definitively

determine the reference distribution using SRM 114p or to determine the best methods to

measure the cement PSD. Therefore, the following recommendations should be considered in

organizing the next round-robin:

• Reduce the number of cements (2-3 maximum)

• Provide with each sample a standard report form, in which the participant is asked to provide

detailed information on procedures and parameters used during the tests.

• A draft protocol could be prepared for each method and the operator could be asked to

measure the specimens using first this draft method and then their usual method at least for

SRM 114p. This will allow the determination of whether the scatter is due solely to the

protocol used or also could be attributed to the instrument used.

• Have several replicate measurements using the same method, instrument and cement

It is the belief of the authors that an ASTM standard should include a standard procedure for

each method that is specialized for cement. It would certainly help if a reference distribution for

a cement such as SRM 114p could be determined. This will help the operator determine if the

PSD measured is within an acceptable error margin.

In conclusion, before a standard test can be proposed, further research needs to be conducted to

determine the correct methodology for any of the tests discussed in this report.
24

6 References

1 "Standard Test Method for Fineness of Portland Cement by the Turbidimeter" ASTM C

115-96, Annual Book of ASTM Standards, Vol. 04.01.

2 Jillavenkatesa A., Dapkunas S. J., Lum L.-S. H., Particle Size Characterization, NIST

Special publication 960-1, 2001.

3 Handbook of Optical Constants of Solids, edited by E.D. Palik, Academic Press, New

York, 1985; Handbook of Optical Constants of Solids II, edited by E.D. Palik, Academic

Press, New York, 1991.

4 M. Cyr and A. Tagnit-Hamou, “Particle size distribution of fine powders by LASER

diffraction spectrometry. Case of cementitious materials,” Materials and Structures, 34,

342-350 (2000).

5 J.D. Lindberg, R.E. Douglass and D.M. Garvey, “Absorption-coefficient-determination

method for particulate materials,” Applied Optics, 33[9], 4314-4319 (1994).

6 N.A. Marley, J.S. Gaffney, J. C. Baird, C.A. Blazer, P.J. Drayton and J.E. Frederick, “An

empirical method for the determination of the complex refractive index of sizefractionated atmospheric aerosols for radiative transfer calculations,” Aerosol Science

and Technology, 34, 535-549 (2001).

7 C.F. Bohren and D.R. Huffman, Absorption and Scattering of Light by Small Particles,

John Wiley & Sons, New York, 1983.

8 ISO 13320-1:1999(E), Particle size analysis — LASER diffraction methods — Part 1:

General principles.

9 J.P.K. Seville, J.R. Coury, M. Ghadiri, and R. Clift, “Comparison of techniques for

measuring the size of fine non-spherical particles,” Particle Characterization, 1, 45-52

(1984).

10 ISO 13319:2000(E), Determination of particle size distributions — Electrical sensing

zone method.

11 T. Allen, Particle Size Measurement, 4th Edition, Chapman and Hall, London, 1990.

12 ISO 13317-1:2001, Determination of particle size distribution by gravitational liquid

sedimentation methods -- Part 1: General principles and guidelines.

13 ISO 13317-3:2001, Determination of particle size distribution by centrifugal liquid

sedimentation methods -- Part 1: General principles and guidelines.

14 ISO 2591-1:1988, "Test sieving -- Part 1: Methods using test sieves of woven wire cloth

and perforated metal plate."

