American Mineralogist, Volume 64, pages 337-351 , 1979

High-temperature crystal chemistry of hydrous Mg- and Fe-cordierites

MrcHeel F. Hocssr_r_e, Jn.r

Department of Geological SciencesVirginia Polytechnic Institute and State [Jniuersity

B lac ksburg, V i rg inia 2 406 I

GoRpoN E. BnowN, Jn.

Department of GeologyStanford Uniuersity

Stadord, C alifu rnia 94 305

Fneo K. Ross nNo G. V. Grsss

Departments of Chemistry and Geological SciencesVirginia Polytechnic Institute qnd State (lniuersity

B lac ksburg, V i rg inia 2 406 I

Abstract

Structural refinements have been completed for a Mg-rich cordierite using data recorded at24",375o,775o and 24"C (after heating to 775") and for an Fe-rich cordierite at 24" and375'C. The mean T-O bond lengths in both cordierites remain unchanged but the meanoctahedral bonds (M-O) lengthen upon heating. The unusually low thermal expansion of theMg-cordierite is the result of its relatively "rigid" tetrahedral framework and the anisotropicexpansion ofoctahedra isolated from each other. This anisotropic expansion leads to a slightrotation of the six-membered rings, a concomitant collapse of the structure parallel to c, andan expansion parallel to a and 6. In the Fe-cordierite, the octahedron is more flattened,resulting in c being smaller and a and b being larger than the cell dimensions of the Mg-cordierite. Upon heating Fe-cordierite, there is no evidence for a rotation of the rings, and a,b, and c increase as the M-O bonds expand.

X-ray Ap maps calculated for the Mg-cordierite showed approximate positions and relativeamounts ofchannel constituents. The peak ascribed to the alkali and other atoms that centersthe six-membered rings becomes elongated parallel to c upon heating through 375.c. How-ever, the peak ascribed to the oxygen associated with HrO in the 24' and 375' maps is absentin the 775'C maps. It reappears in maps computed from the 24" (after heating) data. In bothcordierites, small amounts of hematite were produced during heating (prematurely haltingdata collection on the Fe-cordierite), and apparently formed by combination of octahedraland channel iron with oxygen from the channel water molecules.

A re-examination of the water-orientation in the channels o[ the Mg-cordierite usingneutron and X-ray Ap maps does not clearly show either type I [H-o-H in the (100) planewith the H-H vector parallel to cl or type II [H-o-H in the (100) plane with the H-H vectorparallel to b] water, as previously suggested by spectroscopic studies. Instead, our ap mapsindicate that the water molecule lies in a plane tilted -29o from (100) and that the H-H vectoris t i l ted -l9o from c.

Introductioncordierite, (Mg,Fe)rAlaSiuO,r. nHrO, has attracted

the interest of mineralogists and ceramists because of

I Present address: Department of Ceoloqy, Stanford Univer-sity, Stanford, California 94305.

w3-n4x/79/0304-0337$02.00 317

its widespread formation in moderate- to high-grademetamorphic rocks, its occurrence in a variety ofstructural states involving different degrees of AllSiordering, and its unusually low thermal expansion.Ceramists have found a number of applications forMg-cordierite as a thermal shock resistant material.

HOCHELLA ET AL,: CRYSTAL CHEMISTRY OF CORDIERITES

Among these are use as an insulator for spark plugs,as a refractory coating on metals for internal com-bustion engines, in the production of dolomitic typesof refractories and low-expansion concrete, and as acatalytic support for the treatment of waste gas andautomobile exhaust emissions. Perhaps its most im-portant application in the future will be in the fabri-cation of turbine engines (Gostelow and Restall,1972). Fe-rich cordierite has been produced in indus-try but only as a by-product in blast-furnace linings(Richardson, 1949), in "black cores" in stonewarepipe (Lach, 1974), and even in building-brick (Rath-geber and Fowler, 1966). Because it is more difficultto synthesize than Mg-cordierite and because it oxi-dizes at high temperatures, ceramists have not yetfound specific applications for Fe-rich cordierite.

Despite the extensive use of Mg-cordierite in theceramic industry and the growing geologic impor-tance of both the Mg- and Fe-rich phases (see, e.g.,Currie, 1971;Newton,1972), no detailed study of thebehavior of the cordierite structure at high temper-atures has been undertaken. The present study (seeHochella, 1977) was carried out in order to determinethe crystal structures of hydrous Mg- and Fe-richcordierite as a function of temperature, in an attemptto clarify the unusual thermal-expansion propertiesof this mineral. Also, the effects of heating on boththe channel constituents and the AllSi distribution inthe tetrahedral framework were investigated. Finally,the neutron diffraction data ofCohenet al. (1977)forthe White Well cordierite were re-analyzed, and theorientation of the water molecules within the chan-nels of this structure is discussed.

Experimental detail and observations

Specimen descriptions

The Mg-rich cordierite, designated the White Wellcordierite, was previously described and used in acombined X-ray and neutron diffraction study byCohen et al. (1977). It occurs in a phlogopite schistwhich formed under amphibolite to granulite faciesconditions (Pryce, 1973) and is one of the most Mg-rich specimens yet reported (see Table l). We as-sumed that our crystal (0.30 X 0.22 X 0.22 mm) andthose used by Cohen et al. (1977) had identical chem-ical compositions and crystal structures because theyhad statistically-identical cell dimensions and wereselected from the same specimen (an approximately4-mm cube). The room-temperature intensity data(before heating) were taken from Cohen (1975).

