Canadidn Mineralogist Vol. 15, pp. 4349 (1977)
THEPOLYMORPHISMOF GORDIERITE: II. THECRYSTALSTRUCTURE OF INDIALITE
E. P. MEAGHER Department of Geological Sciences,Unlversity of British Columbia, vancouver S, 8.C., CanadaV6T lws
G. V. GIBBS Department of Geological Sciences,Virginia Polytechnic Institute and State University, Blacksburg,Virginia 24061 U.S.A.
Ansrnecr INrnooucttoN . A least-squar€s refinement of typeJocality india- The earliest quantitative information on the lito [Mgr.eoFeo.6d,l4.r1si4.8gO1P 6 / mcc; a 9.800(3), c "; phase relations of cordierite was provided by 9.345(3)Al shows rtre Iz tetrahedra in tle six-mem- a combined microscopic and thermal study of bered ring of the framework to be significantly the system MgO-AlrOu-SiOz by Rankin & smaller than the linking I tetrahedra. By compari- Mer- son of (I-O> data for cordierite the contents of win (1918) who discovered two forms of Mgz these tetrahedra are estimated to be ([: 0.72 N, AlnSisOre,referred to as cu and #, forms. Th" p 0.28 Si; 7l: 0.30 ,4'1,0,70 Si). Because the Al con- form was considered to be a metastable prod- tent of the f1 tetrahedra differs significantly from uct because, after crystallization from glass at 1.0, the order-disorder changes in cordierite involve temperatures below 950oC, it transformed ir- all the tetrahedral atoms in the framework rather reversibly upon heating to the c form and be- tlan just those in the six-membered ring. The de- cause repeated attempts to transform the c form of long-range order estimated with €ree tle Bragg- to the p form at temperatures below 950'C Williams equation is 0.38. The constraints of P6/mcc symmetry permit a range of intermediate structufal failed. On the other hand, the
Frc. 1.. The structure of indialite (eft, c-axis projection) compared with an idealized drawing of the structure of low cordierite (righl c-axis projectioa). Iq the indialite structure, ?1 sites are Si-rich and Iz are Al-rich. In the low cordierite structure, full 7! Is circles are Si and open ?r, 72 circles are Al.
SisOre{Fig. 1; Miyashiro & Iiyama 1954; Miya- The present study of indialite was undertaken shiro ef al. 1955). Miyashiro (1957) has since to clarify the polymorphism of cordierite by de- suggestedan Al,Si order-disorder transformation termining whetler indialite is truly hexagonal, between cordierite and indialite, analogous to or dimensionally hexagonal but with a lower that exhibited between the alkali feldspars low symmetry and whether the order-disorder microcline and high sanidine. The transforma- changes involve 1 A1 and 5 Si atcvmsin a six- tion in cordierite was assumed to involve the dis- membered ring or 4 Al and 5 Si atoms in the tribution of 1 Al and 5 Si atoms in a six-mem- AlaSLOa tetrahedral framework (Meagher & bered ring; the remaining a Al atoms were as- Gibbs 1965; Meagher 1967). sumed to occupy the tetrahedra outside the ring and not to be involved in the order-disorder B>
'I. TABTE CHEI.{ICALAND PHYSICAL DATA FOR INDTALITE RsnNsrvrnr.Ir
oxlde: Mso Feo* At203 St02 The refinement of indialite was carried out .lo0,4g [elght %: 9.3 7.8 34.7 48.6 Tota.t: in space group P6/ mcc because of the apparent structural relationship between indialite, beryl Unit cell content and low cordierite. Starting atomic positional nornnlized to 18 oxygens: ?[HSl.4OFe0, Sll. 6C14. t t Ag0lA] parameters for indialite were obtained by trans- formation of the refine.d positional parameters group: Space P6,hcc Calculated denslty: 2.59 g/cc for Haddam cordierite (Meagher 1967) to a hexagonal basis. Cell dinenslons: a . 9.900(3)l c . 9.3a5(3)l The structure refinement was calculated with qn-l an IBM 360/67 using p: 14.9 Radlation/filter: Mo/Zr a modified version of the full-matrix least-squares program ORFIS (Bu- Crystalslze: 0.14x 0.10x 0.06mn sing ef al.1964). Scattering curves from the In- ternational Tables for X-ray Ctystallography llumberobserved feflectlons: l6g (L962) were modified for half ionization and corrected for tle real part of the anomalous dis- R " r(lFol-ircl)/rlFol. o.oqz persion. Unobserved reflections were not in- cluded in the refinement and the weighting . tu{ (x w(lrol - lrcl)ztrwFo2)l/2. 