American Mineralogist, Volume 7 2, pages 1 I 7 6- I I 89, I 987

Ashcroftine, ca. KroNaro(YoCa)ro(OH)4(CO3)r6(Sis6Or40).L6HrO, a structure withenormous polyanions

Pnul Bnr.c'N MoonpDepartment of the Geophysical Sciences, The University of Chicago, Chicago, Illinios 60637, U.S.A.

Pn-q.orp K. SrN Guprl.Department of Geology, Memphis State University, Memphis, Tennessee 38152, U.S.A.

Er-rrnn O. Scnr.ntrprnDepartment of Chemistry, University of Missouri, Columbia, Missouri 6521 1, U.S.A.

SrnuNo Mnnr,rNoDipartimento di Scienze della Terra, Universitd di Pisa, 56100 Pisa, Italy

ABSTRACT

The elephantine crystal structure of ashcroftine, end member ca. K,oNa,o(Y,Ca)ro-(OH).(CO3),6(Si56o,oo).l6HrO has been independently investigated (Moore, Sen Gupta,Schlemper : MSS; Merlino : M) in two laboratories. Type material from Narsarsuk,Greenland, afforded crystals for both studies. The ashcroftine average structure is tetragonalholosymmetric, space group I4/m 2/m 2/m, a: 23.994(6), c : 17.512(5) (MSS) and a:24.039(6), c : 17.538(8) (M),2:2. R : 0.058 for 1774 independent { values (MSS) and0.060 for 2276 F" values (M).

The structure is based on at least 39 atoms in the asymmetric unit. Of these, 27 areordered and make up the [K€NarYr4(OH)o(CO3)r6(SiosO128).l0HrO]'8 fraction. The under-lying polyanion is a giant [SiorO,rr] ball whose connections define a polyhedron, hence abalosilicate. It has point symmetry (4/ m 2/ m 2/ m), a near subgroup of (4/ m 3 2/ m) foundfor the related truncated cuboctahedron, an Archimedean solid. Breaks in the batl admitan extensive circumjacent disordered region and together define the L[Sir6O,oo] tubularinosilicate with channels and bulges, oriented parallel to [001]. All terminal oxygens pointoutside, away from the central channel. The ordered carbonate fraction defines, amongother things, ordered [Na(COr)o] clusters. The entire ordered region is called the curd.

The large balls are encrusted with a border region, or limbus, with Y-O, Na-O, and K-O bonds. The disordered region of 12 atoms in the asymmetric unit, or the whey, consistsof partly occupied T(D) : (Si,B), Si; Na(D), K(D), and 6 (6: O'-, OH-, H,O) sites.

It is proposed that the [Sior] core constituted the template for ashcroftine's growth andthat other related monsters may occur in a similar paragenesis.

INrnooucrroN

Gordon (1924) initiated the curious history of the ex-otic ashcroftine. It is appropriate to give a brief reviewof the discovery and subsequent studies on the speciesthat, as we shall see, possesses a most remarkable andunusual crystal structure. Gordon christened it kalithom-sonite, and he found it in "pocket K," one-half meterbelow the surface. This site is near the famous minerallocality Narsarsuk, which is situated 45 km northeast fromJulianehaab, in southwestern Greenland. Most of theclassic mineral occurrences of Steenstrup, Flink, andGordon were confined within a kilometer-wide zone ofaugite-syenite. The exotic minerals occur within small,irregular pegmatitic vugs. The pegmatites are composedof coarse feldspar crystals, aegirine, some arfvedsoniteand eudialyte of which many tons were collected.

"Pocket K" was a vug 15 cm in greatest dimension.

From the augite-syenite rock inward, Gordon noted thesequence of precipitation or paragenesis from oldest toyoungest: aegirine * orthoclase + zinnwaldite * graph-ite - etched quartz crystals - elpidite + albite - cal-cite - kalithomsonite. The kalithomsonite occurred aspink aggregates of fibers that completely filled the cavityremaining in the vug. Despite much digging circumjacentto the pocket, no other pockets with similar contents werediscovered.

Chemical analysis by Whitfield reported in GordonQ92Q is repeated in Table 1. The small kalithomsonitecrystals measuring up to 0.25 x 4 mm in dimension hadsome peculiar properties. Gordon noted cleavages a(l00)less perfect, D(010) perfect, c(001) imperfect; a: 1.535,F : 1 . 5 3 7 , 7 : 1 . 5 4 5 , X : b , Y : a , Z : c ; a n d h eemphasized the optical differences from normal thom-sonite (X: a, Y : c, Z : b, a : 1.535, 0 : 1.531 [sic],

0003404x/87 / | | r2-1 I 76$02.00 rt7 6

.y : 1.541, according to Gordon). Based on the Whitfieldanalysis, he proposed a formula close to KNa(Ca,Mg,-Mn)[AloSirO,s] . 1 0HrO.

Hey and Bannister (1933), in the course of studies onzeolites, re-examined kalithomsonite. They expresseddoubts based on the published optical dalathat kalithom-sonite was a thomsonite at all. Furthermore, the a(100)and b(010) cleavage planes appeared equally developed,and no difference was noted between a and B. X-ray sin-gle-crystal study revealed an enormous unit cell, the larg-est then known for an inorganic substance, a : 34.04(5),c : 17.49(5) [Note: a/y'2 : 24.07 A1. Ottrer salient de-tails: cell contents 40[KNa(Ca,Mg,Mn)AloSiOrs. 8H2O],tentative space group DII : P4r/mnm, @ : 1.536, e :

1.545, small bundles bounded by cleavages a{100},c{001}, specific gravity 2.61(5). Thus, kalithomsonite wasan entirely new species, named ashcroftine after Mr.Frederick Noel Ashcroft, who presented large gifts of zeo-lites to the cabinet of the British Museum of NaturalHistory.

There the matter stood until Moore et al. (1969) at-tempted the crystal structure of ashcroftine in earnest, butthe Patterson synthesis could not possibly be interpretedaccording to the then-accepted composition, so recoursewas made to anr- electron-microprobe scans. It was dis-covered that only trace Al was present; in its stead therewas actually Y with minor amounts of lanthanides. InTable I, we accepted YrO, in lieu of the AlrO, of Gordon(1924). The results: a : 24.044(4), c : 17.553(8) A, spacegroup l4/mmm, I4mm, 1422 or I4m2,proposed formulaKNaCaYrSiuO,r(OH),0'4H,O, Z : 16. Ashcroftine wastherefore proposed to be not a zeolite but possibly relatedto lovozerite (since both species are found associated withnepheline syenites), enthusiasm for the difrcult structureproblem at hand was lost, and further study was aban-doned.

The ashcroftine saga continued. In 1973, Merlino re-ceived the vial of ashcroftine from Moore, who initiallyreceived a portion of Gordon's type material from theU.S. National Museum of Natural History (NMNH95320). Sen Gupta, unaware ofthe other work, receivedcrystals from the British Museum of Natural History (no.BM 1924,867 ; Narsarsuk, Greenland). These samples camefrom the same batch collected by Gordon. Moore wascalled on the scene when an impasse was reached in thestructure determination by Sen Gupta. A seemingly rou-tine problem ballooned into one of considerable com-plexity. When it was discovered that Merlino also reju-venated the problem, we joined forces. The presentcontribution is a combination of two relatively indepen-dent studies, and results from both are given. For ex-ceedingly complicated structures, presentation of two in-dependent sets of data has advantages and lessens thephantasmagoria that occasionally creep into study ofsuchmonsters.

We show that ashcroftine is, for an average structure,tetragonal holosymmetric, space group I4/m 2/m 2/m,a: 24.02, c -- 17.52 L, Z : 2 for a formula unit ca.

t t 7 7

Teeue 1. Ashcroftine chemical analysis and interpretation

' l ' 3- 4'

MOORE ET AL.: ASHCROFIINE AND ITS ENORMOUS POLYANIONS

NaroKrO

MgoCaOMnO

B,O"Alro3Y,O"

sio,H,O (>100 'C )H ,O (<100 'C )

Total

5.653.62c.bc

0.875.720.79

3.s5 4.38 3.936.33 6.04 5.97

2,28 2.53

- t t o -

31.17 30.40 34.38

9.29 9,22 8.934295 4078 42.68

4a3 lu !.

