Quantitative Analysis of Aluminum Dross by the Rietveld Method

A. Gomez1, N. B. Lima2 and J. A. Tenorio1

1Polytechnic School, University of Sao Paulo, Av. Prof. Mello Moraes 2463; Sao Paulo, SP, CEP: 05508-900, Brazil2X-ray Diffraction Laboratory, Nuclear and Energy Research Institute, IPEN, Av. Lineu Prestes 2242; Sao Paulo, SP, Brazil

Aluminum white dross is a valuable material principally due to its high metallic aluminum content. The aim of this work is to develop amethod for quantitative analysis of aluminum white dross with high accuracy. Initially, the material was separated into four granulometricfractions by means of screening. Two samples of each fraction were obtained, which were analyzed by means of X-ray fluorescence and energydispersive spectroscopy in order to determine the elements present in the samples. The crystalline phases aluminum, corundum, spinel, defectspinel, diaoyudaoite, aluminum nitride, silicon and quartz low were identified by X-ray diffraction. The quantitative phase analysis wasperformed by fitting the X-ray diffraction profile with the Rietveld method using the GSAS software. The following quantitative results werefound: 77.8% aluminum, 7.3% corundum, 2.6% spinel, 7.6% defect spinel, 1.8% diaoyudaoite, 2.9% aluminum nitride, and values notsignificant of quartz and silicon. [doi:10.2320/matertrans.MRA2007129]

(Received June 20, 2007; Accepted January 29, 2008; Published March 12, 2008)

Keywords: X-ray diffraction, Rietveld method, quantitative characterization, aluminum dross

1. Introduction

During aluminum smelting, a dross layer is created on thesurface of the molten metal as the aluminum reacts with theatmosphere. Aluminum dross can be classified as three types:white, black and saltcake.1) The generation of white drossoccurs at primary aluminum smelters, this product isinevitable in any process that implies aluminum smeltingand represents between 1 to 10% of the total production.2)

Saltcake and black dross result from the recycling processes.The composition and structure of the dross are not

predictable because several factors influence the oxidationprocess: temperature, alloy composition, furnace height andatmosphere composition.3–6) In general, white dross iscomposed principally of high amounts of metallic aluminumand minor quantities of corundum, aluminum nitride, andother oxides. These constituents are of economic interest, forexample, the metallic aluminum can be recovered byrecycling process, and the corundum is a refractory material.

Qualitative analysis of phases by X-ray diffraction andchemical analysis of elements are some characterizationmethods found in the literature about aluminum dross. Thequantification of phases present in aluminum white dross isdifficult due to strong heterogeneousness, therefore, the X-ray diffraction can be used for this purpose because it permitsidentifying and quantifying the phases present in mixtureswith high accuracy.

Due to the precision, X-ray diffraction (XRD) is the mostuseful technique for quantitative analysis of phases inmulticomponent mixtures, quantification is possible becausethe intensity of the diffraction pattern of a phase in a mixturedepends on its concentration.7,8)

There are several methods of X-ray diffraction to quantifyphases, but the Rietveld method has been perhaps the mostuseful tool in recent years as it accounts for the factors thataffect the reproducibility of the intensity peaks: the peakoverlapping, the presence of amorphous phases, and thepreferred orientation of crystallites. This is possible becausethe totality of the diffraction pattern is used to calculate thephase amount.

The Rietveld method was developed initially for refine-ment of crystalline structures using neutron diffraction.9,10) Inthe refinement procedure, a calculated pattern is fitted to anobserved diffraction pattern by the least-squares method,until the best fit is obtained. The least-squares refinementleads to a minimal residual quantity (Sy):

11)

Sy ¼Xi

wiðyi � yciÞ2 ð1Þ

where wi ¼ 1=yi, yi = observed intensity at the ith step,and yci = calculated intensity at the ith step.

The diffraction pattern is calculated by the simultaneousrefinement of the unit cell and structural parameters, thenother parameters are introduced to compensate the effects ofpreferred orientation, angular shifts, surface roughness, etc.Among the refined parameters, the scale factor s� permitscalculating the relative weighted fractions of the phases:12,13)

w� ¼s�ðZMVÞ�Xn

i¼1

s�ðZMVÞ�ð2Þ

where w� is the weight fraction of the phase �, M� is themolecular weight, Z� is the number of molecules in a cellof unit volume V�.

