AmericanMineralogist, Volume63, pages448460, 1978
Is eachanalcime different?
Ftonnnzo Mrzzt C.N.R. Centrodi Studioper la Cristallografa strutturale cf o Istituto di Mineralogiadell'Uniuersilh, Pauia, Italy
AND ERMANNo GALLI Istituto di Mineralogiae Petrologiadell'Uniuersitit Modena,Italy
bstract
Precedingstudies assigned a cubic symmetry(Ia3d) to analcime,even if possiblelower symmetriesare suggested from contradictoryevidence: e.g., the occurrence of opticalanoma- liesand the presenceof forbiddenreflections in X-ray photographs. In an attempt to check the true symmetryof analcime,the crystal structuresof seven opticallyanisotropic and apparentlyuntwinned crystals from variouslocalities were refined (finalR from 0.02to 0.07for the observedreflections). They were tetragonal (I4r/acd, with cell edges:o ) c in four samplesand a ( c in one sample)and orthorhombic(/bca). These diflerentsymmetries follow from the differentordering of Al in eachof threetetrahedra and from the relateddifferent occupancy of the nearestNa site.Neither tetrahedra occupied only by Al (maximumAl fraction0.5), nor completeoccupancies of Na sites(maximum 0.84) were observed. Simplerelationships were obtained between Al fractionsin tetrahedraand (1) occupancies of the nearestNa sites,(2) latticeparameters, and (3) intensitiesof tripletsof X-ray reflec- tions. A hypothesisis given regarorngthe possiblederivation of all the crystal structuresof analcimefrom the superpositionof three different orientationsof one basic tetragonal structure,with an Al fraction of 0.5 in two equivalenttetrahedra and no Al in the third.
Introduction cimesworthy of a detailedX-ray single-crystalinves- The crystalstructure of analcime,NaAlSirO.. HzO, tigation. was determinedby Taylor (1930)and refinedmany times (Calleri and Ferraris, 1964;Knowles et al,, Experimental 1965;Ferraris et al.,1972),butalways with reference Thick sectionswithout coverglasswere prepared to the cubic spacegroup la3d, althoughit has been from nearlythirty analcimesamples, and we selected known for a long time that many analcimesexhibit with the polarizingmicroscope those samples which somedeviation from cubicsymmetry (Coombs, 1955; were definitely anisotropic at least in some parts. Harada and Sudo, 1976;and quoted references). These non-cubic crystals were always poly- Before our work little was known about the real syntheticallytwinned, and hencewe were forced to symmetryof non-cubicanalcime. Mazzi et al. (1976) selectportions of twins with singleindividuals large showedthe symmetryof non-cubicleucite to betetra- enough for single-crystaldiffractometry and with gonal l4r/a and consideredit a possiblesymmetry sharpcomposition planes. alsofor non-cubicanalcime. Harada and Sudo (1976) As shown by Mazzi et al. (1976) for the related suggesteda monoclinic symmetry as probable for mineral leucite, both merohedricand pseudo-me- analcime,because the extrapolationof B valuesin the rohedrictwins arepossible, and only the latter canbe wairakite-analcimeseries gives A = 90"12' for pure recognizedand avoidedduring the data collection. analcime.We thereforeconsidered non-cubic anal- The following sevensamples were selected for the
0003-004x / 78 / 0506-o148$02. 00 448 MAZZI AND GALLI: ANALCIME completecollection of intensitydata, as typical repre- The symmetryof the intensitiesand systematicex- sentativesof about thirty specimenssubmitted to a tinctionsled to spacegroup I4r/acd for samplesANA preliminary X-ray single-crystalexamination (the l, ANA 2, ANA 3, ANA 5 andANA 6, andto space numberof the specimenin the "Museo di Mineral- group lbca for ANA 4 and ANA 7. These space ogiadell'Universiti di Modena" is in parentheses): groups are compatiblewith the presenceof diffrac- tions (hlh:2h t I : 4n -l 2) observedin the powder ANA 1: Veselinear t]sti nad Labem(also known in patternsand alsodetected in somesingle-crystal pho- German as "Wesselnbei Aussig"), Bo- tographs. These reflectionsviolate la3d symmetry hemia,Czechoslovakia (16-2-21, 47). Crust and wereconsidered for a long time to beevidence of of vitreous transparentcrystals, up to 5 deviationfrom cubic symmetry.Actually the major- mm, intergrownand twinned,filling the ity of thesereflections were "unobserved"in all ex- veinsand coveringa freesurface of an albi- aminedcrystals; when present they were in agreement tizedbasaltic rock (Rammelsberg,1858). with the correspondingspace group (e.g.020. 0100, ANA 2: Val di Fassa,Trento, ltaly (16-2-21,2l). 424 werepresent both in the tetragonaland ortho- Crustof milky whiteand pale pink crystals, rhombiccrystals, whereas 002,0010, 42werc absent up to I cm across,densely intergrown with in tetragonal crystals, but present in the ortho- calciteon a weatheredalkali-basaltic rock rhombic ones)with no evidenceof broadeningor (Braccio,l95l). splitting. ANA 3. ANA 4. ANA 5 and ANA 7: Alta Val Following the X-ray data collection,electron mi- Duron, Val di Fassa,Trento, Italy (all from croprobe analyseswere made on the samecrystals $pecimen16-2-21, 100). Vitreous colorless with an Anl-Sprvreinstrument operated in the wave- transparent crystals, featuring irregular lengthdispersive mode at l5 kV, 0.1pA beamcurrent prismsup to 7 mm long, in radial fibrous (10 nA samplecurrent) and usinga defocusedbeam aggregatesfilling the cavitiesof a Middle (spotsize -50 pm), yieldingthe atomicproportions Triassicweathered basaltic andesite (Mon- reportedin Table 2. On-linedata processingbased eseand Sacerdoti.1970:Yezzalini and Al- upon ZAF corrections(Ziebold and Ogilvie, 1964) berti, 1975). usedAlbee and Ray (1970)correction factors. Syn- ANA 6: Isola dei Ciclopi, Catania,Sicily, Italy (16- theticplagioclase glass, natural albite,and microcline 2-21, 46). Vitreous transparenteuhedral wereused as standards for Si,Al, Ca, Na, and K. Fe, trapezohedron,2 cm across,in a basaltic Mg, Sr, and Ba were also analyzedfor but found to rock (Di Franco, 1926;Knowles et al., be absent.The valuesgiven in Table 2 are the aver- 1965;Ferraris et al., 1972). aged analysesof three points for each specimen, The crystalsfor X-ray measurementswere ground which were homogeneousthroughout. Water loss into spheres,whose dimensions are given in Table I was not determinedbecause of the paucity of the togetherwith otherexperimental conditions. availablematerial. Unit-cell dimensions and diffraction intensities were measuredat room temperaturewith a Philips Refinements 1100 automatic single-crystaldiffractometer and The atomic parametersgiven by Ferraris et al. graphite-monochromatizedradiation. The latticepa- (1972), properly adapted to the 14,/scd and lbca rametersgiven in Table 2 were obtained by least- spacegroups, were used as starting coordinates ofthe squaresrefinement ofthe adjustedangular settings of refinementscarried out with a modified versionof 18reflections. the least-squaresprogram Onrls (Businget al., 1962). Diffraction intensitieswere measured in the @-scan The scattering-factorcurves were calculated from the mode,and backgroundmeasurements were made at values given in International Tablesfor X-Ray Crys- both sidesof each reflection.Three standardreflec- tallography(1974, p.99-l0l) for neutralatoms. A tions, monitored at three-hourintervals, did not secondaryextinction correction(Zachariasen, 1963) show significantchanges in their intensitiesduring was includedin the refinementsof the form: the data collection. Intensitieswere correctedfor F""1"(corr): F.a./(l * Lorentz-polarizationeffects and for absorption,then 0gloo") convertedto lFon"l and o(Fop")according to Davies where Fcar" is the calculated structure factor, and Gatehouse(1973). The reflectionswith lF"o"l' F""r"(corr)the value correctedfor the secondaryex- lessthan 3o(ffioJ were considered as "not observed". tinction, 1o6"the observedintensity and g the ex- MAZZI AND GALLI: ANALCIME
Table 1. Summaryof experimentaland refinementdata
ANA 1 ANA 2 ANA 3 ANA 4 ANA 5 ANA 7
Sphere diameter (m) O.O84 0.1 14 0.174 o.236 o.r92 o. r98 0.236 Radiation MoKC CuIG MoKd Mol((X MoKC CuKCI MoKd , -1. AR (cm ) O.O3O 0.408 0.063 o.085 o. 069 o.7o9 o. 085 Maximum 2@(o; 60 13O 60 6o 60 13Ci 60 Scan width (o) 1.0 2.5 1.O 1.4 2,5 1.O Scan speed (o/sec) o.ozs o.o5 o.o333 o.05 o.o25 o.0625 o.05
Time for each background (sec) 5 IV J 7 ) R< Total measurements 11OO 670 I 106 449r 1111 1263 2630 Total unique reflection" 938 551 94r L9r2 942 554 1874 observed reflections t12> :g(12)) +AS 434 662 r392 677 453 t352 Maximum percent variation in 2.9 2.r 3.6 3.5 3.3 t.7 2.5 standard reflection intensiti-es Anisotropic refinenent cycles 28 ,9 ,9 28 rQ 28 28 Extinction parameter (exrOd) 67(4g) 6350 3) 1060(3 I ) r874(18) r51o(23) L6a3t(233) 506(9) Final R (A11 unique reflections) O.151 0.064 0.06r o.o4r o.o52 o.o42 0.048 Fina1 R (Observed reffections) 0.067 o. o43 o.037 o.o24 o.o3o 0.033 o.o29
E.s.d.rs on the last significant digit in parentheses.