0.061 scheme of Hanson (f965) was applied. Because the Al,Si distribution in the framework was ini- i Total Fe assuniedferrous tially unknown, the atoms at the Tr and Tz tetra- hedral sites were assigned a random distribution scattering curve of 4/9 N + 5/9 Si in the first few cycles of refinements of precision back-reflection Weissen- of the refinement a model based on isotropic temperature coefficients. berg data (c 9.8000(3),c 9.345Q)A) compaf,ewell factor with those determined by Miyashiro et al. (1955) Upon convergence of the refinement (weighted b 9.812, c 9.351A). R-index = 0.085) tetrahedral Al,Si contents were In order to critically 4nalyze the dilfrastion estimated from the a"-O) bond lengths (de- symmetry of indialite, intensity data were col- tails of this procedure are given in Discussion lected on the basis of an orthorhombic cell Section). Following an adju$tment of the scat- (Cccm) with a=1/3b. The crystal was mounted tering curves for the Tr and 7z atoms to match about the c axis and three-dimensional intensity that estimated from <7-O>, and an exGnsion data were colected utilizing equi-inclination of the model to include anisotropic temperature geometry on a manual Weissenberg scintiuation- factor coefficients, a final least-squares refine- connter diffractometer. Zr-filtered Mo radiation ment converged to a weighted R-index of 'positional was used along with a pulse-height discrimina- 0.061{'. Refined and thermal para- tor. Non-equivalent reflections for the orthor- hombic cell were scanned 10.43 within sind rTables and traced on a strip-chart recorder. Relative of structure factors are available, at a nomi- nal intensities \ilere then determined with an in- charge, from the Depository of Unpublished tegrating planimeter Data, CISTI, National ResearchCouncil of Canada, and corrected for Lorentz Ottawa KlA 0S2. and polarization factors. An absorption correc- tion was not applied- In addition to the symmetrically non-equiva- TABLE2. POSITIOMLPARAI4ETERS ND EQUIVAIEI{IISO]IOPIC lent intensities collected for the orthorhombic TE4PERATUREFACTORS FOR INDIALIIE cell, approximately thirty hkU and lrlc/ reflections were recorded to test their equality across all B (ia)* {110} and {31O} planes. Hexagonal equivalent intensities measured on opposite sides of these T1 1/2 1/2 tt4 0.e(1) planes were found to be statistically equal, in- T2 0.3727(4) 0.2668(4) i r.ro(g) dicating hexagonal difftaction symmetry for in- 'U4 dialite. !l t/3 2/3 1.8(2) The indices of the planes in the orthorhombic 0l 0.485r(6) 0.34e4(5) 0.1445(6) r.4(r ) cell were transformed to those defined in terms of the hexagonal cell and tle symmetrically equi- 0.2305(I r ) 0.3093(rI) 0 2.213.) valent intensities wero averaged to give 168 rtsotmplc equlvalent of anlsotroplc tmperature factor (Hrml'l- nou-equivalent hexagonal intensity data. ton 1959). 46 THE CANADIAN MINERALOGIST
TABTE3. AI{ISOTROPICTEI{PENATURE FACIOR COEFFICIEITTST pose the nomenclature outlined in Table 5. The indialite framework consists of ?r tetra- Btt '33 Etz B,l: 823 "22 hedra linked both laterally and vertically to six-membered rings T.l 212(511 213(47) 426(44) 83 o of ?z tetrahedra. The Tr tetrahedron shares two opposite edges with M t^ 346(39) 363(40) 440(36) 204(36) 0 0 octahedra whereas the ?z tetrahedron lacks M 478{58) 478 771(59) 239 o 0 shared edges. Thus, each Oa atom is bonded only to two ?g atoms and each Or is bonded to -79(58) 5(55) ol 2e8(62) 286(69) 632(7r) 99(56) one ?r, one 7a and an M atom. Transformation o2 793(134) 8fi(r03) 814(112) 649(e4) 0 0 of indialite to orthorhombic cordierite results in Or and Oz splitting into two sets, eacb * ValuesarenFrld i 10". The coefflclents are of the form consisting of tlree non-equivalent oxygen (0.,.,tr2+ ...,.. zBtzhk + .,....). atoms labelled Or1, 016 and Or3, and Oa1, Oz6 ,and O"3, respectively. In addition, the Zr atoms split into a set of two non- INDIALITE 1ABLE4. IiIIEMTOiIICDISTAIICES AI.ID BOI.ID ANGLES OF equivalent tetrahedral atoms labelled T'I, ?16 and tbe Tz atoms split into a set of three T,il-o Distanc$ {i) o-oDrstances ([) liil"iil,!,ti9l non-equivalent tetrahedral atoms labelled TzI,
