NIST Special Publication 260-166

Certification of SRM 114q: Part II

(Particle size distribution)

Chiara F. Ferraris

William Guthrie

Ana Ivelisse Avilés

Max Peltz

Robin Haupt

Bruce S. MacDonald
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NIST Special Publication 260-166 

Certification of SRM 114q: Part II

(Particle size distribution)

Chiara F. Ferraris

Max Peltz

Materials and Construction Research Division

Building and Fire Research Laboratory

William Guthrie 

Ana Ivelisse Avilés

Statistical Engineering Division

Information Technology Laboratory

Robin Haupt

Materials and Construction Research Division 

Construction Materials Reference Laboratory

Bruce S. MacDonald 

Measurement Services Division

Technology Services

National Institute of Standards and Technology

Gaithersburg, MD 28099

November 2006

U.S. Department of Commerce

Carlos M. Gutierrez, Secretary

Technology Administration

Robert Cresanti, Under Secretary of Commerce for Technology

National Institute of Standards and Technology

 William Jeffrey, Director
Certain commercial entities, equipment, or materials may be identified in this 

document in order to describe an experimental procedure or concept adequately. Such 

identification is not intended to imply recommendation or endorsement by the 

National Institute of Standards and Technology, nor is it intended to imply that the 

entities, materials, or equipment are necessarily the best available for the purpose.

National Institute of Standards and Technology Special Publication 260-166

Natl. Inst. Stand. Technol. Spec. Publ. 260-166, 64 pages (November 2006)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 2005

_________________________________________

For sale by the Superintendent of Documents, U.S. Government Printing Office

Internet: bookstore.gpo.gov — Phone: (202) 512-1800 — Fax: (202) 512-2250

Mail: Stop SSOP, Washington, DC 20402-0001
iii

Abstract

The standard reference material (SRM) for fineness of cement, SRM 114, is an integral 

part of the calibration material routinely used in the cement industry to qualify cements. 

Being a powder, the important physical properties of cement, prior to hydration, are its 

surface area and particle size distribution (PSD). Since 1934, NIST has provided SRM 

114 for cement fineness and it will continue to do so as long as the industry requires it. 

Different lots of SRM 114 are designated by a unique letter suffix to the SRM number, 

e.g., 114a, 114b, ..., 114q. A certificate that gives the values obtained using ASTM C204 

(Blaine), C115 (Wagner) and C430 (45 μm sieve residue) is included with each lot of the 

material. For the SRM 114p an addendum was developed in 2003 providing the PSD 

curve. The supply of SRM 114p was released in 1994 and depleted in 2004. 

Therefore, a new batch of SRM 114 needed to be developed. This process included 

selection of the cement, packaging the cement in small vials, and determining the values 

for the relevant ASTM tests. In “Certification of SRM 114q: Part I” (SP26-161), the 

development of the values for the ASTM C204 (Blaine), C115 (Wagner) and C430 (45 

μm sieve residue) tests were discussed. In this report, the PSD for SRM 114q is 

presented. 

The measurement of the PSD in this report was based on light scattering technology, or 

as it is commonly referred to, laser diffraction (LD). Other methods could be used to 

develop the PSD of cement but after two round robins and a survey, data obtained from 

other methods were insufficient to allow a statistically valid calculation of the mean PSD. 

The purpose of this report is to complement the description of the process to certify SRM 

114q described in Part I. All measurements used for the development of the PSD 

reference curve are provided along with statistical analyses. 
iv

Acknowledgements

The authors would like to thank all participants of the round-robin (listed below in 

alphabetical order by institution) for providing time and staff to perform the particle size 

distribution (PSD) tests used for certification of this material. 

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

(CCRL), who were instrumental in providing the samples to the round-robin participants. 

The authors would also like to thank some key persons at NIST without whom this 

certification could not have being completed: Mark Cronise and Curtis Fales for 

packaging all the materials; Vince Hackley of the Materials Science and Engineering 

Laboratory for numerous discussions during the planning stage and for providing a 

description of laser diffraction principles; Romayne Hines for helping in distribution of 

the samples for the round-robin; Edward Garboczi (NIST), Paul Stutzman (NIST), Jon 

Martin (NIST) and Charles Hagwood (NIST) for their valuable comments. 

Round-Robin Participants for the PSD (Alphabetical)

Buzzi Unicem USA, New Orleans Slag Facility, New Orleans, LA: Ronald J. Rajki 

California Portland Cement Co., Mojave, CA: Rebecca Lara 

Construction Technology Laboratories, Skokie, IL: Ella Shkolnik 

F.L. Smidth A/S, Laboratory Copenhagen: Bjarne Osbaeck 

Holcim Group Support Ltd., Holderbank: Werner Flueckiger 

Lafarge North America Sugar Creek Plant, Sugar Creek, MO: Nick Ewing 

Lehigh Cement Company Union Bridge, Union Bridge, MD: Jeff Hook 

Mitsubishi Cement Corp., Lucerne Valley, CA: Tom Gepford 

RMC Pacific Materials Inc., Davenport, CA: Chow Yip 

St. Lawrence Cement, Inc., Mississauga, Ontario: John Falletta 

St. Marys Cement, Detroit, MI: Linda Harris 

Texas DOT, Austin, TX: Lisa Lukefahr 
v

Table of Contents 

1 Introduction................................................................................................................. 1 

2 Description of particle size distribution methods ....................................................... 3 

2.1 Introduction......................................................................................................... 3 

2.2 Laser diffraction [4] ............................................................................................ 3 

3 Materials ..................................................................................................................... 7 

3.1 Characteristics of the cement.............................................................................. 7 

3.2 Packaging............................................................................................................ 8 

3.3 Homogeneity determination................................................................................ 8 

4 Experimental design and data analysis ....................................................................... 9 

4.1 Experimental Design........................................................................................... 9 

4.2 Parameters used .................................................................................................. 9 

4.3 Analysis of the Particle Size Distribution Data ................................................ 12 

4.3.1 Introduction............................................................................................... 12 

4.3.2 Data for SRM 114p by LD-D ................................................................... 12 

4.3.3 Data for SRM 114p by LD-W .................................................................. 13 

4.3.4 Data for SRM 114q by LD-D ................................................................... 14 

4.3.5 Data for SRM 114q by LD-W .................................................................. 15 

4.4 Homogeneity..................................................................................................... 15 

4.5 Discussion of results ......................................................................................... 20 

4.5.1 Comparison of SRM 114p with certified values....................................... 20 

4.5.2 Comparison of SRM’s 114p and 114q...................................................... 20 

5 Summary................................................................................................................... 22 

5.1 The PSD for SRM 114q.................................................................................... 22 

5.2 Precision statement based on SRM 114q.......................................................... 22 

5.3 How to use these values.................................................................................... 26 

5.3.1 Introduction............................................................................................... 26 

5.3.2 Conformity determination......................................................................... 26 

6 References................................................................................................................. 28 

7 Appendix................................................................................................................... 30 

7.1 Appendix A: Questionnaire for participants..................................................... 30 

7.2 Appendix B: Data received from the Round-robin........................................... 32 

7.3 Appendix C: Bootstrap method ........................................................................ 41 

7.4 Appendix D: DRAFT Test Method for Particle Size Analysis of Hydraulic 

Cement and Related Materials by Light Scattering. ..................................................... 42 

Copy of the proposed certificate for SRM 114q with the Addendum related to PSD 51 
vi

List of Figures 

Figure 1: LD-D for SRM 114p for each laboratory identified by the CCRL number. Each 

curve is the average of 3 replicates........................................................................... 13 

Figure 2: LD-W for SRM 114p for each laboratory identified by the CCRL number. Each 

curve is the average of 3 replicates........................................................................... 13 

Figure 3: LD-D for SRM 114q for each laboratory identified by the CCRL number. Each 

curve is the average of 3 replicates. The letters ABC stand for each of the 3 vials 

used by each laboratory. ........................................................................................... 14 

Figure 4: LD-W for SRM 114q for each laboratory identified by the CCRL number. Each 

curve is the average of 3 replicates. The letters ABC stand for each of the 3 vials 

used by each laboratory. ........................................................................................... 15 

Figure 5: Comparison of particle size distributions using wet, dry, and combined LD for 

SRM 114p. The x-axis is designed to emphasize the points by spacing them at equal 

distance. .................................................................................................................... 18 

Figure 6: Comparison of particle size distributions using wet, dry, and combined LD for 

SRM 114q. The x-axis is designed to emphasize the points by spacing them at equal 

distance. .................................................................................................................... 19 

Figure 7: Comparison of PSD results for SRM 114p (leftmost interval in each pair) with 

values from the SRM 114p certificate (rightmost interval in each pair) showing the 

agreement of the current results with the certified values. ....................................... 20 

Figure 8: Comparison of particle size distributions for SRM’s 114q and 114p. .............. 21 

Figure 9: Particle size distribution for SRM 114q using LD (combined wet and dry)..... 23 

Figure 10: Plot illustrating the expanded uncertainties of the differences between two 

PSD determinations within- and between-laboratories. CVF = Cumulative volume 

fraction. *Note: Different laboratories have significantly different within-lab 

standard deviations, so some labs will find that smaller differences are statistically 

significant while others will find that larger differences are not significant. ........... 25 

List of Tables 

Table 1: Chemical composition .......................................................................................... 7 

Table 2: Potential cement compounds according to ASTM C150 ..................................... 8 

Table 3: Parameters reported by participants for LD-W .................................................. 10 

Table 4: Parameters reported by participants for LD-D ................................................... 11 

Table 5: ANOVA output from the fit of a nested, random-effects model with factors box 

and lab to the PSD data (LD-D, particle size=32 μm).............................................. 16 

Table 6: Comparison of particle size distribution results for SRM 114p using different 

methods..................................................................................................................... 18 

Table 7: Comparison of particle size distribution results for SRM 114q using different 

methods..................................................................................................................... 19 

Table 8: Particle size distribution for SRM 114q using LD (combined wet and dry)...... 24 

Table 9: Standard uncertainties and expanded uncertainties for the difference of two 

cumulative volume fractions within- and between-labs. .......................................... 24 

Table 10: Simultaneous Expanded Uncertainties for Conformance Assessment with SRM 

114q........................................................................................................................... 27 
1 

1 Introduction 

A standard reference material (SRM) is a material that has been extensively characterized 

with regard to its chemical composition, physical properties, or both. The National 

Institute of Standards and Technology (NIST) provides over 1300 different SRMs to 

industry and academia. These certified materials are used in quality assurance programs, 

for calibration, and to verify the accuracy of experimental procedures. Every NIST SRM 

is provided with a certificate of analysis that gives the official characterization of the 

material’s properties. In addition, supplementary documentation, such as this report, 

describing the development, analysis, and use of SRMs, is also often published by NIST 

to provide the context necessary for effective use of these materials. 

There are several SRMs related to cement (http://ts.nist.gov/ts/htdocs/230/232/232.htm). 

SRM 114 is related to the fineness of cement, as measured by various indirect methods 

giving its surface area and by passing the material through a fine sieve. This SRM is an 

integral part of the calibration materials routinely used in the cement industry to qualify a 

cement. Being a powder, the main physical properties of cement are its surface area and 

particle size distribution (PSD). Since 1934, NIST has provided SRM 114 for cement 

fineness and it will continue to do so as long as the industry requires it. Different lots of 

SRM 114 are designated by a unique letter suffixed to the SRM number. A certificate that 

gives the values obtained using ASTM C 204 (Blaine) [1], C 115 (Wagner) [2], C 430 

(45 μm residue) [3] and measures of the cement particle size distribution (PSD) by laser 

diffraction are included with each lot of the material. 

In 1934, only the results of the Wagner test and the 45 μm residue test were listed. In 

1944, the Blaine test measurement was added to the SRM 114 certificate. In 2003, the 

PSD measured by laser diffraction was added as an information value, i.e., not certified. 

The PSD was obtained under the sponsorship of ASTM Task Group C01.25.01 [4, 5, 6]. 

The SRM 114p was released in 1994, and depleted in 2004. Therefore, a new batch of 

SRM 114 had to be developed. The development process included the selection of a 

cement, packaging of the cement in small vials, and determination of the values for the 

ASTM tests reported. In ref [7], the development of the values for the ASTM C204 

(Blaine), C115 (Wagner) and C430 (45 μm sieve residue) tests were discussed. In this 

report, the establishment of the PSD for SRM 114q is presented. 

The values given in this report were obtained through a round-robin by volunteer 

participants from companies participating in the Cement and Concrete Reference 

Laboratory (CCRL) certification program. The development of the PSD in this report was 

based on the light scattering technology, or as it is commonly referred to, laser diffraction 

(LD). Other methods could be used to measure the PSD of cement but after two round 

robins and a survey [4, 5, 6], there were insufficient data by other methods to allow a 

statistically valid calculation of the mean PSD. 
2 

The purpose of this report is to provide the description of the development of the PSD 

curve. A brief description of the methodology to measure PSD, and all measurements 

used for the PSD determination, are provided along with the statistical analysis. 
3 

2 Description of particle size distribution methods 

2.1 Introduction 

Based on the results of two round-robins conducted under ASTM sponsorship [4, 5, 6], 

and a survey conducted through CCRL during the development of this SRM, the most

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

cement are as follows: 

1. Laser Diffraction (LD) 

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

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

2. Electrical Zone Sensing (Coulter Principle) (EZS) 

3. Sedimentation 

4. Sieving 

5. Scanning Electron Microscopy (SEM) 

The laser diffraction method is used by over 90 % of the cement industry for measuring 

PSD. The other methods could be classified from the most used to the least used in the 

following order: Electrical zone sensing (Coulter Principle or EZS), sedimentation and 

sieving. The SEM method is not yet used by the cement industry as a quality control 

method. 

