NIST Technical Note 1441

Phase Composition Analysis of the 

NIST Reference Clinkers by Optical 

Microscopy and X-ray Powder 

Diffraction

Paul Stutzman

Stefan Leigh

i 
NIST Technical Note 1441

Phase Composition Analysis of the NIST

Reference Clinkers by Optical 

Microscopy and X-ray Powder 

Diffraction

Paul Stutzman

Building and Fire Research Laboratory

Stefan Leigh

Statistical Engineering Laboratory

September 2002

U.S. Department of Commerce

Donald L. Evans, Secretary

Technology Administration

Phillip J. Bond, Under Secretary for Technology

ii 
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 Technical Note 1441

Natl. Inst. Stand. Technol. Tech. Note 1441, 44 pages (September 2002)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 2002

_________________________________________

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 

Certification of the phase compositions of the three NIST Reference Clinkers will be based upon 

more than one independent method. The current reference values were established using an optical 

microscope examination, with additional optical microscope data taken from an ASTM C 1356 round 

robin. The present X-ray powder diffraction (XRD) study provides a second, independent estimate of 

the phase abundance. Reitveld refinement of the powder diffraction data allowed calculation of a set 

of best-fit reference patterns and their scale factors. Because of significant contrast in the linear 

absorption coefficients of ferrite and periclase relative to the estimated mean matrix linear absorption 

coefficient, the scale factors were adjusted for microabsorption effects. The XRD data generally 

agree with the optical data with the exception of aluminate. This disagreement may reflect the 

difficulty in resolving this fine-sized phase using the optical microscope. The XRD data show greater 

precision than replicate measurements by microscopy. 

Measurements from different sources, laboratories, instruments, and methods can exhibit significant 

between-method variability, as well as distinct within-method variances. The data sets were analyzed 

using both unweighted and weighted schemes to establish optimal consensus values and to provide 

meaningful consensus uncertainties. While the consensus mean values of individual phase 

abundance do not vary significantly across methods of combining data sources, the associated 

uncertainty values do. The Mandel-Paule-Vangel-Rukhin maximum likelihood method of combining 

the data sets is favored as this method produces a weighted mean whose weighting scheme does not 

necessarily skew the consensus value in the direction of the large number of XRD values, and it takes 

between- as well as within-method variation explicitly into account. 

i 
Table of Contents 

Abstract................................................................................................................................................... i 

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

Microscopical Analysis...........................................................................................................................5 

X-Ray Powder Diffraction......................................................................................................................5 

Experimental Methods............................................................................................................................5 

Sample preparation..............................................................................................................................5 

Analysis...............................................................................................................................................6 

Microabsorption Corrections..................................................................................................................7 

Data Presentation and Evaluation ...........................................................................................................9 

Quantitative Analysis..............................................................................................................................9 

Graphical Analyses: Box Plots.............................................................................................................15 

Direct Phase Estimates by Microscopy and QXRD .............................................................................16 

RM 8486............................................................................................................................................16 

RM 8487............................................................................................................................................21 

RM 8488............................................................................................................................................24 

Numerical Summaries: Consensus Means and Uncertainties in Phase Abundance .............................28 

The Naive Method.............................................................................................................................28 

The Levenson et al. (BOB) Method: Bound on Bias ........................................................................28 

The Mandel-Paule-Vangel-Rukhin (MPVR) Method: Maximum Likelihood Estimation ...............29 

Summary...............................................................................................................................................30 

Acknowledgements...............................................................................................................................32 

References.............................................................................................................................................32 

Appendix A. Structure Models for Clinker Phases..............................................................................34 

Appendix B: Selective Extractions for Clinker and Cement ...............................................................44 

Salicylic Acid/Methanol Extraction (SAM)......................................................................................44 

Potassium Hydroxide/Sugar Extraction (KOH/Sugar).....................................................................44 

Nitric Acid/Methanol Extraction.......................................................................................................44 

List of Tables 

Table 1: Linear Attenuation Coefficients (μ) (for Cu Kα radiation)......................................................8 

Table 2. RM 2686 mass fraction (percent) by QXRD, optical data (OM), and round robin data (RR) 

following ASTM C 1356 [2]. QXRD analysis of nine vials (1-9) with two splits per vial (a, b), 

with each split analyzed in duplicate (1, 2)....................................................................................12 

Table 3. RM 2687 mass fraction (percent) by QXRD, optical data (OM), and round robin data (RR) 

following ASTM C 1356 [2]. QXRD analysis of nine vials (1-9) with two splits per vial (a, b), 

with each split analyzed in duplicate (1, 2)....................................................................................13 

Table 4. RM 2688 mass fraction (percent) by QXRD, optical data (OM), and round robin data (RR) 

following ASTM C 1356 [2]. QXRD analysis of nine vials (1-9) with two splits per vial (a, b), 

with each split analyzed in duplicate (1, 2)....................................................................................14 

Table 5. RM Clinker QXRD Summary: 95 % Confidence Limits for the Mean (Mass Percent). ......15 

Table 6. Combined QXRD / Optical Analyses Mean and 95 % Uncertainty Interval. ........................31 

ii 
List of Figures 

Figure 1: RM 8486 polished section prepared using a 30 s HF vapor etch with a field width of 260μm 

(upper) and 100μm (lower image). ..................................................................................................2 

Figure 2: RM 8487 polished section prepared using a 30 s HF vapor etch with a field width of 260μm 

(upper) and 100μm (lower image). ..................................................................................................3 

Figure 3: RM 8488 polished section prepared using a 30 s HF vapor etch with a field width of 260μm 

(upper) and 100μ m (lower image). .................................................................................................4 

Figure 4: Crystal structure database entry for belite (β-form)................................................................7 

Figure 5: True versus calculated mass fraction values for a laboratory-prepared mixture of clinker 

phases showing both raw data (diamonds) and data corrected for microabsorption (circles) using 

the Brindley microabsorption correction and a median particle size of 1 μm. ................................8 

Figure 6 Refined data for sample 1a showing raw, best-fit, and difference curves. The tic marks show 

peak positions for (bottom up) alite, belite (β and α forms), ferrite, cubic and orthorhombic 

aluminates, and periclase................................................................................................................10 

Figure 7 A straight normal probability plot of the errors indicates their distribution is well 

approximated by a Gaussian. .........................................................................................................11 

Figure 8. Backscattered electron SEM images of RM 8486 at low (a) and high (b) magnifications 

show the heterogeneous texture and intermediate crystal size with alite (A), belite (B), ferrite (F), 

aluminate (AL), periclase (M), and pores (P). ...............................................................................17 

Figure 9. Box plot for RM 8486 alite phase estimates by QXRD, optical microscopy (OM), and round 

robin (RR). .....................................................................................................................................18 

Figure 10. Box plot for RM 8486 Belite...............................................................................................18 

Figure 11. Box plot for RM 8486 aluminate.........................................................................................19 

Figure 12. Box plot for RM 8486 ferrite...............................................................................................19 

Figure 13. Box plot for RM 8486 periclase. .........................................................................................20 

Figure 14. SEM backscattered electron image of the interstitial phase of RM 8487 shows the intermixing of ferrite (F, bright phase) and aluminate (AL, dark) not observable by optical 

microscopy. Other phases shown here are alite (A), and porosity (P)...........................................21 

Figure 15. Box plot for RM 8487 alite. ................................................................................................22 

Figure 16. Box plot for RM 8487 belite. ..............................................................................................22 

 Figure 17. Box plot for RM 8487 aluminate........................................................................................23 

Figure 18 Box plot for RM 8487 ferrite................................................................................................23 

Figure 19. Box plot for RM 8487 arcanite............................................................................................24 

Figure 20. SEM backscattered electron image of RM 8488 showing alite (A), belite (B), aluminate 

(AL), ferrite (F), and porosity (P). .................................................................................................25 

Figure 21. SEM backscattered electron image of a finer-grained interstitial phase texture in some

fragments of RM 8488, which will be more difficult to point count in the microscope................25 

Figure 22. Box plot for RM 8488 alite. ................................................................................................26 

Figure 23. Box plot for RM 8488 belite. ..............................................................................................26 

Figure 24. Box plot for RM 8488 aluminate.........................................................................................27 

Figure 25. Box plot for RM 8488 ferrite...............................................................................................27 

iii 
Introduction 

Improvements in cement production and prediction of cements' performance properties require the 

application of material science, which, in turn, requires the ability to determine and describe their 

micro- and macrostructures. Improved methods for determining the phase composition of cements 

using X-ray powder diffraction will facilitate this understanding. This project, part of the Partnership 

for High-Performance Concrete Technology at the National Institute of Standards and Technology 

(NIST), involves the development and testing of analytical methods necessary for characterization of 

cements. Rietveld refinements to model the complex X-ray powder diffraction (XRD) patterns of 

cementitious materials will provide phase, chemical, and structural information in order to more 

completely characterize them, and so provide an improved basis for investigating relationships 

among cement properties and performance properties. 

 

RMs 8486, 8487, and 8488 are three NIST reference clinkers used for developing and testing 

methods of quantitative phase analysis [1]. These clinkers were selected as representative of the 

range of North American clinker production with respect to phase abundance, crystal size, and crystal 

distribution. The reference values are currently based upon an optical microscope examination of 

polished, etched sections. The XRD study is intended to provide both an additional estimate using an 

independent method of analysis, and data to examine inter- and intra- sample heterogeneity. The 

combined XRD and optical datasets are used to establish the certified values. 

Reflected light microscopy images illustrate the textures of the three clinkers. Epoxy-impregnated, 

polished specimens are etched with hydrofluoric acid vapor to facilitate phase identification. Alite is 

colored brown and belite, blue to brown. Distinguishing features of the silicate phases are the 

hexagonal crystal outline of alite, and the rounded form and internal lameller structure of belite. 

Ferrite appears white due to its high reflectivity and occurs in both a lath-like or dendritic forms. 

Aluminate appears gray and is often found with the ferrite; both of which are sometimes referred to 

as the interstitial phases. Periclase appears gray and is identified by its equant crystal habit and size. 

Clinker 8486 (Figure 1) is intermediate in crystal size and exhibits heterogeneous phase distribution 

relative to the other clinkers. Alite appears as brown subhedral to anhedral crystals approximately 

25μm in size. Belite occurs in large clusters, as rounded crystals about 15μm in diameter, which 

often exhibits the internal lameller structure. Ferrite occurs as medium- to fine-grained lath-like 

crystals that appear white. Aluminate as gray crystals between the ferrite crystals, and periclase 

occurs as gray, equant crystals up to 15μm in both the matrix and within some alite crystals. 

