American Mineralogist, Volume 73, pages 861-369, 1988

Rietveld refinement of the todorokite structure

Jpprnnv E. PosrDepartment of Mineral Sciences, Smithsonian Institution, Washington, D.C. 20560, U.S.A.

Davro L. BIsnEarth and Space Sciences Division, Los Alamos National I-aboratory, Los Alamos, New Mexico 87545, U.S.A.

AssrRAcr

Rietveld refinements, using powder X-ray data, of the structures of todorokite samplesfrom South Africa and Cuba have confirmed the basic [3 x 3] tunnel structure and, forthe first time, have provided information about the positions of the tunnel cations andwater molecules. Fourier-difference maps and subsequent refinements show a major tunnelsite at about (0.36, 0, 0.35) and smaller more difuse areas of electron density near (0.70,

Vz, 0.38) and (t/2, Vz, t/z). Structure-energy calculations suggest that the first two positions

are occupied by water molecules and the third by cations such as Na and Ca. The differencemaps indicate considerable positional disorder on the tunnel sites, probably caused byvarious tunnel contents and configurations oflower-valence octahedral cations in differentunit cells. The MqO octahedra at the edges of the triple chains have larger mean Mn-Odistances and probably accommodate the larger cations found in todorokite, e.9., Mg2+,Mn3+, Cu2+, Ni2*, etc.

Iwrnooucrrou

The crystal structure of todorokite has been a subjectofinterest and speculation for several decades. Much ofthis attention stems from its role as a major manganeseoxide phase in ocean manganese nodules and the possi-bility that it is the host for Cu, Ni, and other importantmetals found in the nodules (Burns et al., 1983). Todo-rokite also occurs in many terrestrial manganese depositsand in some cases is mined as an ore of manganese. Re-cently, studies have shown that todorokite exhibits de-hydration and cation-exchange behavior similar to manyzeolites, suggesting possible potential as a catalyst mate-rial (Bish and Post, 1984). Unfortunately, like many othertetravalent manganese oxide minerals, todorokite typi-cally occurs as poorly crystalline masses, and to date nocrystals have been found that are suitable for single-crys-tal X-ray or neutron-diffraction studies. Consequently,many questions remain about the crystal chemistry andstructure of todorokite.

Todorokite is a hydrated Na-, Ca-, K-, Mg-bearingmanganese oxide with characteristic X-ray powder-dif-fraction lines at about 9.6, 4.8, and 2.42 A. Chemicalanalyses (e.g., Ostwald, 1986) show a wide range of com-positions and suggest the general formula(Na,Ca,K,Ba,Sr)o r-0, (Mn,Mg,Al)u O,, . 3. 2-4. 5HrO. Formany years, a controversy existed in the literature aboutthe nature of the todorokite crystal structure. On the basisof electron-diffraction data and the commonly fibroushabit, Burns and Burns (1977) proposed a tunnel struc-ture for todorokite, similar to those of the tetravalentmanganese oxide minerals romanechite and hollandite.On the other hand, infrared-spectroscopy data and the

0003404x/88/0708{861$02.00 861

sometimes platy habit exhibited by todorokite supportedthe notion of a layer structure, analogous to birnessite(Potter and Rossman,1979). A third point of view ex-pressed by Giovanoli and coworkers (e.9., Giovanoli andBurki, 1975) maintained that todorokite was in fact nota valid mineral species but rather a mixture of buseriteand/or birnessite and manganite.

In recent years, speculations about the basic todorokitestructure have largely been laid to rest by high-resolutiontransmission electron microscopy (nnrovr) studies thatconfirm the tunnel model proposed by Burns and Burns(l 977) (Chukhrov et al., 1978; Turner and Buseck, 198 l).The nnrpu images reveal that todorokite consists pre-dominantly of triple chains of edge-sharing Mn,O octa-hedra that corner-share to form large tunnels, measuringthree octahedra on a side [3 x 3] (Fig. l). The unit cellnominally has six Mn and 12 O atoms constituting theoctahedral framework, along with the tunnel cations andwater molecules. The todorokite structure is similar tothose of hollandite and romanechite but has larger tun-nels. Hollandite is constructed of double chains of Mn,Ooctahedra forming 12 x 2l tunnels, and romanechite ofdouble and triple chains, resulting in [2 x 3] tunnels. TheHRrEM images ofthe todorokite structure commonly showintergrowths of larger tunnels, e.9., [3 x 4] and [3 x 5],with the basic [3 x 3] units (Chukhrov et al.,1978; Turnerand Buseck, 1981). Unfortunately, the Hnrevr studiescannot provide precise atom positions and bond lengthsfor todorokite, nor do they give any information aboutthe locations of the cations (Na, Ca, K, etc.) and watermolecules that presumably reside in the large tunnels.