Laser diffraction measurements can be performed with the powder either dispersed in air 

or in a liquid. The industry is almost evenly divided between the two techniques and 

some have the capability to use both. 

A full description of each method can be found elsewhere [4, 8]. In this section, we 

present a very brief description of laser diffraction methods. 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. 

2.2 Laser diffraction [4] 

The laser diffraction (LD) 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 (wavelength 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 
4 

methods, depending on the underlying principle or its application. We have chosen 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 ref [8] for a list of equivalent or related methods. 

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 light beam path: 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 electrical energy by interaction with the particles; absorption 

depends on both size and composition. 

The influence of composition is controlled by the complex refractive index, m = n − ik , 

where i = −1 . For non-absorbing (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, 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, a medium is selected that has an imaginary component value 

of k=0). Values of n have been published for many bulk materials [9], but in the case of 

cement, n is routinely estimated based on a mass average of the refractive indices for the 

individual material components [10] and its value was fixed at 1.7 for all round-robins [4, 

5] and in this report. The imaginary refractive component is more difficult to determine 

and/or find in the published literature [11,12], and this often represents a significant 

challenge to the use of scattering methods for fine particle size measurements [13]. 

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 = 1 was fixed for cement 

in this round-robin, although this value is unverified and will likely vary for different 

formulations. In the literature, the value of k=0.1 is also often used for cement. Further 

studies are needed to determine the correct value. 

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 non-spherical 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 
5 

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 with sizes below 100 nm, possibly because of increased 

sensitivity to uncertainties in the refractive index that occur with these materials. Hackley 

et al. [18] determined the range of value of the refractive indices for cement. 

For very large particles (relative to the wavelength of the light used [18]), 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 

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 [14]. For near 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 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 [10,15]. These errors are 

especially prevalent in the size range below one micrometer, where errors exceeding 

100 % are possible. Partial transparency can lead to the appearance of “ghost” particles, 

generally in the size range below one micrometer, produced as an artifact of the 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 LD method requires that the particles be dispersed, either in liquid 

(suspension) or in air (aerosol). The former is commonly referred to as the “wet” method 

(LD-W) while the latter is termed the “dry” method (LD-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 as long as the particles are 

equally well dispersed. For Mie scattering, the higher refractive index contrast in air, 

compared with most liquids, may impact the scattering pattern, without altering the 

results. 

Differences between LD-D and LD-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, e.g., by changing pH or adding chemical dispersing agents, or to break up 

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

dispersion can be achieved in a properly selected liquid medium, i.e., a liquid not 

chemically reactive with the powder and with a different refractive index than the 

powder. 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, 
6 

methanol, and ethanol, are commonly used instead. In the LD-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, non-colloidal-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 one 

micrometer 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. 
7 

3 Materials 

3.1 Characteristics of the cement 

Based on the properties of past lots of SRM 114, CCRL and NIST identified a plant with 

a suitable cement for SRM 114q. The selected plant was Lehigh Cement Company1

, 

Union Bridge, Maryland, which donated 1300 kg of cement. The material selected was 

Type I according to the ASTM C 150 Standard Classification as was SRM 114p. Material 

was collected directly from the finish mill process stream into bags for shipment to NIST. 

The approximate chemical composition has been determined by ASTM Standard Test 

Method C 114-02 to provide additional information on this cement. The analyses of this 

cement (CCRL Portland Cement Proficiency Sample No. 150) were performed by 170 

laboratories. The chemical composition, which is not certified but is provided for 

information only, is shown in Table 1. 

Calculation of the mass fraction of cement compounds, according to ASTM C 150-02, 

are shown in Table 2. These values are not part of the certified values that will be 

published in the certificate. 

The density of the cement was also measured using a modified ASTM C 188 method. 

The modification was to use isopropanol (IPA) as the medium instead of kerosene, with a 

calibrated Le Chatelier flask as described in the ASTM test. Two density measurements 

were done with the results of: 3255 kg/m3

 and 3248 kg/m3 (3.255 g/cm3 and 

3.248 g/cm3). This leads to an average of 3251 kg/m3 ± 0.5 kg/m3 (3.25 g/cm3 ± 0.005 

g/cm3). 

Table 1: Chemical composition 

CaO SiO2 A12O3 Fe2O3 SO3 K2O TiO2 P2O5 Na2O MgO 

loss on 

ignition 

Percent 

by mass 

fraction 64 20.7 4.7 3.2 2.4 0.7 0.3 0.12 0.07 2.2 1.67 

 

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. 
8 

Table 2: Potential cement compounds according to ASTM C150 

Compound Mass Fraction 

C3S (tricalcium silicate) 60 % 

C2S (dicalcium silicate) 14 % 

C3A (tricalcium aluminate) 7 % 

C4AF (tetracalcium alumino-ferrite) 10 % 

3.2 Packaging 

Upon arrival at NIST, the cement was blended in a V-blender (1.7 m3

 or 60 ft3) and then 

transferred to 0.2 m3 (55 gal) drums lined with 0.15 mm (6 mil) polyethylene liners to 

minimize hydration of the cement in storage prior to preparation and packaging. Over 

the next two days, the cement from each drum was sealed in foil bags, each containing 

about 16 kg of cement. The foil bags were stored, and subsequently packaged as 

described below into vials, in a climate-controlled area. 

Each foil bag was packaged into vials, which were then capped and boxed. Each box 

contained approximately 500 sealed vials and the boxes were sequentially labeled from 1 

to 118. Usually about five boxes were filled per day. The more than 59 000 glass vials 

produced, each containing approximately 5 g of cement, were subsequently sealed into 

smaller individual foil bags. The vials were randomly selected (see section 4) and 

shipped to the participating laboratories for measurements. After the analysis of the 

results was completed, the vials were packaged in boxes containing 20 vials each. 

3.3 Homogeneity determination 

It is paramount that all the vials contain essentially similar material; therefore efforts 

were made to determine that the material properties of the powder within the vials could 

be considered identical. Loss of ignition (LOI) measurements were performed and are 

described in ref. [7]. 

PSDs were also measured to determine the best technique to obtain a representative and 

homogeneous specimen from each vial. It was determined that the methodology 

described in the certificate was correct and should be used prior to any PSD 

measurements. The recommendations in the certificate are: 

“Allow the sealed foil bag to equilibrate to testing temperature before opening. Hold the 

pouch at one end and cut off the end of the pouch with scissors. Fluff the cement in 

accordance with ASTM standard C204, Section 3.4 and allow the cement to settle for 2 

min, then measure without delay.” 
9 

4 Experimental design and data analysis 

4.1 Experimental Design 

To determine the box-to-box, lab-to-lab, and vial-to-vial inhomogeneity, each roundrobin participant received 4 vials: one of SRM 114p and three of SRM 114q. The vials 

were randomly selected from boxes that were also randomly selected (from the 118 boxes 

with approximately 500 vials each). For LD-D, the selected boxes were: 2, 6, 13, 24, 45, 

100 and 118. For LD-W, the selected boxes were 19, 29, 33, 88, 92, 94, 101, and 120. 

Participants were asked to perform three replicate measurements using the single SRM 

114p vial and three replicates for each of the three vials of SRM 114q. They were asked 

to report what box number was used for SRM 114q. 

4.2 Parameters used 

In this round-robin, the participants were free to use either method (LD-W or LD-D), but 

they had to respond to a questionnaire (Appendix A) and some parameters were fixed. 

The fixed parameters were: 

Refractive index: 1.7 

Imaginary index: 1 

In LD-W: Isopropanol was requested and the refractive index of isopropanol was set to 

be 1.39 

The responses to the questionnaire are summarized in Table 3 and Table 4. It can be 

noticed that some participants did not return the questionnaire and some elected not to 

use the refractive indices requested or were not aware of them. 

It should be noted that a value of the imaginary index of 0.1 is often selected for cements 

but the value imposed on the participants was 1. In Ref. [18], it has been shown that the 

selection of an imaginary index larger than 0.1 does not affect the results for cement. 

Therefore, the same results should be obtained for imaginary index values of 0.1 to 1. 
10 

Table 3: Parameters reported by participants for LD-W 

Refractive index Ultra sound 

Lab 

# 

Real Imag. Medium Normal Mediuma Concentration 

of cement in the 

mediumb

Dilution 

from stock 

Y/N Durationc Where 

84 1.7 1 1.39 IPA 0.000256 g/mL No Y 10 % for 30 s Inside 92 1.7 1 1.39 IPA No N 

175 1.7 1 1.39 IPA N 209 1.7 1 1.39 Ethanol 20 % No N 284 1.7 1 1.39 IPA 0.001 g/mL No N 557 1.7 1 1.39 No N/A Y 5 min Prior to device 

(bathconcentrate) 

605 1.7 1 1.39 IPA Unknown No Y 40 W for 60 s Inside 690 1.7 1 1.39 No (25/75 

propylene) 

 No N 

736 1.7 1 1.39 No (Ethanol) No Y 100 % for 60 s Inside 932 1.7 1 1.39 No (Ethanol) Unknown No N 

1251 1.7 1 1.39 IPA 0.0003 g/mL No Y 60 s Inside 1916 N/A N/A N/A 1940 1.7 1 1.39 IPA Unknown No Y 60 s Inside 2116 1.7 1 1.39 IPA Y 38 kHz for 60 

s 

Inside 

Notes: a: The participants were requested to use IPA but they were also asked if this was the alcohol that they normally 

asked to indicate what alcohol they used normally. Therefore, this column gives the name of the alcohol that they 

b: The concentration of cement is reported here as given by the participants. The units are as given by the partic

here for information only. 

c: The intensity of the ultrasound is reported here as given by the participants. The units are as given by th

device/manufacturer dependent. Therefore, they cannot be converted to fundamental units. They are given here f

d : The participants were asked to state the model that they used to interpret the data: M= Mie; F= Fraunhofer; B=
11 

Table 4: Parameters reported by participants for LD-D 

Refractive Index 

Lab 

# 

Real Imag. 

Air 

pressure 

[bar] 

Measurement

duration 

[sec] 

Model 

(M/F/B)#

Comments+

73 1.7 1 3.3 12 N/A 

105 1.7 1 6 15 N/A The LD needs at least 5 g for analysis (the whole 

vial) 

124 1.7 1 3.05 3.1 F 148 1.68 N/A 3.4 10 F 151 1.7 1 2 30 F 255 Not used Not used 1 7-12 F 303 N/A N/A N/A 354 1.7 1 4 10 M Material was placed in a 2 oz jar and the jar 

shaken for 10 s before transfer to the PSD device 

619 N/A N/A N/A 736 1.7 1 3 5 M feed rate 37 %; obscuration 1 % to 3 % 

1251 1.7 1 5.7-6.1 30 M 

Note: # : The participants were asked to state the model that they used to interpret their data: M= Mie; F= Fraunhofer; B

+: The comments are as reported by the participants. They refer on how the cement to be tested was treated befor
12 

4.3 Analysis of the Particle Size Distribution Data 

4.3.1 Introduction 

Each participating lab provided three replicates from one pouch2 with SRM 114p and 

three replicates from three different vials for SRM 114q. The data were transmitted in a 

standard spreadsheet. To simplify the data interpretation the cumulative particle size 

distribution were reduced to the following sizes: (1, 1.5, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 

64, 96, 128) μm. All data are shown in Appendix B. 

Each participant laboratory is identified by their CCRL number in this report 

There were 11 participants who provided data with LD-D (44 %) and 14 with LD-W (54 

%). These participants represent 38 % of the laboratories that participated in the roundrobin for the Blaine [3, 4], ASTM C 204 [1]. The lower participation is probably due to 

the lack of a standard test method available for PSD. Nevertheless, the participation was 

sufficient for statistical analysis. 

The statistical analysis of the results allowed the calculation of mean particle size 

distribution for the two cements (SRM 114p and SRM 114q). The heterogeneity between 

the vials was also examined and was incorporated in these results. 

A bootstrap statistical analysis (Appendix C and Ref [4, 5]) was used to calculate the 

mean PSD given in this report. One major conceptual difference from the analysis of the 

results in Ref [4, 5] and those given here is the identification and handling of the outliers. 

The bootstrap procedure used to identify outliers in Ref [4, 5] was probably too 

aggressive because it was based on a percentage of points that fell outside a confidence 

interval for the mean PSD. The alternative chosen for the analysis of the data described in 

this report was to identify curves that significantly differed from the bulk of the data by 

visual inspection. 

The PSD results for SRM 114p and SRM 114q are presented in below, followed by a 

discussion of the results in section 4.4 and 4.5. As discussed in Section 4.5, no 

significant difference was found between the two methods, LD-D and LD-W, therefore a 

single particle size distribution based on the combined results from both methods was 

computed and will be used in the certificate of the SRM 114q. 

4.3.2 Data for SRM 114p by LD-D 

All the curves obtained are shown in Figure 1. Lab 1251 was visually identified as an 

outlier and thus was excluded from subsequent analyses. 

 

2

 The SRM 114p was packaged in pouches directly while the SRM 114q was placed in a vial that was then 

sealed in a pouch. 
13 

Figure 1: LD-D for SRM 114p for each laboratory identified by the CCRL number. 

Each curve is the average of 3 replicates. 

4.3.3 Data for SRM 114p by LD-W 

All the curves obtained are shown in Figure 2. Based on visual inspection, no outliers 

were identified. 

Figure 2: LD-W for SRM 114p for each laboratory identified by the CCRL number. 

Each curve is the average of 3 replicates. 