Clinker 8487 (Figure 2) exhibits a fine crystal size and relatively homogeneous phase distribution, 

with the exception of belite and free lime, which both occur as clusters within the microstructure. 

Alite occurrs as anhedral grains approximately 12μm and comprises the bulk of the clinker. The 

matrix contains subhedral aluminate and fine-grained ferrite. Some of the ferrite is intimately 

intermixed with the aluminate. Some of the pores contain alkali sulfates. This clinker may be 

difficult to examine microscopically because of the fine texture of the aluminate and ferrite and the 

uneven distribution of the belite and free lime. 

Clinker 8488 (Figure 3) is the most coarsely crystalline of the three clinkers and exhibits the most 

homogeneous distribution of the constituent phases. Subhedral to anhedral alite crystals up to 110μm 

form the bulk of the clinker. Belite occurs as rounded, evenly distributed crystals of about 35μm 

diameter. Ferrite occurs with both lath-like and dendritic habit while aluminate crystals may be found 

between ferrite crystals. 

1
Alite

Belite

< Periclase

< Ferrite

< Aluminate 

Figure 1: RM 8486 polished section prepared using a 30 s HF vapor etch with a field width of 260μm 

(upper) and 100μm (lower image). 

2
 

Figure 2: RM 8487 polished section prepared using a 30 s HF vapor etch with a field width of 260μm 

(upper) and 100μm (lower image). 

3
Figure 3: RM 8488 polished section prepared using a 30 s HF vapor etch with a field width of 260μm 

(upper) and 100μ m (lower image). 

4
Microscopical Analysis 

Clinker petrography has long been used in the examination of clinker materials. ASTM 1356M [2] 

provides guidance in phase abundance analysis using a microscopical point-count procedure. The 

original certificate phase abundance estimates were performed using a procedure similar to that of 

ASTM 1356M while the round robin data were collected following that ASTM standard test method. 

The advantages of optical microscopy (OM) over chemical analyses are that it provides direct 

examination of the clinker, characterization of both phase composition and texture, and a rapid, 

relatively simple method for estimating the phase volume fraction via point count analysis. 

Procedures for preparation and examination of clinker may be found in Campbell [3]. 

X-Ray Powder Diffraction 

XRD analysis of clinker has been used in cement studies for the past 60 years, and applied in phase 

abundance analysis over the past 40 years. ASTM 1365 [4] details a standard test method for 

quantitative phase abundance analysis using XRD for determination of ferrite, aluminate, and 

periclase (QXRD). XRD is a direct, bulk analysis technique where the patterns provide phase, 

chemical and crystal structure information data that may afford greater understanding of cement 

property/performance relationships. However, XRD analysis of clinker has proven difficult as the 

multiple phases result in substantial peak overlap. There is also difficulty in securing suitable pure 

phase reference standards. These concerns may be addressed using the Rietveld method for X-ray 

powder diffraction [5]. Public domain code General Structure Analysis System (GSAS) can be used 

to refine the powder diffraction data [6]. 

The Rietveld method allows standardization of powder diffraction analysis through use of calculated 

reference diffraction patterns based upon crystal structure models (Fig. 4). The result is a set of 

refined crystal structure models for each phase in the clinker. From these data one can obtain pattern 

intensity information that may be related to phase abundance. Additional data on the chemical and 

structural properties of each phase may also be obtained. This approach to processing XRD data can 

be used in research and for quality control in cement production, and is used here to analyze the NIST 

Reference Clinkers. This method is acceptable under ASTM C 1365, where users are required to 

qualify their instruments and procedures. Initial crystal structure models were taken from the 

literature [7-11, 14] and are provided in Appendix A. 

Experimental Methods 

Sample preparation 

A representative sampling of each clinker was obtained through use of a random-stratified sampling 

scheme and totaled nine samples. Each of these samples was split into replicates designated a and b 

for a total of 18 specimens. Each replicate was analyzed twice, so for all three clinkers there were 54 

samples and 108 scans. The specimen analysis sequencing was randomized so as to avoid 

confounding with any effects of machine drift. For example, RM 8486 sample 1, replicates a and b, 

were analyzed during scans 12, 46, 32, and 65. 

The clinkers are millimeter-sized fragments to provide a relatively homogeneous material, yet be 

suitable for microscopic analysis. Particle size requirements for XRD necessitate reduction in particle 

5
size to below 10 μm to maximize the number of particles analyzed, improve powder homogeneity 

and packing characteristics, and minimize microabsorption-related problems. 

Each vial of clinker (about 10 g) was split into replicates using the cone-and-quarter technique for

subsampling a material. The clinker is poured onto a weighing paper and the mound is then divided 

into quarters using a small spatula. Opposite quarters are combined as equal splits of the original 

sample. The splits were ground individually to fineness less than about 250 μm using a mortar and 

pestle. Final grinding employed a micronizing mill1,2

 to reduce the clinker to a mean particle size of

about 2 μm in 10 min, using 200-proof ethanol (about 5 ml) as a grinding lubricant. The median 

particle size estimate is based upon a single measurement using an X-Ray absorption particle settling 

system. The ground clinker was vacuum filtered to remove the ethanol, dried at 60 °C, and then 

placed in a sealed vial over desiccant in a vacuum dissector. 

Analysis 

Data were collected using Cu Kα radiation from 2Θ = 18° to 130°, using a step size of 0.02°, a count 

time of 4 s, and a graphite monochromator. The receiving slit was fixed at 0.2 mm and a fixed 

divergence slit approximately 0.9° to satisfied the requirement for a constant irradiated volume as 

GSAS calculates diffraction patterns on a fixed slit basis. 

The first step was to establish suitable experiment files for the crystal structures and peak shapes for 

the phases in each clinker by analyzing chemical extraction residues. Structure models from the 

literature (Figure 1 and Table 1, Appendix A), were used for the refinement. This simplified 

subsequent analyses by allowing refinement of each structure model and the peak shape parameters 

with less interference from the other constituents. These intermediate models and peak shapes were 

used for the analyses of the bulk clinker patterns. In essence, the bulk clinker analyses are patternfitting exercises using reference standards determined from the extraction residue experiments. The 

potassium hydroxide/sucrose extraction (KOSH) concentrates the silicate fraction, the salicyclic 

acid/methanol extraction (SAX) concentrates the interstitial phases, and a 7 %, by volume, nitric acid 

in methanol extraction provides a ferrite and periclase residue [12]. A description of these procedures 

is provided in Appendix B. 

 

Variables refined for each phase include scale, specimen displacement, background, lattice 

parameters, atomic coordinates (subject to Si-O or Ca-O bond length constraints), aluminum and iron 

fractions in ferrite tetrahedral and octahedral sites, peak shapes, and, for alite, preferred orientation. 

Fixing these variables, especially the profile shape parameters, in the subsequent analyses eliminated 

problematic correlations. 

 1 Certain products are identified to more fully describe the analytical procedure. In no case does this 

imply endorsement by the National Institute of Standards and Technology, nor does it mean that they 

are the best available for the purpose. 

2

 McCrone micronizing mill, McCrone Research, Chicago, Illinois.

6
Phase: β-Dicalcium Silicate Formula: Ca2SiO4 ICDD: 33-302 (larnite)

Reference: K.H. Jost, B. Ziemer and R. Seydel “Redetermination of the Structure of 

 β-Dicalcium Silicate,” Acta Cryst. (1977). B33, 1696-1700 

Symmetry: Monoclinic P21/n Z: 4 Mass, Formula Unit: 3.326 g cm-3

Cell Parameters (Å)

a 5.502 b 6.745 c 9.297 β = 94.59° Vol (Å3

): 343.9 

Atomic Parameters 

 x y z B (Å2 )

Ca(1) 0.2738 0.3428 0.5694 0.38

Ca(2) 0.2798 0.9976 0.2981 0.30

Si 0.2324 0.7841 0.5817 0.19

O(1) 0.2864 0.0135 0.5599 0.91

O(2) 0.0202 0.7492 0.6919 0.67

O(3) 0.4859 0.6682 0.6381 0.63

O(4) 0.1558 0.6710 0.4264 0.62

Average interatomic distances 

Si - O: 1.63c, Ca - O: 2.88c

Typical bulk belite composition (from Taylor ‘90, Cement Chemistry) 

Na2O MgO Al2O3 SiO2 P2O5 SO3 K2O CaO TiO2 Mn2O3 Fe2O3

0.1 0.5 2.1 31.5 0.2 0.1 0.9 63.5 0.2 0.0 0.9 

 This reference: (K0.01 Na0.005 Ca0.975 Mg0.01)2 (Fe0.02 Al0.06 Si0.90 P0.01 S0.01)O3.96

Figure 4: Crystal structure database entry for belite (β-form). 

 Microabsorption Corrections 

Microabsorption results in biased phase fraction estimates. The greater the individual phases linear 

attenuation coefficient from that of the mixture, the greater the error of the phase fraction estimate. 

Weakly-absorbing phases exhibit greater intensities than expected, while strongly absorbing phases 

exhibit lower intensities. Calculation of the linear attenuation coefficients for the cement phases 

(Table 1) and for a mixture, RM 8486, shows that ferrite, periclase, and free lime (when present) may 

be expected to have the greatest error unless compensated for. This effect is not problematic in 

studies utilizing standardization mixtures, as the error is inherent in the standardization curve; 

however, in Rietveld analyses this effect may be significant. 

Microabsorption effects are reduced through fine grinding, but trials using binary mixtures of ferrite 

and periclase show they may still be problematic. Use of the Brindley absorption correction changes 

the scale factors based upon the differences between the phase and mixture linear attenuation 

coefficients, with an adjustment made for particle size [13]. Using the actual median particle size of 

2μm resulted in an over correction of the phase fractions of the known mixture. An example showing 

true values versus raw data and Brindley-corrected values based upon a 1μm median particle size, is 

provided in Figure 5. As expected, ferrite and periclase values better reflect the true values based 

upon the laboratory-prepared mixture. The low value for orthorhombic aluminate may partly result 

from impurities in the laboratory material. 