The fit must be evaluated by visual comparison betweenthe observed and calculated pattern; however, some numer-ical criteria are necessary in order to judge whether therefinement is proceeding satisfactorily and when it can bestopped. There are several R values that can be used toevaluate the fit: R-structure factor RF , R-Bragg factor RB,R-pattern factor Rp and the weighted-profile factor Rwp.The Rwp value is defined as:11)

Rwp ¼

Xwiðyi � yciÞ2X

wiy2i

" #1=2

ð3Þ

The expression in the numerator of the Rwp is the minimalresidual quantity being minimized; therefore, this is the mostexpressive of the R’s, and it is the one that best reflects the fitof the calculated pattern diffraction. The RF and RB are based

Materials Transactions, Vol. 49, No. 4 (2008) pp. 728 to 732#2008 The Japan Institute of Metals

on the intensities calculated, thus they are biased towardsthe model being used.14)

The ‘‘goodness of fit’’ (S) is another numerical criterionfrequently used for the evaluation of the success of the fit:12)

S ¼Sy

ðN � PÞ

� �1=2¼

Rwp

Re

ð4Þ

where N is the number of observations, P is the number ofparameters and Re is the expected R value which reflects thequality of the data, Re is defined as:11)

Re ¼ðN � PÞX

wiy2i

" #1=2

ð5Þ

2. Experimental Details

2.1 MaterialAn aluminum white dross with particle size greater than

3.35mm was analyzed in order to develop a method ofquantitative characterization. This dross was produced by aprimary smelter. Initially, the particle-size analysis of thematerial was done by using three sieves with mesh sizesof: 6.35mm, 12.7mm and 25.4mm, four granulometricfractions were obtained: D1 (+3.35mm, �6:35mm), D2(+6.35mm, �12:7mm), D3 (+12.7mm, �25:4mm) andD4 (+25.4mm).

The coarse particle size makes difficult the homogeniza-tion and the quartering of the material; hence, eachgranulometric fraction was crushed in a knife mill in orderto reduce the particle size, and then screened (mesh size1mm). The material greater than 1mm was analyzed bymeans of energy-dispersive spectroscopy and qualitativeX-ray diffraction in order to determine its composition.The powders (�1mm) were used to carry out analysis ofenergy-dispersive spectroscopy, X-ray fluorescence andquantitative X-ray diffraction.

The chemical elements of the powders were foundusing energy-dispersive spectroscopy and X-ray fluores-cence. The crystalline phases were identified by means ofqualitative X-ray diffraction.

The samples for quantitative X-ray diffraction werepulverized in a vibration grinding mill to reduce the particlesto less than 45 mm. Greater reduction of particle size was notdone to avoid material loss. The sample preparation must becarefully performed because grinding for long periods couldinduce structural changes.15)

2.2 Experimental conditionsThe diffraction data were obtained at room temperature

using a Rigaku Multiflex diffractometer with Bragg-Brentano�=2� geometry and Cu k� radiation (40 kV, 20mA). Theangular range was 2� ¼ 6{110�, and it was scanned in stepsof 0.02�. The counting was set at 8 s/step in order to obtainexperimental diffraction profiles with low statistical errors.

2.3 The Rietveld refinementThe weight percentages of the phases were calculated by

applying the Rietveld method using the GSAS software(General Structure Analysis System). The background wasrefined with the analytical function of Chebyschev, and the

peak profile with a modified pseudo-Voigt function. Thefollowing parameters were refined for all phases: individualscale factor, sample displacement, cell parameters, Gaussfactor of the phase profile function and the Lorentz factor ofthe phase profile function.

The asymmetric parameter was refined only for the phasesthat showed lines at low angles. The temperature factors werenot refined. The preferred orientation was corrected byapplying the spherical harmonics function, implemented inGSAS by Von Dreele.16) The surface roughness correction ofSuortti was also applied.17)

3. Results and Discussion

The particle size distribution of the dross is shown inTable 1. In this procedure, the dross was separated into fourgranulometric fractions in order to facilitate the analysis ofthe material.

