Rietveld quantitative X-ray diffraction analysis of NIST fly ash standardreference materials

Ryan S. Winburn, Dean G. Grier, Gregory J. McCarthy, and Renee B. PetersonCenter for Main Group Chemistry, Department of Chemistry, North Dakota State University,Fargo, North Dakota 58105

(Received 1 November 1999; accepted 30 May 2000)

Rietveld quantitative X-ray diffraction analysis of the fly ash Standard Reference Materials (SRMs)issued by the National Institute of Standards and Technologies was performed. A rutile (TiO2)internal standard was used to enable quantitation of the glass content, which ranged from 65% to78% by weight. The GSAS Rietveld code was employed. Precision was obtained by performing sixreplicates of an analysis, and accuracy was estimated using mixtures of fly ash crystalline phasesand an amorphous phase. The three low-calcium (ASTM Class F) fly ashes (SRM 1633b, 2689 and2690) contained four crystalline phases: quartz, mullite, hematite, and magnetite. SRM 1633b alsocontained a detectable level of gypsum, which is not common for this type of fly ash. Thehigh-calcium (ASTM Class C) fly ash, SRM 2691, had eleven crystalline phases and presented achallenge for the version of GSAS employed, which permits refinement of only nine crystallinephases. A method of analyzing different groups of nine phases and averaging the results wasdeveloped, and tested satisfactorily with an eleven-phase simulated fly ash. The results werecompared to reference intensity ratio method semiquantitative analyses reported for most of theseSRMs a decade ago. © 2000 International Centre for Diffraction Data. [S0885-7156(00)00403-6]

I. INTRODUCTION

A review of the chemical composition and mineralogy(crystalline phases) in North American coal combustion flyashes is given by McCarthy et al. (1990). In that publication,fly ashes were classified by analytical CaO content: low-calcium (<10%CaO), intermediate-calcium (10%-19.9%CaO), and high-calcium (3=20% CaO).

The United States National Institute of Standards andTechnologies (NIST) has issued or reissued four StandardReference Material (SRM) fly ashes (NIST SRMP, 1999),principally as standards for trace elements analysis. TheseSRMs were designed to be representative of the range ofcompositions of North American fly ashes (Table I). SRM1633 and 2689 are low-calcium, American Society for Test-ing and Materials (ASTM) Class F fly ashes (ASTM, 1987)derived from combustion of bituminous coal. SRM 2690 and2691 are subbituminous coal fly ashes with higher calciumcontents.

A decade ago, McCarthy and co-workers studied theNIST fly ash SRMs then available by X-ray diffraction(XRD), and reported qualitative (McCarthy and Johansen,1988; McCarthy et al, 1988) and semiquantitative (McCar-thy and Thedchanamoorthy, 1989) crystalline phase analy-

ses. The semiquantitative analyses were done by the refer-ence intensity ratio (RIR) method using rutile as the internalstandard. RIR values were determined in their laboratoryfrom synthetic materials or minerals.

The particular difficulty with quantitative X-ray diffrac-tion (QXRD) analyses of complex multiphase materials,such as these fly ashes, is the extensive overlap of the strongpeaks of many of the phases, which may leave no obviouslyunique peaks to be used for quantitation. McCarthy andThedchanamoorthy (1989) developed a scheme by whichoverlapped peaks that were to be used for RIR quantitationwould have intensity due to other phases subtracted from theanalytical peak prior to quantitation. An example of such ascheme is shown in Figure 1 (McCarthy et al, 1990). This isthe flow chart used for the RIR QXRD analysis of high-calcium fly ashes, such as SRM 2691. McCarthy and Thed-chanamoorthy (1989) recommended that these QXRD resultsbe considered semiquantitative only.

Over the decade since those analyses were done, appli-cation of the Rietveld method (Rietveld, 1969) to QXRD hasbecome common, and implementations of this method thatrun on personal computers are now widely available. Thismethod appears to be better suited than the RIR method for

TABLE I. Chemical compositions of the NIST SRM fly ashes."

SRM

1633a1633b268926902691

ASTMclass

FFFFC

Coaltype"

BitBitBitSubSub

SiO2

48.849.351.555.336.0

A12O,

27.028.424.523.318.5

Fe2O,c

13.411.213.35.16.3

CaO

1.62.13.08.0

25.8

MgO

0.80.81.02.55.2

Na2O

0.20.30.30.31.5

K2O

2.32.42.61.20.4

SO3

0.50.5

0.42.1

TiO,

1.31.31.30.91.5

P2O5

0.50.21.21.2

"Calculated as oxides from elemental analysis data reported on the SRM certificates.bBit=bituminous; Sub=subbituminous.cFe expressed as Fe2O3 although present both as Fe2+ and Fe3+.

163 Powder Diffraction 15 (3), September 2000 0885-7156/2000/15(3)/163/10/$6.00 © 2000 JCPDS-ICDD 163

High-Calcium Fly Ash TABLE II. Mineral names, nominal chemical compositions, XRD codesand other names of crystalline phases normally found in North American flyashes.

Read peak at 31.1' andsubtract 34% (29%) oflAh= 'Ml

Subtract 15% (8%) of I Mufrom peak at 54.1'

Multiply residual by178% = I u .

