x-ray powder diffraction profile refinement of synthetic hercynite

8/14/2019 X-Ray Powder Diffraction Profile Refinement of Synthetic Hercynite

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American Mineralogist, Volume 69, pages 937-942, 1984

X-ray powder diffraction profile refinement of synthetic hercynite

Rooerucr J. Hrt-r-

CSIRO Division of Mineral ChemistryP.O. Box 124. Port Melbourne

Victoria 3207 Australia

Abstract

A full profile X-ray powder diffraction structure refinement has been completed on asample of synthetic hercynite, FeAl2Oa, sing graphite monochromatized uKa step-scandata (20^u* : 140") and a flexible profile shape of the pseudo-Voigt type. The mostsatisfactory onvergence as achieved t R*o = 0.0781 nd Rs : 0.0125 sing ully ionizedatomic scattering factors and a peak shape parameter of the form e = 0.233(17) +

0.0055(3)20: he individual peak shapes vary from 33.7Vo orentzian to 99.8Vo orentziancharacter s 20 ncreases. he derived structural parameters t20"C arei a = 8.15579(6)4,(inversion) = 0.163(5), (0) : 0.2633(2), B : 0.56(3), 0.44(3) and 1.07(5)42 or thetetrahedral Fe), octahedral Al) and oxygen atoms, espectively. Calculated alues or aand x based on the onic model and : 0.163are n good agreement ith the refined values.

Introduction

The crystal chemistry of the spinel hercynite, FeAl2Oa,is of considerable nterest to mineralogists and materialsscientists because of its importance in metamorphic pe-trology (Osborne t al., l98l; Rumble, 1976; urnock andEugster, 1962; Palache et al., 1944, p.687), ceramics(Mason and Bowen, 98l; Meyers et al. , 1980; Baldwin,1955) nd device applications Zhukovskaya t al., 1980;Dehe et al.,1975; Hoffmann and Fischer, 1956). Howev-er, the detailed crystal structure of this phase in particu-lar its cation distribution) remains uncertain, primarilybecause pure hercynite is rarely, if ever, encountered nnature (Turnock and Eugster, 1962; Palache et aI., 1944,p. 692) and because synthetic hercynites in the FeO-Fe2O3-Al2O3 ystem often contain significant levels ofnon-stoichiometry arising from valence state variations,interstitial atoms and oxygen atom vacancies Mason andBowen, 98l; Halloran and Bowen, 1980). ndeed, manyof the natural "hercynites" documented n the literatureare more properly classified as members of the MgAl2O2-FeAlzO+ pleonaste) or Fe3Oa-FeAl2Oa olid solution se-ries.

A compound AB2X4 with the spinel structure crystal-lizes in space group Fd3m with the A cation in site 8d at(l/8 l/E l/8), the B cation n site l6d aI (ll2 ll2 ll2), andthe anion in site 32e at (xxx), when the origin is at l6d(Bragg, 1915;Hafner, 1960; Blass, 1964;Hill et al., 1979).The structure then requires only three parameters (ex-

cluding thermal vibration coefficients) to describe itsatomic arrangement completely: the unit cell size, a, theanion positional coordinate, x, and the cation ordering, or0003-004x/84/09r0-0937$02.00 %7

inversion parameter, . For i : 0 and l, respectively, hespinel has the so-called normal, A[Bz]&, and inverse,B[AB]X4, cation distributions, where the ions indicatedin parenthesis are in octahedral coordination by X, and

the remaining ons (including X) are n tetrahedral coordi-nation. Intermediate cation distributions may be repre-sented as (Ar-i B)[Ai Bz-i]Xn.

For those phases which have been described s FeAlzOrin the literature the unit cell dimensions have beendetermined o lie in the range 8.08-8.164 (Segnit, 1984).This rather large range of values suggests hat not all ofthe samples are stoichiometric and/or they contain someFe3+ or other cation. The oxygen coordinate has beendetermined twice, yielding values of "about" 0.265(Barth and Posnjak, 1932) and 0.2635(l) (Roth, 1964).Estimates of the distribution of Fe2* over the octahedral

and tetrahedral sites obtained rom diffraction and Mtiss-bauer measurements ary between i : 0.0 and 0.25(Osborne et al., 1981; Dickson and Smith; 1976,Yagnikand Mathur, 1968; Barth and Posnjak, 1932;Roth, 1964).

The present study of synthetic hercynite was initiated(1) in order to accurately characterize the crystal struc-ture of this important phase, and (2) as part of a broaderinvestigation into the application of full-profile Rietveld-type powder diffraction structure refinement methods anddetailed peak-shape modelling in the case of two-wave-length X-ray data.