100.00 100.00 100.00

0.875.720.79

26.61

38.09

12.O06.40

99.75

26 61

38.09

4.86.40

99 75. (1) Whitfield in Gordon \19241. (2) Column 1 with Al,O. reckoned as

Y,O3. No AlrO3 was detected by electron-microprobe analysis. The CO'content was determined by vapor-pressure measurement, in a procedurediscussed by Harris (1981). lt was subtracted from H2O (>100 rc) deter-mined by Whitfield in Gordon (1924), assuming that upon ignition both CO,and H2O were lost. (3) Calculated composition based on site occupanciesin Table 3 and the MSS formula in the section on Chemical Composition'(4) The same, but for M. (5) For K,oNaloYr4(OH)1(CO3)'6(Sis6o1.o)'16H,O.

Na,oK,oYro(OH)4(CO3)r6(SiruO'oo)' 1 6HrO. Essential car-bonate groups earlier unreported (but probably incorpo-rated into the water analysis of Whitfield) were uncov-ered, as well as a disordered enormous L[Sis6Oroo] tube,whose ordered bulbous part is in fact derived from thegiant cage [Siord,ro] that is the Archimedean semiregulartruncated cuboctahedron with Si at the vertices and d(anions) at midpoints of the edges, with 48 additionalterminal @ bonded to the Si atoms and protruding out-ward.

The presence of (CO.) groups presented problems inthe chemical interpretation, and it was most desirable todetermine the quantity of carbonate by independentmeans. A. T. Anderson volunteered to measure the con-centration of CO, in a small ashcroftine crystal. The mi-crodetermination, which employs a heating stage, cryo-pump, and vapor-pressure measurement, was announcedby Harris (1981). The gas species were easily discrimi-nated by their solid-vapor equilibria during sublimationof individual components.

Measurement of the single crystal gave 2.8(4) x 10-6cm3 corresponding to a mass of 7.2(10) x 10-6 g. MostCO, was lost between 550 and 1000 "C. The total massof CO, lost below 1250 "C computed to 5.2 x l0 ? g. Thecrystal was reduced to a blebby mass.

The concentration of CO, is therefore 7.2(ll) wto/0. Theproposed value for CO, based on site occupancies in Ta-ble I is 9 .3 wto/o, about 200lo higher than the microdeter-mination, a not at all unreasonable difference for so smalla crystal. In any event, CO, is clearly essential and firmlybonded in ashcroftine's crystal Structure.

ExpBnrunNTAL DETAILS

Acronyms for the two separate studies include MSS for Moore,Sen Gupta,.and Schlemper; and M for Merlino. Crystals of ash-croftine are usually ten times as long as they are thick, of simple

ll78 MOORE ET AL.: ASHCROFTINE AND ITS ENORMOUS POLYANIONS

TeeLe 2. Exoerimental details for ashcroftine

MSS

a (A)c (A)Space groupzFormulap"","'(g cm-")Specific gravityfP (cm-')

Crystal size (pm)DiffractometerMonochromatorMax (sin d)/IScan, deg per minBase scan width (deg)Background countsRadiationMeasured intensitiesIndependent F.

R

Scattering factors

77.89

(B) Intensity measurements50 (ll a,) x 100 (ll aJ x 3s0 (ll c)

Enraf-Nonius cAD-4

0.600-20 2.00.7-1.3

Graphite0.70

0_20 3.61 .20

Stationary, 20 s at beginning and end of scanMoKa (I : 0.71069 A)

24.03e(6)1 7.s38(8)

small, no absorption correctionPhilips PW11oo

253522761> SolF.)l

0 060

(A) Crystal cell data23.994(6)17.512(51

l4ln2lm2lm2

End member ca NaloKloYrl(OH)4(CO3),6(5is6o,oo). 1 6H,O2.602.61(5)

25381774

(C) Refinement of the structure0.0s8

Unit weightsNeutral atoms (lbers and Hamilton, 1974)

* From average of MSS and M cell volumes and formula proposed.f Hey and Bannister (1 933).

tetragonal prismatic development, palest pink in color, andstriated parallel to [001]. Table 2 summarizes the experimentaldetails. In the MSS study, the space group 14/mmm was initiallyassumed. In addition, the N(z)-test for presence or absence ofsymmetry centers (Howells et a1., 1950) also supported the cen-tric model. For cell-parameter refinement, 25 reflections of in-termediate Bragg angle were selected. An empirical ry'-scan facil-itated absorption correction, since the crystal possessed arelatively low average atomic number. The data were then ad-justed for Lorentz and polarization factors, and the empiricalabsorption correction was applied. Symmetry-equivalent reflec-tions were merged to provide a set of 1774 independent.F. val-ues.

Solution ofthe structure proceeded at two stages. The heavieratoms (Y and K) were located by MULTAN (Main et al., 1977),and successive difference syntheses revealed all ordered non-Hatoms in the asymmetric unit. Refinement employed full-matrixleast-squares methods with the program sHELx-76 and was con-tinued until no further changes in positional 4nd anisotropicthermal parameters occurred. The second stage ofstructure de-termination mentioned above involved the disordered part ofthe structure and will be summarized later.

The approach and procedure of M was very similar. Least-squares fitting of 25 Bragg reflections led to cell parameters sim-ilar to MSS but about 0.20lo higher. We have no explanation forthis difference. Lorentz and polarization adjustments were made,but there was no absorption correction owing to the small andfavorable shape of the crystal. The structure solution proceededwith the Patterson synthesis, which located the Y(l) and y(2)atomic positions, followed by successive Fourier syntheses.

In both studies, unit weights were used throughout, and thescattering factors for neutral atoms and real and imaginary dis-persion corrections were taken from Ibers and Hamilton (1974).Refinement minimized > u,( l4 | - F" l), where s ' : unit weight.The conventional R index, where R : P il-F.l - l.F'.il)D F. isgiven in Table 2 for both studies.

A comment on the disordered atoms is necessary, since theseconstituted by far the most difficult part of the structure study.Table 3, which lists the atomic coordinate parameters for ash-croftine from the two studies, is divided into two parts. The firstsection includes all atoms in the asymmetric unit that fully oc-cupy their sites. These could be called the ordered atoms, butthe term is ambiguous as it has many meanings. Since they donot exhibit any obvious pathological behavior, we call these 27independent atoms the healthy atoms. In our designations, weinclude Si(1) to S(3), O(1) to O(14), C(1), C(2), oH(l), ow(1),Ow(2), Y(l), Y(2), K(l), K(2), and Na(l). The second sectionincludes 12 independent atomic positions; these presented by farthe geatest difrculties. All of them have the letter D afrxed totheir designations. One central problem was discriminating part-ly occupied cation sites from disordered water molecules. Here,all nearest and second-nearest bond distances and determinationof coordination polyhedra were important clues toward thehopefully correct choice. Although we kept in frequent com-munication concerning the nature ofthese positions, the concordbetween the two studies is not nearly so evident as in the healthyatoms of the first section where most atom pairs are within theirlimits of estimated standard deviation. These we shall call the12 pathological atoms. Note that M split T(lD) into both a con-tribution by Si and by B after he discovered a small B content(0.5-1.00/0) in ashcroftine by semiquantitative spectrographicanalysis. MSS, on the other hand, treated T(lD) and T(2D) aspartly occupied Si sites. Doubtless the pathological atoms havea small but real contribution toward the parameter convergencefor the entire structure, and possible other disordered atoms(particularly water molecules) in the large central ball were notlocated. Finally, MSS treated Y(l) and Y(2) as Y populations,whereas M included scattering curves for Y and complementaryCa in purported solid solution. Both models, which convergedwell, should have their differences manifested in the thermal-vibration ellipsoids.