Because of the difficulty (and perhaps impossibility) of

862

Fig. 1. Projection ofthe Rietveld-refined todorokite structuredown D. The filled circles represent atoms at y : 0, and the opencircles, those at y : Yr.

obtaining todorokite crystals suitable for single-crystal dif-fraction experiments, we have attempted to refine thecrystal structure of todorokite by the Rietveld method(Rietveld, 1969), using X-ray powder-diffraction data. Inaddition to confirming the [3 x 3] tunnel structure indi-cated by HRrEM studies, a major goal of this study hasbeen to locate the positions of the tunnel cations andwater molecules.

Generally, there are two approaches used to extractstructural information from X-ray powder-diffractiondata. In the first method, the powder-diffraction patternis decomposed into the component Bragg reflections, andthe integrated intensities are measured. These Bragg in-tensities, after correction for multiplicity and Lorentz-polarization effects, are used in the same manner as thosedetermined by single-crystal experiments. This so-calledprofile-fitting procedure works well for relatively simplestructures that yield powder patterns having mostly re-solved Bragg peaks. In the case of todorokite, however,there are no completely resolved reflections in the range8" to 130' 20.lnfact, most ofthe peaks in the todorokitepowder pattern (Figs. 2 and 3) are composed of fromseveral to up to a dozen or more Bragg reflections. Itwould be extremely difficult, if not impossible, to use aprofile-fitting procedure on the todorokite powder X-raypattern. Fortunately, the Rietveld approach does not re-quire determination of individual Bragg intensities. In-stead, each data point in the powder profile is used as anobservation in the structure refinement (Rietveld, 1969).A limitation of the Rietveld method is that one must startwith a model that is a reasonable approximation of theactual structure. Typically, a starting model is conceivedby analogy to similar structures, by distanceJeast-squares(DLS) (Villiger, 1969) calculations, or as in the case oftodorokite, from nnrEvr studies. In the actual refinementprocedure, the atom positions, occupancies, unit-cell pa-rameters, and background coefficients, along with profileparameters such as half-widths, peak asymmetry, etc., arevaried in a least-squares procedure until the calculated

POST AND BISH: RIETVELD REFINEMENT OF TODOROKITE STRUCTURE

powder profile, based on the structure model, best match-es the observed pattern. The Rietveld method has beenused successfully in recent years to refine several struc-tures, using neutron or X-ray powder dala (e.9., Thomp-son and Wood, 1983; Hill, 1984; Hill and Madsen, 1984;Baerlocher, 1984). Most previous Rietveld refinementsusing X-ray data have involved relatively simple struc-tures with few variable parameters; todorokite shouldprovide a more severe test of the technique.

ExpnnrnrnNTAl DETAILS

The two todorokite samples used in this study are from theN'Chwaning Mine, North Cape Province, South Africa (HarvardUniversity no. 126232), and Charco Redondo, Cuba (HarvardUniversity no. 106238). Both samples show a fibrous habit.Electron-microprobe (South African sample) and wet-chemical(Cuban sample) analyses yield the following chemical formu-lae: South Africa-(Nao ooCao ,.Ko o,)(Mn!{,Mgo ot)O,r'4.59HrO;Cuba-(Nao rrCao rrKoouSro orBaoot)(Mnfj.Mgo ooAlo orFeo o,)O,r'3.I HrO. The water values were determined using a Dupont 903Hmoisture-evoluti on analyzer.

Samples for X-ray powder diffraction were ground in an agatemorfar to less than 400 mesh and frontJoaded into a cavity-typesample holder. The data for the samples from South Africa andCuba were collected in the step-scan mode using a Scintag andSiemens automated X-ray powder diffractometer, respectively.Data-collection parameters for the two samples are listed in Table1. The sample from South Africa was repacked and rerun threetimes at a scan rate of l'lmin to check for evidence of preferredorientation. No significant changes in intensities were noticedamong the three data sets, suggesting that preferred orientationeffects are minimal. The powder patterns for the Cuban and SouthAfrican samples show minor impurities of quartz, and quartzand calcite, respectively.

For all of the refinements, the data in the low-angle range (seeTable 2) were excluded because in this region not all ofthe in-cident X-ray beam is striking the sample and therefore relativeobserved intensities are too low. Also, 2d regions (see Table 2)encompassing the strongest lines for quartz and calcite were ex-cluded from the data.