Experimental

The sample of FeAl2Oa sed in the present study wassynthesized n an evacuated ilica ube at 1050"Cor 4 days usinga stoichiometric ixtureof Fe, Fe2O3 nd yAl2O3 ollowedby


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938

Table . Crystal structure efinement esults or hercynite

X-ray profl le(predent study)

HILL: REFINEMENT OF SYNTHETIC HERCYNITE

Neutron ltrtegrated( R o t h , 1 9 5 4 )

E , 1 t 2

0 . 99 ( )

0 . 2535( 1 )

0 . 1 t 4 ( r 0 )

14

0 . 010

where s i. ,n" r.""ii]':::":t^n character or thepeaks n the pseudo-Voigt unction (Hindeleh and John-son, 1978). his program can accept X-ray data obtainedfrom a conventional diffractometer since it allows thesimultaneous efinement f two wavelengths i.e., ar andaz) if their intensity ratio is known (2:l in the presentcase). The weight assigned o the intensity observed ateach step in the pattern s 4 = llYioand the functionminimized n the least-squares rocedure s I/,(Iio- Yi")2,where Ylo nd I'i" are he observed nd calculated ntensi-ties, espectively.

The refined quantities were a scale actor, the pseudo-Voigt profile shape parameters 0 (and er in the finalrefinement ycles), a20 zero parameter, peak ull widthat half maximum F'WHM) unction of the orm: FWHM2

: IJ tan20 + V tan? + W; Caglioti et al. 1958) alculatedfor 3.5 half-widths on either side of the peak position, apeak asymmetry parameter Rietveld, 1969) or reflec-tions with d > 2.24, the unit cell constant, a, the xcoordinate of the oxygen atom, x(O), isotropic thermalparameters, , for all three atoms, and a site occupancyparameter, , arranged o model cooperative ation disor-der over both the octahedral and tetrahedral positions.The background was evaluated by linear interpolationbetween 18 points selected at roughly 7o ntervals n 20over the entire pattern. Note that when he background sestimated by interpolation, rather than by refinement,only those data points within 3.5Vo WHM on either sideof the peak positions are included n the profile refine-ment. The number of "observations" is, therefore, re-duced rom 3076 o 1207.Scattering actors including heanomalous ispersion oefficients) or Fe, Fe2*, Al, Al3*,O and O'- were obtained rom Ibers and Hamilton (1974)and that of 02- was obtained rom Hovestreydt (1983).An experimentally etermined alue of 0.91 was used orthe monochromator olarization correction.

The refinements were initiated using a : 8.159A, x =0.265 , s : 0 .5 , er 0 .0 , : 0 , A( te t . ) B(oct . ) 0 .542 ,B(O) : 1.0A2,and a scale actor and half-width parame-ters estimated by inspection of the observed diffractionpattern. There was no evidence for the presence ofpreferred orientation although several very small peaksdue o a contaminating hase were observed. Refinementwas continued until the parameter hifts n the last cyclewere all less han one quarter of their associated sd's.Combinations f scattering actors corresponding o neu-tral, half-ionized and fully-ionized atoms were carried oconvergence eparately. The pseudo-Voigt es parameterwas only released or the last few cycles of full-matrixrefinement. The complete set of results or the best-fitmodel are given n Table I where hey may be comparedto the integrated ntensity neutron powder diffraction

results of Roth (1964). he raw digital ntensity data havebeen deposited,r but a plot of the observed, calculatedand diference profiles or the final refinement s given nFigure l. A list of observed and calculated ntegrated

Pare[e te t

9 (A )

( t e t , ) ( A 2 )g ( o c t ' ) { 4 2 )

( o ) ( A2)

r(o)

Inverslon, I

SceIe

utv

IT

b zeto

Aay-ettyrr

- t t

No. of ob6ervatlono

e . r s s z l l o ; *

0 . s 6 ( 3 )0 . 44 ( )r . 0 7 5 )

0 , 2633( 2 )

0 . 53 ( 5 )

0 . 00 r 195( 6 )0 . 0 r 5 4 ( 1 r )

- 0 . 0 r 4 r ( 2 t )

0 . 0296( 8 )- 0 . 0857( )

0 . 96 ( 5 )

0 . 2 3 3 ( r 7 )0 . 0055( 3 )

t207

0 . 05680 . 07810 , 0 1 2 5

,R-pR{PP:}

tN-b"a" ln parentheels are the ead.s ln teru of the 1a6t El tni f lcentf lgure to the lft .

t Coefflc lent ln the expregton: nml2 - Uton2o + vtene + t{ (Cegl torte t a l , 1 9 5 E ) .

