Abstract

A 24R nigerite polytype was discovered in tin-bearing skarns at Mt. Garnet in northernQueensland. Its space group is R3z, with rhombohedral lattice parameters a,6: lg.g26(10)A,c.1, : 17.508(3)". The corresponding hexagonal lattice parameters are a6. : 5.730(3), cr,* :55.60(3)A. Its formula, determined from microprobe analysis (combinid with informationfrom the structure determination) is Al,ounSnrorFerr"Zr'rnCaorrMnoo"Sio2,Oro(OH)r. Thecorrect structural model was obtained using crystallochemical reasoning based on structuralprinciples established from an analysis of the related structures of spinet, nolanite, and others.The structure was refned to an R value of 0.044 for 448 symmetry-independent reflectionswith 12 > 3o[Fl, collected using MoKa radiation. The model is based on a close packed an-ion framework (oxygens and hydroxyls) with a 2Llayer mixed stacking sequence along co.*given by ACBABCABCBACABCABACBCABC...(cchcccch...) and with an alternation ofthree types of metal atom layers in the sequence (...or,or,or;orr...), where o and 12 rep-resent the all-octahedral and the mixed octahedral-tetrahedral (l I l) metal atom layers foundin spinel (with composition MrOo), and T, represents the mixed octahedral-tetrahedral metalatom layer found in nolanite, ZnrMqor, corMnror, etc. (with composition Mroo, and oneless tetrahedral metal per unit-cell layer than the T, type). The interLyer articulation of thevarious polyhedra is controlled by the oxygen stacking sequence and is such that tetrahedrashare only corners with octahedra, and octahedra shaie edles and corners. The ...orrorr...part of the structure represents a 4-layet spinel block, with ordering of Al into the octahedralsites and divalent Fe and Zn into the tetrahedral sites. The Sn atoms are fully ordered intothe octahedral sites in the T, layers, whereas the tetrahedral sites in these layers contain pre-dominantly Al.

The structural principles which were used to derive the nigerite-24R structure have beenapplied to predict the structures of related minerals such as nigerite-6H, hcigbomite-gH, andthe taafeite polytypes.

American Mineralogist, Volume 64, pages 1255_1264, lg7g

The crystal structure of nigerite-24R

IeN E. Gnny

CSIRO Division of Mineral Chemistry, p.O. Box 124Port Melbourne, Victoria 3207, Australia

AND BRYAN M. GATPTTOUSN

Chemistry Department,, Monash (Jniyersitv

Clayton, Victoria 3169, Australia

of gahnite, and Bannister et al. noted the structuralcorrespondence in (lll) close-packed oxygen layersin gahnite being parallel to equivalent (0001) layersin nigerite. A close structural relationship betweennigerite, hogbomite, and taafeite polytypes has beensuggested by McKie (1963). The minerals all havetrigonal or hexagonal symmetry, with similar a val-ues and values of c that are nultiples of about 2.3A,the separation between closest-packed oxygen layers.According to McKie's nomenclature, in which adouble oxygen layer is taken as a repeat layer, nige-rite is designated as a 3H polytype (H for hexagonal

Introduction

Nigerite, a tin-bearing oxide mineral, was discov-ered by Jacobson and Webb (1947) n lg44 during aninvestigation of the tin-bearing pegmatites of KabbaProvince, central Nigeria. A subsequent study of thephysical and chemical properties of the mineral byBannislsl et al. (1947) showed that the mineral hadsymmetry 3m, wit}r^ a : 5.72, c : 13.g6,4,. The idealunit-cell composition was given by the formula(Zn,Mg,F e2*)(Sn,Zn)r(Al,Fe3*),rOrr(OH)r. The min_eral was often found as overgrowths on (l I l) planes000.3-004){^/79/ I I t2-1255$02.00 t2s5

r256 GREY AND GATEHOUSE: NIGERITE-24R

symmetry, c = 3 x 4.6A). A new nigerite polytype,with trigonal symmetry and c: 56.2A, was identifiedby Peacor (196'7).In McKie's nomenclature this is al2R polytype, but Peacor suggested that a more real-istic nomenclature system should be based on asingle oxygen layer repeat to account for odd-layernumber repeats, e.g. davidite (Rouse and Peacor,1968). Using this system the two nigerite polytypesare 6H and 24R respectively. In the present paper weadhere to Peacor's suggested nomenclature system.

In a recent mineralogical examination of polishedsections from a tin-bearing magnetite-fluorite-biotitedeposit from Mt. Garnet in northern Queensland, weconflrmed the presence of a tin-rich aluminum oxide,which had been observed in earlier studies on the de-posit (H.W. Fander, private communication, 1976).Single crystals of the phase were excavated from thepolished sections and studied by precession andWeissenberg X-ray diffraction methods. These stud-ies, coupled with microprobe analyses, served tocharacteize the mineral as a 24R nigerite polytype,analogous to the mineral described by Peacor (1967).We report here the single-crystal structure determi-nation for nigerite-24R, and use the results to predictthe structures of some polytypes in the related se-ries-nigerite, hdgbomite, taafeite.

ExPerimental

Drill-core sections containing nigerite were kindlysupplied by Mr. L. A. Newnham, chief geologist atRenison Limited in Tasmania. The samples werefrom a drilling program carried out by Comalco Ltd.at their Mt. Garnet tin deposits in northern Queens-land. In polished section the nigerite appeared assmall rods and plates, generally 5-50pm wide and upto -100 pm long, in a matrix comprising colloform-banded magnetite with fluorite and biotite. Associ-ated minerals included gahnite' corundum, and cas-siterite. The elongated lath-like nigerite crystals wereoften intergrown at an angle of about 120o. Exami-nation of the crystals in a scanning electron micro-scope fitted with an energy-dispersive analyzershowed dominant Al, Sn, together with minor Fe,Zn, andtrace amounts of Ca, Mn.