0

20

40

60

80

100

1 10 100 1000

Size [μm]

Cumulative [%]

73

105

124

148

151

255

303

354

619

736

1251

0

10

20

30

40

50

60

70

80

90

100

1 10 100 1000

Size [μm]

Cumulative [%]

84

92

175

284

557

605

690

736

932

1916

1940

2116
14 

4.3.4 Data for SRM 114q by LD-D 

All the curves obtained are shown in 

Figure 3. No outliers were identified. However, lab 619 was not used in the analyses 

because data for only a single replicate was reported. 

Figure 3: LD-D for SRM 114q for each laboratory identified by the CCRL number. 

Each curve is the average of 3 replicates. The letters ABC stand for each of the 3 

vials used by each laboratory. 

0

10

20

30

40

50

60

70

80

90

100

1 10 100 1000

size [μm]

Cumulative [%]

105A

105B

105C

255A

255B

255C

303A

303B

303C

354A

354B

354C

736A

736B

736C

1251A

1251B

1251C

124A

124B

124C

151A

151B

151C

148A

148B

148C

619A

73A

73B

73C
15 

4.3.5 Data for SRM 114q by LD-W 

All the curves obtained are shown in Figure 4. No outliers were identified. 

Figure 4: LD-W for SRM 114q for each laboratory identified by the CCRL number. 

Each curve is the average of 3 replicates. The letters ABC stand for each of the 3 

vials used by each laboratory. 

4.4 Homogeneity 

Several sources of uncertainty may have affected the results observed for SRM 114q in 

additional to the random measurement error that affects each measurement. Some of the 

sources that may affect these results include heterogeneity of material between vials or 

boxes. Therefore, a statistical analysis was conducted to determine whether the results 

from this round robin show significant box-to-box, lab-to-lab or vial-to-vial scatter. This 

was achieved using the results collected for SRM 114q, since that is the material of 

primary interest for this report and data on multiple vials were measured by each lab. The 

results for SRM 114p were treated analogously, however, when using it as a control to 

confirm that the measurement results obtained in this study were consistent with past 

results. 

To assess the effects of box-to-box and lab-to-lab variation, a nested, random-effects, 

analysis of variance (ANOVA) model [16] was fit to the data for each particle size 

selected (see section 4.3.1). To aid in the interpretation of the results, however, a subset 

of data that provided a balanced design was used to fit the model. The subsetting of the 

data was required because the balance of the original design required all laboratories to 

make measurements using each method (LD-D and LD-W) but not all of the labs 

returned results for each method. 

0

10

20

30

40

50

60

70

80

90

100

1 10 100 1000

size [μm]

Cumulative [%]

932A

932B

932C

1916A

1916B

1916C

92A

92B

92C

175A

175B

175C

605A

605B

605C

1940A

1940B

1940C

84A

84B

84C

736A

736B

736C

284A

284B

284C

557A

557B

557C

2116A

2116B

2116C

690A

690B

690C
16 

For the LD-D measurements, data from boxes 2, 6, 13, and 100 collected by laboratories 

105, 124, 148, 151, 255, 303, 354, and 736, were used, since at least two laboratories 

returned results for vials from each of those four boxes. The data from labs 1251 (box 

45), and 73 (box 118) were not used since those boxes were measured only by one 

laboratory. 

For the LD-W measurements, data from boxes 19, 33, 92, and 129 collected by 

laboratories 92, 175, 284, 557, 605, 932, 1916, and 1940, were used. The data from labs 

2116 (box 29), 209 (box 66 and box 113), 736 (box 88), 84 (box 94), and 690 (box 101) 

were not used since those boxes were measured only by one laboratory. 

Residual plots indicated that the model fit the data well for central particle sizes where 

variation in the measurements was observed. Typical output from the analysis of variance 

for one particle size is shown in Table 5. The low p value (<0.05) corresponding to the F 

test for the significance of lab-to-lab variability provides strong evidence that there is 

significant lab-to-lab variation. The high p value for the F test for box-to-box variability 

(0.1187) indicates that there is not strong evidence of significant box-to-box 

heterogeneity in this data. 

Table 5: ANOVA output from the fit of a nested, random-effects model with factors 

box and lab to the PSD data (LD-D, particle size=32 μm). 

Source 

Degrees of 

Freedom 

Sums of 

Squares 

Mean 

Squares F Statistic p value 

Box-to-Box 3 92.1946 30.7315 3.7132 0.1187166

Lab-to-Lab (in Box) 4 33.1050 8.2763 21.1534 0.0000032

Residuals 16 6.2600 0.3913 

 

To assess vial-to-vial variation or heterogeneity, a one-factor nested ANOVA model for 

the factor vial was fit to the individual data reported by each laboratory for each particle 

size. Then, to control for the increased probability of false positive results that would 

arise from carrying out multiple tests, significance was determined using a simple 

binomial multiple comparisons procedure [19]. 

The multiple comparisons procedure, carried out for each particle size, was implemented 

by interpreting the results of each ANOVA in which vial-to-vial variation was significant 

as the outcome of a Bernoulli trial with probability of success p = 0.05 . Then, because 

the data from each laboratory are considered independent of one another, the probabilities 

of different numbers of successes that could be observed by chance when measuring 

homogeneous cement can be computed to determine how many significant results must 

be observed to conclude with 95 % confidence that the observed vial-to-vial variation is 

significant. 
17 

Using this procedure, it was found that for both the LD-W and LD-D determinations in 

this study, observing two or more significant vial-to-vial results for different labs for each 

particle size would happen less than 5 % of the time if the cement were homogeneous. 

For small particle sizes (below about 10 μm) up to five significant results were observed, 

however, and for larger particle sizes two significant results were observed, indicating 

that this material is not likely to be homogeneous. To account for the heterogeneity 

observed for most particle sizes in the uncertainty of certified PSDs, prediction intervals 

were used at each particle size to account for the vial-to-vial variation in the material for 

distribution to customers. The vial-to-vial standard uncertainty was computed by pooling 

the standard deviations of the mean results for each of the three vials measured within 

each laboratory. This results in a slightly conservative estimate of the standard 

uncertainty due to heterogeneity. The between vial variation was also assumed to follow 

a normal or Gaussian distribution. 

Because there was also significant lab-to-lab variation, replicate measurements within 

labs were averaged so that the certified values would be computed using individual, 

independent values from each laboratory. 

After averaging the replicated determinations made within each lab, the mean particle 

size distributions for wet and dry LD were computed using bootstrap prediction intervals. 

General background on the bootstrap procedure is given in Appendix C. Bootstrap 

intervals were used because for some of the largest particle sizes many laboratories 

observed identical results for each of the three vials they measured, which is inconsistent 

with the typical assumption of normally-distributed data required for uncertainty intervals 

computed using the procedures outlined in the ISO Guide to the Expression of 

Uncertainty in Measurement [20] or the NIST Uncertainty Policy [21]. The bootstrap 

results for the more central particle sizes should give results that are essentially the same 

as the standard results based on Ref [20, 21], however. 

Figure 5 and Table 6 show the results obtained in this study for SRM 114p using both the 

LD-W and LD-D methods for determining the particle size distribution. Results are also 

given for the combined data from the two methods under the assumption that the methods 

do not give significantly different results. The fact that the intervals for the wet, dry, and 

combined show good agreement for all particle sizes indicates that the difference between 

methods is not statistically significant, so only the combined result will ultimately be 

used. Figure 6 and Table 7 show the analogous results for SRM 114q. The particle size 

distribution based on the combined wet and dry methods will be used on the certificate of 

the SRM 114q since the two methods were not statistically distinguishable. 
18 

Figure 5: Comparison of particle size distributions using wet, dry, and combined 

LD for SRM 114p. The x-axis is designed to emphasize the points by spacing them 

at equal distance. 

Table 6: Comparison of particle size distribution results for SRM 114p using 

different methods. 

Particle Wet [%] Dry [%] Combined [%] 

Size 

[μm] 

Lower 

Bound Mean 

Upper 

Bound

Lower 

Bound Mean

Upper 

Bound

Lower 

Bound Mean 

Upper 

Bound

1.0 4.1 5.9 7.7 5.0 5.6 6.1 4.7 5.8 6.9

1.5 6.6 9.0 11.4 8.4 9.3 10.2 7.7 9.1 10.6

2.0 9.9 12.4 15.3 11.6 12.6 13.6 10.9 12.5 14.2

3.0 14.3 17.4 20.8 17.0 18.2 19.3 15.9 17.7 19.5

4.0 18.6 22.0 25.4 21.4 22.8 24.1 20.1 22.3 24.3

6.0 26.2 29.9 33.9 28.7 30.5 32.0 27.8 30.1 32.5

8.0 32.7 36.6 40.4 34.9 36.9 38.8 34.5 36.7 39.1

12.0 44.0 47.7 51.4 45.4 47.5 49.5 45.4 47.6 50.1

16.0 53.3 56.9 60.9 54.0 56.3 58.3 54.3 56.7 58.9

24.0 68.4 71.7 75.5 68.3 70.2 72.1 68.8 71.0 73.2

32.0 79.1 81.9 85.4 78.6 80.2 81.8 79.5 81.2 83.1

48.0 91.0 93.0 94.9 90.6 91.7 92.8 91.2 92.4 93.7

64.0 96.1 97.2 98.3 96.0 96.7 97.5 96.3 97.0 97.7

96.0 98.9 99.3 99.7 98.9 99.4 99.8 99.0 99.3 99.6

128.0 99.4 99.7 99.9 99.3 99.7 100.0 99.4 99.7 99.9

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

Particle Size, μm (spacing of axis labels not to scale)

20 40 60 80 100

Cumulative Volume Fraction, %

LAS-W

LAS-D

Combined

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

Particle Size, μm (spacing of axis labels not to scale)

20 40 60 80 100

Cumulative Volume Fraction, %

LAS-W

LAS-D

Combined
19 

Figure 6: Comparison of particle size distributions using wet, dry, and combined 

LD for SRM 114q. The x-axis is designed to emphasize the points by spacing them 

at equal distance. 

Table 7: Comparison of particle size distribution results for SRM 114q using 

different methods3

. 

Particle Wet [%] Dry [%] Combined [%] 

Size 

[μm] 

Lower 

Bound Mean 

Upper 

Bound

Lower 

Bound Mean

Upper 

Bound

Lower 

Bound Mean 

Upper 

Bound

1.0 3.2 5.2 7.3 4.1 5.1 6.1 3.8 5.1 6.5

1.5 5.5 7.9 10.4 7.0 8.6 10.1 6.2 8.0 9.8

2.0 8.5 11.1 13.8 9.5 11.6 13.5 9.1 11.2 13.3

3.0 12.9 15.9 19.1 14.4 17.0 19.7 13.9 16.3 18.8

4.0 17.1 20.7 24.0 18.6 21.7 24.9 18.1 21.0 24.0

6.0 25.3 29.5 33.4 25.8 30.2 34.2 26.1 29.6 33.3

8.0 33.1 37.3 41.5 32.8 37.9 42.6 33.8 37.6 41.5

12.0 46.0 50.8 55.8 46.3 51.6 56.7 46.8 51.0 55.6

16.0 57.0 62.7 68.4 58.3 63.1 68.3 57.9 62.8 68.0

24.0 77.7 81.3 85.2 76.9 80.2 83.6 78.0 80.8 83.6

32.0 89.2 91.6 94.2 87.8 90.3 92.5 89.4 91.2 92.9

48.0 97.3 98.4 99.6 97.2 98.2 99.2 97.4 98.4 99.4

64.0 98.6 99.7 100.0 99.3 99.8 100.0 98.9 99.7 100.0

96.0 98.8 99.8 100.0 100.0 100.0 100.0 99.1 99.9 100.0

128.0 98.8 99.8 100.0 100.0 100.0 100.0 99.1 99.9 100.0

 

3 This table has been changed from the original version of the report by replacing the values of the upper 

bound on the cumulative particle size distribution that had been reported to be slightly over 100 % by 100 

%. This correction was done to better reflect the physical meaning of the boundary, which for this quantity 

cannot be over 100 %. 

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

Particle Size, μm (spacing of axis labels not to scale)

0 20 40 60 80 100

Cumulative Volume Fraction, %

LAS-W

LAS-D

Combined

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

Particle Size, μm (spacing of axis labels not to scale)

0 20 40 60 80 100

Cumulative Volume Fraction, %

LAS-W

LAS-D

Combined
20 

4.5 Discussion of results 

4.5.1 Comparison of SRM 114p with certified values 

From Figure 7, it can be seen that the results obtained for SRM 114p measured as a 

control for this study are consistent with the values that were given in the SRM 114p 

certificate [1], as indicated by the overlap of the expanded uncertainty intervals. Note that 

these intervals agree within the stated levels of uncertainty despite the fact that they were 

obtained using different values for the imaginary refractive index. A imaginary refractive 

index of 1.0 was used in this round robin and a value of 0.1 was to obtain the results 

shown on the SRM 114p certificate, further confirming the results found in Ref. [18] that 

there is no PSD dependence on the imaginary refractive index for values above 0.1. 

Figure 7: Comparison of PSD results for SRM 114p (leftmost interval in each pair) 

with values from the SRM 114p certificate (rightmost interval in each pair) showing 

the agreement of the current results with the certified values. 

4.5.2 Comparison of SRM’s 114p and 114q 

Figure 8 shows the particle size distributions for SRM 114p and SRM 114q. The SRM 

114q is finer than the SRM 114p. This is not surprising as the certified value for the 45 

μm sieve residue ASTM C430 [3] for SRM 114q is 0.79 % ± 0.19 % while for SRM 

114p the value is 8.24 % ± 0.37 % [16]. 