Subtract 58% (54%) of I Hmfrom 35.5'peak = Isp

No

Subtract (48% of IMo )

from peak at 33.2

Yes

•*O,A

Read peak at 33.8' andmultiply by 81% - IMW

(26%ofIMw)

Figure 1. Flow chart for utilization of the reference intensity ratio methodfor semiquantitative high-calcium fly ash as reported by McCarthy et al.(1990).

characterizing complex multiphase materials such as flyashes. Rietveld QXRD (RQXRD) uses the whole pattern,reducing the effect of peak overlaps. It can model effects dueto sample, such as peak broadening due to crystallite size orstrain, and effects due to specimen mounting, such as speci-men displacement and preferred orientation. RQXRD doesnot require phase pure and representative standards for eachanalyte phase for the production of intensity ratios or scalefactors, as do many other QXRD techniques such as the RIRmethod. However, RQXRD does require crystal structuredata and solid solution chemical compositions for the phasesbeing quantitated. Also, in RQXRD, as with many QXRDtechniques, a crystalline internal standard must be added todetermine absolute weight percentages of crystalline phases,when an amorphous component is also present.

The Rietveld method has been applied to QXRD forsome time (Werner et al, 1979; Hill, 1983; Hill and Howard,1987; Bish and Howard, 1988; O'Connor and Raven, 1988;Hill, 1991; Taylor and Aldridge, 1993). Recently, Winburnet al. (2000) studied the accuracy of the Rietveld method forsystems of the complexity typically found in fly ashes. Theyused reference mixtures with up to eight crystalline phasesand found that for phases present at greater than 1.0 wt %abundance, accuracies of better than ± 10% of the amountpresent were achievable for most analytes.

North American fly ashes typically contain between fourand twelve crystalline phases plus glass (McCarthy, 1988;McCarthy and Johansen, 1988; McCarthy and Thedchan-amoorthy, 1989; McCarthy et al, 1990; McCarthy andSolem, 1991). The phases commonly found in fly ashes andtheir nominal compositions are shown in Table II. The typi-cal mineralogy of low-calcium fly ashes is quartz, mullite,

PhaseNominalformula

XRD codeand other names

QuartzMulliteHematiteMagnetiteLimePericlaseMeliliteMerwiniteAnhydriteTricalcium aluminateBrownmilleriteYe'elimite

SiO2

Al6Si2O13a

Fe2O3

Fe3O4

CaOMgOCa2(Mg, A1)(A1, Si)O7

b

Ca3Mg(SiO4)2

CaSO4

Ca3Al206

Ca4Al2Fe2O10

Ca4Al6012(S04)

QzMuHmMaLm, QuicklimePcMlMwAhC3A, aluminateC4AF, ferrite

C4A3S, sodalitestructure phase

"Refined in this study as the composition A12(A128, Si, 2)O96.b Refined in this study as the akermanite end member, Ca2MgSi207.

hematite, and magnetite. High-calcium ashes have all ofthese phases plus calcium and magnesium-containing com-pounds such as lime, periclase, melilite, merwinite, and an-hydrite. With very few exceptions, well over half the contentof coal combustion fly ashes is glass. [This generalizationapplies to direct coal combustion technologies. Note that theterm ' 'fly ash'' is often (and inappropriately) applied to anyfine particulates resulting from coal utilization. For example,the fines from fluidized bed combustion (FBC) of coal withlimestone as a desulfurization agent are sometimes called"fly ash." In FBC, combustion occurs at a 500-900 °Clower temperature. The chemical composition and mineral-ogy of such materials is quite different from, and the totalcrystalline phase content is typically much greater than, thatof coal combustion fly ash.] According to the data reportedby McCarthy and Thedchanamoorthy (1989), the NIST flyash SRMs contain from 65% to 77% glass.

The objectives of this study were to test the utility of theRietveld QXRD method on multiphase and dominantlyglassy materials using the NIST fly ash SRMs as test cases,and to determine the precision and estimate the accuracy onecan expect from routine analyses of such materials. The termroutine should be noted. Data collection and analysis proto-cols are designed for high throughput of samples accompa-nied by good precision and accuracy. High QXRD through-put in our laboratory means that an hour or two, rather thana half-day or more, is used for data collection. The Rietveldrefinements should be done with as many fixed parameters aspossible in order to keep refinement times on the availablecomputers (at the time of the study: 200+MHz Pentiumclass personal computers with 64-128 Mbytes memory) toan hour or less for most analyses. The target for overallprecision was set at ± 5 % of the amount present consideringall factors from sampling and specimen preparation throughrefinement with the total diffraction pattern, all performed bytwo or more analysts. The target for accuracy of QXRD ofmajor and minor phases was defined as ±10% of the amountpresent in a mixture of four or more crystalline phases in adominantly amorphous matrix.

To determine glass contents, an internal standard wasused. The standard was a coatings grade rutile (TiO2) with a

164 Powder Diffr., Vol. 15, No. 3, September 2000 Winburn et al. 164

submicrometer and relatively uniform particle size. This ma-terial is not 100% crystalline rutile (it has a surface coatingof amorphous alumina tailored for its application as a paintpigment), so to perform the calculations necessary to deter-mine glass content of the fly ashes, it is necessary to have aprimary standard for a crystalline material. NIST SRM 676alumina, which is readily available and widely used an XRDinternal standard for reference intensity ratio determination,has been certified by NIST (NIST SRMP, 1999) to be 98.4%crystalline a-Al2O3. This result was used as the primarystandard in a determination, by the RQXRD method, of thecrystalline phase content of the rutile internal standard. If the98.4% result is changed later, the results of the RQXRDanalyses reported here can be adjusted correspondingly.