tinction parameterto be refined(Table I ). Becauseof ratios,calculated according to Jones(1968) from the the use of a graphite monochromator the expression updatedaverage Z-O distancein each tetrahedron, for B given by Zachariasen (1963) was modified as gavea sum of the products(Al fraction) X (multi- follows: plicity) much lower than the unit-cellcontent of l6 Al; hence a new line for the deduction of the Al o_- | dA* | Q*ccsa2| v * ar' fraction from the T-O distanceswas drawn through "i"n- OT7;""8 the points 1.609(Al fraction : 0 in qrrartz after wherel* is the absorptionfactor, p the linear ab- Zachariasenand Plettinger, 1965) and 1.648,{(Al sorptioncoemcient (for analcime:p(Mo) : 7.19cm-1 fraction : 0.333in cubic analcimeafter Ferrarise, and p(Cu) : 71.58cm-'), Q is the cosineof the al., 1972).The useof this functionallowed the deduc- diffraction angle in the graphite monochromator tion of Al fractionsin accordancewith the chemical (0.95563for Mo and 0.80028for Cu) and d is the composition. Braggangle. Nine further least-squarescycles utilized all dif- Nine least-squarescycles for diffractionswith F > fractionswith ^F > 3o(F) and wererun in the same l2o(F2) were run in groups of three.The first cycle sequenceas before. Refinements were thus completed refinedthe scalefactor, the atomiccoordinates and with the final shifts in the parametersless than the the occupanciesof Na and HrO-bxygen;the second standarddeviations. A lastcycle (with positionaland one refined the extinction parameterand the third temperatureparameters as variables)was run to cal- again refinedthe atomic parametersand the aniso- culatestandard deviations for distances,bond angles, tropic temperaturefactors. At this stagethe AllSi and thermalellipsoid parameters. ratios for singletetrahedral sites were calculatedac- Differenceelectron density maps were carefully in- cording to Jones(1968) from the Z-O bond dis- spectedto searchfor hydrogenatoms of the water tances,to introducemore suitablescattering factor molecule,but without reliableresults in most cases. curvesin the subsequentleast-squares cycles. Only in ANA I and ANA 2 did the differencesyn- Nine more cycleswere calculated in the sameway thesesshow a diffusemaximum at about 0.120.21 for the diffractionswith F > 4o(F); at this stagethe 0.15(multiplicity 36 in spacegroup I4t/acd). It corre- refinementsof the population parametersfor water spondsto the siteH(2) 0.10980.19520.1494 (multi- showedfull occupancyin all samplesand this param- plicity 96 in spacegroup la3d) givenby Ferrariset al. eter was fixed in subsequentcycles. The new Al/Si (re72). MAZZI AND GALLI: ANALCIME 451
The observedand calculatedstructure factors are comparedin Table31. Final atomicparameters and equivalentisotropic temperature factors are listedin Table4. Anisotropicthermal parameters are given in Table 51, and therlnal ellipsoidsdata in Table 61. Bond distancesarid anglesare listed in Table 7 (Si,Al-O framework),9, and l0 (Na octahedra). The resultsof the refinementsare in good agree- ment with the stoichiometricformula, with the ex- ceptionof samplesANA I andANA 2, whichshow a lower Na and Al contentboth from the microprobe analysesand from the refinements(Tables 2 and 8). Discussionof the structure The crystal structureof non-cubicanalcime (Fig. 1) is topologicallyidentical to that of the cubicphase dbscribedby Taylor (1930),Calleri and Ferraris (1964),and Knowleset al. (1965). None of the frameworkatoms shows significantly Fig. l. Thelowerpart (from 2 - 0 to z - l/4) of theunitcellof anisotropicthermal vibration. The Na atomsdisplay non-cubicanalcime, projected along c. Atoms arecoded according markedanisotropy, with the maximumdisplacement to an orthorhombicstructure; numbers in parenthesesgive the z in the directionof the watermolecules and themini- parameters(X 100).The H positionsare thoseassumed for the mum one towards the nearestT sites.The thermal tetragonalsamples ANA I and ANA 2, wherethe Na 2 site is vibrationsof the water moleculegive an elongated nearlyempty. rotation ellipsoidwith the longestaxis perpendicular All the interatomicdistances and anglesagree well to the planeof the threenearest Na atoms. with the valuesgiven in the literature.The Na-O distancesrange from 2.469to 2.555A,the Na-IZ I distancesfrom 2.319to 2.478A(Table 9). When the To receivea copy of Tables3, 5, and 6, orderDocument AM- 78-071from the BusinessOffice, Mineralogical Society of America, Na-siteoccupAncy (Table 8) approaches100 percent Suite 1000lower level, 1909 K Street,NW, Washington,DC (for example,N{,2in ANA 7, Na I in ANA I and 20006.Please remit $1.00in advancefor the microfiche ANA 2), thd Nt-O and Na-Z distancestend to
Table2. Crystaldata
ANA 1 ANA 2 ANA 3 ANA 4 ANA 5 ANA 6 ANA 7
Crystal system Tetrag. Tetrag. Tetrag. Orthorh. Tetrag. Tetrag. Orthorh. s (i) 13.723(7) 13.727e) 13.7 29 Q) r3.733(1 ) 13.7 28 (L) 13.72r(L) 13.7270) !. (A) 13.729(1) t3 .714 0) (A) 13.686(1o) (r) (2) " 13.686(3) t3.709 Q) 13.7 12 13.722(r) 13.735(1) L3.7 40 ior.'." (i3 ) 2577.4 2578.9 2583.9 258 5.3 2586. o 2585.8 2586.6 Space group IL 'l',/ acd 14 acd IL /acd Ibca 14 acd 14./ acd Ibca r/ r/ I Atomic ratios* 5l- 32,74 32.85 3r.94 32.31 32.o6 31.65 32.34 A1 t 5.44 t 5.25 16.14 15.66 16.o6 16.33 15.59 Na r4.78 14.88 r5.74 L5.67 15.41 15.15 r5.7t K o.02 o.02 o.o5 o.o6 o.06 o. o5 o.08 Ca tr tr o.03 o.03 o.08 U. OU o. 03
* Calculated on the basis of p6 oxygens. Ba, Sr, Mg and Fe were also analyzed but found to be absent. Water loss was not determined. (Analysts : R.Rinaldi and G.YezzaLi--ni). E.s.d.ts on the last significant digit in parentheses. 452 MAZZI AND GALLI: ANALCIME