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

Particle Size, μm (spacing of axis labels not to scale)

20 40 60 80 100

Cumulative Volume Fraction, %

Combined

Certified

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

Particle Size, μm (spacing of axis labels not to scale)

20 40 60 80 100

Cumulative Volume Fraction, %

Combined

Certified

This Round-Robin 

SRM 114p Certificate
21 

Figure 8: Comparison of particle size distributions for SRM’s 114q and 114p. 

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

Particle Size, μm (spacing of axis labels not to scale)

0 20 40 60 80 100

Cumulative Volume Fraction, %

SRM 114q

SRM 114p

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

Particle Size, μm (spacing of axis labels not to scale)

0 20 40 60 80 100

Cumulative Volume Fraction, %

SRM 114q

SRM 114p
22 

5 Summary 

5.1 The PSD for SRM 114q 

The SRM 114q particle size distribution (PSD) was determined using laser diffraction 

(LD) techniques in a round-robin evaluation. The values were measured by volunteer 

participants from companies participating in the CCRL proficiency program. Two LD 

methods were included in the tests: LD-D, in which the powder was measured in a dry 

dispersed state as an aerosol (dry) and LD-W, in which the powder was dispersed in a 

non-aqueous liquid medium (wet) . The parameters used to develop the PSD were: 

 The real part of the complex refractive index was 1.7 and the imaginary part was 1.0 

for both methods 

 For LD-W: IPA was used as the medium and the refractive index used for IPA was 

1.39 (imaginary = 0). 

The differences between the results from these two methods was not found to be 

statistically significant, so that data from both methods was combined and used to 

calculate the mean particle size distribution, shown graphically in Figure 9 and in 

tabulated in Table 8. This particle size distribution could be used as a reference to 

validate methodology and instrument operation as described in Section 5.3 below. It 

should be made clear that the uncertainty values shown in Table 8 are intended to 

represent how well the SRM 114q size distribution is known at this time. Therefore, it is 

not expected that all the participant laboratories data would fall within these boundaries. 

In theory, if there were many more laboratories the uncertainty could be even smaller. 

The uncertainty between laboratories and within laboratories is discussed in Section 5.2. 

In summary, the data obtained in this report could be used in the following manner: 

• Table 8 and Figure 9: SRM 114 q values that are on the certificate (how well 

SRM 114q is known) 

Table 9 and Figure 10 and section 5.2: Precision statement that could be used for 

developing a standard test method. Column 2 of 

Table 9 gives the uncertainty for measurements in one laboratory and column 4 of 

• Table 9 gives the uncertainty between laboratories. 

• Table 10 and section 5.3.2: Criteria to determine whether a PSD measurement 

conforms with the measured SRM 114q PSD. 

A draft method to measure the PSD by LD using SRM 114 is given in Appendix D 

(section 7.4). 

5.2 Precision statement based on SRM 114q 

The data from this interlaboratory study was used to obtain typical uncertainties within 

and between laboratories. The results of these determinations are given in 

Table 9 and illustrated in Figure 10. 
23 

To obtain the standard deviation of PSD determinations within a laboratory for a given 

material, the square root of the median of the variances of the three measurements made 

on different vials of SRM 114q by each lab at each particle size was used. These values 

are given in the second column of 

Table 9. The standard deviations for the different particle sizes are indexed by the 

cumulative volume fractions observed for this material, given in the first column of 

Table 9, since the variation depends on the cumulative volume fraction. The particle sizes 

for SRM 114q are not used to index these values because for other materials with 

different particle size distributions the particle sizes associated with each cumulative 

volume fraction will not be the same. 

To reduce the amount of computation that is required to compare two PSD values for a 

particular particle size within a laboratory, the expanded uncertainty of the difference of 

two cumulative volume fractions is given in the third column of 

Table 9. This value gives the acceptable range of two measurements that is likely to be 

caused by random variation. 

Figure 9: Particle size distribution for SRM 114q using LD (combined wet and dry). 

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

Particle Size, ?m (spacing of axis labels not to scale)

0 20 40 60 80 100

Cumulative Volume Fraction, %

Particle Size, μm (spacing of axis labels not to scale)
24 

Table 8: Particle size distribution for SRM 114q using LD (combined wet and dry)4. 

Particle Size, 

μm 

1.0 1.5 2.0 3.0 4.0 6.0 8.0 12.0 16.0 24.0 32.0 48.0 64.0 96.0 128.0

Mean 

Cumulative 

Volume 

Fraction, [%] 

5.1 8 11.2 16.3 21 29.6 37.6 51 62.8 80.8 91.2 98.4 99.7 99.9 99.9

95 % Lower 

Expanded 

Uncertainty 

Bound [%] 

3.8 6.2 9.1 13.9 18.1 26.1 33.8 46.8 57.9 78 89.4 97.4 98.9 99.1 99.1

95 % Upper 

Expanded 

Uncertainty 

Bound [%] 

6.5 9.8 13.3 18.8 24 33.3 41.5 55.6 68 83.6 92.9 99.4 100.0 100.0 100.0

Table 9: Standard uncertainties and expanded uncertainties for the difference of 

two cumulative volume fractions within- and between-labs. 

Cumulative 

Volume 

Fraction 

(CVF), % 

Standard 

Uncertainty of 

CVF's Obtained 

from a Typical Lab*

, 

% 

Expanded 

Uncertainty for the 

Difference of Two 

CVF's Obtained 

from a Typical Lab*

, 

% 

Standard 

Uncertainty of 

CVF's Obtained 

from Different Labs, 

% 

Expanded 

Uncertainty for the 

Difference of Two 

CVF's Obtained 

from Different Labs, 

% 

5.075 0.175 0.496 2.511 7.103 

8.033 0.281 0.794 3.233 9.144 

11.195 0.342 0.969 3.889 10.999 

16.286 0.450 1.274 4.526 12.801 

21.005 0.530 1.500 5.138 14.532 

29.636 0.565 1.598 5.948 16.823 

37.573 0.600 1.696 6.191 17.509 

51.045 0.603 1.706 6.352 17.967 

62.795 0.552 1.561 6.385 18.058 

80.823 0.501 1.417 4.982 14.092 

91.150 0.384 1.085 3.453 9.766 

98.359 0.217 0.614 1.326 3.750 

99.695 0.049 0.139 0.565 1.597 

99.886 0.003 0.009 0.458 1.295 

99.895 0.000 0.000 0.460 1.300 *

Note: Different laboratories have significantly different within-lab standard deviations, some labs will find 

that smaller differences are statistically significant while others will find that larger differences are not 

significant. 

 

4 This table has been changed from the original version of the report by replacing the values of the upper 

bound on the cumulative particle size distribution that had been reported to be slightly over 100 % by 

100 %. This correction was done to better reflect the physical meaning of the boundary, which for this 

quantity cannot be over 100 %. 
25 

Figure 10: Plot illustrating the expanded uncertainties of the differences between 

two PSD determinations within- and between-laboratories. CVF = Cumulative 

volume fraction. *Note: Different laboratories have significantly different within-lab 

standard deviations, so some labs will find that smaller differences are statistically 

significant while others will find that larger differences are not significant. 

Differences larger than the 

Table 9 value for a particular cumulative volume fraction are likely to be caused by 

additional significant sources of variation that should be identified and addressed 

appropriately. The expanded uncertainties were obtained by multiplying the standard 

uncertainties associated with each cumulative volume fraction by the factor 2 2 . The 

2 accounts for the fact that we are computing the uncertainty of the difference of two 

independent measurements while the 2 is the coverage factor used to convert the 

uncertainty from a standard uncertainty to an expanded uncertainty. 

Because the different labs taking part in this study had significantly different levels of 

random variability in their measurements, the within-lab standard uncertainties and the 

uncertainties of the differences between two measurements within a lab represent the 

uncertainties that a typical lab might expect to have. However, the uncertainties within 

some labs could be smaller while the uncertainties within other labs could be larger. 

Uncertainties analogous to those given within a typical laboratory are given for results 

obtained between laboratories in the last two columns of 

0.0

5.0

10.0

15.0

20.0

0.0 20.0 40.0 60.0 80.0 100.0

Cumulative Volume Fraction, %

Expanded Uncertainty of 

Difference in CVF's, %

 Expanded

Uncertainty

for the 

Difference of

Two CVF's

Obtained

from a Typical

Lab*, % 

 Expanded

Uncertainty

for the 

Difference of

Two CVF's

Obtained

from Different

Labs, %
26 

Table 9. The standard uncertainties were obtained by taking the standard deviation of the 

mean PSD values for each laboratory at each particle size. The expanded uncertainties of 

the differences between two measurements were obtained from the standard uncertainties 

by multiplying each standard uncertainty by the factor 2 2 , as was done for the withinlab values. 

5.3 How to use these values 

5.3.1 Introduction 

The purpose of a reference PSD based on an easily accessible reference material is to 

allow the operator to verify the performance of an instrument and the measurement 

procedure being used. If the results are found to be statistically different from the SRM 

certified values, the operator should check the performance of the device, the parameters 

used (such as the refractive indices) or the procedure used (dispersion, ultrasound, 

duration of measurement, et cetera). A proposed procedure to compare the results 

obtained with the SRM 114q is illustrated below. Nevertheless, this procedure is 

considered valid only if the measurements are done using a LD method. From previous 

work [4, 5], it was found that the PSD of a powder is strongly dependent on the 

measurement methodology. The LD distributions might not match a curve obtained using 

SEM, EZS or sedimentation. This is due to the fact that each of these methods is based on 

different assumptions and theories to calculate a particle size from the measurements. For 

instance, LD assumes that the particles are spherical and that the refractive indices of the 

powder are known. The other methods make other assumptions to calculate the PSD from 

the raw data. 

5.3.2 Conformity determination 

The operator should start by measuring at least 3 replicate measurements of the SRM 

114q using the LD procedure and instrument. These results can then be used to determine 

conformity at the following levels: 

• General agreement of the results with other laboratories that participated in this 

round-robin: Because there is no standard test method, a relatively large amount of 

between-lab variation is allowed in this situation 

• Agreement to within-laboratory reproducibility: This level of agreement indicates that 

the user’s results will not differ from the certified value of SRM 114q by more than 

expected based on the within-lab reproducibility of a typical laboratory. 

As stated above, these expanded uncertainty intervals allow for two levels of 

conformance assessment. The first level indicates agreement with the results typically 

obtained by laboratories that participated in the interlaboratory study used for 

certification of the particle size distribution of SRM 114q. Because there is no currently 

agreed upon standard test method for obtaining particles size distributions using laser 

diffraction, however, a relatively large amount of between-lab variation is allowed for in 

these uncertainties, given in column 4 of Table 10. 

For laboratories that would like to assure tighter agreement with SRM 114q, the 

uncertainties in column 3 of Table 10 can be used instead. This level of agreement 
27 

indicates that the user’s results will not typically differ from the certified value of SRM 

114q by more than the within-lab reproducibility of a typical laboratory. 

Table 10: Simultaneous Expanded Uncertainties for Conformance Assessment with 

SRM 114q 

Particle 

Size, 

μm 

Cumulative 

Volume 

Fraction 

(CVF) of SRM 

114q, % 

Simultaneous 95% Expanded 

Uncertainties for the Difference 

Between a Typical Lab and the 

Certified Value of SRM 114q, %

Simultaneous 95% Expanded 

Uncertainties for the Difference 

Between a Typical Lab and the 

Certified Value of SRM 114q 

Including Between Lab 

Variation, % 

1 5.1 2.0 7.6 

1.5 8.0 2.8 9.9 

2 11.2 3.2 11.8 

3 16.3 3.8 13.8 

4 21.0 4.6 15.7 

6 29.6 5.5 18.2 

8 37.6 5.9 19.0 

12 51.0 6.7 19.7 

16 62.8 7.6 20.2 

24 80.8 4.4 15.2 

32 91.2 2.8 10.5 

48 98.4 1.6 4.2 

64 99.7 1.2 2.0 

96 99.9 1.2 1.8 

128 99.9 1.2 1.8 

To use these uncertainties to assess agreement with other laboratories, the user should 

compute the absolute difference in cumulative volume fraction between his or her results 

and the certified values for SRM 114q for each particle size. These differences should 

then be compared to the appropriate expanded uncertainties in columns 3 or 4 of Table 10 

to determine conformance. If the observed absolute difference between the user’s results 

and the certified values for SRM 114q is always less than the corresponding expanded 

uncertainty, then the user can conclude that his or her results are in agreement with other 

laboratories with a confidence level of approximately 95 %. If one or more of the 

observed absolute differences is larger than the corresponding expanded uncertainty, on 

the other hand, this is evidence that the user’s results are not in agreement with the results 

of other laboratories and that changes to the measurement procedures are needed. 

The expanded uncertainty intervals given in Table 10 are computed using the formula 

Conformance Typical Lab SRM 114q

2 2 U ku u = +

where Typical Lab u is the appropriate standard uncertainty obtained from columns 2 or 4 of 
28 

Table 9 and SRM 114q u is obtained by converting the expanded uncertainty intervals given 

for the certified value of SRM 114q in Table 8 using the formula 

SRM 114q

Upper Uncertainty Bound Lower Uncertainty Bound

4

u − = . 

The coverage factor, k, which is used to control the confidence level of the expanded 

uncertainty intervals, is computed so that the confidence level applies simultaneously to 

the 15 comparisons for each particle size certified for the SRM. This is done using the 

Bonferonni inequality [19] and a normal distribution cut-off for 95 % confidence and 

results in a value of k = 2.935 . 