**Aedeftned by E.rvcld (1969).

t tcqefflc lent ln the exptesslonr p.eudo-vol8te

'eo

+I.2O.

t Agreenent lndlces deflned by yostrg.nd prtnce (19E2)i E t . rouShtyequlvelent to t r lce th colvqnt lonel I vl l re obta ined f im tntegratddpeak structure reflneoentE.

annealing t E50"C or 5 days (pers. comm., V.J. Wall, Dept. ofEarth Sciences, Monash University). The maximum amount ofFe3+ s estimated rom Mossbauer measurements obe about Voof the total Pe content (personal communication rom W.A.Dollase, Dept. of Earth Sciences, cLA to V.J. Wall).

The hercynite powder was back-pressed nto a standarda l u mi n i u m holder and mounted in a Phi l ips PW 1050

diffractometer quipped with a PWl7l0 automatic tep-scanningsystem and a diEracted-beam urved graphite monochromator.Intensity measurements ere made at 20'C at ntervals f0.04.20over the range 17-140'20 using CuKa radiation and a stepcounting ime of 5 s. The X-ray tube was operated at 45 kV and26 mA, with l'divergence and receiving slits. These conditionsallowed the collection of profile data for a total of 72 Braggreflections with background ounts n the range 150-1200 nd amaximum peak ntensity of 45,000 ounts. Dead-time orrectionswere applied automatically uring data collection.

Structure refinementThe east-squares tructure efinements were undertak-

en with the full-profile, Rietveld-type, program DBW3.2(Rietveld, 1969;Wiles and Young, l98l) locally modifiedto include the application of a Z&variable profile shapefunction of the form:


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aa . 5

r t0

o ' '

NTs

HILL: REFINEMENT OF SYNTHETIC HERCYNITE 939

SnT|T|C rcntE - FELU4 - FILLY O{Eo nlt6

no DTn [c)

Fig. 1. Observed, calculated and diference X-ray powder diffraction profiles or synthetic hercynite. The observed data areindicated y plus signs and the calculated rofileby the continuous ine overlying hem. The short vertical ines below he patternrepresent he positions of all possible Bragg eflections nd the lower curve shows he value of (yi., - yi.) at each step.

peak intensities, ogether with their d-spacings, or al lpeaks with intensities reater han Vo of the maximum sgiven n Table 2.

With the profile and structural parameters set equal tothe values obtained rom the best-fit model the 12 mostintense Bragg peaks were considered ndividually inrefinements of the scale factor, 20 zero, half-width Wterm, and pseudo-Voigt 0parameter. he resultant peak

I To receive a copy of this data, order Document AM-84-248from the Business Office, Mineralogical Society of America,2000 Florida Avenue, N.W., Washington, D.C. 20009. Pleaseremit $5.00 n advance or the microfiche.

Table 2. Observed nd calculated ntegrated eak ntensities ndd-spacings or hercynite eflections with intensities reater han

lVo of the maximum calculated alue

I f

widths and e0 parameters re plotted as a function of 20 nFigure 2.

Discussion

Structural parameters

Refinement f the model with fully-ionized atom scat-tering factors produced a slightly better fit between heobserved nd calculated profiles, as measured y Ro andR.o, than he neutral and half-ionized models. However,none of the parameters, ncluding he relatively sensitivethermal vibration parameters, 8, and inversion parame-

ter, i, were affected by more than 1.5 combined esdls bythe different orm factor models.

The mean isotropic thermal vibration parameter of0.8242 is in reasonable agreement by X-ray powderdiffraction standards) with the single value 0.99(5)deter-mined for hercynite by Roth (1964) Table l), with thevalues 0.56(4) and 0.3(1)42 determined for synthetic

q(a)

l l

o 2I 10 0

2 2l 1

0 4o 23 32 24 42 61 33 50 00 62 2l )

) )2 60 44 6

I 34 4

I

: t

4

6 . I

6

5

E

I

7)

E

o

9

I

4 . 7092 . 4E 42 . 4592 . O391 . 8 7 1

I . 665

1 . 5 7 0

1 . 4 4 21 , 2 9 01 . 2 4 1l . 2301 . 7 71 . 090

1 . 062

1 . 019

o.96L2

0 . 9418

0 . 93550 . 9 t90. E6940 . E 550o,8324

I . 15 7 . 4

1 0 2 . 617 . 2

t6 . E

4 1 . 4

49 . 1

1 0 . 0

8 . 0

6 . 2

4 . t

r 1 ,

1 . 32 . 1I . 6

1 2 . 62 2 , 2

I . I

5 7 9

I00 . 0

L 7 2

1 7 . 0

4 1 . 5

49.9

9 . 6

7 . 8

1 4 , 9

o.5 ;t

o.4 g

Eo.3 E

0 2 :a

o.t tc

o o

g0 8E

o 0.6

f o.oo

{ o z

. Il-zt

' ' l i /l/ l v

-t-tl-r-l-{l/r

1 0 . 9

1 . 7

22.O

o 20 40 60 80 loo 120 140

? 9 . 1

Fig. 2. Variation of the individual peak pseudo-Voigtparameters solid circles) and peak ull widths at half maximum