The results of the RQXRD analysis are compared tothose obtained previously by McCarthy and Thedchan-amoorthy (1989) using the RIR method for four of the fivefly ashes studied. Because of their certified uniformity andavailability, it is suggested that fly ash SRMs would be use-ful for interlaboratory comparisons and round robins focusedon multiphase materials with high glass contents.

II. MATERIALS AND EXPERIMENTAL PROCEDURES

A. Materials

1. Fly ash standard reference materials

The four fly ash SRMs were purchased from NIST(NIST SRMP, 1999). Their major and minor element chemi-cal compositions, recalculated as oxides, are given in Table1. SRM 1633b (which replaced SRM 1633 and 1633a), wasissued in 1991 for "use in the evaluation of analytical meth-ods for the determination of constituent elements in coal flyash or materials with similar matrix." Like the fly ashes itreplaced, SRM 1633b is derived from combustion of bitumi-nous coal and has a chemical composition that places it inthe ASTM Class F fly ash category (ASTM, 1987). SRM2689 is also derived from bituminous coal, and is also anASTM Class F ash. SRMs 2690 and 2691 come from subbi-tuminous coal, but have significantly different compositions.SRM 2690 is derived from a Colorado subbituminous coal,with the ash having an analytical CaO content (all analyzedCa reported as CaO) of 8.0%. It is a low-calcium fly ash, butwith a CaO content well above the 2.1% and 3.1% of SRM1633b and 2689. SRM 2691 is a high-calcium fly ash with aCaO content of 25.8%, accompanied by a significantlyhigher MgO content than the other fly ashes. The differentcomposition of SRM 2691 gives it a mineralogy distinctfrom that of the other three fly ash SRMs.

2. Internal standard

As was the case in the previous QXRD study, rutile wasselected as the internal standard because it has a linear ab-sorption coefficient in the midrange of the various fly ashphases to be analyzed. Such a selection helps to minimizeintensity error due to microabsorption (Brindley, 1945).

The rutile sample used by McCarthy and Thedchan-amoorthy (1989) was a reagent grade TiO2 fired for severaldays at 1200 °C and ground to < 10 /xm. This rutile was stillavailable for the present study, but when examined by scan-ning electron microscopy (SEM), it was found to have par-

ticle sizes ranging from submicrometer to 5 fim, with a meanof about 2 fjum. In order to minimize microabsorption contri-butions from the internal standard, a rutile with a smaller andmore uniform particle size was employed. DuPont'sTi-Pure® R900 coatings grade titanium dioxide is reportedby the manufacturer to have a mean size of 0.31 yttm and alow dispersion of particle sizes. This material was checkedby SEM and confirmed to have a mean particle size of about0.3 fj.m. DuPont also certifies the material to be >94% rutilewith an alumina surface coat. The material showed no ana-tase (TiO2) or other detectable crystalline impurity in a high-sensitivity X-ray powder pattern. The alumina surface coat-ing is X-ray amorphous.

3. Single phases used in reference mixtures ofsynthetic fly ashes

The materials used for the synthetic fly ashes (referencemixtures) included MIN-U-SIL quartz obtained from U.S.Silica Company, ferric oxide (hematite) from Baker Re-agents, silica gel H and calcium carbonate (calcite) from EMReagents, magnesium oxide (periclase) from Mallinckrodt,and magnetite from CERAC. The mullite used was groundfrom refractory brick. Anhydrite was prepared by heatinggypsum (Mallinckrodt) at 800 °C for 10 h. The remainingphases, tricalcium aluminate, merwinite, brownmillerite, andmelilite (see Table II for compositions), were synthesizedfrom reagent grade chemicals and standard ceramic tech-niques (McCarthy and Thadchanamoorthy, 1989).

Each of the reference phases was checked for crystallinephase purity by qualitative XRD, and for amorphous phasecontent by RQXRD (Winburn, 1999; Winburn et al, 2000).None of the reference phases had any detectable crystallineimpurities. For the phases that had an X-ray amorphous com-ponent, appropriate adjustments were made to referenceweight percentages in the mixtures, and the amorphous con-tent of each phase was included in the overall amorphousphase content of each reference mixture.

B. Specimen preparation

Experimental procedures for XRD studies of fly ashhave been discussed previously (McCarthy et al., 1988) andwill only be summarized here. An approximately 5 g aliquotof the fly ash sample was ground in a McCrone MicronizingMill using an agate mill with ethanol as the grinding me-dium. Qualitative analysis specimens were prepared directlyfrom the slurry obtained from the micronizing process by thesmear method on a glass microscope slide (Davis et al.,1997). The remaining material was allowed to air dry beforebeing used for the quantitative analysis specimens.

For each specimen, 0.9000 g of the SRM fly ash wascombined with 0.1000 g of the rutile internal standard. Eachsample was then ground for 5 min with a mortar and pestleunder 95% ethanol. The specimens were prepared by sidedrifting the sample into an aluminum well mount (McMurdieet al., 1986).