We believe that beyond the 27 atoms in the healthy part of

MOORE ET AL.: ASHCROFTINE AND ITS ENORMOUS POLYANIONS

Teeu 3. Ashcroftine atomic coordinates

t t79

(Healthy part)MSS

s(1 )s(2)s(3)o(1)o(2)o(3)o(4)o(5)o(6)o(7)o(8)o(e)o(10)c(1)o(11)o(12)c(2)o(13)o(14)oH(1)ow(1)ow(2)

-Y(1)-Y(2)K(1)K(21Na(1)

1 0 01 0 01 0 01.001.001.001.001.001.001.001.001.001.001.001.001 0 01.001.001.001 0 01 0 01.001.001 0 01.001.001.00

323232323232325Z

321 61 61 61 61 6321 6t o

32t o

I1 64

321 68I4

o.2414(110.2697(2)0.2188(2)0 2371(4\o.2235(4)0.301 8(3)0.2682(4)0.3247(4)0.1 595(4)0.191 2(4)0.2297(6)0.2807(6)0.2200(7)0.4002(9)0.4261(5)0.3529(7)0 3709(1 1 )0 3596(5)0.3932(6)0.2473(510.1264(71

0.3ss6(1 )0.2679(1 )o.2704(5)0.3057(4)

V2

0.1 51 0(1 )0.063s(1 )0.0630(1 )0.0935(4)0.061 9(4)0.1 780(4)0.0970(4)0.0958(4)0.0875(s)0.1 91 20 1322(5)

000

0.0469(5)0

0.0923(1 0)0.0693(4)0.141 1(6)0.24730.1264

00.1 1 52(1)0 .1618(1)

000

0.4128(2)0.2945(2)0.1 339(2)0.3644(s)0.2264(s)0.4034(s)0.0958(5)0.269s(5)0.1 1 60(8)0.3848(6)

V20.320s(8)0.1 033(8)0 1 s82(1 5)0.1 71 3(7)0.1 31 s(1 0)

0.4353(5)

Y20.2782(9)

00.1 468(1 )

0

0.2417(1)0.2696(1 )0.21 86(1 )0.2368(3)0.2247(4)0.3016(3)0.2684(4)0.3254(3)0.1 591 (4)0.1 905(3)0 2293(5)0.281 1(6)0.2189(7)0.4027(910.4271(4\0.3s1 8(7)0.3709(8)0.3s90(4)0.3944(5)0.2475(5)0.1 285(4)

Y20.3559(1 )o.2677(1)0 2696(4)0.3055(4)

Vz0Y4

0.1513(1) 0.4127(2)0.0637(1) 0.2940(2)0.0631(1) 0.1338(2)0.0943(3) 0.3634(5)0.0622(4) 0 2256(5)0.1784(3) 0.4025(5)0.0961(3) 0.0eso(5)0.0952(3) 02700(4)0.088s(s) 0 1 1s3(9)0.190s 0.3839(6)0.1320(5) v2

0 0.321s(7)0 0.1014(8)0 0.1574(11)

0.0468(4) 0.1698(7)0 0.1320(10)

0.0919(8) Y20.0686(4) 0.4361(5)0.1398(5) v20.2475 Y20.1285 02784(6)

0 00 1145(1) 0.146s(1)0 1616(1) 0

0 V 20 0O V 4

(Pathological part)

Mul . Occ.

r (1D)r(2D)

1 61 6

1 6

1 61 64

t o

1 61 6I88

si 0 38 0.1336(4)s i039 00986(5)

0.30 0.2158(1 0)

0.45 0.4181(10)0.28 0.3900(17)0.42 0

0.49 0.1859(9)0.30 0.0s32(10)0 13 0.1441(37\0.54 0 0983(12)0.36 0 1036(29)0.50 0.1733(1s)

0.1336 0.0622(8)0.0986 0.0905(11)

0.2057(2't)

0.3924(1 5)0.3585(25)

0

0.1859 0.0772(21\0.0532 0.1270(2610.1086(41) 00.0983 0

0 00.1733 0

si 0.20 IB 0.s2 | 0j344(41si 0.28(2) 0.0986(5)

0.25 0.2146(9)

0.50 0.4210(10)0.50 0.3902(10)0 40(6) 0

oH 0.61(4) 0.183s(6)oH 0.28(2) 0.0545(22)o, 0.31(6) 0.1426(30)o, 0.63(8) 0.0948(15)H,O0.66(10) 0.1099(28)oH 0 49(10) 0.1776(24)

0 0.3946(16)0 0.361 1(1 8)0 0.0322(20)

0 1835 0.0746(13)0.054s 0.1238(43)0.1124(28) 00.0948 0

0 00.1776 0

0.1 3440.0986

0.2146

0.0675(8)0.0901 (1 1 )0.2089(20)K(1D)

Na(1 D)Na(2D)Na(3D)

d(1D) OHd(2D) OHd(3D) H,Od(4D) o'd(sD) H,Od(6D) OH

0.2158

000

ivotej Estimated standard errors refer to the last digit. Occ. refers to fractional occupancy at a site; Mul. is number of equivalences in space groupAlmmm.

" ln M, ref ined to Y(1):0.89(1)Y + 011Ca and Y(2): 0.79(2)Y + O.21 Ca MSS employed only Y.

the structure, the inclusion of the 12 atoms in the pathologicalpart leads to art averaged crystal structure at best. Most of thepathological atoms can be traced to the behavior of the disor-dered tetrahedra, T(lD) and T(2D). The T(ID)-T(2D) separa-tion of 1.3 A requires an ordering scheme between the disor-dered tetrahedral sites. In addition, M suggests 0.58 + 0.2Si atthe T(lD) site. Ordering schemes for only one species, say T(lD),can be admitted for full occupancy by l4/mmm or 1422. Forboth ordered and fully occupied T(lD) and T(2D), I4mm, 142m,Immm, and their subgroups are possibilities. To test thesesubgroups was considered but deemed of marginal value, owingto high parameter correlations and, in most cases, a near-dou-bling of variable atomic coordinate parameters. Therefore, weproceeded in 14/ mmm, realizing that an averaged crystal struc-ture would result. Incidentally, such an averaged stnrcture may

well explain a few anomalies (such as nonpositive definite ther-mal ellipsoids) in the refinements.

Table 4 lists the thermal parameters, Table 5' the structurefactors, and Table 6 the bond distances and angles. These tablesreport results of both the MSS and M studies, and all but Table5 are grouped together for easy comparison. Mention should bemade of refinement procedures. In both MSS and M, the atomiccoordinate parameters and anisotropic thermal parameters wererefined for the "healthy" part, and all atoms fully occupied theirsites. For the "pathological" part of the structure, parameter

' To obtain a copy of Table 5, order Document AM-87-360from the Business Ofrce, Mineralogical Society ofAmerica, 1625I Street, N.W., Suite 414, Washington, D.C. 20006, U.S.A. Pleaseremit $5.00 in advance for the microfiche.

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= ^^ @ ^ ^ ^ ^ b ^ ^ ^ ( 9 r J N ^ ^ ^ ^ ^

i i @ N 6 { @ @ + O @ F O O F O @ N o + N O O F F @ O I O 6 t s F O F F C ) r O O @ F Oi r - -- O O - N d ) O 6 c ) N c a ( O @ N ( 6 ( 6 F N 6 F N O O F N + O a O N F O t r ) O O O @ O O @

@ O O b g r N o N O o t r t l O O r O N o ( O F N F r o b O ( ? 6 c ) N ( O N g , N Q - F : f O : f F )N e N - N N N N N F N o N N F O l c \ t F N t t N ( O ( o * r l ) 6 l N F F N N

^^ a6 - ^ 6 - 6 ' ^ ^ ^ __N t N C O N : i O ) @ 6 l r O O ) O N F O r O t O C O N r o ( o ( , < f ( o N O ) F i @ € r N O ( 9 O )

6+. +-d 'Fd ' t r i t 6 'b 'd '= +< EY d iF o n i t i t 6+ . d ' i ( 5= 6d '6 'V V i6 ' i (b 'd 'Vo ( ' ) c D o o i o @ N * o , F @ ; o r o r ; o , o i t r ) 6 1 6 @ o t o ( o o l ( D o , F Q o ) E ) 6 \ f N a o

N F A I N F N F N i i o + ; F F F F N ( O o t f N 6 N b N N N 6 l F

z

6-A '6 'e 6 ' ^ ^^ ^^O + t N r @ F O F N O O F o F - @ o N F ( t o r 6 O N N N O F F - N @ @ h O ) O @ O ,F F N F A t r ( o c ) @ h + ( ' n t b + o 6 < C . ) O ( O O r O N S O r N r O ( O n 6 @d '6 ' <v d5 F= d t i ( vd ' 6 ' a6 ' 6 ' i 6 ' i ( d ' i ( i t 6 . v 5d ' v i 6 ' 6 ' d ' 6 - v d t6 ' d ' t t =6 ' 6 ' d 'N N N 6 N c ) ( o ( o O ( o N N @ @ O i ; + O < O ( o O O r c ) @ @ t N $ F O C ) o ) F O ( o r O QN F t r ) N ( f ) N + N + o - F N N N N N c i i - $ ( t * t O @ N ( 9 * * N N \ f A l b t c ) ( '

a = o 6 ' eFFFgg9899SggasBBSBs

-i

{

5'

{

{

{

I

S

o

X

ooo)E(!(!