The Fe-rich cordierite (Table I ), designated the

Dolni Bory cordierite, was collected from a pegmatitenear Dolni Bory, Western Moravia, Czechoslovakia(Stanek and Miskovsky, 1964), where crystals arereported to attain dimensions up to several decime-ters. Many single crystals were sector-twinned; how-ever, one exhibiting uniform optical extinction wasfound suitable for structure determination. This crys-tal was a nearly equant chip measuring 0.33 X 0.33 X0.27 mm. After orientation by optical spindle-stagetechniques (Bloss, in preparation), crystals of theWhite Well and Dolni Bory cordierites were mountedin high-temperature mullite cement on silica-glass fi-bers and sealed in evacuated silica-glass capillaries toinhibit the oxidation of iron. Each was heated forapproximately 12 hours at l00oC to cure the cementand was then equilibrated for at least l2 hours at thetemperature of the measurement before data collec-tion was begun. Temperature fluctuations for thesingle-crystal heater (see Brown et al., 1973, for de-tails) were recorded continuously on a strip chartduring each high-temperature experiment and werenot more than t l0o.

Thermal expansion measurements

Cell parameters for the White Well cordierite atseven temperatures ranging from 24" to 775o andagain at24"C after heating (see Table 2) were deter-mined by least-squares refinement of the diffractome-

Table l. Cell parameters (24"C), distortion index (A), specificgravity, calculated density (p) and composition of the White Well

and Dolni Bory cordierites

Lrhi te l ie l l Dolni Bory

a 1 7 . 0 8 8 ( 3 ) 1b 9 . 7 3 4 ( 2 )c 9 . 3 5 9 ( 1 )A 0 . 2 5 "s . g . 2 , 5 1p ( c a l c . ) 2 . 5 6 e / c m r

2Formulae (based on 18 oxygens)

A l k a l i s" to. o5*0. o2c"o. oz

M cations "oo. ot'rr. rt"93lo,

T ca t i ons s i 5 .o tA13 .9 :

i J a t e r ( H Z O ) O . S O

r z . z : o ( s ) i9 . 8 3 s ( 3 )9 . 3 r4 (3 )0 . 2 1 '2 . 7 62 . 7 8 g / c n 3

Nto . 15c"0 . o5

otto.ou"ro. , r t " i ]u,

s i4. 9 rAr4. 05

( H z o ) o . o t

1 The nwnbex in parentheses ?epresents the stmdard eruor (lG )resoqLated utth the Last decinal place reported.

2 Whtte WeLL cordierLte eorrposition repoxted by Prgce (1973);Dolni Borg cordierLte eontposition reported by Stanek mdMLskoxsky (L964).

HOCHELLA ET AL.: CRYSTAL CHEMISTRY OF CORDIERITES 339

9.734(2) 9 .359(1)9 .737(2) 9 .357(1)9 . 7 4 1 ( r ) 9 . 3 5 8 ( 1 )9 . 7 4 5 ( 7 ) 9 . 3 5 7 ( r )

9 . 7 5 1 ( 1 ) 9 . 3 5 7 ( 1 )9 . 7 5 5 ( r ) 9 . 3 5 5 ( 1 )9 .7s9(1) 9 .352( r )9 .746( r ) 9 .36r (1 )

9 . 8 3 5 ( 3 ) 9 . 3 r 4 ( 3 )9 .847(2) 9 .328(2)

7 5 5 6 . 7 ( 4 ) O . 2 51 5 5 8 . 2 ( 4 ) O , 2 61 5 5 0 . 0 ( 3 ) 0 . 2 11 5 6 r . 3 ( 3 ) O . 2 7

1 5 6 3 . 1 ( 3 ) O . 2 7L 5 6 4 . 2 ( 3 ) 0 , 2 71 5 6 5 . 1 ( 3 ) O . 2 71 5 6 1 . 8 ( 3 ) O . 2 6

1 5 7 8 . 3 ( 8 ) 0 . 2 11 5 8 5 . 3 ( 3 ) 0 . 2 2

Table 2. Cell edges (A), cell volume (As), and calculated distortionindex (A) Dr temperature for White Well and Dolni Bory

corolerltes

Tenperature ("C) a

Whlte Well cordlerlt€

rz . oss ( : )117.103(3)17 .1r .3 (3)77.123(2)

r 1 . L 3 2 ( 2 )r7 .ko(2)r7 .t49(2)17 .119(2)

17 .230(5)r7 .2s8(3)

sorption corrections were not initially applied to ei-ther the White Well (p : 9.0 cm-') or Dolni Bory (p: 26.3 cm t) cordierite data sets for the followingreasons: (l) Positional parameters obtained fromboth X-ray and neutron refinements for the WhiteWell cordierite of Cohen et al. (1977) are identical towithin 26; the X-ray data were uncorrected for ab-sorption. (2) The relatively low linear-absorption co-efficient and size of the White Well cordierite crystalused in this study result in a differential absorption ofabout 7 percent in the worst case. (3) The Dolni Borycrystal was dislodged and lost from its mount beforeits shape was accurately determined. However, thecrystal was nearly equant and, in the worst case,produced a difference in transmission of - l6 percent.After completion of this study, an absorption calcu-lation for the White Well cordierite crystal was madeusing the program AcNosr written by Coppens el a/.(1965), which showed that transmission varied from0.84 to 0.90. Thus our neglect of an absorption cor-rection in this case should not result in significanterrors in positional parameters. In the case of our Fe-rich cordierite, where absorption is more significant(transmission is predicted to vary between 0.42 and0.49 in the worst cases), the roughly equant shape ofthe crystal would result in a differential absorption ofl0 percent or less between most pairs of reflections.Furthermore, the bond lengths from the two Fe-cordierite refinements are quite reasonable relative tothe Mg-cordierite distances, suggesting that the Fe-cordierite positional parameters were not signifi-cantly affected by differential absorption effects.