15 ISO 565:1990, "Test sieves -- Metal wire cloth, perforated metal plate and electroformed

sheet -- Nominal sizes of openings."
A-25

APPENDICES
A-26
A-27

TABLE OF CONTENT

APPENDIX A: CEMENT CHARACTERISTICS .................................................................. 29

APPENDIX B: PSD DATA AS RECEIVED............................................................................ 37

APPENDIX C: THE BOOTSTRAP METHOD ...................................................................... 44

APPENDIX D-1: PARTICLE SIZE DISTRIBUTION USING ALL DATA CORRECTED

BY THE BOOTSTRAP METHOD........................................................................................... 46

APPENDIX D-2: PARTICLE SIZE DISTRIBUTION USING ONLY DATA FROM

LASER WET CORRECTED BY THE BOOTSTRAP METHOD. ...................................... 47

APPENDIX E: GRAPH FOR EACH METHOD .................................................................... 48
A-28
A-29

Appendix A: Cement characteristics
A-30
A-31
A-32
A-33
A-34
A-35
A-36
A-37

Appendix B: PSD data as received

Lab A B C D F G H I J K L N O Q R S T U V W X

[μm] SEM LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-D LAS-W LAS-W LAS-W EZS Sedim. LAS-W LAS-W LAS-D EZS LAS-W

114P

1 0.5 17.2 10.7 6.9 15.1 6.8 7.1 15.7 0.0 5.2 0.2 0.0 1.3 8.3 0.1 14.4 13.6 3.9 2.2 4.5

1.5 2.0 22.2 14.3 10.3 18.2 11.7 12.6 18.3 0.1 8.3 4.9 0.0 3.6 14.2 0.2 19.9 18.6 7.4 3.9 6.4

2 4.4 25.2 17.0 12.9 20.6 15.2 16.1 20.7 2.2 11.1 13.9 3.9 6.3 18.5 0.5 9.0 23.3 22.4 10.2 6.7 8.33 10.3 29.1 21.4 17.6 23.7 20.5 20.8 25.2 8.9 16.2 32.2 23.0 11.5 25.6 0.8 13.6 27.8 27.4 15.1 8.8 12.34 16.5 32.1 25.2 21.5 27.6 24.8 24.4 29.3 12.9 20.6 44.6 32.0 16.3 29.1 1.1 18.1 31.2 31.2 19.5 12.3 16.46 27.6 37.7 31.9 28.2 35.0 31.8 30.6 36.3 18.9 28.0 56.9 38.1 24.2 36.2 1.7 26.1 37.2 38.5 27.0 15.4 23.98 38.2 43.4 37.5 34.0 40.8 37.6 36.5 42.1 24.1 34.1 66.6 46.7 30.5 42.3 2.4 33.1 43.1 45.4 33.1 21.3 30.4

12 54.8 55.6 47.3 44.1 47.6 47.3 48.0 51.7 34.7 44.1 79.7 63.4 41.0 52.4 3.7 45.2 53.8 59.2 42.8 27.4 41.516 68.2 67.2 55.6 53.0 55.3 55.4 58.6 59.9 45.9 52.5 85.4 78.7 50.0 60.8 4.8 55.2 62.7 71.1 50.9 41.1 51.024 78.8 84.1 69.0 68.7 69.1 69.2 76.6 73.2 63.5 66.1 91.8 93.8 65.0 74.3 5.9 70.0 76.1 86.4 64.3 56.0 66.632 84.1 92.8 79.3 78.9 79.4 79.8 88.4 82.9 75.9 76.2 95.6 98.0 76.6 83.9 6.6 80.3 85.2 93.8 74.9 79.7 78.348 92.7 98.6 91.4 91.8 89.0 92.5 97.8 93.7 90.2 88.2 98.6 99.8 90.3 94.7 10.3 93.6 94.7 98.7 88.3 91.4 91.764 96.3 99.9 96.3 96.7 95.4 97.8 99.6 98.0 95.6 93.7 99.4 100.0 96.3 98.7 15.7 97.6 98.0 99.7 94.5 99.2 97.396 99.4 100.0 98.9 99.2 99.2 99.6 100.0 100.0 98.5 97.4 100.0 100.0 99.4 100.0 45.5 99.3 99.7 100.0 98.7 100.0 100.0

128 99.9 100.0 99.5 99.7 99.5 99.8 100.0 100.0 99.3 98.1 100.0 100.0 99.6 100.0 91.9 99.8 100.0 100.0 99.7 100.0 100.0
A-38

