NIST Technical Note 1815 

PERFORMANCE CRITERIA FOR AN 

ASTM XRF STANDARD TEST METHOD 

FOR CHEMICAL ANALYSIS OF 

HYDRAULIC CEMENTS: 

INTER-LABORATORY STUDY CEMENTS 

E AND F 

Paul Stutzman 

Alan Heckert 
 

 

 

 

 

 

 

 

 

NIST Technical Note 1815 

PERFORMANCE CRITERIA FOR AN 

ASTM XRF STANDARD TEST METHOD 

FOR CHEMICAL ANALYSIS OF 

HYDRAULIC CEMENTS: 

INTER-LABORATORY STUDY CEMENTS 

E AND F 

Paul Stutzman 

Materials and Structural Systems Division 

Engineering Laboratory 

Alan Heckert 

Statistical Engineering Division 

Information Technology Laboratory 

October 2013 

U.S. Department of Commerce 

Penny Pritzker, Secretary 

National Institute of Standards and Technology 

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and 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 Technical Note 1815 

Natl. Inst. Stand. Technol. Tech. Note 1815, 154 pages, October 2013 

CODEN: NTNOEF 
 

 

 

Abstract

Bulk oxide determinations from a pair of portland cements are used to calculate precision and 

accuracy values for X-ray fluorescence (XRF) analysis of both the fused glass bead and the 

pressed powder sample preparation methods. This report is the second in a series on an 

Interlaboratory study on chemical analyses of hydraulic cements by X-ray fluorescence for the 

purpose of estimating precision and qualification criteria. Approximately 24 laboratories 

provided six replicates analyzed in duplicate for two separate portland cements containing ca. 

5 % limestone, covering fifteen analytes, CaO, SiO2, Al2O3, Fe2O3, SO3, MgO, Na2O, K2O, 

TiO2, P2O5, Mn2O3, SrO, ZnO, Cr2O3, and Cl, with the laboratories roughly split between the two 

different sample preparations. Chemical data using traditional chemical analyses (the Reference 

Methods) from the Cement and Concrete Reference Laboratory (CCRL) proficiency test 

program were included for comparison to the XRF results. Precision measures for within- and 

between-laboratory performance are presented as 1σ and 95 % limits (ASTM d2s). Accuracy 

criteria are based upon a two-sided 95 % prediction interval for the mean of two test results, 

defining the range of values one might expect for each analyte relative to a certified value of a 

reference material. 

iii 
Table	of Contents

Abstract..................................................................................................................................................iii

Table of Contents ................................................................................................................................ iv

List of Tables......................................................................................................................................... vi

List of Figures ....................................................................................................................................... vi

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

Development of a Test Method for XRF Analysis of Hydraulic Cements ......................................3

Measurement Precision ................................................................................................................................6

Measurement Accuracy and Method Bias ...............................................................................................6

Outlier Identification .....................................................................................................................................7

The Prediction Interval.................................................................................................................................8

Results – Condensed	Summary...................................................................................................................9

Individual	Oxide Results............................................................................................................................ 13

Summary ......................................................................................................................................................... 13

Acknowledgements ...........................................................................................................................13

SiO2 .................................................................................................................................................................... 14

Al2O3 ................................................................................................................................................................. 20

Fe2O3 ................................................................................................................................................................. 26

CaO.....................................................................................................................................................................
 32

MgO ................................................................................................................................................................... 38

SO3 ..................................................................................................................................................................... 44

Na2O .................................................................................................................................................................. 50

K2O..................................................................................................................................................................... 56

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

P2O5 ................................................................................................................................................................... 68

TiO2 62

Mn2O3................................................................................................................................................................ 74

SrO..................................................................................................................................................................... 80

ZnO .................................................................................................................................................................... 86

Cr2O3..................................................................................................................................................................
 90

Cl ........................................................................................................................................................................ 93

Appendix A. Request for Participants	Letter. ..........................................................................96

Appendix B. XRF Glass	Summary by Material and Replicate.............................................99

Appendix C. XRF Powder Summary	by Material	and Replicate...................................... 101

Appendix D. Raw Data by Analyte. ............................................................................................ 103

SiO2................................................................................................................................................................................... 103

Al2O3 ................................................................................................................................................................................ 107

Fe2O3................................................................................................................................................................................ 110

CaO................................................................................................................................................................................... 113

MgO.................................................................................................................................................................................. 116

SO3 .................................................................................................................................................................................... 119

Na2O.................................................................................................................................................................................
 122

K2O ................................................................................................................................................................................... 125

TiO2 .................................................................................................................................................................................. 128

P2O5.................................................................................................................................................................................. 131

iv 
Cl ....................................................................................................................................................................................... 134

Mn2O3 .............................................................................................................................................................................. 136

ZnO................................................................................................................................................................................... 138

SrO....................................................................................................................................................................................
 141

Cr2O3................................................................................................................................................................................ 143

Acknowledgements ........................................................................................................................ 145

References......................................................................................................................................... 145

v 
 

 

 

 

 

 

 

 

 

 

 

List of Tables

Table 1 ASTM C114 performance criteria for the chemical analysis of portland cements from the 

Report of Working Committee on Methods of Chemical Analysis, June 12, 1946 []............ 2

Table 2 Pooled Results for XRF-Glass, XRF-Powder and Combined Powder and Glass Methods 

with ZnO and Cr2O3 results from combined glass and powder methods. ............................ 11

Table 3 95 % Prediction Interval designed to bracket values of a mean of k = 2, 3, 4 

measurements. The mean of n replicate determinations should differ from the known value 

of the certified reference material (±) by no more than the value shown. ............................ 12

List of Figures

Figure 1 Reference and instrumental methods popularity from CCRL proficiency test data shows 

that over 80 % of the labs use X-ray methods for bulk chemical analysis by either energyor wavelength-dispersive analysis, using either powder or glass specimens.......................... 2

Figure 2 Calculated values for the determination of within and between lab precision. ................ 5

Figure 3 Scatter plot for CaO with XRF-glass as blue circles, XRF-powder as red squares, 

Reference methods as a +, and x striking out excluded data due to exceeding the h or k 

statistics................................................................................................................................... 8

Figure 4 Lab means and standard deviations for cements E (Material 1) and F (material 2)......... 9

Figure 5 h and k statistic plots illustrate the within- (k) and between-laboratory (h) precision and 

are useful in identifying unusual results that may be considered outlying. The dashed lines 

mark the limits for each statistic. .......................................................................................... 10

Figure 6 Box plots for SiO2 for XRF glass and powder, and reference methods. ........................ 14

Figure 7 SiO2 precision statistics by method with bar chart comparing results to current and past 

ASTM C114 limits and previous studies on chemical analysis precision as 1σ, between lab 

(SR). ....................................................................................................................................... 19

Figure 8 Box plots for Al2O3 for XRF glass and powder, and reference methods. ...................... 20

Figure 9 Al2O3 precision statistics by method with bar chart comparing results to current and past 

ASTM C114 limits and previous studies on chemical analysis precision as 1σ, between lab 

(SR). ....................................................................................................................................... 25

Figure 10 Box plots for Fe2O3 for XRF glass and powder, and reference methods. .................... 26

Figure 11 Fe2O3 precision statistics by method with bar chart comparing results to current and 

past ASTM C114 limits and previous studies on chemical analysis precision as 1σ, between 

lab (SR). ................................................................................................................................. 31

Figure 12 Box plots for CaO for XRF glass and powder, and reference methods. ...................... 32

Figure 13 CaO precision statistics by method with bar chart comparing results to current and past 

ASTM C114 limits and previous studies on chemical analysis precision as 1σ, between lab 

(SR). ....................................................................................................................................... 37

Figure 14 Box plots for MgO for XRF glass and powder, and reference methods. ..................... 38

Figure 15 MgO precision statistics by method with bar chart comparing results to current and 

past ASTM C114 limits and previous studies on chemical analysis precision as 1σ, between 

lab (SR). ................................................................................................................................. 43

Figure 16 Box plots for SO3 for XRF glass and powder, and reference methods. ....................... 44

Figure 17 SO3 precision statistics by method with bar chart comparing results to current and 

past ASTM C114 limits and previous studies on chemical analysis precision as 1σ, between 

lab (SR). ................................................................................................................................. 49

vi 
 

 

 

 

 

Figure 18 Box plots for Na2O for XRF glass and powder, and reference methods...................... 50

Figure 19 Na2O precision statistics by method with bar chart comparing results to current and 

past ASTM C114 limits and previous studies on chemical analysis precision as 1σ, between 

lab (SR). ................................................................................................................................. 55

Figure 20 Box plots for K2O for XRF glass and powder, and reference methods. ...................... 56

Figure 21 K2O precision statistics by method with bar chart comparing results to current and 

past ASTM C114 limits and previous studies on chemical analysis precision as 1σ, between 

lab (SR). ................................................................................................................................. 61

Figure 22 Box plots for TiO2 for XRF glass and powder, and reference methods. ...................... 62

Figure 23 TiO2 precision statistics by method with bar chart comparing results to current and 

past ASTM C114 limits and previous studies on chemical analysis precision as 1σ, between 

lab (SR). ................................................................................................................................. 67

Figure 24 Box plots for P2O5 for XRF glass and powder, and reference methods. ...................... 68

Figure 25 P2O5 precision statistics by method with bar chart comparing results to current and 

past ASTM C114 limits and previous studies on chemical analysis precision as 1σ, between 

lab (SR). ................................................................................................................................. 73

Figure 26 Box plots for Mn2O3 for XRF glass and powder, and reference methods. .................. 74

Figure 27 Box plots for SrO for XRF glass and powder methods. ............................................... 80

Figure 28 Box plots for ZnO for XRF glass and powder methods. .............................................. 86

Figure 29 Box plots for Cr2O3 for XRF glass, powder, and reference methods. .......................... 90

Figure 30 Box plots for Cl for XRF glass, powder, and reference methods................................. 93

vii 
 

 

 

Introduction

Chemical analysis of portland cement is used for process control in clinker and cement 

manufacture, for demonstration specification compliance, and for relating chemical properties to 

performance attributes. Reporting requirements for the chemical composition of portland 

cements in North America date back to the 1915 Joint Conference on Uniform Methods of Tests 

and Standard Specifications for Cement, which was written by the American Society of Civil 

Engineers, the American Society for Testing Materials (ASTM), and the United States 

Government, and included the following analytes: SiO2, Fe2O3, Al2O3, CaO, MgO, SO3, Ignition 

Loss, and Insoluble Residue [1]. 

In 1946, work on harmonizing the Federal and ASTM Cement Specifications resulted in the 

development of ASTM C150, Specification for Portland Cement within ASTM C1 on Cement. 

Standard Methods of Chemical Analysis of Portland Cement, ASTM C114-44 was also 

published and contained a performance-based qualification scheme [Table 1] that is very similar 

to that used today where duplicate determinations on different days are made and the two results 

must be within the limit of permissive variation with their average accepted as the correct value 

[2]. Reference cements were used to qualify each laboratory’s process, and the standard method 

required the laboratory to repeat the measurement process if the qualification criteria were not 

met. 

The 1960’s through the 1970’s saw a shift from classical analytical “wet” chemistry 

measurements (referred to as the ‘reference-wet’ and the ‘alternate-wet’ methods) to 

instrumental methods, including atomic absorption spectrometry, X-ray spectrometry, and a 

spectrophotometric/titrimetric scheme. Forrester et al. [3], Midgley [4], Harrison et al. [5], 

Aldridge et al. [6,7], Stutzman and Lane [8], European standard EN 196-2.2 [9], and a National 

Cooperative Highway Research Program report [10] have investigated uncertainty in chemical 

analyses of portland cements, with the latter three being based upon standardized methods. 

ASTM Subcommittee C01.23, Chemical Analysis, amended the precision requirements with 

accuracy requirements in 1977 by replacing the third column in Figure 1 with a maximum 

difference between the mean of two replicate determinations and the value of a certified 

reference material. This amended set of criteria is now Table 1 of ASTM C114 and is the basis 

of method qualification for instrumental methods such as, for example, those by X-ray 

fluorescence (XRF) [2]. While the column one requirements originated in the 1946 edition of 

ASTM C114 and are based upon the reference methods, none of the qualification requirements 

have supporting data available. The development of a standard test for XRF analysis of hydraulic 

cements provides an opportunity to collect the data and calculate appropriate qualification 

values. 

1 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 1 ASTM C114 performance criteria for the chemical analysis of portland cements from 

the Report of Working Committee on Methods of Chemical Analysis, June 12, 1946 [11]. 

Maximum Limits of Permissive Variation 

Component Between two results Between the extreme values in 

three results 

Silicon dioxide, SiO2 0.16 0.24 

Aluminum oxide, Al2O3 0.20 0.30 

Ferric oxide, Fe2O3 0.10 0.15 

Calcium oxide, CaO 0.20 0.30 

Magnesium oxide, MgO 0.16 0.24 

Sulfur trioxide, SO3 0.10 0.15 

Loss on ignition 0.10 0.15 

Sodium oxide, Na2O 0.03 0.05 

Potassium oxide, K2O 0.03 0.05 

Phosphorous pentoxide, P2O5 0.03 0.05 

Managanic oxide, Mn2O3 0.03 0.05 

Insoluble residue 0.10 0.15 

Chloroform - soluble organic substances 0.004 0.006 

Free calcium oxide 0.20 0.30 

water – soluble alkali 0.05 0.08 

Figure 1 Reference and instrumental methods popularity from CCRL proficiency test data shows 

that over 80 % of the labs use X-ray methods for bulk chemical analysis by either energy- or 

wavelength-dispersive analysis, using either powder or glass specimens. 

2 
 

 

Development of a Test Method for XRF Analysis of Hydraulic Cements

Over 80 % of the participants in the CCRL proficiency test program conduct XRF analysis using 

either a wavelength- or an energy-dispersive spectrometer [12]. The percentage of cement 

manufacturers that use XRF analysis is probably higher, and the remaining instrumental and 

traditional chemical methods of analysis are generally reserved as backup in case the principal 

XRF instrument is down for repair. In ASTM C114 terminology, the XRF method, atomic 

absorption and inductively coupled plasma spectrometry fall under rapid methods, whereas much 

longer times are required to perform the traditional wet, gravimetric, titrimetric, and colorimetric 

chemical techniques. Current practice for chemical analysis follows ASTM C114, which states 

that any method of analysis may be used as long as it can be demonstrated to conform to 

precision and bias performance criteria of Table 1 in ASTM C114 [2]. This means that the rapid 

methods require qualification where results of six of seven certified reference materials must fall 

within the qualification criteria of Table 1; the seventh measurement must fall with twice the 

precision criteria in Table 1. The qualification limits were originally published in 1946 and 

remain the same today. Bias criteria were originally based upon the maximum difference of three 

determinations, whereas today the criteria are a maximum limit on the difference of the mean of 

two determinations and an accepted reference value. The National Bureau of Standards 

(currently NIST) issued three portland cement reference materials (1011, 1015, and 1016) in 

January of 1962 with provisional values, which were finalized in 1964. Until this time, no 

comparison to “certified” values was possible. 

ASTM C01.23 initiated an inter-laboratory study for XRF Analysis to establish a data set for 

assessing precision of the method being developed. This method does not provide a set of 

instructions to prepare specimens and perform an analysis, but rather outlines a goal of analysis 

of major and minor elements by XRF with use of either of two specimen preparation procedures: 

pressed powder and fused glass. Guidelines as a draft standard are provided for both the pressed 

pellet and the fused glass preparations. 

For the inter-laboratory study, three pairs of cements were distributed to participants with 

approximately 24 laboratories participating. This report covers the second set of cements, 

referred to as Cements E and F, originating from the CCRL proficiency test program cements 

165 and 166, respectively. Mill sheet data report ca. 3 % limestone, with CCRL 165 limestone 

being 80 % CaCO3 and 166 being 97.4 % CaCO3. Each laboratory was asked to follow their own 

standard operating procedure (SOP), as long as it fell within the draft standard guidelines, and 

prepare and analyze three specimens (replicates) to be analyzed twice each (duplicates) on two 

different days for a total of six specimens and twelve analyses (Appendix A). Subsequent studies 

will contain ASTM C595 1s cements (samples C D), and ASTM C595 1p cements with fly ash 

(samples G H). Results and data from each sample set will be reported separately. 

Sample preparation for XRF can be achieved using either of two distinct methods: a pressed 

powder and a fused glass disk. Pressed powder specimens are typically ground in a tungsten 

carbide ring and puck mill with a binding agent to reduce the particle size and provide a packed 

powder mount that will remain intact for transport and analysis. The advantages of this 

preparation method include the simplicity and better detection limits, while disadvantages 

include the “mineralogical effect”, which requires a similar composition matrix between a 

bracketed calibration and unknown specimens for the calibrations to be valid. The potential for 

3 
 

 

 

 

bias due to the mineralogical effect will be greater for the second, third, and fourth cement pairs, 

which will contain slag additions at the 50 % level and limestone additions at a level of less than 

5 %, and fly ash, respectively. The fused disk preparation eliminates the potentially adverse 

effects of discrete mineral phases by dissolving the cement in a flux and fusing the mixture into a 

homogeneous glass disk. However, the fluxing process is subject to volatization of some analytes 

if the heating process is not carefully controlled. 

The data analysis follows ASTM E691 [13] “Standard Practice for Conducting an Interlaboratory 

Study to Determine the Precision of a Test Method,” and was performed using the Dataplot1 

software. Data were compiled by the CCRL staff into a database and exported to a spreadsheet 

format for subsequent processing and analysis. The terms used in ASTM E691 and the means of 

their calculation are presented in Figure 3, with the last six terms being used subsequently in the 

evaluation and presentation of the results. 

The layout of this report consists of some background for chemical analysis of cements, 

information on the interlaboratory study, methodology behind the precision calculations, a 

summary table for all reported elements, and individual analyte (as oxides) results in table and 

graphical form, along with comparisons to previous studies. The calculations provide precision 

estimates for consideration by the ASTM C01.23 Subcommittee on compositional analysis for 

use in developing a draft standard test method for XRF analysis of hydraulic cements. The draft 

method uses a qualification approach, similar to that used in ASTM C114, having criteria for 

precision as well as accuracy. Unfortunately, the process and data used to develop the ASTM 

C114 Table 1 criteria are no longer available, so while precision is calculated here, criteria for 

accuracy will require careful consideration by the subcommittee. If the predominant sources of 

uncertainty lie in the laboratory protocol – the sample preparation, the calibrations, and the 

analyses – the differences between laboratory results reflect the combined within-laboratory 

uncertainties and laboratory-specific bias based upon protocol. As was done with the XRD test 

method ASTM C1365, bias limits (ASTM C114, Table 1, Column 3) are established using 

prediction intervals for each analyte. 

1 http://www.itl.nist.gov/div898/software/dataplot/homepage.htm 

4 
Figure 2 Calculated values for the determination of within and between lab precision. 

5 
 

Measurement Precision

Uncertainties in bulk oxide measurements originate from a number of sources: consistency and 

bias in specimen preparations, standardization, data collection procedures, and analysis protocol. 

Measurements are estimates of the actual value being measured and ideally have some statement 

of uncertainty. The uncertainty may be estimated through an interlaboratory study, which 

provides estimates on precision, or random error (Type A) and bias, or systematic error (Type B) 

uncertainty. ASTM defines precision as “the closeness of agreement between independent test 

results obtained under stipulated conditions”, (the standard test procedure), which may be 

expressed as a standard deviation (1σ) [14]. Precision is further differentiated by that achieved 

within a laboratory by a single instrument (and operator, or procedure), called repeatability, and 

that between different laboratories, called reproducibility as a single standard deviation or a 95 % 

limit as defined by E691 and presented below: 

Repeatability: Precision under repeatability conditions 

Repeatability limit (r): “The value below which the absolute difference between two 

individual test results obtained under repeatability conditions may be expected to occur 

with a probability of approximately 0.95 (95 %)” 

The repeatability limit is 2.8 (1.96*√2) times the repeatability standard deviation 

Reproducibility: Precision under reproducibility conditions 

Reproducibility limit (R): The value below which the absolute difference between two 

test results obtained under reproducibility conditions may be expected to occur with a 

probability of approximately 0.95 (95 %) 

The reproducibility limit is 2.8 (1.96*√2) times the reproducibility standard 

deviation 

Measurement Accuracy and Method Bias

ASTM defines accuracy as “the closeness of agreement between a test result and a accepted 

reference value” [14], which includes both random and systematic error. The qualification 

criteria in C 114, Table 1, Column 3 addresses accuracy. Bias is defined by ASTM as “the 

difference between the expectation of the test results and an accepted reference value” [14], and 

reflects the systematic error. A meaningful estimate of method bias is more difficult to extract 

from interlaboratory studies if an explicit protocol is not available, even if certified reference 

materials are available. Systematic error introduced by individual lab protocols dominates that of 

the method, making a universal bias correction difficult to estimate and apply. In addition, the 

cements used in this program were not reference materials (due to the number of participants), so 

a bias calculation is not possible. These materials were specially homogenized and packaged as 

part of the CCRL chemical proficiency test program. 

6 
 

 

 

 

 

 

 

 

 

 

 

 

 

Outlier Identification

Participation in the inter-laboratory study (ILS) was open to all interested laboratories and was 

not restricted based on the laboratory staff’s years of experience. In addition, the ILS did not 

specify an explicit method for preparation and analysis. These two factors contributed to the 

overall uncertainty in the measurement data. Some means of identification of outlying data was 

necessary to exclude any outlying results and their influences on the calculated precision and 

consensus values. A graphical representation of this process is provided in Figure 4 where the 

individual replicate data from powder data with results plotted with cement E on the x-axis and 

cement F on the y-axis. The vertical and horizontal axes represent the consensus value means for 

cements E and F, respectively for the original data (before outlier identification). Like a Youden 

plot, this plot of the data pairs provides some insight, based on the degree and directions of 

dispersion of the results. In the absence of bias, the point pattern is roughly circular, and the 

dispersion along a diagonal from the lower-left, to the upper-right quadrant represents systematic 

error, and dispersion that is orthogonal to this direction represents the random error (precision). 

In the example for CaO shows powder preparation (squares), glass preparation (circles) and 

reference methods (+). An X striking out a symbol represents data considered to be an outlier 

based upon that lab’s repeatability or reproducibility. For example, a cluster of circles along the 

upper-right diagonal exhibits good within-lab precision but significant positive systematic error 

for both cements, likely representing either a calibration or preparation error. Data scattered 

perpendicular to the diagonal exhibits systematic error and random error. Finally, on occasion, a 

lab may report an errant value, which might represent an error in the sample preparation or a data 

entry error. In this case, no attempt was made to fix the data, and that analyte from that lab was 

removed for the final analysis to maintain the balanced data set required by E691. 

The plots in Figure 5 of the laboratory mean and standard deviation are also useful for rapid 

visualization of overall performance by laboratory and material. The mean plots represent the 

mean of the three replicates for cements E and F (labeled as Materials 1 and 2) against the 

consensus value. The mean values by laboratory have the effect of averaging out the random 

error in the analyses, providing a more robust estimate for each lab. Lab 1 stands out in 

producing consistently low values, while precision problems of Lab 3 (cement F, material 2) and 

Lab 20 (cement E, material 1) are seen in the standard deviation (SD) plots. 

Quantitative assessment of within- and between-lab precision is represented by the h and k 

statistics [13], which can take the table form or be expressed in a plot. The h and k consistency 

statistics are measures of the lab’s within- and between-laboratory precision, are shown in Figure 

6. These statistics were used to identify outlying lab data in the original data set, which were 

subsequently excluded on an analyte-by-analyte basis. The rationale for this being applied on a 

one time only basis was that it aided in the identification of unusual data due to standardization 

and procedural error, or errors on the reported values due to data entry. No attempt was made to 

evaluate the data and fix errant values due to entry error. ASTM E691 requires a balanced data 

set so if a lab submitted an incomplete data set or was flagged as an outlier due to an errant 

value, the entire data set for that analyte was eliminated. 

7 
 

 

 

The Prediction	Interval

Qualification criteria specified in Table 1 of ASTM C114 include limits on the maximum 

difference between duplicates and an accuracy criterion limiting the maximum difference 

between the mean of two duplicates and a certificate value from a certified reference material. 

These criteria are provided here by the within- and between-laboratory precision statistics and by 

the prediction interval. A prediction interval for a single future observation is an interval having 

a pre-determined probability that it will “contain the next randomly selected observation from a 

population” [15]. The prediction interval approach assumes generally that (1) the underlying 

population is normally distributed, is homogeneous and unchanging and, (2) that the interval will 

be used to bracket numbers based on data from that same underlying population. The 

requirement on the accuracy of the estimates is based upon prediction intervals derived from the 

composite interlaboratory study data and 2-point means of duplicate samples. 

Figure 3 Scatter plot for CaO with XRF-glass as blue circles, XRF-powder as red squares, 

Reference methods as a +, and x striking out excluded data due to exceeding the h or k statistics. 

8 
 

 

 

 

Figure 4 Lab means and standard deviations for cements E (Material 1) and F (material 2). 

Results – Condensed Summary

Table 2 summarizes the results by method. The table reports the 1σ within-laboratory standard 

deviation (Sr), the 1σ between-laboratory standard deviation (sR), and the appropriate ASTM 

d2s (the 95 % limits on the difference between two test results) as r and R, representing a pooled 

standard deviation for the two replicates for both cements E and F for within-laboratory and 

between-laboratory results, respectively. In addition, pooled results for glass and powder 

methods are shown on the right-hand side of the table. More detailed summaries by method and 

material are found in Appendix B for the glass preparation, and in Appendix C for the powder 

preparation. Appendix D contains the data used in this analysis. 

A two-sided 95 % prediction interval for the mean of two test results is presented in Table 2 for 

each analyte. This interval defines the range of values one might expect relative to a certified 

value of a reference material based upon the mean of two separate determinations, similar to the 

criteria of column 3 of Table 1 in ASTM C114, titled “Maximum difference of the average of 

duplicates from CRM certificate values”. 

9 
Figure 5 h and k statistic plots illustrate the within- (k) and between-laboratory (h) precision and 

are useful in identifying unusual results that may be considered outlying. The dashed lines mark 

the limits for each statistic. 

10 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 2 Pooled Results for XRF-Glass, XRF-Powder and Combined Powder and Glass Methods 

with ZnO and Cr2O3 results from combined glass and powder methods. 

Glass Powder Pooled Glass and Powder 

Sr sR r R Sr sR r R Sr sR r R 

CaO 0.097 0.346 0.268 0.959 0.136 0.284 0.377 0.787 0.118 0.316 0.327 0.877 

SiO2 0.056 0.169 0.154 0.469 0.058 0.251 0.161 0.695 0.057 0.214 0.158 0.593 

Al2O3 0.027 0.075 0.074 0.209 0.024 0.099 0.067 0.273 0.025 0.088 0.070 0.243 

Fe2O3 0.011 0.039 0.029 0.108 0.013 0.044 0.037 0.122 0.012 0.041 0.033 0.115 

SO3 0.047 0.081 0.130 0.225 0.029 0.110 0.079 0.304 0.039 0.097 0.107 0.268 

MgO 0.011 0.019 0.031 0.054 0.021 0.046 0.058 0.127 0.017 0.035 0.046 0.098 

Na2O 0.006 0.016 0.017 0.044 0.007 0.022 0.019 0.060 0.006 0.019 0.018 0.052 

K2O 0.004 0.013 0.011 0.036 0.007 0.018 0.020 0.049 0.006 0.015 0.016 0.043 

TiO2 0.004 0.008 0.010 0.023 0.004 0.006 0.010 0.017 0.004 0.007 0.010 0.021 

P2O5 0.002 0.004 0.005 0.011 0.003 0.013 0.009 0.035 0.003 0.009 0.007 0.026 

Mn2O3 0.002 0.007 0.006 0.019 0.003 0.007 0.007 0.019 0.002 0.006 0.005 0.017 

SrO 0.001 0.004 0.002 0.011 0.002 0.006 0.005 0.017 0.001 0.005 0.004 0.014 

ZnO 0.0005 0.0042 0.001 0.012 

Cr2O3 0.0009 0.0019 0.002 0.005 

Cl 0.0016 0.0062 0.005 0.017 

11 
 

 

 

 

 

 

Table 3 95 % Prediction Interval designed to bracket values of a mean of k = 2, 3, 4 

measurements. The mean of n replicate determinations should differ from the known value of the 

certified reference material (±) by no more than the value shown. 

k = 2 k = 3 k = 4 

Glass Powder Glass Powder Glass Powder 

CaO 0.647 0.512 0.554 0.437 0.501 0.394 

SiO2 0.305 0.430 0.260 0.364 0.234 0.326 

Al2O3 0.132 0.173 0.112 0.147 0.101 0.132 

Fe2O3 0.068 0.077 0.058 0.065 0.052 0.059 

SO3 0.146 0.188 0.125 0.159 0.112 0.143 

MgO 0.036 0.077 0.031 0.065 0.028 0.058 

Na2O 0.028 0.038 0.024 0.032 0.021 0.029 

K2O 0.022 0.031 0.019 0.026 0.017 0.024 

TiO2 0.014 0.010 0.012 0.009 0.011 0.008 

P2O5 0.007 0.022 0.006 0.018 0.006 0.016 

Mn2O3 0.014 0.014 0.012 0.012 0.011 0.011 

SrO 0.008 0.013 0.007 0.011 0.006 0.010 

ZnO 0.007 0.007 0.006 

Cr2O3 0.002 0.002 0.002 

12 
 

 

 

Individual	Oxide Results

Each analyte, expressed as oxides, is represented with box plots for both cements E and F that 

include the reference data from the CCRL proficiency test program for these cements. For 

comparison, a table of results for each duplicate and replicate by sample preparation (glass and 

powder), a summary table for the precision calculations by cement, duplicate and replicate, and a 

bar chart illustrating the pooled results against the ASTM C114 criteria and reproducibility 

values calculated in other studies on analytical uncertainty. 

Box plots are a graphical one-way ANOVA, enabling comparison of the two XRF preparation 

and the reference methods results through assessment of the alignment or mis-alignment of 

median values, differences in interquartile ranges, and the extent of the data extremes. The box 

plots characterize the XRF data after outliers from the initial analysis have been removed. 

Important features of the box plot are: 

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

2.	 the median value is identified by the X within the box is used for its resistance to outliers, 

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

4.	 the top and the bottom of the box represent the estimated 75 % and 25 % point, 

respectively, and
 

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

projecting from the box 

Summary

Precision and accuracy estimates from analysis of data from an ASTM interlaboratory test 

program provide the basis for qualification statement for the new XRF standard test method now 

in development. The current qualification criteria are based upon traditional wet chemistry test 

methods, and the original data and means of their calculation of the qualification criteria data are 

not available. Following ASTM E691, precision values for within- and between-laboratory and 

their 95 % limits have been determined. The accuracy criterion in ASTM C114, Table 1 is 

developed here using a two-point mean and 95 % prediction interval. Together, these 

performance criteria will aid in facilitating accurate and consistent analyses of the bulk chemical 

compositions of hydraulic cements. 

Acknowledgements

LeRoy Jacobs, Chair of the XRF task group within C01.23 subcommittee on compositional 

analysis coordinated the effort to develop a standard test procedure for X-ray fluorescence of 

hydraulic cements. His leadership, perseverance and humor kept the effort going. Robin Haupt of 

the Cement and Concrete reference laboratory coordinated the distribution of materials and 

collection. The comments and suggestions of the internal reviewers, Kenneth Snyder and 

Clarissa Ferraris and external reviewer, Donald Broton are appreciated. 

13 
SiO2

SIO2 

22.0 

X 

X 

X 

X 

X 

X 

X 

X 

X 

1 2 3 

21.0 

20.0 

19.0 

18.0 

17.0 

MASS FRACTION MASS FRACTION 

CEMENT E 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE 

SIO2 

20.0 

19.5 

19.0 

18.5 

18.0 

17.5 

17.0 

X 

X 

X 

X 

X 

X 

X 

X 

X 

1 2 3 

CEMENT F
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

Figure 6 Box plots for SiO2 for XRF glass and powder, and reference methods. 

