Carwdian MineralogistVol. 20, pp.239-251 (1982)

ABsrRAcr

The crystal structure of a carbonate-rich can-crinite has been refined to a conventional R indexof 2.8Vo in space gxoup P6s using X-ray-diffractiondata and a model derived using a study by high-resolution transmission electron microscopy anddetailed Fourier sections from a trial refinement.The superstructure observed can be rationalizedsolely in terms of the substitutional arrangement ofinterchannel cations and anions on sites positionallyconsistent with the space-group symmetry. Stack-ing variations differing from the hexagonalABAB ... type are shown not to exist in thismaterial.

Keywords: cancrinite, X-ray diffraction, crystalstructure, high-resolution fansmissiotr electronmicroscopy, superstructure, sodalite, zeolit€.

Sorvrrvrerns

La structure cristalline d'une cancrinite riche encarbonate a 6t6 affin6e dans le $oupe spatial P6ajusqu'i un r6sidu R de 2.8Vo. L'affinement estfond6 sur donn6es de diffraction X et i la lumidred'une 6tude au microscope 6lectronique par trans-mission i haute r6solution et de sections de Fourierd6taill6es r6sultant d'un affinement pr6liminaire.On explique la surstructure observ6e en fonction deI'agencement des substitutions des cations et anionsdans les positions permises par le groupe spatial.On montre qu'aucune d6viation de la s6quenced'empilement hexagonal ABAB.. . n'exrste dansce mat6riau,

(fraduit par la R6daction)

Mots-cl6s: cancrinite, structure cristalline, diffrac-tion X, microscopie 6lectronique par transmissiond haute r6solution, surstructure, sodalitg z6olite.

INtnonucttoN

The cancrinite group of minerals is shar-acterized by an ordered framework of (Al, Si)04 tetrahedra. The hexagonal symmetry is theresult of the close packing of interconnectedand parallel 6-fold rings of alternating AlOrand SiOa tetrahedra in an ABAB. . . type ofstacking sequence (Jarchow 1965), Many mem-berr of the sodalite group of minerals are poly-morphic with members of the cancrinite group.

THE GRYSTAL STRUCTURE OF A CARBONATE-R|CH GANGRTNTTE

H. D. GRUNDY eNp [. HASSANDepartment of Geology, McMaster University, Hamilton, Ontario I3S 4IA

Ilowever, the Iatter have cubic symmetry dueto an ABCABC. . . stacking sequence. Thedifference in stacking sequence gives rise toimportant structural dissimilarities between thetwo mineral groups.

Cancrinite has a large continuous frameworkchannel parallel to the axis of 6-fold rotation(z axis), in which are located interframeworkcations and anions. In sodalite this channel isoffset by the C-type stacking layer to give anetwork of large cages. In addition, cancrinitehas "chains" of small cages parallel to the zaxis. These consist of framework cavities be-tween successive A- or B-type layers (Fig. 1);these cavities also contain cations and anions.The difference in structure between these twogroups suggests that the cancrinite-group min-erals are more likely to be the low-temperaturepolymorphs, as the continuous channel facili-tates diffusion, and thereby decomposition, atelevated temperatures. In the case of the hydroxyvarieties, this has been experimentally verified(van Peteghem & Burley 1962).

Although the frameworks of these groups ofminerals are well defined and essentially a 1:1ratio of AlOe and SiOa tetrahedra, the inter-framework ions are chemically diverse andtypical of zeolitic materials. The large channelsin cancrinite are found to contain Na+, K+,Ca2*, OH-, COr'-, SOe2- or HrO and the smallcages, Na+, K+, Ca2+, OH-, HzO or Cl-; thesodalite-group cavity can contain Na+, K+, Ca"+,OH-, SOn2-, Cl- or HrO. The disorder thatresults from substitution of these ionic speciesfor each other gives P6s symmetry. As a furthercomplicationo vacancies on non-framework sitesare usual in both groups of minerals.

The general features of the crystal structuresof both cancrinite and sodalite are well known(Pauling 1930). However, the detailed structureand the origin of observed superstructures arenot clear. This work reports on some of theresults of a general study of the structure andchemistry of these two groups of minerals.