Table4. Final atomiccoordinates and equivalentisotropic temperature factors (A')
Aton Typ"* Beq: Atom Typei B"qf*
ANA 1 ANA 4 r I gz(e) o.1264(r) o.16r7(1) o.41r8(1) o.76 r r1 16(f) o.1256(o) o.1624(o) o.4r22(o) o.87 12 16(f) o.163I (r ) o.4131 r/8 o.77 r 12 16(f) o .4124\o ) o.1243(o) o.1623(o) o.87 o r 32(e) o.1o50(4) o.3705(4) o.2186(3) 2.40 r 2 r6(f) o.1625(o) o.4123 (o ) o.1252(o) o.88 o z r2(e) o.2218(3) o.1028(3) o.3 633(4 ) r.86 o 11 16(f) o.1o48(1) o.3676(1) o.2189(1) 2.23 o 3 :2(e) o.3631(3) o.2182(3) o.1o51(3 ) 1.84 o 12 16(f) o.3824(1) o.1452(1) o.4686(r) 2.23 Na 1 t6(e) o.1246(4) o r/4 2.80 o 21 16(f) o.2207\L ) o.ro4o(1) o.3641(1) 2.18 Na 2 8(b) o t/+ t/8 2.84 o 22 r6(f) o.1458(1) o.4704(r) o.3851(1) 2.23 w I 6(f) o.1r95(6) o.13O5 r/8 6.03 o 31 16(f) o.3650(1) o.2189(r) 0.1043(r) 2.r7 o 32 16(f) o.469r( r ) o.3853(1) o.1459(1) 2.r4 ANA 2 Na11 8(c) o . 1247(2) o t/ + 2.87 r r lz(e) o.1264(1) o.1618(r) o.4117(r) 1.O5 Na12 8(d) r/4 o.t252(2) o 2.9r r 2 16(f) o.1632(1) o.4132 r/8 o.98 Na2 8(e) o r/+ o.1250(3) 2.55 o 1 32(e) o.1055(3 ) o .37r2l3 ) o .219r(2) 2.64 w 16(f) o.r46(2) o.1268(2)o.1252(3) 6.o2 o 2 32(e) o.22Lr\2) o . ro27(2) o.3638(3) c 19 o 3 3z(e) o.3634(3) o.2190 (2) o.1o56(2) 2.22 4r4--q Na1 16(e) o.1242(3) o r/4 r I 32(e) o .1244lL ) o.r624(r) o.4124(r) o.83 Na2 8(b) o r/4 1/8 2.88 rz 16(f) o.1623(r) o.4123(r) r/8 o.82 w r6(f) o.1r94(4) o.13O6 1/8 6.29 o r 32(e) o.1038(3) o.3640(3)o.22oo(2) 2.32 o 2 32(e) o.2185(2) o.1046(3)o.3666(3) 2.33 ANA 3 0 3 32(s) o.3663(3) o.2zo2(2)o.1o48(2) 2.36 r 1 32(e) o.r258(1) 0.1624(1) o.4123(1) o .78 Na I t6(e) o.r252(4) o r/+ 2.57 r2 16(f) o.1625(1) o.4r25 r/8 0.80 Na 2 8(b) 0 r/+ 1/8 2.87 o 1 32(c) o.ro5o(2) o.3 68o(2) o.219o(2) 2.r4 w 16(f) o.1256(4) o.r244 t/8 6.53 o 2 :z(s) o.2206(2) o.104o(2) o.3642(2) 2.r3 o 3 :z(e) o.3649e) o.2188(2) o.1043(2 ) 2.O7 4N4l Na1 r 6(e) o.r242(3) o t/t 3.o4 r 11 r6(f ) 0.124O(o) o.r621(o) o.4125(o) o.89 Na2 8(b) o r/+ r/8 2.29 r 12 16(f) o.4124 (o ) o.1254(o) o.1626(o) o.87 w 16(f) o.1233(4) o.7267 r/8 6.o1 r2 16(f) o.1622(o) o.4123(o) o.r254(o) o.87 o 11 16(f) o.1039(1) o.3632(2) o.22o6(r) 2.r4 4r4l o 12 16(f) o.386r(2) o.r459(1) o.4698(r) z.rL r 1 32(e) o.1251(o) o.1623(o) o.4rz2(o) o.88 o zL r 6(f) o.218r(1) o.1046(1) o.3658(2) 2.17 r2 16(f) o.1624(o) o.4124 r/8 o.83 o 22 16(f) o.1450(1 ) o.4682 (1 ) o.3825(2) 2.20 o 1 32(e) o.1044(2) o.3665(2) o.2194(1) 2.30 o 31 16(f) o .367 6(2) o.2197(1) o.1o47(r) 2.27 o 2 32(c) o.2196(1) o. r041(2) o.3 6490) 2.34 o 32 r6(f ) o.4704G) o.3845(2) o.1459(1) 2.22 o 3 32(e) o.3654 (2 ) o.2194(1) o.1043(r) 2.23 Na 11 8 (c) o.r257(z) o r/ 4 2.92 Na1 16(e) o.1248 (2 ) o r/4 3.r4 Na12 8 (d) r/4 o.1248 (3 ) o 2.52 Na2 8(b) o r/+ 1/8 2.80 Na2 8(e) o t/+ o.Lz46(2) 2.88 w 16(f) o.1238 (3 ) o.1262 r/8 6. 59 w r 6(f) o.r27| (3) o.1239(3) o.1238(3) 6.03
I Number of positions and Wyckoff notation, **Equivalent isotropic temperature factor after Hanilton (1959). Na-occupancy factors are given in Table 8. W: water molecule. E.s.d.rs on the last significant digit in parentheses. becomeequal (-2.484). When the occupancyof the concentratedonly on oneNa site(say Na 2 in tetra- Na sitesis low (for exampleNa 2 in ANA I andANA gonal ANA I and ANA 2), all the H atomsoccupy 2) the Na-Z distances(2.32A) are smallerthan the only the 32 equivalent positions which face this Na-O ones (2.554'),and the water moleculesare emptysite, thus producing an appreciablemaximum shiftedtowards the vacantNa positions.Of thethree in the differencemaps. This could be the explanation Na sites(Na I 1,Na"l2, Na 2) surroundingeach water of the experimentalevidence described in the preced- position, one must be empty to account for the ing section. stoichiometricunit; very likely the HrO hydrogens A linearrelationship (Fig. 2) existsbetween lattice facethis latter Na site (Fig. 1). When the Na va- constantsand Al fraction in the 7 sites.so that an canciesare variouslydistributed among the threeNa approximatedetermination of the Al occupanciesis sites(cubic analcime, ANA 5), the H atomsare also possiblewithout any structuralrefinement, using the spreadamong the 96 positionscorresponding to the lattice dimensionsonly. The explanationof this H(2) parameters(Ferraris et al., 1972)in the cubic simple relationship becomesclear from Figure l: analcime.On the contrary. when the vacanciesare thereis only onetetrahedral edge parallel to thea axis MAZZI AND GALLI: ANALCIME
Table7. Interatomicdistances (A) and angles(") within the framework*
T-O Atons U-U o-T-o Atoms T-O o-o 0-T-O Atoms T-O-T
4!41 r1-o1' 1.656(5) olf -o2 2.751\7) 111.4(3) o1-01' 2.578(9) 105.7(4) r1'-01-r2 146,4(4) 11-o2 1.675(5) o1'-o3 2.658(6) ro6.1 (3 '.u"r,rnl -ot I rr-o2-'r2 142.8(3) ) Il_3i,) ::, "^'^,12.6s30) rro.e(2) r1-o3 1.671(5) or'-o3' 2.738(6) 111.7 (3) ''*"ur r1-03-r1' r43.6(3) rr-o3, 1.653(5) o2-o3 2.752(7) LLo.7e) ol -nrt I li-33,) ::::^t 2.664('\ ttt.6(3) o2-o3' 2.613(6) 1o3.5(2) Mean 1 664 Mean f.611 03-o3' 2.782(7) I 13.7(3 ) o2-o2: 2.563(8) 1o6.2(4) 4!4_2 Tl-o11 1.649(4) o1'-o2 2.727 (5) Lro.7 \2) ''u"<'ro1-01' 2.594(6) 1o6.6(3) T1'-o1-r2 r47.+\3) r1-o2 r.667(4) o1'-03 2.654(5) 106.7(z) li-31,) r.uu'ttl 11r.0(2) rL-o?-rz L42.9\2) rr-o3 1.660(4) o1l-o3' 2.733 (5) 111.5(2) ',3-3!rl 3i-001,) 11-03-r1' r44.2\Z) 1.657(4 o2-o3 2.740(5) 110.9(2) ''u"*, nr-orr) r1-o3, ) 2.663(5) rrr.r(2) o2-o3r 2.6r6(5) 1o3.8(z) ::,'^-^l Mean 1 .658 Mean 1.615 03-o3' 2.77| (6) 113.3(2) o2-ozt 2.575(7) 106.o(3)