An approximate extinction correction was madeand least-squares refinements were calculated withfirst isotropic and later anisotropic temperature-fac-tor models. Weights based on the counting statisticswere used in all refinements, and reflections wereautomatically rejected at the 2& level for the WhiteWell cordierite and at 3,i for the Dolni Bory cordier-ite . In our refinement of the White Well cordierite, weneglected the channel constituents reported in thechemical analysis (Table l). On the other hand, whileneglecting the water, we included the alkali atoms inour refinement for the Dolni Bory cordierite becauseof their greater abundance. The number of acceptedreflections and the weighted and unweighted R fac-tors for the anisotropic refinements are given for bothcordierites in Table 3. The final positional parametersand anisotropic temperature factors, as well as theisotropic equivalent temperature factors for the non-equivalent atoms in the White Well and Dolni Borycordierites, are listed in Table 4. Observed and calcu-

24280375470

7 rh.e ,lweere in pare,ntheee|, represent the eetinated. stadzyd. ewt (t6)

oI tne L@t @dML qwted

2 Afte" heatirg

ter settings angles for 28 reflections in the 20 range30-40". Similar refinements were carried out for theDolni Bory cordierite using data gathered at 24" and375'C. The refined cell parameters, cell volume, andcalculated distortion index (Miyashiro el al., 1955)for each temperature are listed in Table 2.

Data collection and refinements

Intensity data from one octant of the MoKa spherewere collected over a range of 5" to 60' 20 at temper-atures of 375o, 775o, and, 24"C (after heating) usinggraphite-monochromatized MoK radiation (WhiteWell cordierite) and at 24" and 375oC using Zr-filtered MoK radiation (Dolni Bory cordierite)r. Theupper 20limit was imposed by the heater configura-tion. Two standard reflections (060 and 008) mea-sured every 30 reflections indicated that machine driftand/or crystal movement were within acceptable lim-its, so no drift corrections were applied. Observedintensities for the White Well cordierite were cor-rected for Lorentz-polarization effects assuming a 50percent ideally mosaic monochromator crystal andwere converted to lF(obs)l with a values estimatedusing the equation of Corfield et al. (1967). The ob-served intensities for the Dolni Bory cordierite werecorrected for Lorentz-polarization effects and con-verted to lF(obs)l with the program DereI-rss. Ab-

'z Intensity data for the White Well cordierite were collected atStanford University; data for the Dolni Bory cordierite were col-lected at VPI and SU.

8 Catalogued in the World List of Crystallography ComputerPrograms (3rd edition).

HOCHELLA ET AL.: CRYSTAL CHEMISTRY OF CORDIERITES

Cordier l te TeEDeralure/I of accepted R-factorreflectlons IJNII' 'd2

Table 3. Results of the aniSotropic refinements for the White Welland Dolni Bory cordierites

loss in the intensities of the diffraction data nor evi-dence of oxidation or breakdown. However, unlikecordierite, both of these minerals lack loosely-boundwater molecules and Fe atoms in the channels (Gold-man et al., 1977). Upon heating, these componentsapparently react to produce hematite even in a thor-oughly evacuated capillary. The decrease in the in-tensities of the diffraction data recorded for the DolniBory cordierite indicates that octahedral Fe is alsoinvolved in the reaction to form hematite, which re-sults in partial disruption of the Fe-cordierite struc-ture.

Discussion

Axial expansion

The a cell edge of the White Well cordierite in-creases as a function of temperature at a rate slightlygreater than that of 6, while c undergoes a slight butsystematic shortening up to 775oC (Fig. l). On theother hand, the c cell edge of the Dolni Bory cordier-ite (not plotted) does not shorten upon heating from24" ro 375'C but increases at about the same rate asthe a and b cell dimensions. However, because allparameters of the Dolni Bory cordierite were deter-mined at only two temperatures up to 375"C (Table2), the variation of these parameters and cell volumewith temperature is only qualitatively known over arelatively small temperature range. Therefore, therates of axial and volume expansion for the two cor-dierites cannot be quantitatively compared.

Thermal expansion data for the disordered poly-morph, indialiteu (P6/mcc), measured by Fischer etal. (1974) and by Lee and Pentecost (1976), are com-pared with those for the ordered White Well cordier-ite (Cccm) in Figure l The expansion of the a celledge of White Well cordierite is about l500ppmgreater at 775o than that of indialite, whereas theexpansion along b in the former is practically thesame as that along a in the latter. The contractionalong c in White Well cordierite is significantly less(-800ppm less at 775") than that along c in indialite.Moreover, the variation of c in White Well cordieriteis linear with temperature within the limits of error ofthe results. The thermal expansion measurements forthe two indialites show an initial contraction along cwith temperature, but Fischer et al. find that c begins

u Cordierite may exist in a range of structural states, like alkali

feldspars, depending on the ordering of Al and Si in the tetrahe-

dral framework. The ordered form of cordierite is orthorhombic;

the completely disordered form is hexagonal and has been given

the name indialite.

whire Well 24"c TaftetCohen e t aL . ,

1977)375" C

175"C

24"C (afxerheating)

Dolni Bory 24'C

375"C

0 . 0 3 3 0 . 0 5 1

0 . 0 4 1 0 . 0 6 6

0 . 0 5 6 0 , 0 8 7

0 , 0 3 8 0 . 0 6 1

0 . 0 7 3 0 . 0 6 3

0 . 0 6 1 0 . 0 6 3

105 7

L07 7

994

LL7 6

1203

7L6

r R@M) = t t l re l - l ro l l t l lFol2 R<w) = t Lu ( lFo l - l r . l ) ' / t n { r ; ' l \

lated structure factors are given in Table 5.4 Selectedinteratomic distances and angles uncorrected forthermal motion were calculated with the programORnnes and are given in Table 6.