(It

ol(5

Eo

.9

oo

o

Y

o

+UJ

-

correlations among site occupancies, scattering curves, and ther-mal vibration ellipsoids are high. Refinement varying all suchparameters rarely has much meaning. MSS approximately re-fined occupancy parameters, then fixed them while continuinganisotropic thermal refinement. M allowed occupancies to varybut continued with isotropic refinement.

By adding up the cell contents from the refined crystal struc-ture, an approximate formula for ashcroftine can be computed,as presented in Table I and Table 2. The minor MgO, MnO,and substantial CaO (5 .7 2o/o) were ignored, and all OW (: HrO)and CO, determined from the slmcture study were included inthe oxide content calculated from the formula. Note that allAlrO. of Gordon (1924) was reckoned as YrOr. Clearly, more(HrO) occurs in the structure, but this is probably disordered-hence undetected by X-ray difraction-in the large ball. A1-though the alkali contents are in fair agreement, Whitfield's anal-ysis suggests that CaO indeed goes into solution with YrOr.

Oddly, the calculated density based on the proposed formulastands in surprisingly good agreement with the specific gravitydeterminations of Hey and Bannister (1933). This agreement isprobably fortuitous and is in part the cumulation of many smallerrors (neglect of CaO, uncertain HrO in cell, other absences,possible incorrect atom assignments). For this reason, calculatedspecific gravities ofcomplex minerals, so often used to confirma formula in the literature, can be delusive.

DpscnrprroN oF THE srRUcruRE

The elephantine crystal structure of ashcroftine has re-gions or subunits that possess very high point symmetry,4/m 2/m 2/m and its subgroups. We are particularly con-cerned about specific regions in the structure-in this case,three-that warrant individual description and concludewith a unified description ofthe entire structure.

The first region consists of the ordered silicate and car-bonate fractions of the structure in the unit cell, specifi-cally [SiorO,rr] and 16[CO,l for Z : 2. These two radicalsinclude the first 19 nonequivalent atomic sites in Table3, all ofthem ordered and fully occupying their positions.We call this stable region of the structure the curd. Man-delbrot (1983, p. 76), who introduced this neologism, de-fined it as "a volume within which a physical character-istic becomes increasingly concentrated as a result ofcurdling." On that same page, he defines curdling as"anycascade ofinstabilities resulting in a contraction." In oth-er words, a curd is the limit of a converging set. Thisdefinition, although it is used in the description offractalgeometries, appears quite appropriate in describing crys-tal structures-in this case, the region that is ordered andthat itself conseryes the point symmetry of the spacegroup. We shall also call this region, specifically [Si4tO,28],the fundamental building block of the crystal structure.

The second region follows from the first and is alsodefined by Mandelbrot (1983, p. 76).It is the whey or"the space outside the curd." This term is appropriate asit includes the extensively disordered part composed of12 nonequivalent atomic sites and as we could not findany stable (ordered and fully occupied) sites within thedomain of the whey.

The third region is a portion of the curd and the whey.Specifically, it is the region that is adjacent to the curd

I l 8 l

and to the whey. An appropriate term is limbus. Con-sulting Bethel (1956, p. 488), limbus is of Iatin etymol-ogy and specifically applies to zoology and botany-"aborder distinguished by color or structure." It is proposedthat limbus also applies to chemical crystallography. It iswhere the curd overlaps with the whey. The limbus in-cludes the terminal oxyanions from the curd that alsocoordinate to the adjacent cations: Y(l), Y(2), Na(l),Na(2D), K(l), K(2), and Na(lD).

The curd

The curd is centered at(0 0 Vz), (Vzt/20) for the silicatefraction; and (t/z 0 t/q), (t/z 0 Te), (0 t/z 3/e), and (0 t/z Vt)-which exactly specify the centroids of Na(l)-for the car-bonate fraction. It includes Si(l) to S(3), O(l) to O(10);Na(l); C(l), O(l l), O(12); and C(2), O(13), O(14). Thestoichiometryin the cell is 2[SiurO,rr] and [Na(l)o(COr)rr].All 20 nonequivalent atoms are ordered and their sitesfully populated (Table 3). The curd is shown in Figure Ias a spoke diagram.

The ordered silicate fraction is most interesting. Its di-mensionality is 0, and it is therefore either an oligosilicateunit, the largest yet found in a mineral crystal, or a oy-closilicate. Its composition is [SiorO,rfl, which rules outmonocyclosilicates, where [SUOr,] obtains. This is an ad-equate but incomplete description of the silicate unit inashcroftine. In a remarkable but rarely cited paper byLaves (1932) on silicate classification, particular empha-sis is placed on dimensionality. For dimensionality : n,he derived for stoichiometry of tetrahedral units SiO4,n : 0 ; SiOr, n : 0 , l ;S i rOr, n : 0 , 1, 2,3;andSiO2, n :l, 2, 3 as topological possibilities. The stoichiom€try forashcroftine is l6SirOr. It can be mapped on the surfaceof a ball, that is, it conserves a volume, by merely con-necting the Si cations together (a connection whenever alinking oxyg€n exists). Such arrangements lv€ prefer toconsider a subdivision of the oligosilicates, and we callthem balosilicates, frcm Middle English bal meaning"ball."

One important property of the balosilicate is that theoligosilicate anionic unit maps on a sphere and it pos-s€sses branches (connections or edges), vertices (nodes),and polygons (faces) that together can refer to some poly-hedron. Such systems must have some connections great-er than two about vertices. Two-connected systems (suchas rings) merely divide the sphere into two pieces by theintervening polygon. Liebau (1985) in a masterful dis-cussion on silicate structuresn listed the dicyclosilicatedouble rings. With p : number of tetrahedra within onering, the general formula is [aSirrQrrl-zr. Double rings areknown for p : 3 (synthetic phases), 4 (numerous syn-thetic phases, steacyite, iraqite), 5 (synthetic phases), and6 (synthetic phases, minerals of the osumilite-milaritegroup). It is proposed that all double-ring silicates whoseconnections ofvertices define a polyhedron also be calledbalosilicates.

Connecting the cations together in Figure 2 gives the[Sior] ball. Here, nodes identiff with the Si cations and

MOORE ET AL.: ASHCROFTINE AND ITS ENORMOUS POLYANIONS

l 1 8 2

-1/z)/zX

edges with the connecting oxide anions where the oxidesoccur somewhere near the rnidpoints of these edges. Eightcuts occur above and below the plane of the projectionand are represented diagrammatically as dashed lines. Foreach dashed line, not one oxide occurs, but two. Iftheseeight oxide pairs are fused together, then the stoichiom-etry is [SiorO,ro]. This leads to Figure 3, which is the planof the truncated cuboctahedron, an Archimedean semi-regular solid.

Figure 4 attempts to feature a combination of polyhe-dral and spoke representations of the crystal structure,the central [Sio8Orr8] unit and its enveloping limbus ofY(l)-O, Y(2)-O, K(l)-O, K(2)-O, Na(2D)-O, andNa(3DfO bonds (the last two atom positions in the whey).Also in the whey are T(lD), which is shown here, andT(2D) that seal the dashed ruptures in Figure 2 together.Through additional units such as [T(D),@(D)4(D),O.] or[TrOr] groups, the balls are bridged together along [001].For this reason, the tetrahedral fraction can be consideredtubular with enormous bulges in it. The tubular portionthen is L[TruO,oo], T connoting tetrahedrally coordinatedcations such as Si4+ or B3+. Note that in the process, semi-regularity is destroyed for the ideal truncated cubocta-

MOORE ET AL.: ASHCROFTINE AND ITS ENORMOUS POLYANIONS

x1/zVz

Fig. l. The central curd of ashcroftine as a spoke diagram, showing Si(l) to S(3), C(l), C(2), Na(l), O(17) : OW(2) and O(1)to O(14). These atoms are ordered. The ball centered at (0 0 y, is [SiorO,rJ. Atom sites corresponding to Table 3 are noted, andtheir heights are given as fractional coordinates in z.

xt/z-1/z

slzUzx

hedron (t.c.o.). Instead, from No : 48, N' : 72, and Nz:26 (12 squares, 8 hexagons, 6 octagons), insertion ofdis-ordered T(D) tetrahedra lead to No : 56, N' : 80, lrr, :

26 (12 squares, 4 octagons, 8 heptagons, 2 dodecagons).We shall see later that this insertion leads to a geometricalas well as point-symmetric distortion of the t.c.o. The(4/m 3 2/m) point symmetry of the t.c.o. is degraded toa nearest subsymmetry @/m 2/m 2/m). This is also theaverage point symmetry of ashcroftine's crystal structure.