7
Table 1: Linear Attenuation Coefficients (μ) (for Cu Kα radiation) 

 

Phase Composition μ μ / μ clinker 

Alite 

Belite 

Aluminate 

C4AF 

Free Lime 

Periclase 

Arcanite 

RM 8486 

Ca3SiO5 

Ca2SiO4 

Ca3AL2O6 

Ca2(Al,Fe)2O5

CaO 

MgO 

K2SO4

Bulk Clinker 

308 

294 

260 

496 

398 

100 

226 

290 

1.0 

1.0 

0.9 

1.7 

1.4 

0.3 

0.8 

1.0 

0.0

10.0

20.0

30.0

40.0

50.0

60.0

0 10 20 30 40 50 60

Calculated Mass Fraction %

Known Mass Fraction %

Raw Data

Corrected

Known Raw Data Corrected

C3S 55.6 60.0 55.4

C2S 20 19.7 19.0

C4AF 11.1 8.2 10.8

C3A-c 5.6 6.3 5.8

C3A-o 5.6 3.6 3.2

Periclase 2 2.3 1.6

Figure 5: True versus calculated mass fraction values for a laboratory-prepared mixture of clinker 

phases showing both raw data (diamonds) and data corrected for microabsorption (circles) using the 

Brindley microabsorption correction and a median particle size of 1 μm.

8
Data Presentation and Evaluation 

Figure 5 shows a composite plot of the raw data, the calculated peak locations for each phase (tic 

marks at base of plot), the calculated pattern (green trace), and difference plot. Graphical comparison 

of the observed versus the calculated pattern, residual plots, the normalized error distribution and 

normal probability plots of the residuals (Figure 6) are perhaps the best means by which to judge the 

quality of the fit. For the normal probability plot of the normalized residuals, a linear plot with a zero 

intercept and unit slope indicates that the error is normally distributed. Numerical assessment of the 

fit is made using a chi-squared value, with lower values reflecting an improved fit. The refinement 

was stopped when the fit could not be significantly improved. 

Quantitative Analysis 

Simultaneous refinement of X-ray diffraction patterns of multiple phases allows quantitative analysis 

using equation 1, whose variables (aside from Z) are all refined in the fitting process: 

 Wp = (Sp (ZMV)p) / (Σ [S (ZMV)]) (1) 

where 

Wp = the mass fraction of phase p, 

S = the Rietveld scale factor, 

Z = the number of formula units per unit cell, 

M = the mass of the formula unit, and 

V = the unit cell volume. 

Initial estimates of the phase fractions were used to estimate the linear absorption coefficient of the 

mixture. A second quantitative estimate using a Brindley absorption correction, based upon a mean 

particle size of 1 μm, established the final analyses. Phase abundance estimates of polymorphs of 

specific phases, such as β-C2S and α-C2S or cubic and orthorhombic C3A were summed for 

comparison with the optical microscopy data. 

9
Figure 6. Refined data for sample 1a showing raw, best-fit, and difference curves. The tic marks 

show peak positions for (bottom up) alite, belite (β and α forms), ferrite, cubic and orthorhombic 

aluminates, and periclase. 

10
Figure 7. A straight normal probability plot of the errors indicates their distribution is well 

approximated by a Gaussian. 

11
Table 2. RM 2686 mass fraction (percent) by QXRD, optical data (OM), and round robin data (RR) 

following ASTM C 1356 [2]. QXRD analysis of nine vials (1-9) with two splits per vial (a, b), with 

each split analyzed in duplicate (1, 2). 

Alite Belite Ferrite Aluminate Periclase

1a1 

1a2 

1b1 

1b2 

2a1 

2a2 

2b1 

2b2 

3a1 

3a2 

3b1 

3b2 

4a1 

4a2 

4b1 

4b2 

5a1 

5a2 

5b1 

5b2 

6a1 

6a2 

6b1 

6b2 

7a1 

7a2 

7b1 

7b2 

8a1 

8a2 

8b1 

8b2 

9a1 

9a2 

9b1 

9b2 

OM1 a 

OM1 b 

OM1 c 

OM1 d 

RR1 a 

RR1 b 

RR2 a 

RR2 b 

RR3 a 

RR3 b 

56.4 

56.8 

55.1 

56.1 

56.8 

56.5 

58.5 

58.5 

56.8 

57.0 

58.6 

57.4 

56.3 

56.2 

56.7 

56.9 

55.8 

55.7 

57.2 

57.1 

56.9 

56.8 

57.3 

57.0 

55.9 

56.5 

56.5 

56.9 

56.7 

57.0 

56.9 

56.3 

55.8 

56.9 

56.1 

57.2 

59.0 

56.3 

60.3 

58.1 

56.8 

56.2 

60.0 

60.2 

61.8 

60.6 

21.5 

21.8 

21.1 

20.3 

20.9 

21.7 

20.8 

21.0 

21.5 

21.2 

20.4 

20.6 

21.1 

21.5 

20.9 

20.9 

20.6 

20.8 

21.1 

21.0 

21.5 

21.4 

20.7 

20.5 

21.4 

20.7 

21.5 

21.1 

21.2 

21.1 

20.6 

21.1 

21.4 

20.8 

21.0 

20.8 

23.0 

25.3 

20.6 

23.7 

23.6 

24.1 

23.6 

24.6 

23.9 

25.0 

13.8 

14.0 

16.1 

15.7 

14.6 

14.4 

13.9 

13.5 

14.2 

14.5 

13.7 

14.5 

15.0 

14.9 

14.8 

14.7 

15.7 

15.8 

14.1 

14.1 

14.1 

14.1 

14.2 

15.0 

14.9 

14.8 

14.3 

14.2 

14.4 

14.3 

15.0 

14.8 

15.1 

14.6 

15.3 

14.8 

13.0 

13.1 

14.2 

14.1 

13.5 

14.3 

9.6 

8.1 

3.9 

3.3 

3.6 

3.7 

3.5 

3.4 

3.1 

3.2 

3.3 

3.4 

3.3 

3.5 

3.4 

3.3 

3.5 

3.5 

3.5 

3.5 

3.4 

3.4 

3.4 

3.4 

3.6 

3.5 

3.5 

3.5 

3.4 

3.6 

3.5 

3.5 

3.4 

3.5 

3.5 

3.5 

3.5 

3.4 

1.1 

1.1 

1.0 

1.0 

3.2 

2.5 

1.3 

2.3 

4.3 

4.0 

4.2 

4.3 

4.2 

4.0 

3.7 

3.8 

4.2 

3.9 

3.9 

4.1 

4.2 

4.1 

4.1 

4.1 

4.4 

4.2 

4.2 

4.3 

4.0 

4.3 

4.2 

3.9 

4.3 

4.6 

4.3 

4.1 

4.2 

4.0 

4.1 

4.2 

4.3 

4.2 

4.1 

3.8 

3.0 

3.7 

3.7 

3.7 

1.9 

2.0 

4.7 

3.8 

2.5 

2.8 

 

12
Table 3. RM 2687 mass fraction (percent) by QXRD, optical data (OM), and round robin data (RR) 

following ASTM C 1356 [2]. QXRD analysis of nine vials (1-9) with two splits per vial (a, b), with 

each split analyzed in duplicate (1, 2). 

Alite Belite Ferrite Aluminate Arcanite Free Lime*

1a1 

1a2 

1b1 

1b2 

2a1 

2a2 

2b1 

2b2 

3a1 

3a2 

3b1 

3b2 

4a1 

4a2 

4b1 

4b2 

5a1 

5a2 

5b1 

5b2 

6a1 

6a2 

6b1 

6b2 

7a1 

7a2 

7b1 

7b2 

8a1 

8a2 

8b1 

8b2 

9a1 

9a2 

9b1 

9b2 

OM1 a 

OM1 b 

OM1 c 

OM1 d 

RR1 a 

RR1 b 

RR2 a 

RR2 b 

RR3 a 

RR3 b 

74.7 

74.2 

74.3 

74.4 

74.4 

74.2 

74.6 

74.2 

74.4 

74.4 

74.2 

73.5 

74.5 

73.8 

73.8 

73.6 

73.8 

73.8 

74.2 

74.4 

74.1 

74.0 

74.2 

74.5 

74.2 

74.7 

74.7 

74.9 

73.9 

74.3 

74.1 

73.7 

73.8 

74.0 

74.0 

74.1 

73.19

71.64

73.25

75.46

72.24

72.51

70.42

71.92

76.93

76.11

11.2 

11.2 

11.5 

11.7 

11.6 

11.8 

11.5 

11.6 

11.4 

11.4 

11.4 

11.4 

11.1 

11.4 

11.4 

11.6 

11.4 

11.5 

11.9 

11.8 

11.6 

11.4 

11.6 

11.4 

11.2 

10.8 

11.3 

11.0 

11.3 

11.2 

11.2 

11.7 

11.5 

11.6 

11.9 

11.5 

 7.29 

 9.59 

 7.14 

 6.98 

 9.10 

 9.79 

 9.00 

 8.50 

 8.31 

 8.29 

4.3 

4.7 

4.3 

4.3 

4.3 

4.3 

4.4 

4.3 

4.4 

4.4 

4.6 

4.5 

4.5 

4.8 

4.8 

4.7 

4.8 

4.7 

4.2 

4.3 

4.4 

4.8 

4.5 

4.4 

4.5 

4.5 

4.2 

4.3 

4.9 

4.7 

4.6 

4.7 

4.7 

4.5 

4.3 

4.6 

4.00 

3.72 

2.78 

2.56 

1.46 

0.88 

0.92 

1.20 

1.00 

1.00 

8.3 

8.5 

8.3 

8.1 

8.3 

8.3 

8.0 

8.3 

8.3 

8.3 

8.2 

9.1 

8.4 

8.3 

8.3 

8.4 

8.5 

8.5 

8.1 

8.0 

8.3 

8.3 

8.3 

8.3 

8.6 

8.5 

8.4 

8.4 

8.5 

8.4 

8.6 

8.3 

8.4 

8.3 

8.3 

8.3 

12.43

12.29

12.82

10.82

13.23

13.32

15.63

14.50

13.40

10.40

0.6 

0.6 

0.7 

0.6 

0.6 

0.6 

0.6 

0.7 

0.6 

0.5 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.6 

0.5 

0.5 

0.6 

0.6 

0.6 

0.5 

0.5 

0.6 

0.6 

0.6 

0.6 

0.6 

0.7 

0.6 

0.82 

0.62 

0.98 

1.49 

1.69 

1.48 

0.00 

0.00 

0.00 

0.00 

2.25 

1.91 

3.01 

2.63 

2.24 

1.99 

4.03 

3.88 

1.86 

1.57 

* XRD data did not measure free lime as it was altered during sample preparation and storage. 