Lab A B C D F G H I J K L N O Q R S T U V W X

[μm] SEM LASW LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-D LAS-W LAS-W LAS-W EZS Sedim. LAS-W LAS-W LAS-D EZS LAS-W

131

1 0.6 17.1 11.8 7.1 17.7 6.2 6.8 15.2 0.0 7.1 0.0 0.0 1.0 9.8 0.4 13.6 11.5 4.5 3.6 5.9

1.5 2.3 22.4 16.1 9.7 21.6 10.6 11.8 17.2 0.0 11.6 3.2 0.6 2.9 16.8 1.2 19.6 16.7 8.6 6.8 8.1

2 4.8 25.8 19.3 11.8 24.9 13.8 15.4 19.0 0.6 15.6 12.7 2.7 5.2 21.8 2.5 11.7 23.7 20.9 12.1 12.4 10.33 11.2 30.6 24.4 16.7 28.8 19.1 20.8 23.1 7.9 23.0 34.4 12.2 10.5 29.2 4.7 17.4 29.3 26.5 18.3 17.2 14.94 18.5 34.4 28.9 22.1 33.5 23.8 25.6 27.4 15.3 29.5 49.5 18.1 16.2 34.5 6.8 23.2 33.7 30.8 24.0 25.6 19.66 32.1 41.4 37.2 32.4 42.7 32.5 34.8 35.8 25.2 40.7 63.2 27.0 26.6 43.1 12.1 33.4 41.1 38.5 33.7 32.9 28.58 44.6 49.0 44.4 41.3 49.5 40.0 43.9 43.6 32.8 50.1 72.9 35.0 35.5 50.5 18.8 42.2 48.2 46.1 41.7 45.6 36.5

12 65.2 64.6 56.7 55.2 56.7 52.3 60.6 56.5 46.9 65.1 86.2 49.1 49.9 62.5 34.2 57.1 60.9 61.1 54.2 56.4 50.116 79.0 77.6 66.1 66.0 66.0 62.2 74.1 66.9 60.4 75.8 91.2 61.9 61.1 72.0 44.8 68.7 71.3 73.6 63.9 73.3 61.024 92.4 92.2 79.9 81.1 80.9 77.3 90.5 81.8 79.4 88.6 95.7 79.2 77.6 85.6 55.9 83.0 86.2 88.4 78.4 84.4 77.532 97.4 97.4 88.9 89.7 89.7 87.3 97.0 90.6 89.4 94.9 98.4 89.0 87.5 93.5 61.4 90.9 94.4 94.8 87.7 94.3 87.748 100.0 99.7 96.7 96.9 96.1 96.4 99.8 98.0 97.1 99.4 99.9 97.4 96.8 99.2 68.5 98.6 99.3 98.8 96.6 97.8 97.164 100.0 100.0 98.8 98.9 99.1 99.1 100.0 100.0 99.1 100.0 100.0 99.3 99.9 100.0 76.9 99.6 100.0 99.7 99.2 99.9 99.896 100.0 100.0 99.8 99.7 100.0 99.9 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 99.9 100.0 100.0 100.0 100.0 100.0

128 100.0 100.0 99.7 99.9 100.0 99.9 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
A-39

Lab A B C D F G H I J K L N O Q R S T U V W X

[μm] SEM LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-D LAS-W LAS-W LAS-W EZS Sedim. LAS-W LAS-W LAS-D EZS LAS-W

132

1 0.6 21.5 14.1 10.1 19.3 8.2 9.3 19.0 0.0 7.9 1.1 0.0 1.4 12.3 0.3 17.0 13.3 6.1 5.0 6.3

1.5 2.2 27.9 19.2 15.0 24.2 14.3 16.5 22.2 0.0 12.8 8.0 0.1 4.6 20.8 0.9 24.8 19.3 11.6 9.4 9.6