ExppnnurNtnt,

Although useful models of the crystal struc-

239

THE CANADIAN MINERALOGIST

Frc.l. Stereographic schematic diagSam of the framework of cancrinite viewed down the z axis. The largechannel is defined by the "chains" of interconnectod small cages parallel to the z axrs.

ture of the sodalite-group minerals have beenestablished (Schulz 1970), those for the can'crinite group are less detailed (Jarchow 1965,Nithollon & Vernotte 1955). Therefore, in theinitial stages of the present research program'a structural refinement of a possible "end-member" cancrinite was undertaken to define amodel that would be a useful starting point fortle refinement of chemically more complexspecies. Details of the material chosen are grvenin Table 1.

Long-exposure precession photographs (Fig.2) show a symmetry consistent with the ac-cepted space-group P6' (Jarchow 1965). Thediffraction photographs also show a well-devel-oped superstructure resulting in a supercell con-sistent with a c dimension eight times that ofthe substructure. All observed diffraction max-ima are sharp. Cell dimensions, determined byleast squares from 25 substructure reflectionsautomatically aligned on a 4-circle diffracto-meter, are presented in Table 1 together withother information pertaining to the collectionand refinement of X-ray data. A sphere O.2 mmin diameter was ground and used to collect theintensity data. The crystal was mounted on aSyntex P2r automatic diffractometel using gra-phite-monochromated MoKc radiation andoperated n tlcre 0-20 scan mode. A total of 1918reflections were collected over treo a$ymmetricunits out to a 20 value of 65o, Dwing the dataacquisition, standard reflections collected atregular intervals indicated that there was de-terioration neither in crystal quality nor cry$tal-lographic alignment. The data were corrected

for spherical absorption, Lorentz, polarizationand background effects and subsequently re-duced to structure factors. All crystallographic

TABLE 1 . CRYSIAL DATA FOR CANCRINlTE FROI , I BANCROFT,OI.ITAR I OT

c h e n l c a l C e l Ia n a l y s i s t t C o n t e n t s t t t M l s c e l l a n e o u s

5 t 0 2 3 4 . 3 5 5 l

A l 2 0 3 2 9 . 3 5 A l

F e Z 0 3 . 0 3 F e

i l so .01 l {g

C a o 8 . 1 1 C a

5 . 9 8 a 1 2 . 5 9 0 ( 3 ) A

i l a 2 0 L 7 . 6 6 N a 5 . 9 6

K z O . 1 0 K . 0 2

H z 0 ' 3 , 0 2 H 2 O r . 7 5

H z 0 - . 1 1

c a z 6 . 6 0 c r . 5 7

c ] . 2 r c l . 0 6

5 n . d .

v t t 9 9 . 5 5

c h e n l c a l f o r n u l a e u s e d l n r e f l n e m e n tN a 6 S l 6 A l 6 0 2 4 C a 1 . 5 1 . 6 C 0 3

c 5 . 1 1 7 ( 1 ) A

v z o z . a ( r ) 1 3

S p a c e G r o u p P 6 r7 r -

D e n s l t y C a l c . 2 . 3 7 g n / c .

u 1 0 . 2 8 c n - l

c r y s t a l S l z e s p h e r e0 . 2 n m d l a m e t e r

R a d f i o K a g r a p h l t en o n o c n r o n a t o r

T o t a l n o , o f I l 9 l 8

N o n e q u l v . 9 4 ?l F o l ) 3 o 8 s 5

F l n a l R ( o b s ) = 2 . 8" i ( l F o l _ l F c l ) / r l F o I

F l n a l R r ( o b s ) = 3 . 1. ( l r ( l F o l - l r g l l z /

Lulr ol2)rl2

r - I

6 . 0 2

. 0 3

. 0 3

i s i r e c l n e n 6 8 0 2 4 , I ' l c l i l a s t e r U n l v e r s t t y c o ' l l e c t l o n .F r o m 0 u n g a n n o n T o r n s h ' l p ' o n t a r l o .

t l re t qna lysJs , ' J . l ' l uysson, l ' l c l ' l as te r Un ivers l ty( H r 0 ' b y P e n f l e l d g r a v l m e t r l c n e t h o d ) .

t t t b a 6 e d o n A l + S l ' 1 2

CRYSTAL STRUCTURE OF A CARBONATE-RICI{ CANCRINITE 241

Fre. 2. Z,ero-level [00]-axis X-ray-diffraction photograph of cancrinite,showing strong substructure reflections with generally much weaker super-structure reflections in rows paratrlel to a* (p, = 30o, C\Ko radiation,Ni filter).

calculations were made using the X-RAY76Crystallographic System (Stewart et al, 1976),