(crosses) with 20 for the 12 most intense peaks n the X-raydiffraction pattern of hercynite. The peak width and shaperelationships etermined y refinement f the entire pattern areshown as continuous ines.


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940 HILL: REFINEMENT OF SYNTHETIC HERCYNITE

Table 3. Interatomic distances and angles or hercynite than the unshared ones, and the valence angles aredistorted 6.6o rom their ideal values. The tetrahedronretails its 43m symmetry with a bond ength expanded y0. 9A over he value corresponding o ideal close packingof the anions (x : 0.25), while the octahedron has 3m

symmetry with bond lengths decreased y 0.104 fromtheir ideal values. The bond lengths are consistent withvalues calculated using the observed site populations(Table l) and the efective ionic radii of O2-, Fe2* andAl3* (O'Neill and Navrotsky, 1983).

Parameter esd's

The subject of the accuracy of parameter esd's deter-mined in profile structure refinements has been exten-sively debated n the recent iterature Scott, 1983;Coo-per,1982:' Cooper et al., l98l; Hewat and Sabine, 98l;Prince, l98l; Bacon and Lisher, l9E0; Prince, 1980;

Sakata and Cooper, 1979). hegeneral

onclusion s thatprofile refinement esd's may be underestimated y afactor of 2 or so compared to the results obtained fromintegrated ntensity refinements when the model, nclud-ing both the structure and the profile parts, is not correct.However, in cases, ike the present study, where thedifraction peak profile shape s itself a refineable parame-ter, it may be expected hat the esd's of the structuralparameters more closely reflect the true distributionabout heir mean values. ndeed, while the major contri-butions to the least-squares esidual do lie under thepeaks n Figure I, the satisfactory value for R*o indicatesthat the peak shape model s reasonable, y X-ray stan-dards, n the present case.

Comparison of the profile refinement results obtainedin the present X-ray study with those obtained n theintegrated intensity neutron data refinement of Roth(1964) (Table l) demonstrates hat the values of theparameters themselves are unaffected by the differentrefinement methods. Moreover, he esd's determined orall parameters common to both studies are of very similarmagnitude, ending support o the estimates obtained nthe profile refinement.

Peak shape and half-width

The power of the pseudo-Voigt rofile unction s that tallows a continuous variation in shape rom pure Lorent-zian or Cauchy e = 1.0) hrough o a pure Gaussian e =0.0). ndeed, Young and Wiles 1982) ave concluded hatthe pseudo-Voigt and Pearson VII (Hall et al., 1977) peakshape functions are consistently he best options forRietveld refinements of both X-ray and neutron diflrac-tion data.

In the present study the best fit between he observedand calculated peak shapes was achieved by varying heshape inearly as a function of 20 (Fig. 2). At the low 20end of the diffraction pattern the peaks have about 34VoLorentzian character, whereas at the high 20 end theyapproximate to a pure Lorentzian form. This indicatesthat for a given FWHM, a greater proportion of theintegrated ntensity lies in the peak tails as the diffraction

AO4 etrahedron:

A- o I ' 41o-A-o tx6l

o-0 t '61

806 octahedron:

B-0 Ix51o-o [x5lo ' - 0 ' t "51o-E-o t'61o ' - B- o ' t r 5 l

A - Fe0.84A1O.15

1 . 9 s 4 ( 2 ) A

109 . 47(10)"

3 . 1 9 0 ( 3 ) A

8 - A l t , g 4 F e O , t 6

1 . 9 3 7 ( 2 ) A

2 . 5 7 7 ( ) A . h a r e d e d8e

2.892(I) A undhared edSe

8 3 , 4 1 ( 7 ) "

e 6 . 5 9 ( 7 ) "

oAB3 polyhedroo

o- A t ' I l 1 . 954( 2 ) Ao- 8 t ' 31 1 . 937( 2 ) AA-B t '31 3 . 381( 0 ) AB-B t'31 2.884(0) A scro36 ehered edgeA-0-B tr3l r2o.72(8) 'B-o-B I'31 e6.23(7r"

Shortest A-A - 3.532 A

MgAl2Oa nd ZnAl2Oa, espectively, rom neutron powderdiffraction data (Fischer, 1967), and with the value1.0(2)42 determined or synthetic Fe3Oa rom neutronsingle crystal data (Hamilton, 1958).