During the crushing of each granulometric fraction twokinds of particles were obtained: powder and spheres, whichwere separated by means of screening and then weighed. Themass percentages are shown in Table 2. The spheres wereanalyzed by energy-dispersive spectroscopy (EDS) in ascanning electronic microscopy (SEM). Figure 1 shows theSEM image of a sphere, which is composed of a few ofimpurities (clear zones) immersed in an aluminum matrix.

The results of X-ray diffraction of the spheres (Fig. 2)verified the results of the SEM analysis. Mainly peaks ofmetallic aluminum can be observed, and other small peaks ofimpurities that were not possible to identify. However, it canbe concluded that the spheres are mainly aluminum, and theamount of impurity is small enough to be negligible, whichmeans that during the crushing, a fraction of metallicaluminum is agglomerated to form spheres, and thisprocedure was a means of separating a large portion ofaluminum, in all cases more than 58% of the sample(Table 2).

The chemical analysis of all the powder samples (aftercrushing) made by X-ray fluorescence (XRF), showed the

Table 1 Size distribution of aluminum white dross.

SampleParticle size Cumulative (%)

(mm) Retained Accumulated

D1 +3.35 �6:35 29.6 29.6

D2 +6.35 �12:7 33.2 62.8

D3 +12.7 �25:4 24.9 87.7

D4 +25.4 12.3 100

Total 100.0

Table 2 Mass percentages of powder and spheres obtained after crushing

of dross.

Sample Spheres (+1mm) (%) Powder (�1mm) (%)

D1 59.7 40.3

D2 65.2 34.8

D3 58.2 41.8

D4 61.2 38.8

Quantitative Analysis of Aluminum Dross by the Rietveld Method 729

presence of greater amounts of Al and lesser amounts of Mg,Si, F, Fe, K, Na, Ca, Ti and S. In the EDS analysis high peaksof Al, and minor peaks of O, Fe, Na, Mg, Si and K werefound.

Analysis of the diffraction pattern of the powders revealedthe presence of metallic aluminum (Al), aluminum oxide (�-Al2O3), spinel (MgAl2O4), defect spinel (Mg0:388Al2:408O4),diaoyudaoite (NaAl11O17) and aluminum nitride (AlN).Minor traces of silicon (Si) and quartz low (SiO2) werefound in the samples D3 and D4. The structural data of theobserved phases are shown in Table 3. The diffractionpattern of sample D1 and the principal lines of each phase aremarked and shown in Fig. 3.

Presence of Al, �-Al2O3, MgAl2O4, AlN, Si and �-SiO2

was confirmed in the visual examination of all X-raydiffraction patterns. The Rietveld method was used toidentify the NaAl11O17 and Mg0:388Al2:408O4 phases.

The phases NaAl11O17, Na2O.11(Al2O3), andK1:5Al11O17:25 called �-aluminas15,18–20) have peaks in thesame angular positions with similar intensities. In thechemical analysis both Na and K were found; therefore, inorder to identify the correct phase, it was necessary to fit thepeak profile with each one of these phases. The best fit wasreached with the NaAl11O17.

The phase Mg0:388Al2:408O4 presents peaks in the sameangular positions of the MgAl2O4 but with differentintensities. Refinements were done with each phase, and it

was not possible to adjust the peak profile. A satisfactory fitwas obtained by refining the two phases together.

In order to observe the reproducibility of the results, twopowder samples of each granulometric fraction were ana-lyzed using the Rietveld method. The quality of the refine-ment was confirmed by visual examination as well as by thenumerical criteria. In all samples a good fit between theoriginal and the fitted X-ray diffraction profiles was obtained.The original data and the fitted profiles of samples D1-1,

30 35 40 45 50 55 60 65 70 75 80 85 90-200

0

200

400

600

800

1000

1200

1400

1600

1800

Inte

nsity

(cp

s)

Angle 2θ (degree)

Fig. 2 X-ray diffraction pattern of an aluminum ball.

Table 3 Crystalline phases found in aluminum dross.