A reflection was considered observed if itsmagnitude exceeded that of three standarddeviations based on counting statistics. Thisresulted n 942 unique reflections of which 855were classified as observed. A trial refinemenrof the crystal structure was made by the least-squares method using the structure previouslydetermined by Nithollon & Vernotte (1955) asthe starting model. Scattering factors for neutralatoms were taken from Doyle & Turner (1968).The refinement converged at a conventionalR-index of. e J/6 after varying the scale,positional parameters and anisotropic temper-ature-parameters. The refinement was con-strained according to the chemical formula(Table 1). The refined structure showed satis-factory geometry for the framework. The lengths

of bottr the Si-O and Al-O bonds were com-patible with ordered alternating AlOn and SiOatetrahedra, and the temperature factors for bothAl, Si and the framework oxygen atoms showednothing unusual. The large channel cation waspositionally well defined and had normal tem-perature-factors, in marked contrast to theanion gtoup (COs?-) position, which showedan extremely anisotropic thermal vibration withelongation parallel to the z axis. The small-cage cation, which lies on a special positionon the 3-fold axis, also showed large anisotropyparallel to the e axis, whereas the oxygen inthis cage showed a disc-shaped therrnal ellip-soid elongate perpendicular to the z axis. Theseobservations are in accord with those made byJarchow (1965) from a structure refinement ofsimilar material. A projection of this trial struc-ture down [0O1] is shown in Figure 3.

""Rc?r*o,02

N'/o6

eNA2

242 THE CANADIAN MINERALOGIST

Fro. 3. Diagramatic projection of the trial structure down [001], showing the site nomenclature and alsothe symmery elements for space group P6e

Obviously, the starting model is not adequateto reveal the details of the structure beyondthose already seen by Jarchow (1965). In orderto develop a more useful modeln it is necessaryto review the possible origins of the super-structures observed in the diffraction lrratternof sancrinite specimens. The superstructures aresimilar, in that they are one-dimensional innature and affect the z-axis repeat. The repeats,based on the superstructure, are consistent withintegral numbers of substructure repeats andcan increase the unit cell to as much as 16 timesthat of the substructure (Brown & Cesbron1973). The intensity of the superstructurc re-flections seen on X-ray-diffraction photographs(Fig. 2) are, in general, much weaker thanthose of the substructure. Ilowever, on electron-diffraction photographs, owing to the morecomplex diffraction process, they are muchmore apparent (Fig. 5) and can approach theintensity of the substructure reflections.

Rationalization of the superstructure is basedon two models, both of which are treoreticallyreasonable : 1) substitutional or positional or-dering (or both) of interframework cationsand anions (see Foit et al. 1973), and 2)periodic variation in the stacking sequence ofthe framework giving a sequence transitional be-

tween those of the cancrinite structure ABAB . . .and the sodalite structure ABCABC. . . (seeRinaldi & Wenk 1979). For the C0c'--richcancrinites, the first model appears to be themost appropriate, based on experimental obser-vations. The high+emperature work of Foitet al. (1973) on COa'--rich material showedthat on heating, the superstructure intensitydecreased with time, whereas that of the sub-structure remained constanl On prolonged heat-ing (Chen 1970), the position of &e super-structure reflections changed as a function oftime, indicating its potentially incommensuratenature. The above behavior is difficult to explainby changes in the stacking sequence, which in-volve the reorganization of the framework.Model 2 has been suggested for those caseswhere the intensity of the sulrcrstructure ap-proaches that of the substructure (Merlino &Orlandi 1977a).

Afghanite is an example of a cancrinite ofthis type; it has been assigned a tentative stack-ing sequence of ABABACAC by Merlino &Mellini (1976). Although the elestron-diffrac-tion pattern (Rinaldi & Wenk 1979) shows areasonably intense superstructuren howevern theX-ray-diffraction pattem (Bariand et al. 1968)shows the extra reflections to be very much

CRYSTAL STRUCTURE -OF A CARBONATE.RICH CANCRINITE

weaker than tlose of the substructure. Rinaldi& Wenk (1979) observed lattice fringes withthe TEM for both afghanite s1d flanzinite sad,following the proposals of Merlino & Mellini(1976) and Merlino & Orlandi (1977a, b), in-terpreted these in terms of differing stackingsequences. Cancrinites, which have been asso-ciated with model 2, are in general SOr2--richand COg'--poor. As yet there have ben nosuccessful structure refinements of the proposedpolytypes; published R-indices vary from 16 to3OVo (Rinaldi & Wenk 1979, Baiand. et aI.1968, Barrer et al, L97O, lN'f,azzi et al. L98l).