Crystals excavated from the polished section ap-peared colorless under the binocular microscope anda very pale green in transmitted light. An elongatedtabular crystal measuring

'77 x 35 x 20 pm was se-

lected for the X-ray diffraction study. Initially, pre-

cession and Weissenberg photographs were used toconfirm that it was a single crystal, with trigonal sym-

metry, R3m, R32, or Rlm, and approximate cell di-

mensions a : 5.73, c : 55.6A.For the intensity data collection the crystal was re-

mounted along its long dimension on a Philips

PWllOO 4-circle automatic diffractometer. Thirteen

reflections with 14" < 20 < 29" were carefully cen-

tered and ttre 20 values used in a least-squares refine-

ment to calculate the lattice parameters as reported

in Table l. Intensities were collected with graphite-

monochromated MoKa radiation. A e-20 scan, 3-

30". was used with a variable scan width given by Ad: (0.9 + 0.3 tan d) and a speed of 0.03" sec-'. Two

background measurements, each for half the scan

time, were made for each scan, one at the lower and

one at the upper limit. The intensities were processed

using a program written for the PW 1100 diffrac-

tometer by Hornstra and Stubbe (1972). An absorp-

tion correction was not applied. However, a partial

compensation was achieved by averaging the in-

tensities of equivalent reflections, !(hkl, lhk, klh), in

the rhombohedral cell. (Interscale R factor for equiv-

alent reflections : 0.054.) Thus, the 2834 reflections

measured were reduced to a unique set of 656, of

which 47'7 had F > 3o [P] and were used in the

structure refinement.Scattering factor curves for Sn, Fe, A1, Ca, Zn, arrd

Mn neutral atoms are those of Cromer and Mann(1968). Anomalous dispersion corrections for all

atoms are from Cromer and Liberman (1970)' All

computing was performed on the Monash University

CDC 3200 and Burroughs 6700 and the CsIno CDC7600 computers.

Two nigerite grains in close proxi-mity to the one

excavated for XRD studies were subjected to micro-probe analyses. The results (given in Table 2) show

variations of up to l0 percent in individual element

analyses; the two data sets were averaged to obtain a

typical analysis applicable to the XRD crystal' The

derived unit-cell composition, normalized to 32 an-

ions, is given in Table 2.

A structural model for nigerite and related mineralpolytype-general considerations

The diffraction patterns for nigerite and related

mineral polytypes are dominated by strong spinel-

like subcell reflections. In the case ofthe nigerite-24Rdescribed here, the strongest reflections define a 6R

type sublattice with a: 5.73, c : 13.90A. For com-parison the unit cell for the spinel gahnite, when re-

ferred to hexagonal axes, is also 6R in type and has a: 5.73, c : l4.O4A. As a consequence the three-di-

mensional Patterson map for nigerite showed only

Table l. Nigerite-24R: unit-c€ll parameters

GREY AND GATEHOT]SE: NIGERITE-24R t257

alternates with layers containing both octahedrallyand tetrahedrally coordinated metal atoms [Figs.l(ii) and l(iii)1. To simplify the discussion we havedesignated these layers as O (for octahedral cationsonly), T, (two tetrahedral cations per layer in the unitcell), and T, (one tetrahedral cation) respectively[Fig. l, (i)-(iiDl. For spinel, O and T, layers alter-nate, whereas in both the (ch...) and (h...) structures Oand T, metal atom layers alternate along [0001]. Theinterlayer articulation of polyhedra (Le. betweenmetals in the O and T layers) depends on the-oxygenstacking sequence. Octahedron-octahedron articula-tion occurs by edge-sharing only in (c...), by corner-sharing only in (h...), and by both corner- and edge-sharing in (ch...). These are shown in Figure 2. Tet-rahedron-octahedron articulation occurs only bycorner-sharing in both the (c...) and (ch...) structures,and by corner- and edge-sharing (as in olivine) in the(h...) structures (see Fig. 3). Note that this latter typeof tetrahedron-octahedron articulation is avoided inthe (ch...) structures by having only one of the twoavailable tetrahedral sites in the T, layers occupied.

The unit-cell compositions of the O, Tr, and T,layers (including surrounding oxygens) are MrOo,MrOo, and MrOo respectively, and so the overall com-positions of the (c...), (ch...), and (h...) type com-pounds (normalized to 8 oxygens for comparison) areMuO8, M6O8, and MrO, respectively. It follows thatlong-periodicity structures with mixed stacking se-quences, e.g. cchccchh..., will have compositions in-termediate to MrO, and MuO*. This in fact is true forall the known polytypes of nigerite, hcigbomite, andtaafeite, range MrrnrO" to MuO, (McKie, 1963; Hud-son et al., 1967; Wilson, 1977). We were able to es-

Table 2. Nigerite-24R: electron microprobe analyses

a . = 1 8 . 8 2 6 ( 1 0 ) lrn

d = l U q n n / r t o-'rh

rh

Space group R3m

D . = 4 , 4 2 e c m 'c a r c

u = 7 0 . 4 c n -

1, " * = 5 .730(3) R

cn"* = 5s .60(3) I

nex

spinel-type subcell vectors, and was thus not veryuseful in helping to establish a structural model.However, the similarities in the diffraction data andunit-cell parameters for nigerite, htigbomite, and taa_feite polytypes suggested that a simple structuralprinciple, such as intergrowth of, two basic structuretypes, should relate the structures of the various poly_types. An attempt was thus made to solve the struc_ture of nigerite-24R by using crystallochemical rea_soning to establish the underlying general structuralprinciple for the polytypes. In this approach we wereaided by the available structural information fornigerite and related minerals, as well as publisheddata for related compounds with known strucrures.