Precession photographs of the White Well cordier-ite recorded following the heating experiment showedpowder rings of weak intensity identified as the dif-fraction pattern of hematite. Later, when the DolniBory cordierite was heated above 600"C, the crystalchanged from colorless to amber while the peak in-tensities dropped off drastically, preventing the col-lection of additional data. A second crystal was se-lected and the measurements were repeated, butagain the peak intensities dropped off markedly attemperatures above 600o. Precession photographs re-corded after the second set of measurements showedthe same faint powder rings of the hematite diffrac-tion pattern. Rathgeber and Fowler (1966) carriedout open-air heating experiments at I150" onstoichiometric Fe-cordierite, in which they noticed areddening of the crystals, a 40 percent decrease inmeasured X-ray powder diffraction peak intensity,and the formation of hematite (see also Stunz et al.,1971). On the other hand, hedenbergite, CaFeSizOe,was heated without oxidation as high as 1000' fordata collection by Cameron et al. (1913), using thesame heater and mounting techniques employed inour study. Brown and Prewitt (1973) heated an oli-vine (Far') to 7lOoC in an evacuated capillary with no

{ To receive a copy of Table 5, order Document AM-79-093from the Business Office, Mineralogical Society of America, 1909K Street, N.W., Washington, D.C. 20006. Please remit $1.00 inadvance for the microfiche.

HOCHELLA ET AL.: CRYSTAL CHEMISTRY OF CORDIERTTES

Table 4. Final fractional coordinates and thermal parameters (X 106) for White Well and Dolni Bory cordierites at various temperatures

f D o l n i B o r yAron 24 . c r 375 . c 7 7 5 " c 24" c2 24"C (Cem\ 375oc

341

rrl (A1)

116 (s i )

vzB r r

T r l (S i ) Bzz- B s sB r zB r sB z r

eq

xvz

B r rT16 (A l ) Bzz-

B s gB t zB r rB z tB

eq

x

vz

B r rB z z

T?3 (S i ) B : .p r 2

B r s8 z rB

L l 4L / 4

0 . 2 5 0 2 ( 1 ) q

s7 (3 )133 (8)110 ( 9)1s ( 3 )00

o . 5 2

0r l 2L l439 (3 )

146 (r0)e8 (10)000

o . 4 5

0 .1926 (1 )0 . 0 7 7 8 ( 1 )

038 (2 )8 3 ( 7 )

118 (8)7 ( 3 )00

0 . 3 9

0 .0s08 (1 )0 . 3 0 7 9 ( 1 )

031 (3)

121 (8 )r32 (9 )

8 ( 3 )00

0 . 4 3

-0 . 1352 (1 )o . 2 3 7 5 ( r )

037 (2 )9 e ( 7 )

105 (8)-1 r (3 )

00

0 . 3 9

o . 2 4 7 4 ( r )0. r029 (1)0 .1410 (2 )

7 4 ( 5 )ls3 (13)179 (15 )

e (s)-31 (6)_19 (11)

0 . 6 9

0. 0620 (r )0. 4160 (2 )o . L 5 r 2 ( 2 )

s4 (5 )211 (r3)180 (r5)r7 ( 6 )-2 (6 )

-7r (1r)0 . 6 9

r l 4r l 4

0 .2s00 (2 )93 (4 )

224 (r2)27 2 (L4)2 2 ( s )00

0 . 95

0r l 2L l460 (s )

245 (r5)228 (L7)

000

0 . 8 1

0 . 1920 (1 )0 ,0783 (1 )

060 (4 )

lss (11)239 (11)11 (5)00

0 . 7 1

0 . 0506 (1 )0 . 3076 (1 )

06 2 ( 4 )

220(L2)268 (15)2L (5 )00

0 . 8 3

-0. 1351 (1)0 . 2369 (1 )

057 (4 )

176 (11 )247 G3)-L4 (4)

00

0 . 7 3

o . 2 4 7 0 ( L )0 . 1036 ( 2 )0 .1407 (3 )L37 (7 ) '277 (22)308 (25)24 (e )

-40 (11)_68 (r9)L . 2 5

0 .0620 (1 )o.4166 (2)0. lsr2 (3 )

9 0 ( 7 )37 5(2L)33r (25)

24(Lo)-16 (11)

-rs0 (19 )L . 2 L

L l4r l 4

0 . 2 s 0 0 ( 2 )r25 (6)363 (19)429 (22)3s (8 )00

7 . 4 6

0L /2L l488 (7 )

352(22)342(25)

000

1 . 1 9

0 .1917 ( r )0 . 078s (2 )

087 (5 )

240 (15)37 3 (20)13 (7 )00

1 . 08

0 .0500 (1 )0 .3070 (2 )

091 (6 )

33s (18 )382(22)27 (8 )00

t . 2 3

-0 .1347 ( r )o .2363 (2 )

086 (5 )

27 3 (16)340 (r9)-40 (7 )

00

1 . 0 8

o .2468 (2)0 . 1042 (3 )0 . 1398 (4 )

2L7 (L2)414 (36 )4s0 (38)16 (16 )

-r22(L9)-95 (29)1 . 9 0

0. 0619 ( 2)0 . 4159 (3 )0. 1510 (4 )122 (10)ss0 (33 )s4s (39)23 (L6)

-73 ( r7 )-234 (32)

l . 6 r

L l4I l 4

0 . 2 5 0 2 ( r )s1 (3)

106 (10)17 4(r2)15 (4)00

o . 5 4

0L l2r l 433 (4 )

L7 0(L2)135 (15 )