Foit er al. (L973) also noted that the super-structure reflections were still observable afterthe heating experiments, although greatly re-duced in intensity. It is possible that such re-sidual intensity could perhaps be assigned to atype-2 model. More recently, prolonged heatingat 4O0oC of sacrofanite (Burragato et al. l98O)was shown to have no effect at all on thesuperstrusture, which would suggest that, inthis case, it was due in total to a typ-2 odgn.This material is SOa'9--rich with only minorCO: and HrO and, therefore, differs from theCOa'--rich cancrinites, which readily.lose COgand H:O on heating. In order to determine therole of stacking variations in the cancriniteunder study, it was decided that the structureshould be imaged using high-resolution trans-mission electron microscopy (HRTEM) so that

any periodic variation in the stacking sequencecould be incorpororated into the structuralmodel.

Hrcu-Rpsoruuox TReNsulssroNFr ecrroN Mtcnoscopy

In order to see the stacking sequence, asection sentaining the 6s axis is necessary; themost useful section is parallel to (010), i.e.,perpendicular to [210]. Figure 4 shows aschematic view of the f,ramework down [210],illustrating a hypothetical example of a stack-ing variation ABACBA... that may be ob-served in this projection.

The microscope used was a JEM 1@B oper-ating at 10O kV with objective aperture c€ntredabout the incident beam of 5O g,m (j.e., radiusof * O.42 A-'), u 15O pm condenser apertureand a 200 to 500K magnification factor. Thespecimen wns prepared by ion-fhinning asingle-crystal section obtained from a polishedthin section having the crystal oriented sub-parallel to (O10). Twenty-nine substructur€beams plus the included superstructure intensi-ties were used to produce the bright-field imageshown in Figure 5. The electron-diffractionpattern (Fig. 5) corresponding to the imagewas photographed both before and after imag-ing and was not observed to change. Note thatthis pattern shows 001-type substructure re-

B

A

B

A

cB

A

B

AFrc. 4. Hypothetical diagram of the Al/Si framework projecrted

[2101. Shown is a C-type sfasking fault in the regular ABAB..of stacking sequence.

down. type

244 THE CANADIAN MINBRALOGIST'

Frc. 5. High-resolution ransmission electron micrograph down the [2101. Inset at lower left is theelectron-diffraction pattern used in the imaging process' Inset at lower right is the scaled and orient-ed representation of the calculated image. Inset at top left is a projection of the trial structure down

t2101. The^ rectangular boxes correspond to one substructure cell, the small edge of which is approxi-mate ly5Ainmagn i tude.

CRYSTAL STRUCTURE OF A

flections when / is odd; these are forbidden inspace group P6a and were not observed on theX-ray-diffraction photograph (Fig. 2). On titt-ing the specimen sligbtly, they changed intensityand, therefore, were interpreted as artifacts,mainly due to multiple diffraction, with per-haps a small part due to the superposition of asuperstructure reflection.

Also inset in Figure 5 is a projection of thetrial structure down [210], which is scaled andoriented so as to superimpose directly on arelevant part of ths electron micrografh. Thepositioning was verified by comparing a cat-culated image with the one observed. Calcula:tions were made using the multislice method(Goodman & Moodie 1974, Cowley & Moodie1957) with a program developed by OKeefeet al. (1978) and O'Keefe & Buseck (1979)for the calculation of images of minerals.

Owing to the extreme instability of the sub-stance in the electron beam, it was not possibleto experimentally obtain the usual through-focusseries of images. Instead, calculations were

a',!o2

CARBONATE.RICS CANCRINITE 245

made for a variety of foci in addition to thick-ness. Systematic trends emerged and it waspossible to match the observed image shownin Figure 5 with a thickness of approximately50 A at an underfocus of -900 A. fn Ais image,areas of light contrast correspond to regions oflow electrostatic potential. This calculated imageis also shown correctly scaled and oriented asan inset in Figure 5.

Careful study of the image revealed that thestacking sequence was of the type ABAB...,with neither systematic deviations nor evenrandom stacking faults. Therefore, in this case,a model-2 contribution to the superstructureintensity could be eliminated completely.

RsrrNnMENt oF TrtE Srnucrurs

It has been experimentally established thatthe appearance of the superstructur€ in thissubstance is not due to alternate 5laqking se-quences; furthermore, from the trial refine-ment, it was determined that the AllSi frame-

"@ @."'&-@

88:-x'-Frc. 6. Fourier sections of electron density tlrough the interframework

atom sites derived from the observed structure factors and calculatedphases.