Tl-ol [4]* 1.7r9(5) ol-ol'[2] 2.553(lo) e5.e(3) Tz6 and Tu3. The atoms Or, Oa, Tr and Tz in 'r10.0(3) ot,-ol'[2] 2.816(9) indialite correspond to atoms labelled Or1, Ozl, T'l and TzI in orthorhombic cordierite, ot-ol, 3.032(10) r23.7(3) [2] the L denoting the fact that they are related by <0-0> 2.800 the identity map in the hexagonal polymorph. On the other hand, the atoms labelled o16, Tz-ot[2] 1.674(6) 01-02' [2] 2.693(9) r0e.6(3) 0"6, T16 and ?:6 in cordierite are related by a -02'nl r.623(8) ot-02 [2] 2.688(e) 108.3(2) sixth turn, 6, to Or, Or, Tt and f, in indialite 'r1r.3(7) -02lrl 1.{42(9) 02-02' [1] 2.728(10) whereas the atoms labelled Or3, Og3 and ?s3 '1.653 2.70r(lr) r07.6(3) are related by a third turn, 3, to Or, Ob and 7, "12-or 0t-0tm[r] <0-0> 2.699 in the hexagonal form. Following the scheme
r,r-01 2.roe(5) ot-ol'l3l 2.553(lo) TAELE 5. NOI.IOICTAIURIPROPOSED FOR ATOiS II{ INDNIII! {61 Al{D oRfi otuio,{Blc CInDIERIT! 0t'-01'{31 2,877(10) or'-01'[6] 3.227181
<0-0> 2.971 lndl 8 l lte 0ftho|h@blc cordlerlte th Jh zh to Jo zo
il-01-Tt 129.1(3) 12-02-t2 173.3(7) T1 1/2 1/2 t/4 rll v4 t/4 1/4 T?-01-lt r29.1(3) 116 0 v2 l/4
T2 0.3727 0.266a 0 T2l 0.1841 0.0805 0 t l{unber in souare brackets refeB to mltlpllclty of the bond length. rz6 .0530 .3200 0 123 - .1334 .2393 0 meters are given in Tables 2 and 3, respectivd, and bond length and angle data are given in 0l 0.4851 0.3494 0.1445 0:1 0.2426 0. t069 0.1445 Table 4. Calculation of a three-di.mensional 0]6 .0679 .4172 ,1445 difference Fourier synthesis (F"-F, revealed 0t3 - .1747 .3104 .1445 no significant ,anomalies, indioating an absence of alkali atoms and HrO in ttre structural chan- 02 0.?305 0.3093 0 Dzl 0.1153 0.1941 0 nels of the indialite. 026 - .0394 .2699 0 023 - .1547 .0759 0 DrscussroN t/3 lt 0.t667 l/4 Nomenclature C@rdlnate transfg@tlans fro hqagonal t! C-csnter€d orthorholblc basls Indialite (Frg. 1) is isostructural with beryl for the at@ ln lndlallte related by lndmtity' L slrtb tum, g, and thlrd tun, ].. and, like low cordierite, it is a framework si- 'l: yo . yh - ' xo " xhlz, xh/2, zo zh licate. To facilitate discussion and comparison - 6. xo xhl2 - !h12, ro rh? 1 lhlz, zo " zh oJ the str,uctures of the hexagonal and orttror- " 3, xo - -yhl2, yo xh - !dz, zo - zh hombic potymorphs of MgaAtSLOler \ile pro- " CRYSTAL STRUCTURE OF INDIALITE 47 used for the feldspars (Kroll 1973), tle Al con- =ts3= 0.0) within experimental error despite tents of the ?r and ?s tetrahedra in indialile that for Si- and Al-containing tetra- are denoted as tr and t, respectively, whereas hedra are *0.01A longer than those recorded those of the 7rl, T16, Tzl, ?g6 and Tz3 teta- for corresponding 7g tetrahedra (Iable 5). hedra in orthorhombic cordierite are denoted Cohen et al, (1977) have also asserted that the as frl, tr6, ttl, /s6 and &3, respectively. Glilford cordierite is completely ordered with- in experimental error because its (?-O) values Al, Si contents of tetraltedra are statistically identical with those of ttre White Well corclierite. Following analogous tetrahedral A site refinement using neutron studies on feldspars, Al contents of the Tr and diffraction data recorded for tle White IVell 7g tetrahedra in indialite wete estimated as- cordierite (Cohen et aI. 1977) indicates it to be suming a linear relation betweeen is expected to be longer than rAELE5. EsrtilATtor.t0F Til r SITE OCCUPANCIESIII INDIALITE (7rO) for tetrahedra with identical Al,Si contents, two separate equations were used to Content tlhlte Ue]l Cullford Cordlerlter Cordlerlte estimate the contents of these tetrahedra. These equations were derived utilizing the grmd .Tl0t ..TI-0r, mean ?-O bond lengths, <