Initially, a survey was made of compounds withknown structures, containing close-packed oxygenframeworks, which could be described by hexago_nal/trigonal unit cells with a = 5.j, c = n x 2.3A.[Compounds with large cations occupying anionsites, such as various ferrites, e.g. BaFe,rO,, (Towneset al., 1967), were not considered because the nige_rite-hdgbomite-taafeite polytypes do not containsuch ions.l In addition to spinel, with cubic stackingofclose-packed oxygen layers, (c...), z : 6, there area number of compounds with double-hexagonalstacking, l.e. (ch...), f, : 4, and also. series of com_pounds with simple hexagonal stacking of the oxygenlayers, (h...), n : 2. The former are typified by itremineral nolanite, an iron vanadate, (Fe,V)rO, (Han-son, 1958), and also by compounds ArMorOr, A :Zn,Mg, Mn...(McCanoll et al.,1957), and the simplehexagonal structures are represented by the seriesLiRMorOr, R : Sc, Y, In, Sm...(McCanoll, 1977).The three types of structures, designated (c...), (ch...i,and (h...) according to the oxygen layer stacking,(ABC...), (ABAC...) (AB...) respectively, have someimportant features in common. For instance, thelayer of octahedrally coordinated metal atoms asshown in Figure l(i) occurs in all three structures and

Weight percent

! z**

Atons '

A1SnFeZa

Mns i

2 7 . 7 8t 7 . 6 21 0 . 5 06 . 2 30 . 8 l0 . 2 60 . 4 0

) 7 0 ?

1 5 . 8 9r t . t 26 . 8 ru . t )o . 2 50 . 4 3

t 4 . 6 6 t 4 . 7 32 . r r 1 . 9 12 . 6 8 2 . 8 31 . 3 6 r . 4 80 . 2 9 0 . 2 70 . 0 7 0 . 0 6o . 2 0 0 . 2 2

* Nunber o f a lom per un i t ce l l , nomal ized to30 O + 2 OH, aod w i th a l l i ron as fe r rous .The averaged unit cel1 composition fron I and2 i s A 1 1 4 . 5 9 S n 2 . o t F e z . 7 5 Z n 1 . 4 2 C a g . 2 g M n 6 . g 5S t 6 . 2 1 O 3 6 ( O I I ) 2 .

*x I and 2 are polnt analyses for two differentgrains .

1258 GREY AND GATEHOUSE: NIGERITE.24R

a a a a a

a a a

a a a a a

o

A

a

vl

a

( i i )

o aV t

^o a o

Y

A

a a a

A A

a a

AO .

a a a a a a

( i i i )

Fig. l. Metal atom arrangements between close-packed oxygen layers for (i) the O layer in spinel and nolanite, (ii) the T, layer in

spinel, and (iii) the Tr layer in nolanite. The small solid circles and triangles represent octahedrally and tetrahedrally coordinated metals,

respectively. Oxygen layers and unit-cell outlines are shown in the upfer parts of the figure; the lower half shows th€ extended metal

atom arrangements.

obtained from Patterson and Kasper's Table in Inter-

national Tables for X-ray Crystallography, Yol. lI(1962), p.342-355. Nigerite-24R has an even period,

N : 8, and a primitive rhombohedral lattice, and the

appropriate table shows that eight different stacking

sequences are possible. These were reduced to twoprobable sequences using the criterion that cubic

stacking should predominate, as suggested by thestrong spinel-like subcell. These two possibilities are

designated (6)(2) and (5X3) bV Patterson and Kasper

and comprise stacking sequences (ccccchch...) and(cccchcch...). The observation of an even number of

layers for nigerite-24R (as indeed is the case for allthe reported polytypes of nigerite, hdgbomite, and

taafeite) required that O and T metal atom layers al-

ternate. A further restriction suggested by the survey

of known related structures given above was that T,

layers lay between pairs ofcubic stacked oxygen lay-

ers, ,.e. c-T2-c, and Tr layers lay between cubic- and

( i i )

( i )

tablish the correct structural model for nigerite-24R,and predict models for other polytypes, on the basisthat they were built up from a stacking of O, Tr, andT, layers, the sequence being determined by the oxy-gen-layer stacking scheme. This is outlined below.

Model for nigerite-ZR

Using the realistic assumption that the c-axis peri-odicity (n:24) is determined by the oxygen stackingsequence (rather than by subtle changes in metalatom ordering), the possible layer sequences may be

( i i ) ( i i i )

Fig. 2. Polyhedral representations of interlayer articulation of

octahedra in (i) LiRMqO6, (ii) nolanite' and (iii) spinel+ype

structures.

Fig. 3. Polyhedral representations of interlayer articulation of

tetraiedra and octahedra in (i) LiRMo306 and (ii) spinel and

nolanite tyPe structures.

GREY AND GATEHOUSE: NIGERITE.24R

Table 3. Nigerite-24R: final atomic coordinates and isotropic temperature factors

1259

Atom s i te Occupaney B (82)

M( 1) ocr .'r4(2) ocr.M(3) TET.M(4) ocr .M(5) ocr .M(6) rET.M I 7 \ T F T

M(8) ocr .

o ( 1 )o ( 2 )o ( 3 )o ( 4 )0 ( 5 )0 ( 6 )o ( 7 )o ( 8 )

2 . 1 A 1 + O . 9 f l *Z J N

1 . 2 A 1 + 0 . 8 F e6 A 12 L T

F e * 0 . 8 Z n + O . 2F e + 0 . 6 Z a + O . 4

3 A I

0 .50000o,28684(2)0 . 0 3 0 7 0 ( 6 )0 . 7 5 0 r 3 ( 7 )0 . r 2 4 8 8 ( 8 )0 . s 3 r s 3 ( 4 )0 . 22047 (5 )0 .00000

0 . 1 s s 8 ( 2 )0 . 3 s 0 4 ( 2 )o .4420 (2 )o .0644 (2 )0 . 0439 (2 )0 . 5 6 6 6 ( 2 )0 .7056 (2 )0 . r 8 4 4 ( 2 )