A\ \ \ - - - - - - - l / /'F/

/A\v@v

U6 THE CANADIAN

work was positionally well defined; the super-structure thus must originate from substitu-tional or positional ordering (or both) of thenon-framework ions. Large-scale Fourier mapsof electron density were prepared for the chan-nel and cage volumes using the observed struc-ture-factors and phase information from thetrial refinement, in order to detect details thatwould lead to a better model of the structure.

The envhonment of the small cage was ex-amined; the electron density on the'anion siteO6 (Fig. 6) was se€n to be ellipsoidal in yzsections but triangular in ry sectionS. This tri-angular feature was also noted by Jarchow(1965); his procedure of moving the atom offthe 3-fold axis and disordering it was followed.The cation position NA1 shows an electrondensity distributed as an ellipsoid of rotationabout the 3-fold axis; it is elongate down thisaxis, but not sufficiently extensive to warrant

TABLE 3. OCCUPAI{CIEs, POSTTTOML AND ISOTROPIC I}IERIOL PARAI.IEIERS

Framrk atms

aton equl- slte- 6ffi iffient!o-;F

-

tl on

L z Elequrv)A2

. 4 0 4 3 ( 2 ) . 6 s 7 4 ( 5 ) 1 . 1 6

.5635(2) .728r (7) 1 .59

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

.3566(2) .043e(5) 1.25

.4r25(r) 314 .54

.4r2s( r ) .7510(3) .50

Non-frammrk atomt

t ch@lcal symbol n ls vacancy.ch locatsd ln channel.cg located ln cage.

TABLE 4. AlrlsotRoptci nuprMtunt t6x6tr61gp5 x 104

Frammrf ttom

MINERALOGIST

positionally disordering the atom lryPonsibleior it in more than one position. Therefote,this atomic position was kept identical to thatof the trial structure.

The large channel also was investigated; thecation position approximated an isotropic dis-tribution of density, with no indication of sys-tematic positional disorder. However, the aniongroup COo!- showed extreme anisotropism inthe distribution of density, with the direction ofelongation parallel to the z axis. In the rysections the individual atoms of the groupshowed reasonably circular cross-sections ofdensity. In order to account 1e1 this distribu-tion of density, the position yas split into twononequivalent'positions 1.6 A apart down &ez axis. Refinement was continued using themodified set of atom positions and, on thefinal cycle, after varying all refinable para-meters, the structure converged with a conven-tional R factor of 2.87o.

Fourier maps were again prepared using theFo values and the new phases. The maps nowshowed two well-separated maxima for theCO"s- gtoups (Fig. 6), in accord with thepostulated positions, and three maxima for the06 position. All other atom positions were ex-amined for positional disorder, but none wasfound, and the average structure wul con-sidered to the fully refined at this point. Table 2lists the observed and calculated structurefactors together with their phase angles; thistable is available at nominal charge from Dpos-itory of Unpublished Data, CISTI, NationalResearch Council of Canada, Ottawa, OntarioKIA 0S2. Final positional parameters are shownin Table 3, and the anisotropic temperaturefactors are presented in Table 4.

DEscRrpttoN oF THB Srnucruns

The general features of the structure havebeen described in the introductory paragraphs;only further details will be presented here. Im-portant interatonic distances are shown in Table5, and interframework angles in Table 6. Theaverage tetrahedral bond-lengths (fable 5), 1.612and 1.733 A, can be assigned to Si*.o and Al-Orespectively. A calculation f-ollowing Baur(1978) shows that the 1.612 A distance cor-responds to full occupancy by Si. Therefore,as the ratio of Al:Si is 1:1, by implication the1.733 A distance correspond$ to full occupancyby Al. The framework is therefore fully ordered.Bbnd-valence calculations (Brown & Shannon1973) show that the bond-valence deficiencyon the framework oxygen atoms is predominant-ly satisfied by the cations on the NA2 position,

0l020304n't2

000

stAI

051 c .38 0+.62 [ ] .0s72(8) .1163(8) .6 i29(25) 2 .8 ch to52 c .38 0+.62 U .0587(8) .U94(8) .9134(30) 3.4 ch06 c .33 0 .6246tL2\.3243(42).6875(25) 6.3 caCl a .38 c+.62 [] 0 0 .6729(25) 2,7 chC2 a .38 C+.62 U 0 0 .9134(30) 4.3 chl1A1 b 1.00 lb 213 u3 .1339(U) 3.9 cgM2 c .67 Nar.25 Ca .1232(1) .2490(1) .2959(3) 1.5 ch