2 4.6 31.8 23.2 18.8 28.1 19.0 21.6 25.2 0.9 17.1 17.6 2.4 8.3 26.8 1.6 15.0 29.9 23.9 15.9 17.1 13.03 10.3 37.0 29.6 25.4 32.7 26.5 28.9 31.2 14.3 24.6 35.8 13.0 16.0 35.2 2.6 22.0 36.3 29.9 23.4 23.5 19.54 16.5 41.2 35.2 31.0 38.1 32.8 34.7 36.9 23.8 31.2 48.3 18.0 23.2 41.2 3.5 29.0 41.2 34.2 30.0 34.3 25.56 28.2 49.7 44.7 40.6 48.1 43.2 45.4 46.9 33.8 42.4 62.5 23.9 35.6 51.0 5.6 41.3 50.1 42.6 41.5 43.4 36.28 39.2 59.2 52.8 49.2 56.3 51.7 55.8 55.6 42.1 52.2 73.6 29.2 45.9 59.3 8.3 51.8 58.6 51.2 51.1 58.9 45.5

12 60.3 76.6 67.0 64.8 66.1 65.3 74.4 69.9 60.1 68.0 87.5 40.0 62.2 72.7 13.7 69.9 75.1 69.1 66.2 71.9 61.116 77.2 88.0 78.2 77.5 76.8 76.2 87.0 80.5 78.0 79.2 93.6 51.3 74.6 82.9 18.0 83.4 87.3 83.0 77.3 88.7 73.224 93.8 97.0 91.8 91.7 91.0 90.9 97.4 92.7 94.7 91.7 98.5 67.9 89.4 94.5 22.3 93.9 97.7 95.4 90.3 95.2 88.732 96.9 99.2 96.9 96.9 96.8 97.0 99.6 97.6 98.5 97.1 99.8 79.7 95.9 98.2 23.7 97.6 99.7 98.7 96.0 98.0 95.748 98.5 99.9 98.9 99.5 99.5 99.4 100.0 100.0 100.0 99.8 100.0 94.7 99.6 99.8 27.2 99.4 100.0 99.9 99.2 99.1 99.864 99.4 100.0 99.4 99.9 100.0 99.8 100.0 100.0 100.0 100.0 100.0 99.0 100.0 100.0 31.4 99.7 100.0 100.0 99.4 100.0 100.096 100.1 100.0 99.9 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 62.6 99.8 100.0 100.0 99.4 100.0 100.0

128 100.1 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 99.7 100.0 100.0
A-40

Lab A B C D F G H I J K L N O Q R S T U V W X

[μm] SEM LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-D LAS-W LAS-W LAS-W EZS Sedim. LAS-W LAS-W LAS-D EZS LAS-W

135

1 0.3 15.3 11.4 6.8 15.3 6.0 6.6 14.3 0.0 5.4 0.0 0.0 0.7 8.1 0.1 11.9 10.1 3.8 3.3 4.0

1.5 1.3 20.2 15.6 9.3 18.9 10.4 12.0 15.9 0.0 8.8 2.7 0.0 2.3 14.1 0.4 17.4 14.8 7.3 6.5 4.7

2 3.0 23.6 18.7 11.4 21.8 13.8 15.8 17.6 0.7 11.8 12.2 1.7 4.5 18.5 0.9 10.0 21.2 18.7 10.4 12.6 5.53 8.0 28.2 23.7 16.2 25.4 19.4 21.5 21.5 7.8 17.4 34.5 12.3 9.8 25.1 1.7 15.0 26.5 24.1 15.8 18.4 7.84 14.2 31.6 28.1 21.1 29.6 24.3 26.1 25.7 14.3 22.2 50.0 19.1 15.4 29.8 2.4 20.0 30.5 28.1 20.7 28.7 11.26 26.6 37.4 35.4 29.8 37.2 32.6 33.8 33.7 22.2 30.2 63.0 27.4 25.3 37.2 4.1 28.8 37.0 35.1 28.8 37.3 19.68 37.3 43.2 41.6 36.9 43.1 39.3 40.7 40.7 28.0 36.9 71.8 33.8 33.3 43.6 6.2 36.4 43.1 41.8 35.4 51.1 27.9