RrmNnvrnNT AND Founrnn ANALYSIS

The observed X-ray powder profiles for the two todo-rokite samples are plotted in Figures 2 and3.It is obviousthat most of the peaks in the two patterns appear relativelybroad (FWHM > 0.5'at 30), and although this broad-ening in part can be explained for many of the peaks bythe large number of contributing Bragg reflections (note

reflection markers in Figs. 2 and 3), undoubtedly some ofthe broadening results from structural disorder. As men-tioned above, HRrEM images of the todorokite structureinvariably show octahedral chains ofdifferent widths ran-domly intergrown with the predominant triple chains(Chukhrov etal.,1978; Turner and Buseck, l98l). Also,HRrEM images indicate that the B angle for diferent unitcells can range from 90" to I l0'(Turner, 1982). Both ofthese structural effects probably contribute to the peak

broadening in todorokite powder-difraction patterns. Peakbroadening is especially apparent in the profile for thesample from Cuba (Fig. 2). Similar broadening of certain

Todorok i te . #106238. Cuba

Two - Theta (Degnees)

POST AND BISH: RIETVELD REFINEMENT OF TODOROKITE STRUCTURE

Fig.2. Observed X-ray diffraction pattern for todorokite from Cuba, offset by one major division on the y axis (i.e., the zero-intensity point is 1600). The vertical bars mark positions ofBragg reflections.

863

r u 8 0

i s l

H 4 8

classes of reflections is also observed in X-ray powder-diffraction patterns of hollandites and romanechite, whichalso show chain-width disorder in nnrnv images (Turnerand Buseck, 1979). It is not known how seriously thetodorokite structural disorder affects the Rietveld refine-ment results, but it undoubtedly contributes to a some-what higher value for the profile residual.

The [3 x 3] Mn,O octahedral framework shown in Fig-ure 1 was the starting model for the Rietveld refinements

ofthe todorokite structure. Initial atom positions (Table3) were determined by DLS calculations with programorszo (Baerlocher et al., 1977), based on observed Mn-Oand O-O bond distances from single-crystal X-ray studiesof romanechite and hollandite (Turner and Post, in prep.;Post et al., 1982). Unit-cell parameters for the DLS cal-culations were fixed to observed powder-diffraction valuesfor the todorokite from South Africa. For both DLS mod-eling and subsequent Rietveld refinements, space group

58 65 72 79 86 93T h e t a ( D e g n e e s )

Fig. 3. Observed and calculated X-ray diffraction patterns for South African todorokite using CuKo radiation. The crosses arethe observed data, and the solid line is the calculated profile. The smooth line beneath the patterns is the calculated background.The patterns have been offset by two major divisions along the / axis (i.e., the zero point is at 500). The diference between theobserved and calculated patterns is plotted below. The vertical bars mark all possible Bragg reflections.

x1 14 51Two

Todor0k i te . #126232. S0uth Af r i ca

864

TneLe 1. Data-collection paramerers

South Africa Cuba

RadiationDetectorMonochromatorSlits

PrimaryReceivingSoller

ScanRange ( '2d)Step size (" 2d)Time/step (s)

QuKq CuK/Solid state (Ge)

None None

' l m m 1 m m0.2 mm 0.2 mm

Incident, diffracted

6-1 10 6-1 100.02 0.0240 40

QuKqScintillationGraphite (diffracted beam)

t "1 'Incident, diffracted

8-960.0270

P2/ m was assumed because it is consistent with the sym-metry exhibited by the [3 x 3] octahedral framework andwith the 2/m Laue symmetry shown by electron-diffrac-tion patterns (Turner, 1982). In the absence of any po-sitional information, tunnel cations and water moleculeswere excluded from DLS calculations and from initialstages of refinement.

All Rietveld refinements were carried out using thecomputer program DBw3.2 (Wiles and Young, 1981), asmodified by S. Howard (pers. comm.). During the earlystages of refinement only the following parameters werevaried: scale factor, background coefrcients, unit-cell pa-rameters, full-width parameters, sample displacement, andpeak asymmetry (< 50' 2d). First, only the scale factor wasrefined, and then gradually the remaining parameters wereincluded in successive least-squares cycles. The back-ground was fit using a third-order polynomial, and theobserved peak shapes were approximated with a PearsonVII profile function, limited to ten full-widths on eachside of the peak maximum. The Pearson VII mixing coef-

TneLe 2. Final Rietveld refinement parameters for todorokite

POST AND BISH: RIETVELD REFINEMENT OF TODOROKITE STRUCTURE

ficient was also included as a refinable profile parameter.In the case of the Cuban sample, there was difficulty re-fining full-width parameters, and we were forced to use afull-width that had a fixed 2d dependence. This problemlikely arose because ofdifferences in peak widths for dif-ferent classes ofreflections, caused by structural disorder.Using the DlS-determined fixed Mn,O framework, therefinements converged to weighted profile residuals of0. I 6,0.17, and 0.16 for the South African Ka, KB, and Cubandata sets, respectively. The reasonably low R*o values, atleast for Rietveld refinements using X-ray data, afrrm thatour starting model structure is basically correct.