000

0 . 5 0

0 . 1924 (1 )0 . 07 78 (1 )

032(3)9 r ( 9 )

167 (r2)1 ( 4 )00

0 . 4 4

0. 0508 ( 1)0. 307 9 (1)

032 (3 )

124 (10)1s3 (13)

s (4)0

o . 4 6

-0 . r 3s2 (1 )o .237 4 ( L )

02 3 ( 3 )

133 (9 )141 (11)_13 (4)

00

0 . 4 4

0 .2473 ( r )0. 1034 (2 )0 . 1 4 0 9 ( 2 )

66 ( s )282(16)153 (20)

3 ( 8 )-31 (8)-11 ( r 6 )0 . 7 9

0 . 0623 (1 )o .4166 (2 )0 . 1 5 1 3 ( 2 )

s7 (5 )2 t s ( r 7 )1e8 (21 )-3 ( 8 )10 (8)

-7 2 (r5)0 . 7 3

L l4L l4

o.2502(3)4 r ( 6 )

104 ( ls)64 (1s )L4(7 '00

0 . 3 7

0L l2r /43r (8)

L22(20)44(2o)0

00 . 3 3

0.1901 (1)0 .o1 94 (2 )

037 (6 )38 (14 )64(L7 )L2(7 )00

0 . 3 1

0.0s01 (1)0 . 3 0 7 6 ( 2 )

03 3 ( 7 )64(L6)69 (19 )13 (8)00

o . 2 9

0 . 2 4 4 2 ( 2 )0. 10s2 (3 )0. r415 (3)

69 (r2)r29 (27)93 (28)

-15 ( r4 )-44(t6)-34(24)0 . 5 5

0. 0611 (2 )o.4L44 (4)0 .1522 (4 )

70 (12 )207 (29)134 (33)3 o (14)23(L6)

-s8 (26)0 . 6 9

r l4r l 4

0 .2s01 (4 )94(e)

208(28)L04(26'38 (12)00

0 . 8 0

0L t2Ll4u (10)

2L9 (34 )144 (3s)

000

0 . 5 2

o.L894 (2)0 . 0 7 9 s ( 3 )

065 (e)

L44(25)D,7 (29)

4(L2)00

0 . 58

o.0499 (2)0 .3077 (3 )

043 (e )

L62(28)208(32)39 (13 )00

0 . 6 2

0 . 2 4 3 8 ( 3 )0. 1049 (5 )0 .1412 ( s )101 (16 )296(52)269 (56)18 (23 )

-80 (26 )-40(44)1 . 1 0

0 . 0609 (3 )0 . 41s l ( s )0. 1s09 (5)

9s ( ls)324(48)285 (60)23 (23)

-18 (25)-13r (46)

1 . 1 3

vzB r rB z zR ^ ^

BrzB r sBzzB r

xvzB r rB z zB s :B rzB r sBzzB

-0 .1347 (1 ) - 0 .1350 (2 )0.2343(2) 0.2344(3)

0 034(7) s9(9)43 (1s) r51 (26)73 (16 ) 140 (28 )

-22 (7 ) - r 2 ( r2 )0 00 0

o . 2 8 0 . 5 9

X

v

B r ror I 8zz-

B : :B r zB r rBzzB

eq

x

vzg r r

0 .6 2 , ,r p 3 3

B r zB r sBzzBeq

342 HOCHELLA ET AL.: CRYSTAL CHEMISTRY OF CORDIERITES

Table 4. (continued)

Whlte well

Arom 24"Cr 375"C 775 'C 24"C2

Dolni BorY

24"c (Ccm) 375"c

vzB r r

o r 3 Bzzp 3 3

B r zB r s9zsBeq

-0 . 17 32 (1 )0 . 3 r0 r ( 2 )0 . 1416 (2 )

s4 (4 )2o2(L4)199 ( ls )=11 (6)

20 (6)-29 (11)

0 . 7 0

0 . r 223 (1 )0 . 1839 (2 )

07 0 ( 7 )

248 (2L)386 (2s)s l ( 9 )00

1 . 04

-0. 0430 (1)0 . 2 4 7 6 ( 2 )

0s3 (7 )

301 (21)330(24)-27 (9)

00

0 . 9 7

-0. 1645 (1)o . 07 92 (2 )

0e l ( 7 )

144 (19 )36L (23 )-37 (9)

00

0 . 9 6

0 . 162s (1 )L l 2u448 (3 )

L42 (9 )18r (9)

000 ( 7 )

0 . 5 8

-0 . 17 36 (1 )0. 3090 (2)o . 1418 (3 )111 (7 )342(22)285 (25)-26 (r0)

36 (10)-90 (19)

L . 2 0

0.1220 (2)0 .1846 (4 )

13s (12)368 (35 )718 (s0)133 (16)

00

r . 83

-O.0434 (2')0 .247 I ( 4 )

069 (11)

s94 (39)711 (49 )-31 (15)

00

1 . 8 5

-0. 1641 (2 )0 .07 93 (3 )

0163 (12)189 (30)779 (so)-76 ( l s )

00

L . 7 9

o . t 622 (L )r l 2L l 475 (4 )

259(r4)436 (L6)

00I ( 12 )

1 . t 3

-0.r7 34 (2)0 .3082 (4 )0 .1422 (4 )

L79 (L2)501 (3s)s49 (42)-ss (17 )

95 (18 )-140 (32)

1 . 9 8

0 .1216 (3 )0 .1843 (6 )

016s (18)615 (59)

L2O6(94)2r7 (27)

00

a Q 1

-0.0438 (3)0.2484 (6)

0L22 (L7 )883 (69)87s (76 )

" -L4<26)00

2 . 6 2

-0 . r 630 (3 )0 . 0 7 7 8 ( s )