C. Data collection and qualitative analysis

Data were collected using a Philips X-Pert Multi-purpose Diffractometer in Bragg-Brentano geometry. The

165 Powder Diffr., Vol. 15, No. 3, September 2000 Rietveld quantitative X-ray diffraction analysis 165

TABLE III. Diffractometer and measurement conditions for obtaining qualitative and quantitative powderX-ray diffraction data.

Qualitative analysis Quantitative analysis

Radiation sourceMonochromatorDivergence SlitsAntiscatter SlitsReceiving SlitsDetectorSoller slitsGenerator settingsStarting angle (20)Final angle (20)Step sizeStep time (s)Elapsed time

Cu Ka, long fine focusGraphite diffracted beamVariable4°0.2 mmProportional counter0.04 rad, incident and diffracted beam45 kV, 30 mA6°65°0.025°149 min

Cu Ka, long fine focusGraphite diffracted beam1 °1 °0.2 mmProportional counter0.04 rad, incident and diffracted beam45 kV, 30 mA20°80°0.03°266 min

details of the diffractometer and scan conditions are de-scribed in Table III. In keeping with one of the study objec-tives, to obtain high sample throughput, the quantitativeanalysis scan parameters (20-80° 2 0, 0.03° steps, 2 s/step)selected required a data collection time of only 1.1 h. It hadbeen previously shown in QXRD analyses on eight phasereference mixtures in a dominantly amorphous matrix (Win-burn et ai, 2000) that these conditions yield an accuracysimilar to that obtained from scans with wider angular rangeand longer count times (20-140° 2 6, 0.025° steps, 8 s/step).An experiment to verify that this observation holds true inthis system was performed, comparing the 1.1 h data collec-tion results to the 12 h data collection results, as part of thestudy of precision. For the criteria set forth in the objectivesof this study (i.e., no attempted structure refinement analy-ses), the 1.1 h and 12 h data collection experiments producedsimilar results.

Qualitative analyses were performed using the search/match software JADE (MDI, 1998) applied to the JCPDS-ICDD Powder Diffraction File database (McClune, 1998).

D. Quantitative analysis

The Rietveld code used was the publicly available Gen-eral Structure Analysis System (GSAS) (Larson and VonDreele, 1994). The instrumental parameters were determinedusing the NIST Alumina plate, SRM 1976 (NIST SRMP,1999). The parameters included in the refinements of theinstrumental standard and samples are shown in Table IV.After experimenting with several profile functions, thepseudo-Voigt function of Thompson et al. (1987) was cho-sen to model the peaks. Due to the small amounts of crystal-line phases present, and the resulting low diffraction intensi-ties, atomic positional and displacement ("thermal")parameters were not refined. A microabsorption correctionwas not applied, as discussed later.

Crystal structure data for each phase identified in thequalitative analysis were obtained directly from the litera-ture, or from the ICSD database (1999). A list of structuraldata used in this study and their respective literature refer-ences can be obtained from http://

TABLE IV. Rietveld parameters for the instrumental profile and RQXRD refinements.

Parameter

Instrument zeroSpecimen displacementBackground

Profile functionGUGVGWGPLXLY

Specimen transparencyPeak asymmetryPreferred orientationPeak broadening due to

crystallite sizePeak broadening due to strainLattice dimensionsAtomic positionsAtomic displacements

("thermal parameters")Lorentz polarizationPhase fraction

Instrumental profile refinement

RefinedRefinedChebyshev polynomial

(12 coefficients)Pseudo-VoigtRefinedFixedRefinedRefinedRefinedRefinedRefinedRefined12th order spherical harmonicsRefined

RefinedRefinedFixedFixed

Refined

RQXRD refinements

FixedRefinedChebyshev polynomial

(12-18 coefficients)Pseudo-VoightFixedFixedFixedFixedRefinedFixedFixedFixedNoneNot refined

Not refinedRefinedFixedFixed

FixedRefined

166 Powder Diffr., Vol. 15, No. 3, September 2000 Winburn era/. 166

Theta(deg)

Figure 2. Comparison of X-ray diffraction patterns of NIST fly ash SRMs1633a and 1633b.

qxrd.chem.ndsu.nodak.edu/ccbs. These structure data setswere tested by performing Rietveld refinements on variousindividual and mixed phases following screening of ques-tionable structures (Winburn et al, 1997; Winburn, 1999;Winburn et al., 2000). In most cases the data analysis wascompleted in approximately 15 min on a 266 MHz personalcomputer. The exception was the analysis of SRM 2691,which took about 8 h to complete due to the mineralogicalcomplexity of the sample and the need to run multiple re-finements.

In the version used in this study, the GSAS Rietveld pro-gram had the limitation of allowing refinement of only ninecrystalline phases, or eight analyte phases plus the internalstandard. High-calcium fly ashes typically show nine or morephases. An averaging technique was developed to deal withthis limitation, which is described in detail in the following.The averaging technique was tested on a reference mixtureof eleven crystalline phases, ten of which were identified inSRM 2691.

The normalized results of the RQXRD analysis wereconverted to absolute weight percentages of the crystallinephases using the rutile internal standard which had beenadded in a fixed weight percentage. Amorphous content wasdetermined by difference.

Replicate analyses were done by three analysts havingbackgrounds and experience in XRD procedures rangingfrom novice to expert.