+.08 U

l{on-fr@srk atoEs

uu v22113(e) 218(10)221(10) 115(8)1r5(e) 220(10)r59(10) 225(1r)55(3) 78(3)72(3) 86(3)

124(34) 127(33)147(40) 144(38)e82(1rs) 1073(155)207(60) a)7(60)112(52) rr2(52)312(r0) 312(r0)111(4) 179(5)

atd

020304n12

05105?06a t

c2ltAlt{42

Ul:110(8)268(13)e9(11)9X(10)65(3)7o(3)

o(38)5(4e)

-4e(56)000

-18(5)

801(86)1004(98)332(60)619(16r)

r41t(348)84e(34)271(8)

utl5(8)

14(12)35(8)13(8)2(4)0(4)

uzl17(e)12(11)45(e)45(e)3(4)6(4)

55(29)86(34)

714(201)r03(3r)56(26)

156(5)e4(4)

42(3e)-83(4e)-53(104)

000

-12(5)

t yhsm todperature factor . exp [-2lr!1 ,!r(ut5a1a3hgh3)J

CRYSTAL STRUCTURE OF A CARSONATE-RICII CANCRINITE 2/+7

IAEIE 5. SELECTM IMERAMI,IIC DISTANCESI AfiD BOI{D SIREI{GTI{ uilrTs)fibond A Bond strength (vu) bond

":!l lfffi{iJ l:Blgllir ',:BL-Sq 1.61e(s) r .oogis

' _03

,;ll +ffli+ ,0,",*18#L dll*calculated

(s.l) 1.616 Expected* 4

*'-31.x I 3:333[3] B:ifl[Bl c,-051 x 3:33; Z:3iiti3l o.zoers)' cz-o5z x 3

r,rean ror [8] TJl&- rotur l*330t4l 2.421 ExDect€d L

A Bond strength (vu)

1 .728(3) .762(5)1 .7U(3) .783(5)r .741(3) .738(5)1 .747(31 .721(51I;71l5- Totat 3mT_'

Erpected 3

1.258(9)

1.302(9)

octahedraltrlgonal blpyramld

Na2-01-03-04-o5la-osr3-051D

2.507(3)2.427 (4)2,444(312.440(11)2.431(21)2 .4r2(V l2:tt4*2 .859(3)2 .891(6)TSrz"-

2.507(3)2.427 (4)2.4M(3)2.414(14)2.424(21)

W2.8se(3)

+8#r!L

l,lean

-04ilean

0.154(0)0 . 1 7 7 ( 1 )0,172(0)0 . r73(3)0 .176(6)0 .183(3)

0.088( o)0.084(0)

rotal TIZoF-Expected 1.17

.088(0)

.084(0)ToIET-TZIZ

Expecied 1.17

ila2-01._03-04-oszP-oszP-or2D

lilean-03-04

l'lean

a E a b o v e : b " b e l o waccording to Baur (1978) for st te f l i led r l th Slu n l v e r s a l a r v e sexpected fron slte populafion (see Table Z)

IABLE 6 . SELECTED FRAI . IE I , IORK AI {GLES

which lie within the channel, with the exceptionof the oxygen on the 02 position, which is tooremote and satisfied solely by the cage cation.The calculation shows the bond-valence defi-ciency on 02 to be 0.17 valency units (v.u.).The NAI position is closely co-ordinated tothree 02 oxygen atoms and the oxygen at 06,which is part of a hydrogen-bonded water mole-cule. These hydrogen bonds are weak and,according to Brown (1976), have a valency ofless than 0.1 v.u. As the 06 . . . .O distance mustbe greater than 3 A, this valensy must be dis-persed over five framework oxygen (3 x 02,01 and 03) that are within hydrogen-bondingdistance. The directionality of the hydrogen

bonds formed is the probable cause of the rela-tively well-resolved positional disorder of the06 oxygen atom.

Both the population refinement and the bond-valence sum show the NA1 site to be fullyoccupied by Na+. It is unlikely that this struc-tural position will ever be systematically de-fective, owing to 02 charge requirements, un-less there is a corresponding increase in theSi/Al ratio of the framework. Furthermore,owing to the unresolved positional disorder ofthe NAI and (}6 sites parallel to tle 3 sxis,the cage cations and anions will not contributeto the one-dimensional superstructure of thiscancrinite.

The configuration of the interchannel cationNA2 and anion groups positionally conformsto space group P6s symmetry. I{owever, asthere is only one cation position, the refinementmust show this site to be completely disorderedwith respect to Na, Ca and vacancies.