1!Al 11-o1' 1.648(3) oll-o2 2.744\5) 111.9(2) r'z-!1,) o1-o11 2.59o(6) 105.2(2) Tr'-o1-rz r4s.7(2) (2) r.osor:)o1-02 Tr-o2-T2 143.3(2) r1-o2 1.665(3) 01'-03 2.645Q) 106.5 \ 2.680( 4!4_4 T11-o1z L,657O) ot2-o2r 2.704\3) 111.9(r) r2-o11 1.631(2) 011-0122.584(3) 1o4.8(1) Tr1-o12-T2 145.4(1) 111-021 1.669O) 012-0312.648(3) 1o6.3(1) 'r2-orz 1.631(2) 011-o212.683(3) 110.9(1) TLI-O21-T2 143.4(1) rrr-o31r.652(z) or2-o322.741\3) 111.4(r.) r2-ozr r.627 O) orz-o2z 2.687(3) r10.9(1) T11-031-T12144.0(1) rlr-o3z 1.661(2) o21-o312.737 (3) 111.o(1) T2-o22 1.633(2) otr-ozz 2.741(3) 111.8(r) r11-032-T12 143.8(1) o2r-o32 2.616 (3 ) 103.6(1) orz-o2r 2.7 SZG) rr2.2(r) T12-o11-r2 145,3(1) Mean 1.660 Mean 1.630 'rr2-o22-T2 031-o32 2.757 13) r12.7 (r) o21-o2z2.611(3) 1o6.4(l) 143.8(1) T12-o111.65r(2) orL-o2? 2.703(3) 1r1.7(1) 'rr2-o2z 1.660(2) o11-O312.732\3) 111.4(1) r12-o31 1.656(2) 011-o322.641(3) 106.3(1) rr2-o32 L .649 e) o22-o3r 2.608(3) 1o3.7(1 ) o22-o322.728(3) 111.1(1) Mean 1 .654 031:03 2 2.751 13 ) ANA 5 rr-o1' r.6450) o1'-o2 2.738(3) 112.r(1.) o1-olt 2.601(4) ro4.4e) r1'-01-T2 r44.8(2) '.uou,,r rr-o2-r2 143.8(2) r1-o2 1.656(2) o1'-03 2.632(3) 1o6.2(1 ) I3_3i,1 o1-o2l ^-^^/"\ rlr.o(1)irr^.r (2) -o3' 2.70e(3) T1-O3-T1r r44.2\2) r1-o3 I,651 o1' 2.7 23 Q) 111.4(1) T2-02\ , rfircr ;i,_;;,i 11-o3r 1.646(2) o2-o3 2.724(3) 1r1.1(1) rz-oz,l ol-oz'l 2.727^ -^-,^\\3) 1r2'2r1)a1a.t1 o2-o3' 2.603(3 ) 103.8(1 ) o;,-;21 Mean 1.650 Mean 1.644 03-o3f 2.739Q) 112.4(1) oz-o2) 2.624(4) 106.2(2) 414--0 -02 103.3(3 r1,-01-T2 1+3.3\2) 11-ot' 1.638 (3 ) o1' 2.746(5) rrz.4O) r2-o1,) (: o1-o1, 2.616(6) ) -o3 (5) r. ooa ) Tr-o2-r2 r+4.9\2) T1-o2 1.640(4) o1' 2.619 106.4O) 9i. ?.) 2.724(il 11r.4(z) r1-03 1.633(4) olf-o3l 2.702\3) Lro.7 (z) ',1-f,i,\''o'o<+t UT'.UZ'' r1-o3-r1' 144.8(3) r1-o3' 1.647 (3 ) o2-03 2.699(5) 111.1(2) r.tuttrl rrz.3(2) o2-03' 2.600(5) 104.6(2) 31,--*) Mean 1.640 Mean I.662 03-03' 2.7I 5(6) rrr.8(3) o2_ozt 2.65rO) 106.4(3) 4!41 T1r-O121.638(2) orz-o?t 2.732\3) rr2.7 \r ) 12-011 t.6750) 011-O 12 2.624U) 1o3.3(1) T1r-o12-r2 143.6(1) 'r2-oL2 r1 1-O21 1.64+(2) 012-o312.626(3) 106,4( 1) r.67O(2) ort-o2r 2.753(3) 1r1.1(1) Tr1-o21-T2 144.6(1) T11-O31L.642(2) or2-o32 2.714e) 111.2(1.1 r2-o2L r.66Le) or2-o22 2.7so(3) 111.3(1) r11-031-r12 r45.4(2) ^ F-^/^ \ ir. ^/r\ r1l-o32 1.653(2) o21-o312.712(3) 111.3(1) T2-O22 1.659(2) ott-o22 ..ttw\J) 1r..J\r/ T11-032-T12r44.O\2) o2r-o32 2.596(3) 103.9(1) ot2-o2l 2.77z(3) 1r2.5 (1 ) Tr2-O1r-tZ t42.9\l) Mean 1.6+4 Mean 1.667 031-o322.724(J) 111.5(1) o2l-o22 2.661(3) 1o6.4(1) Tr2-O22-r2 r45.3\2) T12-o11 r.627(2) orL-ozz 2.7o9\3) 112.6(1) T|2-O2Z 1.630(2) o11-o312.684$) 110.6(1) rr 2-o31 | .637 O) o11-O322.608(3) 1o6.4( 1) Tr2-o3z 1.631(2) o22-o3L2.588(3) 1o4.8(1) ozz-o322.687 111.0(1) Mean 1.631 e) 031-0322.7O3\3) 11r.6(1) * Interatomic distances and angles sJMetrically equivalent are bracketed. Atonic positions relationships in orthorhonbic and in tetragonal are as follows: (T11,o11,021,031,Na11)orthorh. correspond to (T1,01,02,o3,Na1) tetrag. and (112,612,922,o32,Na12) o.thorh. correspond to (T1',o1'ro2'ro3r,Nalr) tetrag. E.s,d.rs on the last significant digit in parentheses. 454 MAZZI AND GALLI: ANALCIME In applyingthe least-squaresmethod, the function to be differentiatedis: l-. I f : r(o)l+Klm*n-rp-2(r+'J r+r)l ag LTlt sa ct where K is a constantto be determinedand which CJ derivesfrom the procedurefor the calculation of ct c, conditionedmaxima and minima, andm t n * p - CE 2(r I s + t) = 0 is the conditionthat the sumof all Na's mustequal the sumof all Al's (thecoefficient 2 is the ratio betweenthe multiplicityof the 7 sitesand that of Na sites).By assumingm, n, andp to be Al-fractionin T-site independentvariables, the systemof the following Fig. 2. Linear relationshipbetween Al fractionsin tetrahedra four equationsis obtained: and correspondingunifcell edges;a is plbttedversus Al in T I I (or 7 I in tetragonalanalcimes), b versusAl in T 12and c versusAl in 6f/6m: (4m- 6r - 3s- 3t)/10+ K:0 T 2. The numbersoutside parentheses identify the samples,the numbersin parenthesesare thoseof the 7 sites The straightline 6f/6n : (4n - 3r - 6s - 3t)/36 + K : 0 allowsa simplebut reliablededuction of the Al fractionsfrom the latticeparameters. The dashedlines are at onestandard deviation. 6f/6p: (4p- 3r - 3s - 6t)/X+ K : 0 and it pertainsto Z 1l (Z I in tetragonalanalcime); m*n+p-2(r*s*t):6 similarlyone edge of T 12 (7 l') is parallelto the b The solutionof the systemgives three similar equa- axis,and oneedge of T 2 isparallel to thec axis.Thus tions: the Al occupanciesof each of thesemay be deter- mined from the correspondinglength of a, b, and c. a: (l4r 1- 5s* 5t)/12 n:(5r*l4s* St)/tZ Relationshipbetween the fractionof Al in the ? sites -t and the occupancyof the nearestNa sites , : ( 5r + 5s l4t)/12 A simple relationshipbetween the occupanciesofl As the total Al: (r * s + t) : I for stoichiometric the Na sitesand the fraction of Al in the tetrahedra can be derivedby applyinga least-squaresmethod to minimize the lack of balanceof electrostaticcharge Table 8. Al fraction in T sites and occupancy in Na sites on the oxygensof the framework. Let r, s, and t be the Al fractionsin Z I l, T 12,and Ar\A I Nq 2 Ar'A 3 AIG 4 AI@ 5 Alq 6 AIiA 7 Z 2 respectivelyand let ry, n, and p be the Na occu- panciesin Na I l, Na 12,and Na bondstrength 2.T!e A1-fractlon (x 100) (S) whichreaches one oxygen from - 7ll is [4(l r) J) Zl - r1(r11) 47 42 40 44 30 + 3rl/4: | (r/4),and similarly from 712 it is I - TL2 JO 19 45 50 (s/4), and from 7 2 it is I - (t/4). The bond strength T2 z) I7 I8 30 100 100 99 99 which reachesan oxygenfrom sodiumis respectively At totat 96 89 97 occupanql (x 100) m/6, or n/6, or p/6. The doublenegative charge qf \a eachoxygen is balancedby the bond strengthsof t'he Na I (Na ll) 82 84 79 77 t5 0r 69 85 78 75 81 69 58 62 two nearestZ sitesand by one Na site.The degreeof