13
Table 4. RM 2688 mass fraction (percent) by QXRD, optical data (OM), and round robin data (RR) 

following ASTM C 1356 [2]. QXRD analysis of nine vials (1-9) with two splits per vial (a, b), with 

each split analyzed in duplicate (1, 2). 

Alite Belite Ferrite Aluminate

1a1 

1a2 

1b1 

1b2 

2a1 

2a2 

2b1 

2b2 

3a1 

3a2 

3b1 

3b2 

4a1 

4a2 

4b1 

4b2 

5a1 

5a2 

5b1 

5b2 

6a1 

6a2 

6b1 

6b2 

7a1 

7a2 

7b1 

7b2 

8a1 

8a2 

8b1 

8b2 

9a1 

9a2 

9b1 

9b2 

OM1 a 

OM1 b 

OM1 c 

OM1 d 

RR1 a 

RR1 b 

RR2 a 

RR2 b 

RR3 a 

RR3 b 

67.2 

68.2 

67.5 

66.9 

66.7 

67.3 

67.0 

67.1 

65.8 

66.7 

67.3 

67.5 

68.0 

68.0 

67.3 

67.3 

66.6 

67.4 

67.4 

67.4 

66.1 

66.5 

66.9 

67.4 

68.2 

68.3 

67.5 

68.0 

67.3 

68.0 

68.7 

69.1 

69.0 

68.9 

68.1 

69.2 

65.14

64.98

64.20

65.54

63.40

64.06

65.52

67.72

67.35

67.82

14.8 

13.9 

14.1 

14.7 

14.9 

14.0 

15.0 

15.5 

15.2 

14.8 

14.0 

14.1 

13.7 

14.1 

14.8 

14.9 

15.6 

14.5 

14.8 

14.8 

15.4 

14.7 

15.2 

15.0 

14.6 

14.5 

15.1 

14.7 

14.4 

13.9 

15.2 

15.3 

16.0 

15.4 

15.8 

 14.5 

18.30

19.31

18.48

17.94

19.82

19.37

19.92

17.21

18.09

18.16

14.3 

14.3 

14.8 

14.7 

14.8 

14.9 

14.3 

13.7 

15.1 

14.6 

14.8 

14.6 

14.6 

14.5 

14.2 

14.2 

14.1 

14.3 

14.2 

14.0 

14.7 

14.8 

14.3 

14.0 

13.5 

13.6 

13.9 

13.9 

14.5 

14.3 

12.7 

12.2 

11.7 

12.3 

12.6 

12.7 

13.46

11.56

13.20

10.25

12.77

12.03

7.80 

7.54 

9.80 

8.20 

3.7 

3.7 

3.6 

3.7 

3.6 

3.7 

3.8 

3.7 

3.8 

3.9 

3.8 

3.8 

3.7 

3.5 

3.6 

3.6 

3.7 

3.9 

3.7 

3.7 

3.8 

4.0 

3.7 

3.6 

3.7 

3.6 

3.5 

3.5 

3.9 

3.7 

3.4 

3.4 

3.4 

3.4 

3.5 

3.6 

3.08 

4.15 

3.87 

6.24 

4.02 

4.53 

6.76 

7.54 

4.80 

8.20 

14
Table 5. RM Clinker QXRD Summary: 95 % Confidence Limits for the Mean (Mass Percent).

Limits Lower Mean Upper 

RM 8486 

Alite 

Belite 

Aluminate 

Ferrite 

Periclase 

 56.50 56.75 57.00 

 20.91 21.04 21.17 

 3.41 3.46 3.50 

 14.40 14.61 14.81 

 4.07 4.13 4.20 

Limits Lower Mean Upper 

RM 8487 

Alite 

Belite 

Aluminate 

Ferrite 

Periclase 

 

 73.51 74.18 74.85 

 10.95 11.44 11.92 

 7.98 8.35 8.73 

 4.11 4.51 4.91 

 0.77 0.91 1.05 

Limits Lower Mean Upper 

RM 8488 

Alite 

Belite 

Aluminate 

Ferrite 

 

 65.91 67.55 69.18 

 13.64 14.77 15.90 

 3.36 3.66 3.96 

 12.33 14.02 15.71 

Graphical Analyses: Box Plots 

The box plot is a schematic graphical device for comparing the empirical distributions represented by 

batches of numbers [15]. For these data, the analytical method used (QXRD, OM-1, RR1-n) 

identifies the batches. This plot can be considered a visual one-way analysis of variance (anova) or ttest. The location of the distributions, their spread, and extremes are embedded in the graphical 

display. This allows meaningful comparison of distributional information through rapid assessment 

of the alignment or misalignment of median values and boxes, and differences in spread. 

Important features of the box plot are: 

1. the width of the box is proportional to sample size, 

2. the median value, used as an indicator of location because of its resistance to outliers, is identified

by the X, 

3. the interquartile range ("middle half") of the data are represented by the body of the box, and 

4. the extremes (minimum and maximum) are represented by the ends of the straight lines projecting 

out of the box. 

15
One important consideration for these data are that the QXRD box represents 36 numbers, while the 

RM certificate data (OM) represents only four numbers, and the round robin data (RR) represents just 

two numbers each. The boxes for the RR groups, with only two observations, have the upper line of 

the box equal to one data point, the other line equal to the other, and the X in the middle denoting the 

mean/median of the two observations. 

Direct Phase Estimates by Microscopy and QXRD 

Both microscopical and QXRD methods have been used to estimate phase abundance of clinker and 

are considered direct methods of analysis. Error in microscopy due to incorrect identification of the 

constituent phases is considered to exceed the error due to counting statistics [15] as fineness of the 

constituents may preclude their identification. For the finer-grained clinkers this may be especially 

problematic for periclase, free lime, and the alkali sulfates. 

X-ray powder diffraction analyses are not limited by crystal size and so are suitable for both clinker 

and cements. The accuracy of XRD, given careful experimental procedure, is about 2 % to 5 % 

absolute for alite and belite and 1 % to 2 % for aluminate and ferrite [15]. Grinding to a particle size 

of a few micrometers is a necessary preparation step and a consequence is the improved homogeneity 

of a relatively coarse-grained material, and resulting improved data precision. Generally, one should 

see good agreement between XRD and microscopy for the silicates and the total interstitial phases. 

Limitations of the accuracy derive from the suitability of the reference standards (the structure 

models), and the ability to identify and control correlations between variables. For example, because 

of a high degree of overlap of the strong diffraction peaks from cubic and orthorhombic aluminate, 

their scale (intensity) factors are correlated. These correlations can be controlled through 

determination of the peak profile shape characteristics using a salicylic acid / methanol extraction 

residue enriched in aluminate. In fitting the whole-clinker pattern, these profile shape variables 

served as initial values and, for both aluminate forms, were constrained to be the same. Box plots of 

the initial data set showed an anti-correlation between belite and ferrite. In this case, the peak shape 

of ferrite would broaden at the expense of the intensity factor of belite. This was controlled by 

determining their respective peak profile shape parameters using potassium hydroxide / sucrose and 

nitric acid / methanol extraction residues and holding the shape parameters fixed throughout the 

fitting of the whole-clinker patterns. 

RM 8486 

RM 8486 exhibits an intermediate crystal size and high heterogeneity relative to the other clinkers 

that may result in greater spread in the phase fraction estimates (Figure 7). Alite (Figure 8) shows 

reasonable similarity between XRD, OM-1 and RR-1, with RR-2 and RR-3 being higher. OM-1 with 

its 4 points has significantly greater spread (IQ-range) than the more tightly grouped XRD numbers. 

For belite (Figure 9), the optical points diverge from the XRD yet demonstrate reasonable agreement 

along themselves, although OM-1 again displays large variance, with only the lowest point 

comparing favorably with XRD. 

Aluminate values (Figure 10) do not demonstrate good agreement among XRD and optical data. 

Here OM-1 appears to be a lowlier. This may result from the fine crystal size and resulting difficulty 

in seeing this phase. Ferrite estimates (Figure 11) exhibit reasonable agreement among XRD, OM-1, 

and RR-1, both in terms of level (mean/median) and spread. Periclase estimates (Figure 12) fall into 

two groupings with respect to the mean/median: XRD/OM/RR-2 versus RR-1/RR-3. 

16
240 μm a

P

ALM- F60 μm 

B 

A

b

Figure 8. Backscattered electron SEM images of RM 8486 at low (a) and high (b) magnifications 

show the heterogeneous texture and intermediate crystal size with alite (A), belite (B), ferrite (F), 

aluminate (AL), periclase (M), and pores (P).

17
18

Figure 9. Box plot for RM 8486 alite phase estimates by QXRD, optical microscopy (OM), and round 

robin (RR).

Figure 10. Box plot for RM 8486 Belite.
19

Figure 11. Box plot for RM 8486 aluminate 

Figure 12. Box plot for RM 8486 ferrite.
20

Figure 13. Box plot for RM 8486 periclase.
21

RM 8487 

RM 8487, being the finest-grained of the three clinkers, was expected to be the most difficult to 

analyze using microscopy. Typical microstructures showing a heterogeneous distribution of the 

silicates (alite and belite), may result in the greater uncertainties observed in the optical analyses. 

The ferrite phase ranged from fine-grained to extremely fine- grained and may in some cases be 

difficult to distinguish visually from the aluminate. A backscattered electron scanning electron 

microscope image of the interstitial phases (Figure 13) shows the finely-intermixed aluminate and 

ferrite. This microstructure probably would not be recognized using optical microscopy. The finegrained distribution does not pose difficulties for the X-ray analyses. 

Alite (Figure 14) shows reasonable similarity between XRD, OM-1 and RR-1, with RR-2 and RR-3 

being somewhat lower and higher, respectively. OM-1 with its 4 points has significantly greater 

spread (IQ-range) than the more tightly grouped XRD numbers. For belite (Figure 15), the optical 

points diverge from the XRD yet demonstrate reasonable agreement between themselves, although 

OM-1 again displays large variance. 