0 . 000000.28684(2)0 . 0 3 0 7 0 ( 5 )0 . 7 5 0 r 3 ( 7 )0 . 1 2 4 8 8 ( 8 )0 . 5 3 1 5 3 ( 4 )0 . 2 2 0 4 7 ( s )0. 00000

0 . 1 s s 8 ( 2 )0 . 3 s 0 4 ( 2 )0 .4420 (2 )o . 0 5 4 4 ( 2 )o ,0439 (2 )o . s666 (2)o . 7056 (2 )0 .1844 (2 )

A1A1

0 . 5 0 0 0 0 0 . 2 4 ( 1 0 )0 .28684 (2 ) 0 .31 (2 )o . o 3 0 7 0 ( 6 ) 0 . s 2 ( 6 )o .2s328 ( r4 ) 0 .35 (s )0 . 1 2 4 8 8 ( 8 ) O . 2 2 ( 9 )0 . s 3 1 5 3 ( 4 ) 0 . 3 9 ( 4 )0 . 2 2 0 4 7 ( 5 ) 0 . 6 5 ( s )0 . s0000 0 .33 (8 )

0 . 6 2 5 7 ( 3 ) 0 . 9 4 ( r s )0 . 3 5 0 4 ( 2 ) 0 . e 1 ( 2 s )0 . 9 2 1 3 ( 3 ) 0 . 9 8 ( l s )0 . 0 6 4 4 ( 2 ) 0 . 8 8 ( 2 s )0 . 6 0 2 6 ( 3 ) 0 . 8 2 ( 1 3 )o . s 6 6 6 < 2 ) 0 . 2 6 ( 2 2 )o . 1 4 6 7 ( 3 ) O . 9 7 ( r 4 )0 . 1 8 4 4 ( 2 ) 0 . 7 2 ( 2 4 )

6 02 0 H6 02 06 02 06 02 0

= vacancy

Table 4. Nigerite-24R: selected interatomic distances (A) and angles (degrees)

M(1) (A1) Octahedron

M ( r ) - o ( r ) r . 9 8 2 " ( x 4 )M ( I ) - o ( 2 ) r . 9 0 8 ( x 2 )

Mean I . 957

o (1 ) -o (2 ) 2 .622 ( x4 )0 ( 1 ) - o ( r ) ' 2 . 6 9 3 ( x 2 )0 ( 1 ) - o ( 1 ) t t 2 . 9 L o ( x 2 )o ( r ) r - 0 (2 ) 2 .875 ( x4 )

0 ( 1 ) - M ( 1 ) - o ( 2 )o ( 1 ) - M ( r ) - 0 ( 1 ) 'o ( l ) - M ( r ) - o ( 1 ) "o ( r ) ' - M ( 1 ) - o ( 2 )

o ( 1 ) - M ( 2 ) - 0 ( 1 ) '0 ( r ) -M(2 ) -0 (3 )o ( 3 ) - M ( 2 ) - o ( 3 ) ,

o ( t ) - M ( 3 ) - 0 ( r ) ,o ( l ) - M ( 3 ) - o ( 4 )

84 .13 ( x4 )8 5 . 5 6 ( x 2 )94.44 (x2)95 .27 ( x4 )

79 .38 ( x3 )9 1 . s 9 ( x 6 )96.26 (x3)

M(6 ) - o ( 6 )M(6 ) - 0 ( 7 )

Mean

o ( 7 ) - o ( 7 ) 'o ( 6 ) - o ( 7 )

M( 7 ) - 0 ( s )M( 7 ) - o ( 8 )

Mean

o ( 5 ) - o ( 8 )o ( s ) - o ( 5 ) '

M ( 8 ) - 0 ( 7 )M ( 8 ) - o ( 8 )

Mean

o( 7) -0 (8)o ( 7 ) - o ( 7 ) '0 ( 7 ) - 0 ( 7 ) ' '

o ( 7 ) ' - o ( 8 )

r . 9 4 9r . 9 7 0r . 9 6 5

3 .2033 . 2 1 5

1 , 8 9 8 ( x 4 )1.926 (x2)r . 907

2.523 (x4)2 .527 ( x2 )2.832 (x2)2 .873 ( x4 \

1.1(5) (A1) Octahedron

M ( s ) - o ( s ) 1 . 8 9 4 ( x 3 ) 0 ( 7 ) - M ( s ) - 0 ( 7 ) 'M (s ) -0 (7 ) 1 .922 ( x3 ) 0 (5 ) -M(5 ) -o (5 ) '

Mean I . 908 0 (5 ) -M(5 ) -o (7 )

o ( 7 ) - o ( 7 ) ' 2 . 5 2 7 ( x 3 )0 ( s ) -o ( s ) ' 2 , 529 ( x3 )o (5 ) -0 (7 ) 2 .858 ( x6 )

M(6) (Fe,Zn) Tetrahedron

82.2283.7996 ,99

(x3)(x3)(x6)

M ( 2 ) ( S n ) O c t a h e d r o n

M ( 2 ) - o ( l ) 2 . 1 0 8 ( x 3 )M(2 ) -0 (3 ) 2 .003 ( x3 )

Mean 2.056

0 ( r ) - o ( l ) ' 2 , 6 9 2 ( x 3 )0 ( l ) - 0 ( 3 ) 2 . 9 4 8 ( x 6 )o ( 3 ) - 0 ( 3 ) r 2 . 9 8 4 ( x 3 )

o ( 7 ) - M ( 6 ) - o ( 7 ) ' I 0 8 . 7 3 ( x 3 )( x3 ) o (6 ) -M(6 ) -0 (7 ) 110 .21 ( x3 )

(x3)(x3)

M(3) (A f ,Fe) Te t rahedronM(7) (Fe,Zn) Tetrahedron

1 .925 ( x3 ) o (5 ) -M(7 ) -0 (8 ) 106 .22 ( x3 )2 .00s 0 ( s ) -M(7 ) -o (5 ) ' 1 r2 .52 ( x3 )I . 9 4 5