6 References 

1. “Standard Test Method for Fineness of Hydraulic Cement by Air Permeability 

Apparatus”, ASTM C204-00 Volume: 04.01 

2. “Standard Test Method for Fineness of Portland Cement by the Turbidimeter”, 

ASTM C115-96a (2003) Volume: 04.01 

3. “Standard Test Method for Fineness of Hydraulic Cement by the 45-μm (No. 325) 

Sieve”, ASTM C430-96 (2003) Volume: 04.01 

4. Ferraris, C.F, Hackley V.A., Aviles A.I., Buchanan C.E., "Analysis of the ASTM 

Round-Robin Test on Particle Size Distribution of Portland Cement: Phase I" NISTIR 

6883, May 2002 (http://ciks.cbt.nist.gov/monograph, Part I, chapter 3, section 8a) 

5. Ferraris, C.F, Hackley V.A., Aviles A.I., Buchanan C.E., "Analysis of the ASTM 

Round-Robin Test on Particle Size Distribution of Portland Cement: Phase II" 

NISTIR 6931, December 2002 (http://ciks.cbt.nist.gov/monograph, Part I, chapter 3, 

section 8b) 

6. Ferraris C.F., Hackley V.A., Avilés A.I., “Measurement of Particle Size Distribution 

in Portland Cement Powder: Analysis of ASTM Round-Robin Studies”, Cement, 

Concrete and Aggregate Journal, Dec. 2004, vol. 26 #2, pp 71-81 

7. Ferraris, C.F. , Guthrie W., Avilés A.I., Haupt, R., B. McDonald “Certification of 

SRM 114q; Part I”, NIST SP260-161, July 2005 

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

Special publication 960-1, 2001. 

9. 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. 

10. 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). 
29 

11. J.D. Lindberg, R.E. Douglass and D.M. Garvey, “Absorption-coefficientdetermination method for particulate materials,” Applied Optics, 33[9], 4314-4319 

(1994). 

12. 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). 

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

Particles, John Wiley & Sons, New York, 1983. 

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

General principles. 

15. 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). 

16. SRM 114p Certificate: 

https://srmors.nist.gov/certificates/view_cert2gif.cfm?certificate=114q Or by 

selecting “Standard Reference Materials” from the website www.NIST.GOV and 

typing in 114p 

17. Montgomery, Douglas C., Design and Analysis of Experiments, 2nd Edition, John 

Wiley and Sons, New York, 1984. 

18. Hackley V., Lum L-S., Gintautas V., Ferraris C., “Particle Size Analysis by Laser 

Diffraction Spectrometry: Applications to Cementitious Powders”, NISTIR 7097, 

March 2004. 

19. Miller, R.G., Simultaneous Statistical Inference, 2nd edition, Springer-Verlag, New 

York, 1981. 

20. Guide to the Expression of Uncertainty in Measurement, International Organization 

for Standardization (ISO), Geneva, Switzerland, 1993. 

21. Taylor, B.N. and Kuyatt, C.E., “Guidelines for Evaluating and Expressing the 

Uncertainty of NIST Measurement Results”, NIST TN 1297, 1994. 
30 

7 Appendix 

7.1 Appendix A: Questionnaire for participants 

Note: Underlined and in bold the values that were assigned by NIST 

SECTION A: Laser Diffraction (wet): specimen dispersed in a liquid 

Device brand and model: 

 

Parameters to use (mandatory)

3⁄4 Medium: Isopropanol (IPA) 

Is this the medium that you normally use (circle one): Yes No 

If no, please specify what you normally use: 

 

3⁄4 Complex refractive index used for powder: Real: 1.7 Imaginary: 1.0

3⁄4 Refractive index (real) used for medium: 1.39

3⁄4 Do not use a surfactant 

Some information on your method

3⁄4 Concentration of the dispersion: [g/mL] (if known) 

Diluted from more concentrated stock? YES NO 

If yes, give stock concentration [g/L]: _____ 

• Note: use particle density of 3.2 g/mL for calculation of solids concentration. Also 

indicate density used for medium [g/mL]: ________________ 

3⁄4 Ultrasonication of sample suspension (circle one): Yes No 

If yes, please specify intensity and duration: 

 

3⁄4 Was ultrasonic treatment performed (circle one): 

(a) inside PSD device; (b) prior to introduction into device; (c) both 

• If (b) or (c), please identify type of external ultrasonicator used (circle one) 

bath submersible horn 
31 

• If (b) or (c), was the external ultrasonication performed on a (circle one) 

concentrate or dilute dispersion* 

*refers to a suspension at or near the solids concentration used in the actual measurement 

Test and results: 

3⁄4 Duration of the measurement in the PSD device [sec]: 

3⁄4 Model used to interpret the results: (circle one): Mie Fraunhofer Both 

Notes: (add any information that could be useful to better describe the procedure used): 

SECTION B: Laser Diffraction (Dry): specimen dispersed in air 

Device brand and model: 

 

Parameters to use (mandatory)

3⁄4 Complex refractive index used for powder: Real: 1.7 Imaginary: 1.0

Particle dispersion: 

3⁄4 Dispersion procedure: (circle one) compressed air vacuum 

If compressed air, pressure setting used [bar] 

Test and results: 

3⁄4 Duration of the measurement in the PSD device [s]: 

3⁄4 Model used to interpret the results: (circle one): Mie Fraunhofer Both 

Notes: (add any information that could be useful to better describe the procedure used): 
32 

7.2 Appendix B: Data received from the Round-robin SRM 114 p by LD-D

Size Cumulative Particle size distribution by Laboratory (CCRL Code) [%] 

[μm] 1251 255 736 105 354 303 124 151 148 619 

1 5.1 5.6 5.00 6.04 6.6 5.6 6.7 3.8 5.1 

1.5 8.3 10.0 8.00 10.70 10.1 9.5 11.4 7.1 7.7 

2 11.0 13.4 10.88 14.05 13.4 13.0 14.7 10.0 10.2 14.26 3 15.5 18.8 16.26 19.50 19.3 19.3 19.3 14.9 15.0 21.14 4 19.3 23.2 20.96 24.38 24.3 24.8 22.8 18.9 19.4 26.19 6 25.4 31.2 28.61 32.66 32.0 34.0 29.1 25.7 26.5 33.86 8 30.3 38.1 34.71 39.23 38.1 41.4 35.8 31.6 32.3 39.96 

12 37.6 48.5 44.68 49.29 48.2 52.9 48.0 42.0 42.1 50.65 16 43.1 56.2 53.09 57.22 56.9 62.1 57.6 51.2 50.7 59.56 24 52.3 69.3 66.79 69.86 70.5 76.0 71.4 66.6 65.2 73.50 32 60.2 79.2 76.87 79.43 80.7 85.3 81.0 77.8 76.1 83.35 48 70.2 91.4 89.09 90.81 91.4 95.1 92.7 90.8 89.4 94.16 64 74.9 97.0 95.16 95.71 95.8 99.1 97.7 96.3 95.9 98.11 96 77.9 100.0 99.57 98.84 98.1 100.0 100.0 99.2 99.8 99.86 

128 79.2 100.0 100.00 99.67 98.5 100.0 100.0 99.7 100.0 100.00 
33 

SRM 114 p by LD-W

Size Cumulative Particle size distribution by Laboratory (CCRL Code) [%]

[μm] 932 1916 92 175 605 1940 84 736 284 557 2116 20

1 2.6 9.2 2.0 10.7 5.6 5.0 4.9 5.4 10.5 2

1.5 5.2 11.7 5.5 5.1 17.1 8.6 8.2 8.9 8.8 16.3 3

2 20.0 7.6 14.0 9.4 8.1 21.1 11.4 10.8 13.8 11.6 20.3 53 24.2 12.1 19.2 15.9 13.4 27.4 16.1 15.4 21.0 16.3 26.5 94 28.3 16.3 24.6 21.1 17.7 32.6 20.2 19.2 26.9 20.3 31.7 136 35.7 24.0 33.7 29.4 24.9 40.7 26.9 25.7 35.6 26.8 39.6 218 41.7 30.9 40.5 36.6 31.5 47.2 32.7 31.2 42.9 32.4 45.9 29

12 50.9 42.4 50.5 48.1 41.3 58.3 42.8 41.0 53.6 42.4 57.6 4016 58.8 52.0 58.3 57.6 49.2 67.7 51.6 49.8 62.6 51.2 67.2 5024 71.2 66.1 71.1 72.6 65.3 81.2 66.1 64.6 76.8 65.7 80.6 6532 80.6 76.1 80.9 82.6 78.6 88.8 76.7 75.8 85.7 76.4 88.9 7648 91.8 87.7 92.4 92.7 91.7 96.0 89.5 89.3 95.5 89.0 97.6 9064 96.8 93.6 97.3 96.5 96.2 99.0 95.4 95.6 99.9 94.4 99.9 9596 99.7 98.2 99.9 98.9 98.8 100.0 99.1 99.5 100.0 97.4 100.0 99

128 100.0 99.5 100.0 99.6 99.7 100.0 99.8 99.8 100.0 97.9 100.0 99
34 

SRM 114 q by LD-D

Size Cumulative Particle size distribution by Laboratory (CCRL Code) [%] 

[μm] 1251 255 736 

Box 45 45 45 2 2 2 13 13 13 100? 

1 6.1 7.3 5.4 5.2 5.4 5.2 4.8 4.8 4.8 5.6 

1.5 10.0 11.8 8.7 9.4 9.8 9.4 7.7 7.6 7.7 10.0 

2 13.2 15.7 11.6 12.8 13.2 12.8 10.5 10.4 10.6 13.2 3 18.7 22.2 16.4 18.6 19.0 18.6 15.9 15.9 16.0 18.5 4 23.5 27.7 20.5 23.6 23.9 23.5 20.8 20.8 21.0 23.5 6 31.8 37.0 27.8 32.6 32.9 32.6 29.5 29.5 29.8 32.4 8 39.1 44.7 34.3 40.4 40.8 40.5 37.2 37.2 37.6 40.2 

12 51.3 56.7 45.5 52.7 53.1 52.8 51.1 51.0 51.3 53.2 16 60.8 65.6 55.2 62.4 62.9 62.5 63.0 62.8 63.0 64.0 24 73.5 76.5 72.2 78.8 79.6 78.9 80.3 80.1 80.1 80.4 32 83.5 84.7 84.2 89.4 90.2 89.5 90.3 90.2 90.1 90.4 48 94.8 94.9 95.5 97.5 98.1 97.7 98.5 98.5 98.5 98.6 64 98.6 98.9 99.0 99.5 99.7 99.6 100.0 100.0 100.0 100.0 96 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 

128 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 
35 

SRM 114 q by LD-D (continued 1)

Size Cumulative Particle size distribution by Laboratory (CCRL Code) [%] 

[μm] 354 303 124 

Box 6 6 6 6 6 6 2 2 2 13 

1 6.1 5.9 5.9 4.9 5.0 5.0 5.9 6.0 6.0 1.5 

1.5 9.4 9.2 9.2 8.5 8.5 8.4 10.0 10.3 10.2 3.3 

2 12.7 12.5 12.4 11.8 11.8 11.5 13.1 13.3 13.3 5.1 3 18.7 18.5 18.5 18.2 18.2 17.6 17.6 17.9 17.9 8.5 4 24.0 23.9 23.8 24.3 24.2 23.3 21.2 21.6 21.6 11.4 6 33.0 33.0 32.9 35.1 35.1 33.7 28.4 28.9 28.9 16.5 8 40.8 40.9 40.8 44.5 44.5 42.8 36.3 36.9 36.9 22.4 

12 54.7 54.8 54.8 59.9 59.8 58.2 51.7 52.3 52.3 35.3 16 66.5 66.7 66.7 72.1 72.0 70.8 64.3 64.8 64.9 48.4 24 82.8 83.0 83.0 87.8 87.7 87.1 81.8 82.3 82.4 71.7 32 92.5 92.7 92.6 95.2 95.1 94.9 91.3 91.9 92.0 86.0 48 99.0 99.1 99.0 99.8 99.8 99.8 98.4 98.7 98.7 96.5 64 100.0 100.0 100.0 100.0 100.0 100.0 99.8 99.8 99.8 98.8 96 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 

128 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 
36 

SRM 114 q by LD-D (continued 2)

Size Cumulative Particle size distribution by Laboratory (CCRL Code) [%] 

[μm] 148 619 73 

Box 100 100 100 24? 118 118 

1 4.4 4.4 4.4 5.7 5.7 

1.5 7.0 6.9 7.0 9.0 9.0 

2 9.5 9.4 9.5 12.3 12.1 12.1 3 14.4 14.1 14.3 18.5 17.9 18.1 4 18.8 18.5 18.6 23.4 23.2 23.5 6 26.3 25.9 26.0 31.5 32.6 33.1 8 32.9 32.6 32.6 38.5 41.2 41.8 

12 45.5 45.2 45.3 51.5 56.5 57.1 16 57.3 57.0 57.1 62.9 68.9 69.4 24 75.9 75.8 75.8 81.0 85.4 85.6 32 87.8 87.8 87.8 92.0 93.7 93.8 48 97.9 97.9 97.9 99.3 99.3 99.3 64 100.0 100.0 100.0 100.0 100.0 100.0 96 100.0 100.0 100.0 100.0 100.0 100.0 

128 100.0 100.0 100.0 100.0 100.0 100.0 
37 

SRM 114 q by LD-W

Size Cumulative Particle size distribution by Laboratory (CCRL Code) [%] 

[μm] 932 1916 92 

Box 19 19 19 92? 92? 92? 120 120 120 33 

1 2.1 2.2 2.1 10.1 9.2 9.8 

1.5 4.3 4.4 4.3 13.2 12.3 13.0 3.8 

2 17.4 18.9 18.1 6.6 6.7 6.6 16.0 15.0 15.7 6.6 3 21.1 23.3 22.3 11.3 11.4 11.1 21.4 20.4 21.0 11.9 4 25.2 27.6 26.6 15.9 16.1 15.8 26.7 25.7 26.2 16.6 6 33.2 35.5 34.8 24.9 25.1 24.7 35.9 34.8 35.3 25.3 8 40.5 42.4 41.9 33.3 33.5 33.2 43.1 42.1 42.6 33.6 