Aluminate values (Figure 16) do not demonstrate good agreement between XRD and optical data, 

with XRD values lower than the optical data. Ferrite values show a reverse trend (Figure 17), with 

XRD values slightly higher than optical. These findings may result from the fine crystal size which 

made it difficult to see this phase using the optical microscope. Alkali sulfate was identified by 

optical microscopy and was identified in the bulk XRD patterns as arcanite. The XRD and OM-1 data 

show reasonable agreement. 

Figure 14. SEM backscattered electron image of the interstitial phase of RM 8487 shows the intermixing of ferrite (F, bright phase) and aluminate (AL, dark) not observable by optical microscopy. 

Other phases shown here are alite (A), and porosity (P). 
22

Figure 15. Box plot for RM 8487 alite. 

Figure 16. Box plot for RM 8487 belite.
23

Figure 17. Box plot for RM 8487 aluminate. 

Figure 18. Box plot for RM 8487 ferrite.
24

Figure 19. Box plot for RM 8487 arcanite.

RM 8488 

Clinker 8488 was expected to be the easiest to characterize using optical microscopy because of its 

more coarsely-grained texture (Figure 19). There were two distinct interstitial phase textures though: 

a coarse-grained texture exhibiting large lath-like aluminate and blocky ferrite crystals, and a finegrained texture with extremely fine-grained aluminate crystals within a fine-grained dendritic ferrite. 

The latter poses difficulties in resolving differences between ferrite and aluminate for optical 

analyses. 

The silicate phases appear to show an negative correlation between the XRD and optical analyses, 

with XRD values of alite (Figure 20) being slightly greater and belite (Figure 21) slightly lower than

the corresponding values from the optical analyses. Optical data (OM-1) show a tighter spread 

(interquartile range) than XRD for both silicates. This may reflect the coarse-grained nature and 

relative ease of identification of the silicates in this clinker. 

Aluminate and ferrite values (Figures 22 and 23) demonstrate good agreement between XRD and 

optical data with the exception of optical round robin sets two and three. Again, this may result from

the fine crystal size and resulting difficulty in observing this phase and in the experimental approach 

(magnification) used in performing the optical point count. 
25

PF 

ALB

A

120 μm

Figure 20. SEM backscattered electron image of RM 8488 showing alite (A), belite (B), aluminate 

(AL), ferrite (F), and porosity (P).

120 μm 

Figure 21. SEM backscattered electron image of a finer-grained interstitial phase texture in some

fragments of RM 8488, which will be more difficult to point count in the microscope. 
26

Figure 22. Box plot for RM 8488 alite. 

Figure 23. Box plot for RM 8488 belite.
27

Figure 24. Box plot for RM 8488 aluminate.

Figure 25. Box plot for RM 8488 ferrite.
Numerical Summaries: Consensus Means and Uncertainties in Phase Abundance 

Often a reference material is certified based on data from more than one measurement method. This

situation occurs when no single method can provide the necessary level of accuracy and/or when 

there is no single method whose sources of uncertainty are well understood and quantified. 

Measurements from different sources, different laboratories, different instruments, and different 

methods can exhibit significant between-method variability, as well as distinct within-method 

variances. A common goal in the analysis of such data is to compute a best consensus value and to 

attach a meaningful consensus uncertainty to that value. The results of the combined XRD and 

optical microscopy data sets are presented in Table 6. Three methods for combining these data sets 

are presented and discussed below. 

The Naive Method 

 

A naive approach [16,17] is to regard the different method results for the same analyte as being 

repeated estimates of a single true mean, and to compute the consensus mean as the unweighted mean 

of the different group means, and the consensus uncertainty as: 

( )

n

s

t(n−1) × (2) 

where n is the number of groups, the ordinary sample standard deviation s is computed on the mean 

values themselves, and t is the appropriate tabulated value of the Student t percent point function for 

achieving 95 % confidence. A very high t value for the case n=2 (t ≈ 13) typically precludes using 

this approach when only two groups are available. Otherwise, this method is useful in that it is 

simple, is probably something that many practitioners would attempt to use, and will often give a 

consensus value identical or very close to other naturally weighted methods. The naive method yields 

a less conservative uncertainty than those provided by other methods that take other sources of error 

into account, but it can serve as a baseline for those methods. 

 

The Levenson et al. (BOB) Method: Bound on Bias

The point of departure for a new method of consensus mean/uncertainty estimation proposed by 

Levenson et al. at NIST [18], is that the intent of using multiple methods is to quantify systematic 

effects (biases) of individual methods by using the variation across the multiple methods results. 

However, if the number of methods is small−two to four, as is the case here−then the sample standard 

deviation of the method means will be a poor estimator of the uncertainty of the systematic effects. 

To overcome this deficiency, this method uses a Type B model [19] for the uncertainty of the 

systematic effects. In practice, a uniform distribution, bounded by the range of method results, has 

been found to be effective as a Type B model. Variants of the method make explicit use of betweenmethod bias (or bias squared), computed as the difference between the largest group mean and 

smallest group mean or between the largest and grand average of the group means [20], as a proxy for 

between-method variance. Here we explicitly combine in quadrature an estimate of within-method 

variation obtained by pooling the standard errors associated with each method with an estimate of 

between-method variation obtained by dividing half the max-mean minus the min-mean range by the 

square root of three to convert to a uniform standard error. 

28
The Mandel-Paule-Vangel-Rukhin (MPVR) Method: Maximum Likelihood Estimation 

Another approach to computing consensus estimates is to get an explicit estimate of the intermethod 

(intergroup) variance, and sum that with a pooled estimate of the within-method (within-group) 

variance, using the combination to weight the contributions from the different methods to form a 

consensus mean. An estimation equation approach for the determination of the between-group 

variance developed by Mandel and Paule [21] has often been used at NIST, particularly in the 

certification of standard reference materials. Vangel-Rukhin [22] showed that the Mandel-Paule 

solution can be interpreted as an approximation to maximum likelihood. We compute the MPVR 

estimates of the inter method variances here and add them to a standard pooled estimates of the 

within method variances, take the square root to get an estimate of the overall standard errors, and 

multiply by an expansion factor of 2. This method has the virtues of explicitly quantifying withingroup and between-group variation, and being rooted in a broadly applicable important general 

method of mathematical statistics, namely maximum likelihood. The drawback is that the estimation 

equation solution and formulations of its variance are strictly speaking only asymptotically correct, so 

that MPVR estimates are better for data sets where many (e.g. >10) methods/groups are present. 

Comparing the consensus means and uncertainties obtained across the comparable sets of RM/analyte 

data, one can observe the following. Consensus means agree very well across all sets. Naive and 

BOB must agree because they are both unweighted means of (group) means. But the weighting 

scheme of MPVR (maximum likelihood) in general either doesn't move the consensus away from the 

unweighted mean−at least to within the reportable precision−or perturbs it only very slightly. 

Comparing the consensus uncertainties as calculated here, one can observe the general pattern: 

U(naive) < U(BOB) < U(MPVR). U(naive) is actually computed from an incorrect, or overly 

naive, underlying statistical model, one that assumes that all the varying groups' data come from

a single parent normal population (same mean, same variance). Consequently U(naive) will, 

typically, lower bound the other estimates, and represents an anticonservative, and probably 

incorrect, estimate of the overall variation. U(BOB), on the other hand, makes no such naive 

population assumption, and takes explicitly into account intermethod biases. The U(BOB) estimates 

here represent credible consensus uncertainties. U(MPVR) estimates calculated from formula [19] of 

Vangel-Rukhin [22], representing confidence intervals about the consensus mean, would in fact - 

experience suggests - agree rather closely with the BOB estimates. However, here we have elected to 

combine pooled-across-group within-variance in quadrature with the MPVR estimate of betweenvariance, and multiply by an expansion factor of 2, to get numbers that can be thought of as 

representing over-conservative confidence intervals, or less-than-conservative prediction intervals for 

the consensus means. Because of the discrepancies among the methods clearly visible in the various 

box plot figures in this publication, we elect to use these slightly inflated MPVR uncertainties as the 

certification numbers for the respective SRM's and listed in Table 6. 

29
Summary 

Phase compositional data from X-ray powder diffraction were compared and combined with that

obtained using optical microscopy for three NIST RM clinkers. Rietveld refinement of the XRD data 

facilitated calculation of suitable reference standards for quantitative analyses. The optical data were 

collected using a point-counting procedure following ASTM C 1356. 

Comparison of the phase composition data sets using box plots provides a means of displaying and 

evaluating the data distributions, including their locations, spreads, and extremes. The data sets 

generally show reasonable agreement in the estimates of the individual phase abundance. The data 

do not always agree as well in the estimates of aluminate and ferrite. This may be the result of the 

fine size of the interstitial material crystals and the resulting difficulty in their microscopic 

identification. The XRD data generally exhibit greater precision than that of the microscopy point 

counts. This may reflect the homogenization of the sample as a result of the fine grinding required for 

XRD analyses and the larger sampling volume (about twice) for powder diffraction compared to 

microscopy. In the case of the microscope values for RM 8488, the coarser texture of the clinker may 

allow for easier phase identification. 

Certification of a Reference Material is often based upon more than one measurement method. X-ray 

powder diffraction and microscopy analyses are the intended use of these clinkers and so were used 

for determining the phase abundance. To establish best consensus values and meaningful 

uncertainties, three methods of combining these data sets were applied. The mean values of 

individual phase abundance do not vary from method to method, but the 95 % uncertainty interval 

values do, depending upon the method. 

In selecting a single method to report consensus values, the maximum likelihood (MPVR method) 

would be favored. The MPVR method produces a weighted mean with a weighting scheme that does 

not necessarily skew the consensus value in the direction of the large number of XRD values and 

generally produces the most conservative uncertainty interval. The MPVR method also takes 

explicitly into account between- as well as within-method variance. The RM clinker certificate 

values and uncertainties, based upon the MPVR method, are provided in Table 6. 

30
Table 6. Combined QXRD / Optical Analyses Mean and 95 % Uncertainty Interval.

RM 8486 ALITE BELITE FERRITE ALUMINATE PERICLASE 

Naive Method 

2-σ

58.6 

2.6 

23.3 

1.7 

14.1* 

1.0 

2.3 

1.7 

3.3 

1.2 

Levenson et al. 

2-σ BOB

58.6 

2.8 

23.3 

2.2 

14.1 

1.1 

2.3 

1.5 

3.3 

1.4 

MPVR 

2-σ MLE 

58.6 

4.0 

23.3 

2.8 

14.1* 

1.4 

2.3 

2.1 

3.3 

1.9 

* ferrite mean and 2-σ values are based upon 2-source (XRD, OM-1) data alone.