14 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SiO2, Cement E, Glass, Replicate 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 20.4507 0.1215 -0.1219 -0.73 1.97 

2 20.8033 0.0450 0.2307 1.37 0.73 

3 20.2757 0.0474 -0.2969 -1.77 0.77 

4 20.4997 0.0270 -0.0729 -0.43 0.44 

5 20.6917 0.0343 0.1191 0.71 0.56 

6 20.6883 0.0605 0.1157 0.69 0.98 

7 20.5300 0.0329 -0.0426 -0.25 0.53 

8 20.7353 0.0904 0.1627 0.97 1.47 

9 20.4788 0.0152 -0.0938 -0.56 0.25 

Average of cell averages = 20.57261 

Standard Deviation of cell averages = 0.16817 

Repeatability Standard Deviation = 0.06155 

Reproducibility Standard Deviation = 0.17731 

Critical Values h,k = 2.23, 1.73 

SiO2, Cement F, Glass, Replicate 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 18.7622 0.0983 -0.0789 -0.54 1.93 

2 18.9417 0.0479 0.1006 0.69 0.94 

3 18.5590 0.0260 -0.2820 -1.94 0.51 

4 18.8252 0.0319 -0.0159 -0.11 0.63 

5 19.0233 0.0388 0.1823 1.25 0.76 

6 18.9217 0.0387 0.0806 0.55 0.76 

7 18.7833 0.0197 -0.0577 -0.40 0.39 

8 18.9948 0.0677 0.1538 1.06 1.33 

9 18.7582 0.0404 -0.0829 -0.57 0.79 

Average of cell averages = 18.84104 

Standard Deviation of cell averages = 0.14566 

Repeatability Standard Deviation = 0.05083 

Reproducibility Standard Deviation = 0.15287 

Critical Values h,k = 2.23, 1.73 

15 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SiO2, Cement E, Glass, Replicate 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 20.4933 0.1167 -0.0883 -0.49 1.99 

2 20.8717 0.0671 0.2900 1.62 1.14 

3 20.2676 0.0355 -0.3141 -1.75 0.60 

4 20.5050 0.0283 -0.0766 -0.43 0.48 

5 20.6933 0.0314 0.1117 0.62 0.54 

6 20.6683 0.0426 0.0867 0.48 0.73 

7 20.5167 0.0234 -0.0650 -0.36 0.40 

8 20.7432 0.0845 0.1616 0.90 1.44 

9 20.4755 0.0184 -0.1061 -0.59 0.31 

Average of cell averages = 20.58162 

Standard Deviation of cell averages = 0.17959 

Repeatability Standard Deviation = 0.05868 

Reproducibility Standard Deviation = 0.18741 

Critical Values h,k = 2.23, 1.73 

SiO2, Cement F, Glass, Replicate 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 18.8043 0.0931 -0.0527 -0.35 1.86 

2 18.9750 0.0404 0.1180 0.79 0.80 

3 18.5647 0.0425 -0.2924 -1.96 0.85 

4 18.8480 0.0416 -0.0090 -0.06 0.83 

5 19.0217 0.0232 0.1646 1.10 0.46 

6 18.9683 0.0500 0.1113 0.75 1.00 

7 18.7900 0.0329 -0.0670 -0.45 0.65 

8 18.9962 0.0598 0.1391 0.93 1.19 

9 18.7450 0.0337 -0.1120 -0.75 0.67 

Average of cell averages = 18.85702 

Standard Deviation of cell averages = 0.14923 

Repeatability Standard Deviation = 0.05018 

Reproducibility Standard Deviation = 0.15610 

Critical Values h,k = 2.23, 1.73 

16 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SiO2, Cement E, Powder, Replicate 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 20.6467 0.0612 0.0891 0.46 0.99 

2 20.8367 0.0505 0.2791 1.45 0.81 

3 20.7317 0.0232 0.1741 0.90 0.37 

4 20.4100 0.0522 -0.1476 -0.77 0.84 

5 20.6217 0.0725 0.0641 0.33 1.17 

6 20.8417 0.1030 0.2841 1.47 1.66 

7 20.5267 0.0437 -0.0309 -0.16 0.70 

8 20.3350 0.0572 -0.2226 -1.15 0.92 

9 20.4833 0.0388 -0.0742 -0.39 0.63 

10 20.4083 0.0436 -0.1492 -0.77 0.70 

11 20.2917 0.0914 -0.2659 -1.38 1.47 

Average of cell averages = 20.55758 

Standard Deviation of cell averages = 0.19280 

Repeatability Standard Deviation = 0.06206 

Reproducibility Standard Deviation = 0.20095 

Critical Values h,k = 2.34, 1.75 

SiO2, Cement F, Powder, Replicate 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 19.0483 0.0183 -0.1063 -0.38 0.37 

2 19.1583 0.0786 0.0037 0.01 1.58 

3 19.0900 0.0566 -0.0646 -0.23 1.14 

4 18.8683 0.0426 -0.2863 -1.02 0.86 

5 19.1417 0.0574 -0.0130 -0.05 1.15 

6 19.3017 0.0643 0.1470 0.52 1.29 

7 19.0533 0.0398 -0.1013 -0.36 0.80 

8 19.1333 0.0472 -0.0213 -0.08 0.95 

9 18.7467 0.0294 -0.4080 -1.45 0.59 

10 19.3183 0.0431 0.1637 0.58 0.87 

11 19.8408 0.0410 0.6862 2.44 0.83 

Average of cell averages = 19.15462 

Standard Deviation of cell averages = 0.28179 

Repeatability Standard Deviation = 0.04971 

Reproducibility Standard Deviation = 0.28542 

Critical Values h,k = 2.34, 1.75 

17 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SiO2, Cement E, Powder, Replicate 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 19.0617 0.0426 -0.1036 -0.35 0.74 

2 19.1433 0.0942 -0.0220 -0.07 1.63 

3 19.1017 0.0462 -0.0636 -0.21 0.80 

4 18.8400 0.0529 -0.3253 -1.09 0.92 

5 19.1883 0.0818 0.0230 0.08 1.42 

6 19.3167 0.0622 0.1514 0.51 1.08 

7 19.0483 0.0214 -0.1170 -0.39 0.37 

8 19.1400 0.0400 -0.0253 -0.09 0.69 

9 18.7717 0.0279 -0.3936 -1.32 0.48 

10 19.2967 0.0301 0.1314 0.44 0.52 

11 19.9100 0.0823 0.7447 2.50 1.43 

Average of cell averages = 19.16530 

Standard Deviation of cell averages = 0.29760 

Repeatability Standard Deviation = 0.05776 

Reproducibility Standard Deviation = 0.30223 

Critical Values h,k = 2.34, 1.75 

SiO2, Cement F, Powder, Replicate 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 19.0617 0.0426 -0.1036 -0.35 0.74 

2 19.1433 0.0942 -0.0220 -0.07 1.63 

3 19.1017 0.0462 -0.0636 -0.21 0.80 

4 18.8400 0.0529 -0.3253 -1.09 0.92 

5 19.1883 0.0818 0.0230 0.08 1.42 

6 19.3167 0.0622 0.1514 0.51 1.08 

7 19.0483 0.0214 -0.1170 -0.39 0.37 

8 19.1400 0.0400 -0.0253 -0.09 0.69 

9 18.7717 0.0279 -0.3936 -1.32 0.48 

10 19.2967 0.0301 0.1314 0.44 0.52 

11 19.9100 0.0823 0.7447 2.50 1.43 

Average of cell averages = 19.16530 

Standard Deviation of cell averages = 0.29760 

Repeatability Standard Deviation = 0.05776 

Reproducibility Standard Deviation = 0.30223 

Critical Values h,k = 2.34, 1.75 

18 
 

 

 

 

 

 

 

 

 

 

 

 

 

XRF Glass, Replicate 1 

Material Xbar 

1 20.5726 

2 18.8410 

sx

0.1682 

0.1457 

sr

0.0616 

0.0508 

sR

0.1773 

0.1529 

r

0.17 

0.14 

R

0.50 

0.43 

XRF Glass, Replicate 2 

Material Xbar 

1 20.5816 

2 18.8570 

sx

0.1796 

0.1492 

sr

0.0587 

0.0502 

sR

0.1874 

0.1561 

r

0.16 

0.14 

R

0.52 

0.44 

XRF Powder Replicate 1 

Material Xbar 

1 20.5576 

2 19.1546 

sx

0.1928 

0.2818 

sr

0.0621 

0.0497 

sR

0.2010 

0.2854 

r

0.17 

0.14 

R

0.56 

0.80 

XRF Powder Replicate 2 

Material Xbar 

1 20.5750 

2 19.1653 

sx

0.1878 

0.2976 

sr

0.0620 

0.0578 

sR

0.1961 

0.3022 

r

0.17 

0.16 

R

0.55 

0.85 

Figure 7 SiO2 precision statistics by method with bar chart comparing results to current and past
 

ASTM C114 limits and previous studies on chemical analysis precision as 1σ, between lab (SR).
 

19 
Al2O3

AL2O3 

4.8 

4.9 

5.0 

X 

X 

X 

4.6

ION 

4.1 

4.2 

4.3 

4.5 

4.5 

MASS FRACT

X 

X 

X 

X 

X 

X 

1 2 3 

CEMENT E 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE 

AL2O3 

7.0 

6.5 

X 

X 

X 

X 

X 

X 

X 

X 

X 

1 2 3 

MASS FRACTION 

6.0 

5.5 

5.0 

4.5 

4.0 

CEMENT F
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

Figure 8 Box plots for Al2O3 for XRF glass and powder, and reference methods. 

20 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Al2O3, Cement E, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 4.3992 0.0265 -0.0459 -0.56 0.93 

2 4.6093 0.0534 0.1643 1.99 1.87 

3 4.4967 0.0273 0.0516 0.62 0.96 

4 4.4307 0.0107 -0.0144 -0.17 0.37 

5 4.4812 0.0267 0.0361 0.44 0.93 

6 4.4450 0.0164 0.0000 0.00 0.58 

7 4.3017 0.0299 -0.1434 -1.74 1.05 

8 4.4869 0.0205 0.0419 0.51 0.72 

9 4.3700 0.0352 -0.0750 -0.91 1.23 

10 4.4298 0.0143 -0.0152 -0.18 0.50 

Average of cell averages = 4.44504 

Standard Deviation of cell averages = 0.08263 

Repeatability Standard Deviation = 0.02857 

Reproducibility Standard Deviation = 0.08665 

Critical Values h,k = 2.29, 1.74 

Al2O3, Cement F, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 5.2623 0.0263 -0.0741 -1.19 0.96 

2 5.4653 0.0474 0.1289 2.07 1.72 

3 5.3600 0.0245 0.0236 0.38 0.89 

4 5.3027 0.0141 -0.0337 -0.54 0.51 

5 5.3692 0.0251 0.0327 0.52 0.91 

6 5.3250 0.0138 -0.0115 -0.18 0.50 

7 5.2583 0.0240 -0.0781 -1.25 0.87 

8 5.3913 0.0231 0.0548 0.88 0.84 

9 5.3133 0.0418 -0.0231 -0.37 1.52 

10 5.3170 0.0129 -0.0195 -0.31 0.47 

Average of cell averages = 5.33645 

Standard Deviation of cell averages = 0.06238 

Repeatability Standard Deviation = 0.02753 

Reproducibility Standard Deviation = 0.06725 

Critical Values h,k = 2.29, 1.74 

21 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Al2O3, Cement E, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 4.4060 0.0250 -0.0383 -0.50 1.02 

2 4.5877 0.0374 0.1433 1.87 1.53 

3 4.4933 0.0151 0.0490 0.64 0.62 

4 4.4296 0.0151 -0.0148 -0.19 0.62 

5 4.4840 0.0141 0.0397 0.52 0.58 

6 4.4417 0.0204 -0.0027 -0.03 0.84 

7 4.2967 0.0388 -0.1477 -1.93 1.59 

8 4.4866 0.0252 0.0423 0.55 1.03 

9 4.3950 0.0243 -0.0493 -0.64 0.99 

10 4.4228 0.0122 -0.0215 -0.28 0.50 

Average of cell averages = 4.44433 

Standard Deviation of cell averages = 0.07652 

Repeatability Standard Deviation = 0.02444 

Reproducibility Standard Deviation = 0.07971 

Critical Values h,k = 2.29, 1.74 

Al2O3, Cement F, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 5.2705 0.0223 -0.0580 -0.94 0.88 

2 5.4483 0.0387 0.1198 1.95 1.52 

3 5.3533 0.0350 0.0248 0.40 1.38 

4 5.2980 0.0099 -0.0305 -0.50 0.39 

5 5.3417 0.0153 0.0132 0.21 0.60 

6 5.3317 0.0172 0.0032 0.05 0.68 

7 5.2333 0.0294 -0.0952 -1.55 1.16 

8 5.3929 0.0188 0.0644 1.05 0.74 

9 5.2933 0.0356 -0.0352 -0.57 1.40 

10 5.3220 0.0111 -0.0065 -0.11 0.44 

Average of cell averages = 5.32851 

Standard Deviation of cell averages = 0.06140 

Repeatability Standard Deviation = 0.02542 

Reproducibility Standard Deviation = 0.06564 

Critical Values h,k = 2.29, 1.74 

22 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Al2O3, Cement E, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 4.4700 0.0126 -0.0551 -0.54 0.54 

2 4.5433 0.0121 0.0182 0.18 0.51 

3 4.5167 0.0103 -0.0084 -0.08 0.44 

4 4.5300 0.0477 0.0049 0.05 2.03 

5 4.5067 0.0197 -0.0184 -0.18 0.84 

6 4.5450 0.0176 0.0199 0.20 0.75 

7 4.3900 0.0167 -0.1351 -1.33 0.71 

8 4.6117 0.0293 0.0866 0.85 1.24 

9 4.3961 0.0144 -0.1290 -1.27 0.61 

10 4.7417 0.0284 0.2166 2.12 1.21 

Average of cell averages = 4.52511 

Standard Deviation of cell averages = 0.10192 

Repeatability Standard Deviation = 0.02354 

Reproducibility Standard Deviation = 0.10416 

Critical Values h,k = 2.29, 1.74 

Al2O3, Cement F, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 5.1300 0.0167 0.0115 0.12 0.66 

2 5.3517 0.0240 0.2332 2.41 0.95 

3 5.1733 0.0308 0.0549 0.57 1.22 

4 5.0783 0.0366 -0.0401 -0.41 1.45 

5 5.0400 0.0179 -0.0785 -0.81 0.71 

6 5.0333 0.0207 -0.0851 -0.88 0.82 

7 5.0467 0.0121 -0.0718 -0.74 0.48 

8 5.0733 0.0163 -0.0451 -0.47 0.65 

9 5.1762 0.0376 0.0577 0.60 1.49 

10 5.0818 0.0253 -0.0367 -0.38 1.00 

Average of cell averages = 5.11847 

Standard Deviation of cell averages = 0.09685 

Repeatability Standard Deviation = 0.02522 

Reproducibility Standard Deviation = 0.09954 

Critical Values h,k = 2.29, 1.74 

23 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Al2O3, Cement E, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 4.4483 0.0286 -0.0670 -0.76 1.22 

2 4.5433 0.0151 0.0280 0.32 0.64 

3 4.5117 0.0098 -0.0037 -0.04 0.42 

4 4.5317 0.0527 0.0163 0.18 2.25 

5 4.5033 0.0163 -0.0120 -0.14 0.70 

6 4.5367 0.0186 0.0213 0.24 0.80 

7 4.3883 0.0172 -0.1270 -1.44 0.74 

8 4.6200 0.0110 0.1046 1.19 0.47 

9 4.4011 0.0137 -0.1142 -1.30 0.59 

10 4.6692 0.0183 0.1538 1.74 0.78 

Average of cell averages = 4.51537 

Standard Deviation of cell averages = 0.08815 

Repeatability Standard Deviation = 0.02338 

Reproducibility Standard Deviation = 0.09070 

Critical Values h,k = 2.29, 1.74 

Al2O3, Cement F, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 5.1433 0.0225 0.0158 0.16 0.91 

2 5.3567 0.0258 0.2291 2.36 1.05 

3 5.1783 0.0133 0.0508 0.52 0.54 

4 5.0833 0.0408 -0.0442 -0.46 1.65 

5 5.0400 0.0126 -0.0875 -0.90 0.51 

6 5.0317 0.0160 -0.0959 -0.99 0.65 

7 5.0483 0.0117 -0.0792 -0.82 0.47 

8 5.0833 0.0207 -0.0442 -0.46 0.84 

9 5.1770 0.0363 0.0495 0.51 1.47 

10 5.1333 0.0279 0.0058 0.06 1.13 

Average of cell averages = 5.12753 

Standard Deviation of cell averages = 0.09709 

Repeatability Standard Deviation = 0.02468 

Reproducibility Standard Deviation = 0.09967 

Critical Values h,k = 2.29, 1.74 

24 
 

 

 

 

 

 

 

 

 

 

 

 

 

XRF Glass, Replicate 1 

Material Xbar 

1 4.4450 

2 5.3365 

sx

0.0826 

0.0624 

sr

0.0286 

0.0275 

sR

0.0866 

0.0672 

r

0.08 

0.08 

R

0.24 

0.19 

XRF Glass, Replicate 2 

Material Xbar 

1 4.4443 

2 5.3285 

sx

0.0765 

0.0614 

sr

0.0244 

0.0254 

sR

0.0797 

0.0656 

r

0.07 

0.07 

R

0.22 

0.18 

XRF Powder Replicate 1 

Material Xbar 

1 4.5154 

2 5.1275 

sx

0.0882 

0.0971 

sr

0.0234 

0.0247 

sR

0.0907 

0.0997 

r

0.07 

0.07 

R

0.25 

0.28 

XRF Powder Replicate 2 

Material Xbar 

1 4.5251 

2 5.1185 

sx

0.1019 

0.0968 

sr

0.0235 

0.0252 

sR

0.1042 

0.0995 

r

0.07 

0.07 

R

0.29 

0.28 

Figure 9 Al2O3 precision statistics by method with bar chart comparing results to current and 

past ASTM C114 limits and previous studies on chemical analysis precision as 1σ, between lab 

(SR). 

25 
Fe2O3

X 

X 

X 

X 

X 

X 

X 

X 

X 

2.5 

2.6 

2.7 

2.8 

3.0 

3.0 

X 

X 

X 

X 

X 

X 

X 

X 

X 

2.0 

2.1 

2.2 

2.3 

2.5 

2.5 

FE2O3 

1 2 3
 

CEMENT E
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

FE2O3
 

1 2 3
 

CEMENT F
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

Figure 10 Box plots for Fe2O3 for XRF glass and powder, and reference methods. 

26
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fe2O3, Cements E, Glass, Rep. 1 

Laboratory Cell Cell 

Number Mean SD d h k

1 2.8658 0.0071 -0.0191 -0.49 0.96 

2 2.9133 0.0140 0.0284 0.73 1.87 

3 2.8795 0.0045 -0.0054 -0.14 0.60 

4 2.8373 0.0067 -0.0476 -1.22 0.90 

5 2.8317 0.0075 -0.0533 -1.37 1.01 

6 2.8983 0.0041 0.0134 0.34 0.55 

7 2.8883 0.0098 0.0034 0.09 1.32 

8 2.8936 0.0067 0.0087 0.22 0.90 

9 2.9683 0.0041 0.0834 2.14 0.55 

10 2.8730 0.0038 -0.0119 -0.31 0.51 

Average of cell averages = 2.88492 

Standard Deviation of cell averages = 0.03897 

Repeatability Standard Deviation = 0.00747 

Reproducibility Standard Deviation = 0.00747 

Critical Values h,k = 2.29, 1.74
 

Fe2O3, Cements F, Glass, Rep. 1 

Laboratory Cell
 Cell
 

Number Mean SD d h k
 

1 2.3672 0.0114 -0.0605 -0.39 0.03 

2 2.3897 0.0115 -0.0380 -0.24 0.03 

3 2.3736 0.0027 -0.0541 -0.35 0.01 

4 2.3475 0.0062 -0.0801 -0.51 0.02 

5 2.3333 0.0137 -0.0943 -0.61 0.04 

6 2.3900 0.0063 -0.0376 -0.24 0.02 

7 2.8600 1.1856 0.4324 2.78 3.16 

8 2.3872 0.0073 -0.0404 -0.26 0.02 

9 2.4600 0.0063 0.0324 0.21 0.02 

10 2.3678 0.0077 -0.0598 -0.38 0.02 

Average of cell averages = 2.42763 

Standard Deviation of cell averages = 0.15562 

Repeatability Standard Deviation = 0.37501 

Reproducibility Standard Deviation = 0.37501 

Critical Values h,k = 2.29, 1.74 

27 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fe2O3, Cements E, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 2.8758 0.0080 -0.0095 -0.26 0.86 

2 2.9120 0.0138 0.0266 0.72 1.49 

3 2.8795 0.0054 -0.0058 -0.16 0.58 

4 2.8360 0.0097 -0.0494 -1.34 1.05 

5 2.8283 0.0117 -0.0570 -1.55 1.27 

6 2.8983 0.0041 0.0130 0.35 0.44 

7 2.8933 0.0052 0.0080 0.22 0.56 

8 2.8939 0.0066 0.0086 0.23 0.72 

9 2.9583 0.0147 0.0730 1.98 1.60 

10 2.8780 0.0059 -0.0074 -0.20 0.64 

Average of cell averages = 2.88536 

Standard Deviation of cell averages = 0.03683 

Repeatability Standard Deviation = 0.00922 

Reproducibility Standard Deviation = 0.03778 

Critical Values h,k = 2.29, 1.74 

Fe2O3, Cements F, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 2.3762 0.0068 -0.0032 -0.10 0.75 

2 2.3898 0.0114 0.0104 0.31 1.24 

3 2.3739 0.0046 -0.0055 -0.16 0.50 

4 2.3405 0.0105 -0.0389 -1.15 1.15 

5 2.3317 0.0160 -0.0478 -1.41 1.75 

6 2.3933 0.0052 0.0139 0.41 0.56 

7 2.3750 0.0055 -0.0044 -0.13 0.60 

8 2.3873 0.0079 0.0079 0.23 0.86 

9 2.4567 0.0082 0.0773 2.29 0.89 

10 2.3698 0.0094 -0.0096 -0.28 1.03 

Average of cell averages = 2.37942 

Standard Deviation of cell averages = 0.03379 

Repeatability Standard Deviation = 0.00916 

Reproducibility Standard Deviation = 0.03481 

Critical Values h,k = 2.29, 1.74 

28 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fe2O3, Cements E, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 2.9117 0.0098 -0.0098 -0.24 0.70 

2 2.8867 0.0082 -0.0348 -0.85 0.58 

3 2.9200 0.0126 -0.0015 -0.04 0.91 

4 2.9233 0.0216 0.0018 0.04 1.55 

5 2.8767 0.0082 -0.0448 -1.10 0.58 

6 2.8967 0.0121 -0.0248 -0.61 0.87 

7 2.9283 0.0075 0.0068 0.17 0.54 

8 2.9367 0.0103 0.0152 0.37 0.74 

9 2.9102 0.0276 -0.0114 -0.28 1.98 

10 3.0250 0.0045 0.1035 2.53 0.32 

Average of cell averages = 2.92151 

Standard Deviation of cell averages = 0.04091 

Repeatability Standard Deviation = 0.01396 

Reproducibility Standard Deviation = 0.04285 

Critical Values h,k = 2.29, 1.74 

Fe2O3, Cements F, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 2.3867 0.0082 -0.0007 -0.02 0.64 

2 2.4000 0.0063 0.0126 0.28 0.50 

3 2.4033 0.0151 0.0160 0.36 1.18 

4 2.4483 0.0117 0.0610 1.37 0.92 

5 2.3033 0.0082 -0.0840 -1.88 0.64 

6 2.3517 0.0075 -0.0357 -0.80 0.59 

7 2.3717 0.0098 -0.0157 -0.35 0.77 

8 2.3767 0.0103 -0.0107 -0.24 0.81 

9 2.3746 0.0284 -0.0128 -0.29 2.23 

10 2.4575 0.0042 0.0701 1.57 0.33 

Average of cell averages = 2.38737 

Standard Deviation of cell averages = 0.04461 

Repeatability Standard Deviation = 0.01272 

Reproducibility Standard Deviation = 0.04610 

Critical Values h,k = 2.29, 1.74 

29 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fe2O3, Cements E, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 2.9100 0.0089 -0.0108 -0.30 0.67 

2 2.8950 0.0084 -0.0258 -0.71 0.63 

3 2.9133 0.0082 -0.0074 -0.20 0.62 

4 2.9250 0.0187 0.0042 0.12 1.41 

5 2.8767 0.0103 -0.0441 -1.22 0.78 

6 2.8983 0.0133 -0.0224 -0.62 1.00 

7 2.9300 0.0000 0.0092 0.25 0.00 

8 2.9400 0.0089 0.0192 0.53 0.67 

9 2.9093 0.0284 -0.0115 -0.32 2.14 

10 3.0100 0.0045 0.0892 2.46 0.34 

Average of cell averages = 2.92076 

Standard Deviation of cell averages = 0.03629 

Repeatability Standard Deviation = 0.01325 

Reproducibility Standard Deviation = 0.03825 

Critical Values h,k = 2.29, 1.74 

Fe2O3, Cements F, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 2.3917 0.0117 0.0032 0.07 0.88 

2 2.3967 0.0082 0.0082 0.18 0.61 

3 2.4050 0.0138 0.0165 0.35 1.03 

4 2.4483 0.0117 0.0598 1.29 0.88 

5 2.3000 0.0000 -0.0885 -1.90 0.00 

6 2.3550 0.0105 -0.0335 -0.72 0.79 

7 2.3733 0.0103 -0.0152 -0.33 0.77 

8 2.3767 0.0103 -0.0118 -0.25 0.77 

9 2.3726 0.0276 -0.0159 -0.34 2.07 

10 2.4658 0.0128 0.0773 1.66 0.96 

Average of cell averages = 2.38851 

Standard Deviation of cell averages = 0.04653 

Repeatability Standard Deviation = 0.01334 

Reproducibility Standard Deviation = 0.04810 

Critical Values h,k = 2.29, 1.74 

30 
 

 

 

 

 

 

 

 

 

 

 

 

 

XRF Glass, Replicate 1 

Material Xbar 

2.8849 

2.4276 

XRF Glass, Replicate 2 

Material Xbar 

1 2.8854 

2 2.3794 

sx

0.0390 

0.1556 

sx

0.0368 

0.0338 

sr

0.0075 

0.3750 

sr

0.0092 

0.0092 

sR

0.0396 

0.3760 

sR

0.0378 

0.0348 

r

0.02 

1.05 

r

0.03 

0.03 

R

0.11 

1.05 

R

0.11 

0.10 

XRF Powder Replicate 1 

Material Xbar 

1 2.9215 

2 2.3874 

sx

0.0409 

0.0446 

sr

0.0140 

0.0127 

sR

0.0428 

0.0461 

r

0.04 

0.04 

R

0.12 

0.13 

XRF Powder Replicate 2 

Material Xbar 

1 2.9208 

2 2.3885 

sx

0.0363 

0.0465 

sr

0.0133 

0.0133 

sR

0.0383 

0.0481 

r

0.04 

0.04 

R

0.11 

0.13 

Figure 11 Fe2O3 precision statistics by method with bar chart comparing results to current and 

past ASTM C114 limits and previous studies on chemical analysis precision as 1σ, between lab 

(SR). 

31 
CaO

CAO 

64.0 

63.5 

63.0 

62.5 

62.0 

61.5 

61.0 

X 

X 

X 

X 

X 

X 

X 

X 

X 

1 2 3 

MASS FRACTION MASS FRACTION 

CEMENT E 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE 

CAO 

65.0 

64.5 

64.0 

63.5 

63.0 

62.5 

62.0 

X 

X 

X 

X 

X 

X 

X 

X 

X 

1 2 3 

CEMENT F
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

Figure 12 Box plots for CaO for XRF glass and powder, and reference methods. 

32 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CaO, Cements E, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 62.5033 0.0831 0.0540 0.13 0.99 

2 62.3887 0.0507 -0.0606 -0.14 0.60 

3 61.7987 0.1038 -0.6506 -1.56 1.23 

4 62.3083 0.1373 -0.1410 -0.34 1.63 

5 62.4900 0.0352 0.0407 0.10 0.42 

6 62.4203 0.1047 -0.0290 -0.07 1.24 

7 63.3233 0.0615 0.8740 2.09 0.73 

8 62.3617 0.0413 -0.0876 -0.21 0.49 

Average of cell averages = 62.44929 

Standard Deviation of cell averages = 0.41814 

Repeatability Standard Deviation = 0.08427 

Reproducibility Standard Deviation = 0.42516 

Critical Values h,k = 2.15, 1.72 

CaO, Cements F, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 63.0267 0.1127 -0.2645 -1.13 1.28 

2 63.3952 0.0348 0.1040 0.44 0.40 

3 62.9720 0.0983 -0.3191 -1.36 1.12 

4 63.3967 0.0703 0.1055 0.45 0.80 

5 63.3033 0.0480 0.0122 0.05 0.55 

6 63.2237 0.0898 -0.0675 -0.29 1.02 

7 63.7250 0.1461 0.4339 1.85 1.66 

8 63.2865 0.0390 -0.0046 -0.02 0.44 

Average of cell averages = 63.29113 

Standard Deviation of cell averages = 0.23504 

Repeatability Standard Deviation = 0.08788 

Reproducibility Standard Deviation = 0.24835 

Critical Values h,k = 2.15, 1.72 

33 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CaO, Cements E, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 62.5467 0.0734 0.1011 0.26 0.63 

2 62.4373 0.0524 -0.0082 -0.02 0.45 

3 61.7898 0.0866 -0.6557 -1.70 0.75 

4 62.3200 0.1311 -0.1255 -0.33 1.13 

5 62.5050 0.0333 0.0595 0.15 0.29 

6 62.4277 0.1119 -0.0179 -0.05 0.96 

7 63.2017 0.2470 0.7561 1.96 2.13 

8 62.3362 0.0235 -0.1094 -0.28 0.20 

Average of cell averages = 62.44554 

Standard Deviation of cell averages = 0.38611 

Repeatability Standard Deviation = 0.11621 

Reproducibility Standard Deviation = 0.40042 

Critical Values h,k = 2.15, 1.72 

CaO, Cements F, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 63.0500 0.1182 -0.2526 -0.97 1.25 

2 63.3920 0.0184 0.0894 0.34 0.19 

3 62.9587 0.0713 -0.3440 -1.32 0.75 

4 63.3967 0.0589 0.0940 0.36 0.62 

5 63.3050 0.0561 0.0024 0.01 0.59 

6 63.2273 0.0837 -0.0753 -0.29 0.88 

7 63.8233 0.1941 0.5207 1.99 2.05 

8 63.2682 0.0314 -0.0345 -0.13 0.33 

Average of cell averages = 63.30265 

Standard Deviation of cell averages = 0.26103 

Repeatability Standard Deviation = 0.09464 

Reproducibility Standard Deviation = 0.27496 

Critical Values h,k = 2.15, 1.72 

34 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CaO, Cements E, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 62.7733 0.0513 0.0832 0.52 0.48 

2 62.6883 0.0886 -0.0018 -0.01 0.84 

3 62.7000 0.1166 0.0099 0.06 1.10 

4 62.8567 0.0942 0.1665 1.04 0.89 

5 62.4550 0.1126 -0.2351 -1.47 1.06 

6 62.5067 0.1407 -0.1835 -1.14 1.33 

7 62.5617 0.0313 -0.1285 -0.80 0.30 

8 62.7267 0.1218 0.0365 0.23 1.15 

9 62.9428 0.1397 0.2527 1.58 1.32 

Average of cell averages = 62.69013 

Standard Deviation of cell averages = 0.16023 

Repeatability Standard Deviation = 0.10579 

Reproducibility Standard Deviation = 0.18709 

Critical Values h,k = 2.23, 1.73 

CaO, Cements F, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 63.9883 0.0445 0.2820 0.89 0.32 

2 63.7433 0.1109 0.0370 0.12 0.80 

3 63.8533 0.1768 0.1470 0.46 1.28 

4 63.3050 0.0550 -0.4013 -1.26 0.40 

5 63.5650 0.1790 -0.1413 -0.44 1.30 

6 63.5483 0.1783 -0.1580 -0.50 1.29 

7 63.2433 0.0622 -0.4630 -1.45 0.45 

8 64.2050 0.0993 0.4987 1.57 0.72 

9 63.9053 0.2128 0.1990 0.62 1.54 

Average of cell averages = 63.70633 

Standard Deviation of cell averages = 0.31842 

Repeatability Standard Deviation = 0.13801 

Reproducibility Standard Deviation = 0.34244 

Critical Values h,k = 2.23, 1.73 

35 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CaO, Cements E, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 62.7783 0.0854 0.0656 0.42 0.53 

2 62.6617 0.0659 -0.0511 -0.33 0.41 

3 62.7150 0.1219 0.0022 0.01 0.75 

4 62.8017 0.0674 0.0889 0.57 0.42 

5 62.4300 0.0940 -0.2828 -1.80 0.58 

6 62.5317 0.1093 -0.1811 -1.15 0.68 

7 62.7317 0.3928 0.0189 0.12 2.43 

8 62.8067 0.1015 0.0939 0.60 0.63 

9 62.9582 0.1378 0.2454 1.56 0.85 

Average of cell averages = 62.71276 

Standard Deviation of cell averages = 0.15691 

Repeatability Standard Deviation = 0.16173 

Reproducibility Standard Deviation = 0.21545 

Critical Values h,k = 2.23, 1.73 

CaO, Cements F, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 64.0567 0.0631 0.3331 1.01 0.47 

2 63.7850 0.0729 0.0614 0.19 0.55 

3 63.8700 0.1774 0.1464 0.44 1.33 

4 63.3083 0.0337 -0.4153 -1.26 0.25 

5 63.5283 0.1735 -0.1953 -0.59 1.30 

6 63.5983 0.1972 -0.1253 -0.38 1.48 

7 63.2400 0.0613 -0.4836 -1.46 0.46 

8 64.2167 0.0763 0.4931 1.49 0.57 

9 63.9090 0.1967 0.1854 0.56 1.48 

Average of cell averages = 63.72359 

Standard Deviation of cell averages = 0.33049 

Repeatability Standard Deviation = 0.13298 

Reproducibility Standard Deviation = 0.35208 

Critical Values h,k = 2.23, 1.73 

36 
 

 

 

 

 

 

 

 

 

 

 

 

XRF Glass, Replicate 1 

Material Xbar 

1 62.4493 

2 63.2911 

sx

0.4181 

0.2350 

sr

0.0843 

0.0879 

sR

0.4252 

0.2484 

r

0.24 

0.25 

R

1.19 

0.70 

XRF Glass, Replicate 2 

Material Xbar 

1 62.4455 

2 63.3026 

sx

0.3861 

0.2610 

sr

0.1162 

0.0946 

sR

0.4004 

0.2750 

r

0.33 

0.27 

R

1.12 

0.77 

XRF Powder Replicate 1 

Material Xbar 

1 62.6901 

2 63.7063 

sx

0.1602 

0.3184 

sr

0.1058 

0.1380 

sR

0.1871 

0.3424 

r

0.30 

0.39 

R

0.52 

0.96 

XRF Powder Replicate 1 

Material Xbar 

1 62.7128 

2 63.7236 

sx

0.1569 

0.3305 

sr

0.1617 

0.1330 

sR

0.2154 

0.3521 

r

0.45 

0.37 

R

0.60 

0.99 

Figure 13 CaO precision statistics by method with bar chart comparing results to current 

and past ASTM C114 limits and previous studies on chemical analysis precision as 1σ, 

between lab (SR). 