0243(20)298(45)850 (70 )

- l s s ( 2s )00

2 . 3 2

0. 1626 (1)r l 2L l 4

109 (7 )385 (20)655(26)

00

30 (20)1 . 68

-0 . 17 33 (1 )0 .3102 ( 2 )o .L4L4 (2 )

60 (s )L7 4 (L7 )2O9 (2r)-20 (8 )

21 (8)-3 9 (rs)

0 . 7 0

0 .1222 (2 )0 .1844 (3 )

073 (8 )

178 (2s )401 (36)

61 (12 )00

0 . 98

-o .0432 (2 )o .2487 (3 )

058 (8)

26r(2s)360 (34)-33 (12)

00

0 . 98

-0.L646(2)o. 0803 (3 )

88 (8)r4o(2s)4L2 (35 )

-2(r2)00

1 . 0 0

0 . 1624 (1 )Uzr l444 (3)

L22(rr)22s(t3)

005 (L0)

0 . 5 9

-0.r1 29 (2)0 .3053 (4 )0 .L428 (4 )

8o (13 )r86 (30)e4 (30)

-2L(L4)3 (1s)

-84 (2s)o . 6 7

0. 1188 (3 )0 .1822 (6 )

072(2o)

L7 6(45)4O4(64)

66(20)00

o . 9 7

-0. 043s (4)0 . 2449 (6 )

040 (20)

363 (56)4e4(66)-16(25)

00

L . 2 0

-0. 1615 (4 )0 . 0 7 7 8 ( 5 )

090 (19 )

101 (40)382 ( s9 )

7 (22)

00 . 9 3

0 . r 632 (1 )t / 2L l 447 (4 )

11e (8 )L62 (9 )

00

12 (10)0 . 5 3

-0.r7 29 (3)0. 3049 (s)0.L421 (5)

65 (L7 )4s4 (s6)254 (60)-45(23)

46(22)_25(4s)

1 . 14

0 .1200 (5 )0. 1833 (8)

0r37 (27)270(78)7 02 (r09)109 (38)

00

L . 7 r

-0. 04 34 (4 )0.2462(9'

0s6 (2s )

579 (94)607 (r01)

-107 (38)00

r . o /

-o.L607 (7)0 . o 7 6 6 ( 7 )

0190 (29)l ls (70)621 (r04)-69 (3s )

00

L . O Z

0 .1632 (1 )L l 2r l480 (5 )

256 ( ls)402 (18)

00

11 (17 )1 . 11

x

v

B r rBzzB g :9 r zB r c9zsB

eq

x

zB r rB z zB s rB t zF r sB z gB

eq

x

zB r rB z zB : sB r zB r gB z sB

eq

xvzB r rR ^ -

B : sBtzB r rBzsBeq

ozL

oz6

oz3

I ALL 24"c data fron cohen et aL. (L97?)

2 A|ter heating

3 B"o i.e the isotropic equiualent of the anisott'opic tqnperaAne factore cdlcul'ated using the erp"easion(HdniLton, L969)

Beq = 4 /a l \ t ta2 * Bzzb2 + Bzsc2 * 2Btzabcos(

* 2 \zgbccosd + 2Br3accosg\

a The ntmbete in parenthesis pefe" to the estinated sta/tdard ernor (tG) associ.ated dith the Laet decinnl pLace

reported.

HOCHELLA ET AL..' CRYSTAL CHEMISTRY OF CORDIERITES 343

Table 6. T-O and M-O interatomic distances (A) and O-T-O angles (') for the five tetrahedral sites us. temperature in White Well andDolni Bory cordierites

I l l l i te well Dolni BoryDis tance/ Mu l t i -Ans le D l ic i t y 24"C 375"C 175"c 775?ct 24"C2 24"C 375"C

T11-011

;:*'

013"-T11-O13 |

o11-Tr1-o13"-ot3 '

- o t l '

!1ean

u';l:l016-T16-o16,

-o t6 " '

"""r-otu"T21 '01 l

-o23'

;:::

orl -Tr1-orlm

-ozL-oz3'

"';]:l-"''T23-013

-oz3

;:::

0r3-Tr3-0r3n-o

z6'oz3

o'u;l:l-""

T26-0L6

-ozL

;:::

or6-Tr6-or6m-oz6-ozL

o2l-T26-026Mean

T2I-OzL-T26

T 2L-O23-'r23T23-O26-T26

L , 7 4 8 ( 4 ) 1 . 7 5 6 ( s )

L . 7 4 8 ( 4 ) 1 . 7 5 0 ( 5 )

t . 7 4 8 ( 2 ) 1 . 7 s 3 ( 3 )

1 1 0 . 4 ( 3 ) 1 1 0 . 3 ( 4 )

9 6 . 9 ( 2 ) 9 7 . 2 ( 2 )

t 2 2 . 7 ( 2 ) L 2 2 . 4 ( 2 )

109 .3 ( 2 ) 109 . 3 ( 4 )

1 0 9 . 8 ( 1 ) 1 0 9 . 8 ( 1 )

r . 627 (4 ) 1 .631 (5 )

r . 6 2 7 ( 2 ) r . 6 3 1 ( 3 )

l r 7 . 6 ( 3 ) 1 1 8 . 3 ( 4 )

l r 1 . 9 ( 3 ) 1 1 0 . 9 ( 4 )

9 9 . 3 ( 3 ) 9 9 . 7 ( 3 )

109 .6 (1 ) L09 .6 (2 )

1 . 6 3 4 ( 4 ) 1 . 6 3 6 ( 5 )

L .623 (6 ) 1 ,616 (7 )

1 .591 (5 ) L .576 (7 )