Both the site-population refinement (Table 3)and bond-valence sums (Table 5) confirm thechemistry (Table 1) of the NA2 site. The COaz-groups lie on two nonequivalent 2-fold posi-tions; the population refinement shows theseto be equally occupied by O.4 of a C\cs2- group.Because of the close proximity of the positions,only one can be occupied at any one timeand, therefore, the maximum possible ocsupancyfor total disorder would be 0.5 groups per site.Bond-valence calculations (Table 5) about the

0 l - T t - 0 2

- 0 40 2 - I t - 0 3

-0403- T l - 04

I'le an

1 0 7 . 2 ( r l1 0 e . 1 ( 2 )1 0 6 . 0 ( 2 )1 r 4 . 7 ( 2 )1 1 4 . 6 ( 2 ' )1 0 4 . 8 ( 1 )Toe-:?**

t e t r a h e d r a l

1 0 8 . 2 { 2 ) 0 r - ' t 2 - o 21 0 7 . 1 ( 1 ) _ 0 31 1 0 . 5 ( 1 ) - 0 4112.4(2 ' 02- ' t2 -031 1 2 . 2 ( 2 ) - 0 4I 0 6 . 5 ( 2 ) 0 3 - T 2 - 0 4T0-t5- ilean

b r l d g l n g

T 1 - 0 1 - T 2 1 4 2 . 3 ( 2 \T 1 - 0 2 - T 2 1 5 2 . 8 ( 2 \T r - 0 3 - T 2 t 3 z . g l 2 \rr-04-rz nz.glzl

l , fean TO.z-

THE CANADIAN MINENALOGIST

cation site NA2 show that the two possible co-ordinations of NA2 (depending on which COg'-position is occupied; see Fig. 7) are electrostati-cally equivalent. However, the refinement doesshow a shghtly larger temperature-factor forthe COa'- group associated with octahedral co-ordination, which could, rn turn, be interpretedas a slightly higher occupancy due to a correla'tion that exists between these two parameters.However, as both Na and Ca are usually ir-regularly co-ordinated, a preference is not ex-pected in this case. The substantial temperature-factor component parallel to the z axis for theCOro- is probably due, in part, to a more subtlepositional disorder, depending on the type ofcation (Na or Ca) or vacancy that it is co-ordinating. However, there is no marked aniso'tropy of the NA2 site, indicating that the frame-work tends to be insensitive to the tyln of cationor vacancy on this si!e. Chemical variation onthe NA2 site is accommodated solely by the

positioning of the anion groups within the chan-nel.

OnrcrN oF THE Surensrrucrune

According to the space-group symmetry, thechemical formula shows that there is a defi-ciency in each NA2 cation site of 0.08 ions anda deficiency of double that in the COas- $oup.Therefore, the substitutions that must be con-sidered are Na d Cad vacancy for the NA2position and COa-<2 yacancy for the channel-anion positions. Superstructures might easilyarise from ordeiing of such vacancies. Aspreviously discussed, it seems unlikely that thecage environment contributes significantly tothe superstructure. However, owing to the va-riety of orientations possible for the water mole-cule, it is conceivable that these can indirectlystabilize certain vacancies in the large channelby providing extra charge to the 01 framework

Frc. 7. Stereographic drawing in tle vicinity of the NA2 cation site showing the position o-f framework

uod "g

r-Jgr6up o*yg"o- uio-t co"rainutiog this site for tle two arrangiements of the COrs-

groups.

CRYSTAL STRUCTURE OF A CARBONATE-RICH CANCRINITB

pz

1o.24 t5.56 20..4 3072 55.84 rKr96

x o x o t l o r o t r o , o

249

A

!uPar$flJcfirneporlod

E vccontx tullo tullo full

Frc. 8. Ordering pattern used for tle generation of the ca,lculated superstructure, tle intensities of whichare compared with those observed in Table 7.

c€ Ptonecq pbneCoz} ploneNor done

oxygen when required through hydrogen bond-ing. By far the most important contribution tothe superstructure is from the arrangement ofthe interchannel cations, anions and vacansies.

The period of the superstructure along z is4O.94 A; from the results of the chemical anal-ysis (Table 1), the channel contains approxi-mately 32 Na+, 12 Ca'+ and 13 COs2- persupercell. The stoichiometric composition shouldbe 48 (Na+ * Ca,+; and 16 COa2- groups(32 positions half-occupied). Therefore, thenature of the superstructure is controlled by3 to 4 COa2--group omissions with subsequentrearrangement of cations and vacansies on theNA2 position.