Refined unit-cell parameters for the two samples arelisted in Table 2. For powder patterns having many over-lapping reflections, as in the case oftodorokite, Rietveldrefinement is probably the method of choice for deter-mining accurate unit-cell parameters. Small discrepanciesbetween the values for the two samples are likely a man-ifestation of compositional differences.

In an attempt to locate the positions ofthe tunnel species,Fourier-difference maps were calculated using the ob-served Bragg intensities as determined by the Rietveldrefinement procedure described above. These intensitieswere corrected for multiplicity and Lorentz-polarizationeffects and converted into structure factors for use in thexRAy?6 crystallographic computing package (Stewart,1976). Using the same DLS todorokite structure as above,an overall scale factor was refined and a three-dimensionaldifference-Fourier map was computed for each of the to-dorokite data sets, witn O.:-A resolution. Sections fromthe maps are pictured in Figures 4 and 5.

When interpreting difference maps based on Rietveldintensities, it is important to consider that the results are

South Africa

Kp

a (A)b (A)c (A)B f )v(4.)Pearson Vll coef.Asymmetry parameterFWHM f 2d at 30')tOverall BExcluded regions (')

ParametersBragg reflections

P +F","nn

s 764(1 )2.8416(4)9 .551 (1 )

94.06(1 )264.32

1.0s(3)0.006(3)0.590.06(8)6-20

26.5-26.929.3-29.665.3-66.0

36401

0.0890 . 1 1 30.046

9.763(2)28454(4)9.55e(1)

94.1 6(1 )264 83

1.06(3)-0.03(1)

0.45-0.50(8)

6-201 8.6-19.022.7-22.8423.84-24.'t826.4-26.7458.38-58.78\to

5490 1060.1 350.054

e.78e(6)2.834(1)9.551(4)

93.72(3)264.46-0.50(6)f-0.04(1)

1 .630.6s(8)6-2 I

353 1 0

0.0970.124

-$

. Full-width at one-half maximum peak height- . 4 : > , { l l obq - t ca t c i l }D i { t obq } .t R o: [),{W(lobs, - lcalc),}/2r{w,(lobs),}],/,.+ Pseudo-voight coefficient.$ F"^* not calculated.

TneLe 3. Todorokite atom positions

POST AND BISH: RIETVELD REFINEMENT OF TODOROKITE STRUCTURE 865

Taele 4. Bond distances (A) for todorokite

DLS

South Africa Mn1 -O2( x 4)-O3( x 2)

Mean

Mn2-O1( x 2)-o2-o3( x 2)-o4

Mean

o1-o1

-o3-o4-o4'

o2-o2

-o3-o3'

H,O(1)-O1

-o6-H,O(1)-H,O(3)

Mn3-O5( x 4)-06( x 2)

Mean

Mn4-O1-O4(x2)-o5-06( x 2)

Mean

o4-o4-o5-o6

o5-o5-o5'-o6-o6'

o6-06

Kp

1 .851 .901 .87

1 .821 .751 .80

Mn1 x

zXvzx

zx

zx

zx

zxvzxvzxvzxvzxvz

xvz

xvz

'/2

'/2

00.76900.00200Y20.978

o.7670 162'/2

0.1020.41800.0960.679'/2

0.0980.92000.1 450.911

0 3970.8880u . o c /

Y2V20o.76400.00200Vz0.990f2

0.7590.180v2

0 . 1 1 60.40300.0690.663V20 . 1 1 00.90800.1500.993V20.4720.88900.666

1 9 51.891 9 41 9 81 9 4

2.842.812.602.933.02

2.842.282.232.78

Vz V2V2 Y20 00.764 0.7660 00.002 0.0010 00 0V2 V20.974 0.975V2 Y20 765 0.7680 178 0 .176Vz Y20 . 1 1 9 0 . 1 1 70.41 8 0.4190 00.079 0.0660.665 0.649V2 V20.090 0.0800 917 0.9320 00 .150 0 .1480.913 0.902V2 Vz0.407 0.4000.880 0.8950 00.649 0.6530.363 0.4050 00.353 0.4140.92 0.860 696 0.644f2 v2

0 380 0.3850.42 0.90Vz YzY2 Y2V2 V20.48 0.64

1 0 n1 .922.051 .981 .96

2.842.842.65

2.842.382.562.75

2.84

2,793.492 . 1 12.842.30

2.842.88

o3-o3-o4

o4

U5

o6

H,O(1)

H,O(2)

H,O(3)

Notes.' (1) lsotropic temperature factors fixed to B : 0.8 for Mn, 1.0 forO, and 5.0 for HrO. Overall isotropic temperature factors were refined (seeTable 2). (2) The estimated errors determined by the Rietveld refinementsare typically 0 001 for Mn, 0.002 for O, and 0 006 for H,O. The actualerrors are probably several times these values, at least for the anions (seediscussion of errors in text).

biased by the model structure, typically to a greater degreethan in single-crystal experiments. This is because theobserved Bragg intensities determined by the Rietveldprogram for overlapping peaks are assumed to have thesame ratios as the corresponding calculated intensities.Consequently, the amount of information contained onthe resulting diference-Fourier maps is typically less (andelectron-density maxima are lower) than on comparablemaps resulting from single-crystal data. For example, dif-ference maps calculated for analcime (Bish and Post, un-pub. results), in the same manner as described for todo-rokite, show only 2 to 5 e /A' peaks for the Na and watersites. It is noteworthy, however, that for analcime all ofthe cavity species were accurately located on the maps,and there were no extra peaks larger than 0.5 e-lA'.