Two independent carbonate groups and Na(l) com-plete the curd. The [Na(l)O'] polyhedron serves in partas a bridge between the [Y(l)O'] polyhedra along [100]and [010]. Four [C(I)O(I2)O(ll),] polyhedra surroundthe central Na(l) that is fixed on the tetragonal scaleno-hedral point (4m2). Four O(l l)-O(l l)' edges are identi-fied with edges of the [Na(l)O(I1)'] polyhedron that is acube (polyhedron no. 257 of Britton and Dunitz. 1973),distorted by unequal edge lengths toward the direction ofa square antiprism (polyhedron no. 128). These linkagesand the tc(2)o(14)o(13),1 polyhedron show up as islandsin Figure l, the latter appearing like crossed swords. Theoxygen atoms in this latter [C(2)O3] group are also linkedwith Y(l) through edge-sharing via O(13)-O(14). The for-

Center of ISiorO,rr]z = lz

si (3) t .r 3

mer [C(l)Or] group also shares an O(l l)-O(12) edge withY(1). As the [CO3] groups are constrained by mirrorplanes, they act as structural struts, and [C(l)O3] bridgesby two O(11)-O(12) edges to Y(l) along [00] (and [010]);lC(2)O3l bridges by two O(13)-O(14) edges to Y(l) along[001 ] .

The limbus

The border or edge between the ordered curd and thedisordered whey includes the remaining ordered cationsY(l), Y(2), K(1), and K(2). They define a laurel wreatharound the central [Sio8orr8] curd, and the chicken-eggquestion arises: just which portion of the total structurewas the template for the remainder? A possible answercan be found in assessing the point symmetries. Thecentral laurel wreath has overall composition8Ye+Or8d(D)rOH, which includes one of the disorderdanions. It involves a sequence of Y(I)-Y(2)-Y(2)-Y(l) face-sharing polyhedra (Fig. 5). The polyhedra are now dis-cussed. The [Y(I)OJ polyhedron is ideally a D2d do-decahedron (polyhedron no. l4), a common coordinationpolyhedron of order eight about lanthanides. For exam-ple, in cerite, CerFe3t(SiO4)6(SiO3OHXOH)3, all threenonequivalent lanthanide positions are based onthe DZddodecahedron. The [Y(2)OE] polyhedron is more elusivesince it includes disordered f(lD), but if full occupancyof this anion is granted, the polyhedron is also of ordereight. With Y(2) at z : 0, coordinating O(3), O(a), and

r 183

aNo (1 ) 1 .25

o \ S i ( l ) t . 4 |

(2) ! .29 Y(2) .00

. v ( t ) r . t s

@(lD) with general z define a distorted trigonal prism;two coordinating atoms at z :0, OH(l), and O(14) formthe two lateral caps and complete the polyhedron that isa bicapped trigonal prism (polyhedron no. 52). The max-

Fig. 3. The Archimedean semiregular truncated cuboctahe-dron down an axis normal to the octagonal face. Mirror planesand twofold and fourfold rotors are drawn in. The polyhedronhas No : 48 vertices and Nr : 72 edges.

MOORE ET AL.: ASHCROFTINE AND ITS ENORMOUS POLYANIONS

r f2).so

aNo ( 2D)+ 1 A

K(2).00

s i ( 2 D ) ! 0 9

si(r D) r.07

K(10 ) ! .21

No (1D )+ 1 q

a

Fig.2. The central ball drawn as [Sior] connections, with mirror planes and twofold and fourfold rotors drawn in. The linkingoxygen atoms are approximately at the midpoints ofthe "edges." The breaks ofthe edges for the truncated cuboctahedron are shownas dashed lines. There are eight such dashed lines, each representing two oxygens instead ofone such that SioEO,r' * O, : SiosO,23.Surrounding cations in the border or limbus and cations in the disordered whey are also shown, heights as fractional coordinatesin z following Table 3.

ITrr{rr]

-;I

SxI

S\I

S

NII,x

aN

I

Soo

G@oboo

ooG

ooE

qo

o6(Do

oF

E6E b9 Et g' 9 6d o

c o

=s'* ,4.x v

C A= E.9) e; >@ . .( o b

EEF O

y , =

b gEg @

x s of ; t >. E s b6 n ol u u J =

* N O

t x I\

- : - . i " ho N @ t s o ) 6 0 r N o r FF O s t F F F O F t O O

@ F O ( 9 O @ O r ) . @ bo + + + $ o o + ' o o

^ ^ ^ oS C 6 ' C 6 ' - 9 5 g ed'b'< =E d' oq r u? qN s i ; ; ; N 9 = t ho s $ \ f $ ( D } : = :

N

^ ^ ^ ^ O F ^ ^@ ( O O ) O F F N N- - N O N 6 O O O UA I N A t ( o C O O T C O N c ) 6(t, (") (t) (7) (D (o o N * @

N N N A I N N N N N N

o o

19-^^6 '=+- O o \o t r ) $ o F F F F ! 2 r N

o o o o o o o o h o- ! r -L - r l l l r ; r

F F F T < T

r l ) r o @ r o : i < )

O @ N F O € $r * . O € N d ) N O )

bbbg. eeP===PF - O r @ $ ( od r C \ t O t r rb ( o @ @ @

O F O @ O @ t6 @ @ @ O @ @O I A I A I N N N N

o @ ( o r o 6 F . t r )q q a ? q q q a i 'o @ N N O O O

o ^ o o o o o F F F oF @ F F

F F N O ) r Jo ) F N N Fo @ @ @ @

O O F N c O c O ( r )o o @ @ @ @ @N N N N N N N

q?+$$ $??Ss?sggg$a ieOO-04a a a a o o o o o o

6 I N F F

N r + @ O ( 9 0 ,q \ q q q aN N N N O I r )

N A I C J Ft \ r i ( o F t @q \ q q o q 9 aN 6 t A r d ) N C 9 i r

z

^ \t o

o *- - ". )()( .,d '6 'E'Y Y E,J-r H 6'6'X88i 88iN F N F

993+' odddd 'F 'q

t l t t h AN N N N > : >Y Y Y Y < YN N 6 t +

t f

oAI

o^ o

r EO GN i -

oI

a

I

z@

oo t N o 6 0O F ( r d ) F NN t r ) G ' ( 9 t r ) ( D

(o* r o 6 l ( o @ t -O I F ( O g ) F 6 l a

s i t r i n i n i d d i S ,YY

9- ^. . ^9-

F+9s?+eN N N N N N Y

F N F N N F

a.L.!-L.1-1-N @ N ( o ( o T O@ o o @ o * s@ N @ O r ( ) r O ,

* * r r O O O O - - O= = r - -! U = g ro c o o r N ( Y )@ @ F F Oq ? q q q q . , . . - .- O O - = = = N

N @ O b @ O Yu ? u ? q q q q NA I A I N N N N

@ o N @ @ 6r ) @ ( 7 ) o @ O : fr O F . O r @ ( D N O ,

F o ^ ^ O o O O F F OF r ( o o t

F ( O O s t @t s o o N o6 0 @ @ 6

t @ o N s t @ o6 b @ @ @ @ @N N N N N N N

q+F+ g sFtFss s99904 o6s000ia a a a o o o o o o

^a \ ^ : - ^ 6 ' ^ -aSr== gsre Xg, = N6 6 6 t n 6 a ' i 6 = =r l r lJ- r a- t lJ-F N € O N O F F N @ @

o o o o o o o o o o-!-J--L J- -t-t- ll -L-L= = = E 9 9 9 9 9 9@ a a o a a a a < n a

F F @ F A l r

N O O N N O OA I N N t r ) $ @ ( '

N N N N N N N

F F * F C ) NF O O O ( O n ON N N O I O O

N N O I N N N N

O ) F . F O O ) F N N I( ' T F O O N O O @ r FO S ( t N < ) O C O @ r f ; *a ? a ? c ? c ? a c ? u ? \ a 66 r N N N A r A t 6 1 6 t 6 r ( i

, -@O -o l q qO F O

= . L F N NF N

o @ @N 6,1 6t

F $ Nq q qN N N

o oeS,a q q e6 0 0 >F N N

- 6

N N N

N -F N ON N O IN N N

o ^ ^ ^F O r @ F ' r N

d'dd'd F, 6r l l l x rF F f F Y F

Y Y Y Y < Y* N N s f C !