III. RESULTS AND DISCUSSIONA. Qualitative analysis

The mineralogy of SRM 1633a was described by Mc-Carthy and Johansen (1988) and McCarthy and Thedchan-amoorthy (1989). In 1993, SRM 1633b replaced 1633a.X-ray diffractograms of SRM 1633a and 1633b are shown inFigure 2. The diffraction patterns were very similar, withquartz, mullite, hematite, and magnetite present in additionto diffuse scattering due to the amorphous content. However,SRM 1633b also contains a small amount of gypsum(CaSO4-2H2O), as indicated by the unique peaks at 11.8°

and 29.1° 20. While anhydrite is occasionally identified inClass F coal combustion fly ash, identification of its dihy-drate gypsum was unexpected.

SRMs 2689 and 2690 show the mineralogy typical of aClass F fly ash. The only crystalline phases identifiable werequartz, mullite, hematite, and magnetite. A small amount oflime (CaO) was also present in 2689. Lime was not reportedin SRM 2689 by McCarthy and Johansen (1988) or McCar-thy and Thedchanamoorthy (1989). The greater sensitivity toweak peaks of the newer diffractometer used in the presentstudy could account for the observation of a trace of lime.Lime does not occur commonly in ASTM Class F fly ashesderived from bituminous coal (McCarthy et al., 1990).

SRM 2691 has the most complex mineralogy of theSRM fly ashes. The phases identified were quartz, mullite,hematite, lime, periclase, merwinite, melilite, C3A, brown-millerite, anhydrite, and ye'elimite (see Table II for nominalchemical compositions). McCarthy and Johansen (1988) andMcCarthy and Thedchanamoorthy (1989) also reported mag-netite, but no observable hematite, in diffraction patterns ofSRM 2691. They did report that hematite was observable inmagnetically enriched fractions of SRM 2691.

B. Quantitative analysis

1. Rutile internal standard

In order to use DuPont's 0.3 fim Ti-Pure® R900 rutile asan internal standard, it was first necessary to determine itsrutile content. NIST SRM 676 corundum (NIST SRMP,1999) was selected as the primary standard for crystallinephase content by XRD. The amorphous content of this SRMwas recently reported by Cline and Von Dreele (1998) to be1.6%. The known crystallinity of this SRM allows for thedetermination of the crystallinity of any material in a mixtureof the analyte in question and the corundum SRM. The 0.3/j,m rutile was mixed in a 1:1 ratio with the corundum SRM.Using the Rietveld refinement parameters given in Table IV,and making the appropriate correction in the nominally50:50 wt % mixture of rutile and corundum for the fact thatthe corundum was only 98.4% crystalline, the rutile wasfound to contain an X-ray amorphous fraction totaling 5.6%of the total mass, i.e., the material was 94.4% crystallinerutile.

2. Microabsorption

In their studies of the accuracy possible with RQXRD ofreference mixtures, Winburn (1999), Winburn et al. (2000)reported that a postrefinement correction for microabsorptionaccording to Brindley (1945) and Taylor (1991) was desir-able for the most accurate results in complex, multiphasemixtures of compounds having large differences in linearabsorption coefficients. The microabsorption correction ofBrindley (1945) requires the particle size of each componentin the system be known. Winburn (1999) and Winburn et al.(2000) also showed that using poor estimates of particle sizesin microabsorption corrections was usually worse than usingno microabsorption correction at all. Because obtaining theparticle sizes of all of the crystalline phases in fly ash isdifficult at best and beyond the scope of routine fly ashQXRD, no microabsorption correction was applied. Use ofthe 0.3 /zm rutile, combined with the fact that the linear

167 Powder Diffr., Vol. 15, No. 3, September 2000 Rietveld quantitative X-ray diffraction analysis 167

SRM 1633b Qz = 5.7(0.6)%Mu = 21.2(2.1)%Hm = 2.1(0.3)%Ma = 4.0(0.6)%Gp = 0.9(0.2)%Amorphous = 66.1 %

7.0 8.0X10E 1

Figure 3. Rietveld refinement of SRM 1633b with rutile internal standard.Crosses represent the experimental pattern, the upper solid line representsthe calculated pattern, and the lower solid line is the difference plot. Hashmarks indicate possible XRD peak positions for crystalline phases (frombottom to top): quartz (Qz), mullite (Mu), hematite (Hm), magnetite (Ma),gypsum (Gp), and rutile.

absorption coefficient of rutile is in the midrange of fly ashphases, helped minimize microabsorption errors.

3. Precision

In order to estimate the precision of RQXRD quantita-tion of crystalline and noncrystalline phases, the more re-cently issued SRM 1633b was analyzed by three analystsstarting from six aliquots of the SRM. A typical Rietveld plotfor one of the finished refinements is shown in Figure 3.

The results and the associated statistics are given inTable V. Among the crystalline phases, precision expressedas relative standard deviation (RSD) ranged from 2% to 8%for the four principal phases in this low-calcium fly ash. Thetwo most abundant phases had the lowest relative standarddeviations, as might be expected from the better countingstatistics of their Bragg peaks. The least abundant phase,gypsum at 1.0 wt%, had the largest RSD, 13%. The overallprecision of the RQXRD analyses is perhaps best representedby the weighted average RSD. In this case, the overall pre-cision for the five crystalline phases is 3.5%, and for allphases (including the dominant glass component) is 2.3%.Both of these results were within the target precision of± 5 % .