All of the significant electron-density peaks (>0.3 e /

3.13 H,O(2FO32.71 -o42.38 -O52.84 -H,O(2)2.35 -H,O(3)

H,O(3FH,O(3) 284

Note.'Bond distances are calculated from atom positions determined forthe Kd data set for the sample from South Africa. Errors as determinedby the Rietveld refinement are about one in the last place, but as explainedin the text, actual errors are probably several times larger.

A,; on the difference maps for the three todorokite datasets are centered at levels y : 0 and y : t/z and are locatedin the tunnel region of the structure or near framework-atom positions. The Mn and O atoms in the [3 x 3]framework also have y coordinates of 0 and t/z and areplotted for reference on the Fourier sections in Figures 4and 5. Corresponding map sections for both samples arevery similar, suggesting that they reveal real structuralinformation rather than just artifacts. The most significantarea of electron density in each map is centered at about(0.37, 0, 0.37); the peak for the Cuban material is slightlylarger (2.3 vs. 1.8 e-tA\ and better defined than that forthe South African sample. The next largest difference peaksare about 1.0 to 1.5 e /A'located at approximately (2h,t/2, t/t). The map for the South African K0 data set showsa 1.5 e- / A3 peak at (Yz, lz, t/z), but the other two differencemaps have peaks at that position that are only about halfas large. Scatterings of small peaks occur in the vicinitiesof (2/2, 0, t/t) and (t/t, Vz, t/) in all ofthe maps. The todorokitechemical formulae given above indicate approximatelyfour water molecules per unit cell; thus most of the elec-tron density in the tunnels must be due to water, whichprobably explains some of the diffirseness of the differencepeaks.

For the remainder of the Rietveld refinement process,all of the tunnel cation species were assumed to be water.Water sites were included in the todorokite structure mod-el, corresponding to the major areas of electron densityon the difference maps (see Table 3). The temperature

866

ooFig. 4. Difference-Fourier maps at y : 0, superimposed onto

projections of the todorokite framework looking down D (B :90'), for samples from (a) South Africa (Ka), and (b) Cuba. Themaps were calculated using the DLS framework and Rietveld-derived observed Bragg intensities. The filled circles representatoms at y : 0, and the open circles, those at y : t1r. The largecircles indicate O and the small circles Mn atoms. The contourinterval is 0.4 e-lA,. The unit cell is indicated bv the dottedlines.

factors for the water positions were fixed to .B : 5.0, andthe positions and occupancy factors were refined alongwith the profile parameters. When we attempted to refineisotropic temperature factors for the water positions, theyincreased to very large values (B > l0), especially forH,O(2). This might in part result from high correlationswith occupancy factors. Yet, in Rietveld refinements, tem-perature parameters can implicitly correct for other prob-lems of an experimental nature associated with the dataset, so they may be suspect. It is also likely, however, thatthe large temperature factors are indicating a large degreeof positional disorder on the water sites, similar to whatis observed in many zeolite structures, where .B values forwater sites are commonly > l0 (e.g., Rinaldi et al., 197 4,where -B values for phillipsite ranged from 7 to l9).

Inclusion of the water sites in the refinements signifi-cantly reduced the R*o values (by 0.04 to 0.05). Resultsfor the South Africa Ka data indicate that the HrO(l) sitehas the largest occupancy; however, the KB refinementlocates a slightly diferent position for H,O(1) and assignsnearly equal occupancies to HrO(l) and HrO(2). TheH,O(2) positions are also slightly different among the threecases. We did not attempt to refine water sites for each ofthe several small peaks shown on the difference maps inthe region around HrO(2). Each of the refinements showabout 0.4 to 0.6 water molecules at (t/2, Vz, t/z) and nothingat (2/t, 0, 7). The sliehtly different water positions resultingfrom the various data sets are most likely a consequenceof the smeared-out nature of the tunnel electron density.