Na 12 74 52 lack of balanceis given by: : + 73 48 U S(7.) S(D + Na2 23 L7 48 52 58 77 80 S(Na) -2.The actualimbalance for eachoxygen is: 25 zb 4s 46 62 82 89 Na total t 93 92 103 r01 r02 100 101 U(Oll) :2p - 3(s+ t)/t2 97 92 97 100 100 99 L00 U(o t2):2p - 3(r+ t)lii 5 VaIueF obtaineal frcrn the last refilement c1rcle; for all U(O2r) : 2m- 3(r+ t)/12 values the stardard deviation is ! on the last signtflcant dlgit. The occqnrcies calculated frcrn the equationr : - n = I.322' + 0.225 (see text) a-re irEitten h ltalics belo'r U(O22) 2n 3(s+ t)/r2 each correspording Na-occupancy. f Na total vatrues are half the sum of the occupancies of U(O31) : 2n- 3(r+ s)/r2 tlEee sites because of the nrltipliciw of Na-positiots (in tetragonal analcirEs take the fiJst value twice). U(O32) : 2m- 3(r+ s)/12 MAZZI AND GALLI: ANALCIIIE 4)) analcimes,the three equationsare slmplifiedas fol- Table 9. Bond distances(A) in the Na-coordination polyhedra* lows: Sample Bond Distance Distance m : 0.75r+ 5/12; n: 0.75s+ 5/12: ANA t Na1-O2 2.485 ( 6) Na2-o1l 2.539 | 5) p:0.75t+5/12 Nal-o3' 2.469(6) Na2-01r, Na 1-W 2.478 (6) Na 2 - W 2.319(r1 ) Accordingto the aboveequations, the Na occu- ANA 2 Nal-02 2.487Q) Na 2 - O 1\ 2, 555(4) pancyof an octahedronwould dependonly on the Al Na1-O3l 2,479 Q) Na2-01r, Na I - W 2.47I (4) Na 2 -W 2.319(8) fraction in the tetrahedronwhich sharesone edge ANA Na1-02 2.498(4) Na2-o1l 3 z.5zz(l\ with the Na octahedron.The plot of Na occupancy Na1-O3l 2.483Q) Na 2 - O 1r, versusAl fraction of Figure 3 contains all points Na I - W 2.442 \4 ) Na 2 -W 2.395(8 ) Na11-021 2.+96\3) Na 2 - O 11 2.518(3) correspondingto the observedvalues and the 4Ir4 calcu- Na11-032 2.487Q) Na 2 - O 12 2.516(3) latedline: Na occupancy: 0.75(Alfraction) + 5/12 Na 11 - W 2.442\3) Na 2 -w 2.398 (3 ) (line A). The agreementis fairly good, except for Na12-O22 2.502(3) points with low Al fractions. Na12-031 2.490\3) Most likely this dis- Na 12 - W 2.443 \3 ) agreement follows from actual more complexrela- ANA Nal-02 2.49+ (2) na2-Ot\ 5 2.508(3 ) tionshipsthan the simple ones assumed in thepreced- Na1-O3l 2.496(2) Na2-Oltl Na 1 - W 2.438(3 Na 2 -W 2,404(3 ing derivation. For instance possible ) ) a weak ( ANA 6 Na1-o2 2. 503 5.) Na2-O1l 2.48s(4) hydrogenbond betweenwater and oxygensof the Na1-O3l 2.516(5) Na2-Olrl Na 1-W 2.42r14 ) Na2-W 2,437 \9 ) - -O 1l (3) 4{4_Z Na 11 o 2l 2.490(3) Na 2 2.487 Na11-O32 2.5o8(3 ) Na 2 - 0 12 2.483 (3) Na ll - W z.qzz(t) Na 2 -W 2.4s7G) Na12-O22 2.511(3) Na12-O31 2. 52+(3) Na 12 - W 2.396(4) * Bond distances symetrically equivalent are bracketed. All the above distances repeated twice for sjmetry. For the meaning of the Pri[ed atoms see second footnote in Table 7. E.s.d.rs on the last sigDificant digit in parentheses. '/rt tetrahedralframework could be considered.Actually t the Z-O distances,which range from 3.336 to 3.574A(Table l0), are largerthan the conventional onesfor a hydrogenbond. Furthermore,they occur betweentwo verticesof the same Na octahedron. However,the shortestdistances (W-O I : 3.344in ANA I and ANA 2) takeplace between vertices of an octahedronaround Na 2. in which the cationicsite is practicallyempty. One might infer that in the general casesome hydrogen bonds would occur with oxygens O I I (O 1) andO 12(O l') whenthe Na 2 positionis vacant(Fig. I ) and,in thesame way, with O 22(O 2') andO 3l (O 3) or O 2l (O 2) andO 32(O 3') when Al-fractioninT-site the Na Il (Na l) or Na 12 (Na l') positionsare empty. Fig. 3. Plot of Na occupancy against the Al fraction in the Calling w the possibleweak H-bond nearest 7 site: Na I I (or Na I in tetragonal analcimes) versusAl in strength, Z ll (or I l), Na 12 versusAl in 7 12 and Na 2 versus Alin 72. which would reach one oxygen of the tetrahedral The A line, Na occupancy : 0.75(Al fraction) I 5/12, was framework, the charge balance equations written calculated from the charge balanceon oxygenswithout considering abovewould be increasedby a term, namelyYz(m + the HrO hydrogens. The line of best fit (line B), Na occupancy : n - p)w for O ll and'O12, Vz(m - n t p)wfor O22 1.32(Al fraction) + 0.23, corresponds to that calculated and O 31,and finallyVr(-m -t n t p)w for O 2l and considering also the HrO hydrogens; the dashed lines are at one standard deviation. Numbers outside parenthesescorrespond to o 32. samples, numbers in parenthesesidentify T and/or Na sites. By the procedurefollowed in the precedingcalcu- MAZZI AND GALLI: ANALCIME Table 10.Distances (A) of waterfrom frameworkoxygensi ANA 1 ANA 2 ANA 3 ANA 4 ANA 5 ANA 6 ANA 7 w-or (orr1\ 3.392(4) 3.443(s) 3.336(e) 3.346(7) 3.390(6) 3.392(5) 3.4rt (7) w-ot,(orz11 3.387 (4 ) 3.414(s) w-ot (orr11 3.ss8(5) 3.s49(7) 3.ss6(s) w-olr(oL2)l 3.53e(e) 3.551(7) 3.s640) 3.s64(s) 3.sss(s) 3.563(s) w-o2(o21)\ 3.442(4) 3.376(s) 3.5oo(11) 3.497(8) 3 .440(8 ) 3.426 (6) 3.3e3(e) w-o2r(o22)J 3.44t (4) 3.37 4 (s) w-o2(o21)l 3.552(5) 3.562(5) 3.570(7) 3.s74(s) 3.5s4(s) 3.ss8(4) w-o2r(o22)l 3.s66(s) 3.s6s(s) 3.ss6(s) w-o3 (o3l)\ 3.3e6(4) 3.405(s) 3.379(s) 3.390(4) 3.3e3(4) 3 .400(3 ) 3.4zr ( 5) w-o3r(osz)l 3.394(4) 3.$7 (s) r,r-o3(orr11 3.s62(5) 3.s63(s) 3.sq(7) 3 . s72(5) 3.56r (5) 3 . s66(4) 3.566(5) w-o3r(o32), 3.s64(s) 3.ss8(s) i Interatornic d.istances sJrmmetrically equivalent are bracketed. For the rneaning of the primed atoms see second footnote in Table /. E.s.d.rs on the last significant digit in parentheses. lation,the occupancy(say m) of a sodiumsite is: atomsoccupy 50 percentof the 32 Z I sitesand no 7 2 sites.Consequently the cubic cell is flattenedwith a 9(l - 6w)r+ 6w(48w- 13)+ 5 ) c; ANA l, ANA 2 and,to a lesserextent, ANA 3 l44w3w-l)+12 aregood examples of this type.