Crystalline Phase Space Group Unit cell parameters

a, b, c �, �, �

Aluminum Al F m -3 m 4.04975, 4.04975, 4.04975 90, 90, 90

Corundum �-Al2O3 R -3 c H 4.75890, 4.75890, 12.9910 90, 90, 120

Spinel MgAl2O4 F d -3 m Z 8.07500, 8.07500, 8.07500 90, 90, 90

Defect Spinel Mg0:388Al2:408O4 F d -3 m Z 7.97830, 7.97830, 7.97830 90, 90, 90

Diaoyudaoite NaAl11O17 P 63 m m c 5.60200, 5.60200, 22.6259 90, 90, 120

Aluminum nitride AlN P 63 m c 3.11100, 3.11100, 4.97800 90, 90, 120

Quartz low SiO2 P 31 2 1 4.91300, 4.91300, 5.40500 90, 90, 120

Silicon Si F d -3 m S 5.43040, 5.43040, 5.43040 90, 90, 90

Fig. 1 SEM image of an aluminum sphere, being aluminum the gray

phase.

10 20 30 40 50 60 70 80 90 100 110

0

2000

4000

6000

8000

10000

b

Inte

nsity

(cp

s)

Angle 2θ (degree)

e e

cd

bcd f

b

cd

a

b

acd

aa

bf

cd a

a. Alb. α-Al

2O

3

c. MgAl2O

4

d. Mg0.388

Al2.408

O4

e. NaAl11

O17

f. AlN

Fig. 3 Identified phases in the sample D1 of aluminum dross.

730 A. Gomez, N. B. Lima and J. A. Tenorio

D2-1, D3-1 and D4-1, as well as the difference between theseprofiles are shown in Figs. 4 to 7 respectively.

The Rietveld refinement results are shown in Table 4,including the weight percent and the numerical criteria of thepowder samples.

These results represent only the weighted fractions of thephases contained in powder samples obtained during thecrushing. The total weight fractions were recalculated takinginto account the mass of the spheres (Table 2), which were

composed only of aluminium. The results are shown inTable 5.

The reproducibility of the results was confirmed bycomparing the differences found between each pair ofsamples. For example, the maximal difference of 1.6%between the first pair of samples (D1) was found for Al. In thepair of samples D2, a difference of 1% was found for theMg0:388Al2:408O4, the other phases presented minor differ-ences. For the samples D3 and D8, the maximal differencewas 2.4% for phases NaAl11O17 and Mg0:388Al2:408O4

respectively.To calculate the percentage of total weight of each phase in

the dross, it is necessary consider the particle size distributionshown in Table 1. The results are given in Table 6, includingthe mean weight and difference values.

The maximal difference in percentage of 0.7% was foundfor the phase NaAl11O17, which is the minor phase present inthe sample and higher errors are expected. For the otherphases, the differences, do not exceed 0.4% of the weightpercents, these results confirm the precision of the developedmethod. The weight percents of Si and SiO2 are not found inTable 6 because the values are not significant.

10 20 30 40 50 60 70 80 90 100-2000

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Inte

nsity

(cp

s)

Angle 2θ (degree)

Original data profile Fitted data profile Difference

a)

403530-2000

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Inte

nsity

(cp

s)

Angle 2θ (degree)

Original data profile Fitted data profile Difference

b)

Fig. 4 a) Rietveld refinement of the sample D1-1, b) detail of the Rietved

refinement of sample D1-1 (angles 2� from 30� to 40�).

10°-500

0

500

1000

1500

2000

2500

3000 Original data profile Fitted data profile Difference

Inte

nsity

(cp

s)

Angle 2θ (degree)

20° 30° 40° 50° 60° 70° 80° 90° 100°

Fig. 7 Rietveld refinement of the sample D4-1.

10 20 30 40 50 60 70 80 90 100-2000

0

2000

4000

6000

8000

10000

12000

Original data profile Fitted data profile Difference

Inte

nsity

Angle 2θ (degree)

Fig. 6 Rietveld refinement of the sample D3-1.

10 20 30 40 50 60 70 80 90 100-2000

0

2000

4000

6000

8000

10000 Original data profile Fitted data profile Difference

Inte

nsity

(cp

s)

Angle 2θ (degree)

Fig. 5 Rietveld refinement of the sample D2-1.