In the final stages of refinement, the positions of Mnand O atoms were allowed to vary along with the waterpositions and occupancy factors and profile parameters(total variables : 36). Individual isotropic temperaturefactors were held fixed to B : 0.8 for Mn and, B : 1.0 forO atoms. Final observed and calculated profiles for theSouth African Ka refinement are compared in Figure 3.The flnal residuals and atomic parameters are listed inTables 2 and 3, respectively, and bond distances are listed

POST AND BISH: RIETVELD REFINEMENT OF TODOROKITE STRUCTURE

ob

Fig. 5. Difference-Fourier maps at y : yt. For further expla-nation, see Fig. 4 caption.

in Table 4. The refined Mn positions resulting from thethree data sets agree quite closely, therefore giving us con-fidence in their accuracy. The general agreement amongthe O-atom positions for the various refinements is alsoreasonably good although they show more variation thanthe Mn positions, especially the 05 determined for theCuban data. Most of the variation among the sets of re-fined atom positions probably is caused by disorder and/or minor preferred orientation in the samples. Slight dif-ferences in atom positions in the two samples are expectedbecause of differences in composition and unit-cell pa-rameters. Atom positions determined using the Ka dataset from South Africa were used to calculate the bondlengths in Table 4 because this refinement yielded thelowest profile and Bragg residuals. The slightly higher re-siduals for the South African KB profile probably resultfrom the much lower count rates (approximately 40 cpsfor the largest peak) and poorer counting statistics.

DrscussroNl

The refinement results are consistent with the [3 x 3]tunnel structure proposed by Turner and Buseck (1981),and the final Mn,O atom positions compare quite wellwith the DLS model of the octahedral framework (Table3). Unfortunately, it is difrcult to assess the accuracy ofour refined todorokite atom positions and, consequently,bond distances. The estimated errors determined by theRietveld refinement are based on counting statistics in thedata but do not account for errors in the profile functions,nor for sample-related problems such as preferred ori-entation and structural disorder. In particular, we havefound that atomic coordinates can be significantly affectedby preferred orientation of crystallites in the sample. Forexample, refinements that we have carried out on hollan-dite and romanechite (Post and Bish, in prep.) show thatgreatly improved fits are obtained between Rietveld andsingle-crystal results when preferred orientation is mini-mized (by grinding samples to smaller particle sizes andby side-loading sample holders). It appears that the largesteffect of nonrandom samples is on the positions of thelight elements such as oxygen; for both romanechite andhollandite, the Rietveld-refined Mn positions are not sig-nificantly different from the values determined by single-

crystal refinements. As mentioned above, the todorokitepowder patterns do not show evidence ofsignifrcant pre-ferred orientation problems; however, the possibility ofminor effects cannot be dismissed.

Octahedral framework

The Mn-O distances resulting from the Rietveld re-finement of romanechite (which has a structure similar tothat oftodorokite and also exhibits disorder) agree withsingle-crystal values to within 0.10 A or less; most agreewithin 0.05 A. It is probably reasonable to assume thatthe todorokite distances in Table 4 have similar uncer-tainties. For the most part, the todorokite Mn-O distancesfall within the range (1.87-2.12 A) shown by single-crystalstudies on romanechite, hollandite, and cryptomelane (Postet al., 1982; Turner and Post, in prep.). The distances inthe Mnl octahedron, however, are anomalously short andprobably reflect errors in the refinement.

Although it is not possible to discuss precise details ofthe todorokite framework because of the uncertainties inthe bond distances, some general characteristics are evi-dent. For example, the average Mn2-O and Mn4-O bondlengths (1.94 and 1.96 A, respectively) are considerablylonger than the mean Mn l-O and Mn3-O distances ( I .80and 1.87 A, respectively), suggesting that the larger lower-valence cations, e.g., Mn3+ and Mg2+ (necessary to offsetthe charges on the tunnel cations), preferentially occupythe Mn2 and Mn4 octahedral sites. This is consistent withsingle-crystal results for romanechite that show Mn3+ or-dering into the octahedral sites at the edges ofthe triplechains (Post and Turner, 1986). Similarly, a recent re-finement of a synthetic [2 x 5] tunnel manganese oxidestructure (Tamada and Yamamoto, 1986) shows the larg-est octahedra to be at the edges of the quintuple chain.Presumably, the larger Mn2 and Mn4 sites also accom-modate cations such as Cu2+, Co2+, and Ni2+ that com-monly occur in todorokite (Ostwald, 1986). According tothe chemical analysis of the todorokite from South Africa,if all of the Mg cations are in the Mn2 or Mn4 octahedra,they fill approximately 100/o of those sites. Using typicalMna+-O and Mgz* O distances of 1.9 I and 2. I 0 A (Shan-non, 1976), respectively, one calculates for these sites anaverage cation-O bond length of 1.93 A, compared to1.94 and 1.96 A in Table 4. The slightly longer refineddistances suggest that perhaps the experimental distancesare in error or that Mn3+ also is present in the sites. With-out knowing the amount of hydroxyl in the structure, ifany, and the distribution of Mg between the tunnel andoctahedral positions, it is not possible to calculate exactlythe amount of Mn3+ in the framework. The Mn2 andMn4 octahedra do not, however, show significant evi-dence of Jahn-Teller distortion that should accompanylarge amounts of Mn3+ on these sites.