37 
MgO

MGO 

3.0 

2.9 

2.7 

X 

X 

X 

X 

X 

X 

X 

X 

X 

1 2 3 

MASS FRACTION

2.7 

2.5 

2.5 

2.4 

2.2 

2.2 

CEMENT E
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

MGO 

2.4 X 

2.3 

2.0 

2.2

MASS FRACTION

X 

X 

X 

X 

X 

X 

2.0 X X 

1.9 

1 2 3
 

CEMENT F
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

Figure 14 Box plots for MgO for XRF glass and powder, and reference methods. 

38 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MgO, Cements E, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 2.5422 0.0138 -0.0223 -1.30 1.05 

2 2.5683 0.0133 0.0039 0.22 1.01 

3 2.5685 0.0056 0.0040 0.23 0.42 

4 2.5483 0.0075 -0.0161 -0.94 0.57 

5 2.5783 0.0133 0.0139 0.81 1.01 

6 2.5583 0.0075 -0.0061 -0.36 0.57 

7 2.5744 0.0259 0.0099 0.58 1.97 

8 2.5468 0.0033 -0.0176 -1.03 0.25 

9 2.5950 0.0138 0.0305 1.78 1.05 

Average of cell averages = 2.56447 

Standard Deviation of cell averages = 0.01718 

Repeatability Standard Deviation = 0.01316 

Reproducibility Standard Deviation = 0.02096 

Critical Values h,k = 2.23, 1.73 

MgO, Cements F, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 2.1110 0.0083 0.0018 0.11 0.87 

2 2.1150 0.0105 0.0058 0.36 1.10 

3 2.1055 0.0051 -0.0037 -0.23 0.53 

4 2.0900 0.0063 -0.0192 -1.19 0.67 

5 2.1350 0.0084 0.0258 1.60 0.88 

6 2.0933 0.0137 -0.0158 -0.98 1.44 

7 2.1253 0.0080 0.0161 1.00 0.84 

8 2.0892 0.0085 -0.0200 -1.24 0.89 

9 2.1183 0.0133 0.0092 0.57 1.40 

Average of cell averages = 2.10917 

Standard Deviation of cell averages = 0.01612 

Repeatability Standard Deviation = 0.00950 

Reproducibility Standard Deviation = 0.01831 

Critical Values h,k = 2.23, 1.73 

39 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MgO, Cements E, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 2.5463 0.0128 -0.0184 -1.00 1.12 

2 2.5683 0.0117 0.0036 0.20 1.03 

3 2.5699 0.0114 0.0052 0.28 1.00 

4 2.5483 0.0075 -0.0164 -0.89 0.66 

5 2.5800 0.0089 0.0153 0.83 0.79 

6 2.5450 0.0105 -0.0197 -1.07 0.92 

7 2.5756 0.0184 0.0109 0.59 1.62 

8 2.5507 0.0098 -0.0141 -0.76 0.86 

9 2.5983 0.0075 0.0336 1.83 0.66 

Average of cell averages = 2.56472 

Standard Deviation of cell averages = 0.01842 

Repeatability Standard Deviation = 0.01138 

Reproducibility Standard Deviation = 0.02115 

Critical Values h,k = 2.23, 1.73 

MgO, Cements F, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 2.1168 0.0053 0.0064 0.44 0.53 

2 2.1200 0.0141 0.0095 0.67 1.40 

3 2.1038 0.0062 -0.0066 -0.46 0.62 

4 2.0900 0.0000 -0.0205 -1.43 0.00 

5 2.1333 0.0121 0.0229 1.60 1.20 

6 2.1000 0.0110 -0.0105 -0.73 1.09 

7 2.1144 0.0122 0.0040 0.28 1.21 

8 2.0942 0.0074 -0.0163 -1.14 0.73 

9 2.1217 0.0133 0.0112 0.78 1.32 

Average of cell averages = 2.11048 

Standard Deviation of cell averages = 0.01429 

Repeatability Standard Deviation = 0.01008 

Reproducibility Standard Deviation = 0.01699 

Critical Values h,k = 2.23, 1.73 

40 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MgO, Cements E, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 2.6483 0.0382 -0.0038 -0.07 1.47 

2 2.5700 0.0089 -0.0821 -1.56 0.35 

3 2.6617 0.0371 0.0095 0.18 1.43 

4 2.6417 0.0117 -0.0105 -0.20 0.45 

5 2.5917 0.0172 -0.0605 -1.15 0.67 

6 2.6000 0.0200 -0.0521 -0.99 0.77 

7 2.7067 0.0367 0.0545 1.03 1.42 

8 2.6350 0.0187 -0.0171 -0.32 0.72 

9 2.7000 0.0190 0.0479 0.91 0.73 

10 2.7417 0.0360 0.0895 1.70 1.39 

11 2.6232 0.0274 -0.0289 -0.55 1.06 

12 2.7058 0.0139 0.0537 1.02 0.54 

Average of cell averages = 2.65214 

Standard Deviation of cell averages = 0.05277 

Repeatability Standard Deviation = 0.02589 

Reproducibility Standard Deviation = 0.05782 

Critical Values h,k = 2.38, 1.76 

MgO, Cements F, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 2.0467 0.0258 -0.0152 -0.51 1.70 

2 2.1067 0.0137 0.0448 1.51 0.90 

3 2.0483 0.0133 -0.0135 -0.46 0.87 

4 2.0467 0.0151 -0.0152 -0.51 0.99 

5 2.0467 0.0082 -0.0152 -0.51 0.54 

6 2.0633 0.0137 0.0015 0.05 0.90 

7 2.0500 0.0167 -0.0119 -0.40 1.10 

8 2.0517 0.0194 -0.0102 -0.34 1.28 

9 2.0783 0.0147 0.0165 0.56 0.97 

10 2.1050 0.0084 0.0431 1.45 0.55 

11 2.0948 0.0163 0.0329 1.11 1.07 

12 2.0042 0.0074 -0.0577 -1.95 0.48 

41 

Average of cell averages = 2.06186 

Standard Deviation of cell averages = 0.02966 

Repeatability Standard Deviation = 0.01521 

Reproducibility Standard Deviation = 0.03274 

Critical Values h,k = 2.38, 1.76 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MgO, Cements E, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 2.6283 0.0214 -0.0212 -0.42 0.90 

2 2.5700 0.0089 -0.0795 -1.56 0.38 

3 2.6800 0.0316 0.0305 0.60 1.33 

4 2.6417 0.0098 -0.0079 -0.15 0.41 

5 2.5933 0.0207 -0.0562 -1.10 0.87 

6 2.6050 0.0207 -0.0445 -0.87 0.87 

7 2.7017 0.0331 0.0521 1.02 1.39 

8 2.6417 0.0183 -0.0079 -0.15 0.77 

9 2.7000 0.0167 0.0505 0.99 0.70 

10 2.7467 0.0403 0.0971 1.91 1.69 

11 2.6236 0.0307 -0.0259 -0.51 1.29 

12 2.6625 0.0061 0.0130 0.25 0.26 

Average of cell averages = 2.64954 

Standard Deviation of cell averages = 0.05091 

Repeatability Standard Deviation = 0.02382 

Reproducibility Standard Deviation = 0.05536 

Critical Values h,k = 2.38, 1.76 

MgO, Cements F, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 2.0650 0.0152 -0.0002 -0.01 0.94 

2 2.1050 0.0164 0.0398 1.51 1.01 

3 2.0533 0.0216 -0.0119 -0.45 1.33 

4 2.0467 0.0082 -0.0185 -0.70 0.50 

5 2.0450 0.0197 -0.0202 -0.77 1.22 

6 2.0633 0.0137 -0.0019 -0.07 0.84 

7 2.0483 0.0133 -0.0169 -0.64 0.82 

8 2.0567 0.0207 -0.0085 -0.32 1.28 

9 2.0750 0.0122 0.0098 0.37 0.76 

10 2.1067 0.0137 0.0415 1.58 0.84 

11 2.0967 0.0153 0.0315 1.20 0.95 

12 2.0208 0.0191 -0.0444 -1.69 1.18 

Average of cell averages = 2.06521 

Standard Deviation of cell averages = 0.02630 

Repeatability Standard Deviation = 0.01620 

Reproducibility Standard Deviation = 0.03018 

Critical Values h,k = 2.38, 1.76 

42 
 

 

 

 

 

 

 

 

 

 

 

 

XRF Glass, Replicate 1 

Material Xbar 

1 2.5645 

2 2.1092 

sx

0.0172 

0.0161 

sr

0.0132 

0.0095 

sR

0.0210 

0.0183 

r

0.04 

0.03 

R

0.06 

0.05 

XRF Glass, Replicate 2 

Material Xbar 

1 2.5647 

2 2.1105 

sx

0.0184 

0.0143 

sr

0.0114 

0.0101 

sR

0.0211 

0.0170 

r

0.03 

0.03 

R

0.06 

0.05 

XRF Powder Replicate 1 

Material Xbar 

1 2.6521 

2 2.0619 

sx

0.0528 

0.0297 

sr

0.0259 

0.0152 

sR

0.0578 

0.0327 

r

0.07 

0.04 

R

0.16 

0.09 

XRF Powder Replicate 2 

Material Xbar 

1 2.6495 

2 2.0652 

sx

0.0509 

0.0263 

sr

0.0238 

0.0162 

sR

0.0554 

0.0302 

r

0.07 

0.05 

R

0.15 

0.08 

Figure 15 MgO precision statistics by method with bar chart comparing results to 

current and past ASTM C114 limits and previous studies on chemical analysis precision 

as 1σ, between lab (SR). 

43 
SO3

SO3 

3.7

3.5 

3.5 

3.4 

1 2 3 

X 

X 

X 

X 

X 

X 

X 

X 

X 

MASS FRACTION MASS FRACTION

3.2 

3.2 

3.0 

3.0 

2.8 

2.7 

CEMENT E 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE 

SO3 

4.0

3.5 

3.0 

2.5 

2.0 

X 

X 

X 

X 

X 

X 

X 

X 

X 

1 2 3 

CEMENT F
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

Figure 16 Box plots for SO3 for XRF glass and powder, and reference methods. 

44 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SO3, Cements E, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 3.2318 0.0211 -0.0036 -0.07 1.63 

2 3.2450 0.0182 0.0095 0.18 1.41 

3 3.2867 0.0103 0.0512 0.94 0.80 

4 3.2942 0.0062 0.0587 1.08 0.48 

5 3.2183 0.0133 -0.0171 -0.31 1.03 

6 3.2550 0.0055 0.0195 0.36 0.42 

7 3.1785 0.0086 -0.0570 -1.05 0.66 

8 3.1283 0.0160 -0.1071 -1.97 1.24 

9 3.2813 0.0070 0.0459 0.84 0.54 

Average of cell averages = 3.23547 

Standard Deviation of cell averages = 0.05440 

Repeatability Standard Deviation = 0.01294 

Reproducibility Standard Deviation = 0.05567 

Critical Values h,k = 2.23, 1.73 

SO3, Cements F, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 3.6952 0.0851 0.0130 0.16 2.64 

2 3.6830 0.0306 0.0008 0.01 0.95 

3 3.7183 0.0160 0.0362 0.45 0.50 

4 3.7220 0.0085 0.0399 0.50 0.26 

5 3.6150 0.0122 -0.0672 -0.84 0.38 

6 3.7083 0.0117 0.0262 0.33 0.36 

7 3.7889 0.0098 0.1067 1.33 0.30 

8 3.5050 0.0197 -0.1772 -2.21 0.61 

9 3.7038 0.0099 0.0217 0.27 0.31 

Average of cell averages = 3.68218 

Standard Deviation of cell averages = 0.08024 

Repeatability Standard Deviation = 0.03228 

Reproducibility Standard Deviation = 0.08548 

Critical Values h,k = 2.23, 1.73 

45 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SO3, Cements E, Glass, Rep.2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 3.2390 0.0205 0.0051 0.10 1.49 

2 3.2278 0.0177 -0.0060 -0.11 1.29 

3 3.2883 0.0147 0.0545 1.02 1.07 

4 3.2960 0.0066 0.0621 1.17 0.48 

5 3.2150 0.0187 -0.0189 -0.35 1.36 

6 3.2533 0.0103 0.0195 0.37 0.75 

7 3.1789 0.0094 -0.0550 -1.03 0.68 

8 3.1317 0.0098 -0.1022 -1.92 0.71 

9 3.2747 0.0086 0.0408 0.77 0.63 

Average of cell averages = 3.23386 

Standard Deviation of cell averages = 0.05334 

Repeatability Standard Deviation = 0.01378 

Reproducibility Standard Deviation = 0.05480 

Critical Values h,k = 2.23, 1.73 

SO3, Cements F, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 3.6765 0.0175 0.0074 0.09 0.20 

2 3.5815 0.2541 -0.0876 -1.07 2.97 

3 3.7183 0.0098 0.0492 0.60 0.11 

4 3.7194 0.0072 0.0503 0.61 0.08 

5 3.6133 0.0163 -0.0558 -0.68 0.19 

6 3.7033 0.0082 0.0342 0.42 0.10 

7 3.7898 0.0090 0.1207 1.47 0.10 

8 3.5217 0.0232 -0.1474 -1.79 0.27 

9 3.6980 0.0104 0.0289 0.35 0.12 

Average of cell averages = 3.66910 

Standard Deviation of cell averages = 0.08224 

Repeatability Standard Deviation = 0.08570 

Reproducibility Standard Deviation = 0.11350 

Critical Values h,k = 2.23, 1.73 

46 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SO3, Cements E, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 3.2233 0.0163 0.0412 0.47 0.70 

2 2.9800 0.0110 -0.2021 -2.32 0.47 

3 3.2117 0.0319 0.0295 0.34 1.37 

4 3.1783 0.0147 -0.0038 -0.04 0.63 

5 3.2867 0.0258 0.1045 1.20 1.11 

6 3.2400 0.0522 0.0579 0.66 2.23 

7 3.0967 0.0121 -0.0855 -0.98 0.52 

8 3.2217 0.0133 0.0395 0.45 0.57 

9 3.2667 0.0103 0.0845 0.97 0.44 

10 3.1593 0.0168 -0.0229 -0.26 0.72 

11 3.1392 0.0166 -0.0430 -0.49 0.71 

Average of cell averages = 3.18213 

Standard Deviation of cell averages = 0.08724 

Repeatability Standard Deviation = 0.02334 

Reproducibility Standard Deviation = 0.08980 

Critical Values h,k = 2.34, 1.75 

SO3, Cements F, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 3.7033 0.0121 0.0028 0.02 0.37 

2 3.3900 0.0434 -0.3105 -2.68 1.34 

3 3.6867 0.0393 -0.0138 -0.12 1.21 

4 3.6800 0.0219 -0.0205 -0.18 0.67 

5 3.8067 0.0516 0.1062 0.91 1.59 

6 3.8367 0.0175 0.1362 1.17 0.54 

7 3.7217 0.0232 0.0212 0.18 0.71 

8 3.7517 0.0147 0.0512 0.44 0.45 

9 3.7633 0.0288 0.0628 0.54 0.89 

10 3.6930 0.0205 -0.0075 -0.07 0.63 

11 3.6725 0.0507 -0.0280 -0.24 1.56 

Average of cell averages = 3.70050 

Standard Deviation of cell averages = 0.11606 

Repeatability Standard Deviation = 0.03247 

Reproducibility Standard Deviation = 0.11978 

Critical Values h,k = 2.34, 1.75 

47 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SO3, Cements E, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 3.2317 0.0147 0.0615 0.60 0.64 

2 2.9783 0.0098 -0.1918 -1.87 0.42 

3 3.2017 0.0319 0.0315 0.31 1.38 

4 3.1833 0.0052 0.0132 0.13 0.22 

5 3.2917 0.0256 0.1215 1.18 1.11 

6 3.2333 0.0575 0.0632 0.61 2.49 

7 3.1017 0.0117 -0.0685 -0.67 0.51 

8 3.2267 0.0103 0.0565 0.55 0.45 

9 3.2667 0.0103 0.0965 0.94 0.45 

10 3.1526 0.0143 -0.0175 -0.17 0.62 

11 3.0042 0.0038 -0.1660 -1.62 0.16 

Average of cell averages = 3.17016 

Standard Deviation of cell averages = 0.10274 

Repeatability Standard Deviation = 0.02314 

Reproducibility Standard Deviation = 0.10489 

Critical Values h,k = 2.34, 1.75 

SO3, Cements F, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 3.7133 0.0082 0.0131 0.11 0.24 

2 3.3917 0.0431 -0.3085 -2.62 1.28 

3 3.6883 0.0417 -0.0119 -0.10 1.24 

4 3.6883 0.0256 -0.0119 -0.10 0.76 

5 3.8083 0.0500 0.1081 0.92 1.49 

6 3.8417 0.0147 0.1415 1.20 0.44 

7 3.7183 0.0204 0.0181 0.15 0.61 

8 3.7567 0.0121 0.0565 0.48 0.36 

9 3.7633 0.0250 0.0631 0.54 0.74 

10 3.6924 0.0213 -0.0078 -0.07 0.63 

11 3.6400 0.0614 -0.0602 -0.51 1.83 

Average of cell averages = 3.70022 

Standard Deviation of cell averages = 0.11770 

Repeatability Standard Deviation = 0.03363 

Reproducibility Standard Deviation = 0.12164 

Critical Values h,k = 2.34, 1.75 

48 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

XRF Glass, Replicate 1 

Material Xbar 

1 3.2355 

2 3.6822 

sx

0.0544 

0.0802 

sr

0.0129 

0.0323 

sR

0.0557 

0.0855 

r

0.04 

0.09 

R

0.16 

0.24 

XRF Glass, Replicate 2 

Material Xbar 

1 3.2339 

2 3.6691 

sx

0.0533 

0.0822 

sr

0.0138 

0.0857 

sR

0.0548 

0.1135 

r

0.04 

0.24 

R

0.15 

0.32 

XRF Powder Replicate 1 

Material Xbar 

1 3.1821 

2 3.7005 

sx

0.0872 

0.1161 

sr

0.0233 

0.0325 

sR

0.0898 

0.1198 

r

0.07 

0.09 

R

0.25 

0.34 

XRF Powder Replicate 2 

Material Xbar 

1 3.1702 

2 3.7002 

sx

0.1027 

0.1177 

sr

0.0231 

0.0336 

sR

0.1049 

0.1216 

r

0.06 

0.09 

R

0.29 

0.34 

Figure 17 SO3 precision statistics by method with bar chart comparing results to current 

and past ASTM C114 limits and previous studies on chemical analysis precision as 1σ, 

between lab (SR). 

49 
Na2O

NA2O 

0.2

MASS FRACTION 

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

X 

X 

X 

X 

X 

X 

X 

X 

X 

1 2 3 

CEMENT E
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

NA2O 

0.1 

0.2 X 

X 

0.1 

0.1 

X X 

0.1 

0.1 

0.1 

MASS FRACTION 

X 

X 

X 

0.1 

0.1 

0.1 X X 

1 2 3
 

CEMENT F
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

Figure 18 Box plots for Na2O for XRF glass and powder, and reference methods. 

50 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Na2O, Cements E, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1580 0.0021 0.0035 0.22 0.30 

2 0.1835 0.0083 0.0290 1.78 1.18 

3 0.1350 0.0084 -0.0195 -1.20 1.19 

4 0.1523 0.0025 -0.0022 -0.14 0.36 

5 0.1299 0.0047 -0.0246 -1.51 0.67 

6 0.1702 0.0023 0.0157 0.96 0.33 

7 0.1410 0.0049 -0.0135 -0.83 0.71 

8 0.1519 0.0080 -0.0026 -0.16 1.15 

9 0.1600 0.0141 0.0055 0.34 2.02 

10 0.1632 0.0050 0.0087 0.53 0.71 

Average of cell averages = 0.15448 

Standard Deviation of cell averages = 0.01628 

Repeatability Standard Deviation = 0.00700 

Reproducibility Standard Deviation = 0.01749 

Critical Values h,k = 2.29, 1.74 

Na2O, Cements F, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1503 0.0010 0.0056 0.39 0.17 

2 0.1657 0.0059 0.0210 1.45 0.99 

3 0.1283 0.0075 -0.0164 -1.13 1.27 

4 0.1446 0.0015 -0.0001 -0.01 0.25 

5 0.1211 0.0023 -0.0236 -1.63 0.39 

6 0.1622 0.0037 0.0175 1.21 0.62 

7 0.1338 0.0062 -0.0109 -0.75 1.05 

8 0.1443 0.0124 -0.0004 -0.03 2.10 

9 0.1400 0.0000 -0.0047 -0.32 0.00 

10 0.1567 0.0067 0.0120 0.83 1.14 

Average of cell averages = 0.14470 

Standard Deviation of cell averages = 0.01447 

Repeatability Standard Deviation = 0.00594 

Reproducibility Standard Deviation = 0.01545 

Critical Values h,k = 2.29, 1.74 

51 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Na2O, Cements E, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1593 0.0023 0.0041 0.28 0.47 

2 0.1805 0.0065 0.0253 1.70 1.30 

3 0.1433 0.0052 -0.0119 -0.80 1.03 

4 0.1532 0.0014 -0.0020 -0.13 0.29 

5 0.1298 0.0039 -0.0254 -1.71 0.79 

6 0.1715 0.0031 0.0163 1.10 0.63 

7 0.1425 0.0056 -0.0127 -0.86 1.13 

8 0.1507 0.0087 -0.0045 -0.30 1.73 

9 0.1567 0.0052 0.0015 0.10 1.03 

10 0.1645 0.0039 0.0093 0.63 0.78 

Average of cell averages = 0.15521 

Standard Deviation of cell averages = 0.01484 

Repeatability Standard Deviation = 0.00501 

Reproducibility Standard Deviation = 0.01553 

Critical Values h,k = 2.29, 1.74 

Na2O, Cements F, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1503 0.0008 0.0036 0.27 0.14 

2 0.1682 0.0051 0.0214 1.59 0.85 

3 0.1350 0.0055 -0.0117 -0.87 0.92 

4 0.1441 0.0016 -0.0026 -0.20 0.27 

5 0.1235 0.0027 -0.0233 -1.72 0.45 

6 0.1615 0.0019 0.0148 1.09 0.31 

7 0.1347 0.0062 -0.0121 -0.89 1.04 

8 0.1505 0.0140 0.0038 0.28 2.35 

9 0.1433 0.0052 -0.0034 -0.25 0.87 

10 0.1563 0.0049 0.0096 0.71 0.82 

Average of cell averages = 0.14674 

Standard Deviation of cell averages = 0.01350 

Repeatability Standard Deviation = 0.00594 

Reproducibility Standard Deviation = 0.01455 

Critical Values h,k = 2.29, 1.74 

52 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Na2O, Cements E, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1600 0.0025 0.0010 0.05 0.36 

2 0.1433 0.0052 -0.0156 -0.78 0.72 

3 0.1400 0.0110 -0.0190 -0.94 1.54 

4 0.1633 0.0052 0.0044 0.22 0.72 

5 0.1567 0.0052 -0.0023 -0.11 0.72 

6 0.1767 0.0151 0.0177 0.88 2.11 

7 0.1495 0.0036 -0.0095 -0.47 0.51 

8 0.1750 0.0055 0.0160 0.80 0.77 

9 0.1285 0.0022 -0.0305 -1.52 0.31 

10 0.1967 0.0052 0.0377 1.87 0.72 

Average of cell averages = 0.15896 

Standard Deviation of cell averages = 0.02011 

Repeatability Standard Deviation = 0.00713 

Reproducibility Standard Deviation = 0.02114 

Critical Values h,k = 2.29, 1.74 

Na2O, Cements F, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1570 0.0028 -0.0009 -0.04 0.46 

2 0.1400 0.0000 -0.0179 -0.82 0.00 

3 0.1367 0.0151 -0.0213 -0.97 2.54 

4 0.1700 0.0000 0.0121 0.55 0.00 

5 0.1550 0.0055 -0.0029 -0.13 0.92 

6 0.1767 0.0052 0.0187 0.86 0.87 

7 0.1455 0.0027 -0.0124 -0.57 0.45 

8 0.1817 0.0041 0.0237 1.08 0.69 

9 0.1245 0.0044 -0.0334 -1.53 0.74 

10 0.1925 0.0042 0.0345 1.58 0.71 

Average of cell averages = 0.15795 

Standard Deviation of cell averages = 0.02188 

Repeatability Standard Deviation = 0.00593 

Reproducibility Standard Deviation = 0.02254 

Critical Values h,k = 2.29, 1.74 

53 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Na2O, Cements E, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1623 0.0023 0.0025 0.13 0.29 

2 0.1417 0.0041 -0.0182 -0.92 0.53 

3 0.1400 0.0141 -0.0198 -1.00 1.83 

4 0.1650 0.0055 0.0052 0.26 0.71 

5 0.1600 0.0000 0.0002 0.01 0.00 

6 0.1817 0.0172 0.0218 1.11 2.22 

7 0.1532 0.0025 -0.0067 -0.34 0.32 

8 0.1767 0.0052 0.0168 0.85 0.67 

9 0.1277 0.0043 -0.0321 -1.63 0.56 

10 0.1900 0.0000 0.0302 1.53 0.00 

Average of cell averages = 0.15982 

Standard Deviation of cell averages = 0.01973 

Repeatability Standard Deviation = 0.00774 

Reproducibility Standard Deviation = 0.02096 

Critical Values h,k = 2.29, 1.74 

Na2O, Cements F, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1543 0.0054 -0.0028 -0.13 0.77 

2 0.1383 0.0041 -0.0188 -0.90 0.58 

3 0.1383 0.0133 -0.0188 -0.90 1.90 

4 0.1650 0.0055 0.0079 0.38 0.78 

5 0.1533 0.0052 -0.0038 -0.18 0.74 

6 0.1733 0.0103 0.0162 0.78 1.48 

7 0.1488 0.0039 -0.0083 -0.40 0.55 

8 0.1800 0.0063 0.0229 1.10 0.91 

9 0.1260 0.0046 -0.0311 -1.49 0.66 

10 0.1933 0.0052 0.0362 1.74 0.74 

Average of cell averages = 0.15709 

Standard Deviation of cell averages = 0.02088 

Repeatability Standard Deviation = 0.00699 

Reproducibility Standard Deviation = 0.02183 

Critical Values h,k = 2.29, 1.74 

54 
 

 

 

 

 

 

 

 

 

 

 

 

XRF Glass, Replicate 1 

Material Xbar 

1 0.1545 

2 0.1447 

sx

0.0163 

0.0145 

sr

0.0070 

0.0059 

sR

0.0175 

0.0155 

r

0.02 

0.02 

R

0.05 

0.04 

XRF Glass, Replicate 2 

Material Xbar 

1 0.1552 

2 0.1467 

sx

0.0148 

0.0135 

sr

0.0050 

0.0059 

sR

0.0155 

0.0145 

r

0.01 

0.02 

R

0.04 

0.04 

XRF Powder, Replicate 1 

Material Xbar 

1 0.1590 

2 0.1579 

sx

0.0201 

0.0219 

sr

0.0071 

0.0059 

sR

0.0211 

0.0225 

r

0.02 

0.02 

R

0.06 

0.06 

XRF Powder, Replicate 2 

Material Xbar 

1 0.1598 

2 0.1571 

sx

0.0197 

0.0209 

sr

0.0077 

0.0070 

sR

0.0210 

0.0218 

r

0.02 

0.02 

R

0.06 

0.06 

Figure 19 Na2O precision statistics by method with bar chart comparing results to current 

and past ASTM C114 limits and previous studies on chemical analysis precision as 1σ, 

between lab (SR). 

55 
K2O

K2O 

0.8 

X 

X 

X 

X 

X 

X X 

X 

1 2 3 

MASS FRACTION MASS FRACTION 

0.7 

0.7 

0.6 

0.6 

CEMENT E 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE 

K2O 

1.2 

X 

X 

X 

X 

X 

X 

X 

X 

X 

1 2 3 

1.2 

1.2 

1.1 

1.1 

CEMENT F
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

Figure 20 Box plots for K2O for XRF glass and powder, and reference methods. 

56 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

K2O, Cements E, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.7238 0.0044 -0.0087 -1.06 1.52 

2 0.7383 0.0041 0.0058 0.70 1.43 

3 0.7364 0.0030 0.0039 0.47 1.06 

4 0.7256 0.0032 -0.0070 -0.85 1.14 

5 0.7317 0.0041 -0.0009 -0.11 1.43 

6 0.7400 0.0000 0.0075 0.91 0.00 

7 0.7277 0.0027 -0.0049 -0.59 0.93 

8 0.7326 0.0016 0.0001 0.01 0.55 

9 0.7300 0.0000 -0.0025 -0.31 0.00 

10 0.7218 0.0029 -0.0107 -1.30 1.00 

11 0.7500 0.0000 0.0175 2.12 0.00 

Average of cell averages = 0.73254 

Standard Deviation of cell averages = 0.00824 

Repeatability Standard Deviation = 0.00286 

Reproducibility Standard Deviation = 0.00864 

Critical Values h,k = 2.34, 1.75 

K2O, Cements F, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 1.1612 0.0066 -0.0130 -0.84 1.36 

2 1.1850 0.0055 0.0108 0.69 1.12 

3 1.1794 0.0032 0.0052 0.33 0.65 

4 1.1636 0.0056 -0.0106 -0.68 1.14 

5 1.1817 0.0041 0.0075 0.48 0.83 

6 1.1733 0.0052 -0.0009 -0.06 1.06 

7 1.1665 0.0029 -0.0077 -0.49 0.59 

8 1.1620 0.0047 -0.0122 -0.78 0.96 

9 1.1700 0.0063 -0.0042 -0.27 1.29 

10 1.1602 0.0028 -0.0140 -0.90 0.57 

11 1.2133 0.0052 0.0391 2.51 1.06 

Average of cell averages = 1.17420 

Standard Deviation of cell averages = 0.01561 

Repeatability Standard Deviation = 0.00489 

Reproducibility Standard Deviation = 0.01623 

Critical Values h,k = 2.34, 1.75 

57 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

K2O, Cements E, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.7238 0.0033 -0.0071 -1.16 0.90 

2 0.7350 0.0055 0.0040 0.65 1.49 

3 0.7354 0.0026 0.0045 0.73 0.72 

4 0.7263 0.0048 -0.0046 -0.75 1.30 

5 0.7300 0.0000 -0.0010 -0.16 0.00 

6 0.7350 0.0055 0.0040 0.65 1.49 

7 0.7273 0.0027 -0.0036 -0.59 0.73 

8 0.7326 0.0020 0.0016 0.27 0.54 

9 0.7300 0.0000 -0.0010 -0.16 0.00 

10 0.7218 0.0031 -0.0091 -1.48 0.84 

11 0.7433 0.0052 0.0124 2.01 1.41 

Average of cell averages = 0.73098 

Standard Deviation of cell averages = 0.00616 

Repeatability Standard Deviation = 0.00366 

Reproducibility Standard Deviation = 0.00701 

Critical Values h,k = 2.34, 1.75 

K2O, Cements F, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 1.1615 0.0072 -0.0138 -0.85 1.54 

2 1.1850 0.0055 0.0097 0.60 1.17 

3 1.1786 0.0013 0.0033 0.20 0.27 

4 1.1634 0.0032 -0.0119 -0.73 0.69 

5 1.1867 0.0052 0.0114 0.70 1.10 

6 1.1733 0.0052 -0.0020 -0.12 1.10 

7 1.1708 0.0042 -0.0045 -0.27 0.90 

8 1.1620 0.0043 -0.0133 -0.82 0.92 

9 1.1733 0.0052 -0.0020 -0.12 1.10 

10 1.1585 0.0014 -0.0168 -1.04 0.29 

11 1.2150 0.0055 0.0397 2.45 1.17 

Average of cell averages = 1.17529 

Standard Deviation of cell averages = 0.01621 

Repeatability Standard Deviation = 0.00469 

Reproducibility Standard Deviation = 0.01677 

Critical Values h,k = 2.34, 1.75 

58 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

K2O, Cements E, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.7417 0.0075 0.0044 0.53 1.43 

2 0.7333 0.0052 -0.0039 -0.47 0.98 

3 0.7383 0.0041 0.0011 0.13 0.77 

4 0.7483 0.0041 0.0111 1.34 0.77 

5 0.7367 0.0052 -0.0006 -0.07 0.98 

6 0.7467 0.0052 0.0094 1.14 0.98 

7 0.7287 0.0037 -0.0086 -1.04 0.69 

8 0.7300 0.0000 -0.0072 -0.88 0.00 

9 0.7450 0.0084 0.0078 0.94 1.58 

10 0.7237 0.0051 -0.0135 -1.63 0.96 

Average of cell averages = 0.73724 

Standard Deviation of cell averages = 0.00828 

Repeatability Standard Deviation = 0.00528 

Reproducibility Standard Deviation = 0.00958 

Critical Values h,k = 2.29, 1.74 

K2O, Cements F, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 1.1817 0.0117 -0.0080 -0.37 1.49 

2 1.1800 0.0089 -0.0096 -0.44 1.14 

3 1.1883 0.0075 -0.0013 -0.06 0.96 

4 1.1983 0.0075 0.0087 0.40 0.96 

5 1.1883 0.0075 -0.0013 -0.06 0.96 

6 1.2383 0.0075 0.0487 2.25 0.96 

7 1.1683 0.0055 -0.0213 -0.98 0.70 

8 1.1650 0.0055 -0.0246 -1.14 0.70 

9 1.2100 0.0089 0.0204 0.94 1.14 

10 1.1780 0.0055 -0.0117 -0.54 0.70 

Average of cell averages = 1.18963 

Standard Deviation of cell averages = 0.02165 

Repeatability Standard Deviation = 0.00783 

Reproducibility Standard Deviation = 0.02280 

Critical Values h,k = 2.29, 1.74 

59 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

K2O, Cements E, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.7383 0.0041 0.0014 0.17 0.82 

2 0.7317 0.0041 -0.0053 -0.66 0.82 

3 0.7400 0.0063 0.0031 0.38 1.26 

4 0.7467 0.0052 0.0097 1.22 1.03 

5 0.7383 0.0041 0.0014 0.17 0.82 

6 0.7450 0.0055 0.0081 1.01 1.09 

7 0.7285 0.0036 -0.0084 -1.05 0.71 

8 0.7300 0.0000 -0.0069 -0.87 0.00 

9 0.7467 0.0082 0.0097 1.22 1.63 

10 0.7242 0.0049 -0.0127 -1.59 0.99 

Average of cell averages = 0.73694 

Standard Deviation of cell averages = 0.00800 

Repeatability Standard Deviation = 0.00500 

Reproducibility Standard Deviation = 0.00922 

Critical Values h,k = 2.29, 1.74 

K2O, CementsF, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 1.1833 0.0082 -0.0062 -0.28 0.85 

2 1.1800 0.0110 -0.0095 -0.44 1.14 

3 1.1900 0.0063 0.0005 0.02 0.66 

4 1.2017 0.0098 0.0122 0.56 1.02 

5 1.1883 0.0075 -0.0012 -0.05 0.78 

6 1.2367 0.0052 0.0472 2.17 0.54 

7 1.1698 0.0055 -0.0197 -0.90 0.57 

8 1.1667 0.0052 -0.0228 -1.05 0.54 

9 1.2100 0.0063 0.0205 0.94 0.66 

10 1.1686 0.0205 -0.0209 -0.96 2.13 

Average of cell averages = 1.18951 

Standard Deviation of cell averages = 0.02178 

Repeatability Standard Deviation = 0.00960 

Reproducibility Standard Deviation = 0.02348 

Critical Values h,k = 2.29, 1.74 

60 
 

 

 

 

 

 

 

 

 

 

 

 

 

XRF Glass, Replicate 1 

Material Xbar 

1 0.7325 

2 1.1742 

sx

0.0082 

0.0156 

sr

0.0029 

0.0049 

sR

0.0086 

0.0162 

r

0.01 

0.01 

R

0.02 

0.05 

XRF Glass, Replicate 2 

Material Xbar 

1 0.7310 

2 1.1753 

sx

0.0062 

0.0162 

sr

0.0037 

0.0047 

sR

0.0070 

0.0168 

r

0.01 

0.01 

R

0.02 

0.05 

XRF Powder Replicate 1 

Material Xbar 

1 0.7372 

2 1.1896 

sx

0.0083 

0.0217 

sr

0.0053 

0.0078 

sR

0.0096 

0.0228 

r

0.01 

0.02 

R

0.03 

0.06 

XRF Powder Replicate 2 

Material Xbar 

1 0.7369 

2 1.1895 

sx

0.0080 

0.0218 

sr

0.0050 

0.0096 

sR

0.0092 

0.0235 

r

0.01 

0.03 

R

0.03 

0.07 

Figure 21 K2O precision statistics by method with bar chart comparing results to current 

and past ASTM C114 limits and previous studies on chemical analysis precision as 1σ, 

between lab (SR). 