(2) The l6 Al atoms when / * s * , : l. This equationis obviously occupyno f I sitesand 100percent of the 16 T 2 transformedinto the precedingone, m: (9r + 5)/12 sites.This secondmodel was described for analcime : 0.75r+ 5/12,if w : 0. With w :0.072,i.e. aweak by Meier (1973), but it actually conflictswith the interactionbetween oxygens and HrO hydrogens,one upper limit for the Al fraction (60 percent)empha- obtainsm : 1.32r+ 0.23.This equationis the same sizedat the beginningof this section.Therefore the as that of the regressionline (Fig. 3, line B) drawn maximumallowed Al contentsfor this modelwould throughthe wholeset of the experimentaldata (linear be 6.4Al atomsin 20 percentof the 7l sites,and 9.6 correlationcoefficient: 0.96). Al in 60 percentof T 2 sites,and, as a consequence, the cubic cell is elongatedwith a I c. ANA 6 hasan (Al,Si) Order-disorderin tetrahedra Al distributionof this kind. As explainedabove, there is a definiterelationship On the whole, the two ordering schemesin the betweenthe Na occupancyin one site and the Al tetragonalsystem are simpleand clear;things are a fractionin the nearbytetrahedron. Because the upper little more complicatedin the orthorhombicsystem, limit of Na occupancyis obviously100 percent, ac- spacegroup lbca. FirsLof all, the orientationis not cordingto line B (Fig. 3) the Al fractionin any site obvious,because an interchangeof the axesdoes not shouldnot be largerthan 60 percent.As a matterof affect the style of the extinctions. Therefore we fact, no Al fraction larger than 50 percenthas been choosea "pseudotetragonal"orientation, a and b - - -bl; found in this work. mostsimilar,namely l, o | > | o bl < lt The possibleschemes of (Si,Al) orderingin anal- we alsochoose a 2 b. cime can be summarizedas follows. In cubic anal- What happensin the orthorhombicsystem is re- cime all 48 tetrahedraare symmetricallyequivalent, lated to the two ordering schemespossible in the and hencethe 16Al atomsmust occupyat random tetragonalsystem, namely in one casethe unit cell is onethird of them.In the tetragonalspace group I4r/ flattenedwith (a + b)/2 ) c, and in the otherone it is acd the 48 tetrahedraare split into two groups:the Z elongatedwith (a + b)/2 < c. I sites(multiplicity 32) and7n 2 sites(multiplicity 16). First case,(a + b)/2 ) c: the tetragonalI I siteis Two orderingschemes are possible:(l) the 16 Al split into two sites,Z 1l and T 12,eachwith multi- MAZZI AND GALLI.. ANALCIME 457 plicity 16.The Al fraction,which is 50 percentin I I tionsd, e, andf areeasily obtained from d : r -t s -t, (ANA l, ANA 2), is slightlydifferent in ?'ll and Z e : r - s * t, andf = -r * s * l. The atomic 12 (44 percentand 38 percent),the remainingsmall parametersof the basic structure(Table I I ) were fractionof Al beingplaced in T 2 (exampleANA 4). calculatedby linearextrapolation of the atomicpa- Secondcase, (a + t)/Z ( c: the I I site is again rametersversus Al fractionin T 2 for the determined split into two sites Z I I and T 12. The Al fraction tetragonalstructures (ANA l, 2, 3, 5 and 6); obvi- whichis 25percent in Z I (ANA 6),is not equalin the ouslyenough, they are verysimilar to thoseof ANA two newsites (30 percent and l9 percent),the remain- I andANA 2. A recalculationof the atomicparame- ing largefraction of Al (50percent) being placed in Z ters for the variousanalcimes, starting from thoseof 2 (exampleANA 7). the basicstructure and using the appropriatevalues The differencebetween the two orthorhombiccases for d, e, andf, gaveresults in agreementwith those follows from the "pseudotetragonal"orientation of obtainedfrom the structuraldeterminations (stan- the crystallographicaxes: the latter casevanishes if dard deviations0.0002 for Z and Na sites,0.0005 for one retainsonly the conventionalchoice of the axes O sitesand 0.0009 for W sites).The occupancyof Na in the orthorhombicsystem b ) a ) c. in Na I I andNa l2 wasfixed at 0.88and that of Na 2 at 0.24(Fig. 3, line B). The thermalfactors for the Interpretation of the different types of analcime as atomsof the basicstructure were an averageof those derivedfrom a singlebasic tetragonal structure in ANA I andANA 2. The variouscrystal structures of analcimestudied Any structurefactor Fc'(hkl) of an analcimede- herecan be consideredas built upon one basictetra- finedby a triplet d, e, andfcan becalculated from the gonalstructure 0.5/0.5/0, i.e., 0.5 is theAl fractionin structurefactors Fc(hkl), Fc(lhk) and Fc(klh) of the Z ll and T 12(T I andT I' in tetragonalanalcime) basicstructure by meansof the relations: and no Al is in T 2; this structureis verynear to those of ANA I andANA 2.Thedifferent analcimes would I Fc'(hkl): d Fc(hkl)+ e Fc(lhk)+ f Fc(klh) derivefrom the superpositionof threeportions (say Fc'(thk): d Fc(thk)+ e Fc(klh)+ Fc(hkl) d, e,andf,withd 1-e * f : l) of the basicstructure, I f suchportions being rotated by 120'arounda diago- I Fc'(klh): d Fc(klh)+ e Fc(hkl)+ f Fc(lhk) nal of the unit cell(3-fold axis of cubicanalcime). This interpretationmakes it possibleto devisea On the other hand, if the Fc' valuesare replacedby simpleway of identifyingthe natureof a specimenof the observed ones (Fo') for the actual structure of an analcimethrough intensitymeasurements of only analcime,the solution of the above systemof three threereflections. Ifr, s, and t arethe Al fractionsin Z equationsallows one to calculated, e, andf from only ll, T 12, and T 2 respectively,the volume propor- one triplet of reflections,and hence the Al fractions r, Table 11.Atomic coordihatesand anisotropictemperature factors (X lClo)assigned to the basicstructure * Atom Type Occupancy