RM 8487 ALITE BELITE FERRITE ALUMINATE PERICLASE ARCANITE 

Naive 

Method 

2-σ

73.5 

2.5 

9.1 

1.8 

2.2 

2.0 

12.1 

3.1 

0.4 

1.2 

1.1 

1.2 

Levenson et 

al. 

2-σ BOB

73.5 

3.2 

9.1 

2.2 

2.2 

2.1 

12.1 

4.0 

0.3 

0.5 

1.1 

0.6 

MPVR 

2-σ MLE 

73.6 

3.8 

9.1 

2.8 

2.2 

3.1 

12.1 

4.9 

0.4 

0.9 

1.0 

1.0 

RM 8488 ALITE BELITE FERRITE ALUMINATE 

Naive Method 

2-σ

66.1 

2.1 

17.9 

2.3 

11.0 

3.2 

5.2 

1.9 

Levenson et al. 

2-σ BOB

66.1 

2.4 

17.9 

2.9 

11.0 

3.8 

5.2 

2.3 

MPVR 

2-σ MLE 

66.1 

3.4 

17.9 

3.7 

11.1 

5.1 

5.0 

2.9 

31
Acknowledgements 

The authors gratefully acknowledge the comments and suggestions of the reviewers, Chiara Ferraris, 

Edward Garboczi, and Leslie Struble. This work was supported by the Partnership on High 

Performance Concrete Technology and the Standard Reference Materials Program at the National 

Institute of Standards and Technology. 

References 

1. Kanare, H.M., "Production of Portland Cement Clinker Phase Abundance Standard Reference 

Materials SRMs 2686, 2687, 2688," Final Report, Construction Technology Laboratories, Skokie, IL 

1987. Also see individual clinker RM certificates. 

2. ASTM C 1356M - 96 Standard Test Method for Quantitative Determination of Phases in Portland 

Cement Clinker by Microscopical Point-Count Procedure. In Annual Book of ASTM Standards Vol. 

4.01 American Society for Testing and Materials, West Conshohocken, PA 1999. 

3. D.H. Campbell, Microscopical Examination and Interpretation of Portland Cement and Clinker, 

2nd ed., The Portland Cement Association Research and Development Serial No. 1754, 1999, 202 pp. 

4. ASTM C 1365 - 98 Standard Test Method for Determination of the Proportion of Phases in 

Portland Cement and Portland Cement Clinker Using X-Ray Powder Diffraction Analysis. In Annual 

Book of ASTM standards Vol. 4.01 American Society for Testing and Materials, West 

Conshohocken, PA 1999. 

5 R.A. Young, ed., The Rietveld Method, International Union of Crystallography Monographs on 

Crystallography 5, Oxford University Press.

6. A.C. Larson and R.B. VonDreele, "GSAS General Structure Analysis System," Operational 

Manual, Los Alamos National Laboratory LAUR 86-748, 2000. 

7. F. Nishi, Y. Tak uchi and I. Maki, "Tricalcium silicate Ca3O[SiO4]: The Monoclinic 

Superstructure," Zeitschrift fÔr Kristallographie 172, 297-314 (1985). 

8. P. Mondal and J.W. Jeffery, "The Crystal Structure of Tricalcium Aluminate, Ca3Al2O6," Acta 

Cryst., (1975). B31 689. 

9. K.H. Jost, B. Ziemer, and R. Seydel, "Redetermination of the Structure of -Dicalcium Silicate, 

Acta Cryst. (1977) B33, 1696-1700. 

10. A.A. Colville and S. Geller, "The Crystal Structure of Brownmillerite, Ca2FeAlO5," Acta Cryst. 

(1971) B27, 2311. 

11. Y. Tak uchi, F. Nishi, and I. Maki, "Crystal-Chemical Characterization of the 3 CaO  Al2O3-

Na2O Solid Solution Series," Zeitschrift fÔr Kristallographie 152, 259-307 (1980). 

12. W.A. Klemm and J. Skalny, "Selective Dissolution of Clinker Minerals and Its Applications, 

Martin Marietta Technical Report 77-32, 1977, 26 pp. 

32
13. J.C. Taylor and C.E. Matulis, "Absorption Contrast Effects in the Quantitative XRD Analysis of 

Powders by Full Multi-phase Profile Refinement," J. Appl. Cryst. 1991, 24, 14-17. 

14. H.F.W. Taylor, Cement Chemistry, 2nd edition, Thomas Telford, London, 1997, 459 pp. 

15. A. Heckert and J. J. Filliben, Dataplot Reference Manual , 

http://www.itl.nist.gov/div898/software/dataplot/ 

16. Neter, J. Kutner, M.H. Nachtsheim, C.J., Wasserman, W., APPLIED LINEAR STATISTICAL 

MODELS 4th edtn., Irwin/McGraw-Hill Chicago 1996. 

17. Taylor, B.N. and Kuyatt, Chris E. "Guidelines for Evaluating and Expressing 

the Uncertainty of NIST Measurement Results," NIST Technical Note 1297 USDOC 1994. 

18. M.S. Levenson D.L. Banks K.R. Eberhardt, L.M. Gill, W.F. Guthrie, H.K. Liu, 

M.G. Vangel, J.H. Yen, and N.F. Zhang, ``An Approach to Combining Results 

from Multiple Methods Motivated by ISO GUM,'' NIST JOUR RESEARCH vol. 105 #4, JulyAugust 2000, pp. 571-579. 

19. Guide to the Expression of Uncertainty in Measurement ISO Switzerland 1st ed. 1993. 

20. S.B. Schiller and K.R. Eberhardt, "Combining data from independent chemical analysis methods'' 

Spectrochimica Acta vol. 46B, no. 12, 1991 pp. 1607-1613. 

21. Mandel, J., EVALUATION AND CONTROL OF MEASUREMENTS

Marcel Dekker, New York, 1991 sections 4.4-4.5 

 

22. Rukhin, A.L. Vangel, M.G., ``Estimation of a Common Mean and Weighted 

Means Statistics, ''JOURNAL OF THE AMERICAN STATISTICAL ASSOCN. 

March 1998 Vol. 93 no. 441 pp. 303-308.

33
Appendix A. Structure Models for Clinker Phases 

Phase: Alite Formula: Ca3SiO5 ICDD: 42-551 

Reference: F. Nishi, Y. Tak uchi and I. Maki, "Tricalcium silicate Ca3O[SiO4]: 

The monoclinic superstructure," Zeitschrift für Kristallographie 172, 297-314 (1985) 

Z: 36 Space Group: Cm Density: 2.935 g cm-3

Cell Parameters (Å)

a b c β Vol. (Å3

)