As noted previously, the diffraction patterns in this studywere collected using scan parameters that resulted in a datacollection time of approximately 1 h. To test the hypothesisthat a larger scan range and a longer count time may havegiven a different and potentially more accurate result, a scancovering an additional 60°, counting for 8 s/step instead of 1s/step, and employing a smaller step size (0.025° instead of0.03°) was done. The last column of Table V gives the resultof this analysis. The values from this 10.75 h scan are statis-tically identical to the mean of the six measurements madewith 1.1 h scans. Quantitative phase abundance was the pur-pose of this study, and the observation that relatively lowangle data (20°-80° 28) were sufficient for this purposeshould not be generalized to structure refinement experi-ments, where higher angle data are critical.

4. Averaging procedure

Eleven crystalline phases were identified from the quali-tative analysis of SRM 2691. The internal standard adds atwelfth phase. GSAS is limited to nine phases in any onerefinement. This restriction was addressed with an averagingtechnique. A total of six refinements were performed, eachincluding rutile, quartz, mullite, merwinite, and tricalciumaluminate (C3A). Each of the remaining phases was in-cluded in a minimum of three refinements. The results of thesix refinements were then averaged to give the final reportedvalues.

5. Accuracy

The accuracy of the RQXRD analyses of the fly ashSRMs cannot be determined because NIST has not certifiedtheir crystalline phase content. In order to get an estimate ofpotential accuracy, two simulated fly ashes containing mostof the crystalline phases in low-calcium and high-calcium flyashes were prepared. These mixtures were diluted with aknown amount of silica gel, which was used to mimic theglass component of fly ash in typical fly ashes, as reported byMcCarthy et al. (1990). The results are given in Tables VI(a)and VI(b).

For the simulated low-calcium fly ash, which was de-signed to have only about 26% total crystalline phases, re-coveries ranged from 3% to 15% of the actual amounts.Overall, the weighted error for the crystalline phases wasabout 7%. The internal standard method yielded an amor-

TABLE V. Six replicate RQXRD analyses, in weight percent, and precision statistics for SRM 1633b plus aseventh analysis with wider angular range and longer count time.a

Phase

QuartzMulliteHematiteMagnetiteGypsumGlass

Weighted

1

6.221.3

2.13.71.1

65.6

relative standard

2

5.721.2

2.14.00.9

66.1

deviation

3

6.522.62.64.41.1

62.8

4

6.122.0

2.13.81.1

64.9

5

5.921.9

2.23.91.2

64.9

6

6.021.8

2.13.80.8

65.5

Mean SDb

6.121.8

2.23.91.0

65.0

CrystallineAI:

0.20.50.20.20.11.1

phases1 phases

RSDC

4%2%8%6%

13%2%

3.5%2.3%

7

9

6

"Data collection parameters: 20°-140° 2 0, 0.025° step, 8 s/step.bSD=standard deviation.c RSD=relative standard deviation.

168 Powder Diffr., Vol. 15, No. 3, September 2000 Winburn et al. 168

TABLE VI. (a) RQXRD analysis of a simulated low-calcium fly ash.(b)RQXRD analysis of a simulated high-calcium fly ash using the averagingtechnique.

PhaseReference

wt. % RQXRDRelative

error"

(a) Quartz 8.1Mullite 11.1Hematite 4.0Magnetite 3.3Amorphous 73.5

Weighted relative error1"

(b) Quartz 7.3Mullite 4.8Hematite 1.7Magnetite 0.4Melilite 1.6Merwinite 2.6Periclase 1.6Calcite 3.1Anhydrite 3.4Tricalcium aluminate 2.2Brownmillerite 0.9Amorphous 70.5

Weighted relative error

7.210.83.92.8

75.3

Crystalline phasesAll phases

6.84.21.50.32.12.92.02.84.01.70.7

71.0

Crystalline phasesAll phases

11%3%3%

15%2%

7.2%3.6%

6%12%8%

21%25%14%21%9%

16%20%21%

1%

12.9%4.3%

1100*(|reference—RQXRD|)/reference; wt %.bS (reference wt. % * relative error)/2 reference; wt %.

phous content within 2% of the known amount, whichbrought the overall weighted average accuracy to about±4%.

The simulated high-calcium fly ash, which was designedprimarily to test the averaging procedure, contained elevencrystalline phases, and all but two of the crystalline phasesidentified by quantitative analysis in SRM 2691. The calciumaluminosulfate ye'elimite was not available, and was substi-tuted by a small amount of magnetite ( — 0.4%). Lime,which tends to hydrate in moist air, was substituted by cal-cite, CaCO3. The amorphous phase, silica gel, made upabout 71 % of the mixture, and all of the eleven phases werepresent at the low concentrations likely to be encountered inactual high-calcium fly ashes.

The results for this simulated high-calcium fly ash aregiven in Table VI(b). All crystalline phases except quartzwere mixed to abundances less than 5 wt%. The relativeerrors ranged from 6% to 25%, with the highest relative er-rors occurring for the least abundant phases. There was agood balance of over- and underdetermination of the crystal-line phases, and once again the determination of the amor-phous content is in excellent agreement with the knownamount.

6. Recommended estimated standard errors

In the previous section it was shown that very good re-coveries of the phases in a simulated low-calcium fly ash,and good recoveries in a mineralogically complex simulatedhigh-calcium fly ash, can be obtained by the experimentalmethods employed here.