61 
TiO2

TIO2 

0.2 X 

0.2 X X 

0.2 X X 

0.2 

MASS FRACTION 

X X X 

0.2 

0.2 

0.1 X 

1 2 3
 

CEMENT E
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

TIO2 

0.2

MASS FRACTION 

0.2 

0.2 

0.2 

0.2 

0.2 

X 

X 

X 

X 

X 

X 

X 

X 

X 

1 2 3 

CEMENT F
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

Figure 22 Box plots for TiO2 for XRF glass and powder, and reference methods. 

62 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TiO2 Cements E, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.2280 0.0030 -0.0035 -0.44 0.76 

2 0.2323 0.0050 0.0009 0.11 1.29 

3 0.2350 0.0055 0.0035 0.46 1.40 

4 0.2302 0.0006 -0.0012 -0.16 0.14 

5 0.2469 0.0017 0.0155 1.99 0.43 

6 0.2283 0.0041 -0.0031 -0.40 1.05 

7 0.2217 0.0041 -0.0098 -1.26 1.05 

8 0.2247 0.0014 -0.0068 -0.87 0.35 

9 0.2220 0.0032 -0.0095 -1.22 0.82 

10 0.2350 0.0055 0.0035 0.46 1.40 

11 0.2300 0.0037 -0.0015 -0.19 0.94 

12 0.2433 0.0052 0.0119 1.53 1.32 

Average of cell averages = 0.23145 

Standard Deviation of cell averages = 0.00777 

Repeatability Standard Deviation = 0.00391 

Reproducibility Standard Deviation = 0.00855 

Critical Values h,k = 2.38, 1.76 

TiO2 Cements F, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.2243 0.0026 -0.0019 -0.22 0.80 

2 0.2188 0.0038 -0.0073 -0.89 1.17 

3 0.2317 0.0041 0.0055 0.66 1.26 

4 0.2246 0.0008 -0.0016 -0.19 0.24 

5 0.2396 0.0019 0.0134 1.62 0.57 

6 0.2217 0.0041 -0.0045 -0.54 1.26 

7 0.2200 0.0000 -0.0062 -0.75 0.00 

8 0.2190 0.0021 -0.0072 -0.87 0.65 

9 0.2162 0.0024 -0.0100 -1.21 0.74 

10 0.2350 0.0055 0.0088 1.06 1.70 

11 0.2234 0.0052 -0.0028 -0.34 1.60 

12 0.2400 0.0000 0.0138 1.67 0.00 

Average of cell averages = 0.22618 

Standard Deviation of cell averages = 0.00829 

Repeatability Standard Deviation = 0.00323 

Reproducibility Standard Deviation = 0.00880 

Critical Values h,k = 2.38, 1.76 

63 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TiO2 Cements E, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.2277 0.0024 -0.0037 -0.50 0.61 

2 0.2275 0.0061 -0.0039 -0.52 1.53 

3 0.2383 0.0041 0.0070 0.94 1.03 

4 0.2292 0.0012 -0.0021 -0.28 0.30 

5 0.2418 0.0036 0.0104 1.41 0.90 

6 0.2300 0.0000 -0.0014 -0.18 0.00 

7 0.2217 0.0041 -0.0097 -1.31 1.03 

8 0.2260 0.0021 -0.0054 -0.72 0.53 

9 0.2217 0.0013 -0.0096 -1.30 0.34 

10 0.2333 0.0052 0.0020 0.27 1.30 

11 0.2341 0.0060 0.0027 0.36 1.50 

12 0.2450 0.0055 0.0136 1.84 1.38 

Average of cell averages = 0.23136 

Standard Deviation of cell averages = 0.00742 

Repeatability Standard Deviation = 0.00396 

Reproducibility Standard Deviation = 0.00825 

Critical Values h,k = 2.38, 1.76 

TiO2 Cements F, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.2242 0.0021 -0.0024 -0.31 0.63 

2 0.2237 0.0029 -0.0029 -0.38 0.84 

3 0.2267 0.0052 0.0001 0.02 1.51 

4 0.2247 0.0009 -0.0018 -0.24 0.27 

5 0.2377 0.0042 0.0112 1.49 1.22 

6 0.2250 0.0055 -0.0015 -0.20 1.60 

7 0.2200 0.0000 -0.0065 -0.87 0.00 

8 0.2190 0.0017 -0.0075 -1.00 0.49 

9 0.2164 0.0013 -0.0102 -1.35 0.37 

10 0.2333 0.0052 0.0068 0.90 1.51 

11 0.2259 0.0022 -0.0006 -0.08 0.64 

12 0.2417 0.0041 0.0151 2.01 1.19 

Average of cell averages = 0.22652 

Standard Deviation of cell averages = 0.00753 

Repeatability Standard Deviation = 0.00342 

Reproducibility Standard Deviation = 0.00815 

Critical Values h,k = 2.38, 1.76 

64 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TiO2 Cements E, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.2283 0.0041 -0.0017 -0.44 1.25 

2 0.2300 0.0000 -0.0001 -0.02 0.00 

3 0.2400 0.0000 0.0099 2.49 0.00 

4 0.2300 0.0000 -0.0001 -0.02 0.00 

5 0.2250 0.0055 -0.0051 -1.27 1.68 

6 0.2300 0.0000 -0.0001 -0.02 0.00 

7 0.2300 0.0000 -0.0001 -0.02 0.00 

8 0.2250 0.0055 -0.0051 -1.27 1.68 

9 0.2305 0.0019 0.0004 0.10 0.57 

10 0.2333 0.0052 0.0033 0.82 1.58 

11 0.2272 0.0038 -0.0029 -0.74 1.18 

12 0.2317 0.0026 0.0016 0.40 0.79 

Average of cell averages = 0.23008 

Standard Deviation of cell averages = 0.00399 

Repeatability Standard Deviation = 0.00327 

Reproducibility Standard Deviation = 0.00498 

Critical Values h,k = 2.38, 1.76 

TiO2 Cements F, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.2233 0.0052 0.0018 0.30 1.19 

2 0.2217 0.0041 0.0001 0.02 0.94 

3 0.2367 0.0052 0.0151 2.52 1.19 

4 0.2217 0.0041 0.0001 0.02 0.94 

5 0.2217 0.0075 0.0001 0.02 1.74 

6 0.2250 0.0055 0.0035 0.58 1.26 

7 0.2200 0.0000 -0.0015 -0.26 0.00 

8 0.2100 0.0000 -0.0115 -1.92 0.00 

9 0.2197 0.0012 -0.0019 -0.31 0.28 

10 0.2200 0.0063 -0.0015 -0.26 1.46 

11 0.2187 0.0033 -0.0028 -0.47 0.77 

12 0.2200 0.0000 -0.0015 -0.26 0.00 

Average of cell averages = 0.22153 

Standard Deviation of cell averages = 0.00600 

Repeatability Standard Deviation = 0.00434 

Reproducibility Standard Deviation = 0.00719 

Critical Values h,k = 2.38, 1.76 

65 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TiO2 Cements E, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.2300 0.0000 0.0000 0.01 0.00 

2 0.2300 0.0000 0.0000 0.01 0.00 

3 0.2400 0.0000 0.0100 2.28 0.00 

4 0.2300 0.0000 0.0000 0.01 0.00 

5 0.2233 0.0052 -0.0066 -1.50 1.67 

6 0.2317 0.0041 0.0017 0.39 1.32 

7 0.2300 0.0000 0.0000 0.01 0.00 

8 0.2250 0.0055 -0.0050 -1.12 1.77 

9 0.2282 0.0015 -0.0018 -0.41 0.48 

10 0.2350 0.0055 0.0050 1.14 1.77 

11 0.2263 0.0031 -0.0037 -0.83 1.00 

12 0.2300 0.0000 0.0000 0.01 0.00 

Average of cell averages = 0.22996 

Standard Deviation of cell averages = 0.00441 

Repeatability Standard Deviation = 0.00310 

Reproducibility Standard Deviation = 0.00524 

Critical Values h,k = 2.38, 1.76 

TiO2 Cements F, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.2217 0.0041 0.0004 0.07 1.04 

2 0.2200 0.0000 -0.0013 -0.21 0.00 

3 0.2383 0.0041 0.0171 2.85 1.04 

4 0.2217 0.0041 0.0004 0.07 1.04 

5 0.2183 0.0041 -0.0029 -0.49 1.04 

6 0.2233 0.0052 0.0021 0.35 1.31 

7 0.2200 0.0000 -0.0013 -0.21 0.00 

8 0.2133 0.0052 -0.0079 -1.33 1.31 

9 0.2200 0.0017 -0.0013 -0.21 0.42 

10 0.2217 0.0075 0.0004 0.07 1.91 

11 0.2169 0.0026 -0.0044 -0.74 0.65 

12 0.2200 0.0000 -0.0013 -0.21 0.00 

Average of cell averages = 0.22127 

Standard Deviation of cell averages = 0.00598 

Repeatability Standard Deviation = 0.00394 

Reproducibility Standard Deviation = 0.00698 

Critical Values h,k = 2.38, 1.76 

66 
 

 

 

 

 

 

 

 

 

 

 

XRF Glass, Replicate 1 

Material Xbar sx sr sR r R

1 0.2315 0.0078 0.0039 0.0085 0.01 0.02 

2 0.2262 0.0083 0.0032 0.0088 0.01 0.02 

XRF Glass, Replicate 2 

Material Xbar sx sr sR r R

1 0.2314 0.0074 0.0040 0.0083 0.01 0.02 

2 0.2265 0.0075 0.0034 0.0082 0.01 0.02 

XRF Powder, Replicate 1 

Material Xbar sx sr sR r R

1 0.2301 0.0040 0.0033 0.0050 0.01 0.01 

2 0.2215 0.0060 0.0043 0.0072 0.01 0.02 

XRF Powder, Replicate 2 

Material Xbar sx sr sR r R

1 0.2300 0.0044 0.0031 0.0052 0.01 0.01 

2 0.2213 0.0060 0.0039 0.0070 0.01 0.02 

Figure 23 TiO2 precision statistics by method with bar chart comparing results to current 

and past ASTM C114 limits and previous studies on chemical analysis precision as 1σ, 

between lab (SR). 

67 
P2O5

P2O5 

0.1

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

X 

X 

X 

X 

X 

X 

X 

X 

X 

1 2 3 

MASS FRACTION MASS FRACTION 

CEMENT E 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE 

P2O5 

0.1

0.1 

0.1 

0.1 

0.1 

0.1 

0.1 

X 

X 

X 

X 

X 

X 

X 

X 

X 

1 2 3 

CEMENT F
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

Figure 24 Box plots for P2O5 for XRF glass and powder, and reference methods. 

68 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P2O5, Cements E, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1407 0.0031 0.0044 1.16 1.52 

2 0.1308 0.0017 -0.0055 -1.44 0.84 

3 0.1369 0.0010 0.0006 0.17 0.46 

4 0.1353 0.0025 -0.0010 -0.26 1.23 

5 0.1400 0.0000 0.0037 0.98 0.00 

6 0.1367 0.0008 0.0004 0.10 0.40 

7 0.1395 0.0016 0.0032 0.85 0.80 

8 0.1300 0.0000 -0.0063 -1.66 0.00 

9 0.1367 0.0038 0.0004 0.12 1.86 

Average of cell averages = 0.13629 

Standard Deviation of cell averages = 0.00378 

Repeatability Standard Deviation = 0.00206 

Reproducibility Standard Deviation = 0.00422 

Critical Values h,k = 2.23, 1.73 

P2O5, Cements F, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1367 0.0010 0.0022 0.61 0.51 

2 0.1300 0.0030 -0.0045 -1.27 1.45 

3 0.1340 0.0010 -0.0005 -0.14 0.49 

4 0.1311 0.0028 -0.0034 -0.96 1.38 

5 0.1400 0.0000 0.0055 1.55 0.00 

6 0.1347 0.0005 0.0002 0.05 0.25 

7 0.1370 0.0028 0.0025 0.71 1.35 

8 0.1300 0.0000 -0.0045 -1.27 0.00 

9 0.1371 0.0033 0.0026 0.73 1.61 

Average of cell averages = 0.13450 

Standard Deviation of cell averages = 0.00354 

Repeatability Standard Deviation = 0.00204 

Reproducibility Standard Deviation = 0.00400 

Critical Values h,k = 2.23, 1.73 

69 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P2O5, Cements E, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1397 0.0010 0.0029 0.71 0.59 

2 0.1302 0.0015 -0.0066 -1.64 0.83 

3 0.1368 0.0009 0.0000 -0.01 0.49 

4 0.1373 0.0024 0.0005 0.13 1.35 

5 0.1400 0.0000 0.0032 0.79 0.00 

6 0.1372 0.0008 0.0004 0.09 0.43 

7 0.1393 0.0019 0.0025 0.62 1.05 

8 0.1300 0.0000 -0.0068 -1.68 0.00 

9 0.1408 0.0038 0.0040 0.99 2.15 

Average of cell averages = 0.13681 

Standard Deviation of cell averages = 0.00406 

Repeatability Standard Deviation = 0.00177 

Reproducibility Standard Deviation = 0.00436 

Critical Values h,k = 2.23, 1.73 

P2O5, Cements F, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1372 0.0010 0.0021 0.69 0.52 

2 0.1318 0.0034 -0.0032 -1.06 1.83 

3 0.1344 0.0006 -0.0007 -0.24 0.32 

4 0.1335 0.0025 -0.0015 -0.50 1.31 

5 0.1400 0.0000 0.0049 1.62 0.00 

6 0.1350 0.0013 -0.0001 -0.02 0.68 

7 0.1370 0.0025 0.0019 0.63 1.35 

8 0.1300 0.0000 -0.0051 -1.66 0.00 

9 0.1367 0.0021 0.0017 0.55 1.13 

Average of cell averages = 0.13507 

Standard Deviation of cell averages = 0.00305 

Repeatability Standard Deviation = 0.00187 

Reproducibility Standard Deviation = 0.00349 

Critical Values h,k = 2.23, 1.73 

70 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P2O5, Cements E, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1373 0.0014 0.0005 0.04 0.48 

2 0.1400 0.0000 0.0032 0.25 0.00 

3 0.1333 0.0052 -0.0035 -0.26 1.82 

4 0.1450 0.0055 0.0082 0.63 1.94 

5 0.1400 0.0000 0.0032 0.25 0.00 

6 0.1380 0.0015 0.0012 0.09 0.55 

7 0.1400 0.0000 0.0032 0.25 0.00 

8 0.1000 0.0000 -0.0368 -2.81 0.00 

9 0.1517 0.0010 0.0149 1.14 0.36 

10 0.1375 0.0014 0.0007 0.05 0.49 

11 0.1418 0.0049 0.0050 0.38 1.74 

Average of cell averages = 0.13679 

Standard Deviation of cell averages = 0.01309 

Repeatability Standard Deviation = 0.00283 

Reproducibility Standard Deviation = 0.01334 

Critical Values h,k = 2.34, 1.75 

P2O5, Cements F, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1363 0.0012 -0.0011 -0.10 0.37 

2 0.1400 0.0000 0.0025 0.22 0.00 

3 0.1350 0.0055 -0.0025 -0.22 1.67 

4 0.1417 0.0041 0.0042 0.37 1.24 

5 0.1383 0.0041 0.0009 0.08 1.24 

6 0.1405 0.0044 0.0030 0.27 1.34 

7 0.1400 0.0000 0.0025 0.22 0.00 

8 0.1067 0.0052 -0.0308 -2.72 1.57 

9 0.1538 0.0010 0.0164 1.44 0.30 

10 0.1417 0.0015 0.0042 0.37 0.46 

11 0.1382 0.0022 0.0008 0.07 0.66 

Average of cell averages = 0.13748 

Standard Deviation of cell averages = 0.01132 

Repeatability Standard Deviation = 0.00329 

Reproducibility Standard Deviation = 0.01172 

Critical Values h,k = 2.34, 1.75 

71 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P2O5, Cements E, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1378 0.0010 0.0017 0.14 0.31 

2 0.1400 0.0000 0.0039 0.30 0.00 

3 0.1333 0.0052 -0.0028 -0.21 1.61 

4 0.1433 0.0052 0.0072 0.56 1.61 

5 0.1383 0.0041 0.0023 0.17 1.28 

6 0.1353 0.0037 -0.0008 -0.06 1.16 

7 0.1400 0.0000 0.0039 0.30 0.00 

8 0.1000 0.0000 -0.0361 -2.80 0.00 

9 0.1518 0.0012 0.0158 1.22 0.37 

10 0.1377 0.0018 0.0016 0.12 0.55 

11 0.1392 0.0048 0.0032 0.25 1.51 

Average of cell averages = 0.13608 

Standard Deviation of cell averages = 0.01289 

Repeatability Standard Deviation = 0.00320 

Reproducibility Standard Deviation = 0.01322 

Critical Values h,k = 2.34, 1.75 

P2O5, Cements F, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1365 0.0018 -0.0013 -0.11 0.51 

2 0.1400 0.0000 0.0022 0.19 0.00 

3 0.1333 0.0052 -0.0044 -0.38 1.50 

4 0.1417 0.0041 0.0039 0.34 1.19 

5 0.1400 0.0000 0.0022 0.19 0.00 

6 0.1417 0.0055 0.0039 0.34 1.59 

7 0.1417 0.0041 0.0039 0.34 1.19 

8 0.1067 0.0052 -0.0311 -2.69 1.50 

9 0.1543 0.0012 0.0166 1.43 0.35 

10 0.1415 0.0015 0.0037 0.32 0.44 

11 0.1381 0.0025 0.0004 0.03 0.72 

Average of cell averages = 0.13777 

Standard Deviation of cell averages = 0.01154 

Repeatability Standard Deviation = 0.00343 

Reproducibility Standard Deviation = 0.01196 

Critical Values h,k = 2.34, 1.75 

72 
 

 

 

 

 

 

 

 

 

 

 

 

 

XRF Glass, Replicate 1 

Material Xbar 

1 0.1363 

2 0.1345 

sx

0.0038 

0.0035 

sr

0.0021 

0.0020 

sR

0.0042 

0.0040 

r

0.01 

0.01 

R

0.01 

0.01 

XRF Glass, Replicate 2 

Material Xbar 

1 0.1368 

2 0.1351 

sx

0.0041 

0.0030 

sr

0.0018 

0.0019 

sR

0.0044 

0.0035 

r

0.00 

0.01 

R

0.01 

0.01 

XRF Powder Replicate 1 

Material Xbar 

1 0.1368 

2 0.1375 

sx

0.0131 

0.0113 

sr

0.0028 

0.0033 

sR

0.0133 

0.0117 

r

0.01 

0.01 

R

0.04 

0.03 

XRF Powder Replicate 2 

Material Xbar 

1 0.1361 

2 0.1378 

sx

0.0129 

0.0115 

sr

0.0032 

0.0034 

sR

0.0132 

0.0120 

r

0.01 

0.01 

R

0.04 

0.03 

Figure 25 P2O5 precision statistics by method with bar chart comparing results to current 

and past ASTM C114 limits and previous studies on chemical analysis precision as 1σ, 

between lab (SR). 

73 
Mn2O3

MN2O3 

MASS FRACTION 

0.2 X
 

X
 

0.2 

X
 

X
 

X 0.2 X
 

X
 

0.1 X
 

X
 0.1 

1 2 3
 

CEMENT E
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

MN2O3 

MASS FRACTION 

0.0 X
 

0.0 

0.0 X
 

0.0 X
 X
 

X
 

X
 

0.0 X
 X
 

X
 

0.0 

0.0 

1 2 3
 

CEMENT F
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

Figure 26 Box plots for Mn2O3 for XRF glass and powder, and reference methods. 

74
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Mn2O3, Cements E, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.2033 0.0029 -0.0006 -0.06 1.40 

2 0.2100 0.0000 0.0060 0.61 0.00 

3 0.2100 0.0000 0.0060 0.61 0.00 

4 0.2073 0.0014 0.0034 0.34 0.65 

5 0.2025 0.0009 -0.0015 -0.15 0.42 

6 0.1830 0.0017 -0.0210 -2.12 0.80 

7 0.2117 0.0041 0.0077 0.78 1.95 

Average of cell averages = 0.20397 

Standard Deviation of cell averages = 0.00988 

Repeatability Standard Deviation = 0.00210 

Reproducibility Standard Deviation = 0.01006 

Critical Values h,k = 2.05, 1.70 

Mn2O3, Cements F, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0558 0.0023 0.0008 0.24 0.77 

2 0.0600 0.0000 0.0050 1.51 0.00 

3 0.0533 0.0052 -0.0017 -0.51 1.71 

4 0.0582 0.0015 0.0031 0.95 0.49 

5 0.0544 0.0016 -0.0007 -0.20 0.55 

6 0.0502 0.0004 -0.0049 -1.48 0.14 

7 0.0533 0.0052 -0.0017 -0.51 1.71 

Average of cell averages = 0.05503 

Standard Deviation of cell averages = 0.00329 

Repeatability Standard Deviation = 0.00302 

Reproducibility Standard Deviation = 0.00429 

Critical Values h,k = 2.05, 1.70 

75 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Mn2O3, Cements E, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.2057 0.0016 0.0046 0.84 0.92 

2 0.2067 0.0016 0.0056 1.02 0.92 

3 0.2024 0.0011 0.0014 0.25 0.62 

4 0.2022 0.0012 0.0011 0.20 0.66 

5 0.2013 0.0029 0.0003 0.05 1.62 

6 0.1990 0.0024 -0.0020 -0.36 1.37 

7 0.1900 0.0000 -0.0110 -2.00 0.00 

Average of cell averages = 0.20104 

Standard Deviation of cell averages = 0.00551 

Repeatability Standard Deviation = 0.00178 

Reproducibility Standard Deviation = 0.00574 

Critical Values h,k = 2.05, 1.70 

Mn2O3, Cements F, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0535 0.0005 -0.0035 -0.58 0.39 

2 0.0558 0.0023 -0.0012 -0.19 1.66 

3 0.0537 0.0004 -0.0033 -0.55 0.28 

4 0.0552 0.0004 -0.0018 -0.30 0.29 

5 0.0527 0.0012 -0.0043 -0.72 0.87 

6 0.0581 0.0025 0.0011 0.19 1.78 

7 0.0700 0.0000 0.0130 2.16 0.00 

Average of cell averages = 0.05700 

Standard Deviation of cell averages = 0.00601 

Repeatability Standard Deviation = 0.00139 

Reproducibility Standard Deviation = 0.00615 

Critical Values h,k = 2.05, 1.70 

76 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Mn2O3, Cements E, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.2043 0.0015 0.0005 0.06 0.59 

2 0.2100 0.0000 0.0062 0.72 0.00 

3 0.2100 0.0000 0.0062 0.72 0.00 

4 0.2082 0.0019 0.0043 0.50 0.76 

5 0.2023 0.0033 -0.0016 -0.18 1.30 

6 0.1855 0.0014 -0.0184 -2.14 0.54 

7 0.2067 0.0052 0.0028 0.33 2.02 

Average of cell averages = 0.20385 

Standard Deviation of cell averages = 0.00858 

Repeatability Standard Deviation = 0.00255 

Reproducibility Standard Deviation = 0.00889 

Critical Values h,k = 2.05, 1.70 

Mn2O3, Cements F, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0555 0.0005 0.0012 0.33 0.22 

2 0.0600 0.0000 0.0057 1.60 0.00 

3 0.0517 0.0041 -0.0027 -0.75 1.67 

4 0.0577 0.0018 0.0033 0.94 0.72 

5 0.0535 0.0019 -0.0008 -0.24 0.78 

6 0.0503 0.0012 -0.0040 -1.13 0.50 

7 0.0517 0.0041 -0.0027 -0.75 1.67 

Average of cell averages = 0.05433 

Standard Deviation of cell averages = 0.00355 

Repeatability Standard Deviation = 0.00244 

Reproducibility Standard Deviation = 0.00419 

Critical Values h,k = 2.05, 1.70 

77 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Mn2O3, Cements E, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.2043 0.0015 0.0005 0.06 0.59 

2 0.2100 0.0000 0.0062 0.72 0.00 

3 0.2100 0.0000 0.0062 0.72 0.00 

4 0.2082 0.0019 0.0043 0.50 0.76 

5 0.2023 0.0033 -0.0016 -0.18 1.30 

6 0.1855 0.0014 -0.0184 -2.14 0.54 

7 0.2067 0.0052 0.0028 0.33 2.02 

Average of cell averages = 0.20385 

Standard Deviation of cell averages = 0.00858 

Repeatability Standard Deviation = 0.00255 

Reproducibility Standard Deviation = 0.00889 

Critical Values h,k = 2.05, 1.70 

Mn2O3, Cements F, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0555 0.0005 0.0012 0.33 0.22 

2 0.0600 0.0000 0.0057 1.60 0.00 

3 0.0517 0.0041 -0.0027 -0.75 1.67 

4 0.0577 0.0018 0.0033 0.94 0.72 

5 0.0535 0.0019 -0.0008 -0.24 0.78 

6 0.0503 0.0012 -0.0040 -1.13 0.50 

7 0.0517 0.0041 -0.0027 -0.75 1.67 

Average of cell averages = 0.05433 

Standard Deviation of cell averages = 0.00355 

Repeatability Standard Deviation = 0.00244 

Reproducibility Standard Deviation = 0.00419 

Critical Values h,k = 2.05, 1.70 

78 
 

 

 

 

 

 

 

 

 

 

 

 

XRF Glass, Replicate 1 

Material Xbar 

1 0.2040 

2 0.0550 

sx

0.0099 

0.0033 

sr

0.0021 

0.0030 

sR

0.0101 

0.0043 

r

0.01 

0.01 

R

0.03 

0.01 

XRF Glass, Replicate 2 

Material Xbar 

1 0.2010 

2 0.0570 

sx

0.0055 

0.0060 

sr

0.0018 

0.0014 

sR

0.0057 

0.0061 

r

0.00 

0.00 

R

0.02 

0.02 

XRF Powder Replicate 1 

Material Xbar 

1 0.2039 

2 0.0543 

sx

0.0086 

0.0035 

sr

0.0026 

0.0024 

sR

0.0089 

0.0042 

r

0.01 

0.01 

R

0.02 

0.01 

XRF Powder Replicate 2 

Material Xbar 

1 0.2039 

2 0.0543 

sx

0.0086 

0.0035 

sr

0.0026 

0.0024 

sR

0.0089 

0.0042 

r

0.01 

0.01 

R

0.02 

0.01 

79 
SrO

SRO 

0.13

0.13 

X 

X 

X 

X 

X 

X 

1 1. 2 

MASS FRACTION 

0.12 

0.12 

0.11 

0.11 

0.11 

CEMENT E
 

1 = GLASS, 2 = PRESSED POWDER
 

SRO 

0.08 

0.09 X 

X 

X 

X 

0.07

MASS FRACTION

X 

0.07 

0.07 X 

1 1. 2 

CEMENT F 

1 = GLASS, 2 = PRESSED POWDER 

Figure 27 Box plots for SrO for XRF glass and powder methods. 