3 . I 44 ( x3 )3 . 2 0 1 ( x 3 )

M(8) (A1) octahedron

o ( 7) -M( 8) -o (8)o (7 ) -M(8 ) -o (7 )o (7 ) -M(8 ) -o (7 ) "o ( 7 ) ' - M ( 8 ) - o ( 8 )

M ( 3 ) - o ( I ) r . 8 3 7 ( x 3 )M ( 3 ) - o ( 4 ) 1 . 8 7 3

Mean I .846

o ( I ) - o (4 ) 2 ,981 ( x3 )o ( I ) - o ( I ) r 3 . 0 3 7 ( x 3 )

1 1 1 . 5 7 ( x 3 )1 0 7 . 2 8 ( x 3 )

M(4) (A1) ocrahedron

M(4 ) -o (3 ) 1 .87e ( x2 ) o ( s ) -M(4 ) -0 ( s ) 'M (4 ) -o (6 ) | . e23 0 (3 ) -M(4 ) -o (6 )M(4 ) -o (4 ) r . 936 o (4 ) -M(4 ) -o ( s )M(4 ) -o (5 ) I . 960 ( x2 ) o (3 ) -M(4 ) -0 (5 )

Mean 1 .923 0 (3 ) -M(4 ) -0 (3 ) |o ( s ) -M( 4 ) - 0 ( 6 )

o ( 5 ) - o ( 5 ) ' 2 . s 2 e o ( 3 ) - M ( 4 ) - 0 ( 4 )0 (3 ) -0 (6 ) 2 . s r9 ( x2 )o ( ) - o ( s ) 2 .605 ( x2 )o (3 ) -o (5 ) 2 .181 ( x2 )0 ( 3 ) - o ( 3 ) ' 2 . 7 4 7o (s ) -o (6 ) 2 .877 ( x2 )0 (3 ) -0 (4 ) 2 ,866 ( x2 )

80 , 3782.97 (x2)8 3 . 9 s ( x 2 )92.82 (x2)9 3 . 9 2

97.40 (x2)

82 . s8 ( x4 )83 .50 ( x2 )96.50 (x2)97.42 (x4)

* S tandard dev ia t lons fo r M-M, M-0 , and O-O are 0 .003, O.OO5, and 0 ,008 8 , respec t ive ly , and fo r ang le O-M-O0. 16 degrees .

1260 GREY AND GATEHOUSE: NIGERITE.24R

Origin

e c { s n B c A B c B A

h c c h c c c c h c c

T t O T t o r z o r z o r t o r t

Fig. 4. Anion layer sequence (first two lines) and metal atom

layer sequence (third line) for dgerite-24R.

hexagonal-stacked oxygen layers, le. c-T,-h. It wasalso possible to make some reasonable assumptionsconcerning the metal atom distributions in the trialmodels. Firstly, by analogy with gahnite, it was ex-pected that the spinel-like slabs would contain alumi-num in octahedral sites and large divalent ions, Zn2*and Fe2*, in the tetrahedral sites. Secondly, Sno* hasa marked preference for octahedral coordination inspinel (Djega-Mariadassov et al., 1973). lt is not ex-pected to order with the much smaller Al3* in the Olayers and was thus assigned to T, layers.

Subject to the restrictions outlined above, only asmall number of models remained to be tested. Struc-ture factor calculations for these possible models in-dicated a centrosymmetric model (R1m), with the(5X3) oxygen stacking sequenoe as correct.

Refinement of the structure

The origin location was established in the spacegroup R3n by assigning O-layer mbtals (aluminums)to the special positions 3(e) and 3(d), i.e. 0 Yz th and t/z

0 0 (rhombohedral axes). Initially, with Al atoms as-signed to the O-layers and an average structure fac-tor curve for M atoms in the T layers, full refinementof coordinates of all atoms proceeded smoothly to anR of about 0.15. At this stage, a di-fference Fourierand temperature factor refinement allowed a specificassignment of Sn, Fe, etc. to the different metal atomsites in the T layers. With a new set of scatteringcurves, refinement of all coordinates and isotropictemperature factors proceeded to an R value of 0.065.The refined temperature factors showed a wide rangeof values, from -0.40(20) to 1.57(33), and a differ-ence Fourier displayed a number of peaks of densitygreater than 2e A-', in unrealistic positions (e.9.within -2A from metal atoms). Examination of thestructure factor table showed that 30 of the weakestreflections (3olPl < P < aolFl) had F" values sys'tematically higher than F" by a factor of 2 or more.These reflections were given zero weight in the sub-sequent refinement. Further cycles of full matrix re-finement of positional and isotropic thermal parame-

ters led to convergence at R :0.044, rvR : 0.033, andR(F) : 0.058, for 448 observed reflections. The re-fined atomic coordinates (in the rhombohedral cell)and thermal parameters are listed in Table 3. Thethermal parameters for oxygens are now within thenarrow range expected for a close-packed oxide [ex-cept for 0(6), which had a B value of -0.40(20) be-fore removal of the 30 affected reflections]. A finaldifference Fourier showed no features above 0.5eA-'.

Calculated bond lengths are given in Table 4 andobserved and calculated structure factors are listed inTable 5.'