12 55.6 55.3 52.0 48.0 50.1 49.6 53.2 52.0 39.1 47.9 83.8 45.6 45.6 54.2 10.3 49.5 54.1 55.3 46.0 62.0 42.116 69.0 66.6 60.5 57.1 58.0 57.9 64.1 61.1 50.6 57.0 88.0 57.2 55.3 63.1 13.5 60.0 63.5 67.2 54.8 77.6 53.024 85.7 81.7 73.9 71.7 71.9 71.6 81.5 75.4 68.7 71.6 92.3 74.6 70.6 77.1 17.2 74.9 78.2 83.3 69.3 87.2 69.432 95.4 91.2 83.8 82.1 81.9 82.0 91.9 85.3 81.1 82.2 95.3 87.0 81.7 86.9 18.7 84.7 88.0 91.8 80.2 95.5 80.648 99.7 98.1 94.6 93.5 90.8 93.9 98.9 95.6 93.9 94.2 97.9 98.7 93.9 96.7 23.2 96.7 97.2 98.1 92.6 98.3 93.164 100.1 99.7 98.2 97.5 96.4 98.5 99.9 99.1 98.0 98.6 99.1 100.0 98.5 99.5 26.2 99.2 99.5 99.5 97.4 99.9 97.996 100.1 100.0 99.5 99.3 99.2 99.8 100.0 100.0 99.9 100.0 100.0 100.0 100.0 100.0 57.2 99.8 100.0 100.0 99.9 100.0 99.9

128 100.1 100.0 99.7 99.7 99.2 99.9 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
A-41

Lab A B C D F G H I J K L N O Q R S T U V W X

[μm] SEM LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-W LAS-D LAS-W LAS-W LAS-W EZS Sedim. LAS-W LAS-W LAS-D EZS LAS-W

136

1 0.3 14.4 9.9 6.3 14.9 5.6 5.7 13.8 0.0 4.8 0.2 0.0 0.6 7.9 0.2 11.3 10.0 3.4 3.7 4.7

1.5 1.4 19.2 13.8 9.6 18.4 9.8 10.6 15.9 0.0 7.8 4.4 0.2 2.3 13.6 0.5 17.0 14.7 6.4 7.0 6.9

2 3.4 22.4 16.7 12.2 21.2 13.1 14.3 18.0 0.8 10.5 12.7 3.7 4.5 17.6 1.0 9.0 21.0 18.3 9.0 12.5 9.23 8.8 26.8 21.4 16.9 24.7 18.5 19.7 22.4 7.4 15.4 29.8 14.5 9.7 23.6 1.8 14.0 26.4 23.3 13.5 17.1 14.24 14.8 30.0 25.3 20.9 28.9 23.4 24.1 26.6 13.2 19.8 41.7 19.6 14.8 28.0 2.6 19.0 30.5 27.0 17.8 24.7 19.36 26.3 35.7 32.3 27.8 36.5 31.8 31.7 34.4 20.7 27.3 54.0 26.0 23.8 35.2 4.4 27.7 37.4 34.0 25.2 31.0 28.48 36.7 41.4 38.4 33.7 42.5 38.6 38.4 41.0 26.2 33.7 63.7 31.4 31.0 41.5 6.6 35.0 43.9 40.5 31.3 41.7 35.8