33.3594 7.0800 18.6823 94.231 4299 

Atomic Parameters 

Atom x y z name Uiso 

Ca 0.0050 0.0000 0.0073 CA01 0.023 

Ca 0.6673 0.0000 0.1746 CA02 0.023 

Ca 0.3216 0.0000 0.3318 CA03 0.023 

Ca -0.0056 0.0000 0.5008 CA04 0.023 

Ca 0.6636 0.0000 0.6705 CA05 0.023 

Ca 0.3365 0.0000 0.8283 CA06 0.023 

Ca 0.5942 0.0000 -0.0651 CA07 0.023 

Ca 0.2590 0.0000 0.0908 CA08 0.023 

Ca -0.0805 0.0000 0.2656 CA09 0.023 

Ca 0.5865 0.0000 0.4380 CA10 0.023 

Ca 0.2568 0.0000 0.5982 CA11 0.023 

Ca -0.0742 0.0000 0.7693 CA12 0.023 

Ca 0.7385 0.0000 -0.0997 CA13 0.023 

Ca 0.3991 0.0000 0.0749 CA14 0.023 

Ca 0.0640 0.0000 0.2465 CA15 0.023 

Ca 0.7279 0.0000 0.4026 CA16 0.023 

Ca 0.3994 0.0000 0.5693 CA17 0.023 

Ca 0.0670 0.0000 0.7420 CA18 0.023 

Ca -0.0819 0.2833 -0.0858 CA19 0.023 

Ca 0.5825 0.2538 0.0949 Ca20 0.023 

Ca 0.2435 0.2503 0.2485 Ca21 0.023 

Ca -0.0913 0.2558 0.4202 Ca22 0.023 

Ca 0.5764 0.2562 0.5897 Ca23 0.023 

Ca 0.2452 0.2419 0.7499 Ca24 0.023 

Ca 0.0052 0.2341 -0.1545 Ca25 0.023 

Ca 0.6737 0.2312 0.0109 Ca26 0.023 

Ca 0.3360 0.2321 0.1792 Ca27 0.023 

Ca -0.0014 0.2410 0.3453 Ca28 0.023 

Ca 0.6659 0.2290 0.5122 Ca29 0.023 

Ca 0.3355 0.2379 0.6788 Ca30 0.023 

Ca 0.8300 0.2735 -0.0109 Ca31 0.023 

Ca 0.4873 0.2512 0.1583 Ca32 0.023 

Ca 0.1515 0.2702 0.3312 Ca33 0.023 

Ca 0.8196 0.2641 0.4896 Ca34 0.023 

Ca 0.4917 0.2808 0.6577 Ca35 0.023 

34
Ca 0.1606 0.2712 0.8240 Ca36 0.023 

Si 0.0833 0.0000 0.4288 Si1 0.007 

Si 0.2384 0.0000 -0.0838 Si2 0.007 

Si 0.4292 0.0000 0.7460 Si3 0.007 

Si 0.5699 0.0000 0.7506 Si4 0.007 

Si -0.0943 0.0000 0.0741 Si5 0.007 

Si -0.1015 0.0000 0.5918 Si6 0.007 

Si 0.0966 0.0000 -0.0851 Si7 0.007 

Si 0.1637 0.0000 0.1591 Si8 0.007 

Si 0.1628 0.0000 0.6629 Si9 0.007 

Si 0.2340 0.0000 0.4118 Si10 0.007 

Si 0.4214 0.0000 0.2509 Si11 0.007 

Si 0.5008 0.0000 0.0039 Si12 0.007 

Si 0.4975 0.0000 0.5004 Si13 0.007 

Si 0.5682 0.0000 0.2442 Si14 0.007 

Si 0.7600 0.0000 0.0882 Si15 0.007 

Si 0.7563 0.0000 0.5803 Si16 0.007 

Si -0.1748 0.0000 0.3338 Si17 0.007 

Si -0.1693 0.0000 -0.1575 Si18 0.007 

O 0.9900 0.0000 0.2450 O1a 0.022 

O 0.9880 0.0000 0.2450 O1b 0.022 

O 0.0380 0.0000 0.1190 O2a 0.022 

O 0.0520 0.0000 0.1240 O2b 0.022 

O 0.0300 0.0000 0.5990 O3a 0.022 

O 0.0380 0.0000 0.6100 O3b 0.022 

O -0.0040 0.0000 0.7530 O4a 0.022 

O -0.0050 0.0000 0.7540 O4b 0.022 

O 0.3720 0.0000 -0.0770 O5a 0.022 

O 0.3730 0.0000 -0.0470 O5b 0.022 

O 0.3290 0.0000 0.0750 O6a 0.022 

O 0.3310 0.0000 0.0770 O6b 0.022 

O 0.2890 0.0000 0.2110 O7a 0.022 

O 0.2890 0.0000 0.2230 O7b 0.022 

O 0.3620 0.0000 0.4410 O8a 0.022 

O 0.3620 0.0000 0.4420 O8b 0.022 

O 0.3250 0.0000 0.5830 O9a 0.022 

O 0.3340 0.0000 0.5950 O9b 0.022 

O 0.2820 0.0000 0.7240 O10a 0.022 

O 0.2930 0.0000 0.7320 O10b 0.022 

O 0.6660 0.0000 -0.0930 O11a 0.022 

O 0.6750 0.0000 -0.0810 O11b 0.022 

O 0.6270 0.0000 0.0490 O12a 0.022 

O 0.6340 0.0000 0.0670 O12b 0.022 

O 0.7060 0.0000 0.2850 O13a 0.022 

O 0.7040 0.0000 0.2900 O13b 0.022 

O 0.6480 0.0000 0.4210 O14a 0.022 

O 0.6550 0.0000 0.4140 O14b 0.022 

O 0.6080 0.0000 0.5640 O15a 0.022 

O 0.6220 0.0000 0.5670 O15b 0.022 

O 0.7050 0.0000 0.7630 O16a 0.022 

35
O 0.7090 0.0000 0.7710 O16b 0.022 

O 0.9490 0.0000 0.3760 O17a 0.022 

O 0.9570 0.0000 0.4010 O17b 0.022 

O 0.9600 0.0000 0.8970 O18a 0.022 

O 0.9650 0.0000 0.9070 O18b 0.022 

O 0.1110 0.0000 0.3570 D11 0.018 

O 0.0350 0.0000 0.4080 D12 0.018 

O 0.0960 0.1870 0.4740 D13 0.018 

O 0.2150 0.0000 -0.0110 U24 0.018 

O 0.2860 0.0000 -0.0630 U25 0.018 

O 0.2260 0.1840 -0.1330 U26 0.018 

O 0.4500 0.0000 0.6680 D31 0.018 

O 0.3790 0.0000 0.7300 D32 0.018 

O 0.4430 0.1830 0.7910 D33 0.018 

O 0.5490 0.0000 0.8300 U44 0.018 

O 0.6160 0.0000 0.7670 U45 0.018 

O 0.5550 0.1880 0.7040 U46 0.018 

O -0.1180 0.0000 0.1490 U54 0.018 

O -0.0440 0.0000 0.0930 U55 0.018 

O -0.1070 0.1870 0.0270 U56 0.018 

O -0.1230 0.0000 0.6690 U64 0.018 

O -0.0540 0.0000 0.6080 U65 0.018 

O -0.1170 0.1860 0.5420 U66 0.018 

O 0.1190 0.0000 -0.1610 D71 0.018 

O 0.0480 0.0000 -0.1030 D72 0.018 

O 0.1100 0.1890 -0.0380 D73 0.018 

O 0.0740 0.0000 -0.0090 U74 0.018 

O 0.0550 0.0000 -0.1380 U75 0.018 

O 0.1250 0.1890 -0.0730 U76 0.018 

O 0.1410 0.0500 0.0800 G81 0.018 

O 0.1340 -0.1230 0.2080 G82 0.018 

O 0.2050 -0.1230 0.1510 G83 0.018 

O 0.1760 0.1970 0.2020 G84 0.018 

O 0.1850 0.0000 0.5870 D91 0.018 

O 0.1140 0.0000 0.6450 D92 0.018 

O 0.1760 0.1890 0.7100 D93 0.018 

O 0.1400 0.0000 0.7390 U94 0.018 

O 0.2120 0.0000 0.6810 U95 0.018 

O 0.1410 0.1890 0.6270 U96 0.018 

O 0.1400 0.0500 0.5840 G91 0.018 

O 0.1330 -0.1230 0.7120 G92 0.018 

O 0.2040 -0.1230 0.6550 G93 0.018 

O 0.1750 0.1970 0.7060 G94 0.018 

O 0.2550 0.0000 0.3350 D101 0.018 

O 0.2680 0.0000 0.4800 D102 0.018 

O 0.2060 0.1890 0.4150 D103 0.018 

O 0.2120 0.0000 0.4870 D104 0.018 

O 0.2830 0.0000 0.4300 D105 0.018 

O 0.2210 0.1890 0.3650 D106 0.018 

O 0.4440 0.0000 0.1750 D111 0.018 

36
O 0.3720 0.0000 0.2330 D112 0.018 

O 0.4350 0.1891 0.2980 D113 0.018 

O 0.3990 0.0000 0.3270 U114 0.018 

O 0.3820 0.0000 0.1930 U115 0.018 

O 0.4500 0.1890 0.2570 U116 0.018 

O 0.4780 0.0000 0.0080 U124 0.018 

O 0.5500 0.0000 0.2200 U125 0.018 

O 0.4870 0.1890 -0.0430 U126 0.018 

O 0.4780 0.0500 -0.0750 G121 0.018 

O 0.4660 -0.1230 0.0400 G122 0.018 

O 0.5420 -0.1230 -0.0040 G123 0.018 

O 0.5130 0.1970 0.0470 G124 0.018 

O 0.5200 0.0000 0.4250 D131 0.018 

O 0.4480 0.0000 0.4830 D132 0.018 

O 0.5110 0.1890 0.5470 D133 0.018 

O 0.5200 0.0500 0.5800 G131 0.018 

O 0.5260 -0.1280 0.4510 G132 0.018 

O 0.4560 0.1230 0.5080 G133 0.018 

O 0.4810 0.1970 0.4630 G134 0.018 

O 0.5910 0.0000 0.1690 D141 0.018 

O 0.6020 0.0000 0.3120 D142 0.018 

O 0.5400 0.1890 0.2480 D143 0.018 

O 0.5460 0.0000 0.3200 U144 0.018 

O 0.6170 0.0000 0.2620 U145 0.018 

O 0.5550 0.1890 0.1970 U146 0.018 

O 0.7820 0.0000 0.0130 D151 0.018 

O 0.7110 0.0000 0.0700 D152 0.018 

O 0.7730 0.1890 0.1350 D153 0.018 

O 0.7380 0.0000 0.1640 U154 0.018 

O 0.7260 0.0000 0.0200 U155 0.018 

O 0.7880 0.1890 0.0850 U156 0.018 

O 0.7880 0.0000 0.5050 D161 0.018 

O 0.7070 0.0000 0.5650 D162 0.018 

O 0.7690 0.1910 0.6260 D163 0.018 

O 0.7340 0.0000 0.6560 U164 0.018 

O 0.7170 0.0000 0.5220 U165 0.018 

O 0.7870 0.1800 0.5940 U166 0.018 

O -0.1970 0.0000 0.4090 U174 0.018 

O -0.1260 0.0000 0.3520 U175 0.018 

O -0.1880 0.1890 0.2870 U176 0.018 

O -0.1970 0.0500 0.2550 G171 0.018 

O -0.2040 -0.1230 0.3830 G172 0.018 

O -0.1340 -0.1230 0.3260 G173 0.018 

O -0.1630 0.1970 0.3770 G174 0.018 

O -0.1520 0.0500 0.4130 G175 0.018 

O -0.1450 -0.1230 0.2850 G176 0.018 

O -0.2160 -0.1230 0.3420 G177 0.018 

O -0.1870 0.1970 0.2910 G178 0.018 

O -0.1920 0.0000 -0.0820 U184 0.018 

O -0.1200 0.0000 -0.1400 U185 0.018 

37
O -0.1830 0.1890 -0.2040 U186 0.018 

O -0.1920 0.0500 -0.2370 G181 0.018 

O -0.1990 -0.1230 -0.1080 G182 0.018 

O -0.1280 -0.1230 -0.1650 G183 0.018 

O -0.1580 0.2100 -0.1250 G184 0.018 

38
Phase: β-Dicalcium Silicate Formula: Ca2SiO4 ICDD: 33-302 

 (larnite) 

Reference: K.H. Jost, B. Ziemer and R. Seydel "Redetermination of 

the Structure of β-Dicalcium Silicate," Acta Cryst. (1977). B33, 

1696-1700 

Z: 4 Space Group:P21/n Density: 3.326 g cm-3

Cell Parameters (Å) 

a b c β Vol. (Å3

)

5.502 6.745 9.297 94.59° 343.9 

Atomic Parameters 

 

 x y z Uiso 

Ca(1) 0.2738 0.3428 0.5694 0.004813 

Ca(2) 0.2798 0.9976 0.2981 0.003800 

Si 0.2324 0.7841 0.5817 0.002406 

O(1) 0.2864 0.0135 0.5599 0.011525 

O(2) 0.0202 0.7492 0.6919 0.008486 

O(3) 0.4859 0.6682 0.6381 0.007979 

O(4) 0.1558 0.6710 0.4264 0.007852 

39
Phase: Brownmillerite (C4AF) Formula: Ca2FeAlO5 ICDD: 30-226 

Reference: A.A. Colville and S. Geller, "The Crystal Structure of 

Brownmillerite, Ca2FeAlO5," Acta Cryst. (1971) B27, 2311 

Space Group:Ibm2 Z: 4 Density: 3.683 g cm-3

 

Cell Parameters (Å)

a b c Vol.(Å3

)

5.584 14.60 5.374 438.12 

Atomic Parameters 

x y z Occ. 