Description of the structure

The structure of nigerite is based on a close-packedoxygen framework with a 24-layer repeat along thehexagonal c axis (8-layer true repeat in the primitiverhombohedral cell). The layer sequence is shown inFigure 4, together with the stacking representationfor each oxygen layer (c or h) and the metal atomlayer sequence. The oxygen sequence is(cchcccch...) and the metal atom layer sequence is(OT,OT,OT,OT,. . . ) . The.. . OT,OT,. . . sequencerepresents a four-layer slab of spinel structure. The...OT,OT,... metal layer sequence is the same asthat for the double-hexagonal-close-packed nolanitestructure, and the O-T'-O interlayer polyhedral ar-ticulations are the same [see Figs. 2(ii) and 3(i)].However, the oxygen layer sequence is different, vt2.hcch for nigerite and hchc for nolanite, and this re-sults in different T,-O-T, interlayer polyhedral link-ages, as shown in Figure 5, which gives a polyhedralrepresentation corresponding to the asymmetric unitin the triply-primitive hexagonal cell. The O, T,, andT, layers are marked, as well as the various metalatoms. For convenience in interpreting Figure 5, theatomic coordinates have been converted to those per-taining to the hexagonal cell and are given in Table6. To show the magnitude of the various deviationsfrom an ideal close-packed model, the z parametersare also given in angstroms. It is apparent that thereare considerable distortions both in the planarity ofthe oxygen layers, and in the close packing ofthe ox-ygens within the layers. For example, the ideallycoplanar O(l) and O(2) atoms differ by more than0.2A in thek z parameter, and the y parameters of0(5) and 0(7) also di-ffer by more than 0.2A from the

t To obtain a copy of Table 5, order Document AM-79-ll5from the Business Office, Mineralogical Society of America, 2000Florida Avenue, NW, Washington, D.C' 20009. Please remit $1.00in advance for the microfiche.

c

h

GREY AND GATEHOUSE: NIGERITE-24R 126r

found as an overgrowth. Complete correspondencerequires divalent ions Fe'*, Zn'* in the tetrahedralsites, whereas the observed average bond lengths(Table 3) suggest some trivalent Al in these sites.Note the opposite senses of the ratios of the apical tobasal M-O bond lengths for the two tetrahedral sites,M(6) and M(7), in the spinel block.

A difficulty was encountered in determining theoccupancy of the octahedral site M(l) in the O layer.With Al assigned to this site, a reasonable temper-ature factor was obtained only when the occupancywas reduced to 0.70 (Table 3). The average M(l)-Obond length, 1.957(5)A, is somewhat higher than ex-pected for Al, reflecting a lower average polyhedralbond strength due to the partial occupancy. Allow-ance for iron in this site would decrease the partialoccupancy parameter still further.

Whereas in the T, layers small ions (Al'*) occupythe octahedral site and large ions (Fe'*,Zn'*) occupythe tetrahedral sites, the reverse is true in the T, lay-ers, with large octahedral Sno* and small tetrahedralAl3*. As a consequence of adjusting to the various-sized polyhedra, the M(4)O6 octahedra in the inter-vening O layer are considerably distorted, withM(4)-O bond lengths in the range 1.879(5)-1.960(5)A. By comparison, the M(8)O. octahedra inthe O layers in the spinel block are more regular,with a M(8)-O range of 1.898(5)-1.926(5)A.

Table 6. Nigerite-24R: "t#ff;flTtes

in the hexagonal cell

Atom Atomsi te type

Frac t iona l coord lna tesx y z

,(8) Lay ertyPe

Fig. 5. Polyhedral model of nigerite-24R in a hexagonal cellrepresentatron.

ideal values (y : 5/6 znd 2/3 respectively). The oc-tahedral metal M(2) (tin) in the T, layer shows a dis-placement of 0.27 A, whereas the metals in the O lay-ers are almost exact ly midway between thesandwiching oxygen layers.

Metal aton ordering

Metal atom ordering in a number of sites is quiteunambiguous. In particular the octahedral site in theT, layers is fully occupied by tetravalent tin. The av-erage Sn2*-O bond length of 2.056(5),{ agrees with acalculated value of 2.06A, using Shannon and pre-witt's (1969) ionic radii tables. (The oxygen radiusappropriate to the average coordination number 3.5was used.) The ordering of Al into the octahedralsites in the spinel block is also clearly establishedfrom the structure refinement. The observe6 trl:$bond lengths of 1.908(5) IM(5) in T, layerl and1.907(s) [M(8) in O layer] and 1.923(5) [M(4) in Olayerl lie within the range 1.885-1.924 observed forAl atoms in the octahedral sites in the spinel blocksof various B-aluminas (e.g. Dernier and Remeika,1976; Kodama and Muto, 1976). In fact the spinelblock in nigerite resembles quite closely gahnite,ZnAlrOo (Saalfeld, 1964), on which nigerite is often

\ 0 0 0 . 0 0

0 . 8 2 3 3 0 . 6 4 6 6 0 . 0 2 1 0 r . r 7r / 3 2 / 3 0 . 0 r 7 r 0 . 9 5

M ( 1 ) A 1

0 ( i ) oo (2 ) oH

r4(2) snM(3 ) A l ,Fe

0

c

h

0

T2

0 .493 r 0 .98620 0

2 / 3 r / 30 0

0 0L / 3 2 / 32 / 3 r / 3

0 . 0 4 6 5 2 . 5 90 . 0 3 0 7 r . 7 L

o . 0 6 4 9 3 . 6 10 . 0 6 4 4 3 . 5 8

o ( 3 )o ( 4 )

M ( 4 )

o ( 5 )o ( 6 )

0o

A1

0o

0 . 1 6 7 7 0 . 3 3 5 5 0 . 0 8 2 2 4 . 5 7

o . 8 5 2 9 0 . 7 0 5 8 0 , r 0 3 2 5 . 1 4r l 3 2 1 3 0 . 1 0 0 1 5 . 5 7

M ( s ) A 1M ( 6 ) F e , Z nM ( 7 ) F e , Z n

o ( 7 ) oo ( 8 ) o

M ( 8 ) A 1

0 . 1 4 7 0 0 . 2 9 4 12 / 3 1 1 3

r / 3 1 / 6

o . t 2 4 8 6 . 9 40 . 1 3 5 1 7 . 5 r0 . r r 2 9 6 . 2 8

o . 1 4 7 4 8 . 2 00 . 1 4 8 9 8 . 2 8

1 1 6 9 . 2 7

GREY AND GATEHOUSE: NIGERITE-24R

urtgrn

n s J c e c B A

h c c h c c h

o T z 0 T t o T l

Fig. 6. Anion layer sequence (first two lines) and metal atomlayer sequence (third line) for nigerite-6H.