80 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SrO, Cements E, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1272 0.0008 -0.0004 -0.10 1.12 

2 0.1300 0.0000 0.0024 0.60 0.00 

3 0.1306 0.0005 0.0030 0.74 0.77 

4 0.1200 0.0000 -0.0076 -1.87 0.00 

5 0.1307 0.0012 0.0031 0.76 1.81 

6 0.1270 0.0006 -0.0005 -0.13 0.94 

Average of cell averages = 0.12757 

Standard Deviation of cell averages = 0.00406 

Repeatability Standard Deviation = 0.00067 

Reproducibility Standard Deviation = 0.00410 

Critical Values h,k = 1.92, 1.68 

SrO, Cements F, Glass, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0853 0.0005 -0.0007 -0.20 0.98 

2 0.0900 0.0000 0.0040 1.13 0.00 

3 0.0884 0.0004 0.0024 0.68 0.78 

4 0.0800 0.0000 -0.0060 -1.72 0.00 

5 0.0875 0.0005 0.0015 0.42 1.04 

6 0.0849 0.0010 -0.0011 -0.31 1.83 

Average of cell averages = 0.08603 

Standard Deviation of cell averages = 0.00351 

Repeatability Standard Deviation = 0.00053 

Reproducibility Standard Deviation = 0.00355 

Critical Values h,k = 1.92, 1.68 

81 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SrO, Cements E, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1275 0.0005 -0.0002 -0.05 0.67 

2 0.1300 0.0000 0.0023 0.56 0.00 

3 0.1307 0.0004 0.0030 0.74 0.50 

4 0.1200 0.0000 -0.0077 -1.88 0.00 

5 0.1308 0.0013 0.0031 0.76 1.63 

6 0.1272 0.0013 -0.0005 -0.12 1.62 

Average of cell averages = 0.12771 

Standard Deviation of cell averages = 0.00410 

Repeatability Standard Deviation = 0.00081 

Reproducibility Standard Deviation = 0.00416 

Critical Values h,k = 1.92, 1.68 

SrO, Cements F, Glass, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0855 0.0005 -0.0005 -0.14 1.18 

2 0.0900 0.0000 0.0040 1.15 0.00 

3 0.0884 0.0004 0.0024 0.70 0.88 

4 0.0800 0.0000 -0.0060 -1.72 0.00 

5 0.0872 0.0008 0.0012 0.34 1.62 

6 0.0849 0.0005 -0.0011 -0.32 1.10 

Average of cell averages = 0.08599 

Standard Deviation of cell averages = 0.00349 

Repeatability Standard Deviation = 0.00046 

Reproducibility Standard Deviation = 0.00351 

Critical Values h,k = 1.92, 1.68 

82 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SrO, Cements E, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1300 0.0006 0.0029 0.64 0.39 

2 0.1300 0.0000 0.0029 0.64 0.00 

3 0.1300 0.0000 0.0029 0.64 0.00 

4 0.1300 0.0000 0.0029 0.64 0.00 

5 0.1200 0.0000 -0.0071 -1.59 0.00 

6 0.1289 0.0005 0.0018 0.40 0.33 

7 0.1198 0.0019 -0.0073 -1.62 1.19 

8 0.1283 0.0041 0.0012 0.27 2.51 

Average of cell averages = 0.12714 

Standard Deviation of cell averages = 0.00450 

Repeatability Standard Deviation = 0.00162 

Reproducibility Standard Deviation = 0.00474 

Critical Values h,k = 2.15, 1.72 

SrO, Cements F, Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0877 0.0005 0.0033 0.49 0.25 

2 0.0900 0.0000 0.0056 0.84 0.00 

3 0.0850 0.0055 0.0006 0.09 2.60 

4 0.0900 0.0000 0.0056 0.84 0.00 

5 0.0700 0.0000 -0.0144 -2.15 0.00 

6 0.0882 0.0002 0.0038 0.56 0.12 

7 0.0843 0.0023 -0.0001 -0.01 1.07 

8 0.0800 0.0000 -0.0044 -0.66 0.00 

Average of cell averages = 0.08440 

Standard Deviation of cell averages = 0.00670 

Repeatability Standard Deviation = 0.00210 

Reproducibility Standard Deviation = 0.00697 

Critical Values h,k = 2.15, 1.72 

83 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SrO, Cements E, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.1302 0.0008 0.0031 0.73 0.40 

2 0.1300 0.0000 0.0029 0.69 0.00 

3 0.1300 0.0000 0.0029 0.69 0.00 

4 0.1300 0.0000 0.0029 0.69 0.00 

5 0.1200 0.0000 -0.0070 -1.65 0.00 

6 0.1287 0.0005 0.0017 0.39 0.24 

7 0.1208 0.0010 -0.0062 -1.46 0.52 

8 0.1267 0.0052 -0.0004 -0.09 2.74 

Average of cell averages = 0.12705 

Standard Deviation of cell averages = 0.00426 

Repeatability Standard Deviation = 0.00188 

Reproducibility Standard Deviation = 0.00460 

Critical Values h,k = 2.15, 1.72 

SrO, Cements F, Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0882 0.0008 0.0031 0.45 0.48 

2 0.0900 0.0000 0.0049 0.72 0.00 

3 0.0883 0.0041 0.0033 0.47 2.63 

4 0.0900 0.0000 0.0049 0.72 0.00 

5 0.0700 0.0000 -0.0151 -2.18 0.00 

6 0.0886 0.0004 0.0036 0.52 0.29 

7 0.0853 0.0014 0.0003 0.04 0.88 

8 0.0800 0.0000 -0.0051 -0.73 0.00 

Average of cell averages = 0.08506 

Standard Deviation of cell averages = 0.00691 

Repeatability Standard Deviation = 0.00155 

Reproducibility Standard Deviation = 0.00705 

Critical Values h,k = 2.15, 1.72 

84 
 

 

 

 

 

 

 

 

 

 

 

 

 

XRF Glass, Replicate 1 

Material Xbar sx sr sR r R

1 0.1276 0.0041 0.0007 0.0041 0.00 0.01 

2 0.0860 0.0035 0.0005 0.0035 0.00 0.01 

XRF Glass, Replicate 2 

Material Xbar sx sr sR r R

1 0.1277 0.0041 0.0008 0.0042 0.00 0.01 

2 0.0860 0.0035 0.0005 0.0035 0.00 0.01 

XRF Powder Replicate 1 

Material Xbar sx sr sR r R

1 0.1271 0.0045 0.0016 0.0047 0.00 0.01 

2 0.0844 0.0067 0.0021 0.0070 0.01 0.02 

XRF Powder Replicate 2 

Material Xbar sx sr sR r R

1 0.1270 0.0043 0.0019 0.0046 0.01 0.01 

2 0.0851 0.0069 0.0016 0.0071 0.00 0.02 

85 
ZnO

ZNO 

0.029 

X 

X 

X 

X 

X 

X 

1 2 3 

MASS FRACTION MASS FRACTION 

0.024 

0.019 

0.014 

0.009 

CEMENT E 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE 

ZNO 

0.029 

0.024 

0.019 

0.014 

0.009 

0.004 

0.000 

X 

X 

X 

X 

X 

X 

1 2 3 

CEMENT F
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

Figure 28 Box plots for ZnO for XRF glass and powder methods. 

86 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ZnO, Cement E, Glass and Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0140 0.0000 0.0001 0.02 0.00 

2 0.0135 0.0005 -0.0004 -0.10 1.16 

3 0.0164 0.0004 0.0025 0.58 0.86 

4 0.0100 0.0000 -0.0039 -0.91 0.00 

5 0.0130 0.0000 -0.0009 -0.21 0.00 

6 0.0100 0.0000 -0.0039 -0.91 0.00 

7 0.0247 0.0007 0.0108 2.51 1.45 

8 0.0105 0.0005 -0.0034 -0.79 1.16 

9 0.0129 0.0008 -0.0010 -0.23 1.62 

10 0.0140 0.0006 0.0001 0.03 1.35 

Average of cell averages = 0.01391 

Standard Deviation of cell averages = 0.00432 

Repeatability Standard Deviation = 0.00047 

Reproducibility Standard Deviation = 0.00434 

Critical Values h,k = 2.29, 1.74 

ZnO, Cement F, Glass and Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0132 0.0004 0.0001 0.02 0.81 

2 0.0127 0.0005 -0.0004 -0.10 1.03 

3 0.0154 0.0004 0.0024 0.59 0.81 

4 0.0100 0.0000 -0.0031 -0.76 0.00 

5 0.0120 0.0000 -0.0011 -0.27 0.00 

6 0.0100 0.0000 -0.0031 -0.76 0.00 

7 0.0234 0.0006 0.0103 2.57 1.15 

8 0.0097 0.0005 -0.0034 -0.85 1.03 

9 0.0121 0.0010 -0.0010 -0.25 1.90 

10 0.0124 0.0006 -0.0007 -0.18 1.27 

Average of cell averages = 0.01307 

Standard Deviation of cell averages = 0.00402 

Repeatability Standard Deviation = 0.00050 

Reproducibility Standard Deviation = 0.00405 

Critical Values h,k = 2.29, 1.74 

87 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ZnO, Cement E, Glass and Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0140 0.0000 0.0001 0.02 0.00 

2 0.0138 0.0004 -0.0001 -0.02 0.91 

3 0.0164 0.0004 0.0025 0.58 0.91 

4 0.0100 0.0000 -0.0039 -0.89 0.00 

5 0.0132 0.0004 -0.0007 -0.17 0.91 

6 0.0100 0.0000 -0.0039 -0.89 0.00 

7 0.0250 0.0005 0.0111 2.53 1.14 

8 0.0107 0.0005 -0.0032 -0.74 1.15 

9 0.0127 0.0008 -0.0012 -0.28 1.69 

10 0.0133 0.0006 -0.0006 -0.15 1.43 

Average of cell averages = 0.01390 

Standard Deviation of cell averages = 0.00438 

Repeatability Standard Deviation = 0.00045 

Reproducibility Standard Deviation = 0.00440 

Critical Values h,k = 2.29, 1.74 

ZnO, Cement F, Glass and Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0132 0.0004 0.0000 0.01 0.90 

2 0.0128 0.0004 -0.0003 -0.07 0.90 

3 0.0153 0.0005 0.0021 0.53 1.14 

4 0.0100 0.0000 -0.0031 -0.77 0.00 

5 0.0120 0.0000 -0.0011 -0.27 0.00 

6 0.0100 0.0000 -0.0031 -0.77 0.00 

7 0.0236 0.0007 0.0105 2.58 1.46 

8 0.0097 0.0005 -0.0035 -0.85 1.14 

9 0.0118 0.0005 -0.0013 -0.32 1.07 

10 0.0128 0.0007 -0.0003 -0.07 1.57 

Average of cell averages = 0.01312 

Standard Deviation of cell averages = 0.00406 

Repeatability Standard Deviation = 0.00045 

Reproducibility Standard Deviation = 0.00408 

Critical Values h,k = 2.29, 1.74 

88 
 

 

 

 

 

 

 

XRF Glass and Powder, Replicate 1 

Material Xbar sx sr sR r R

1 0.0139 0.0043 0.0005 0.0043 0.00 0.01 

2 0.0131 0.0040 0.0005 0.0040 0.00 0.01 

XRF Glass and Powder , Replicate 2 

Material Xbar sx sr sR r R

1 0.0139 0.0044 0.0004 0.0044 0.00 0.01 

2 0.0131 0.0041 0.0005 0.0041 0.00 0.01 

89 
Cr2O3

CR2O3 

0.039 

0.034 

X 

X 

X 

X 

X 

X 

X 

1 2 3 

MASS FRACTION MASS FRACTION 

0.029 

0.024 

0.019 

0.014 

0.009 

CEMENT E 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE 

CR2O3 

0.019 

X 

X 

X 

X 

X 

X 

X 

1 2 3 

0.014 

0.009 

0.004 

0.000 

CEMENT F
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

Figure 29 Box plots for Cr2O3 for XRF glass, powder, and reference methods. 

90 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cr2O3, Cement E, Glass and Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0302 0.0012 0.0026 1.29 1.27 

2 0.0272 0.0004 -0.0004 -0.21 0.44 

3 0.0272 0.0004 -0.0004 -0.19 0.43 

4 0.0275 0.0005 -0.0001 -0.04 0.60 

5 0.0243 0.0008 -0.0033 -1.63 0.89 

6 0.0291 0.0016 0.0016 0.78 1.69 

Average of cell averages = 0.02759 

Standard Deviation of cell averages = 0.00200 

Repeatability Standard Deviation = 0.00092 

Reproducibility Standard Deviation = 0.00217 

Critical Values h,k = 2.92, 1.68 

Cr2O3, Cement F, Glass and Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0135 0.0008 0.0013 1.04 0.99 

2 0.0112 0.0004 -0.0010 -0.79 0.49 

3 0.0139 0.0005 0.0018 1.38 0.61 

4 0.0115 0.0005 -0.0007 -0.53 0.65 

5 0.0108 0.0013 -0.0013 -1.05 1.58 

6 0.0121 0.0010 -0.0001 -0.05 1.22 

Average of cell averages = 0.01218 

Standard Deviation of cell averages = 0.00127 

Repeatability Standard Deviation = 0.00084 

Reproducibility Standard Deviation = 0.00149 

Critical Values h,k = 2.92, 1.68 

91 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cr2O3, Cement E, Glass and Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0305 0.0005 0.0030 1.58 0.79 

2 0.0270 0.0000 -0.0005 -0.27 0.00 

3 0.0270 0.0005 -0.0005 -0.26 0.69 

4 0.0277 0.0008 0.0002 0.08 1.18 

5 0.0247 0.0005 -0.0028 -1.50 0.74 

6 0.0282 0.0012 0.0007 0.36 1.72 

Average of cell averages = 0.02751 

Standard Deviation of cell averages = 0.00190 

Repeatability Standard Deviation = 0.00069 

Reproducibility Standard Deviation = 0.00200 

Critical Values h,k = 2.92, 1.68 

Cr2O3, Cement F, Glass and Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0128 0.0004 0.0007 0.56 0.52 

2 0.0110 0.0006 -0.0011 -0.86 0.80 

3 0.0138 0.0004 0.0017 1.28 0.52 

4 0.0115 0.0005 -0.0006 -0.47 0.69 

5 0.0105 0.0012 -0.0016 -1.24 1.55 

6 0.0131 0.0011 0.0010 0.74 1.40 

Average of cell averages = 

Standard Deviation of cell averages = 

Repeatability Standard Deviation = 

Reproducibility Standard Deviation = 

Critical Values h,k = 2.92, 1.68 

0.01211 

0.00129 

0.00079 

0.00148 

XRF Glass and Powder Replicate 1 

Material Xbar 

1 0.0276 

2 0.0122 

sx

0.0020 

0.0013 

sr

0.0009 

0.0008 

sR

0.0022 

0.0015 

r

0.00 

0.00 

R

0.01 

0.00 

XRF Glass and Powder Replicate 2 

Material Xbar 

1 0.0275 

2 0.0121 

sx

0.0019 

0.0013 

sr

0.0007 

0.0008 

sR

0.0020 

0.0015 

r

0.00 

0.00 

R

0.01 

0.00 

92 
 

Cl

CHLORINE 

0.150 

0.100 

X 

X 

X 

XX 

X 

X 

X 

X 

1 2 3 

MASS FRACTION 

0.050 

0.000 

CEMENT E
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

CHLORINE 

0.050 X 

0.040 

0.030

CTION 

0.000 

0.010 

MASS FRA

0.020

X 

X 

X 

XX 

X 

X 

X 

1 2 3
 

CEMENT F
 

1 = GLASS, 2 = PRESSED POWDER, 3 = REFERENCE
 

Figure 30 Box plots for Cl for XRF glass, powder, and reference methods. 

93 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cl, Cement E, Glass and Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0158 0.0004 0.0008 0.13 0.73 

2 0.0110 0.0006 -0.0040 -0.63 1.14 

3 0.0100 0.0000 -0.0050 -0.79 0.00 

4 0.0105 0.0005 -0.0045 -0.71 0.99 

5 0.0160 0.0006 0.0010 0.15 1.14 

6 0.0268 0.0008 0.0118 1.85 1.38 

Average of cell averages = 0.01502 

Standard Deviation of cell averages = 0.00635 

Repeatability Standard Deviation = 0.00056 

Reproducibility Standard Deviation = 0.00637 

Critical Values h,k = 1.92, 1.68 

Cl, Cement F, Glass and Powder, Rep. 1 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0128 0.0004 0.0016 0.29 0.18 

2 0.0077 0.0005 -0.0036 -0.67 0.23 

3 0.0067 0.0052 -0.0046 -0.85 2.33 

4 0.0072 0.0008 -0.0041 -0.76 0.34 

5 0.0125 0.0008 0.0012 0.23 0.38 

6 0.0208 0.0010 0.0095 1.76 0.47 

Average of cell averages = 0.01127 

Standard Deviation of cell averages = 0.00540 

Repeatability Standard Deviation = 0.00222 

Reproducibility Standard Deviation = 0.00577 

Critical Values h,k = 1.92, 1.68 

94 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cl, Cement E, Glass and Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0162 0.0004 0.0009 0.13 0.45 

2 0.0117 0.0008 -0.0036 -0.56 0.91 

3 0.0100 0.0000 -0.0053 -0.81 0.00 

4 0.0107 0.0008 -0.0046 -0.71 0.91 

5 0.0158 0.0008 0.0005 0.08 0.84 

6 0.0274 0.0017 0.0121 1.87 1.86 

Average of cell averages = 0.01530 

Standard Deviation of cell averages = 0.00650 

Repeatability Standard Deviation = 0.00090 

Reproducibility Standard Deviation = 0.00655 

Critical Values h,k = 1.92, 1.68 

Cl, Cement F, Glass and Powder, Rep. 2 

Laboratory 

Number 

Cell 

Mean 

Cell 

SD d h k

1 0.0130 0.0000 0.0015 0.27 0.00 

2 0.0082 0.0004 -0.0033 -0.60 0.19 

3 0.0067 0.0052 -0.0048 -0.87 2.38 

4 0.0073 0.0005 -0.0042 -0.75 0.24 

5 0.0123 0.0005 0.0008 0.15 0.24 

6 0.0215 0.0009 0.0100 1.80 0.41 

Average of cell averages = 0.01150 

Standard Deviation of cell averages = 0.00556 

Repeatability Standard Deviation = 0.00217 

Reproducibility Standard Deviation = 0.00591 

Critical Values h,k = 1.92, 1.68 

XRF Glass and Powder Replicate 1 

Material Xbar sx sr sR r R

1 0.0150 0.0063 0.0006 0.0064 0.00 0.02 

2 0.0113 0.0054 0.0022 0.0058 0.01 0.02 

XRF Glass and Powder Replicate 2 

Material Xbar sx sr sR r R

1 0.0153 0.0065 0.0009 0.0066 0.00 0.02 

2 0.0115 0.0056 0.0022 0.0059 0.01 0.02 

95 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix A. Request for Participants Letter.

ASTM Round Robin for C01.23.03 Task Force Group 

Instructions 

The ASTM C01.23.03 task force group wishes to thank you for agreeing to be a part of the Round Robin 

(RR) which will define the precision and, hopefully, the bias of the X-ray fluorescence spectrometric 

(XRF) elemental analysis of hydraulic cements. Many versions of an XRF analytical procedure exist as set 

up and used by cement producers, cement users, commercial laboratories and general users. Generally, all 

parties are interested in producing a high quality, accurate analysis for industrial use. The Cement and 

Concrete Laboratory (CCRL) in cooperation with the ASTM Inter-Laboratory Study (ILS) has agreed to 

provide samples of Portland cement (meeting ASTM C150 guidelines) and various other mixtures of 

Portland cement and other compounds for the XRF analysis in this RR. Statistical analysis of the returned 

data will be compiled for the task force by NIST statisticians. 

Method 

The “10th Preliminary Draft” of “Standard Test Method for the Major and Minor Elements in Cement by XRay Fluorescence” produced by the task force group is available by down loading from a special webbased program set up by CCRL for the specific purpose of this RR. The method is specifically, a 

generalized approach to the XRF analysis of hydraulic cements, and is subject to revision when data is 

collected to show any confusion, indecision, or conflicts in the “10th Preliminary Draft.” There have 

already been “lots” of “discussions” and changes to the method, and there may be more changes. Some 

have already been suggested by task force members and other interested parties that may be implemented 

when actual data begins to roll in. 

In the interest of collecting data from the RR before I go to a nursing home, we should start to collect now. 

Again the method is a generalized approach to XRF analysis of hydraulic cements, and the individual 

Standard Operating Procedures (SOP) used in your individual laboratory should fit in the generalized 

guidelines. Please follow the method as closely as possible so that your specific laboratory data can be 

utilized for comparison to all the other data. 

The method actually has two preparation schemes for presentation to the XRF, fused disk and pressed 

powder. If your laboratory has the capability to do both preparation methods, please, please, do so. 

In Part 4.2.2 of the “10th Preliminary Draft,” it specifically states “Part 2 of the method is not generally 

applicable to the analysis of blended cements, including those blended with silica fume, limestone, 

pozzolans, fly ash, slag, and any combination thereof higher than the amounts of additions found in 

Portland cements meeting Specification C 150.” For the purposes of this RR data collection only, 

ignore this statement and run pressed pellets, if you have the capability, for comparison with the 

fused disk preparation. We need to establish the precision and truth of this statement and a comparison 

will determine if this statement is correct and help establish precision data on the pressed pellet mixtures by 

XRF. 

96 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Data Return 

The data return for this RR is by accessing the CCRL web site for examination and determining what needs 

to be reported. It will be much easier if you report data on-line in a similar fashion as CCRL data is now 

reported; the statistician will love you. If you are unable to report data on-line, fill out the data and send to 

me (by FAX) and I’ll key punch it in for your data return. By making a request to CCRL, on this RR you 

can obtain more sample, if you are going to do samples by pressed powder Ask for three vials of about 30 

grams on each of the RR samples for powder prep and one sample vial if sample prep is fused disk only. 

If you have the capability, we ask you to run powder prep and fused pellet on the two samples being mailed 

from CCRL. So for instance, there will be Sample A fused pellet data return and Sample A pressed pellet 

data return; then Sample B fused pellet data return and Sample B pressed pellet data return. There will be 

potentially 4 data return sheets for each sample in the mailing from CCRL. The first two samples mailed 

from CCRL are guaranteed to be C150 Portland Cements. The next two to four mailings of sample pairs 

will be mixtures. 

If you can’t do fused pellets, please participate in the pressed pellet RR, and conversely if you can’t do 

pressed pellets, do fused pellets. All data will be used and gratefully appreciated by the task force group 

and task group chairman. We estimate that this RR study will take a minimum of 11⁄2 years to 21⁄2 years, a 

mere moment in the large ASTM scheme of things, but the data will hopefully live forever. 

1. The section at the top should be filled out for company and individual returning the data, but, in general, 

no data will be identified with the lab unless you wish it to be. This ID is in case we have to contact you to 

clear up some misunderstanding or finger trouble with the data entry. 

2. Please give as much data on the Fusion Bead preparation as possible. Flux composition, Non-wetting 

agent, etc. For the Pressed Pellet, as much info as possible, Binder composition, Grinding aid and etc. 

3. Look at the return data sheet, what is intended here is to make on Day 1, three pellets: fusion and/or 

pressed pellets, and analyze each pellet twice, then report on the properly identified data sheets. Day 2 of 

your choosing, make three pellets: fusion and/or pressed pellets, and run each one twice, and report results 

on the proper data return sheets. 

4. If possible (and only if possible) on your instrument, give the raw element intensities and/or raw 

background intensities before calculations and applied corrections. In the case of each element you only 

need to answer the Calibration/correction model question once, not every time on each prep. 

97 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.	 LOI should be run and reported each sample prep day. Insoluble Residue and Free Lime need 

only to be run once, each prep day and only if the sufficient data is returned for the XRF data. The 

RR is primarily an XRF RR; the other data at the end of the CCRL data return will be used if 

needed. 

6. Data should be reported to the CCRL web site with one more significant digit than the smallest 

uncertainty (or standard deviation) value of your best standard elemental value for the element being 

reported back to CCRL. Report determined values no later than three (3) months after receipt of 

samples in your laboratory. (i. e., SRM 1880a has a certified value for CaO of 63.83% +/- 0.46, report 

to three decimals for CaO unless you have lower values on reference materials that were used. ZnO is 

certified at 0.005% +/- 0.001, so report to four decimals in weight percent, unless you have used 

reference standards which have a lower +/- values.) 

LeRoy Jacobs 

ASTM C01.23.03 Task Force Group Chairman 

Wyoming Analytical Lab, Inc. 

1511 Washington Ave. 

Golden, CO 80401 

Ph (303) 278-2446 

FAX (303) 278-2439 

e:mail walxray@aol.com 

98 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix B. XRF Glass Summary by Material and Replicate.

Analyte Material Xbar sx sr sR r R n 

CaO 1 62.4493 0.4181 0.0843 0.4252 0.24 1.19 8 

2 63.2911 0.235 0.0879 0.2484 0.25 0.7 

1 62.4455 0.3861 0.1162 0.4004 0.33 1.12 

2 63.3026 0.261 0.0946 0.275 0.27 0.77 

SiO2 1 20.5726 0.1682 0.0616 0.1773 0.17 0.5 9 

2 18.841 0.1457 0.0508 0.1529 0.14 0.43 

1 20.5816 0.1796 0.0587 0.1874 0.16 0.52 

2 18.857 0.1492 0.0502 0.1561 0.14 0.44 

Al2O3 1 4.445 0.0826 0.0286 0.0866 0.08 0.24 10 

2 5.3365 0.0624 0.0275 0.0672 0.08 0.19 

1 4.4443 0.0765 0.0244 0.0797 0.07 0.22 

2 5.3285 0.0614 0.0254 0.0656 0.07 0.18 

Fe2O3 1 2.8796 0.0409 0.0078 0.0415 0.02 0.12 10 

2 2.3715 0.0384 0.0148 0.0407 0.04 0.11 

1 2.8854 0.0368 0.0092 0.0378 0.03 0.11 

2 2.3794 0.0338 0.0092 0.0348 0.03 0.1 

SO3 1 3.2355 0.0544 0.0129 0.0557 0.04 0.16 9 

2 3.6822 0.0802 0.0323 0.0855 0.09 0.24 

1 3.2339 0.0533 0.0138 0.0548 0.04 0.15 

2 3.6691 0.0822 0.0857 0.1135 0.24 0.32 

MgO 1 2.5645 0.0172 0.0132 0.021 0.04 0.06 9 

2 2.1092 0.0161 0.0095 0.0183 0.03 0.05 

1 2.5647 0.0184 0.0114 0.0211 0.03 0.06 

2 2.1105 0.0143 0.0101 0.017 0.03 0.05 

Na2O 1 0.1545 0.0163 0.007 0.0175 0.02 0.05 10 

2 0.1447 0.0145 0.0059 0.0155 0.02 0.04 

1 0.1552 0.0148 0.005 0.0155 0.01 0.04 

2 0.1467 0.0135 0.0059 0.0145 0.02 0.04 

K2O 1 0.7325 0.0082 0.0029 0.0086 0.01 0.02 11 

2 1.1742 0.0156 0.0049 0.0162 0.01 0.05 

1 0.731 0.0062 0.0037 0.007 0.01 0.02 

2 1.1753 0.0162 0.0047 0.0168 0.01 0.05 

TiO2 1 0.2315 0.0078 0.0039 0.0085 0.01 0.02 12 

2 0.2262 0.0083 0.0032 0.0088 0.01 0.02 

1 0.2314 0.0074 0.004 0.0083 0.01 0.02 

2 0.2265 0.0075 0.0034 0.0082 0.01 0.02 

99 
 

 

 

 

 

Analyte (continued) Material Xbar sx sr sR r R n 

P2O5 1 0.1363 0.0038 0.0021 0.0042 0.01 0.01 9 

2 0.1345 0.0035 0.002 0.004 0.01 0.01 

1 0.1368 0.0041 0.0018 0.0044 0 0.01 

2 0.1351 0.003 0.0019 0.0035 0.01 0.01 

Mn2O3 1 0.204 0.0099 0.0021 0.0101 0.01 0.03 7 

2 0.055 0.0033 0.003 0.0043 0.01 0.01 

1 0.201 0.0055 0.0018 0.0057 0 0.02 

2 0.057 0.006 0.0014 0.0061 0 0.02 

SrO 1 0.1276 0.0041 0.0007 0.0041 0 0.01 6 

2 0.086 0.0035 0.0005 0.0035 0 0.01 

1 0.1277 0.0041 0.0008 0.0042 0 0.01 

2 0.086 0.0035 0.0005 0.0035 0 0.01 

ZnO 1 0.0139 0.0043 0.0005 0.0043 0 0.01 10 

glass and powder 2 0.0131 0.004 0.0005 0.004 0 0.01 

Cr2O3 1 0.0276 0.002 0.0009 0.0022 0 0.01 6 

glass and powder 2 0.0122 0.0013 0.0008 0.0015 0 0 

Cl 6 

glass and powder 

100 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix C. XRF Powder Summary by Material and Replicate.

Analyte Material Xbar n sx sr sR r R 

CaO 1 62.6901 0.1602 0.1058 0.1871 0.3 0.52 9 

2 63.7063 0.3184 0.138 0.3424 0.39 0.96 

1 62.7128 0.1569 0.1617 0.2154 0.45 0.6 

2 63.7236 0.3305 0.133 0.3521 0.37 0.99 

SiO2 1 20.5576 0.1928 0.0621 0.201 0.17 0.56 11 

2 19.1546 0.2818 0.0497 0.2854 0.14 0.8 

1 20.575 0.1878 0.062 0.1961 0.17 0.55 

2 19.1653 0.2976 0.0578 0.3022 0.16 0.85 

Al2O3 1 4.5251 0.1019 0.0235 0.1042 0.07 0.29 10 

2 5.1185 0.0968 0.0252 0.0995 0.07 0.28 

1 4.5154 0.0882 0.0234 0.0907 0.07 0.25 

2 5.1275 0.0971 0.0247 0.0997 0.07 0.28 

Fe2O3 1 2.9215 0.0409 0.014 0.0428 0.04 0.12 10 

2 2.3874 0.0446 0.0127 0.0461 0.04 0.13 

1 2.9208 0.0363 0.0133 0.0383 0.04 0.11 

2 2.3885 0.0465 0.0133 0.0481 0.04 0.13 

SO3 1 3.1821 0.0872 0.0233 0.0898 0.07 0.25 11 

2 3.7005 0.1161 0.0325 0.1198 0.09 0.34 

1 3.1702 0.1027 0.0231 0.1049 0.06 0.29 

2 3.7002 0.1177 0.0336 0.1216 0.09 0.34 

MgO 1 2.6521 0.0528 0.0259 0.0578 0.07 0.16 12 

2 2.0619 0.0297 0.0152 0.0327 0.04 0.09 

1 2.6495 0.0509 0.0238 0.0554 0.07 0.15 

2 2.0652 0.0263 0.0162 0.0302 0.05 0.08 

Na2O 1 0.159 0.0201 0.0071 0.0211 0.02 0.06 10 

2 0.1579 0.0219 0.0059 0.0225 0.02 0.06 

1 0.1598 0.0197 0.0077 0.021 0.02 0.06 

2 0.1571 0.0209 0.007 0.0218 0.02 0.06 

K2O 1 0.7372 0.0083 0.0053 0.0096 0.01 0.03 10 

2 1.1896 0.0217 0.0078 0.0228 0.02 0.06 

1 0.7369 0.008 0.005 0.0092 0.01 0.03 

2 1.1895 0.0218 0.0096 0.0235 0.03 0.07 

TiO2 1 0.2301 0.004 0.0033 0.005 0.01 0.01 12 

2 0.2215 0.006 0.0043 0.0072 0.01 0.02 

1 0.23 0.0044 0.0031 0.0052 0.01 0.01 

2 0.2213 0.006 0.0039 0.007 0.01 0.02 

101 
 

 

 

 

 

Analyte (continued) Material Xbar sx sr sR r R n 

P2O5 1 0.1368 0.0131 0.0028 0.0133 0.01 0.04 11 

2 0.1375 0.0113 0.0033 0.0117 0.01 0.03 

1 0.1361 0.0129 0.0032 0.0132 0.01 0.04 

2 0.1378 0.0115 0.0034 0.012 0.01 0.03 

Mn2O3 1 0.2039 0.0086 0.0026 0.0089 0.01 0.02 7 

2 0.0543 0.0035 0.0024 0.0042 0.01 0.01 

1 

2 

SrO 1 0.1271 0.0045 0.0016 0.0047 0 0.01 8 

2 0.0844 0.0067 0.0021 0.007 0.01 0.02 

1 0.127 0.0043 0.0019 0.0046 0.01 0.01 

2 0.0851 0.0069 0.0016 0.0071 0 0.02 

102 
 

 

 

 

 

 

 

 

Appendix D. Raw Data by Analyte.

Data by oxide after initial outlier removal for SiO2, Al2O3, Fe2O3, CaO, MgO, SO3, Na2O, K2O, TiO2, and 

Cl. Data are organized with the XRF-glass results to the left and XRF-powder to the right. A lab identifier 

is provided in the first column of each preparation method and the six replicate measurements for that lab 

and analyte for duplicate 1 and then duplicate two. Duplicate measurements represent a repeat 

measurement on the same specimen. The final column labeled cement indicates cement E (1) or cement F 

(2). Since outliers were evaluated on an analyte-by analyte basis, a specific lab designation may not be the 

same lab across all analytes. For example, if lab 1 had a high between-lab precision for Al2O3, its data 

were removed and the labs reordered so no gap in the numbering existed. 