12 58.5 53.1 48.7 44.0 49.6 49.0 50.2 51.6 37.0 44.1 77.0 42.4 42.6 52.0 10.8 47.4 55.7 53.3 41.4 50.8 47.216 70.8 64.2 56.6 53.1 57.5 57.2 60.6 60.1 47.9 52.6 83.1 53.5 52.2 60.7 14.2 57.2 65.8 64.5 49.7 65.8 56.224 90.5 80.9 69.2 67.9 71.1 70.5 77.4 73.4 65.0 66.1 89.8 69.7 67.9 74.3 17.5 71.3 81.3 80.2 63.2 77.3 70.732 96.7 90.4 78.8 78.5 80.9 80.5 88.3 82.9 76.7 76.2 94.0 80.8 79.7 83.9 19.3 80.7 90.9 89.3 73.8 91.1 81.548 100.0 97.6 90.3 91.0 89.8 92.2 97.4 93.6 90.3 88.8 98.0 94.7 92.7 94.8 24.4 94.1 98.2 97.1 87.4 96.7 93.764 100.0 99.5 95.5 96.1 95.9 97.5 99.5 98.0 95.5 94.9 99.3 99.0 97.7 98.8 27.3 98.3 99.7 99.3 93.9 99.9 98.496 100.0 100.0 98.7 98.9 99.7 99.9 100.0 100.0 98.7 99.2 100.0 100.0 99.7 100.0 57.2 99.6 100.0 100.0 98.7 100.0 100.0

128 100.0 100.0 99.3 99.6 100.0 100.0 100.0 100.0 99.5 99.9 100.0 100.0 99.9 100.0 100.0 99.9 100.0 100.0 99.8 100.0 100.0

A-43
A-44

Appendix C: The Bootstrap Method

Suppose a random sample ( ) n x , x ,Kx = 1 2 x from an unknown probability distribution F has

been observed and we wish to estimate a parameter of interest θ = t( ) F on the basis of x. For

this purpose, we calculate an estimate θ = s( ) x ˆ from x. How accurate is θˆ ? The bootstrap1 was

introduced in 1979 as a computer-based method for estimating the standard error of θˆ.

The bootstrap is a data-based simulation method for statistical inference. It allows scientists to

explore data and draw valid statistical inferences without worrying about mathematical formulas

and derivations. The bootstrap parameter estimate is available no matter how mathematically

complicated the estimator θ = s( ) x ˆ may be. In its non-parametric form, the bootstrap provides

standard errors and confidence intervals without the usual normal-theory assumptions.

The bootstrap method draws repeated samples (with replacement) from the observed sample

itself to generate the sampling distribution of a statistic (a data set of size n has 2n-1 nonempty

subsets).

Bootstrapping of a statistic θ = s( ) x ˆ consists of the following steps:

1. B samples are drawn with replacement from the original data set x, with each sample the

same size as the original data set. Call these bootstrap samples *1 *2 *B x , x ,Kx .

2. The statistic of interest θˆ is computed for each bootstrap sample, that is ( ) ( ) b b s ˆ * θ = x for

b =1,2,KB. The mean, standard deviation, and percentiles of these B values form the

basis for the bootstrap approach to inference.

Implementation of these steps in a computer language is not difficult. A necessary ingredient for

any bootstrap program is a high quality uniform number generator. It is important to keep in

mind that the bootstrap (and associate methods) are not tools that are used in isolation but rather

are applied to other statistical techniques. For this reason, they are most effectively used in an

integrated environment for data analysis. In such an environment, a bootstrap procedure has the

ability to call other procedures with different sets of inputs (data) and then collect them together

and analyze the results. The S, S-PLUS2

, Gauss, and Matlab packages are examples of

integrated environment. In this report, we use the S-PLUS function summary.bootstrap(). For

each data-column, 1000 samples of the data (with replacement) or replicates were generated and

the mean of these samples was calculated. The 2.5th and 97.5th empirical percentiles for the

replicates of the parameter estimate (sample mean) are the lower and upper bounds of the data

set, respectively.

 

1

 The use of the term bootstrap derives from the phrase to pull oneself up by one’s bootstrap. It is not the same as

the term “bootstrap” used in computer science meaning to “boot” a computer from a set of core instructions, though

the derivation is similar.

2

 Commercial equipment, instruments, and materials mentioned in this report are identified to foster understanding.

Such identification does not imply recommendation or endorsement by the National Institute of Standards and

Technology (NIST), nor does it imply that the materials or equipment identified are necessarily the best available for

the purpose.
A-45
A-46

APPENDIX D-1: Particle size distribution using all data corrected by the bootstrap method.