1 . 6 2 1 ( 3 ) 1 . 6 1 6 ( 3 )

107 . 6 (3) L07 .2(4)

1 1 0 . 0 ( 2 ) 1 0 9 . 7 ( 3 )

108 .7 ( 2 ) 108 .7 ( 3 )

111 .8 (3 ) r Lz .5 (4 )

r09 .5 ( 1 ) 109 .4 ( 2 )

r . 6 4 1 ( 3 ) 1 . 6 3 8 ( s )

1 . 6 0 7 ( 6 ) 1 . 6 1 s ( 7 )

1 . s 7 s ( 6 ) r . 5 8 6 ( 7 )

1 . 6 1 6 ( 2 ) 1 . 6 r e ( 3 )

108 .3 ( 3 ) 108 .8 ( 4 )

111 . 9 ( 2 ) 111 . s ( 3 )

L 0 7 . 0 ( 2 ) 1 0 7 . 4 ( 3 )

1 1 0 . 5 ( 3 ) 1 1 0 . 2 ( s )

r 0 9 . 4 ( 1 ) 1 0 9 . 5 ( 2 )

L . 7 7 3 ( 4 ) L . 7 7 r ( 5 )

1 . 7 1 1 ( 6 ) L . 7 2 r ( 7 )

L . 7 2 6 ( 6 ) L . 7 2 L ( 7 )

r . 7 4 6 ( 3 ) L . 7 4 6 ( 3 )

10s .9 ( 3 ) 10s . 3 ( 4 )

Log .2 (2 ) 108 .1 ( 3 )

1 1 0 . 6 ( 2 ) 1 1 0 . 5 ( 2 )

r r - 2 .9 (3 ) r 14 .0 (4 )

r09 .4 ( r ) 109 .4 ( 1 )

u 3 . 3 ( 4 ) 1 7 5 . 1 ( 6 )

1 7 9 . 0 ( 4 ) r 7 8 . 0 ( 6 )

1 6 2 . 9 ( 4 ) 1 6 3 . 6 ( 6 )

1 7 r . 7 ( 2 ) L 7 2 . 2 ( 3 )

I2l12l

t 1 lI2)t2lt r 1

t 4 l

t2l

l2lt2l

t2lt l lt l l

t l lt21tzl

1 1 1

I2l

t 1 lt 1 1

t 1 l

I 2 lt-21

t 1 1

t-21t l lt l l

t 1 l1 2 lL2lt r l

t . 7 6 0 ( 2 ) L . 7 5 6 ( 2 ) 1 . 7 s 8 ( 3 ) L . 7 5 s r . 7 5 8 ( 2 )

L . 7 5 7 ( 2 ) L . 7 5 r ( 2 ) 1 . 7 5 1 ( 3 ) L . 1 6 2 L . 7 i l . ( 2 )

1 . 7 s 8 ( 1 ) 1 . 7 5 3 ( 1 ) r . 7 5 4 ( 2 ) L . 7 5 9 1 . 7 5 9 ( 1 )

1 0 9 . 6 ( 1 ) 1 0 9 . 3 ( 2 ) 1 0 9 . 6 ( 3 ) r - 0 9 . 0 1 0 e . 6 ( 1 )

94 .1 ( L ) 9s .3 (1 ) 95 .6 (2 ) 95 .3 94 .8 (1 )

125 .9 ( 1 ) L24 .6 ( r ) L25 .2 (2 ) L25 .4 125 .9 ( 1 )

1 0 9 . 0 ( 1 ) 1 0 8 . 7 ( 2 ) r 8 0 . 2 ( 2 ) 1 0 e . 3 1 0 8 . 8 ( 2 )

110 .0 ( r ) 110 .0 (1 ) 109 .9 (1 ) 109 .9 110 .0 (1 )

I . 626 (2 ) L .62s (2 ) 1 .631 (3 ) L .626 L .628 (2 )

L .626 (2 ) r . 62s (2 ) 1 .631 (3 ) L .626 r , 628 (2 )

1 1 9 . 7 ( 1 ) r 2 0 . 0 ( 2 ) 1 1 9 . 6 ( 3 ) 1 1 9 . s 1 2 0 . 0 ( 1 )

1 1 0 . i ( 1 ) 1 1 0 . 6 ( 2 ) 1 1 0 . 7 ( 3 ) 1 1 0 . 8 1 1 0 . 8 ( 1 )

9 8 . 7 ( 1 ) 9 8 . s ( 2 ) 9 8 . 7 ( 2 ) 9 8 . 8 9 8 . 2 ( 1 )

1 0 9 . 7 ( 1 ) 1 0 9 . 7 ( 1 ) r 0 9 . 7 ( r ) L 0 7 . 7 r 0 9 . 7 ( r )

L . 6 3 6 ( 2 ) 1 . 6 3 8 ( 3 ) 1 . 6 3 3 ( 3 ) r . 6 3 7 1 . 6 3 8 ( 2 )

1 . 6 0 r ( 2 ) r . 6 0 7 ( 3 ) 1 . 6 0 3 ( s ) 1 . 6 0 2 1 . 6 1 3 ( 3 )

1 . s 8 3 ( 2 ) r . s 8 4 ( 3 ) r , s 8 s ( s ) 1 . s 8 4 1 . s 8 9 ( 3 )

1 . 6 1 4 ( 1 ) r . 6 1 7 ( 2 ) r . 6 1 4 ( 2 ) 1 . 6 1 s 1 . 6 1 9 ( 1 )

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

1 0 9 . 7 ( 1 ) r 0 9 . 7 ( r ) 1 0 e . 8 ( 2 ) 1 0 9 . 9 1 0 9 . s ( 1 )