SiO2

SiO2: Glass Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 20.225 20.295 

1 20.458 20.489 

1 20.489 20.514 

1 20.447 20.469 

1 20.495 20.54 

1 20.59 20.653 

2 20.825 20.605 

2 20.568 20.337 

2 20.728 20.615 

2 20.337 20.475 

2 20.244 20.22 

2 20.558 20.681 

3 20.81 20.91 

3 20.74 20.85 

3 20.83 20.81 

3 20.82 20.84 

3 20.76 20.83 

3 20.86 20.99 

4 20.328 20.317 

4 20.32 20.292 

4 20.302 20.2654 

4 20.213 20.218 

4 20.253 20.273 

4 20.238 20.24 

5 20.457 20.505 

5 20.476 20.523 

5 20.507 20.464 

5 20.519 20.544 

5 20.525 20.51 

5 20.514 20.484 

6 20.69 20.69 

6 20.63 2064 

6 20.72 20.71 

6 20.71 20.71 

6 20.68 20.68 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

SiO2: Powder Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 20.74 

1 20.6 

1 20.58 

1 20.69 

1 20.66 

1 20.61 

2 20.88 

2 20.83 

2 20.77 

2 20.91 

2 20.82 

2 20.81 

3 21.08 

3 21.12 

3 21.45 

3 20.56 

3 19.78 

3 20.26 

4 20.73 

4 20.7 

4 20.71 

4 20.76 

4 20.75 

4 20.74 

5 20.33 

5 20.37 

5 20.43 

5 20.45 

5 20.47 

5 20.41 

6 20.64 

6 20.75 

6 20.61 

6 20.54 

6 20.62 

20.73 1 

20.72 1 

20.63 1 

20.69 1 

20.72 1 

20.67 1 

20.87 1 

20.88 1 

20.78 1 

20.89 1 

20.75 1 

20.76 1 

21.14 1 

21.14 1 

21.43 1 

20.64 1 

19.81 1 

20.38 1 

20.81 1 

20.69 1 

20.74 1 

20.79 1 

20.78 1 

20.75 1 

20.29 1 

20.39 1 

20.38 1 

20.52 1 

20.49 1 

20.44 1 

20.62 1 

20.75 1 

20.66 1 

20.57 1 

20.64 1 

103 
6 20.72 20.73 

7 20.71 20.64 

7 20.69 20.69 

7 20.64 20.65 

7 20.6 20.67 

7 20.72 20.62 

7 20.77 20.74 

8 20.47 20.52 

8 20.55 20.54 

8 20.56 20.54 

8 20.55 20.48 

8 20.52 20.52 

8 20.53 20.5 

9 20.745 20.7473 

9 20.699 20.711 

9 20.609 20.628 

9 20.819 20.833 

9 20.854 20.847 

9 20.686 20.693 

10 21.28 20.62 

10 20.59 20.81 

10 20.77 20.62 

10 21.32 20.64 

10 20.68 20.84 

10 20.75 20.59 

11 20.479 20.462 

11 20.495 20.489 

11 20.453 20.446 

11 20.472 20.491 

11 20.492 20.49 

11 20.482 20.475 

12 21.47 21.43 

12 21.45 21.47 

12 21.46 21.43 

12 21.38 21.43 

12 21.39 21.4 

12 21.42 21.43 

1 18.724 18.773 

1 18.745 18.815 

1 18.783 18.814 

1 18.607 18.666 

1 18.812 18.802 

1 18.902 18.956 

2 18.759 18.661 

2 18.831 18.765 

2 18.822 18.776 

2 19.13 18.975 

2 19.003 18.96 

2 18.802 18.807 

3 19 18.98 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

6 

7 

7 

7 

7 

7 

7 

8 

8 

8 

8 

8 

8 

9 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

11 

11 

11 

11 

11 

11 

12 

12 

12 

12 

12 

12 

13 

13 

13 

13 

13 

13 

14 

14 

14 

14 

14 

14 

1 

20.57 20.55 1 

20.78 20.86 1 

20.88 20.89 1 

20.99 20.98 1 

20.69 20.69 1 

20.89 20.88 1 

20.82 20.83 1 

20.48 20.5 1 

20.52 20.56 1 

20.47 20.49 1 

20.56 20.53 1 

20.56 20.57 1 

20.57 20.56 1 

20.36 20.38 1 

20.37 20.4 1 

20.3 20.3 1 

20.24 20.22 1 

20.34 20.36 1 

20.4 20.39 1 

20.48 20.5 1 

20.49 20.5 1 

20.45 20.49 1 

20.43 20.44 1 

20.53 20.54 1 

20.52 20.56 1 

20.8 20.79 1 

20.71 20.72 1 

20.76 20.77 1 

20.78 20.76 1 

20.68 20.69 1 

20.73 20.73 1 

20.4 20.4 1 

20.43 20.46 1 

20.47 20.47 1 

20.34 20.31 1 

20.39 20.42 1 

20.42 20.4 1 

20.856 20.868 1 

20.883 20.934 1 

21.053 21.065 1 

20.795 20.819 1 

20.852 20.859 1 

20.775 20.803 1 

20.195 20.39 1 

20.36 20.375 1 

20.335 20.3 1 

20.165 20.395 1 

20.39 20.385 1 

20.305 20.275 1 

19.05 19.06 2 

104 
3 18.89 18.93 

3 18.98 18.96 

3 18.92 18.96 

3 18.97 18.97 

3 18.89 19.05 

4 18.583 18.635 

4 18.594 18.597 

4 18.531 18.548 

4 18.549 18.532 

4 18.564 18.526 

4 18.533 18.55 

5 18.787 18.807 

5 18.799 18.836 

5 18.824 18.888 

5 18.878 18.863 

5 18.825 18.897 

5 18.838 18.797 

6 19.05 19.03 

6 18.99 18.99 

6 19.09 19.05 

6 19 19.02 

6 19 19 

6 19.01 19.04 

7 18.89 18.89 

7 18.92 18.93 

7 18.87 18.99 

7 18.92 19.02 

7 18.97 18.97 

7 18.96 19.01 

8 18.78 18.77 

8 18.79 18.76 

8 18.78 18.83 

8 18.75 18.76 

8 18.79 18.79 

8 18.81 18.83 

9 18.985 18.967 

9 18.942 18.953 

9 18.904 18.927 

9 19.085 19.074 

9 18.998 18.994 

9 19.055 19.062 

10 18.94 18.97 

10 19.01 19.03 

10 18.92 18.86 

10 18.92 18.97 

10 19.01 19 

10 18.89 18.89 

11 18.753 18.758 

11 18.79 18.791 

11 18.804 18.771 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

5 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

6 

7 

7 

7 

7 

7 

7 

8 

8 

8 

8 

8 

8 

9 

9 

9 

19.07 19.06 2 

19.07 19.05 2 

19.03 19.14 2 

19.03 19.01 2 

19.04 19.05 2 

19.25 19.24 2 

19.2 19.16 2 

19.21 19.21 2 

19.13 19.15 2 

19.13 19.13 2 

19.03 18.97 2 

19.23 19.26 2 

19.1 18.96 2 

19.18	 19.29 2 

19 19.01 2 

19.3 19.38 2 

19.23 19.3 2 

19.16 19.14 2 

19.12 19.14 2 

19.03 19.05 2 

19.14 19.15 2 

19.04 19.06 2 

19.05 19.07 2 

18.82 18.77 2 

18.87 18.83 2 

18.82 18.84 2 

18.93 18.91 2 

18.89 18.8 2 

18.88 18.89 2 

19.15 19.16 2 

19.23 19.35 2 

19.17 19.17 2 

19.13 19.15 2 

19.06 19.18 2 

19.11 19.12 2 

19.38 19.38 2 

19.29 19.33 2 

19.29 19.28 2 

19.32 19.34 2 

19.34 19.36 2 

19.19 19.21 2 

19.11 19.08 2 

19.02	 19.02 2 

19 19.05 2 

19.08 19.05 2 

19.05 19.06 2 

19.06 19.03 2 

19.18 19.16 2 

19.11 19.14 2 

19.16 19.16 2 

105 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11 18.767 18.714 2 

11 18.689 18.706 2 

11 18.746 18.73 2 

12 19.76 19.66 2 

12 19.76 19.73 2 

12 19.7 19.75 2 

12 19.67 19.7 2 

12 19.68 19.61 2 

12 19.65 19.71 2 

9 

9 

9 

10 

10 

10 

10 

10 

10 

11 

11 

11 

11 

11 

11 

12 

12 

12 

12 

12 

12 

13 

13 

13 

13 

13 

13 

14 

14 

14 

14 

14 

14 

19.14 19.16 2 

19.05 19.06 2 

19.16 19.16 2 

18.72 18.75 2 

18.72 18.74 2 

18.75 18.77 2 

18.8 18.82 2 

18.75 18.78 2 

18.74 18.77 2 

19.6 19.61 2 

19.51 16.61 2 

19.56 19.58 2 

19.58 19.58 2 

19.49 19.5 2 

19.55 19.55 2 

19.34 19.3 2 

19.34 19.32 2 

19.38 19.34 2 

19.3 19.29 2 

19.26 19.27 2 

19.29 19.26 2 

19.704 19.713 2 

19.58 19.585 2 

19.569 19.564 2 

19.367 19.38 2 

19.406 19.419 2 

19.515 19.519 2 

19.885 19.895 2 

19.85 20.015 2 

19.785 19.83 2 

19.865 19.91 2 

19.865 19.995 2 

19.795 19.815 2 

106 
 

Al2O3

Al2O3: Glass Preparation Al2O3: Powder Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 4.355 4.366 

1 4.402 4.411 

1 4.403 4.403 

1 4.386 4.393 

1 4.418 4.428 

1 4.431 4.435 

2 4.678 4.654 

2 4.655 4.562 

2 4.624 4.598 

2 4.533 4.547 

2 4.578 4.575 

2 4.588 4.59 

3 4.51 4.49 

3 4.45 4.51 

3 4.49 4.49 

3 4.51 4.49 

3 4.49 4.47 

3 4.53 4.51 

4 4.4479 4.4557 

4 4.4293 4.4243 

4 4.4262 4.4341 

4 4.4265 4.4148 

4 4.4374 4.4326 

4 4.4168 4.4159 

5 4.512 4.505 

5 4.448 4.483 

5 4.462 4.494 

5 4.498 4.464 

5 4.463 4.477 

5 4.504 4.481 

6 4.42 4.43 

6 4.46 4.47 

6 4.45 4.45 

6 4.43 4.41 

6 4.46 4.44 

6 4.45 4.45 

7 4.34 4.31 

7 4.27 4.25 

7 4.33 4.3 

7 4.29 4.33 

7 4.27 4.25 

7 4.31 4.34 

8 4.468 4.4651 

8 4.4942 4.5033 

8 4.4654 4.459 

8 4.4998 4.5137 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

Lab Duplicate 1 Duplicate 2 Cement 

1
 

1
 

1
 

1
 

1
 

1
 

2
 

2
 

2
 

2
 

2
 

2
 

3
 

3
 

3
 

3
 

3
 

3
 

4
 

4
 

4
 

4
 

4
 

4
 

5
 

5
 

5
 

5
 

5
 

5
 

6
 

6
 

6
 

6
 

6
 

6
 

7
 

7
 

7
 

7
 

7
 

7
 

8
 

8
 

8
 

8
 

4.49 

4.46 

4.48 

4.46 

4.47 

4.46 

4.53 

4.55 

4.55 

4.56 

4.53 

4.54 

4.93 

4.98 

4.85 

4.76 

4.72 

4.78 

4.52 

4.53 

4.52 

4.52 

4.51 

4.5 

4.54 

4.55 

4.61 

4.51 

4.49 

4.48 

4.49 

4.48 

4.52 

4.53 

4.5 

4.52 

4.57 

4.55 

4.53 

4.52 

4.55 

4.55 

4.41 

4.41 

4.41 

4.29 

4.45 1
 

4.49 1
 

4.47 1
 

4.44 1
 

4.43 1
 

4.41 1
 

4.53 1
 

4.55 1
 

4.56 1
 

4.56 1
 

4.53 1
 

4.53 1
 

4.95 1
 

4.94 1
 

4.87 1
 

4.79 1
 

4.74 1
 

4.8 1
 

4.5 1
 

4.51 1
 

4.51 1
 

4.51 1
 

4.53 1
 

4.51 1
 

4.54 1
 

4.55 1
 

4.62 1
 

4.52 1
 

4.49 1
 

4.47 1
 

4.5 1
 

4.48 1
 

4.5 1
 

4.53 1
 

4.51 1
 

4.5 1
 

4.54 1
 

4.55 1
 

4.54 1
 

4.52 1
 

4.51 1
 

4.56 1
 

4.44 1
 

4.42 1
 

4.44 1
 

4.37 1
 

107
 
8 4.5178 4.5106 

8 4.4764 4.4679 

9 4.41 4.41 

9 4.33 4.41 

9 4.38 4.36 

9 4.41 4.4 

9 4.34 4.42 

9 4.35 4.37 

10 4.432 4.429 

10 4.443 4.417 

10 4.43 4.417 

10 4.443 4.445 

10 4.404 4.413 

10 4.427 4.416 

11 4.71 4.88 

11 4.66 4.67 

11 4.65 4.65 

11 4.94 4.96 

11 4.83 4.84 

11 4.89 4.88 

1 5.249 5.263 

1 5.247 5.26 

1 5.271 5.273 

1 5.228 5.242 

1 5.277 5.276 

1 5.302 5.309 

2 5.453 5.44 

2 5.543 5.506 

2 5.484 5.482 

2 5.448 5.437 

2 5.465 5.424 

2 5.399 5.401 

3 5.36 5.37 

3 5.32 5.34 

3 5.36 5.37 

3 5.39 5.36 

3 5.35 5.39 

3 5.38 5.29 

4 5.3279 5.3046 

4 5.3006 5.3045 

4 5.3034 5.2869 

4 5.2973 5.3081 

4 5.3024 5.2847 

4 5.2847 5.2994 

5 5.365 5.358 

5 5.336 5.317 

5 5.389 5.354 

5 5.378 5.349 

5 5.401 5.339 

5 5.346 5.333 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

8 

8 

9 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

11 

11 

11 

11 

11 

11 

12 

12 

12 

12 

12 

12 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

4.36 4.37 1 

4.36 4.38 1 

4.38 4.38 1 

4.37 4.37 1 

4.41 4.41 1 

4.39 4.38 1 

4.38 4.38 1 

4.41 4.41 1 

4.62 4.63 1 

4.65 4.62 1 

4.62 4.63 1 

4.56 4.6 1 

4.61 4.62 1 

4.61 4.62 1 

4.3957 4.3957 1 

4.3839 4.396 1 

4.414 4.4198 1 

4.408 4.4136 1 

4.3993 4.4001 1 

4.3756 4.3817 1 

4.71 4.675 1 

4.745 4.69 1 

4.77 4.645 1 

4.705 4.67 1 

4.75 4.685 1 

4.77 4.65 1 

5.12 5.12 2 

5.12 5.13 2 

5.16 5.16 2 

5.12 5.12 2 

5.14 5.16 2 

5.12 5.17 2 

5.39 5.39 2 

5.36 5.36 2 

5.36 5.38 2 

5.34 5.34 2 

5.34 5.35 2 

5.32 5.32 2 

5.25 5.22 2 

5.12 5.1 2 

5.14 5.15 2 

5.14 5.12 2 

5.21 5.24 2 

5.22 5.25 2 

5.19 5.18 2 

5.2 5.2 2 

5.14 5.18 2 

5.2 5.18 2 

5.13 5.17 2 

5.18 5.16 2 

108 
 

 

 

 

 

 

 

 

 

 

 

 

6 5.35 5.32 

6 5.32 5.33 

6 5.33 5.36 

6 5.31 5.34 

6 5.32 5.33 

6 5.32 5.31 

7 5.22 5.2 

7 5.28 5.24 

7 5.28 5.23 

7 5.24 5.2 

7 5.27 5.27 

7 5.26 5.26 

8 5.3525 5.3681 

8 5.385 5.38 

8 5.3823 5.3942 

8 5.4065 5.386 

8 5.4053 5.4135 

8 5.4161 5.4155 

9 5.32 5.28 

9 5.25 5.28 

9 5.35 5.35 

9 5.32 5.28 

9 5.28 5.25 

9 5.36 5.32 

10 5.314 5.332 

10 5.338 5.319 

10 5.323 5.302 

10 5.305 5.321 

10 5.319 5.331 

10 5.303 5.327 

11 5.57 5.58 

11 5.56 5.79 

11 5.61 5.61 

11 6.11 6.09 

11 5.71 5.74 

11 5.73 5.74 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

5 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

6 

7 

7 

7 

7 

7 

7 

8 

8 

8 

8 

8 

8 

9 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

11 

11 

11 

11 

11 

11 

12 

12 

12 

12 

12 

12 

5.09 5.1 2 

5.08 5.09 2 

5.07 5.07 2 

5.14 5.15 2 

5.06 5.06 2 

5.03 5.03 2 

5.03 5.04 2 

5.03 5.05 2 

5.07 5.05 2 

5.02 5.02 2 

5.05 5.05 2 

5.04 5.03 2 

5.03 5.02 2 

5.01 5.02 2 

5.03 5.03 2 

5.07 5.06 2 

5.02 5.02 2 

5.04 5.04 2 

5.02 5.04 2 

5.04 5.07 2 

5.05 5.04 2 

4.97 4.98 2 

4.97 4.97 2 

4.9 4.98 2 

5.04 5.05 2 

5.03 5.04 2 

5.06 5.06 2 

5.05 5.05 2 

5.04 5.03 2 

5.06 5.06 2 

5.09 5.08 2 

5.07 5.08 2 

5.09 5.11 2 

5.08 5.1 2 

5.05 5.05 2 

5.06 5.08 2 

5.2413 5.2395 2 

5.1843 5.1853 2 

5.178 5.1806 2 

5.1374 5.1391 2 

5.1405 5.143 2 

5.1758 5.1744 2 

5.105 5.12 2 

5.09 5.165 2 

5.055 5.11 2 

5.0958 5.13 2 

5.1 5.17 2 

5.045 5.105 2 

109 
 

Fe2O3

Fe2O3: Glass Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 2.86 

1 2.871 

1 2.859 

1 2.86 

1 2.869 

1 2.876 

2 2.92 

2 2.911 

2 2.923 

2 2.907 

2 2.89 

2 2.929 

3 2.84 

3 2.83 

3 2.81 

3 2.82 

3 2.83 

3 2.83 

4 2.8786 

4 2.8757 

4 2.8746 

4 2.8862 

4 2.8785 

4 2.8833 

5 2.836 

5 2.832 

5 2.84 

5 2.837 

5 2.849 

5 2.83 

6 2.84 

6 2.82 

6 2.83 

6 2.84 

6 2.83 

6 2.83 

7 2.9 

7 2.9 

7 2.89 

7 2.9 

7 2.9 

7 2.9 

8 2.9013 

8 2.9014 

8 2.8897 

8 2.8947 

2.878 

2.874 

2.869 

2.866 

2.88 

2.888 

2.92 

2.916 

2.93 

2.902 

2.891 

2.913 

2.82 

2.85 

2.83 

2.82 

2.83 

2.85 

2.8757 

2.8805 

2.8708 

2.8813 

2.8854 

2.8834 

2.84 

2.849 

2.823 

2.835 

2.842 

2.827 

2.84 

2.81 

2.83 

2.84 

2.82 

2.83 

2.9 

2.9 

2.89 

2.9 

2.9 

2.9 

2.9014 

2.9019 

2.891 

2.8945 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

Fe2O3: Powder Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 2.92 

1 2.92 

1 2.91 

1 2.92 

1 2.9 

1 2.9 

2 2.91 

2 2.89 

2 2.92 

2 2.85 

2 2.77 

2 2.85 

3 2.9 

3 2.91 

3 2.92 

3 2.93 

3 2.93 

3 2.93 

4 2.94 

4 2.91 

4 2.91 

4 2.96 

4 2.91 

4 2.91 

5 2.88 

5 2.88 

5 2.88 

5 2.86 

5 2.88 

5 2.88 

6 2.9 

6 2.89 

6 2.88 

6 2.91 

6 2.89 

6 2.91 

7 2.92 

7 2.92 

7 2.93 

7 2.93 

7 2.93 

7 2.94 

8 2.94 

8 2.94 

8 2.93 

8 2.95 

2.92 1
 

2.92 1
 

2.9 1
 

2.9 1
 

2.91 1
 

2.91 1
 

2.9 1
 

2.92 1
 

2.91 1
 

2.87 1
 

2.79 1
 

2.86 1
 

2.9 1
 

2.92 1
 

2.92 1
 

2.92 1
 

2.91 1
 

2.91 1
 

2.93 1
 

2.92 1
 

2.91 1
 

2.96 1
 

2.91 1
 

2.92 1
 

2.88 1
 

2.88 1
 

2.89 1
 

2.86 1
 

2.87 1
 

2.88 1
 

2.9 1
 

2.89 1
 

2.88 1
 

2.9 1
 

2.9 1
 

2.92 1
 

2.93 1
 

2.93 1
 

2.93 1
 

2.93 1
 

2.93 1
 

2.93 1
 

2.94 1
 

2.94 1
 

2.95 1
 

2.95 1
 

110
 
8 2.8851 2.8857 

8 2.8893 2.889 

9 2.97 2.95 

9 2.97 2.98 

9 2.97 2.96 

9 2.96 2.94 

9 2.97 2.97 

9 2.97 2.95 

10 2.874 2.883 

10 2.867 2.879 

10 2.874 2.886 

10 2.876 2.875 

10 2.877 2.875 

10 2.87 2.87 

1 2.363 2.371 

1 2.365 2.378 

1 2.369 2.377 

1 2.349 2.367 

1 2.374 2.377 

1 2.383 2.387 

2 2.375 2.384 

2 2.385 2.381 

2 2.389 2.387 

2 2.408 2.402 

2 2.397 2.406 

2 2.384 2.379 

3 2.33 2.35 

3 2.3 2.32 

3 2.31 2.29 

3 2.31 2.29 

3 2.3 2.31 

3 2.31 2.3 

4 2.3734 2.3705 

4 2.3714 2.3695 

4 2.3694 2.3694 

4 2.376 2.377 

4 2.3761 2.377 

4 2.3751 2.3799 

5 2.348 2.347 

5 2.353 2.343 

5 2.346 2.354 

5 2.352 2.327 

5 2.35 2.343 

5 2.336 2.329 

6 2.33 2.33 

6 2.32 2.32 

6 2.35 2.35 

6 2.33 2.33 

6 2.32 2.31 

6 2.35 2.35 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

8 

8 

9 

9 

9 

9 

9 

9 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

5 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

6 

7 

7 

7 

7 

7 

7 

2.94 2.93 1 

2.92 2.93 1 

3.025 3.01 1 

3.02 3.01 1 

3.03 3.005 1 

3.02 3.005 1 

3.025 3.015 1 

3.03 3.015 1 

2.38 2.4 2 

2.39 2.38 2 

2.38 2.39 2 

2.4 2.41 2 

2.38 2.39 2 

2.39 2.38 2 

2.32 2.35 2 

2.33 2.35 2 

2.34 2.34 2 

2.3 2.31 2 

2.32 2.32 2 

2.32 2.31 2 

2.41 2.42 2 

2.4 2.41 2 

2.39 2.39 2 

2.43 2.42 2 

2.4 2.4 2 

2.39 2.39 2 

2.46 2.46 2 

2.44 2.45 2 

2.45 2.45 2 

2.46 2.46 2 

2.45 2.44 2 

2.43 2.43 2 

2.32 2.3 2 

2.3 2.3 2 

2.3 2.3 2 

2.3 2.3 2 

2.3 2.3 2 

2.3 2.3 2 

2.35 2.35 2 

2.34 2.34 2 

2.35 2.35 2 

2.36 2.36 2 

2.35 2.36 2 

2.36 2.37 2 

2.36 2.36 2 

2.38 2.38 2 

2.37 2.38 2 

2.36 2.36 2 

2.38 2.38 2 

2.38 2.38 2 

111 
 

 

 

 

 

 

 

 

 

 

 

 

7 2.39 2.39 

7 2.39 2.39 

7 2.39 2.39 

7 2.4 2.4 

7 2.38 2.39 

7 2.39 2.4 

8 2.4011 2.4026 

8 2.3876 2.3878 

8 2.3809 2.3804 

8 2.3841 2.3853 

8 2.3825 2.3826 

8 2.3872 2.385 

9 2.46 2.46 

9 2.47 2.47 

9 2.46 2.45 

9 2.46 2.45 

9 2.46 2.46 

9 2.45 2.45 

10 2.37 2.366 

10 2.371 2.361 

10 2.354 2.37 

10 2.373 2.36 

10 2.375 2.382 

10 2.364 2.38 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

8 2.39 2.39 2 

8 2.37 2.37 2 

8 2.38 2.37 2 

8 2.38 2.39 2 

8 2.38 2.37 2 

8 2.36 2.37 2 

9 2.46 2.45 2 

9 2.46 2.48 2 

9 2.46 2.47 2 

9 2.46 2.45 2 

9 2.45 2.475 2 

9 2.455 2.47 2 

112 
 

CaO

CaO: Glass Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

3 62.54 62.57 

3 62.44 62.53 

3 62.58 62.63 

3 62.39 62.48 

3 62.47 62.45 

3 62.6 62.62 

4 62.409 62.452 

4 62.452 62.415 

4 62.31 62.47 

4 62.349 62.351 

4 62.4 62.504 

4 62.412 62.432 

5 61.67 61.766 

5 61.947 61.946 

5 61.77 61.693 

5 61.83 61.813 

5 61.869 61.739 

5 61.706 61.782 

6 62.32 62.32 

6 62.08 62.11 

6 62.31 62.35 

6 62.51 62.52 

6 62.29 62.29 

6 62.34 62.33 

7 62.48 62.49 

7 62.51 62.53 

7 62.45 62.47 

7 62.47 62.49 

7 62.55 62.56 

7 62.48 62.49 

8 62.514 62.585 

8 62.564 62.53 

8 62.316 62.308 

8 62.45 62.447 

8 62.325 62.347 

8 62.353 62.349 

9 63.28 62.99 

9 63.29 63.47 

9 63.26 63.14 

9 63.4 62.95 

9 63.4 63.54 

9 63.31 63.12 

10 62.331 62.328 

10 62.38 62.325 

10 62.321 62.315 

10 62.326 62.341 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

CaO: Powder Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 62.8 

1 62.68 

1 62.81 

1 62.82 

1 62.76 

1 62.77 

2 62.74 

2 62.75 

2 62.56 

2 62.78 

2 62.6 

2 62.7 

5 62.67 

5 62.87 

5 62.59 

5 62.74 

5 62.77 

5 62.56 

6 62.75 

6 62.8 

6 62.8 

6 63.01 

6 62.91 

6 62.87 

7 62.5 

7 62.45 

7 62.41 

7 62.26 

7 62.53 

7 62.58 

8 62.41 

8 62.39 

8 62.36 

8 62.54 

8 62.67 

8 62.67 

9 62.61 

9 62.54 

9 62.53 

9 62.59 

9 62.55 

9 62.55 

10 62.73 

10 62.78 

10 62.92 

10 62.55 

62.87 1 

62.76 1 

62.84 1 

62.66 1 

62.7 1 

62.84 1 

62.72 1 

62.67 1 

62.75 1 

62.63 1 

62.63 1 

62.57 1 

62.67 1 

62.89 1 

62.67 1 

62.75 1 

62.78 1 

62.53 1 

62.72 1 

62.81 1 

62.72 1 

62.88 1 

62.85 1 

62.83 1 

62.43 1 

62.4 1 

62.39 1 

62.29 1 

62.53 1 

62.54 1 

62.47 1 

62.49 1 

62.45 1 

62.44 1 

62.65 1 

62.69 1 

62.61 1 

63.53 1 

62.53 1 

62.62 1 

62.56 1 

62.54 1 

62.78 1 

62.89 1 

62.94 1 

62.7 1 

113 
10 62.42 62.381 

10 62.392 62.327 

3 63.12 63.15 

3 63.12 63.13 

3 63.13 63.16 

3 62.9 62.86 

3 62.89 63.01 

3 63 62.99 

4 63.4 63.42 

4 63.382 63.401 

4 63.391 63.372 

4 63.349 63.372 

4 63.456 63.39 

4 63.393 63.397 

5 62.859 62.937 

5 62.836 62.883 

5 63.014 62.994 

5 63.066 62.904 

5 63.035 63.081 

5 63.022 62.953 

6 63.37 63.4 

6 63.27 63.28 

6 63.41 63.42 

6 63.42 63.43 

6 63.47 63.44 

6 63.44 63.41 

7 63.34 63.38 

7 63.27 63.29 

7 63.25 63.26 

7 63.38 63.37 

7 63.29 63.28 

7 63.29 63.25 

8 63.283 63.292 

8 63.333 63.327 

8 63.089 63.1 

8 63.224 63.238 

8 63.151 63.162 

8 63.262 63.245 

9 63.73 63.78 

9 63.87 64.07 

9 63.64 63.65 

9 63.59 63.77 

9 63.93 64.05 

9 63.59 63.62 

10 63.322 63.224 

10 63.314 63.291 

10 63.308 63.255 

10 63.301 63.315 

10 63.237 63.259 

10 63.237 63.265 

1 

1 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

10 

10 

11 

11 

11 

11 

11 

11 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

5 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

6 

7 

7 

7 

7 

7 

7 

8 

8 

8 

8 

8 

8 

9 

9 

9 

9 

9 

9 

62.69 62.69 1 

62.69 62.84 1 

62.847 62.93 1 

62.897 62.938 1 

63.194 63.175 1 

62.926 62.968 1 

62.993 62.993 1 

62.8 62.745 1 

63.97	 64.16 2 

64 64.01 2 

64.04 63.98 2 

63.91 64.05 2 

64.01	 64.05 2 

64 64.09 2 

63.75 63.83 2 

63.74 63.84 2 

63.95 63.77 2 

63.72 63.84 2 

63.63 63.78 2 

63.67 63.65 2 

63.81 63.82 2 

64.15 64.17 2 

63.93 63.95 2 

63.75 63.77 2 

63.63 63.65 2 

63.85 63.86 2 

63.31 63.31 2 

63.28 63.34 2 

63.41 63.29 2 

63.29 63.33 2 

63.29 63.33 2 

63.25 63.25 2 

63.67 63.57 2 

63.44 63.41 2 

63.58 63.59 2 

63.69 63.65 2 

63.27 63.24 2 

63.74 63.71 2 

63.39 63.43 2 

63.32 63.37 2 

63.5 63.59 2 

63.78 63.87 2 

63.7 63.79 2 

63.6 63.54 2 

63.3 63.27 2 

63.17 63.16 2 

63.26 63.25 2 

63.29 63.31 2 

63.16 63.17 2 

63.28 63.28 2 

114 
 

 

 

 

 

 

 

 

 

 

 

 

10 64.28 64.31 2
 

10 64.25 64.24 2
 

10 64.33 64.27 2
 

10 64.18 64.23 2
 

10 64.07 64.12 2
 

10 64.12 64.13 2
 

11 64.203 64.226 2
 

11 64.022 64.001 2
 

11 63.975 63.93 2
 

11 63.66 63.678 2
 

11 63.662 63.736 2
 

11 63.91 63.883 2
 

115 
 

MgO

MgO: Glass Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 2.517 

1 2.544 

1 2.541 

1 2.546 

1 2.546 

1 2.559 

2 2.56 

2 2.56 

2 2.56 

2 2.56 

2 2.58 

2 2.59 

3 2.5776 

3 2.5689 

3 2.5678 

3 2.5678 

3 2.5688 

3 2.56 

4 2.55 

4 2.55 

4 2.56 

4 2.54 

4 2.55 

4 2.54 

5 2.56 

5 2.57 

5 2.57 

5 2.59 

5 2.59 

5 2.59 

6 2.56 

6 2.55 

6 2.57 

6 2.56 

6 2.55 

6 2.56 

7 2.5675 

7 2.6158 

7 2.5894 

7 2.5683 

7 2.5666 

7 2.5389 

8 2.55 

8 2.542 

8 2.55 

8 2.545 

2.523 

2.55 

2.548 

2.544 

2.552 

2.561 

2.55 

2.57 

2.56 

2.58 

2.58 

2.57 

2.5698 

2.5708 

2.563 

2.5916 

2.5631 

2.561 

2.56 

2.54 

2.55 

2.55 

2.55 

2.54 

2.58 

2.57 

2.57 

2.59 

2.58 

2.59 

2.55 

2.54 

2.53 

2.55 

2.54 

2.56 

2.5773 

2.564 

2.5557 

2.6061 

2.5859 

2.5645 

2.554 

2.543 

2.541 

2.543 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

MgO: Powder Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 2.71 

1 2.67 

1 2.61 

1 2.61 

1 2.64 

1 2.65 

2 2.56 

2 2.58 

2 2.57 

2 2.58 

2 2.57 

2 2.56 

3 2.68 

3 2.66 

3 2.7 

3 2.69 

3 2.6 

3 2.64 

4 2.65 

4 2.63 

4 2.64 

4 2.66 

4 2.63 

4 2.64 

5 2.56 

5 2.6 

5 2.59 

5 2.6 

5 2.59 

5 2.61 

6 2.61 

6 2.62 

6 2.61 

6 2.57 

6 2.61 

6 2.58 

7 2.66 

7 2.72 

7 2.73 

7 2.66 

7 2.73 

7 2.74 

8 2.62 

8 2.63 

8 2.61 

8 2.64 

2.65 1
 

2.61 1
 

2.6 1
 

2.62 1
 

2.65 1
 

2.64 1
 

2.56 1
 

2.58 1
 

2.58 1
 

2.57 1
 

2.57 1
 

2.56 1
 

2.68 1
 

2.69 1
 

2.72 1
 

2.7 1
 

2.63 1
 

2.66 1
 

2.64 1
 

2.63 1
 

2.64 1
 

2.66 1
 

2.64 1
 

2.64 1
 

2.56 1
 

2.59 1
 

2.59 1
 

2.62 1
 

2.59 1
 

2.61 1
 

2.61 1
 

2.63 1
 

2.62 1
 

2.58 1
 

2.61 1
 

2.58 1
 

2.65 1
 

2.72 1
 

2.72 1
 

2.67 1
 

2.72 1
 

2.73 1
 

2.64 1
 

2.64 1
 

2.61 1
 

2.64 1
 

116
 
8 2.545 2.558 

8 2.549 2.565 

9 2.58 2.59 

9 2.58 2.6 

9 2.6 2.59 

9 2.59 2.6 

9 2.61 2.61 

9 2.61 2.6 

1 2.109 2.113 

1 2.111 2.121 

1 2.115 2.117 

1 2.103 2.114 

1 2.125 2.125 

1 2.103 2.111 

2 2.13 2.14 

2 2.11 2.13 

2 2.11 2.12 

2 2.12 2.12 

2 2.12 2.11 

2 2.1 2.1 

3 2.1086 2.1047 

3 2.1086 2.1144 

3 2.1007 2.1066 

3 2.0975 2.1014 

3 2.1083 2.0975 

3 2.1092 2.0985 

4 2.09 2.09 

4 2.09 2.09 

4 2.1 2.09 

4 2.09 2.09 

4 2.09 2.09 

4 2.08 2.09 

5 2.13 2.13 

5 2.14 2.12 

5 2.13 2.12 

5 2.15 2.14 

5 2.13 2.15 

5 2.13 2.14 

6 2.08 2.08 

6 2.11 2.11 

6 2.11 2.11 

6 2.09 2.1 

6 2.09 2.1 

6 2.08 2.1 

7 2.1304 2.1274 

7 2.1151 2.0926 

7 2.1286 2.1148 

7 2.1277 2.1235 

7 2.1341 2.1109 

7 2.1156 2.1174 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

8 

8 

9 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

11 

11 

11 

11 

11 

11 

12 

12 

12 

12 

12 

12 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

2.65 2.66 1 

2.66 2.66 1 

2.72 2.72 1 

2.72 2.71 1 

2.7 2.68 1 

2.7 2.71 1 

2.69 2.7 1 

2.67 2.68 1 

2.75 2.75 1 

2.77 2.78 1 

2.76 2.78 1 

2.67 2.67 1 

2.75 2.75 1 

2.75 2.75 1 

2.6135 2.6048 1 

2.6256 2.6272 1 

2.6696 2.6756 1 

2.5855 2.5833 1 

2.6288 2.6262 1 

2.6164 2.6247 1 

2.695 2.67 1 

2.7 2.66 1 

2.725 2.66 1 

2.69 2.67 1 

2.705 2.655 1 

2.72 2.66 1 

2.02 2.08 2 

2.05 2.06 2 

2.07 2.04 2 

2.07 2.07 2 

2.01 2.06 2 

2.06 2.08 2 

2.13 2.13 2 

2.1 2.1 2 

2.11 2.11 2 

2.11 2.11 2 

2.1 2.1 2 

2.09 2.08 2 

2.05 2.06 2 

2.03 2.01 2 

2.05 2.06 2 

2.05 2.06 2 

2.07 2.07 2 

2.04 2.06 2 

2.07 2.05 2 

2.03 2.04 2 

2.03 2.04 2 

2.05 2.06 2 

2.05 2.05 2 

2.05 2.04 2 

117 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8 2.077 2.101 2 

8 2.095 2.104 2 

8 2.1 2.088 2 

8 2.092 2.092 2 

8 2.089 2.095 2 

8 2.082 2.085 2 

9 2.11 2.11 2 

9 2.11 2.13 2 

9 2.11 2.11 2 

9 2.14 2.14 2 

9 2.13 2.13 2 

9 2.11 2.11 2 

5 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

6 

7 

7 

7 

7 

7 

7 

8 

8 

8 

8 

8 

8 

9 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

11 

11 

11 

11 

11 

11 

12 

12 

12 

12 

12 

12 

2.04 2.04 2 

2.04 2.01 2 

2.05 2.05 2 

2.06 2.07 2 

2.05 2.05 2 

2.04 2.05 2 

2.06 2.06 2 

2.08 2.08 2 

2.06 2.06 2 

2.08 2.08 2 

2.05 2.05 2 

2.05 2.05 2 

2.07 2.06 2 

2.04 2.04 2 

2.05 2.04 2 

2.07 2.07 2 

2.03 2.04 2 

2.04 2.04 2 

2.04 2.05 2 

2.04 2.03 2 

2.03 2.04 2 

2.07 2.08 2 

2.05 2.06 2 

2.08 2.08 2 

2.06 2.06 2 

2.09 2.08 2 

2.09 2.08 2 

2.06 2.06 2 

2.08 2.08 2 

2.09 2.09 2 

2.1 2.11 2 

2.1 2.11 2 

2.11 2.1 2 

2.12 2.13 2 

2.1 2.09 2 

2.1 2.1 2 

2.1171 2.1211 2 

2.102 2.0983 2 

2.1072 2.1037 2 

2.0809 2.0786 2 

2.0761 2.0826 2 

2.0853 2.0957 2 

2.01 2.02 2 

2.01 2.045 2 

1.995 2 2 

2.01 2.02 2 

2.005 2.04 2 

1.995 2 2 

118 
 

 