12 53.0 54.0 53.7 47.8 48.0 47.8 55.0 54.2 54.5 48.1 16 64.0 64.4 64.1 59.9 60.1 60.1 65.0 64.6 64.7 60.7 24 81.1 80.4 80.0 76.7 76.8 77.0 80.8 81.1 80.7 79.6 32 91.2 90.1 89.8 87.0 87.0 87.3 90.5 91.0 90.6 90.0 48 99.0 98.2 98.3 96.1 96.0 96.2 98.5 98.7 98.6 97.5 64 100.0 100.0 100.0 98.8 98.8 98.9 100.0 100.0 100.0 99.2 96 100.0 100.0 100.0 99.9 99.9 99.9 100.0 100.0 100.0 99.9 

128 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 
38 

SRM 114 q by LD-W (continued 1)

Size Cumulative Particle size distribution by Laboratory (CCRL Code) [%] 

[μm] 605 1940 84 

Box 120 120 120 92 92 92 94 94 94 88 

1 1.2 1.1 1.1 9.6 12.0 9.5 4.7 4.9 4.9 4.3 

1.5 3.7 3.6 3.5 14.2 17.4 14.5 7.3 7.7 7.6 7.4 

2 6.4 6.1 6.0 18.2 20.9 18.4 9.8 10.4 10.3 10.2 3 11.5 11.3 11.1 24.6 27.4 24.9 14.8 15.4 15.4 15.2 4 16.0 15.9 15.7 30.2 33.3 30.3 19.3 19.9 19.9 19.5 6 24.5 24.4 24.2 39.3 44.3 39.3 27.2 27.7 27.8 27.0 8 32.7 32.5 32.3 47.0 51.5 46.9 34.3 34.7 34.8 33.9 

12 44.2 44.3 44.1 60.6 66.6 60.7 47.4 47.6 47.7 46.9 16 54.6 54.7 54.5 72.5 80.3 72.5 59.1 59.3 59.4 58.6 24 76.8 77.0 76.7 89.9 94.1 89.7 77.2 77.3 77.3 76.6 32 90.4 90.6 90.2 97.7 98.6 97.6 88.4 88.5 88.3 87.8 48 97.8 97.9 97.6 100.0 100.0 100.0 98.0 98.0 97.8 97.6 64 99.4 99.5 99.3 100.0 100.0 100.0 100.0 100.0 99.9 99.9 96 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 

128 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 
39 

SRM 114 q by LD-W (continued 2)

Size Cumulative Particle size distribution by Laboratory (CCRL Code) [%] 

[μm] 284 557 2116 

Box 33 33 33 19 19 19 29 29 29 1

1 3.1 2.8 2.9 4.5 4.5 4.6 9.1 9.0 9.2 2

1.5 6.0 5.6 5.7 7.7 7.7 7.9 13.3 13.0 13.3 4

2 9.8 9.4 9.5 10.6 10.5 10.7 17.3 17.0 17.3 53 15.7 15.3 15.5 15.6 15.4 15.8 24.0 23.4 23.8 64 22.0 21.5 21.6 20.0 19.7 20.1 29.8 29.0 29.3 86 33.2 32.9 32.8 27.3 26.9 27.5 39.2 38.1 38.3 158 42.7 42.8 42.6 34.0 33.4 34.2 46.8 45.8 45.8 23

12 56.9 57.3 56.9 46.6 45.7 46.7 60.7 59.8 59.6 4016 68.3 69.1 68.5 58.3 57.0 58.4 73.5 72.4 71.9 5424 84.8 85.7 85.4 77.1 75.2 76.9 91.5 90.5 90.2 7732 93.4 94.1 94.2 88.6 86.3 88.2 98.2 98.1 98.1 9448 99.1 99.5 99.5 97.1 94.0 96.7 99.9 100.0 100.0 1064 100.0 99.9 100.0 98.9 95.5 98.6 100.0 100.0 100.0 1096 100.0 99.9 100.0 98.9 95.5 98.6 100.0 100.0 100.0 10

128 100.0 100.0 100.0 98.9 95.5 98.6 100.0 100.0 100.0 10
40 

SRM 114 q LD-W (continued 3)

Size Cumulative Particle size distribution by Laboratory (CCRL Code) [%] 

[μm] 209 1251 

Box 66 66 113 57 57 57 

1 1.7 2.0 1.9 9.8 9.7 9.7 

1.5 3.3 3.3 3.4 13.5 13.3 13.5 

2 5.2 4.9 5.2 15.3 15.1 15.3 3 9.5 8.9 9.4 19.2 19.0 19.2 4 14.1 13.4 13.8 24.5 24.4 24.7 6 23.0 22.3 22.7 36.0 36.0 36.5 8 31.2 30.8 31.0 45.3 45.3 46.2 

12 45.7 45.6 45.7 59.6 59.7 60.2 16 57.9 58.0 58.1 73.9 74.0 75.6 24 76.6 76.6 77.0 93.7 93.6 95.4 32 88.3 88.1 88.6 99.5 99.3 99.7 48 98.0 97.9 98.3 100.0 100.0 100.0 64 99.9 99.9 100.0 100.0 100.0 100.0 96 100.0 100.0 100.0 100.0 100.0 100.0 

128 100.0 100.0 100.0 100.0 100.0 100.0 
41 

7.3 Appendix C: Bootstrap method 

Suppose a random sample ( ) n x , x ,Kx x = 1 2 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 θ

ˆ ? 

The bootstrap was introduced in 1979 as a computer-based method for estimating the 

standard error of θ

ˆ. 

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 nonparametric 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 θ

ˆ 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 associated 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, SPLUS, 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 2.5 % and 97.5 % empirical percentiles for the replicates of 

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

respectively.
42 

7.4 Appendix D: DRAFT Test Method for Particle Size Analysis of Hydraulic 

Cement and Related Materials by Light Scattering. 

DRAFT – NOT APPROVED BY ASTM

1. Scope 

1.1.This test method covers the determination of the particle size distribution of 

hydraulic cement and related compounds by means of the laser diffraction 

technique, reported as volume percent of particulate materials.5

 

1.2.This test method applies to analyses with both non-aqueous dispersions and in 

gaseous dispersion. 

1.3.This test method is applicable to the measurement of particulate materials in the 

size range of 0.4 μm to 2000 μm. 

1.4.The values stated in SI units are to be regarded as the standard. 

1.5.This standard does not purport to address all of the safety concerns, if any, 

associated with its use. It is the responsibility of the user of this standard to 

establish appropriate safety and health practices and determine the applicability 

of regulatory limitations prior to use. 

2. Reference documents 

2.1. ASTM standards 

B 822 Test Method for Particle Size Distribution of Metal Powders and Related 

Compounds by Light Scattering6

C 219 Terminology Relating to Hydraulic Cement 

C 115 Test Method for Fineness of Portland Cement by the Turbidimeter7 

C430 Standard Test Method for Fineness of Hydraulic Cement by the 45-μm (No. 325) 

Sieve 

C 204 Test Method for Fineness of Hydraulic Cement by Air Permeability Apparatus7

E 1458 Test Method for Calibration Verification of Laser Diffraction Particle Sizing 

Instruments using Photomask Reticles8

E 1617 Practice for Reporting Particle Size Characterization Data8

2.2.ISO standards 

ISO 13320-1 (E), Particle Size Analysis — Laser Diffraction Methods — Part 1: General 

Principles. 

ISO 14887:2000, Sample Preparation -- Dispersing Procedures for Powders in Liquids. 

3. Terminology 

3.1.Definitions:

For definitions of terms used in this test method, refer to Terminology C219 

3.2.Definition of Terms Specific to this Standard: 

 5

 This test method is a modification of Test Method B 822, so that it can be used for hydraulic 

cement. 6

 Annual Book of ASTM Standards, Vol. 02.05 7

 Annual Book of ASTM Standards, Vol. 04.01 8

 Annual Book of ASTM Standards, Vol. 14.02 
43 

3.2.1. laser diffraction, n – a method for determining the particle size distribution 

based on the detection and analysis of the angular distribution of scattered light, 

produced by a laser, passing through a dilute dispersion of particles. 

3.2.2. Background, n – extraneous scattering of light by elements other than the 

particles to be measured; includes scattering by contamination in the measurement 

path. 

3.2.3. Mie theory, n - the electromagnetic theory that describes the scattering of light 

by spherical particles. 

3.2.4. Fraunhofer diffraction, n - the optical theory that describes the low-angle 

scattering of light by particles that are large compared with the wavelength of the 

incident light. 

3.2.5. multiple scattering, n – The rescattering of light by a particle in the path of 

light scattered by another particle. This typically occurs in dispersions with high 

particle concentrations. 

3.2.6. wet method, n - The particles are dispersed in isopropyl alcohol, then 

recirculated through the path of the light beam. 

3.2.7. dry method, n - The particles are dispersed in air, then passed through the path 

of the light beam. 

3.2.8. d10, d50 and d90 –particle size values corresponding to a cumulative 

distribution at 10 %, 50 % and 90 % respectively. 

3.2.9. span – The width of the differential particle size distribution, calculated using 

the following formula: 

50

90 10 ( )

d

d d

span − =

4. Summary of the Test Method 

4.1 The wet method involves a sample of cement powder dispersed in isopropyl 

alcohol (IPA) and recirculated through the path of the light beam. A dry sample can be 

pushed under air pressure or pulled under vacuum so that it flows through the light beam. 

The particles pass through the beam and scatter light. Photodetector arrays collect the 

scattered light, which is then converted to electrical signals and analyzed by a computer. 

The signals are converted to a particle size distribution (PSD) using an optical model 

based on Fraunhofer diffraction or Mie scattering. Scattering information is analyzed 

assuming spherical particles. Calculated particle sizes are therefore presented as 

equivalent spherical diameters. Additional information pertaining to the general 

principles of PSD analysis by light scattering can be found in ISO Standard 13320-1 or in 

the publications by Ferraris et al.9, 1011 

 9

 Ferraris, C.F, Hackley V.A., Aviles A.I., Buchanan C.E., "Analysis of the ASTM Round-Robin Test 

on Particle Size Distribution of Portland Cement: Phase I" NISTIR 6883, Nat. Inst. Of Stds. And 

Tech., May 2002 (http://ciks.cbt.nist.gov/~garbocz/nist6883/nistir6883.htm) 10 Ferraris, C.F, Hackley V.A., Aviles A.I., Buchanan C.E., "Analysis of the ASTM Round-Robin Test 

on Particle Size Distribution of Portland Cement: Phase II" NISTIR 6931, December 2002 
44 

5. Significance and use 

5.1.Accurate measurement of the PSD of cement powder is a beneficial tool for 

process monitoring in the cement industry. In addition, the PSD is a key factor in 

on-going computational efforts to simulate microstructure development and 

predict the performance of cement-based materials. 

5.2. The only other relevant standard method is Test Method C 115, a sedimentation 

method. Designed primarily to determine fineness of cement in terms of surface 

area per unit mass, this sedimentation method also provides a non-mandatory 

procedure to determine the PSD down to a particle size of 7.5 μm. This lower 

limit is not acceptable for proper description of the PSD of hydraulic cement. 

5.3. The Blaine procedure for fineness of cement, given in Test Method C 204, does 

not provide the PSD, but provides the specific surface area based on the air 

permeability of a compacted specimen of cement. 

5.4.The fineness of cement is also measured using Test Method C 430. This method 

is limited to the measurement of the percentage of particles less than 45 μm, and 

therefore does not provide the full PSD. 

5.5. The laser diffraction method is capable of measuring powders with a size 

distribution ranging from 0.4 μm to 2000 μm, covering the full size range in 

hydraulic cement. The interpretation of the measurements is related to the type of 

light scattering model used, either Fraunhofer or Mie. The limitation of this test 

method is that it is not a direct measurement of particle size. In order to calculate 

the PSD, some assumptions must be made: (1) the particles are spherical; (2) the 

refractive indices of the particles and of the medium are known (needed for the 

Mie model only). Also, to correctly measure the particles, the powder must be 

dispersed so that individual particles, and not agglomerates of particles, will 

scatter light independently. 

5.5.1 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, 

assuming a circular cross-section geometry for the diffracting entities. The 

range of validity for this test 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. In Fraunhofer diffraction, the pattern does not depend on the 

refractive index, so in theory there is no difference between using a liquid or 

a gas as a dispersing medium. 

 5.5.2 For non-spherical particles like cement, Mie theory provides a 

volume-weighted equivalent spherical diameter. An accurate representation 

of the “true” size distribution by Mie scattering depends on knowledge of 

the complex refractive index, and will be affected by the degree of particle 

non-sphericity and the dispersion procedure used to prepare the test 

specimen. For Mie scattering, the higher refractive index contrast in air, 

 11 Ferraris C.F., Hackley V.A., Avilés A.I., “Measurement of Particle Size Distribution in Portland 

Cement Powder: Analysis of ASTM Round-Robin Studies”, Cement, Concrete and Aggregate Journal, 

Dec. 2004, vol. 26 #2, p71-81. 
45 

compared with most liquids, may somewhat affect the scattering pattern, but 

should not alter the PSD results significantly. 

 5.5.3 It is important to recognize that the results obtained by this test 

method may disagree with the results obtained from other methods for 

particle size determination using different physical principles. The results 

are influenced strongly by the physical principles employed by each method 

of particle size analysis. The results of any indirect particle sizing method 

should not be regarded as absolute when comparing with results obtained by 

other methods. 