However, there are other factors that will lead to uncer-tainty and error in any result obtained from RQXRD analy-

TABLE VII. Recommended estimated standard errors (eses) to apply to theresults of Rietveld quantitative X-ray diffraction analyses of fly ashes. Seethe text for an explanation of ese.

Phase < 1 % l%-5%

AnhydriteBrownmillerite

GypsumHematiteLimeMagnetiteMeliliteMerwiniteMullitePericlaseQuartzYe'elimite

25%30%30%25%15%25%25%30%30%25%30%15%30%

15%25%25%15%15%15%15%25%25%15%20%15%25%

10%15%15%10%10%10%10%15%15%10%10%10%15%

ses of materials as complex as fly ashes. The most importantof these is the chemical composition of solid solution phases.Among the phases in the high-calcium fly ashes, mullite,magnetite, melilite, merwinite, brownmillerite, andye'elimite (see Table II for nominal compositions) all exhibitsolid solution ranges. In simpler systems with greater con-centrations and resultant diffraction peak intensities, onemight include refinement of the site occupancies of thesephases to obtain a better approximation of actual solid solu-tion compositions, which should lead to more accurate analy-ses.

For this study, a single composition was chosen for eachof the solid solution phases, and it is likely that this compo-sition does not match the actual composition in the fly ashSRMs. For example, the melilite solid solution was refinedas akermanite, Ca2MgSi207, even though the actual compo-sition probably contains a significant gehlenite, Ca2Al2Si07,component as well as substitution by other ions such as Na+,Fe2+, and Fe3+ on various sites. The actual solid solutioncompositions, or composition ranges, of these phases mighthave been obtainable from exhaustive elemental analysis byanalytical electron microscopy, but such analyses are beyondthe scope of routine, high throughput, analysis.

Taking into account the range of errors obtained for vari-ous phases in the reference mixtures, and the indeterminateeffect of solid solution composition, a set of estimated stan-dard errors (eses) linked to phase abundance has been devel-oped (Table VII). These eses will be used in the RQXRDresults reported here, and it is recommended that they beapplied by others who would use the methods, data collec-tion, and RQXRD analysis procedures described here.

7. RQXRD of NIST fly ash SRMs

The analysis of the crystalline phases in the most re-cently issued SRM, 1633b, was presented in Table V as sixreplicate analyses, with their mean values and standard de-viations. Results of the three replicate RQXRD analyses ofthe NIST fly ash SRMs (including the older 1633a) are sum-marized in Tables VIII(a)-VIII(d). The reported eses in thelatter tables derive from the recommendations in Table VII.A comparison of these results to those obtained previouslyby the semiquantitative RIR method is also summarized inthese tables.

169 Powder Diffr., Vol. 15, No. 3, September 2000 Rietveld quantitative X-ray diffraction analysis 169

TABLE VIII. (a) Three replicate RQXRD analyses of SRM 1633a, and RIR QXRD results reported byMcCarthy and Thedchanamoorthy (MT) (1989). (Estimated standard error, ese, from Table VII.) (b) Threereplicate RQXRD analyses of SRM 2689, and RIR QXRD results reported by McCarthy and Thedchanamoor-thy (1989). (c) Three replicate RQXRD analyses of SRM 2690, and RIR QXRD results reported by McCarthyand Thedchanamoorthy (1989). (d) Three replicate RQXRD analyses of SRM 2691, and RIR QXRD resultsreported by McCarthy and Thedchanamoorthy (1989).

(a)

(b)

(c)

(d)

Phase

QuartzMulliteHematiteMagnetiteGlass

QuartzMulliteHematiteMagnetiteLimeGlass

QuartzMulliteHematiteMagnetiteGlass

QuartzMulliteHematiteMagnetitePericlaseLimeMerwiniteC3AAnhydriteBrownmilleriteMeliliteYe'elimiteGlass

7.021.2

2.25.4

5.510.52.54.30.1

12.88.90.70.6

7.75.12.1

2.10.64.43.82.84.52.10.4

RQXRD

6.821.02.05.6

5.29.52.33.8

Trace

12.69.30.50.5

8.85.60.9

2.20.93.94.42.84.71.80.4

7.020.42.05.0

5.210.42.64.40.2

12.38.30.50.7

8.75.31.4

2.70.55.74.72.55.32.30.7

Mean (ese)

6.9(0.7)20.9(2.1)

2.0(0.3)5.3(0.5)

64.9(6.5)

5.3(0.5)10.1(1.0)2.5(0.4)4.2(0.6)0.1

77.8(7.8)

12.6(1.3)8.8(0.9)0.6(0.2)0.6(0.2)

77.4(7.7)

8.4(0.8)5.3(0.5)1.5(0.2)

2.3(0.5)0.7(0.2)4.7(1.2)4.3(1.1)2.7(0.4)4.8(1.2)2.1(0.5)0.5(0.2)

66.3(6.6)

MT RIR QXRD

5.719.92.46.2

65.8

4.09.93.64.9-

77.6

11.411.2

1.276.2

8.44.2

1.32.41.05.82.81.3

Trace1.6

<1.0- 6 9

Table VIII(a) reports the results for SRM 1633a, alongwith the estimated standard errors indicated in Table VII.The two methods give comparable results, with the RIRmethod reporting somewhat less quartz and mullite and morehematite and magnetite. Applying the eses to the RQXRDresults gives a match only for mullite and glass, but theagreement of the RIR results with the RQXRD results forquartz, hematite, and magnetite is within two eses. Overall,considering the use of simple peak heights and the need toproportion the analytical peak intensity for hematite andmagnetite with the RIR method (McCarthy and Thedchan-amoorthy, 1989), the agreement is surprisingly good.