SO3

SO3: Glass Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 3.1930 3.2030 

1 3.2280 3.2330 

1 3.2350 3.2410 

1 3.2550 3.2640 

1 3.2370 3.2430 

1 3.2430 3.2500 

2 3.2580 3.2470 

2 3.2480 3.2120 

2 3.2730 3.2420 

2 3.2260 3.2220 

2 3.2290 3.2040 

2 3.2360 3.2400 

3 3.2900 3.3000 

3 3.2700 3.2700 

3 3.2800 3.2800 

3 3.2900 3.2900 

3 3.2900 3.2800 

3 3.3000 3.3100 

4 3.2929 3.2939 

4 3.2919 3.2850 

4 3.2996 3.3026 

4 3.2847 3.2945 

4 3.2936 3.3025 

4 3.3024 3.2975 

5 3.2100 3.2100 

5 3.2100 3.2000 

5 3.2000 3.1900 

5 3.2300 3.2200 

5 3.2300 3.2400 

5 3.2300 3.2300 

6 3.2600 3.2700 

6 3.2500 3.2500 

6 3.2500 3.2600 

6 3.2600 3.2500 

6 3.2500 3.2500 

6 3.2600 3.2400 

7 3.1869 3.1839 

7 3.1865 3.1885 

7 3.1685 3.1683 

7 3.1821 3.1825 

7 3.1796 3.1842 

7 3.1675 3.1658 

8 3.1400 3.1300 

8 3.1000 3.1200 

8 3.1300 3.1400 

8 3.1400 3.1400 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

SO3: Powder Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 3.24 

1 3.21 

1 3.24 

1 3.23 

1 3.22 

1 3.2 

2 2.98 

2 2.99 

2 2.99 

2 2.98 

2 2.96 

2 2.98 

3 3.15 

3 3.24 

3 3.22 

3 3.22 

3 3.21 

3 3.23 

4 3.19 

4 3.2 

4 3.16 

4 3.18 

4 3.17 

4 3.17 

5 3.31 

5 3.3 

5 3.29 

5 3.25 

5 3.31 

5 3.26 

6 3.16 

6 3.27 

6 3.26 

6 3.19 

6 3.29 

6 3.27 

7 3.09 

7 3.08 

7 3.09 

7 3.1 

7 3.11 

7 3.11 

8 3.22 

8 3.2 

8 3.22 

8 3.23 

3.24 1 

3.23 1 

3.24 1 

3.25 1 

3.22 1 

3.21 1 

2.98 1 

2.99 1 

2.98 1 

2.98 1 

2.96 1 

2.98 1 

3.14 1 

3.23 1 

3.21 1 

3.2 1 

3.21 1 

3.22 1 

3.18 1 

3.19 1 

3.18 1 

3.19 1 

3.18 1 

3.18 1 

3.31 1 

3.3 1 

3.3 1 

3.26 1 

3.32 1 

3.26 1 

3.17 1 

3.27 1 

3.27 1 

3.15 1 

3.28 1 

3.26 1 

3.11 1 

3.08 1 

3.1 1 

3.1 1 

3.11 1 

3.11 1 

3.22 1 

3.21 1 

3.23 1 

3.23 1 

119 
8 3.1200 3.1200 

8 3.1400 3.1400 

9 3.2840 3.2730 

9 3.2750 3.2590 

9 3.2800 3.2840 

9 3.2870 3.2790 

9 3.2900 3.2790 

9 3.2720 3.2740 

1 3.6680 3.6770 

1 3.6540 3.6720 

1 3.6690 3.6720 

1 3.6310 3.6480 

1 3.8650 3.6950 

1 3.6840 3.6950 

2 3.6410 3.6540 

2 3.6760 3.0670 

2 3.6690 3.6690 

2 3.7190 3.7390 

2 3.7190 3.7030 

2 3.6740 3.6570 

3 3.6900 3.7200 

3 3.7200 3.7000 

3 3.7400 3.7300 

3 3.7200 3.7200 

3 3.7200 3.7200 

3 3.7200 3.7200 

4 3.7187 3.7110 

4 3.7128 3.7294 

4 3.7147 3.7118 

4 3.7218 3.7198 

4 3.7336 3.7247 

4 3.7306 3.7199 

5 3.6000 3.6000 

5 3.6100 3.6000 

5 3.6100 3.6000 

5 3.6100 3.6200 

5 3.6300 3.6200 

5 3.6300 3.6400 

6 3.7100 3.6900 

6 3.7000 3.7100 

6 3.7100 3.7100 

6 3.6900 3.7000 

6 3.7200 3.7000 

6 3.7200 3.7100 

7 3.7760 3.7759 

7 3.7995 3.7964 

7 3.7816 3.7816 

7 3.7989 3.7967 

7 3.7836 3.7915 

7 3.7937 3.7966 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

8 

8 

9 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

11 

11 

11 

11 

11 

11 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

5 

5 

5 

5 

5 

5 

3.22 3.23 1 

3.24 3.24 1 

3.27 3.28 1 

3.28 3.27 1 

3.27 3.27 1 

3.26 3.25 1 

3.25 3.27 1 

3.27 3.26 1 

3.1705 3.1515 1 

3.1705 3.1515 1 

3.1773 3.1776 1 

3.1462 3.1449 1 

3.1575 3.1558 1 

3.1336 3.1345 1 

3.155 3.005 1 

3.13 3 1 

3.15 3.005 1 

3.155 3.005 1 

3.13 3 1 

3.115 3.01 1 

3.71 3.72 2 

3.71 3.72 2 

3.68 3.71 2 

3.7 3.71 2 

3.71 3.7 2 

3.71 3.72 2 

3.33 3.33 2 

3.43 3.43 2 

3.38 3.39 2 

3.37 3.37 2 

3.38 3.38 2 

3.45 3.45 2 

3.63 3.66 2 

3.7 3.69 2 

3.75 3.76 2 

3.68 3.65 2 

3.67 3.66 2 

3.69 3.71 2 

3.67 3.67 2 

3.67 3.69 2 

3.71 3.72 2 

3.65 3.65 2 

3.68 3.71 2 

3.7 3.69 2 

3.86 3.86 2 

3.76 3.76 2 

3.86 3.86 2 

3.76 3.77 2 

3.76 3.76 2 

3.84 3.84 2 

120 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8 3.5200 3.5400 2 

8 3.5200 3.5200 2 

8 3.4800 3.4900 2 

8 3.5200 3.5500 2 

8 3.5100 3.5300 2 

8 3.4800 3.5000 2 

9 3.7090 3.7170 2 

9 3.7160 3.6940 2 

9 3.7120 3.6960 2 

9 3.6940 3.6910 2 

9 3.6920 3.6880 2 

9 3.7000 3.7020 2 

6 

6 

6 

6 

6 

6 

7 

7 

7 

7 

7 

7 

8 

8 

8 

8 

8 

8 

9 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

11 

11 

11 

11 

11 

11 

3.82 3.83 2 

3.83 3.84 2 

3.83 3.83 2 

3.87 3.87 2 

3.84 3.84 2 

3.83 3.84 2 

3.72 3.71 2 

3.69 3.69 2 

3.73 3.73 2 

3.76 3.75 2 

3.72 3.72 2 

3.71 3.71 2 

3.75 3.75 2 

3.75 3.75 2 

3.75 3.76 2 

3.74 3.75 2 

3.78 3.78 2 

3.74 3.75 2 

3.74 3.74 2 

3.76 3.76 2 

3.72 3.73 2 

3.79 3.79 2 

3.79 3.79 2 

3.78 3.77 2 

3.7037 3.7 2 

3.7154 3.7171 2 

3.7118 3.7114 2 

3.6639 3.6617 2 

3.6778 3.6755 2 

3.6851 3.6885 2 

3.61 3.66 2 

3.7 3.56 2 

3.705 3.695 2 

3.605 3.67 2 

3.7 3.565 2 

3.715 3.69 2 

121 
 

Na2O

Na2O: Glass Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 0.156 

1 0.161 

1 0.157 

1 0.158 

1 0.156 

1 0.16 

2 0.193 

2 0.191 

2 0.184 

2 0.18 

2 0.17 

2 0.183 

3 0.13 

3 0.13 

3 0.13 

3 0.13 

3 0.14 

3 0.15 

4 0.1515 

4 0.1524 

4 0.1524 

4 0.1485 

4 0.1524 

4 0.1563 

5 0.1281 

5 0.1316 

5 0.138 

5 0.1238 

5 0.1285 

5 0.1293 

6 0.172 

6 0.17 

6 0.167 

6 0.168 

6 0.173 

6 0.171 

7 0.143 

7 0.141 

7 0.132 

7 0.147 

7 0.142 

7 0.141 

8 0.16532 

8 0.14847 

8 0.15666 

8 0.14982 

0.157 

0.159 

0.159 

0.161 

0.157 

0.163 

0.183 

0.185 

0.189 

0.173 

0.173 

0.18 

0.15 

0.14 

0.14 

0.14 

0.14 

0.15 

0.1554 

0.1515 

0.1534 

0.1524 

0.1524 

0.1543 

0.1331 

0.1276 

0.1361 

0.1257 

0.1284 

0.128 

0.175 

0.172 

0.166 

0.174 

0.171 

0.171 

0.136 

0.144 

0.142 

0.148 

0.149 

0.136 

0.16305 

0.14848 

0.15591 

0.14861 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

Na2O: Powder Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 0.163 

1 0.16 

1 0.157 

1 0.157 

1 0.161 

1 0.162 

2 0.14 

2 0.14 

2 0.15 

2 0.14 

2 0.14 

2 0.15 

3 0.16 

3 0.13 

3 0.13 

3 0.14 

3 0.14 

3 0.14 

4 0.17 

4 0.16 

4 0.17 

4 0.16 

4 0.16 

4 0.16 

5 0.15 

5 0.16 

5 0.16 

5 0.15 

5 0.16 

5 0.16 

6 0.19 

6 0.19 

6 0.19 

6 0.16 

6 0.16 

6 0.17 

7 0.144 

7 0.154 

7 0.152 

7 0.151 

7 0.147 

7 0.149 

8 0.17 

8 0.17 

8 0.18 

8 0.18 

0.162 1
 

0.159 1
 

0.166 1
 

0.162 1
 

0.163 1
 

0.162 1
 

0.14 1
 

0.14 1
 

0.15 1
 

0.14 1
 

0.14 1
 

0.14 1
 

0.16 1
 

0.12 1
 

0.13 1
 

0.15 1
 

0.14 1
 

0.14 1
 

0.17 1
 

0.17 1
 

0.17 1
 

0.16 1
 

0.16 1
 

0.16 1
 

0.16 1
 

0.16 1
 

0.16 1
 

0.16 1
 

0.16 1
 

0.16 1
 

0.2 1
 

0.19 1
 

0.2 1
 

0.16 1
 

0.17 1
 

0.17 1
 

0.156 1
 

0.151 1
 

0.153 1
 

0.15 1
 

0.153 1
 

0.156 1
 

0.17 1
 

0.18 1
 

0.17 1
 

0.18 1
 

122
 
8 0.14229 

8 0.14863 

9 0.17 

9 0.15 

9 0.14 

9 0.18 

9 0.16 

9 0.16 

10 0.161 

10 0.159 

10 0.17 

10 0.157 

10 0.165 

10 0.167 

1 0.152 

1 0.15 

1 0.149 

1 0.151 

1 0.15 

1 0.15 

2 0.165 

2 0.172 

2 0.172 

2 0.158 

2 0.167 

2 0.16 

3 0.12 

3 0.12 

3 0.13 

3 0.13 

3 0.13 

3 0.14 

4 0.145 

4 0.1441 

4 0.1431 

4 0.147 

4 0.1451 

4 0.1431 

5 0.1222 

5 0.1201 

5 0.1201 

5 0.1239 

5 0.1228 

5 0.1176 

6 0.166 

6 0.158 

6 0.158 

6 0.165 

6 0.161 

6 0.165 

0.15104 1 

0.137 1 

0.16 1 

0.15 1 

0.16 1 

0.16 1 

0.16 1 

0.15 1 

0.168 1 

0.166 1 

0.165 1 

0.168 1 

0.158 1 

0.162 1 

0.149 2 

0.151 2 

0.15 2 

0.151 2 

0.151 2 

0.15 2 

0.172 2 

0.174 2 

0.172 2 

0.162 2 

0.165 2 

0.164 2 

0.14 2 

0.14 2 

0.14 2 

0.13 2 

0.13 2 

0.13 2 

0.1421 2 

0.146 2 

0.1441 2 

0.1422 2 

0.1451 2 

0.1451 2 

0.1268 2 

0.1231 2 

0.1262 2 

0.1203 2 

0.1237 2 

0.1207 2 

0.164 2 

0.159 2 

0.161 2 

0.162 2 

0.16 2 

0.163 2 

8 

8 

9 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

5 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

6 

0.18 0.18 1 

0.17 0.18 1 

0.13181 0.1303 1 

0.12829 0.1319 1 

0.1293 0.13239 1 

0.12894 0.12486 1 

0.1272 0.12338 1 

0.12524 0.12324 1 

0.19 0.19 1 

0.2 0.19 1 

0.2 0.19 1 

0.19 0.19 1 

0.2 0.19 1 

0.2 0.19 1 

0.159 0.16 2 

0.155 0.158 2 

0.153 0.151 2 

0.16 0.159 2 

0.159 0.147 2 

0.156 0.151 2 

0.14 0.13 2 

0.14 0.14 2 

0.14 0.14 2 

0.14 0.14 2 

0.14 0.14 2 

0.14 0.14 2 

0.15 0.15 2 

0.15 0.15 2 

0.15 0.15 2 

0.12 0.13 2 

0.13 0.13 2 

0.12 0.12 2 

0.17 0.16 2 

0.17 0.17 2 

0.17 0.17 2 

0.17 0.16 2 

0.17 0.16 2 

0.17 0.17 2 

0.15 0.15 2 

0.16 0.15 2 

0.15 0.16 2 

0.16 0.16 2 

0.15 0.15 2 

0.16 0.15 2 

0.18 0.19 2 

0.17 0.16 2 

0.18 0.17 2 

0.18 0.18 2 

0.18 0.17 2 

0.17 0.17 2 

123 
7 0.128 

7 0.145 

7 0.131 

7 0.137 

7 0.132 

7 0.13 

8 0.1321 

8 0.14767 

8 0.157 

8 0.15734 

8 0.14441 

8 0.12748 

9 0.14 

9 0.14 

9 0.14 

9 0.14 

9 0.14 

9 0.14 

10 0.161 

10 0.166 

10 0.146 

10 0.157 

10 0.154 

10 0.156 

0.132 2 

0.142 2 

0.131 2 

0.143 2 

0.131 2 

0.129 2 

0.12917 2 

0.14105 2 

0.16856 2 

0.15703 2 

0.15827 2 

0.14918 2 

0.14 2 

0.15 2 

0.14 2 

0.15 2 

0.14 2 

0.14 2 

0.153 2 

0.161 2 

0.153 2 

0.15 2 

0.161 2 

0.16 2 

7 

7 

7 

7 

7 

7 

8 

8 

8 

8 

8 

8 

9 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

0.144 0.148 2 

0.145 0.143 2 

0.15 0.149 2 

0.146 0.15 2 

0.142 0.155 2 

0.146 0.148 2 

0.18 0.18 2 

0.18 0.18 2 

0.18 0.17 2 

0.18 0.18 2 

0.19 0.19 2 

0.18 0.18 2 

0.12855 0.1331 2 

0.12978 0.12912 2 

0.12115 0.12421 2 

0.12243 0.12013 2 

0.11872 0.12337 2 

0.12637 0.12628 2 

0.19 0.2 2 

0.2 0.19 2 

0.19 0.19 2 

0.19 0.2 2 

0.195 0.19 2 

0.19 0.19 2 

124 
 

K2O

K2O: Glass Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 0.719 

1 0.723 

1 0.724 

1 0.732 

1 0.722 

1 0.723 

2 0.74 

2 0.74 

2 0.74 

2 0.73 

2 0.74 

2 0.74 

3 0.7387 

3 0.7407 

3 0.7377 

3 0.7335 

3 0.7335 

3 0.7345 

4 0.7235 

4 0.728 

4 0.721 

4 0.7243 

4 0.7299 

4 0.7267 

5 0.73 

5 0.73 

5 0.73 

5 0.74 

5 0.73 

5 0.73 

6 0.74 

6 0.74 

6 0.74 

6 0.74 

6 0.74 

6 0.74 

7 0.728 

7 0.728 

7 0.727 

7 0.729 

7 0.723 

7 0.731 

8 0.732 

8 0.7352 

8 0.7321 

8 0.7336 

0.721 

0.722 

0.728 

0.725 

0.72 

0.727 

0.73 

0.74 

0.73 

0.73 

0.74 

0.74 

0.7377 

0.7367 

0.7387 

0.7325 

0.7326 

0.7345 

0.7217 

0.7315 

0.7236 

0.7223 

0.7328 

0.7261 

0.73 

0.73 

0.73 

0.73 

0.73 

0.73 

0.73 

0.73 

0.74 

0.74 

0.74 

0.73 

0.727 

0.726 

0.724 

0.732 

0.728 

0.727 

0.731 

0.7359 

0.7316 

0.7341 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

K2O: Powder Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 0.75 

1 0.74 

1 0.75 

1 0.74 

1 0.74 

1 0.73 

2 0.73 

2 0.73 

2 0.74 

2 0.73 

2 0.73 

2 0.74 

3 0.73 

3 0.74 

3 0.74 

3 0.74 

3 0.74 

3 0.74 

4 0.75 

4 0.74 

4 0.75 

4 0.75 

4 0.75 

4 0.75 

5 0.74 

5 0.74 

5 0.74 

5 0.73 

5 0.74 

5 0.73 

6 0.74 

6 0.75 

6 0.75 

6 0.74 

6 0.75 

6 0.75 

7 0.725 

7 0.724 

7 0.734 

7 0.73 

7 0.729 

7 0.73 

8 0.73 

8 0.73 

8 0.73 

8 0.73 

0.74 1
 

0.74 1
 

0.74 1
 

0.74 1
 

0.74 1
 

0.73 1
 

0.73 1
 

0.73 1
 

0.73 1
 

0.73 1
 

0.73 1
 

0.74 1
 

0.73 1
 

0.75 1
 

0.74 1
 

0.74 1
 

0.74 1
 

0.74 1
 

0.75 1
 

0.75 1
 

0.74 1
 

0.75 1
 

0.74 1
 

0.75 1
 

0.74 1
 

0.74 1
 

0.74 1
 

0.74 1
 

0.74 1
 

0.73 1
 

0.74 1
 

0.75 1
 

0.74 1
 

0.75 1
 

0.74 1
 

0.75 1
 

0.726 1
 

0.724 1
 

0.734 1
 

0.728 1
 

0.728 1
 

0.731 1
 

0.73 1
 

0.73 1
 

0.73 1
 

0.73 1
 

125
 
8 0.7306 0.731 

8 0.7322 0.7321 

9 0.73 0.73 

9 0.73 0.73 

9 0.73 0.73 

9 0.73 0.73 

9 0.73 0.73 

9 0.73 0.73 

10 0.724 0.72 

10 0.717 0.724 

10 0.724 0.724 

10 0.72 0.721 

10 0.724 0.725 

10 0.722 0.717 

11 0.75 0.74 

11 0.75 0.74 

11 0.75 0.74 

11 0.75 0.74 

11 0.75 0.75 

11 0.75 0.75 

1 1.162 1.161 

1 1.17 1.17 

1 1.154 1.152 

1 1.157 1.158 

1 1.168 1.17 

1 1.156 1.158 

2 1.18 1.19 

2 1.19 1.18 

2 1.18 1.18 

2 1.19 1.19 

2 1.19 1.19 

2 1.18 1.18 

3 1.1818 1.1779 

3 1.1828 1.1789 

3 1.1818 1.1798 

3 1.1753 1.1802 

3 1.1764 1.1773 

3 1.1783 1.1773 

4 1.1688 1.167 

4 1.1561 1.1588 

4 1.1587 1.1653 

4 1.1656 1.1644 

4 1.1622 1.165 

4 1.1702 1.1601 

5 1.18 1.18 

5 1.18 1.19 

5 1.19 1.19 

5 1.18 1.19 

5 1.18 1.19 

5 1.18 1.18 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

8 

8 

9 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

5 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

6 

0.73 0.73 1 

0.73 0.73 1 

0.74 0.75 1 

0.75 0.75 1 

0.75 0.75 1 

0.73 0.73 1 

0.75 0.75 1 

0.75 0.75 1 

0.7204 0.7211 1 

0.7191 0.7202 1 

0.7307 0.7312 1 

0.7189 0.7189 1 

0.7284 0.7284 1 

0.725 0.7255 1 

1.17 1.19 2 

1.18 1.18 2 

1.19 1.19 2 

1.17 1.17 2 

1.18 1.19 2 

1.2 1.18 2 

1.17 1.16 2 

1.19 1.19 2 

1.18 1.18 2 

1.17 1.18 2 

1.18 1.18 2 

1.19 1.19 2 

1.18 1.18 2 

1.19 1.19 2 

1.2 1.2 2 

1.18 1.19 2 

1.19 1.19 2 

1.19 1.19 2 

1.19 1.19 2 

1.2 1.2 2 

1.2 1.21 2 

1.19 1.19 2 

1.21 1.21 2 

1.2 1.21 2 

1.19 1.19 2 

1.18 1.18 2 

1.2 1.2 2 

1.18 1.18 2 

1.19 1.19 2 

1.19 1.19 2 

1.23 1.23 2 

1.24 1.24 2 

1.24 1.24 2 

1.23 1.23 2 

1.24 1.24 2 

1.25 1.24 2 

126 
 

 

 

 

 

 

 

 

 

 

 

 