* datr frcr Cohenet al. (1977) $ nomlized on the basl3 of 9 tetrahedral atoN Long- and short-range order s nonislized on the basls ol 18 oxygenatm. Using the estimated Al,Si contents of the. te- trahedra, a Bragg-Williams (1934) long-range order parameter of 0.38 is salculated and it is TABLE HIPoTHFIICAL 7. Tl, T2 SIIE oCCUPAI{CrESAltD C0RRESP0I{DINC now apparent that a range of intermediate Al,Si BRAGG-|ILI.IAI'ISLOI{G RAI{GE ORDER PAMMETERS FOR IIIDIALIIE order is possible within the constraints of P6/ mcc Al.Sl occupancy Bragg-Hlll lG parmter s1m.metryjust as tlere is a range of intermediate order within the constraints of. C2/ m for the tt ' o'44 0.00 alkali feldspan. Ideally, one can conceive of Al, t2 r 0.44 Si distributions in indialite which rezult in Bragg- Williams parameters rangng from 0.0 to 0.75 as \ " 0.67 - illustrated in Table 7. One may consider the Al, t2 0.33 Si distribution for the 0.60 and 0.75 degree of tl . 0.0 orde.r to be mlikd for crystal-chemical rea$ons; 0,60 however, the to long-range order o'at extent which \ " may develop in indialite has yet to be deter- ' tr' 1.0 mined. ,: 0.t5 t2 . o.17 The discussion to now has dealt exclusively with long-rringe order; nevertheless one cannot 48 THE cANADTAN MINERALOGIST preclude the possibility that short-range ordered sr-ing the ordered distribution wi'thin the ring domains exist in indialite. Although no conclu- would follow, the orientation of the ordered sive evidence for their existence in indialite has unit cell within the hexagonal indialite host been found, Langer & Schreyer (1969), in a would be as shown in Figure 2b which coincides study of synthetic cordieri'te, observed a discre- with the orientation of the ordered cordierite pancy between the infrared spectra and powder cell depicted in Figure lb. Likewise, a prefer- diffrastion data which they believe could be a ence by Si for each of the other two 7r tetrahe- result of the incipient development of short- dra would lead to local domains with orienta- range ordered ds6ains folloryed by the develop- tions as shown in Figures 2c and 2d. Based upon rnent of long-range ordering with further anneal- this model, there are three possible orientations ing. within the hexagonal host which the short-range A. simple model for the development and ordered domains may assume. Continued growth orientation of short:range ordered domains in in- and enlargement of these ordered domains may dialite can be constructed based upon the pre- ultimately lead to the formation of the familir ferential selection of tetrahedra. within the te- polysynthetic or triUing twin in cordierite trahedral frarnework, by Si and A1. Ideally, in (Meagher & Gibbs 1965; Meagher 1967) which totalfy disordered indialite, there is .a 5/9 prob- will be discussedin terms of a possible two-step ability of finding Si in either the Tr or Tz tetra- order-disorder mechanism in a forthcoming pa- hedra. In partly ordered indialite the ?r and, Tz per. tetrahedra may differ in Al,Si content but there It is of interest to calculate the long-range is an equal probability of finding Si in eash.of average Al,Si contents of the ?r and 7z tetrahe- the three equivalent 7r tetrahedra outside the dra in a stoichiometric indialite which is com- six-membered ring (Fig. 2a). Likewise, there is posed of equal amounts of these short-range or- an equal probability of finding Si in each of the dered domains. Such a calculation yields an oc- six equivalent ?a tetrahedra within the six-mem- cupancy of /r = 0.67 and tz=O.33 with a long- bered ring. ff, however, in some localized vol- range order pa'rameter of 0.30 (fable 7). This ume, Si should preferentially occupy one of the agrees within experimental error with the Al, Si three ?r tetrahedra nutside of the,.ring, and as- content determined in the refined indialite struc-