A further consequence of metal atom ordering isan alternation in the magnitude of the oxygen layerseparations, corresponding to the T and O metalatom layer alternation. The average oxygen inter-layer separations are about 2.55 and 2.05A across Tand O metal atom layers respectively. A similar alter-nation (2.67 and,2.02{) was observed in the oxygenlayer separations in the (ch. . .) structure CorMnrO'(Riou and Lecerf, 1975).

The site occupancies derived during the structurerefinement (Table 3) give a unit-cell compositionAl,orSnroFerrZn,oOro(OH)r. This is in reasonableagreement with the average composition calculatedfrom the microprobe analysis (Table 2), especially ifthe minor elements, Si and Mn, are grouped with Aland Fe respectively. The location of the large cal-cium atom was not ascertained from the structure re-finement. It may be distributed over some of the an-ion sites [calcium occupies an anion site in the close-packed oxide mineral loveringite (Gatehouse et al.,1978)1. Note that the above composition requiressome iron as ferric to achieve charge balance. Ferriciron is most likely located with aluminum in the tet-rahedral site M(3).

Electrostatic valence sums

Indirect support for partial occupancy of the vari-ous sites in nigerite is that the resulting calculatedelectrostatic valence sums for the oxygens are gener-ally close to theoretical (see Table 7). If we allow forfull occupancy of site M(l), oxygen O(l) becomes se-

Table 7. Nigerite-24R: electrostatic valence sums of cations about

Anions Coordlnation CatLons xvi

verely oversaturated, with a )Vi value of 2.32. TabIe7 shows that the O(2) site is occupied by OH, havinga )Vi of 1.05. In the calculation of the unit-cell com-position, we thus normalized to 30 O + 2 OH. Fi-nally, the undersaturated O(3) site, )Vi : 1.67, is re-flected in the O(3)-M bonds all being about 0.05Ashorter than the average values.

Prediction of structures for nigeritefH and relatedstructures

As discussed above, the correct structural modelfor nigerite-24R was arrived at using crystallochem-ical reasoning based on the following principles:(a) The structure is based on a close-packed oxygen

framework with a mixed (cubic, hexagonal)stacking sequence. The long cn"* axis periodicityis due to the ordering sequence of cubic- andhexagonal-stacked layers. This sequence must beconsistent with the symmetry and size of the unitcell and the requirement of dominant cubicstacking.

(b) Between the oxygen layers, ordering of metalatoms gives rise to three possible arrangements,O, T,, and T, (see Fig. l).

(c) The sequence of O and T layers is determined bythe oxygen-layer stacking sequence. Type O lay-ers must alternate with type T layers. T, layersoccur between cubic- and hexagonal-stacked ox-ygen layers. T, layers lie between cubic-stackedoxygen layers.

(d) In the T, layers, the unoccupied tetrahedral siteis an olivine-like site, re. sharing the basal edgeswith three octahedra from the adjacent layer (al-though partial occupancy of this site may be pos-sible).

Having confirmed these general structural principlesfor nigerite-24R, it should be possible to apply themto predict the structure of other compounds related tonigerite, but with diferent c".* axis periodicities.These include other nigerite polytypes, hogbomites,and taafeites.

OriginI

J

A

zT t

Fig. 7. Anion layer sequence (first two lines) and metal atomlayer sequence (third line) for hcigbomite-8H.

o ( l )o (2 )o (3 )o (4 )o ( s )o (5 )o (7 )o (8 )

2 . 0 2I . 0 5r . 6 72 , 1 5Z . U J

2 , 0 32 . 0 12 . 0 5

I M ( 1 ) + M ( 2 ) + M ( 3 )3 M ( l )M(2 ) + 2 M(4 )M(3 ) + 3 M(4 )2 r4(4) + M(s) + M(5)3 M(4 ) + M(6 )M ( s ) + M ( 6 ) + 2 u ( 8 )M(7 ) + 3 M(8 )

n - "

. o T ^I I

An almost trivial example is provided by the six-layer nigerite polytype first described by Bannister etal. (1947). This mineral has trigonal symmerry, 32,with c : 13.86A : 6 x 2.31A and with possible spacegroups P3ml or P3lm. From Table 7.1.5B of Patter-son and Kasper (1962), there is only one possible an-ion layer sequence with dominant cubic stacking. Itis designated l(3)l(3)l and has symmerry P6,mmc (i.e.the trigonal symmetry for nigerite-6H must resultfrom the metal atom arrangement). The oxygen andmetal atom layer stacking sequences are given in Fig-ure 6; i.e. the oxygen sequence is (cch...) and themetal sequence is OTrOT,OTr.... Nigerite-6H differsfrom nigerite-24R in having only two, rather thanfour, metal layers in the spinel block. If we use theknown occupancies in the ...OT,OT,... and ...OTr...blocks obtained for nigerite-24R, we can derive aunit-cell composition for nigerite-6H. Allowing thesame fractional occupancies, OH- at a two-fold site,etc. (see Table 3) we have

SnrAl,ouFe, "rZno r rOrr(OH), (not balanced) (l)

For comparison, the analysis obtained by Bannisteret al. (1947) for nigerite-6H is

Sn, ,rAl,o rrFe, nuZno_r"Mno 33022 ,u(OH)r 84 Q)

It appears that in nigerite polytypes the stackingsequence adopted depends on the tin content, i.e. themineral adopts the sequence that allows all the tinatoms to fully occupy (or almost so) the available oc-tahedral sites in T, layers. In going from nigerite-24Rto nigerite-6H, the ratio of T, to T, layers increases toaccommodate the higher tin content of the latter.