Although they are both formed by combustion of bitu-minous coals, SRM 2689 [Table VIII(b)] is a less crystallinefly ash (79% glass) than SRM 1633a (65% glass). The twomethods again give comparable results for the four majorcrystalline phases and glass, with essentially equivalent(within one ese) results for mullite and magnetite, but withpoorer agreement for quartz and hematite. As noted earlier, atrace of lime was detected and quantitated in the presentstudy.

The mineralogy of SRM 2690 [Table VIII(c)] has quartzdominant over mullite. Close inspection of the diffractionpattern of SRM 2690 given by McCarthy and Johansen(1988) helps to explain the differences in mullite analyses,

and the resulting discrepancy in iron oxides analysis. Mul-lite's analytical peak at 26.2° occurs only as a shoulder onthe strong 26.6° quartz peak. Consequently, visual peakheight estimates are subject to large uncertainty. Overdeter-mination of mullite apparently resulted in too much subtrac-tion of a secondary mullite peak overlap from the analyticalpeak of hematite at 33.2°, because McCarthy and Thedcha-namoorthy (1989) reported no hematite in this fly ash. (Theydid indicate that hematite was present in magnetically en-riched ash fractions.) With no intensity from the secondarypeak of hematite to subtract from the analytical peak of mag-netite at 35.5°, magnetite is overdetermined. Profile fittingsoftware was not used in the older RIR methodology, butwould certainly have helped to minimize some of these over-lap problems and produce closer agreement with the moreaccurate RQXRD determinations. Interestingly, the total ironoxide content is the same for both methods. It is also inter-esting to note the similarity of the sum of quartz and mullitecontents obtained by the two methods, which results in closeagreement on glass content.

SRM 2691, the high-calcium Class C fly ash, had themost complex mineralogy. Qualitative analysis identified 12likely phases in the sample, including both hematite andmagnetite. RQXRD analysis failed to find any significant

170 Powder Diffr., Vol. 15, No. 3, September 2000 Winburn et al. 170

intensity attributable to magnetite. (There was a trace ofmagnetite detected in a magnetically enriched fraction.) Con-fidence that magnetite was present only at small concentra-tions in the bulk sample is increased by the result from thesimulated Class C ash mentioned previously, where as littleas 0.4% magnetite was quantified.

The remaining 11 phases were analyzed using the aver-aging strategy described above. Except for the iron oxides,RQXRD results for SRM 2691 [Table VIII(d)] were similarto those reported previously for the RIR method. WithRQXRD it was found that hematite could be analyzed andmagnetite could not. To the contrary, McCarthy and Jo-hansen (1988) and McCarthy and Thedchanamoorthy (1989)reported that magnetite was present and hematite was not. Aswith the SRM 2690, the total iron oxide content is similar forboth methods, and the differences are probably due to themore subjective process of peak selection and peak heightmeasurement in the RIR method (Bender et ai, 1993).

IV. CONCLUSIONS

Rietveld quantitative X-ray diffraction analysis can beapplied to mineralogically complex fly ashes (often eight totwelve crystalline components) with high amorphous con-tents (typically 60-90 wt%). A protocol for routine analy-ses, requiring about 1 h for data collection and typically lessthan 1 h for quantitative analysis, was established. Using thisprotocol with six aliquots of a NIST fly ash SRM, overallprecision (weighted relative standard deviation) was found tobe better than 5%. A 10.75 h diffraction scan with double thescan range and a fourfold increase in the count time gavestatistically identical RQXRD results. (The 1 h data collec-tion described was found sufficient for QXRD; however, it isnot recommended for structure refinements.) Using referencemixtures of simulated fly ashes, which contain reagent gradematerials analogous to the crystalline phases found in com-plex CCB systems, accuracy for actual CCB systems wasassessed. Recommendations for reporting estimated standarderrors (eses) for RQXRD of fly ash and other CCBs weremade.

The crystalline and glass phase content of the four NISTfly ash Standard Reference Materials were determined. Theresults were compared to semiquantitative analyses of theSRMs performed a decade ago by the reference intensityratio method. For most of the crystalline phases, and theglass phase, the results from the RIR method analyses weresimilar to the results reported here. Differences were attrib-uted to the subjective methods of dealing with overlappingpeaks in the RIR method. The time necessary for data col-lection and analysis is comparable for the two measurements,but RQXRD is more effective in dealing with overlappingpeaks and other sample and specimen effects, and it shouldgive much better overall accuracy.

Because of their certified uniformity and availability, itis suggested that fly ash SRMs would be useful for interlabo-ratory comparisons and round robins focused on multiphasematerials with high glass contents.

ACKNOWLEDGMENTS

This research is supported by the Department of Energy(DE-FG22-96PC96207). An Undergraduate Research Fel-

lowship to R.B.P. was provided by NSF OSR-9452892. Jen-nifer L. Parker provided technical assistance as one of theanalysts.

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