d projection Flc.' 2. C-axis of the arrangementof Tr tetrahedra about tle M octabedrou in (a) :tudislite and (b), (c) and (d) tbee possible ordered arrangementsof 1 Si (full circle) and 2 Al (open circles). CRYSTAL STRUCTURE OF INDIALITE 49 ture for which fr = 0.72, lz = 0.30 and the long- riintgenogaphische untersuchung von magnesium- range order pararneter is 0.38. This agreement silikaten. N eues Jahrb. Mineral. Abt. 58, 21G227. may be fortuitous, however, since equal amounts HANsoN, A. W. (1965): The crystal structure of the of the tlree domains need not occur and, at the agulenen $trinitrobenzene complex. Acta Cryst. present t:me, T{e can only acknowledge the pos- Lg, 19-26. siblo existence of short-range ordered domains KRoLL, H. (1973): Estimation of the Al,Si distribu- in this indialite. tion of feldspars from the lattice translations Tr[110] and Tr[110]. Conft, Mineral, Petrologl 39, 141-156. AcKNowLEDcEMENTS LANcnR, K. & Scm,evnn, W. (1969): Infrared antl powder X-ray diffraction studies on the poly- The National Researsh Council of Canada morphism of cordierite, Mgz(ALSiOre). Amer. and the National Science Foundation (Grant Mineral. 54, t442-I459. DES71-0M86-A03) are thanked for their gen- Mnecrnn, E. P. (1967): The Crystal Structure and. erous financial support of this study. We also Polymorphism of Cordierite. Ph.D. Thesis, The th,ank Professor A. Miyashiro of Tokyo Uni- Pennsylvania Stato University, University Park, versity for donating the specimen used in our Pennsylvania. study. & Grnns, G. V. (1965): Crystal structure and polymorphism of cordierite. Program Abstr, Geol. Soc. Amer. Ann, Meet. Kansas City, 105' REFERENCES 106. Brncn,A. E. & Arner, A. L. (1968): Empiricalcor- MryAsHrRo, A. (1957) : Cordierite-indialite relations. rection factors for the electron microanalysis of Amer. l. Sci, 255, 43-62, silicatesand oxides.I. Geol, 76, 382-403. & Ileue, T. (1954): A preliminary uote Bnecc, W. L. & Wnrrervrs,E. J. (1934): The effect on a new mineral, indialite, polymorphic with cor- of thermal agitation on atomic arrangementsin dieite. Proc. Imp. Acad. Japan 30, 74G751. alloys.Proc. Roy. Soc.4145,699:730, -, -, Yervreserr, M. & Mryesnrno, .BusrNc,W. R., MenrrN,K. O. & LBw, H. A. (1964): T. (1955): The polSrmorphism of cordierite and ORFFE, a fofiran crystallographic function and indialite. Arner, J. Sci. 253, 185-m8. enor prograrn.Oak Ridse Nat. Lab. Rep. ORNL- RANKTN,G. A. & MEnwnrr, H. E. (1918): The tei- TM-306. nary system MgO-Al:Og-SiO". Amer, l, Sci. 45, Bvsrndrvr,A. (1942): The crystal structure of cor- 30r-325. dierite. Ark- Kemi. Min. Geol, 1.5B, l-5, Snarn, f. V. (1954): A review of tle Al-O and ConnN,J. P., Ross, F. K. & GBss, G. Y. (1977): Si-O distances,Acta Cryst. 7, 479487. An X-ray and neuron diffraction study of hy- & Ben-rv, S. W. (1963): Secondreview of dous low cordierite. Amer. Mineral. (in press). Al-O and Si-O tetrahedraldistances. Acta Cryst, Fnnuon, L. L. (1918): Preliminary note on the 16,801-811. burning of coal seams at the outcrop. ?raas. SrruNz, H., TnxxvsoN, C. & Uenrr,, P.-J. (1971): M.G.I.Ind.12, 50-63. Cordierite moryhology, physical properties, struc- FoLrNsBBgR. E. (1941): Optical propertiesof cor- ture, inclusionsand oriented intergrowth. Minerals dierito in relation to alkalies in the cordierite-beryl Sci,Eng.8, 3-18. strucfitre. Amer. Minerat. 26, 485-500. TAKANE,K. & Terrucru, T. (1936): The crystal Grsss, G. V. (1966): The polymorphismof cordie- structur€ of cordierite. lap. Assoc. Mineral. Pe' rite: I. The crystal structure of low cordrerite. trology Econ. Geol. L6, l0l-127 (in Japanes). Amer. Minerat. 51, 1068-1087. Manwcript receivedSeptember 1976, emendcdNov' Gosslrn, B. & Mus$NUc, F. (1928): Vergleicherde ember1976.