In order to generate a likely pattern fromthe great number of possibilities, assumptionswere made so that the problem could be con-verted to a one-dimensional calculation. Thiswould make a computer simulation of all thesuperstructure intensity-patterns feasible. If weshoose to match only 0O/-type reflections, weare concerned only with an arrangement ofpoints of differing weigbt of electron densityalong the z axiso these are in known positions.In order to simplify the problem still furtherwe can consider only four types of points cor-responding to 3Ca, 3Na, 3COa or 3 vacancies,for neutral atoms points of weight 60, 33, 30, 0,respectively. Using the superperiodic spacing(40.94 A), the known positions of the points,and X-ray and electron scattering factors forneutral atoms (Doyle & Turner 1968), we cancalculate the intensities of tle fr)l reflectionsusing the standard structurc-factorequations.After correcting for Lorentz and polarizationeffects, these calculated intensities can be com-pared directly with the observed patterns ofintensity.

As we know the number of points involvedand with the assumption that they are only ofthe types described above, a computer program

was written to generate all possible combina-tions. The best match in pattern is showndiagrammatically in Figure 8 and the corre-sponding match in intensity in Table 7. Thecomparison is done only on a semiquantativebasis; a closer fit could perhaps be attained byallowing weights to vary and then optimizingthe difference between observed and calculatedintensities, perhaps by the least-squares method.However, eying to the difficulty of measuringenough of tlese weak superstructure-reflectionsto obtain good statistical integrity, it was not

TABLE 7. @sERvm AND cALcULATED supERsrRucTURE tlrrtslrtEs (00r)r

X-ray dlffractlon

observed cal cul ated

I

3 hldden4 b v5 lncldent6 bem7 scatter

15 1916 _----- SUBSIRUCIUREL7 hlddenl8 by rhlte19 radlatlotr20 streak

Electron diffractlonlt

observed calculated

hldden byIncldentbeam scatter

100 10020 20

1

l011L213 100 10014 50 55

I .-- SIBS1RUCIURE (EXTINCT) present _ 4o ^

9n

1 1

82

24

02I

2L22 62 3 0 024 - stBstRucwR[ (ExIn{cT) _ 2252621 10n29 203031

4140

28186

00020

32 - suBslRucn RE

i t lnds bas m super-period of 40.94 A.tf ylsually estlmted fM photographs taken for varylng lengths of

exposure onty smt-quanttt! i lve. Blanks In tdble corresDond tounobserved lntensltJr values. DynaElcal aspects of electiondlffractlon not cmsidered.

250 THE CANADIAN MINERALOGIST

possible to do this with this substance. Even so,the fit is sufficiently good to show that a rep-resentative superstructure can be generated solelyfrom the ordering of interchannel ions.

CoNcl-ustoxs

We conclude from this work that a usefulmodel has been developed to investigate can'crinite-type structures and, by association, cer-tain aspects of the structure of the sodalitegroup of minerals. The absence of stacking se-quences different from the type ABAB... hasbeen experimentally established and, therefore,in this case, precludes their role in the genera-tion of the observed superstructure. The posi-tions and intensities of the sulrcrstructule re-flections can be adequately relationalized bysubstitutional disorder on atom sites that arepositionally defined by the P6a slmmetr!. Apossible arrangement for Na+, Ca2*, COgt- andvacancy over the available sites according to theresults of the chemical analysis has been estab-lished through computer simulation of the 001superstructure intensities and semiquantitativecomparison with the observed pattern. However,a more rigorous approach using modulationtheory may be more fruitful for explaining thesuperstructures of more complex cancrinite-typematerials.

ACKNoWLEDGEMENTS

Financial assistance was rendered by anNSERC operating grant to H. D. Grundy andby an NSF grant (EAR 7916315) to P. R.Buseck. Electron microscopy was performed inthe Arizona State University Facility for HighResolution Electron Microscopy, establishedwith support from the NSF Regional Instru-mentation Facilities Ptogtam, grant CHB 79-16098. In particular, we thank Dr. P. R. Buseckfor his support and encouragement and alsoDr. I. McKinnon and Mr, M. J. Wheatley fortheir patience and instruction in the use of theelectron microscopes.

RrnsnnNcrs

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CRYSTAL STRUCTURE OF A CARSONATB-RICII CANCRINITB 251

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Received- Qaober 1981, revised manuscrlpt ac-cepted March 1982,