6 1.17 1.17 

6 1.17 1.17 

6 1.17 1.18 

6 1.18 1.18 

6 1.17 1.17 

6 1.18 1.17 

7 1.167 1.174 

7 1.166 1.172 

7 1.172 1.174 

7 1.165 1.165 

7 1.165 1.174 

7 1.164 1.166 

8 1.1534 1.1541 

8 1.1629 1.1634 

8 1.1622 1.1609 

8 1.1667 1.1665 

8 1.1615 1.1623 

8 1.1655 1.1647 

9 1.17 1.18 

9 1.18 1.17 

9 1.16 1.17 

9 1.17 1.18 

9 1.17 1.17 

9 1.17 1.17 

10 1.161 1.16 

10 1.16 1.158 

10 1.165 1.159 

10 1.158 1.157 

10 1.16 1.16 

10 1.157 1.157 

11 1.21 1.21 

11 1.21 1.21 

11 1.22 1.22 

11 1.21 1.22 

11 1.21 1.21 

11 1.22 1.22 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

7 

7 

7 

7 

7 

7 

8 

8 

8 

8 

8 

8 

9 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

1.162 1.163 2 

1.168 1.17 2 

1.17 1.172 2 

1.167 1.169 2 

1.178 1.179 2 

1.165 1.166 2 

1.16 1.16 2 

1.16 1.17 2 

1.17 1.17 2 

1.16 1.16 2 

1.17 1.17 2 

1.17 1.17 2 

1.2 1.21 2 

1.22 1.21 2 

1.2 1.2 2 

1.21 1.21 2 

1.21 1.21 2 

1.22 1.22 2 

1.1781 1.1751 2 

1.1826 1.128 2 

1.1817 1.1817 2 

1.1675 1.1682 2 

1.1772 1.178 2 

1.1806 1.1805 2 

127 
 

TiO2

TiO2: Glass Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 0.223 

1 0.229 

1 0.229 

1 0.228 

1 0.227 

1 0.232 

2 0.23 

2 0.235 

2 0.24 

2 0.233 

2 0.225 

2 0.231 

3 0.24 

3 0.24 

3 0.24 

3 0.23 

3 0.23 

3 0.23 

4 0.2306 

4 0.2306 

4 0.2306 

4 0.2295 

4 0.2305 

4 0.2295 

5 0.2444 

5 0.2462 

5 0.2468 

5 0.247 

5 0.2477 

5 0.2495 

6 0.23 

6 0.23 

6 0.23 

6 0.23 

6 0.22 

6 0.23 

7 0.22 

7 0.22 

7 0.22 

7 0.23 

7 0.22 

7 0.22 

8 0.226 

8 0.225 

8 0.225 

8 0.223 

0.229 

0.231 

0.225 

0.225 

0.227 

0.229 

0.236 

0.22 

0.229 

0.222 

0.232 

0.226 

0.24 

0.23 

0.24 

0.24 

0.24 

0.24 

0.2286 

0.2306 

0.2296 

0.2286 

0.2276 

0.2305 

0.2388 

0.2445 

0.2452 

0.2361 

0.2429 

0.2433 

0.23 

0.23 

0.23 

0.23 

0.23 

0.23 

0.22 

0.22 

0.22 

0.22 

0.22 

0.23 

0.227 

0.222 

0.226 

0.226 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

TiO2: Powder Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 0.23 

1 0.23 

1 0.23 

1 0.23 

1 0.22 

1 0.23 

2 0.23 

2 0.23 

2 0.23 

2 0.23 

2 0.23 

2 0.23 

3 0.24 

3 0.24 

3 0.24 

3 0.24 

3 0.24 

3 0.24 

4 0.23 

4 0.23 

4 0.23 

4 0.23 

4 0.23 

4 0.23 

5 0.23 

5 0.22 

5 0.22 

5 0.23 

5 0.23 

5 0.22 

6 0.23 

6 0.23 

6 0.23 

6 0.23 

6 0.23 

6 0.23 

7 0.23 

7 0.23 

7 0.23 

7 0.23 

7 0.23 

7 0.23 

8 0.23 

8 0.22 

8 0.22 

8 0.23 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.24 1
 

0.24 1
 

0.24 1
 

0.24 1
 

0.24 1
 

0.24 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.22 1
 

0.22 1
 

0.22 1
 

0.23 1
 

0.22 1
 

0.23 1
 

0.23 1
 

0.24 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.23 1
 

0.22 1
 

0.22 1
 

0.22 1
 

128
 
8 0.223 0.228 

8 0.226 0.227 

9 0.2228 0.2217 

9 0.2203 0.2203 

9 0.2205 0.223 

9 0.2217 0.2236 

9 0.2279 0.2204 

9 0.2187 0.2213 

10 0.24 0.24 

10 0.24 0.24 

10 0.24 0.23 

10 0.23 0.23 

10 0.23 0.23 

10 0.23 0.23 

11 0.2261 0.2335 

11 0.2267 0.2341 

11 0.2325 0.2374 

11 0.2321 0.2342 

11 0.2349 0.2416 

11 0.2275 0.2236 

12 0.24 0.24 

12 0.24 0.24 

12 0.24 0.24 

12 0.25 0.25 

12 0.24 0.25 

12 0.25 0.25 

1 0.226 0.225 

1 0.221 0.228 

1 0.222 0.223 

1 0.224 0.223 

1 0.225 0.222 

1 0.228 0.224 

2 0.225 0.224 

2 0.214 0.222 

2 0.216 0.224 

2 0.219 0.227 

2 0.219 0.226 

2 0.22 0.219 

3 0.23 0.22 

3 0.23 0.23 

3 0.24 0.23 

3 0.23 0.22 

3 0.23 0.23 

3 0.23 0.23 

4 0.2239 0.2259 

4 0.2258 0.2258 

4 0.2239 0.2239 

4 0.224 0.224 

4 0.225 0.224 

4 0.2249 0.2249 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

8 

8 

9 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

11 

11 

11 

11 

11 

11 

12 

12 

12 

12 

12 

12 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

0.22 0.23 1 

0.23 0.23 1 

0.228 0.229 1 

0.23 0.226 1 

0.229 0.227 1 

0.232 0.229 1 

0.231 0.23 1 

0.233 0.228 1 

0.23 0.24 1 

0.23 0.24 1 

0.23 0.23 1 

0.24 0.23 1 

0.24 0.24 1 

0.23 0.23 1 

0.2312 0.2203 1 

0.2254 0.2266 1 

0.2251 0.2272 1 

0.2319 0.2283 1 

0.2274 0.2264 1 

0.2219 0.229 1 

0.23 0.23 1 

0.23 0.23 1 

0.235 0.23 1 

0.23 0.23 1 

0.23 0.23 1 

0.235 0.23 1 

0.22 0.23 2 

0.22 0.22 2 

0.23 0.22 2 

0.22 0.22 2 

0.22 0.22 2 

0.23 0.22 2 

0.22 0.22 2 

0.22 0.22 2 

0.22 0.22 2 

0.23 0.22 2 

0.22 0.22 2 

0.22 0.22 2 

0.24 0.24 2 

0.24 0.24 2 

0.24 0.24 2 

0.23 0.24 2 

0.23 0.24 2 

0.24 0.23 2 

0.23 0.22 2 

0.22 0.22 2 

0.22 0.22 2 

0.22 0.22 2 

0.22 0.23 2 

0.22 0.22 2 

129 
5 0.2382 0.2389 

5 0.2378 0.2372 

5 0.2379 0.238 

5 0.2421 0.235 

5 0.2404 0.2325 

5 0.2411 0.2448 

6 0.22 0.23 

6 0.22 0.22 

6 0.22 0.23 

6 0.22 0.22 

6 0.22 0.23 

6 0.23 0.22 

7 0.22 0.22 

7 0.22 0.22 

7 0.22 0.22 

7 0.22 0.22 

7 0.22 0.22 

7 0.22 0.22 

8 0.221 0.22 

8 0.217 0.219 

8 0.221 0.219 

8 0.22 0.219 

8 0.219 0.216 

8 0.216 0.221 

9 0.2191 0.2165 

9 0.2146 0.217 

9 0.2193 0.2147 

9 0.2155 0.2184 

9 0.2145 0.2157 

9 0.2141 0.2158 

10 0.24 0.24 

10 0.24 0.23 

10 0.24 0.24 

10 0.23 0.23 

10 0.23 0.23 

10 0.23 0.23 

11 0.221 0.2256 

11 0.2292 0.222 

11 0.2306 0.2269 

11 0.2183 0.2286 

11 0.2206 0.2267 

11 0.2204 0.2257 

12 0.24 0.24 

12 0.24 0.24 

12 0.24 0.24 

12 0.24 0.25 

12 0.24 0.24 

12 0.24 0.24 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

5 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

6 

7 

7 

7 

7 

7 

7 

8 

8 

8 

8 

8 

8 

9 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

11 

11 

11 

11 

11 

11 

12 

12 

12 

12 

12 

12 

0.22 0.22 2 

0.23 0.22 2 

0.22 0.22 2 

0.23 0.22 2 

0.22 0.22 2 

0.21 0.21 2 

0.22 0.22 2 

0.22 0.23 2 

0.22 0.23 2 

0.23 0.22 2 

0.23 0.22 2 

0.23 0.22 2 

0.22 0.22 2 

0.22 0.22 2 

0.22 0.22 2 

0.22 0.22 2 

0.22 0.22 2 

0.22 0.22 2 

0.21 0.22 2 

0.21 0.21 2 

0.21 0.21 2 

0.21 0.21 2 

0.21 0.22 2 

0.21 0.21 2 

0.219 0.219 2 

0.218 0.222 2 

0.22 0.218 2 

0.221 0.219 2 

0.219 0.222 2 

0.221 0.22 2 

0.23 0.21 2 

0.22 0.22 2 

0.22 0.23 2 

0.22 0.22 2 

0.22 0.23 2 

0.21 0.22 2 

0.224 0.2183 2 

0.217 0.2176 2 

0.2144 0.218 2 

0.2171 0.2145 2 

0.2204 0.213 2 

0.2194 0.2198 2 

0.22 0.22 2 

0.22 0.22 2 

0.22 0.22 2 

0.22 0.22 2 

0.22 0.22 2 

0.22 0.22 2 

130 
 

P2O5

P2O5: Glass Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 0.139 

1 0.14 

1 0.139 

1 0.139 

1 0.14 

1 0.147 

2 0.132 

2 0.128 

2 0.133 

2 0.131 

2 0.131 

2 0.13 

3 0.1368 

3 0.1358 

3 0.1378 

3 0.1377 

3 0.1377 

3 0.1358 

4 0.1339 

4 0.1377 

4 0.139 

4 0.1339 

4 0.1349 

4 0.1324 

5 0.14 

5 0.14 

5 0.14 

5 0.14 

5 0.14 

5 0.14 

6 0.136 

6 0.137 

6 0.136 

6 0.137 

6 0.136 

6 0.138 

7 0.141 

7 0.138 

7 0.138 

7 0.141 

7 0.141 

7 0.138 

8 0.13 

8 0.13 

8 0.13 

8 0.13 

0.138 

0.14 

0.14 

0.139 

0.141 

0.14 

0.129 

0.132 

0.129 

0.132 

0.13 

0.129 

0.1378 

0.1368 

0.1358 

0.1377 

0.1358 

0.1367 

0.1361 

0.14 

0.1333 

0.139 

0.1378 

0.1379 

0.14 

0.14 

0.14 

0.14 

0.14 

0.14 

0.138 

0.136 

0.137 

0.137 

0.138 

0.137 

0.136 

0.14 

0.139 

0.139 

0.141 

0.141 

0.13 

0.13 

0.13 

0.13 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

P2O5: Powder Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 0.138 

1 0.138 

1 0.137 

1 0.139 

1 0.137 

1 0.135 

2 0.14 

2 0.14 

2 0.14 

2 0.14 

2 0.14 

2 0.14 

3 0.14 

3 0.13 

3 0.14 

3 0.13 

3 0.13 

3 0.13 

4 0.14 

4 0.15 

4 0.15 

4 0.14 

4 0.15 

4 0.14 

5 0.14 

5 0.14 

5 0.14 

5 0.14 

5 0.14 

5 0.14 

6 0.139 

6 0.139 

6 0.139 

6 0.139 

6 0.136 

6 0.136 

7 0.14 

7 0.14 

7 0.14 

7 0.14 

7 0.14 

7 0.14 

8 0.1 

8 0.1 

8 0.1 

8 0.1 

0.137 1
 

0.137 1
 

0.138 1
 

0.139 1
 

0.139 1
 

0.137 1
 

0.14 1
 

0.14 1
 

0.14 1
 

0.14 1
 

0.14 1
 

0.14 1
 

0.14 1
 

0.14 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.14 1
 

0.15 1
 

0.14 1
 

0.14 1
 

0.15 1
 

0.14 1
 

0.14 1
 

0.14 1
 

0.14 1
 

0.14 1
 

0.13 1
 

0.14 1
 

0.133 1
 

0.133 1
 

0.131 1
 

0.136 1
 

0.141 1
 

0.138 1
 

0.14 1
 

0.14 1
 

0.14 1
 

0.14 1
 

0.14 1
 

0.14 1
 

0.1 1
 

0.1 1
 

0.1 1
 

0.1 1
 

131
 
8 0.13 0.13 

8 0.13 0.13 

9 0.14 0.1376 

9 0.1381 0.1369 

9 0.1303 0.1415 

9 0.1371 0.1421 

9 0.1405 0.1473 

9 0.1344 0.1394 

1 0.135 0.137 

1 0.137 0.136 

1 0.137 0.138 

1 0.136 0.136 

1 0.138 0.138 

1 0.137 0.138 

2 0.13 0.133 

2 0.126 0.134 

2 0.129 0.134 

2 0.129 0.132 

2 0.131 0.133 

2 0.135 0.125 

3 0.1343 0.1343 

3 0.1343 0.1343 

3 0.1353 0.1353 

3 0.1334 0.1334 

3 0.1344 0.1344 

3 0.1324 0.1344 

4 0.1306 0.1337 

4 0.1344 0.1293 

4 0.1296 0.134 

4 0.1347 0.136 

4 0.1279 0.1325 

4 0.1294 0.1357 

5 0.14 0.14 

5 0.14 0.14 

5 0.14 0.14 

5 0.14 0.14 

5 0.14 0.14 

5 0.14 0.14 

6 0.134 0.133 

6 0.135 0.134 

6 0.135 0.135 

6 0.135 0.136 

6 0.135 0.136 

6 0.134 0.136 

7 0.137 0.136 

7 0.135 0.14 

7 0.141 0.14 

7 0.138 0.137 

7 0.138 0.135 

7 0.133 0.134 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

8 

8 

9 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

11 

11 

11 

11 

11 

11 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

5 

5 

5 

5 

5 

5 

0.1 0.1 1 

0.1 0.1 1 

0.151 0.151 1 

0.15 0.152 1 

0.152 0.15 1 

0.152 0.153 1 

0.153 0.153 1 

0.152 0.152 1 

0.135 0.137 1 

0.139 0.137 1 

0.138 0.138 1 

0.138 0.14 1 

0.137 0.135 1 

0.138 0.139 1 

0.1446 0.1446 1 

0.1394 0.1425 1 

0.1367 0.1329 1 

0.1504 0.1418 1 

0.1396 0.14 1 

0.1402 0.1337 1 

0.137 0.133 2 

0.136 0.138 2 

0.137 0.137 2 

0.137 0.137 2 

0.134 0.137 2 

0.137 0.137 2 

0.14 0.14 2 

0.14 0.14 2 

0.14 0.14 2 

0.14 0.14 2 

0.14 0.14 2 

0.14 0.14 2 

0.13 0.13 2 

0.13 0.13 2 

0.13 0.13 2 

0.14 0.14 2 

0.14 0.14 2 

0.14 0.13 2 

0.14 0.14 2 

0.14 0.15 2 

0.14 0.14 2 

0.15 0.14 2 

0.14 0.14 2 

0.14 0.14 2 

0.14 0.14 2 

0.14 0.14 2 

0.14 0.14 2 

0.13 0.14 2 

0.14 0.14 2 

0.14 0.14 2 

132 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8 0.13 0.13 2 

8 0.13 0.13 2 

8 0.13 0.13 2 

8 0.13 0.13 2 

8 0.13 0.13 2 

8 0.13 0.13 2 

9 0.1372 0.1369 2 

9 0.1413 0.1334 2 

9 0.1325 0.1372 2 

9 0.1403 0.1395 2 

9 0.1351 0.138 2 

9 0.1361 0.1354 2 

6 

6 

6 

6 

6 

6 

7 

7 

7 

7 

7 

7 

8 

8 

8 

8 

8 

8 

9 

9 

9 

9 

9 

9 

10 

10 

10 

10 

10 

10 

11 

11 

11 

11 

11 

11 

0.142 0.14 2 

0.147 0.152 2 

0.141 0.143 2 

0.136 0.14 2 

0.135 0.138 2 

0.142 0.137 2 

0.14 0.14 2 

0.14 0.14 2 

0.14 0.15 2 

0.14 0.14 2 

0.14 0.14 2 

0.14 0.14 2 

0.11 0.11 2 

0.1 0.1 2 

0.11 0.11 2 

0.11 0.11 2 

0.1 0.11 2 

0.11 0.1 2 

0.154 0.155 2 

0.152 0.153 2 

0.154 0.153 2 

0.154 0.156 2 

0.155 0.155 2 

0.154 0.154 2 

0.143 0.14 2 

0.143 0.144 2 

0.14 0.14 2 

0.14 0.141 2 

0.141 0.142 2 

0.143 0.142 2 

0.1388 0.1407 2 

0.1396 0.1389 2 

0.1346 0.1352 2 

0.1407 0.141 2 

0.1369 0.1356 2 

0.1388 0.1374 2 

133 
 

Cl

Cl Glass and Powder 

Lab Duplicate 1 Duplicate 2 Cement Method 

1 0.015 0.016 1 P 

1 0.016 0.016 1 P 

1 0.016 0.017 1 P 

1 0.016 0.016 1 P 

1 0.016 0.016 1 P 

1 0.016 0.016 1 P 

1 0.013 0.013 2 P 

1 0.013 0.013 2 P 

1 0.013 0.013 2 P 

1 0.013 0.013 2 P 

1 0.013 0.013 2 P 

1 0.012 0.013 2 P 

2 0.011 0.011 1 G 

2 0.012 0.012 1 G 

2 0.011 0.012 1 G 

2 0.011 0.013 1 G 

2 0.01 0.011 1 G 

2 0.011 0.011 1 G 

2 0.008 0.008 2 G 

2 0.008 0.008 2 G 

2 0.007 0.008 2 G 

2 0.007 0.008 2 G 

2 0.008 0.009 2 G 

2 0.008 0.008 2 G 

3 0.01 0.01 1 P 

3 0.01 0.01 1 P 

3 0.01 0.01 1 P 

3 0.01 0.01 1 P 

3 0.01 0.01 1 P 

3 0.01 0.01 1 P 

3 0.01 0 2 P 

3 0.01 0.01 2 P 

3 0.01 0.01 2 P 

3 0.01 0.01 2 P 

3 0 0.01 2 P 

3 0 0 2 P 

4 0.01 0.01 1 P 

4 0.011 0.012 1 P 

4 0.01 0.01 1 P 

4 0.011 0.011 1 P 

4 0.01 0.01 1 P 

4 0.011 0.011 1 P 

4 0.008 0.008 2 P 

4 0.007 0.007 2 P 

4 0.007 0.007 2 P 

4 0.008 0.007 2 P 

134 
4 0.006 0.008 2 P 

4 0.007 0.007 2 P 

5 0.016 0.015 1 P 

5 0.016 0.016 1 P 

5 0.015 0.017 1 P 

5 0.017 0.016 1 P 

5 0.016 0.016 1 P 

5 0.016 0.015 1 P 

5 0.011 0.012 2 P 

5 0.012 0.012 2 P 

5 0.013 0.013 2 P 

5 0.013 0.012 2 P 

5 0.013 0.012 2 P 

5 0.013 0.013 2 P 

6 0.02743 0.02738 1 G 

6 0.02741 0.02858 1 G 

6 0.02616 0.02717 1 G 

6 0.02644 0.02472 1 G 

6 0.02748 0.0297 1 G 

6 0.02572 0.02708 1 G 

6 0.02109 0.02184 2 G 

6 0.01991 0.02143 2 G 

6 0.01985 0.02078 2 G 

6 0.02024 0.02162 2 G 

6 0.02116 0.02039 2 G 

6 0.02258 0.02296 2 G 

135 
 

Mn2O3

Mn2O3: Glass Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 0.203 

1 0.206 

1 0.206 

1 0.206 

1 0.207 

1 0.207 

2 0.21 

2 0.21 

2 0.208 

2 0.209 

2 0.209 

2 0.217 

3 0.2013 

3 0.2032 

3 0.2023 

3 0.2041 

3 0.2032 

3 0.2012 

4 0.203 

4 0.201 

4 0.202 

4 0.203 

4 0.203 

4 0.203 

5 0.203 

5 0.2 

5 0.202 

5 0.201 

5 0.199 

5 0.202 

6 0.2002 

6 0.1986 

6 0.2033 

6 0.1995 

6 0.2014 

6 0.196 

7 0.19 

7 0.19 

7 0.19 

7 0.19 

7 0.19 

7 0.19 

1 0.051 

1 0.053 

1 0.052 

1 0.052 

0.204 

0.206 

0.205 

0.204 

0.208 

0.207 

0.205 

0.205 

0.208 

0.207 

0.209 

0.206 

0.2013 

0.2023 

0.2013 

0.2032 

0.2041 

0.2022 

0.203 

0.201 

0.202 

0.204 

0.201 

0.202 

0.206 

0.202 

0.203 

0.199 

0.199 

0.199 

0.1976 

0.199 

0.2015 

0.1985 

0.2021 

0.1956 

0.19 

0.19 

0.19 

0.19 

0.19 

0.19 

0.053 

0.054 

0.054 

0.053 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

2
 

2
 

2
 

2
 

Mn2O3: Powder Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 0.206 

1 0.202 

1 0.199 

1 0.207 

1 0.204 

1 0.202 

2 0.21 

2 0.21 

2 0.21 

2 0.21 

2 0.21 

2 0.21 

3 0.21 

3 0.21 

3 0.21 

3 0.21 

3 0.21 

3 0.21 

4 0.206 

4 0.207 

4 0.209 

4 0.207 

4 0.209 

4 0.206 

5 0.2026 

5 0.2022 

5 0.203 

5 0.2026 

5 0.2035 

5 0.2009 

6 0.183 

6 0.182 

6 0.181 

6 0.182 

6 0.185 

6 0.185 

7 0.21 

7 0.21 

7 0.22 

7 0.21 

7 0.21 

7 0.21 

1 0.059 

1 0.054 

1 0.053 

1 0.058 

0.206 1
 

0.206 1
 

0.203 1
 

0.203 1
 

0.205 1
 

0.203 1
 

0.21 1
 

0.21 1
 

0.21 1
 

0.21 1
 

0.21 1
 

0.21 1
 

0.21 1
 

0.21 1
 

0.21 1
 

0.21 1
 

0.21 1
 

0.21 1
 

0.206 1
 

0.21 1
 

0.207 1
 

0.211 1
 

0.208 1
 

0.207 1
 

0.2017 1
 

0.1975 1
 

0.1998 1
 

0.206 1
 

0.2056 1
 

0.2031 1
 

0.187 1
 

0.184 1
 

0.185 1
 

0.184 1
 

0.187 1
 

0.186 1
 

0.2 1
 

0.21 1
 

0.21 1
 

0.2 1
 

0.21 1
 

0.21 1
 

0.056 2
 

0.055 2
 

0.055 2
 

0.056 2
 

136
 
1 0.053 0.053 

1 0.055 0.054 

2 0.059 0.059 

2 0.06 0.053 

2 0.058 0.058 

2 0.056 0.055 

2 0.055 0.056 

2 0.056 0.054 

3 0.0526 0.0535 

3 0.0526 0.0535 

3 0.0526 0.0535 

3 0.0526 0.0545 

3 0.0536 0.0536 

3 0.0536 0.0536 

4 0.056 0.055 

4 0.055 0.056 

4 0.055 0.055 

4 0.056 0.055 

4 0.055 0.055 

4 0.054 0.055 

5 0.052 0.054 

5 0.052 0.054 

5 0.054 0.052 

5 0.053 0.051 

5 0.052 0.052 

5 0.052 0.053 

6 0.057 0.0627 

6 0.0586 0.0558 

6 0.0593 0.058 

6 0.0598 0.0573 

6 0.0589 0.0587 

6 0.0534 0.0563 

7 0.07 0.07 

7 0.07 0.07 

7 0.07 0.07 

7 0.07 0.07 

7 0.07 0.07 

7 0.07 0.07 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

1 

1 

2 

2 

2 

2 

2 

2 

3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

5 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

6 

7 

7 

7 

7 

7 

7 

0.055 0.055 2 

0.056 0.056 2 

0.06 0.06 2 

0.06 0.06 2 

0.06 0.06 2 

0.06 0.06 2 

0.06 0.06 2 

0.06 0.06 2 

0.06 0.06 2 

0.05 0.05 2 

0.05 0.05 2 

0.06 0.05 2 

0.05 0.05 2 

0.05 0.05 2 

0.06 0.057 2 

0.06 0.061 2 

0.057 0.057 2 

0.057 0.058 2 

0.058 0.057 2 

0.057 0.056 2 

0.0572 0.055 2 

0.0532 0.0511 2 

0.0541 0.0549 2 

0.0545 0.0531 2 

0.0524 0.0514 2 

0.0548 0.0554 2 

0.05 0.049 2 

0.05 0.051 2 

0.051 0.049 2 

0.05 0.05 2 

0.05 0.051 2 

0.05 0.052 2 

0.06 0.06 2 

0.05 0.05 2 

0.05 0.05 2 

0.05 0.05 2 

0.06 0.05 2 

0.05 0.05 2 

137 
 

ZnO

ZnO 

Lab Duplicate 1 Duplicate 2 

2 0.014 0.014 

2 0.014 0.014 

2 0.013 0.014 

2 0.013 0.013 

2 0.013 0.014 

2 0.014 0.014 

3 0.0156 0.0156 

3 0.0166 0.0166 

3 0.0166 0.0166 

3 0.0166 0.0166 

3 0.0166 0.0166 

3 0.0166 0.0166 

6 0.01 0.01 

6 0.01 0.01 

6 0.01 0.01 

6 0.01 0.01 

6 0.01 0.01 

6 0.01 0.01 

8 0.011 0.011 

8 0.01 0.01 

8 0.01 0.011 

8 0.011 0.011 

8 0.01 0.01 

8 0.011 0.011 

9 0.01207 0.01227 

9 0.01331 0.01306 

9 0.01292 0.01376 

9 0.01362 0.01287 

9 0.01193 0.01153 

9 0.01368 0.01246 

10 0.014 0.0129 

10 0.0137 0.0127 

10 0.0144 0.0136 

10 0.0151 0.0144 

10 0.0137 0.013 

10 0.0133 0.0129 

1 0.014 0.014 

1 0.014 0.014 

1 0.014 0.014 

1 0.014 0.014 

1 0.014 0.014 

1 0.014 0.014 

4 0.01 0.01 

4 0.01 0.01 

4 0.01 0.01 

4 0.01 0.01 

Cement 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

Method 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

G 

P 

P 

P 

P 

P 

P 

P 

P 

P 

P 

138 
4 0.01 

4 0.01 

5 0.013 

5 0.013 

5 0.013 

5 0.013 

5 0.013 

5 0.013 

7 0.0246 

7 0.0236 

7 0.0246 

7 0.0254 

7 0.0248 

7 0.0255 

2 0.013 

2 0.013 

2 0.012 

2 0.013 

2 0.013 

2 0.012 

3 0.0156 

3 0.0156 

3 0.0146 

3 0.0156 

3 0.0156 

3 0.0156 

6 0.01 

6 0.01 

6 0.01 

6 0.01 

6 0.01 

6 0.01 

8 0.009 

8 0.01 

8 0.009 

8 0.01 

8 0.01 

8 0.01 

9 0.01316 

9 0.01214 

9 0.01218 

9 0.01031 

9 0.01203 

9 0.01256 

10 0.0131 

10 0.0124 

10 0.0125 

10 0.0115 

10 0.0117 

10 0.0129 

0.01 

0.01 

0.014 

0.013 

0.013 

0.013 

0.013 

0.013 

0.025 

0.0248 

0.0241 

0.0256 

0.0251 

0.0253 

0.012 

0.013 

0.013 

0.013 

0.013 

0.013 

0.0156 

0.0146 

0.0146 

0.0156 

0.0156 

0.0156 

0.01 

0.01 

0.01 

0.01 

0.01 

0.01 

0.009 

0.01 

0.01 

0.01 

0.009 

0.01 

0.01168 

0.01226 

0.01152 

0.01164 

0.01254 

0.01126 

0.0133 

0.0133 

0.0133 

0.0126 

0.013 

0.0115 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

P
 P
 P
 P
 P
 P
 P
 P
 P
 P
 P
 P
 P
 P
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 G
 

139 
1 0.014 

1 0.013 

1 0.013 

1 0.013 

1 0.013 

1 0.013 

4 0.01 

4 0.01 

4 0.01 

4 0.01 

4 0.01 

4 0.01 

5 0.012 

5 0.012 

5 0.012 

5 0.012 

5 0.012 

5 0.012 

7 0.0233 

7 0.0227 

7 0.0235 

7 0.0243 

7 0.0229 

7 0.0237 

0.014 

0.013 

0.013 

0.013 

0.013 

0.013 

0.01 

0.01 

0.01 

0.01 

0.01 

0.01 

0.012 

0.012 

0.012 

0.012 

0.012 

0.012 

0.0233 

0.0238 

0.0224 

0.0241 

0.0237 

0.0242 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

P 

P 

P 

P 

P 

P 

P 

P 

P 

P 

P 

P 

P 

P 

P 

P 

P 

P 

P 

P 

P 

P 

P 

P 

140 
 

SrO

SrO: Glass Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 0.126 

1 0.127 

1 0.127 

1 0.128 

1 0.127 

1 0.128 

2 0.13 

2 0.13 

2 0.13 

2 0.13 

2 0.13 

2 0.13 

3 0.1309 

3 0.1309 

3 0.1309 

3 0.1299 

3 0.1309 

3 0.1299 

4 0.12 

4 0.12 

4 0.12 

4 0.12 

4 0.12 

4 0.12 

5 0.13 

5 0.132 

5 0.129 

5 0.131 

5 0.132 

5 0.13 

6 0.1263 

6 0.1264 

6 0.1278 

6 0.127 

6 0.1277 

6 0.127 

1 0.085 

1 0.085 

1 0.085 

1 0.085 

1 0.086 

1 0.086 

2 0.09 

2 0.09 

2 0.09 

2 0.09 

0.127 

0.127 

0.127 

0.128 

0.128 

0.128 

0.13 

0.13 

0.13 

0.13 

0.13 

0.13 

0.1309 

0.1309 

0.1309 

0.1299 

0.1309 

0.1309 

0.12 

0.12 

0.12 

0.12 

0.12 

0.12 

0.13 

0.132 

0.13 

0.13 

0.133 

0.13 

0.1264 

0.1277 

0.1285 

0.1288 

0.1262 

0.1256 

0.085 

0.086 

0.085 

0.085 

0.086 

0.086 

0.09 

0.09 

0.09 

0.09 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

1
 

2
 

2
 

2
 

2
 

2
 

2
 

2
 

2
 

2
 

2
 

SrO: Powder Preparation 

Lab Duplicate 1 Duplicate 2 Cement 

1 0.13 

1 0.131 

1 0.13 

1 0.129 

1 0.13 

1 0.13 

2 0.13 

2 0.13 

2 0.13 

2 0.13 

2 0.13 

2 0.13 

3 0.12 

3 0.12 

3 0.12 

3 0.12 

3 0.11 

3 0.12 

4 0.13 

4 0.13 

4 0.13 

4 0.13 

4 0.13 

4 0.13 

5 0.13 

5 0.13 

5 0.13 

5 0.13 

5 0.13 

5 0.13 

6 0.12 

6 0.12 

6 0.12 

6 0.12 

6 0.12 

6 0.12 

7 0.1296 

7 0.1293 

7 0.1289 

7 0.1291 

7 0.1284 

7 0.1282 

8 0.118 

8 0.117 

8 0.12 

8 0.121 

0.13 1
 

0.13 1
 

0.129 1
 

0.131 1
 

0.131 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.12 1
 

0.12 1
 

0.12 1
 

0.12 1
 

0.11 1
 

0.12 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.13 1
 

0.12 1
 

0.12 1
 

0.12 1
 

0.12 1
 

0.12 1
 

0.12 1
 

0.1281 1
 

0.1292 1
 

0.1285 1
 

0.1285 1
 

0.1293 1
 

0.1288 1
 

0.119 1
 

0.121 1
 

0.121 1
 

0.121 1
 

141
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2 0.09 0.09 

2 0.09 0.09 

3 0.0886 0.0886 

3 0.0886 0.0886 

3 0.0886 0.0886 

3 0.0876 0.0876 

3 0.0886 0.0886 

3 0.0886 0.0886 

4 0.08 0.08 

4 0.08 0.08 

4 0.08 0.08 

4 0.08 0.08 

4 0.08 0.08 

4 0.08 0.08 

5 0.088 0.088 

5 0.087 0.087 

5 0.087 0.086 

5 0.088 0.088 

5 0.087 0.087 

5 0.088 0.087 

6 0.0843 0.0846 

6 0.0848 0.0843 

6 0.0844 0.0858 

6 0.0841 0.0848 

6 0.0867 0.0847 

6 0.0853 0.085 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

8 

8 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

5 

5 

5 

5 

5 

5 

6 

6 

6 

6 

6 

6 

7 

7 

7 

7 

7 

7 

8 

8 

8 

8 

8 

8 

0.121 0.122 1 

0.122 0.121 1 

0.088 0.089 2 

0.088 0.089 2 

0.088 0.087 2 

0.087 0.088 2 

0.088 0.088 2 

0.087 0.088 2 

0.09 0.09 2 

0.09 0.09 2 

0.09 0.09 2 

0.09 0.09 2 

0.09 0.09 2 

0.09 0.09 2 

0.08 0.08 2 

0.08 0.08 2 

0.08 0.08 2 

0.08 0.08 2 

0.08 0.08 2 

0.08 0.08 2 

0.09 0.09 2 

0.08 0.08 2 

0.09 0.08 2 

0.09 0.09 2 

0.09 0.08 2 

0.09 0.09 2 

0.09 0.09 2 

0.09 0.09 2 

0.09 0.09 2 

0.09 0.09 2 

0.09 0.09 2 

0.09 0.09 2 

0.07 0.07 2 

0.07 0.07 2 

0.07 0.07 2 

0.07 0.07 2 

0.07 0.07 2 

0.07 0.07 2 

0.0883 0.089 2 

0.088 0.0888 2 

0.088 0.0889 2 

0.0886 0.0888 2 

0.088 0.0878 2 

0.0881 0.0884 2 

0.082 0.083 2 

0.083 0.085 2 

0.082 0.085 2 

0.087 0.087 2 

0.086 0.086 2 

0.086 0.086 2 

142 
 

Cr2O3

Cr2O3 

Lab Duplicate 1 Duplicate 2 Cement 

2 0.027 0.027 1 

2 0.028 0.027 1 

2 0.027 0.027 1 

2 0.027 0.027 1 

2 0.027 0.027 1 

2 0.027 0.027 1 

2 0.012 0.012 2 

2 0.011 0.011 2 

2 0.011 0.011 2 

2 0.011 0.011 2 

2 0.011 0.011 2 

2 0.011 0.01 2 

3 0.0274 0.0274 1 

3 0.0274 0.0264 1 

3 0.0274 0.0264 1 

3 0.0273 0.0273 1 

3 0.0273 0.0273 1 

3 0.0264 0.0273 1 

3 0.0136 0.0146 2 

3 0.0146 0.0136 2 

3 0.0146 0.0136 2 

3 0.0136 0.0136 2 

3 0.0136 0.0136 2 

3 0.0136 0.0136 2 

6 0.024 0.025 1 

6 0.026 0.025 1 

6 0.024 0.025 1 

6 0.024 0.024 1 

6 0.024 0.025 1 

6 0.024 0.024 1 

6 0.01 0.01 2 

6 0.013 0.012 2 

6 0.01 0.01 2 

6 0.01 0.01 2 

6 0.01 0.009 2 

6 0.012 0.012 2 

7 0.0277 0.0286 1 

7 0.0309 0.0299 1 

7 0.0272 0.0291 1 

7 0.0308 0.027 1 

7 0.0296 0.0272 1 

7 0.0287 0.0273 1 

7 0.0126 0.0143 2 

7 0.0115 0.011 2 

Method 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

143 
7 0.0107 0.0133 

7 0.0117 0.0131 

7 0.0136 0.0136 

7 0.0126 0.0131 

8 0.02 0.02 

8 0.02 0.02 

8 0.02 0.02 

8 0.02 0.02 

8 0.02 0.02 

8 0.02 0.02 

8 0 0.01 

8 0 0 

8 0 0 

8 0 0 

8 0 0 

8 0 0 

1 0.03 0.03 

1 0.03 0.031 

1 0.029 0.03 

1 0.029 0.03 

1 0.031 0.031 

1 0.032 0.031 

1 0.013 0.013 

1 0.014 0.013 

1 0.013 0.013 

1 0.013 0.013 

1 0.015 0.013 

1 0.013 0.012 

4 0.016 0.015 

4 0.016 0.014 

4 0.015 0.015 

4 0.016 0.016 

4 0.014 0.015 

4 0.015 0.015 

5 0.028 0.029 

5 0.028 0.028 

5 0.027 0.027 

5 0.028 0.028 

5 0.027 0.027 

5 0.027 0.027 

5 0.012 0.012 

5 0.011 0.012 

5 0.011 0.011 

5 0.012 0.011 

5 0.012 0.012 

5 0.011 0.011 

2 

2 

2 

2 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

144 
 

 

 

Acknowledgements

We wish to recognize LeRoy Jacobs, who provided the enthusiasm and his talents to the 

ASTM C1.23 task group in coordinating the inter-laboratory study. The time, efforts of 

all of the participants in this trial program and Robin Haupt of the Cement and Concrete 

Reference laboratory for sample distribution and collecting data are acknoledged. The 

comments and suggestions of reviewers Clarissa Ferraris, Kenneth Snyder and Don 

Broton are gratefully acknowledged. This project was supported by the Early-Age 

Performance of Concrete project within the Sustainable Engineering Materials program at 

NIST. 

References

1 Data Considered by Committee C-1 of the American Society for Testing Materials in 

Preparing the Standard Specifications and Tests for Portland Cement (serial Designation 

C 9-17), Committee C-1, American Society for Testing Materials, Philadelphia, PA, July 

1919. 

2 C114-11b, “Standard Test Method for Chemical Analysis of Hydraulic Cement,” 

Annual Book of ASTM Standards, Vol. 4.01, ASTM International, West Conshohocken, 

PA. 

3 J.A. Forrester, T.P. Lees, and A.E. Moore, “The Precision of Standard Cement Analysis 

nd its Effect on the Calculated Compound Composition,” S.C.I. Monograph No. 18, The 

Analysis of Calcareous Materials, 447-451 (1964)

4 H.G. Midgley, “Compound calculation in the phases in Portland cement clinker,” 

Cement Technology, Vol. 1, No. 3, 1970, pp. 1-5.

5 A.M. Harrisson, H.F.W. Taylor and N.B. Winter, “Electron-Optical Analysis of the 

Phases in a Portland Cement Clinker, with some Observations on the Calculation of 

Quantitative Phase Composition”, Cement and Concrete Research, Vol. 15, pp. 775-780, 

1985. 

6 L.P. Aldridge and R.P. Eardley, “Effects of analytical errors on the Bogue calculation of 

compound composition,” Cement Technology, 4, 1973, pp. 177-182.

7 L.P. Aldridge, “Errors in the analysis of cement,” Cement Technology, 7, 1976, pp. 8-

11 

8 P.E. Stutzman, and D.S. Lane, “Effects of Analytical Precision on Bogue Calculations 

of Potential Portland Cement Composition,” Journal of ASTM International, Vol. 7, No. 

6, paper ID JAI102697

9 EN 196-2, Methods of Testing Cement – Part 2: Chemical analysis of cement, 

10 NCHRP 139, “Precision Estimates for AASHTO Test Method T 105, Determined 

Using CCRL Proficiency Sample Data”. NCHRP Project 09-26A, June 2009, 

http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_w139.pdf

11 Report of Working Committee on Methods of Chemical Analysis, June 12, 1946, W.C. 

Hanna, Chairman

12 R. Haupt, personal communication 

145 
 

13 ASTM E 691 “Standard Practice for Conducting an Interlaboratory Study to Determine
 

the Precision of a Test Method,” Annual Book of ASTM Standards, Vol. 14.02, ASTM
 

International, West Conshohocken, PA.

14 ASTM E177 “Standard Practice for Use of the Terms Precision and Bias in ASTM
 

Test Methods,” Annual Book of ASTM Standards, Vol. 14.02, ASTM International, 

West Conshohocken, PA.

15 G.J. Hahn and W.Q. Meeker, Statistical Intervals: A Guide for Practitioners, John 

Wiley and Sons, New York, 1991.
 

146