The prediction of the structure for hcigbomite-8H(1.e. hrigbomite-4H using McKie's nomenclature) isquite straightforward, using the principles listed (a)-(d) above. This mineral has hexagonal symmetry,possible space groups P6rmc, P62c, and P6r/mmc,with cn.* : 18.354 : 8 x 2.29A (McKie, 1963). FromTable 7.1.5B of Patterson and Kasper (1962) the onlystacking sequence with dominant cubic stacking isthat designated l(4)l(4)1. This has symmetry P6,mmc,and the origin for the oxygen stacking is located onan oxygen. In order that O and M metal atom layersalternate across the origin oxygen layer, a non-cen-trosymmetric space group has to be used. The oxygenand metal atom layer sequences are given in Figure7. Thus, in this structure both the spinel block andthe MrO* block are only two metal-atom layers wide.The ideal unit-cell composition (re. partial occu-pancy not considered) is MrrOrr: MrrOr. Generally,compositions reported for 8H-hdgbomites contain

GREY AND GATEHOUSE: NIGERITE-24R

higher metal contents and suggest partial occupancyof the second tetrahedral site in the T, layers; e.g. thecomposition recently determined for zincian h6gbo-mite-8H by Wilson (1977), (Mg,Fe,Zn,Al,Ti...),,u2(O,OH)8, requires 5OVo occupancy of each of the sec-ond tetrahedral sites in the T, layers. We are cur-rently refining the structure of an 8H-hdgbomitepolytype, and the present R factor of -0.08 confirmsour correct prediction of the structure using the prin-ciples described above.

The taafeite minerals are interesting in that theyform 8H and 18R polytypes with similar diffractionpatterns to hdgbomite and nigerite polytypes, but thecompositions of both are MuOr, within experimentalerror (Hudson et al., 1967). In this case it seems thesame structural principles apply, but the second tet-rahedral site in the T, layers is fully occupied, pre-sumably by the very small Be'* ion which composi-tionally charucterues the taafeite minerals.

AcknowledgmentsWe thank Mr. L. A. Newnham of Renison Ltd. for supplying

the specimens of nigerite, and Mr. P. Kelly, Melbourne UniversityGeology Department, for carrying out the microprobe analyses.We acknowledge the help of Dr. Bruce Poppleton of Csrno withthe computing.

References

Bannister, F. A., M. A. Hey and H. P. Stadler (1947) Nigerite, anew tin mineral. Mineral. Mag., 28, 129-136.

Cromer, D. T. and D. Liberman (1970) Relativistic calculation ofanomalous scattering factors for X-rays. "/. Chem. Phys., 53,189 l -1898.

- and J. B. Mann (1968) X-ray scattering factors computedfrom numerical Hartree-Fock wave functions. Acta Crystallogr.,424.32t-324.

Dernier, P. D. and J. P. Remeika (1976) Structural determinationof single-crystal K B-alumina and cobalt-doped K B-alumina. ./.Solid. State Chem., 17,245-253.

Djega-Mariadassou, C., F. Basile, P. Poix and A. Michel (1973)Pr€paration et propri6tes cristallographiques des phasesFe3-"Sn Oa. Ann. Chim., & 15-20.

Gatehouse, B. M., I. E. Grey, I. H. Campbell and P. Kelly (1978)The crystal structure of loveringite-a new member of thecrichtonite group. Am. Mineral., 63,28-36.

Hanson, A. W. (1958) The crystal structure of nolanite. Acta Crys-tallogr., 1 1,7O3-7O9.

Hornstra, J. and G. Stubbe (1972) PWI100 Data Processing Pro-grarn. Philips Research Labs, Eindhoven, Holland.

Hudson, D. R., A. F. Wilson and I. M. Threadgold (1967) A newpolytype of taafeite-a rare beryllium mineral from the gran-ulites of central Australia. Mineral. Mag., 36,305-310.

Jacobson, R. and J. S. Webb (1947) The oc€unence ofnigerite, anew tin mineral in quartz-sillimanite-rocks from Nigeria. Min-eral. Mag., 28, I 18-128.

Kodama, T. and G. Muto (1976) The crystal structure of Tl-d-alu-mina. "/. Solid State Chem.. 17.61-70.

1263

1264 GREY AND GATEHOUSE: NIGERITE.24R

McCarroll, W. H. (1977) Structural relationships in A2Mo3Ogmetal atom cluster oxides. I norg. Chem., I 6, 335 l-3353.

--, L. Kaw and R. Ward (1957) Ternary oxidcs of quad-rivalent molybdenum. J. Am. Chem. Soc. 79,5410-5414.

McKie, D. (1963) The hdgbomite polytypes. Mineral. Mag., 3j,563-580.

Patterson, A. L. and J. S. Kasper (1962) Close packing. lt Inter-national Tables for X-ray Crystallography, Yol. II, chapter 7.1.Kynoch Press, Birmingham.

Peacor, D. R. (1967) New data on nigerite. Am Mineral., 52,86+866.

Riou, A. and A. Lecerf (1975) Structure cristalline de Co2Mn3O6.Acta Crystallogr., B 3 I, 2487 -2490.

Rouse, R. C. and D. R. Peacor (1968) The relationship betweensenaite, magnetoplumbite and davidite. Am. Mineral., 53, 869-879.

Saalfeld, H. (1964) Structurdaten von Gahnit. Z. Kristallogr., 120,476478.

Shannon, R. D. and C. T. Prewitt (1969) Effective ionic radii inoxides and fluorides. ,4aa Crystallogr., 825,925-946.

Townes, W. D., J. H. Fang and A. J. Perrotta (1967) The crystalstructure and refinement of ferrimagnetic barium ferrite,BaFe12O1e. Z. Kristallogr., I 2 5, 437 -449.

Wilson, A. F. (1977) A zincian h6gbomite and some other hdgbo-mites from the Strangways Range, Central Australia. Mineral.Mag.,41,33'l-34.

Manuscript received, October 2, 1978;

acceptedfor publication, June 26, 1979.