The Mn2 and Mn4 positions (see Fig. l) are shiftedfrom the centers of their coordination octahedra, awayfrom the Mnl and Mn3 cations, respectively. Similar shiftsare observed in romanechite (Turner and Post, in prep.)and hollandite (Post et al., 1982) and probably serve to

867

minimize repulsive forces between neighboring Mn cat-10ns.

In all of our discussions we have assumed that the Mgcations are in octahedral sites and the Na, K, Ca, Ba, Sr,and water are in the tunnels. Cation-exchange experimentsusing the sample from Cuba show that Ba and Sr replacesome of the Ca but not Mg (Bish and Post, in prep.),consistent with the notion that Mg is not in the tunnels.Furthermore, six-coordination is typical for Mg in mostother minerals. In the samples used for this study, thereis sufficient Mg in the octahedral sites such that Mn3+ isnot needed for charge balance, unless significant amountsof hydroxyl anions are present in the structures. The pres-ence of Mg and/or Cu, Ni, Co, etc., instead of Mn3+ asthe lower-valence octahedral cation perhaps serves to sta-bilize todorokite under conditions in which Mn3+ cannotexist (Burns et al., 1983), e.g., highly oxidizing environ-ments.

Tunnel water and cations

The difference-Fourier maps in Figures 4 and 5 and thesubsequent refinements show a major area of electrondensity in the tunnels at about (0.38, 0, 0.38) that wetentatively identify as water, which is known to be themajor tunnel species. The distance of this site from thenearest O atoms is about 2.40 L, which is slightly shortcompared to typical O-O(water) distances. The refinedH,O(2) position is only 2.ll L from 05. The differencemap, however, suggests agreat deal ofpositional disorderover these sites, thus making it difiicult to determine exactbond distances. The disorder possibly arises from variousarrangements of lower-valence cations over the octahedralsites and/or different B angles in different unit cells (asobserved in nnrrvr studies). Structure-energy calculationsfor hollandite minerals show clearly that the positions ofthe tunnel cations in these structures are a function of theconfiguration of the lower-valence octahedral cations sur-rounding the tunnel sites in a given unit cell (Post andBurnham, 1986a). Also, the chemical formulae for mosttodorokite samples show several kinds oftunnel cations,all with occupancies less than one. Therefore, the tunnelcontents of various unit cells are different, which un-doubtedly contributes to the positional disorder. Fur-thermore, the actual water positions might be displacedoffof the mirror planes, which would result in longer HrO-O bond lengths. Structure-energy calculations, describedbelow, in fact indicate that this is likely the case.

Preliminary structure-energy calculations support theassumption that the electron density at about (0.36, 0,0.35) [HrO(l)] is due to water. Calculations using the com-puter program wvrrN (Busing, l98l) and modified elec-tron-gas short-range energy terms (Post and Burnham,1986b) yield minimum-energy water positions at about(0.37, 0.03, 0.37), regardless of the lower-valence cationarrangement on the octahedral sites or the number ofwater molecules and cations in the tunnels. The modelswith four water molecules per unit cell (typical todorokiteanalyses show 3.2 to 4.5 water molecules per cell) deter-

POST AND BISH: RIETVELD REFINEMENT OF TODOROKITE STRUCTURE

868 POST AND BISH: RIETVELD REFINEMENT OF TODOROKITE STRUCTURE

mine a second minimum-energy position at about (0.6,0.6, 0.4). The difference maps in Figure 5 show electrondensity in this region of the tunnel, and the refinement ofthe South African Ka data yielded a tunnel position at(0.7, 0.5, 0.38) [H,O(2)] with an occupancy slightly lessthan that of HrO(l). The K0 refinement placed HrO(2) at(0.64, 0.5, 0.39). The calculations consistently show thesecond water site 0. I to 0.6 A off of the mirror plane at! : t/2. Structure-energy minimizations with Ca and Nacations along with the water indicate that the cations oc-cupy a range ofpositions in the center ofthe tunnel near(t/2, Vz, t/z), depending on the number of water moleculesin the tunnel and the arrangement oflower-valence cationsin the octahedral framework. Such a positionally disor-dered site is consistent with the Fourier maps showingsmeared-out electron density and the refinement ofa smalloccupancy factor (0.5 O atoms) at (t/2, t/2, Yz).