Ca 0.0273 0.1087 0.4920 1.00 

Fe 0.0 0.0 0.0 0.76 

Al 0.0 0.0 0.0 0.24 

Al 0.9283 0.2500 0.9533 0.76 

Fe 0.9283 0.2500 0.9533 0.24 

O 0.2523 0.9861 0.2491 1.00 

O 0.0680 0.1439 0.0246 1.00 

O 0.8607 0.2500 0.6193 1.00 

Vibrational Parameters

U11 U22 U33 U12 U13 U23

Ca 0.004500 0.000800 0.007900 0.001000 -0.000200 0.000000 

Fe 0.001500 0.011000 0.002900 0.000000 0.000000 0.000000 

Al 0.001500 0.011000 0.002900 0.000000 0.000000 0.000000 

Al 0.001200 0.000400 0.002500 0.000000 -0.000700 0.000000 

Fe 0.001200 0.000400 0.002500 0.000000 -0.000700 0.000000 

O 0.002700 0.001100 0.006900 -0.000500 -0.000200 -0.000600 

O 0.005500 0.001200 0.002200 0.000600 -0.001600 0.000200 

O 0.003600 0.000200 0.007400 0.000000 -0.000700 0.000000 

40
Phase: Tricalcium Aluminate Formula: Ca3Al2O6 ICDD: 38-1429 

Reference: P. Mondal and J.W. Jeffery, "The Crystal Structure of 

Tricalcium Aluminate, Ca3Al2O6", Acta Cryst. (1975). B31, 689. 

Space Group: Pa3 Z: 24 Density: 3.027 g cm-3 

Cell Parameters (Å) a 15.263 Vol (Å3

): 3556 

Atomic Parameters 

 x y z 

Ca(1) 0.0000 0.0000 0.0000 

Ca(2) 0.5000 0.0000 0.0000 

Ca(3) 0.2561 0.2561 0.2561 

Ca(4) 0.3750 0.3750 0.3750 

Ca(5) 0.1386 0.3763 0.1272 

Al(1) 0.2526 0.0133 0.0197 

Al(2) 0.2444 0.2335 0.0046 

O(1) 0.2777 0.1241 0.0103 

O(2) 0.4835 0.1315 0.2536 

O(3) 0.2664 0.2841 0.1049 

O(4) 0.2350 0.4047 0.2921 

O(5) 0.3491 -0.0385 -0.0174 

O(6) 0.1500 -0.0104 -0.0242

Vibrational Parameters

 U11 U22 U33 U32 U31 U21

Ca(1) 0.0060 0.0060 0.0060 0.0280 0.0280 0.0280 

Ca(2) 0.0084 0.0084 0.0084 0.0001 -0.0001 0.0001 

Ca(3) 0.0079 0.0079 0.0079 0.0013 0.0013 0.0013 

Ca(4) 0.0117 0.0117 0.0117 0.0027 0.0027 0.0027 

Ca(5) 0.0079 0.0090 0.0223 -0.0010 0.0051 0.0026 

Ca(6) 0.0060 0.0092 0.0096 -0.0011 0.0023 0.0011 

Al(1) 0.0056 0.0058 0.0080 -0.0022 -0.0003 -0.0011 

Al(2) 0.0078 0.0059 0.0065 -0.0011 0.0015 0.0009 

O(1) 0.0170 0.0097 0.0176 -0.0002 -0.0025 -0.0390 

O(2) 0.1380 0.0086 0.0188 -0.0039 0.0014 -0.0013 

O(3) 0.0083 0.0159 0.0147 0.0044 -0.0062 -0.0081 

O(4) 0.0142 0.0094 0.0191 -0.0011 0.0770 0.0054 

O(5) 0.0090 0.0159 0.0147 0.0044 -0.0062 -0.0081 

O(6) 0.0066 0.0154 0.0142 0.0062 0.0047 0.0010 

41
Phase: Tricalcium Aluminate, Orthorhombic Formula: Na2xCa3-xAl2O6 ICDD: 32-150 

Reference: Yoshio Takéuchi and Fumito Nishi, “Crystal-chemical characterization of the 3 CaO · 

Al2O3-Na2O solid-solution series,” Zeitschrift für Kristollographie 152, 259-307 (1980), pp. 259-307 

Space Group: Pbca, Z: 4 Density: 2.555 g cm-3

Cell Parameters (Å)

a b c Vol. (Å3)

 10.879 10.845 15.106 3564.5 x 0.5 

Atomic Parameters 

 x y z Uiso Occupancy 

Ca1 0.00260 0.00230 0.51866 0.013425 1.0 

Ca2 -0.00300 0.01680 0.24027 0.010639 1.0 

Ca3 0.00873 0.26471 0.13216 0.010639 1.0 

Ca4 0.25522 0.27092 0.25253 0.141850 1.0 

Ca5 0.26315 0.24684 0.49821 0.013045 .696 Ca, .304 Na 

Na 0.00260 -0.01560 -0.00730 0.035716 1.0 

Al1 -0.00430 -0.21416 0.11621 0.006966 .888 Al, .061 Fe, .051 Si 

Al2 0.23742 -0.00420 0.11250 0.007219 .868 Al, .072 Fe, .060 Si 

Al3 0.24050 0.00420 -0.10879 0.007979 .831 Al, .092 Fe, .077 Si 

O1 -0.14470 -0.13520 0.11010 0.020391 1.0 

O2 0.11420 -0.10520 0.13130 0.022924 1.0 

O3 0.28570 -0.02580 0.00170 0.015578 1.0 

O4 -0.01250 -0.28660 0.21780 0.023177 1.0 

O5 0.02150 -0.29420 0.01800 0.017985 1.0 

O6 0.35710 -0.07150 0.17160 0.016845 1.0 

O7 0.19040 0.14770 0.13140 0.017605 1.0 

O8 0.16380 -0.12810 -0.14440 0.015198 1.0 

O9 0.37220 0.06720 -0.15800 0.016085 1.0 

42
Phase: Arcanite Formula: K2SO4 ICDD: 5-613 

Reference: R.T. Robinson, "The Crystal Structure of β-K2SO4 and of 

β-K2PO3F," J. Phys. Chem., Vol. 62, August, 1958, pp. 925-928. 

Space Group: Pnam Z=4 Density: 2.666 g cm-3

Cell Parameters (Å)

a b c Vol.(Å3)

6.456 10.080 5.776 434.104 

Atomic Parameters 

 x y z Occupancy Uiso 

K 0.176800 0.081800 0.250000 1.00 K1 0.017731 

K -0.011500 0.704600 0.250000 1.00 K2 0.017731 

S 0.235800 0.415500 0.250000 1.00 S3 0.017731 

O 0.031500 0.403200 0.250000 1.00 O4 0.017731 

O 0.297000 0.557900 0.250000 1.00 O5 0.017731 

O 0.299700 0.348400 0.041000 1.00 O6 0.017731

Phase: Periclase Formula: MgO ICDD: 4-829 

Reference: R.W. G. Wyckoff, Crystal Structures, 2nd ed., Interscience Publishers, New York, 1963 

Space Group: Fm-3m Z=1 Density: 3.582 g cm-3

Cell Parameters (Å) Vol.(Å3

) 

a 4.2117 74.7 

Atomic Parameters 

x y z Occupancy Uiso 

MG 0.000000 0.000000 0.000000 1.00 MG1 0.016229 

O 0.500000 0.500000 0.500000 1.00 O2 -0.001858 

Phase: Lime Formula: CaO ICDD: 37-1497 

Reference: R.W. G. Wyckoff, Crystal Structures, 2nd ed., Interscience Publishers, New York, 1963 

Space Group: Fm-3m Z=1 Density: 3.346 g cm-3

Cell Parameters (Å) Vol.(Å3

)

A 4.8109 111.319 

Atomic Parameters 

x y z Occupancy Uiso 

Ca 0.000000 0.000000 0.000000 1.00 Ca1 0.013803 

O 0.500000 0.500000 0.500000 1.00 O2 -0.000121 

43
44

Appendix B: Selective Extractions for Clinker and Cement 

Salicylic Acid/Methanol Extraction (SAM) 

The SAM extraction dissolves alite, belite, and free lime leaving a residue of interstitial phases 

aluminate and ferrite as well as periclase, alkali sulfates, and for cements, calcium sulfates. 

Concentration aids qualitative and quantitative analysis by reducing diffraction peak overlaps from 

the silicates and increases the diffraction intensities of the phases in the residue. Performing this 

extraction on a cement that has not been heat-treated preserves the calcium sulfate addition forms 

(gypsum, bassanite, and anhydrite). 

The SAM solution consists of 20 g of salicylic acid in 300 ml of methanol. Stir about 5 g of 

powdered clinker or cement in a stoppered flask containing 300 ml of SAM solution for about 2 h. 

Allow the suspension to settle for about 15 min then vacuum filter using a 0.45 μm filter and Buchner 

funnel. Wash the residue with methanol, dry at 100 °C, and store in a vacuum desiccator. Measuring 

the mass loss allows the QXRD values to be re-calculated on a whole-sample basis and provides an 

additional estimate for total silicate content. 

 

Potassium Hydroxide/Sugar Extraction (KOH/Sugar) 

The KOH/sugar extraction dissolves the interstitial phases of aluminate and ferrite leaving a residue 

of silicates and minor phases. First, prepare an extraction solution with 7.5 g of KOH and 7.5 g of 

sucrose in 75 ml of distilled water. Stir 2.25 g of powdered clinker or cement (heat-treated cement) 

into a 95 °C KOH/sugar solution for 1 min. Filter the solution using a 0.45 μm filter and Buchner 

funnel, wash residue with 12 ml of water followed by 25 ml of methanol, dry residue at 100 °C, and 

store in a vacuum desiccator. 

This extraction has the propensity to be difficult to filter. Maintaining the suspension at 95 °C while 

filtering may reduce this problem as does the use of a larger diameter filter paper. In more difficult 

cases, extraction of cement that has not been ground beyond that from the manufacturer may allow 

for a successful extraction. The mass loss is not measured for this extraction as the SAM extraction 

data are generally sufficient. 

Nitric Acid/Methanol Extraction 

This extraction dissolves the silicates and aluminates leaving a residue of ferrite and (if present) 

periclase. The extraction solution is 7 % nitric acid in methanol. Ten grams of ground clinker or 

cement are stirred in to 500 ml of the nitric acid/methanol solution for 30 min. The residue is then 

filtered, rinsed with pure methanol, dried, and stored in a vacuum desiccator. Mass loss is generally 

not measured for this extraction.