5.5.4 A key aspect of the procedure is to ensure dispersion of the cement 

particles. To verify the adequacy of the procedure that is used, the PSD of a 

sample of SRM 11412 is measured, and the resulting PSD is compared with 

the reference PSD. Lack of agreement means that the procedure for 

dispersing the cement sample needs to be modified or that the instrument is 

not functioning properly. 

6. Interferences 

6.1.Air bubbles entrained in the circulating fluid will scatter light and be reported as 

particles. Circulating fluids may require degassing, and shall be bubble-free upon 

visual inspection. The presence of air bubbles can also be detected by the 

presence of two peaks in the particle size distribution, with the second peak being 

at about 1500 μm or higher. 

6.2.In most devices using a fluid, there is the option of dispersing the particles by 

applying an ultrasound vibration to the suspension. This method is highly 

effective in dispersing the particles but it could also increase the temperature of 

the medium. Therefore, after satisfactory dispersion is achieved, the suspension 

should be allowed to regain an equilibrium temperature. Typically a wait of about 

10-15 min is enough. 

6.3.Contaminants, such as particles or foreign substances dispersed in IPA, scatter 

light, and thus are reported as part of the PSD. 

6.4.The presence of oil, water, or foreign substances in air will cause clogging or 

agglomeration in dry dispersal that will bias the particle size results. The air 

supplied shall be free of such substances. 

6.5.Agglomeration or settling of particles during analysis will cause erroneous results. 

Dispersions shall be prepared in accordance with the instrument manufacturer’s 

instructions, and a stable dispersion shall be maintained throughout the analysis. 

A sufficient flow rate for wet dispersions shall be maintained during the analysis 

in order to prevent settling of large particles. 

6.6.A low concentration of particles in the dispersion may result in poor data 

repeatability. A high concentration of particles in the dispersion may cause 

excessive light attenuation and multiple scattering, resulting in an erroneous PSD. 

Follow the instrument manufacturer’s instructions in determining the correct light 

attenuation level. 

 12 SRM 114 can be obtained from NIST. To order go to the URL: www.nist.gov and select “Standard 

Reference Materials” under the heading “NIST Products and Services”. 
46 

7. Apparatus 

7.1.Particle Size Analyzer, based on Fraunhofer diffraction or Mie scattering, or a 

combination of both models. Use care to ensure that the analyzer system or its 

subsystems are appropriate for the size range of hydraulic cement or related 

compounds. 

7.2.Liquid or air sample handling system – to transport the dispersed test specimen 

across the light beam. 

8. Reagents and materials 

8.1.IPA – isopropyl alcohol, reagent grade, to be used with the wet method 

8.2.Dry, clean air for air dispersion – follow suggestions of manufacturer for 

providing acceptable air supply or vacuum. 

8.3.Fine Sand – as recommended by the manufacturer to clean the instrument after a 

measurement using the dry method. 

8.4.SRM 114 – current reference cement available from NIST12. A letter indicating 

the lot numbers follows the number 114. This material is provided with a 

certificate including a reference PSD. This reference PSD is obtained by statistical 

analysis of test results from an ASTM sponsored round-robin9, 10 for SRM 114P 

and from NIST sponsored round-robins for subsequent reference materials. 

9. Sampling and Sample Size 

9.1.Obtain a representative specimen of hydraulic cement. The amount needed for the 

wet method is less than 1 g and for the dry method is about 3 g to 4 g. The exact 

amount depends on the loading method adopted. 

Note 1– The operator needs to ensure that fines are not lost. It is suggested that 

samples should be homogenized in closed vessels, and settled layers should be 

gently recombined before extracting the final samples. 

9.2.For the wet method, disperse the specimen either in the device or external to the 

device. Follow the manufacturer’s recommendations to determine the most 

appropriate method. 

9.3.For the dry method, load the specimen directly on the device feeder. 

10. Calibration and Standardization 

10.1. Verify proper operation of the instrument using Test Method E 1458 or the 

manufacturer’s calibration procedure. 

10.2. Hydraulic cement SRM 114 is intended to be used as a reference material. The 

use of SRM 114 will not permit direct calibration of the instrument, i.e., an 

instrument correction factor should not be calculated. The scope of the SRM 114 

is to provide the means to the operator to develop an appropriate procedure for 

measuring PSD by optimizing the parameters of the instrument. To use SRM 114, 

conduct a test using a method as described in section 11. To use these 

uncertainties to assess agreement with other laboratories, the user should compute 

the absolute difference in cumulative volume fraction between his or her results 

and the certified values for SRM 114q for each particle size. These differences 
47 

should then be compared to the appropriate expanded uncertainties in columns 3 

or 4 of Table 5 in Appendix A of the SRM 114q certificate to determine 

conformance. If the observed absolute difference between the user’s results and 

the certified values for SRM 114q is always less than the corresponding expanded 

uncertainty, then the user can conclude that his or her results are in agreement 

with other laboratories with a confidence level of approximately 95 %. If one or 

more of the observed absolute differences is larger than the corresponding 

expanded uncertainty, on the other hand, this is evidence that the user’s results are 

not in agreement with the results of other laboratories and that changes to the 

measurement procedures are needed. 

Note 2: For more details on this methodology see ref [13] 

11. Procedure 

11.1. Install the desired sample delivery system and select the applicable instrument 

range, as indicated by the manufacturer’s instructions. 

11.2. Allow the instrument to warm up for at least 20 min. 

11.3. If necessary, establish the correct optical alignment according to the 

requirements of the manufacturer. 

Note 3 – It is advisable that optical alignment be checked upon startup, whenever the sample 

delivery system is changed and frequently. 

11.4. Measure the background in the mode in which the analysis will be conducted. 

Ensure that the carrier (air or IPA) is flowing through the light path while 

measuring background. Background values shall not exceed the specifications of 

the manufacturer. If the background values exceed the manufacturer’s 

specifications, perform the necessary procedures as specified by the manufacturer 

to bring the background values within acceptable limits. 

11.5. Extract a test portion from the cement sample. Refer to the manufacturer’s 

recommendation to ensure that the quantity of test material is acceptable to 

achieve optimum light scattering conditions. A wide range of sample sizes is 

acceptable, depending on the median particle size (d50), particle density 

(mass/volume), refractive indexes and sample delivery system. 

11.6. Select the appropriate run time for the test portion. This procedure is very 

specific to the equipment and material and is generally gauged by the run-to-run 

repeatability and by the use of SRM 114 (see section 10). 

11.7. Select the appropriate refractive indices. Recommended refractive indices of 

cement are real 1.7, imaginary 0.1; recommended refractive index for IPA: real 

1.378, imaginary 0. 

11.8. Select the desired data output parameters, according to the manufacturer’s 

requirements. Usually, the PSD reported is the cumulative distribution. To 

simplify data interpretation, the following particle sizes are to be used: 0.5, 1, 1.5, 

 

13 Ferraris, C.F.; Avilés A.I.; Guthrie W.; Peltz M.; Haupt, R.; MacDonald B.; Certification of SRM 114q;

Phase II (Particle Size Distribution), NIST SP260-166 (2006). 
48 

2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, and 128 μm. Other sizes can be reported 

without affecting the quality of the results. 

11.9. Transfer the test portion directly to the sample delivery system. For the wet 

method, allow recirculation for at least 20 s prior to beginning measurement. For 

the dry method, engage the sample switch to allow the sample to begin flow past 

the light source before starting measurement. 

11.10. Select the appropriate measurement parameters. For the wet method, 

parameters such as ultrasonication intensity and time, flow rate, and measurement 

duration are to be selected. For dry method, parameters such as intensity of 

vibration applied to the sample feeder, air pressure or vacuum level are to be 

selected. Refer to the instrument manual for further specifications. 

11.11. Perform the sample analysis according to the manufacturer’s instructions. 

11.12. Collect at least three sets of PSDs and calculate the average value for each 

particle size on the same test portion of the wet method and on three different test 

portions for the dry method. 

11.13. For the wet method, drain and fill the sample dispersion system in 

preparation for the next sample analysis. Drain and rinse as necessary, to achieve 

background values within the acceptable operating limits, as specified by the 

manufacturer. 

11.14. For the dry method, brush or vacuum to remove all particles throughout the 

sample system. Purge with air or use fine sand to remove particles remaining in 

the sample system, as described in the manufacturer’s instructions. 

11.15. Follow the manufacturer’s instructions to determine the frequency and the 

procedure for cleaning the lenses. 

12. Report 

12.1. Practice E 1617 specifies three levels of detail for reporting PSD data. It is up 

to the supplier and user of the data to agree on the level of reporting required. As 

a minimum, report the following information: 

12.1.1. The instrument name and model number used and the range selected 

12.1.2. The method of dispersing the test portion, i.e., wet or dry 

12.1.3. The instrument measurement run time 

12.1.4. The parameters selected under 11.10 

12.1.5. The number of replicates that were used to calculate the average 

12.1.6. The 10 %, 50 % and 90 %, (d10, d50 and d90 respectively) diameters. These 

values can be used to calculate the span 

12.1.7. The cumulative (volume % versus diameter) PSD. This could be provided in 

electronic form as well. 

13. Precision and Bias 

13.1. Precision statement – The analysis of the interlaboratory round-robin, 

sponsored by NIST for the development of the next SRM 114 presented here, 

was used to develop the precision values. 

13.1.1. Within-Laboratory Precision — The standard deviation of PSD 

determinations within a laboratory for a given material, are given in the 

second column of Table 1. The standard deviations for the different particle 
49 

sizes, indexed by the cumulative volume fractions observed for this material, 

are given in the first column of Table 1. Criteria for comparing two PSD 

values for a particular particle size within a laboratory, the expanded 

uncertainty of the difference of two cumulative volume fractions, is given in 

the third column of Table 1. This value gives the acceptable range of two 

measurements that is likely to be caused by random variation. 

13.1.2. Multilaboratory Precision — Between laboratory uncertainties are given 

in the last two columns of Table 1. The standard uncertainties were obtained 

by taking the standard deviation of the mean PSD values for each laboratory 

at each particle size. 

13.2. Bias – This test method has no determinable bias as the values obtained can 

only be defined in terms of this test method. 

14. Keywords 

laser diffraction; light scattering; cement; particle size distribution; PSD 

Table 1: Standard uncertainties and expanded uncertainties for the difference of two 

cumulative volume fractions within and between laboratories 

Cumulative 

Volume 

Fraction 

(CVF), % 

Standard 

Uncertainty of 

CVF's Obtained 

from a Typical 

Lab*

, % 

Expanded 

Uncertainty for 

the Difference of 

Two CVF's 

Obtained from a 

Typical Lab*

, % 

Standard 

Uncertainty of 

CVF's Obtained 

from Different 

Labs, % 

Expanded 

Uncertainty for 

the Difference of 

Two CVF's 

Obtained from 

Different Labs, %

5.075 0.175 0.496 2.511 7.103 

8.033 0.281 0.794 3.233 9.144 

11.195 0.342 0.969 3.889 10.999 

16.286 0.450 1.274 4.526 12.801 

21.005 0.530 1.500 5.138 14.532 

29.636 0.565 1.598 5.948 16.823 

37.573 0.600 1.696 6.191 17.509 

51.045 0.603 1.706 6.352 17.967 

62.795 0.552 1.561 6.385 18.058 

80.823 0.501 1.417 4.982 14.092 

91.150 0.384 1.085 3.453 9.766 

98.359 0.217 0.614 1.326 3.750 

99.695 0.049 0.139 0.565 1.597 

99.886 0.003 0.009 0.458 1.295 

99.895 0.000 0.000 0.460 1.300 

 *

Note: Different laboratories have significantly different within-lab standard deviations, so some 

labs will find that smaller differences are statistically significant while others will find that larger 

differences are not significant. 
50 

National Institute of Standards & Technology 

Certificate of Analysis 

Standard Reference Material® 114q 

Portland Cement Fineness Standard 

This Standard Reference Material (SRM) is intended for use in calibrating fineness testing equipment according to ASTM 

Standard Methods. The SRM unit consists of 20 glass vials with plastic caps containing powdered cement (each vial is 

contained in a sealed foil bag). Each vial contains approximately 5 g of cement. 

Certified Values and Uncertainties: A NIST certified value is a value for which NIST has the highest confidence in its 

accuracy and that all known or suspected sources of bias have been investigated or accounted for by NIST. The certified 

values for specific surface area and sieve residue are given in Table 1. The certified values for the surface area are the mean 

of results from analyses performed by cooperating laboratories. The certified value for sieve residue was calculated from a 

quadratic fit of NIST data using three sieves having openings ranging from 38 μm to 56 μm. 

The expanded uncertainties of the certified values for specific surface area were calculated according to the NIST uncertainty 

policy described in the NIST Technical Note 1297 [1], and are at the 95 % confidence level. The uncertainties include 

measurement variability within and between laboratories. The surface area uncertainties also include material variability and 

the uncertainty of the surface area values for the superseded SRM 114p Portland Cement Fineness Standard, which was used 

as the calibrant for this material. The expanded uncertainty for the sieve residue was computed using a Bayesian analysis and 

is also at the 95 % probability level. The expanded uncertainty accounts for the variability of random measurement effects, 

sieve calibrations, and material inhomogeneity.

Table l. Certified Values 

 Measurand ASTM Method Certified Value and Expanded 

 Uncertainty 

Specific Surface Area C 204-96a(a) 

(Blaine) 

 3818 cm2

/g ± 78 cm2/g 

 (381.8 m2

/kg ± 7.8 m2/kg) 

Specific Surface Area C 115-96a(b) 

(Wagner) 

 2183 cm2

/g ± 160 cm2/g 

 (218 m2

/kg ± 16 m2/kg) 

Sieve Residue (45 μm residue) C430-96(c)

 

 0.79 % ± 0.19 % 

(a) Standard Test Method for Fineness of Portland Cement by Air Permeability Apparatus [Blaine]. 