P" F* l3tt F', l3rsPrs T 11 32(e) o.5Al-+0.5si o.t266 o. 1619 o.4118 10 10 11 0 0 I T2 r6(f) o.o A1+ 1.o si o.L63z o.4132 L/8 11 11 902 o1 S2(e) 1.oo o.1o52 o.371o o.2187 37 42 17 -1 10 4 o2 ez(e) 1.oo o.22LT o.Lo26 o.3630 10 29 35 7 2 o o3 gz(e) 1.oo 0.3631 o.2183 o.1052 30 L7 27 -6 -4 4 Na 11 t6(e) o.88 o.L242 o t/+ 36 38 38 o o -t, Na2 8(b) o.z4 o t/ + r/8 35 35 45 -30 0 o w r6(f) 1.oo o. 1194 o.1306 r/8 80 80 80 18 37 37 * Number of positions and Wyckoff notation. The anisotropic temperature factor has the form: "*o{-n2/3rr-u'Frr-r'Frr- znufrr- zn pn- zutp4) 458 MAZZI AND CALLI: ANALCIME Table 12. Comparison between the observed and calculated quantities relevant to the interpretation ofanalcimes as domains ofthe basic structure with three different orientations 6. A}B 1 AI\A 22 A}G 3 ATB 4 AIr{A5 AIG, 6 A}A 7 lro' {eeo1;a 107.3 107.6 105.5 L29.9 131.2 141..5 157.5 r53.9 lFo' (605)l3 156.5 166.4 167.0 155.3 I52.3 149.5 141.5 L3L.2 lFo' (066)l3 156.9 145.3 A 100 92 79 63 64 40 9 0 99 L0L 62 60 42 15 4 0 2 5 I7 24 30 45 61 e <7 <0 20 24 29 42 OU 12 39 f ?A fo 27 30 r 50 47 42 40 44 35 50 40 42 36 29 32 19 q Jd 3B 4U + 0 z 5 L7 I8 45 50 20 29 42 48 ti.'tz o oltu 7T 70(7r) 7r(7t) 30(54) 25 (65') 9 (60) 18(s4) 40(s7) lEb'(2 o o)| 60 62 22 zu 9 l-527 lFc'(to o o)lq 48 47 (48) 48(.48l. 20(43) 17 (44',, 6 (40) 12(36) 27(38) lFor(10 0 0)l 4l 40 25 19 15 27 I Rs t "basic stnrcture"; Fot (660), rot (606) ard Fo'(066) are in this case Ec values. 2 lotal aluninr.un i.s sigrnificantly tess ttran 1. 3 Fo' values rprrnalized acoordilg to: Fot15691+ro'(606)+For(066) = Fc(660)+Fc(606)+Fc(066)= 440.5. h Fc' (2 0 O) ard Fc' (10 0 0) calculated by usllrg d, e ard f obtaineC frcnr reflectjons 660, 606 and 066; calculated values for a tr,dl of the "basic strtrctlre"in parentheses. = Values equal to tlrose of the preceding line because of the tetragonal sym€try. d,e ard f are the fractions (x 100) of the"basic structure"i r, s ard t are the Al-fractions (x 100) in T 11, T 12 ard T 2: values obtained frcrn the crystal structure analyses are i:r ronan, those obtained frcrn reflections 660, 506 ad 066 are jn italics. For the meaning of For ard Fcr see teJft. r, and l. The followingrelations: tions, the observedstructure factors of reflections 660.606. and 066 resulted in themost suitable ones to Fc'(hkl) + Fc'(lhk) + Fc'(klh) = Fc(hkl) givea goodagreement between the fractionsd, e, and + Fc(lhk) + Fc(klh) : KlFo'(hkl) + Fo'(lhk) + /obtained from the structuralstudies and those from the applicationof the aboveequations (for their Fc obtainedby summing the terms of the values,see first columnof Table l2). The errorsare of equationscan be usedto put the Fo'values"r"it:i3llon an considerablyreduced by usingthe abovetriplet of absolutescale through the determinationof K. reflectionsrather than others, becausein the basic The abovesystem is much simplifiedif reflections structureonly the atomsof one Na siteand of one such as hhl, lhh, and hlh are used.Because for the related 7 site give their maximum contributionsto basictetragonal structure Fc(lhh) : Fc(hlh),and d Ie each of these three reflections:i.e., Na 2 and T 2 + _f: | , eachFct (KFo') valuebecomes dependent on affectonly 660,Na I I and 7nI I contributeuniquely only one variabled, or e, or f: to 066,whereas Na 12 and T 12 influenceonly 606. Tablel2 showsthe resultSof the calculationsfor the : - - 4 fKFo'(hht) F c(lhh)l/IFc(hhl) Fc(thh)l sevenanalcimes. - structures s : lKFo'(hlh) - Fc(thh)l/lFc(hht\ Fc(lhh)l Perhapsthe interpretationof the crystal of analcimesfounded on the basictetragonal struc- = - - 1 [KFo'(thh) Fc(lhh)]/lFc(hhl) Fc(thh)l ture0.5/0.5/0is morethan formal:two out of seven Following severaltests on varioustriplets of reflec- of our specimens,from different localities(ANA I MAZZI AND GALLI: ANALCIME 459 andANA 2),havea crystalstructure very near to the ture. In analcimethe individualsof the pseudo-me- basicstructure and actually,at leastin the examined rohedrictwinning behave as a realsingle crystal. In specimens,no Al fraction in each tetrahedronis high- and low-temperatureleucite the Si-Al sub- largerthan 0.5;such an amountis indeedthe maxi- stitutionis alwaysdisordered, whereas in analcime mum allowablefor the distributionof oneAl atomin different degreesof ordering allow the existenceof two equivalentsites (Z ll and T 12)in a tetragonal four main kind of symmetries:cubic (la3d), tetra- structure.Should this upper limit 0.5be confirmed by gonal(I4r/acd) with a ) c, tetragonalwith a I c,and successivestudies, then the crystalstructures of anal- orthorhombic(Ibca), with all the possibleinter- cimescould be reallybuilt up by smalldomains of the mediatevarieties. This fact justifiesthe title of the basictetragonal structure in three or fewerdifferent paper,which is a paraphraseof a famousstatement orientations. about feldsparsby Fritz Laves. Of courseonly the aboveindirect evidencecan However,the varioustypes of analcimecould be support this interpretation,because when the do- interpretedon the basisof only one basictetragonal mains are small enough no differencebetween a structure(I4r/acd) in threedifferent orientations, re- "structurewith domains"and a "true single-crystal latedby l20o rotationaround [11], the singledo- structure"can be seenby X-ray diffraction.A grad- mainsbeing small enoughto simulatea real single ual increaseof thedimensions of suchdomains would prystal.If the volumeproportions of the threeorien- transforma "single crystalwith domains" into a tationsare calledd, e, and/(Table l2), thenwhen twin; in the extremesituation, the Fc and Fc'values d : e : f = l/3 the diffractionsymmetry is cubic, in