^:-N F

N r- - - . X X . .

6 , d g ' Y Y EA A h - - :u ! > 9 + >o o < o o <F N N F

@ I O F O ( O b NN @ O * @ N * -

+r ; i= ; i ; ( / ,^ ^ Q ^ O O O F F F OO @ F OO N O N Oo ) F F o I Fb ( o ( o ( o @

@ N O + @ O Ou ? q q q q q qN 6 I N N N N N

q??q$ 8FssgB$> A A A A A A >

= 9 = 9 < e e U e g g <a a @ a o o o o o o

a-@O ' Fo o oo r 6 l o

- - F N NO F r F F F

o o o )d? C\l o|

N F -

(9 lo \tC I N N

N N O I

o o )

4 i q g ,o o o ON F N

N O( ) o oN ( D N

N No h Nq q 6 lN N N

< ! r

E

o

r r ) r t @ + @ *o h b @ o o +* r i a i c i o + o i

! - t - L L O O O F F F O@ n o 6

O O F + OO ) A l d ) O t Fr o @ ( o ( o @

N O $ $ @ F t fu ? u ? q q q \ qO I A I N A I N N R I

a

at)c)o,(!

(g

oo

at)o

oE

o

(oUJ

F

o

o

(!

o

og,

(!z

* * r + t tX X X X

N N I t so o @ N oN + h N ( oN N N ( r ) G )

: f ( o $X X X

F F ! €

o ) ( o * c Jt c o N ( ' , ,N N N O I

^ \o o o ob N I N

EE t ' 55-L-! ! ! AA

( ' ) ( o > c ) g )6 6 \ 6 6z z z z

t -a .a -1o N c ) oF F N f r ,o i t € c o oN O r < f ( o OO O F O O

N N F @ ON I O N F N( o o @ o N

O O ( O N i ' -F - N N O N

N N ( O .

* @ F Nn o @ b

o o o o o

N N Ot ( o F O ,N O t s ON O I A I N

N N ON * r O O *N ( O ( o ( D O6 I N N N O

:f * (Y) (t) $O @ N b O Fl O F r A I O C O

N ( " ) ( ' ) O O N

^^ )='

b r $ < t t ;N S O F @ OT N N N O N

N ( D ( 9 ( o ( ' N

G'

r t ( ' , * ;@ o N oq a ? @ a ?N N N N

6 ' -^F F O

Y Y Y od66- Pstsrs, b6 6 6 >z z z <N N F

N t r J I O O '

r o @ o ( 9 @o o o N C oo o o N o

N O N TO h F @ F* 6 @ O r NN N N N N

F A l d ) \ i

o r o o r o o =r i d + A i c r t i yo o o N o F

e-64'6"SYYYga o o o h8**gir N F N

nN

^ ) fN N N ( ' ) ;6 '5Yr 5 -N ( 9 F - C J O 'N N N N O

=6'E KJ U > 6

999. Io o o 6 ' o6 6 6 > 6z z z < zN N F

rire ti giii*o o o h o o a o o o h

F=Fi FP 8*E: iN r r N r F N N r

o

0c3h FYYQYSY6.A6'6 H aF F F F < F

Y Y Y Y < YF F F N

N O O No r r ) r o N @t b ( o r o 6N C ! N N N

o o b o

o O F O l n 'S F . r ) N g )O O F F O

N r O @ h NN N F f FN O @ O 6

O r O $ c O -N N O @ O

A I N t r )r O @ F . g )o r r , ( o 6

A I N t r ' ! t! t O l O ) O O ,I t o ( o N r oN N N N N

N N r O ( ? )< t N c ) F $$ 6 0 0 @

N N N N N

N ( ' , o *

b o * o ) @

O O F N ( Oo o o * o

N O N ( " ) b

F O N N r O ,o N @ @ c ) o

N O N To b @ o N* 6 $ N @N N N O O J

=o@g

ar N N @ t f

gO 6 N N O

r t d o o i d -o O o ) : f O t i- - 9

oN N N r O 6 )s f F - o ) $ r i ( ' oq q \ q a ? \ a-

trN N ( 7 ) Os N < f @ t$ 6 r O N ( oN N N O N

Y

EG

@o

o(5(L

g

(o

N

5.=

x

(oUJ

F

r 186 MOORE ET AL.: ASHCROFTINE AND ITS ENORMOUS POLYANIONS

c=0

) v t t t . t z

^ t t mv z ' t2 -

c = l m

Fig. 4. Ashcroftine's central [SiorO,rJ ball drawn as stippled polyhedra projected down [010]. Some cations in the limbus andwhey are shown. At least five different [TrOr] bridges between the neighboring balls can occur along [001]. One of them-Si(lDlO(3DFS(ID) [: T(1D)-4(4DFT(ID) in text]-is shown. Heights are given as fractional coordinates in y. Note that the top andbottom portions ofadjacent balls along [001] are drawn in as unshaded polyhedra.

IY{2).r6

i,rrr.rl

imal point symmetries for Y(l)O, and Y(2)O, are D2d:(42m) and g2y : (mm2) respectively. The twelve-coor-dinated K(l) cation is situated near the center of and justoutside the large octagonal windows of the central curd(Figs. 2, 4, and 5) and occurs within a distortedlK( I )O(8),O(9),O(1 ).O( I 3),1 tetracapped square prism, theO(8) and O(9) defining the caps. The polyhedron hasmaximal point symmetry C2v: (mm2). The K(2) cationis ten-coordinated with composition [K(2)O(10)rO-(12),O(14),0(4)"1 and also appears in Figures 2, 4, and 5.This cation is further removed from the central curd,more situated in the direction of the interceding channels.It is a distorted czs-bicapped square prism, the two O(14)caps in the plane of central K(2). The maximal pointsymmetry is also (mm2). For larger cations, it is oftendifficult to decide which are the nearest-neighbor dis-tances. Therefore, in Table 6, which lists bond distances,the first cation-cation distance is also listed separately.

This completes description of the curd and limbic por-tions of the ashcroftine crystal structure that contain 27independent atoms out of at least 39 independent atomsin the crystal structure. It is believed that the point sym-metry D4h: (4/m 2/m 2/m) for the ordered fragment of

the [SiorO,rr] ball suggests that it is indeed a fundamentalbuilding block (f.b.b.). In fact, the two distinct Y@, poly-hedra possess neither symmetry nor any simple expla-nation for their structural design other than that [Si48O,r8]forced their affangement and with them, the arrange-ments of all the other atoms in the limbus and in thewhey. It is suggested that in the chicken-egg paradox, theegg came first and was the balosilicate fraction.

The whey

In the whey, the tetrahedrally coordinated cations aresymbolized by T and the ligands by d. All atoms aresuffixed by D to indicate their disordered nature. Thedisordered portion of the crystal structure is composed ofat least twelve nonequivalent "pathological" atoms (Ta-ble 3). This portion of the study constituted by far themost tedious and frustrating part. Since MSS and Mworked on the structure largely independently, it is grat-ifying that at least approximate convergence was attainedfor the disordered atoms even though the methods fortheir deciphering and refinement were somewhat differ-ent.

Nomenclature for the six disordered cations includes

1,.,0 o,,o,o)')*,,,.*

MOORE ET AL.: ASHCROFTINE AND ITS ENORMOUS POLYANIONS 1 1 8 7

x'

l o { r ) .25( <.\KI

Fig. 5. The limbus in ashcroftine that encrusts the central curd. The Y(l)-O and Y(2)-O polyhedra are stippled. Some Na(l)4,Na(lDlO, K(l)-O and K(2lO bonds are shown. The laurel wreath shown here is centered at(t/zUz 0), and some elements ofsymmetry are shown. Heights are given in fractional coordinates n z.