The nversion parameter alue of0.l63(5), correspond-ing to the cation distribution

(Fes saAls. 6)lv[Fe0 6All ro]utOo,

lies n the middle of the range = 0.0-0.25 determined orhercynite in the past, and is very close to the value0.154(10) btained by Roth (1964) Table l). The largerange exhibited by the previous X-ray and Mcissbauerdeterminations s probably a reflection of the difficulty inestimating the areas of weak shoulder peaks in theMcissbauer pectra and/or problems associated ith non-stoichiometry and phase mpurity in the earlier samples.

The refined positional parameter or oxygen, 0.2633(2),is very close o the value obtained by Roth (1964), nd heunit cell size, 8.15579(6)A, alls ar the upper end of the

range ofliterature values clustering round 8.16A Segnit,1984). he a and x values determined n the present tudymay be compared with values of 0.2640 and 8.136Acalculated with the relationships f Hill et al. (1979) singthe observed nversion parameter and the spinel-opti-mized cation adii of O'Neill and Navrotsky (1983).Notethat the lattice parameter determined from the profilerefinement, even allowing for the cubic symmetry andwell crystallized nature of the sample used, s unusuallyprecise because of the requirement hat the calculatedand observed profiles match all along heir steep sides aswell as at the peak center.

The bonding dimensions esulting rom the determineda and x values are summarized n Table 3. As expectedfor a spinel with x > 0.25, he three edges hared etweenadjacent octahedra are shorter (in this case by 0.324)


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angle ncreases. A similar increase n Lorentzian charac-ter has been observed n other X-ray and neutron difrac-tion studies undertaken n our laboratories (Hill andHoward, n preparation) nd n the case of FelOa neutrondiffraction data by Santoro and Prince (1980), who sug-

gested that the variation in shape could be related tostructural distortions and/or the presence of particulardistributions of crystallite sizes within the sample ana-lyzed.

For hercynite he neglect ofthe peak shape ependenceon 20 not only results n a significantly oorer it betweenthe observed and calculated peak profiles Rwp = 9.999compared to 0.07E), but also results in a systematicoverestimation of the atomic thermal vibration parame-ters. However, in spite of this, none of the structuralparameters are affected by more than two combinedstandard deviations.

When individual strong peaks are isolated from thepattern as a whole and refinements are made of theindividual e0 and W parameters, he resultant FWHMvalues ie close o the relationship etween half-widthand20 determined rom the overall U, V and W parameters(Fig. 2). The similarity between he orm of the ndividualpeak width variation with 20 and the variation producedby the Cagliotiet al. (1958) ormula not only ndicates hatthe Caglioti et al. relationship etween half-width and 20is satisfactory or X-ray data, but also shows that thecrystallites are relatively isotropic in shape and un-strained. The systematic variation in the individual evalues can not, therefore, be related o the presence ofeither of these properties n the sample. The only parame-ter with which e shows even a modest correlation coeffi-cient (0.42) is the peak width parameter 1,7and thisrelationship s to be expected.

The source of the profile shape change therefore re-mains undetermined. ossible xplanations ould nvolvethe effect of thermal diffuse scattering, changes n thediffractometer esolution unction, or variable crystallitesize contributions o different parts ofthe pattern. n anyevent, if the presence of peak shape variations withinpowder patterns proves o be widespread t is clear hat a2&dependence or the profile shape unction should be

routinely implemented n the profile refinement proce-dure. For hercynite he function = ao I e1 20 ade-quately accounts or the shape ariation Fig. 2), but thismay not be the case or other samples.

AcknowledgmentsI am grateful o my colleagues . C. Madsen or assistance

during ata ollection nd Dr E. R. Segnit or discussions boutnatural ercynite rystal hemistry, nd o Dr H. G. Scott f theCSIRODivision f Materials cience or his constructive riti-cismof an early version f the manuscript.

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942 HILL: REFINEMENT OF SYNTHETIC HERCYNITE

Meyers, C. E., Mason, T. O., Petuskey, W.T., Halloran, . W. ,and Bowen, H. K. (19E0) hase equilibria n the system Fe-Al-O. Journal of the American Ceramic Society, 63,659-663 .

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Manuscript eceived, September 4, 1983;acceptedfor publication, May I, 19E4.

x-ray powder diffraction profile refinement of synthetic hercynite

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