 (b Standard Test Method for Fineness of Portland Cement by the Turbidimeter [Wagner]. 

 (c) Standard Test Method for Fineness of Hydraulic Cement by the 45 μm (No. 325) Sieve. 

Expiration of Certification: The certification of SRM 114q is valid, within the measurement uncertainties specified, until 

31 December 2016, provided the SRM is handled in accordance with the instructions given in this certificate (see 

“Instructions for Use”). This certification is nullified if the SRM is contaminated or otherwise modified. 

Maintenance of Certification: NIST will monitor representative samples from this SRM lot over the period of its 

certification. If substantive changes occur that affect the certification before the expiration date, NIST will notify the 

purchaser. Registration (see attached sheet) will facilitate notification. 

 James St. Pierre, Chief 

 Materials and Construction Research Division 

Gaithersburg, MD 20899 Robert L. Watters, Jr., Chief 

Certificate Issue Date: 24 March 2005 Measurement Services Division 

See Certificate Revision History on Last Page 
51 

The preparation of the material and the coordination of the technical measurements leading to certification were performed 

by C. Ferraris of the NIST Materials and Construction Research Division. 

Statistical consultation on measurement design and analysis of the certification data was performed by W.F. Guthrie and A.I. 

Avilés of the NIST Statistical Engineering Division. 

The support aspects involved in the issuance of this SRM were coordinated through the NIST Standard Reference Materials 

Program by B.S. MacDonald of the NIST Measurement Services Division. 

INSTRUCTIONS FOR USE 

Stability and Use: This material is considered to be extremely hygroscopic. Based on measurements in 1993 of several 

earlier renewals of SRM 114, the properties certified are stable as long as the foil bag remains sealed. The specific surface 

area of cement changes on exposure to the moisture in air. Therefore, this cement should be used immediately after opening 

the outer foil bag. 

Allow the sealed foil bag to equilibrate to testing temperature before opening. To open the pouch, cut off the end with 

scissors. Fluff the cement in accordance with ASTM Standard C204, Section 3.4, allow the cement to settle for 2 minutes, 

and then perform the measurement. 

Material Selection and Packaging: The desired properties were determined to be generally the same as those selected for 

the previous issues of SRM 114; however, in order to better represent current cements, the material selected for SRM 114q 

consists of a finer particle size distribution than previously issued. The Cement and Concrete Reference Laboratory (CCRL) 

and NIST identified a plant with suitable cement: Lehigh Cement Company (Union Bridge, Maryland)14 donated 1300 kg of 

appropriate cement for this SRM. The material selected was Type I according to the ASTM C 150 Standard Classification 

and had a mass fraction of less than 8 % tricalcium aluminate (C3A). The material was collected for shipment to NIST 

directly from the finish mill process stream into bags. Upon arrival at NIST, the cement was blended in a V-blender (1.68 

m3

) and then transferred to 208 L (55 gallon) drums lined with 0.015 cm (6 mil) polyethylene liners to minimize hydration of 

the cement in storage prior to preparation and packaging. Over the next two days, the cement from each drum was sealed in 

foil bags, each containing about 16 kg of cement. The foil bags were stored in a climate-controlled area. The contents of each 

bag were subsequently packaged into vials. The vials were then capped and packaged in boxes of about 500 vials per box. 

The boxes were sequentially labeled from 1 to 118. About 5 boxes were filled per day. Nearly 59 000 glass vials, each 

containing approximately 5 g of cement, were produced. Each vial was then individually sealed in a foil bag. Vials were 

selected from the lot by stratified random sampling [2] for both homogeneity and certification analyses. Selected vials were 

shipped to the participating laboratories for measurements. The remaining vials were packaged into SRM unit boxes of 20 

vials each. 

Homogeneity Assessment and Certification Analyses: Homogeneity testing of the material was performed on 48 randomselected samples. Measurements of the loss of ignition (LoI) showed no reversible moisture take-up by the cement during 

packaging. The data received from the round-robin participants were also checked for laboratory-to-laboratory (or day-today in the case of sieve residue) variability, box-to-box variability, and vial-to-vial variability. No significant box-to-box or 

vial-to-vial variability was detected except for the Wagner or sieve residue tests, and therefore it was determined that the 

samples were homogeneous for the ASTM measurements. Significant vial-to-vial variability was observed using the Blaine 

test and the certified values reflect this source of uncertainty. 

Certification analyses for specific surface areas using ASTM Standard Test Methods C 115-96a and C 204-00 were 

performed on two samples at each of the participating laboratories. SRM 114p Portland Cement Fineness Standard was used 

for calibration. Raw data were submitted by each laboratory to NIST for tabulation and calculation of surface areas, which 

for the Blaine test, assumed a density of 3.15 g/cm3

. The density was measured twice at NIST: the results were 3.255 g/cm3 

and 3.248 g/cm3. 

Certification analyses according to ASTM Standard Test Method C 430-96 for the 45 μm sieve residue were performed at 

NIST on 40 samples from 20 vials of cement. 

Laboratories performing certification analyses are members of the CCRL (http://www.ccrl.us) proficiency program. The full 

list is provided in the report describing the details of the certification process [2]. 

 14Certain commercial equipment, instruments, or materials are identified in this certificate in order to specify adequately the 

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

Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.
52 

Information Values: NIST information values are considered to be of interest to the SRM user, but are not certified because 

insufficient information is available to assess adequately the uncertainty associated with the values or only a limited number 

of analyses were performed. Information values for SRM 114q are given in Tables 2 and 3. Table 2 provides the 

approximate chemical composition determined by ASTM Standard Test Method C114-02. The analysis of this cement 

(CCRL Portland Cement Proficiency Sample No. 150) was performed by 70 to 170 laboratories; the number of participating 

laboratories depends on the value measured. 

Table 2. Information Values for Chemical Composition 

 Compound Mass Fraction Compound Mass Fraction 

 (%) (%) 

 CaO 64.0 K2O 0.70 

 SiO2 20.7 TiO2 0.30 

 A12O3 4.7 P2O5 0.12 

 Fe2O3 3.2 Na2O 0.07 

 SO3 2.4 MgO 2.2 

 Loss on Ignition 1.67 

Table 3 provides the calculation of cement compounds according to ASTM C 150-02. 

Table 3. Information Values for Cement Compounds (Calculation from Table 2) 

Compound Mass Fraction 

 (%) 

 C3S (tricalcium silicate) 60 

 C2S (dicalcium silicate) 14 

 C3A (tricalcium aluminate) 7 

 C4AF (tetracalcium alumino-ferrite) 10 

REFERENCES 

[1] Taylor, B.N.; Kuyatt, C.E.; NIST Technical Note 1297, Guidelines for Evaluating and Expressing the Uncertainty of 

NIST Measurement Results (1993). 

[2] Ferraris, C.F.; Avilés A.I.; Guthrie W.; Haupt, R. MacDonald B.; Certification of SRM 114q; Phase I, NIST SP260-161 

(2005). 

Certificate Revision History: 24 March 2005 (This technical revision corrects the certified values and expanded uncertainties for the measurand); 23 

March 2005 (Original certificate date). 

Users of this SRM should ensure that the certificate in their possession is current. This can be accomplished by contacting 

the SRM Program at: telephone (301) 975-6776; fax (301) 926-4751; e-mail srminfo@nist.gov; or via the Internet 

http://www.nist.gov/srm. 
53 

Addendum 

Standard Reference Material® 114q 

Portland Cement Fineness Standard 

Particle Size Distribution: The SRM 114q particle size distribution (PSD) was determined using laser 

diffraction (LD) techniques in a round-robin evaluation. Two LD methods were included in the tests: 

LD-W, in which the powder was dispersed in a liquid medium (wet) and LAS-D in which the powder 

was measured in a dry dispersed state as an aerosol (dry). The values given in this addendum were 

obtained through a round-robin inter-laboratory study by volunteer participants from companies 

participating in the CCRL certification program. Because the results obtained from the two methods 

were not found to be statistically different, the results were combined to calculate a mean PSD for LD, 

shown graphically in Figure 1 and tabulated in Table 4. A complete discussion of the test procedures and 

statistical analysis is provided in Ref. [3]. 

This particle size distribution could be used as a reference to validate methodology and instrument 

operation as described in Ref. [3], notes and Appendix below. 

The parameters used to develop the PSD were: 

 For LD-D and LD-W: the complex refractive index for the cement used had a real part of 1.7 and an 

imaginary part of 1.0 

 For LD-W: IPA was used as the medium and the refractive index (real) used for IPA was 1.39; the 

imaginary part was zero.

Table 4. Table 4. Statistical results for the particle size distribution of SRM 114q using LD 

methodology [3] 

Particle Size, μm 1.0 1.5 2.0 3.0 4.0 6.0 8.0 12.0 16.0 24.0 32.0 48.0 64.0 96.0 128.0

Mean Cumulative 

Volume Fraction, 

[%] 

5.1 8 11.2 16.3 21 29.6 37.6 51 62.8 80.8 91.2 98.4 99.7 99.9 99.9 

95 % Lower 

Expanded 

Uncertainty 

Bound [%] 

3.8 6.2 9.1 13.9 18.1 26.1 33.8 46.8 57.9 78 89.4 97.4 98.9 99.1 99.1 

95 % Upper 

Expanded 

Uncertainty 

Bound [%] 

6.5 9.8 13.3 18.8 24 33.3 41.5 55.6 68 83.6 92.9 99.4 100.5 100.7 100.7
54 

Figure 1. Graphical depiction of the particle size distribution of SRM 114q using LD (either wet or dry 

dispersion). 

NOTES 

The purpose of a reference PSD based on an easily accessible reference material is to verify the efficacy 

of an instrument and the procedure being used. 

If the results are found to be statistically different from the SRM certified values, the operator should 

check the performance of the device, the parameters used (such as the refractive indices) or the 

procedure used (dispersion, ultrasound, duration of measurement, et cetera). For more details on the 

procedure, see Ref. [3]. 

REFERENCES 

[3] Ferraris, C.F.; Avilés A.I.; Guthrie W.; Peltz M.; Haupt, R.; MacDonald B.; Certification of SRM 114q; Phase II (Particle 

Size Distribution), NIST SP260-166 (2006). 

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

Particle Size, ?m (spacing of axis labels not to scale)

0 20 40 60 80 100

Cumulative Volume Fraction, %

Particle Size, μm (spacing of axis labels not to scale)
55 

Appendix: Conformity determination 

The operator should start by measuring the SRM 114q at least 3 times using his own procedure and an 

instrument based on LD. These results can then be used to determine conformity at the following levels: 

• General agreement of the results with other laboratories: Because there is no standard test method, a 

relatively large amount of between-lab variation is allowed in this situation 

• Agreement to within-laboratory reproducibility: This level of agreement indicates that the user’s 

results will not differ from the certified value of SRM 114q by more than expected based on the 

within-lab reproducibility of a typical laboratory. 

Table 5: Simultaneous Expanded Uncertainties for Conformance Assessment with SRM 114q 

Particle 

Size, 

μm 

Cumulative 

Volume 

Fraction 

(CVF) of SRM 

114q, % 

Simultaneous 95% Expanded 

Uncertainties for the Difference 

Between a Typical Lab and the 

Certified Value of SRM 114q, %

Simultaneous 95% Expanded 

Uncertainties for the Difference 

Between a Typical Lab and the 

Certified Value of SRM 114q 

Including Between Lab 

Variation, % 

1 5.1 2.0 7.6 

1.5 8.0 2.8 9.9 

2 11.2 3.2 11.8 

3 16.3 3.8 13.8 

4 21.0 4.6 15.7 

6 29.6 5.5 18.2 

8 37.6 5.9 19.0 

12 51.0 6.7 19.7 

16 62.8 7.6 20.2 

24 80.8 4.4 15.2 

32 91.2 2.8 10.5 

48 98.4 1.6 4.2 

64 99.7 1.2 2.0 

96 99.9 1.2 1.8 

128 99.9 1.2 1.8 

As stated above, these expanded uncertainty intervals allow for two levels of conformance assessment. 

The first level indicates agreement with the results typically obtained by laboratories that participated in 

the interlaboratory study used for certification of the particle size distribution of SRM 114q. Because 

there is no currently agreed-upon standard test method for obtaining particles size distributions using 

laser diffraction, a relatively large amount of between-lab variation is allowed for in these uncertainties, 

given in column 4 of Table 5. 

For laboratories that would like to assure tighter agreement with SRM 114q, the uncertainties in column 

3 of Table 5 can be used instead. This level of agreement indicates that the user’s results will not 

typically differ from the certified value of SRM 114q by more than the within-lab reproducibility of a 

typical laboratory. 

To use these uncertainties to assess agreement with other laboratories, the user should compute the 

absolute difference in cumulative volume fraction between his or her results and the certified values for 

SRM 114q for each particle size. These differences should then be compared to the appropriate 

expanded uncertainties in columns 3 or 4 of Table 5 to determine conformance. If the observed absolute 

difference between the user’s results and the certified values for SRM 114q is always less than the 

corresponding expanded uncertainty, then the user can conclude that his or her results are in agreement 

with other laboratories with a confidence level of approximately 95 %. If, on the other hand, one or 
56 

more of the observed absolute differences is larger than the corresponding expanded uncertainty, this is 

evidence that the user’s results are not in agreement with the results of other laboratories and that 

changes to the measurement procedures are needed. 

For more details on how the values were obtained see reference [3]. 
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