T(lD) and T(2D) for tetrahedrally coordinated small cat-ions and K(lD), Na(lD), Na(2D), and Na(3D) for largercations; @(lD) to d(6D) designate the disordered coordi-nating ligands (O'-, OH-, HrO). K(lD) is close to theinversion center at (% Vn V+) with K(lD)-K(lD)' = 2.3 Iand therefore occupies at most half its site. Na(lD) andNa(2D) with Na(lD)-Na(2D) t 0.9 A occur in a com-plementary relation with each other. M proposes half-occupancy at each site, whereas MSS suggest a moreasymmetrical distribution. Na(3D) is in a fixed positionat (0 0 0) in MSS (note severe thermal anisotropy in Table4), whereas M chose (0 0 z), the distance between the twocentroids being 0.56 A. In the first case Na(3D) is in atwelve-coordinate site, with four @(5D) and eieht d(2D)at vertices; in the latter case Na(3D) is in an eight-coor-dinate site, with four d(5D) and four d(2D) at vertices. Acomplementary relation exists between two disorderedanions, d(lD) and @(6D). These evidently coordinate toY(2). But d(lD)-d(6D) I 1.4 A requires occupancies foradjacent pairs d(lD) : 0.0, d(6D) : 1.0 or 4(lD) : 1.0,d(6D) : 0.0 or coordination numbers for Y(2) of sevenand eight, respectively.

At least five spanners or bridges can be identifred be-

tween [SiorO,rJ balls along [001]. One of these-T(lDFd(4DFT(lD)-is shown as a spoke diagram in Figure 4and is one of the unlikely ones. From 0(6)-0(6;r'r."tut"Oby the mirror plane at z :0, the distance along [001] isr4.0 A, roughly the gap spanned by a [TrO'Ou] oligosil-icate dimer where O' is shared by two T. For the ballcentered at (0 0 Yz), the tetrahedral centers are T : T(lD),T(2D), and the geometrically permissible O' links are O' :

d(3D), d(4D), and d(6D). The possible arrangements arelisted in Table 6 with corresponding T-4-T' angles. Thefirst three range between 120' and 180o, and the remain-ing two are between 7 5 and 90'. The first three, mostlikely candidates for spanners between balls, are T(2DFd(4DFT(2D) * 176, T(ID)+(3DFT(ID) = r25o,andT(1DF0(4DFT(2D) I 130". All involve, beside the cen-tral linking 0, 20(6) basal termini on each side.

Although the pathological part of the structure pos-sesses twelve only partly occupied sites, assessing the po-tential-anion formal charges (and the anionic species) ispossible by inspecting their coordinating cations. Thed(lD) and d(6D) sites are approximately each half-oc-cupied. The d(lD) is coordinated bv 2Y(2) and disor-dered lT(lD) and lK(lD). The X{(lD) distances are

l 188

larger than average, and we prefer to assign d(lD) : OH-.The d(6D) is coordinatedby 2Y(2), and these distancesare short. We suggest d(6D) : OH . The @(4D) is coor-dinated by 2T(lD) + 2T(2D), but the individual cationsare approximately half-population on average. We pro-posed d(4D) : O'z-. The 4(2D) is coordinated bV T(2D)and the Na(3D) in the coordination cuboctahedron. Lo-cally, if all sites were populated, the cluster would belNa( 3 D)d( 5 D) 4(T (2D),OgD)d(2 D),0(6 )o)"1, or [Na-(HrO)o(TrO,)ol. Since d(5D) coordinates only to Na(3D),we suggest d(5D) : HrO. The 4(2D) has site populationmuch like T(2D), which is a bit lower than Na(3D). Wesuspect that these atoms-@(2D), T(2D), and Na(3D)-are coupled together, and this means that fQD): OH .Finally, there is @(3D). This is a possible T(lD)+(3D)-T(lD) bridge. The @(3D) population at this site is veryuncertain, as seen in Table 3. With such uncertaintiescoupled with fragmentary evidence, 0(3D) could be O'z-[if both T(lD) are populated] or OH- [if one T(lD) ispopulatedl or HrO [ifboth T(lD) are locally empty]. MSSassign 4(3D) : t/z(H.O + O' ), V2(HrO + OH-), or Yz(H,O+ H,O), etc., where M assigns 0(3D) : O'z as the bridg-ing oxygen between two symmetry-related B cations inthe T(lD) site. The ligand species proposed for each site@ is listed in Table 3.

Within the disordered whey, two clusters in the limitcan be proposed: [Na(H,O)u(T,d,)J for Na(3D) and[KO3(HrOXT@J] for K(lD) where the anionic unit is notspecified for @. This suggests that by other means, theseunits may be more precisely defined, but our X-ray dif-fraction experiments clearly cannot offer more than anaveraged structure.

Chernical composition

Do the proposed occupancies in ashcroftine make anysense in light of Whitfield's chemical analysis in Table 1?As mentioned earlier, YrO, was discovered instead ofAlrOr, and the presence of minor BrO, was detected byM. From structure analysis and vapor-pressure measure-ment, the presence of substantial CO, must be acceptedas a fact, and this was doubtless lost during ignition(H,O > 100 "C) in Whitfield's analysis. From any pointof view, a total analysis of ashcroftine would be exceed-ingly difficult even with contemporary techniques. There-fore, we elected to take the site occupancies ofboth stud-ies in Table 3, reconstruct formulae, and compute contentsas oxides.

From MSS, after balancing charge by adding requisiteCa2* in place of Y3*, for Z : 2 we get K,o ooNa, urYro rr-Ca. orSiro ,60130 ,6(OH)rr 32(CO3),6 00(HrO),, or. From M, af-ter changing l.88OH- to l.88HrO, the composition isK,o ooNa,o roYro ruCa. o.Sir, ,oB. ,uO ,r, oo(OH),, ,o(COr),u oo-(HrO),o rr. An "end-member" formula can be written: forZ : 4, K,Na,Y,,(OH),(CO3)s(Si,sO?J. 8H,O. Naturally, forsuch a complex substance with extensive disorder andother substituents, such a formula is only approximate.

Table I shows tolerable agreement between Whitfield'sanalysis and the structure results. Clearly, Ca2* enters into

MOORE ET AL.: ASHCROFTINE AND ITS ENORMOUS POLYANIONS

the familiar solution with Y3*. Note that the thermal pa-rameters of MSS in Table 4 are larger than those of M,which indicates a lower mean atomic number than Y3* atthese sites. It is also evident that most HrO (>100 "C)can be interpreted as (CO) in the structure, along withthe smaller contributions made by (OH) , tightly bound(H,O), etc.

It is interesting to note that neither structure study pickedup all the water reported in Whitfield's analysis. Onlyabout 7 60/o total water reported was recovered, as detailedabove. This suggests that much water in ashcroftine isdisordered and undetectable by X-ray study. Consideringthe size of the giant ball, the possible content of zeoliticwater could be quite substantial.

Dimensions of the truncated cuboctahedron (ball)

The crystal structures of at least five silicates and alu-minosilicates that possess the t.c.o. as a fundamentalbuilding block are known. If a t.c.o. is constructed fromplastic tetrahedra and Tygon tubings ofequal length, thepolyhedral skeleton is rigid and compact (i.e., minimalvolume of circumsphere). The eight edges are removed,as discussed earlier for ashcroftine, and eight extra tetra-hedra and eight extra bonds are inserted. The new poly-hedron, which is not even semiregular, expands along thetwo principal directions a, and c. This is because theinterior T-T-T angles are more obtuse, a consequence ofthe insertion ofeight extra tetrahedra.

The distance between opposing octagonal facets wascalculated. For an edge length /, we selected the sum oftwo Si-O distances, or Si-O-Si. Selecting d(Si-O) : 1.6A, t : t.Z A. ttre diameter (D) between octagonal facesis easy to derive: it is D : 2(lzl + I/rtl + l/\/21) :

Qrt + Dl : 3.828 /. For the ideal t.c.o., D : 12.2 Afort : 3 . 2 A .

Reasonably refined structures were used to calculatediameters between octagons and are discussed accordingto decreasing values of D. Ashcroftine is the only tetrag-onal structure, so we calculated D(a') and D(c) parallel to

[00] and [001], respectively. From Figure 2, Si(2) evi-dently determines D(4,) and Si(3) determines D(c). Thevalues are D( a,) : 12.9 A and D(c) : 12.8 A, respectively.Ifwe put the average back into our equation for octagonaldiameter of the t.c.o., we get T-O : 1.68 A, a rather largevalue for an Si-O distance average. Clearly, the ball inashcroftine is not strictly a semiregular t.c.o. In ashcrof-tine, OW( 1) is the only identified species that occurs withinthe ball, and K(l) is next, being situated just outside theoctagonal windows.