Cem ent 131

0

80604020

100

1 10 100

Particle size [μ m ]

Cumulative [%]

ABCDFGHIJKNOQSTUVWX

Cem ent 132

0

80604020

100

1 10 100

Particle size [μ m]

Cumulativ e [%]

ABCDFGHIJKNOQSTUVWX

Cem ent 135

0

80604020

100

1 10 100

particle size [μ m]

Cumulativ e [%]

ABCDFGHIJKNOQSTUVWX

Cem ent 136

0

80604020

100

1 10 100

particle size [μ m]

Cumulativ e [%]

ABCDFGHIJKNOQSTUVWX
A-47

APPENDIX D-2: Particle size distribution using only data from Laser wet corrected by thebootstrap method.

Cem ent 131

0

80604020

100

1 10 100

particle size [μ m ]

Cumulative [%]

BCDFGHIJKNOQTUX

Cem ent 132

0

80604020

100

1 10 100

particle size [μ m]

Cumulativ e [%]

BCDFGHIJKNOQTUX

Cem ent 135

0

80604020

100

1 10 100

particle size [μ m]

Cumulativ e [%]

BCDFGHIJKNOQTUX

Cem ent 136

0

80604020

100

1 10 100

particle size [μ m]

Cumulativ e [%]

BCDFGHIJKNOQTUX
A-48

Appendix E: Graph for each methodAll distributions from the various participants and for each cement as measured with LAS-W

131

0

80604020

100

1 10 100

Particle size [μ m]

Cumulativ e [%]

BCDFGHIJKNOQTUX

132

0

80604020

100

1 10 100

Particle size [μ m]

Cumulativ e [%]

BCDFGHIJKNOQTUX

135

0

908070605040302010

100

1 10 100

Particle size [μ m]

cumulativ e [%]

BCDFGHIJKNOQTUX

136

0

908070605040302010

100

1 10 100

particle size [μ m]

cumulativ e [%]

BCDFGHIJKNOQTUX
A-49

All distributions from the various participants and for each cement as measured with LAS-D

131

0

80604020

100

1 10 100

Particle s s ize [μ m ]

Cum ulative [%]

LV

132

0

80604020

100

1 10 100

Particle s s ize [μ m ]

Cum ulative [%]

LV

135

0

80604020

100

1 10 100

Particle s s ize [μ m ]

Cum ulative [%]

LV

136

0

80604020

100

1 10 100

Particle s s ize [μ m ]

Cum ulative [%]

LV

114P

0

80604020

100

1 10 100

Particle s s ize [μ m ]

Cum ulative [%]

LV
A-50

All distributions from the various participants and for each cement as measured with EZS method

114P

0

80604020

100

1 10 100 1,000

Particle size [μm]

Cumulative [% ]

RW

131

0

80604020

100

1 10 100 1,000

Particles size [μm]

Cumulative [% ]

RW

135

0

80604020

100

1 10 100 1,000

Particles size [μm]

Cumulative [% ]

RW

136

0

80604020

100

1 10 100 1,000

Particle Size [μm]

Cumulative [% ]

RW

132

0

80604020

100

1 10 100 1,000

Particles size [μm]

Cumulative [% ]

RW
A-51

All distributions for each cement as measured with SEM and Sedimentation

114P

0

80604020

100

1 10 100

Particle s s ize [μ m ]

Cum ulative [%]

A -SEMS-Sed.

131

0

80604020

100

1 10 100

Particle s s ize [μ m ]

Cum ulative [%]

A -SEMS-Sed.

132

0

80604020

100

1 10 100

Particle s s ize [μ m ]

Cum ulative [%]

A -SEMS-Sed.

135

0

80604020

100

1 10 100

Particle s s ize [μ m ]

Cum ulative [%]

A -SEMS-Sed.

136

0

80604020

100

1 10 100

Particle s s ize [μ m ]

Cum ulative [%]

A -SEMS-Sed.