the precedingsystem of equationsshould be re- when e : f < 1/3 the diffraction symmetryis tetra- placedby Fc2and Fc'2. A calculationof the srrucrure gonala ) c, (Table2), if e : f > l/3 the diffraction factorsfoi the variousanalcimes, made on the hy- symmetryis tetragonala I c, and finally in general pothesisof the presenceof twins of the basicstruc- whend I e j/the diffractionsymmetry is ortho- ture,gave for nearlyall reflectionsresults ve.ny similar rhombic. to thoseobtained for singlecrystals. Only'the weak If onewants to knowthe possible geological mean- reflections200,020,002, and l0 00, 0 l0 0, 00 l0 are ing of all theseanalcimes, the main problem is to find sensitivein distinguishingthe two possibilities.For a routineidentification procedure for them;powder instance in a set of tetragonal single crystals, diffractometry,the main tool of mineralogicalidenti- lFc'(200)l decreasesfrom 7l to 0 going from the fication,is clearlyuseless. At the present,the only basicstructurc (d:e:f : l:0:0) to the cubic one(d:e'.f : possibleway is X-ray single-crystalinvestigation, l:l:l), then it increasesagain to 35 for a structure whichhowever may be reducedto the accuratemea- with d:e.f: 0:I :1. In the caseof twinningthat value surementsof the latticeparameters and/or of the decreasesregularly from 7l to 50 alongthe entireset intensitiesof 600.606. and 066 reflections.Of course of suchtetragonal structures. No indicationof this suchmethods can be appliedonly in the presenceof kind of twinningwas, however, detected in the struc- twin domainslarge enough to permitthe detachment tures herestudied, as the observedstructure factors of a suitableuntwinned fragment. for 200and l0 00 werenever larger than those calcu- lated for a singlecrystal (Table 12) and no peak Acknowledgments broadeningor splitting was experimentallyevi- The authors wish to thank Professor G. Gottardi for his interest and helpful suggestionsand Drs. R. Rinaldi, denced.Similarly, no twinningwas determined G. Rossi, and L. opti- Ungaretti for the critical reading of the manuscript. The Consiglio cally in any of the crystalfragments selected for the Nazionale delle Ricerche of Italy is also acknowledged for geneial presentstudy. support of this work and for financing the electron microprobe laboratory at the Istituto di Mineralogia e Petrologia of the Uni- Conclusions versity of Modena, whose facilities were used in the present work. Bothanalcime and the relatedmineral leucite show References pseudo-merohedrictwinning, detectableby optical Albee, A. L. and L. Ray (1970) Correction factors for electron methodsand by the splittingof the X-ray reflections, probe microanalysis of silicates,oxides, carbonates,phosphates, with twin individualsoften large enough to be exam- and sufphates.Anal. Chem ,42, 1408-1414. ined separatelyby X-ray single-crystalmethods. In Bruccio,A. (1951)I minerali della Valle di Fassa.Dove si trovano leucitethese apparent single individuals still show e come si presentano. Natura,42, 25-70. Busing, W. R., K. O. Martin and H. (1962) merohedrictwinning, with domains A. Levy Onrr-s, a largeenough to Fortran crystallographic least-squares program. U.S. Natl. be revealedduring the resolutionof the crystalstruc- Tech. Inform. Seru. ORNL-TM-305 460 MAZZI AND GALLI: ANALCIME Calleri, M. and G. Ferraris (1964) Struttura dell'analcime: Mazzi,F., E. Galli and G. Gottardi (1976)The crystal structure of NaAlStO"'HzO. Atti Accad.Sci. Torino,98, 82I-846. tetragonalleucite. A m. M ineral., 61, 108-I I 5. Coombs,D. S. (1955)X-ray observationson wairakiteand non- Meier, W. H. (1973)Symmetry aspects of zeolite frameworks. cubicanalcime. Mineral. Mag., 30, 699-708. Aduancesin ChemistrySeries 121, 39-51. Davies,J. E. and B. M. Gatehouse(1973) The crystaland molecu- Monese,A. and M. Sacerdoti(1970) L'analcime contenuto nelle lar structureof unsolvatedp-Oxo-bis-[N,N'-ethylenebis (sa- lave basichetriassiche dell'alta val Duron (Val di Fassa-TN). licylaldiminato)iron(III)1.A cta Crystallogr.,829, 1934-1942. Ann Unio.Ferrara, Sci. Mineral. Petogr.,1 (no. 3),4l-46. Di Franco,S. (1926)L'analcite e il basaltoanalcitico dell'Isola dei Rammelsberg,C. (1858)Ueber die Zusammensetzungdes Anal- Ciclopi. Boll. Soc. Geol.Ital.,45, l-'1. cimes.Pogg. Ann , /05,317-319. Ferraris.G.. D. W. Jonesand J. Yerkess(19'12) A neutron-diffrac- Taylor,W. H. (1930).The structureof analcite(NaAISLO.'HzO). tion studyof thecrystal structure of analcime,Na Al SLO". HzO. Z. Kristallogr., 74, l-19. Z. Kristallogr , 135,240-252. Yezzalin| G. and A. Alberti (1975)Le zeoliti dell'Alpe di Siusi Hamilton,w. C. (1959)On the isotropictemperature factor equiv- Rend.Soc. Mineral. Petol. Ital., 3l, 7ll-^119. alent to a given anisotropictemperature factor. Acta Crystal- Zachariasen,W. H. (1963)The secondaryextinction correction. logr.,12,609-610. Acta Crystallogr.,16, 1139-1144. Harada,K. andT. Sudo(1976) A considerationon thewairakite- -and H. A. Plettinger(1965) Extinction in quartz.Acta Crys' analcimeseries. Is valid a new mineralname for sodium ana- tallogr., 18,'110-7 14. logueof monoclinicwairakite? Mineral. J.,8,247-251. Ziebold,T. O. and R. E. Ogilvie(1964) An empiricalmethod for Intemational Tablesfor X-Ray Crystallography(1974) Vol. IV. efectronmicroanalysis. Anal. Chem.,36, 322-327. Kynoch Press,Birmingham. Jones,J. B. (1968)Al-O and Si-O tetrahedraldistances in alu- minosilicateframework structures. Acta Crystallogr.,B 24,355- 358. Knowles,C. R., F. F. Rinaldiand J. V. Smith(1965) Refinement Manuscript receiued, July 25, 1977; accepted of the crystalstructure of analcime.Indian Mineral.,6, 127-140. for publicalion, January 16, 1978.