The above description of the water positions in thetodorokite tunnels is consistent with infrared spectroscopystudies of todorokite (Potter and Rossman, 1979) indi-cating the presence of water molecules in several well-defined crystallographic sites and, in addition, a disor-dered water component. If, as the energy calculations sug-gest, the tunnel cations are near (t/z,Vz,Vz) and HrO(l) andHrO(2) are fully occupied in a given unit cell, then thecations are octahedrally coordinated by the water mole-cules. The distances from HrO(l) to (t/2, t/2, t/z) are ap-proximately 2.30 to 235 A, which are reasonable for(Ca,Na)-O bond lengths. The larger K and Ba, on theother hand, might occupy positions near the walls of thetunnels, perhaps accounting for some of the smaller dif-ference peaks in Figures 4 and 5. The multiple peaksevident on the difference maps in the vicinities of therefined water sites probably represent different water (and/or cation) positions, depending on the tlpe oftunnel cat-ion (if any), the number of water molecules, and the con-figuration oflower-valence octahedral cations in a givenunit cell. The difference maps and the energy calculationsindicate that the most favorable and well-defined waterposition [HrO(l)] is in the more open corner of the tunnel.Most likely, only after this larger site is filled do watermolecules occupy other tunnel positions.

BrnNnssrrs ro ToDoRoKITE TRANSFoRMATIoN

Recently, Golden et al. (1986, 1987) synthesized to-dorokite by heating birnessite under saturated steam pres-sure at 155 "C. Several observations support their sug-gestion that birnessite might also be the precursor to mostnatural todorokite. One of these is the trilling patternformed by twinned fibers that is observed in electron-microscope images and is almost diagnostic oftodorokite.This twinning is readily explained in the context of abirnessite to todorokite transformation. Assuming thatthe todorokite tunnels form by constructing triple-chainwalls that connect adjacent Mn,O octahedral sheets inbirnessite, then any ofthree different orientations oftun-nels can result, at 120" to each other, in different layersbecause of the threefold svmmetrv of the octahedral sheets.

This is consistent with electron-microscope photographsof todorokite showing stacked layers in which the tunnelsin any given layer are oriented in one direction but arerotated 120'relative to tunnels in other layers (Turnerand Buseck, l98l).

A birnessite parent also explains why the chain-widthdisorder (e.g., quadruple, quintuple, etc., chains) observedin unrrvr photographs of todorokite (Chukhrov et al.,1978; Turner and Buseck, l98l) occur only in one crys-tallographic direction (lla). The direction of disorder isparallel to the original birnessite octahedral sheets. Duringthe transformation to todorokite, some tunnels other than

[3 x 3] form (e.g., [3 x 4], [3 x 5], etc.), and, becausethe original layer separation in birnessite constrains onedimension of the tunnels, larger chain widths can formonly along the layer direction.

Considering the approximately 7-A spacing of the oc-tahedral layers ofbirnessite versus the 9.6-A separationbetween triple chains in todorokite, it is necessary for thebirnessite structure to expand to essentially a buseritestructure (layer spacing of about 9.6 A) before transform-ing to todorokite. In fact, experiments by Golden et al.(l 986) indicate that synthetic birnessite easily hydrates tobuserite in an aqueous environment, suggesting that theactual transformation, therefore, is buserite (which mightor might not have formed from birnessite) to todorokite.

Suuuanv

Rietveld refinements, using X-ray powder data, of thestructures of two todorokite samples have confirmed thebasic [3 x 3] tunnel structure and have provided, for thefirst time, information about the positions of the tunnelcations and water molecules. Fourier-diference maps re-veal a major tunnel water and/or cation positionat (0.37,0, 0.35), along with other sites near (0.70, Yz, 0.38) and(Yz, lz, lz). Structure-energy calculations suggest that cat-ions such as Na and Ca reside near (lz, lz, t/z), where theyare octahedrally coordinated by water molecules occu-pying the other two tunnel positions. Considerable posi-tional disorder on the tunnel sites probably arises fromdifferent arrangements of lower-valence octahedral cat-ions in different unit cells and from variety in the tunnelcontents.

The refined Mn-O bond distances indicate that the oc-tahedra on the edges ofthe triple chains are larger thanthose in the middle and therefore likely accommodate thelarger, lower-valence cations, 0.g., Mg'*, Mn3+, Cu2+, Ni2+,etc.

The formation of todorokite from a birnessite or bus-erite parent is consistent with the trilling twin patternobserved in most todorokite and with the nnrru obser-vation of chain-width disorders occurring in only onecrystallographic direction.

AcxNowr,rncMENTs

We are grateful to Ray Young and Scott Howard for assistance with theDBW3 2 Computer program

PoST AND BISH: RIETVELD REFINEMENT oF ToDoRoKITE STRUCTURE 869

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MaNuscnrpr RECEIVED Ocroser 19, 1987

M.a.rr-rscmrr AccEPTED Mencs 18, 1988