Linde zeolite A was refined by Pluth and Smith (1980).Here, Na(l) is just in the hexagonal faces, and Na(3) isinside the ball, displaced from the hexagonal window.Na(2) is on the octagonal faces. D : 12.3 A for this struc-ture.

The synthetic zeoliteZK-S (Meier and Kokotailo, 1965)has Nat inside the ball. D : l2.l A for this structure.

Paulingite, solved and refined by Gordon et al. (1966),is a natural zeolite with an enormous cubic cell (a: 35.1

Al. eU cations lie outside the ball. D : 12.0 A for thisstructure.

The NHo-rho zeolite (McCusker, 1984) is reminiscentof K(l) in ashcroftine: the NHf ion is in the plane of theoctagonal window. D : I1.8 A for this structure.

For the cubic zeolites, the range of four independentvalues is D: l l .8-12.3, with an average T-O: 1.57 A.These values contrast with D : 12.9 A and T-O : 1.68A for ashcroftine. No definite conclusions can be madeabout occupancies within the ball. In some structures,cations and/or water molecules have been located; in oth-ers, the ball is "empty," at least from X-ray studies. Fromthe analytical data on ashcroftine, it is believed that theremaining water is present in the ball and that it is dis-ordered at room temperature to the extent that X-raydiffraction experiments do not detect it, reminiscent ofthe extensive missing water in the giant pore or channelstructure of cacoxenite (Moore and Shen, 1983).

CoNcr,usroN

Two reasonably refined crystal structures of the ele-phantine ashcroftine were obtained. At least 39 atomsoccur in the asymmetric unit, and 12 of these are disor-dered. The fundamental building block is an ordered largeball, a broken truncated cuboctahedron, with tetragonalsymmetry @/m 2/m 2/m) and with composition [SiorO,rr].The region between balls separated by ca. 4.0 A along[001] is extensively disordered, and these balls have T-@-T spanners between them. If we select T(lD)+(4DFT(lD) as an ordered oligosilicate, the linking @(4D), theassociated 0(6) from [Sio8O,,8], and @(lD) [which alsolinks to two encrustin1Y(2)1, the anhydrous [SirOr] span-ner is created, or ![SiruO,oo], which becomes a tubularinosilicate with large bulbs oriented parallel to [001]. Add-ing all the ordered atoms in Table 3 together, we obtain[KrNarYr"(OH)"(CO3),6(Si,6Or40). 1 0H2O]'0-. The chargeis balanced by additional disordered alkali cations.

The [SiorO,rl ball includes O(l) to O(10). Ofthese, O(l),O(2), O(7), O(8), O(9), and O(10) knit the ball togetherby Si-O-Si bridges. These Si-O-Si angles are listed inTable 6 and range from 138'to 143". They are essentiallyelectrostatically neutral. The remaining O(3), O(4), O(5),and 0(6) stick out from the ball to create a burr. Theseoxygens are electrostatically neutralized by Y(l), Y(2),K(1) and K(2) bonds. Only 0(6), the broken segment ofthe t.c.o., links to the disordered tetrahedral cations, T(D).In fact, for the entire L[Si56Or40], all terminal oxygens stickout like a burr such that the central pipe or tube has novertices pointing into its domain. Yet again, the notionof the central ball as a template for the remainder of thestructure is appealing.

Ashcroftine stands alone among the nepheline syenitesecondary minerals in possessing an enormous silicatepolyanion allied to the truncated cuboctahedron. A muchsmaller semiregular solid occurs in the nepheline syeniteaccessory tugtupite, as the [BeoAlosi,6oos] truncated oc-tahedron that defines the modular unit of a sodalite-typeframework. We speculate that a cubic structure related to

I 1 8 9

ashcroftine but with an isotropic distribution of crust orlimbus around it may indeed exist as a late-stage nephelinesyenite phase, associated with calcite, etc., and that thecubic symmetry may contribute to the elusive characterofsuch a hypothetical phase.

AcrNowlnlcMENTS

Donation of rype ashcroftine by the Bntish Museum of Natural Historyand by the U.S. National Museum of Natural History is greatly appreci-ated We cannot stress too much the importance of type material, andacknowledgement of such should not pass in silence.

P.B.M. appreciates support by the National Science Foundation (GrantEAR 84-08164) and the evident continued sympathy by that agency forhis continued fascination and study ofmineralogical monstrosities. P.K.S.wishes to thank the Tennessee computalion facilities at the TennesseeEarthquake Information Center for use oftheir vAX computer.

S.M. acknowledges the Consiglio Nazionale delle Ricerche (Centro perlo studio della Geologia Dinamica e Strutturale dell'Appennino, Pisa) forfinancial support and the researchers at Centro per la Cristallografia Strut-turale (Pavia) for their help in intensity-data collection.

RrrnnnNcrcs crrnnBethel, J.P., Ed. (1956) Webster's new collegiate dictionary (second edi-

tion), p. 488. G. and C Memam Co., Springfield, Massachusetts.Britton, D., and Dunitz, J.D (1973) A complete catalogue ofpolyhedra

with eight or fewer vertices. Acta Crystallographica,429,362-371.Gordon, E K, Samson, S., and Kamb, W.B. (1966) Crystal structure of

the zeolite paulingite Science, I 54, 1004-1007Gordon, S.G (1924) Minerals obtained in Greenland on the secondAcad-

emy-Vaux expedition, 1923 Proceedings of the Academy of NaturalSciences of Philadelphia, 76, 249-268.

Harris, D.M. (1981) The microdetermination of HrO, CO, and SO. inglass using a 1280'C microscope vacuum heating stage, cryopumping,and vapor pressure measurements from 77 to 273 K Geochimica etCosmochimica Acta. 4 5. 2023-2036

Hey, M H, and Bannister, F.A. (1933) Studies on the zeolites. Part IV.Ashcroftine (kalithomsonite of S.G. Gordon). Mineralogical Magazine,23 ,30s -308 .

Howells, E R, Phillips, D.C., and Rogers, D. (1950) The probability dis-tribution ofX-ray intensity. II. Experimental investigation on the X-raydetection of center of symmetry. Acta Crystallographica, 3, Zl0-214.

Ibers, J.A., and Hamilton, W.C. (1974) Intemational tables for X-raycrystallography, vol. 4, p. 99-100 Kynoch Press, Birmingham, England.

Laves. F (1932) Zur Klassifikation der Silikate Zeitschrift liir Kristallo-graphie, 82, l-14.

Liebau, F. (l 985) Structural chemistry of silicates: Structure, bonding andclassification, p 97-99 Springer-Verlag, New York.

Main, P , Woolfson, M.M., Lessinger, L., Germain, S., and Declerq, J.P.(1977) uurTAx ?4, a system of computer programs for the automaticsolution ofcrystal structures. University ofYork, England (1974)

Mandelbrot, B B. (1983) The fractal geometry of nature, p. 74-83. W. H.Freeman and Co., New York.

McCusker, L.B. (1984) Crystal structures ofthe ammonium and hydrogenforms of zeolite rho. Zeolites, vol 4, p. 5l-55. Butterworth and Co.Ltd.. London.

Meier, W.M., and Kokotailo, G.T. (1965) The crystal structure of syntheticzeolite ZK-5. Zeitschrift fiir Kristallographie, 121, 211-219.

Moore, P B , and Shen, J ( 1983) X-ray structural study of cacoxenite, amineral phosphate. Nature, 306, 356-358.

Moore, P.B., Bennett, J.M., and Louisnathan, S.J (1969) Ashcroftine isnot a zeolite! Mineralogical Magazine,37, 515-517.

Pluth, J.J., and Smith, J.V. (1980) Accurate redetermination of the crystalstructure of dehydrated zeolite A. Absence of near zero coordinationof sodium Refinement of Si, Al<rdered superstructure. AmericanChemical Society Journal, 102, 47 04-47 08.

MeNuscnrpr REcETvED FesnuARv 4, 1987Maxuscnrpr AccEPTED Jurv 2.1987

MOORE ET AL.: ASHCROFTINE AND ITS ENORMOUS POLYANIONS