Quantitative Analysis of Aluminum Dross by the Rietveld Method 731

4. Conclusions

The Rietveld method showed good precision for thequantitative analysis of phases present in white dross withhigh aluminum amounts. The characterization and samplingmethod employed revealed good precision taking intoaccount the reproducibility of results from samples ofeach set. A careful sample preparation to obtain representa-tive results with the totality of the material is veryimportant.

With the Rietveld method, it is possible to quantify theamounts of all phases present in the sample simultaneously.In other methods each phase must be quantified independ-ently.

Compared with other X-ray diffraction methods, such asthe internal standard method, the Rietveld method hasnumerous advantages: having better accuracy, and requiringneither an additional internal standard nor calibration curveand sample homogenization.

The identification of NaAl11O17 and Mg0:388Al2:408O4

was possible only with the aid of the Rietveld method.

Acknowledgments

The authors wish to thank Jim Hesson for the grammaticalEnglish correction of the manuscript, and Dr CarlosOliveira Paiva Santos for comments and discussion aboutthe refinement.

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Table 4 Results of the Rietveld refinement of samples D1 to D4.

D1-1 D1-2 D2-1 D2-2 D3-1 D3-2 D4-1 D4-2

Al (mass%) 50.8 (1) 48.1 (1) 38.8 (1) 39.7 (1) 56.0 (1) 55.1 (1) 4.1 (2) 2.8 (1)

�-Al2O3 (mass%) 14.3 (1) 15.8 (1) 20.1 (1) 19.1 (1) 14.2 (1) 13.6 (1) 37.7 (2) 37.2 (2)

MgAl2O4

(mass%)9.6 (2) 6.7 (2) 10.0 (2) 10.8 (2) 3.3 (2) 2.7 (1) 1.2 (1) 6.0 (2)

Mg0:388Al2:408O4

(mass%)15.1 (2) 19.3 (2) 22.0 (2) 19.2 (2) 16.0 (2) 14.9 (2) 35.8 (2) 29.4 (3)

NaAl11O17

(mass%)6.7 (2) 4.8 (2) 3.5 (1) 5.6 (2) 1.5 (1) 7.3 (2) 0.4 (1) 2.8 (2)

AlN (mass%) 3.7 (1) 5.4 (1) 5.6 (1) 5.6 (1) 8.5 (1) 6.0 (1) 20.6 (2) 21.6 (2)

SiO2 (mass%) — — — — 0.2 (0) 0.2 (0) — —

Si (mass%) — — — — 0.3 (0) 0.2 (0) 0.2 (0) 0.2 (0)

S 2.36 1.86 1.79 1.77 1.80 1.65 2.52 2.90

Rwp (%) 7.52 6.60 6.70 6.49 6.83 6.80 8.38 8.69

RE (%) 4.89 4.84 5.00 4.88 5.08 5.29 5.27 5.11

Table 5 Phase composition of samples D1 to D4.

D1-1 D1-2 D2-1 D2-2 D3-1 D3-2 D4-1 D4-2

Al 80.0 79.0 78.9 79.2 81.7 81.3 62.9 62.4

�-Al2O3 5.7 6.4 6.9 6.6 5.9 5.7 14.6 14.3

MgAl2O4 3.9 2.7 3.4 3.7 1.4 1.1 0.5 2.3

Mg0:388Al2:408O4 6.1 7.8 7.6 6.6 6.7 6.2 13.8 11.4

NaAl11O17 2.7 1.9 1.2 1.9 0.6 3.0 0.2 1.1

AlN 1.5 2.2 1.9 1.9 3.5 2.5 7.9 8.3

SiO2 0.0 0.0 0.0 0.0 0.1 0.1 0.0 0.0

Si 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1

Table 6 Weight percent of phases present in aluminum white dross.

Phase Al �-Al2O3 MgAl2O4 Mg0:388Al2:408O4 NaAl11O17 AlN

(%) (%) (%) (%) (%) (%)

DX-1 78.0 7.3 2.7 7.7 1.4 2.9

DX-2 77.6 7.3 2.6 7.5 2.1 2.9

Mean 77.8 7.3 2.6 7.6 1.8 2.9

Difference 0.4 0.0 0.1 0.2 0.7 0.0

732 A. Gomez, N. B. Lima and J. A. Tenorio