1 0 8 . 3 ( 1 ) 1 0 8 . 4 ( 1 ) 1 0 8 . 9 ( 2 ) 1 0 8 . s 1 0 8 . 3 ( 1 )

113 .3 ( 1 ) r 13 .3 ( 1 ) r L3 .2 (2 ) 113 .3 113 .6 ( 1 )

1 0 9 . 4 ( 1 ) r 0 9 . 4 ( 1 ) 1 0 9 . s ( 1 ) 1 0 9 . s 1 0 9 . 4 ( 1 )

r . 634 (2 ) 1 .640 (3 ) L .644 (4 ) r . 638 L .637 (2 )

r . 6 1 9 ( 2 ' r . 6 1 4 ( 3 ) L . 6 2 2 ( 5 ) r . 6 2 Q 1 . 6 1 3 ( 3 )

1 . s 7 8 ( 2 ) 1 . s 7 4 ( 3 ) 1 . 5 6 3 ( 5 ) 1 . 5 8 0 L . 5 7 7 ( 3 )

1 . 617 (1 ) r , 6L7 (2 ) 1 . 618 (2 ) r . 619 1 .616 (1 )

108 .2 (1 ) 108 .0 (2 ) 108 .0 (3 ) L07 .9 r 07 .9 (2 )

111 .6 (1 ) 1 r r , 8 (1 ) 111 .8 (2 ) r r 1 .7 111 ,6 (1 )

106 .8 ( 1 ) 106 .5 ( 1 ) 106 .6 (2 ) 106 .8 106 .7 ( 1 )

111 . s ( 1 ) 111 .8 ( 1 ) 111 . 7 ( 1 ) 111 . 6 111 .6 ( 1 )

1 0 9 . 4 ( 1 ) 1 0 9 . 4 ( 1 ) 1 0 9 . 4 ( 1 ) 1 0 9 . 4 1 0 e . 4 ( 1 )

1 . 7 7 3 ( 2 ) L . 7 7 9 ( 3 ) L . 7 7 9 ( 4 ) L . 7 1 5 L . 7 7 9 ( 2 )

L . 7 L 6 ( 2 ) r . 7 1 1 ( 3 ) 1 . 7 1 5 ( 5 ) L . 7 L 7 1 . 7 1 5 ( 3 )

r . 7 0 6 ( 2 ) 1 . 7 1 0 ( 3 ) r . 7 0 7 ( 5 ) L . 7 0 1 1 . 7 1 0 ( 3 )

r , 7 4 2 ( r ) 1 . 7 4 5 ( 1 ) L . 7 4 6 ( 2 ) r . 7 4 4 r . 7 4 6 ( L )

1 0 s . 8 ( 1 ) 1 0 5 . 3 ( 2 ) 1 0 5 . 0 ( 3 ) 1 0 5 . 6 1 0 s . s ( 1 )

1 0 7 , 8 ( 1 ) 1 0 7 . 8 ( 1 ) 1 0 8 . 0 ( 2 ) 1 0 7 . 8 1 0 7 . 7 ( 1 )

109 .9 (1 ) 109 .8 (1 ) LOg .6 (2 ) 109 .8 109 .8 (1 )

l 1s , 2 ( 1 ) l 1s .7 ( 1 ) 116 . l ( 1 ) 115 . s 11s . 7 ( 1 )

109 .4 ( r ) r oe .4 (1 ) 109 .4 (1 ) r 09 ,4 10e .4 (1 )

1 7 6 . 4 ( 2 ) 1 7 6 . 3 ( 3 ) 1 7 6 . 3 ( 4 ) 1 7 6 . 3 1 7 6 . 3 ( 2 )

L 7 9 . s ( 2 ) 1 7 9 . 0 ( 3 ) L 7 9 , 5 ( 4 > 1 8 0 . 0 1 7 9 , 0 ( 2 )

1 6 3 . s ( 2 ) 1 6 4 . 3 ( 3 ) 1 6 4 . 8 ( 4 ) 1 6 4 . 0 1 6 4 . 3 ( 2 )

1 7 3 . 0 ( 1 ) 1 7 3 . 2 ( r ) r 7 3 . 5 ( 2 ) r 7 3 . 4 L 7 3 . 2 ( r )

l 2 l

t 2 l

l .2 l

344 HOCHELLA ET AL,: CRYSTAL CHEMISTRY OF CORDIERITES

Table 6. (continued)

I,ftrl.te WelI Dolnl Bory

24"c 375"CDietance/ ltrlt1-Anele Dllcltv 24"c 375oc 775oc 775ocr 24"c2

T21-011-T11

T26-016-T16

T23-013-Tr1

Mean

Tlt-or1-M

T11-O13-M

T16-O16-M

T21-O11-M

T23-O13-M

T 26-OL6-trMean

Ml-O15-o11'

;3:'

L27 .2(L)

132 .9 ( 1 )

r .28.2 (1)

12e .4 ( 1 )

94 .9 (1 )

94 .6 (1 )

9 5 . 0 ( 1 )

L37 .7 (L)

r37 . 1 ( 1 )

131 . 9 ( 1 )

lr.s. 3 (r)

2.rr3<2)2.L0O(2)

2.Lrs<2)2. r.08 (1)

L27 .2 (L)132. 8 (1)

128. 7 (1 )

r29 . 6 (r)

e4 .8 (1 )

e4 .6 (1 )

9 s . r ( 1 )r37 . 6 (1)

135.3 (1 )

131.8 (1 )

115.0( r . )

2.LLL<2)2 .Lr6 (2 )

2.L27 (2)

2 .119 (1)

r27 .7 (2)

L32 .6 (2 )

L 2 9 . L ( 2 )

129 . 8 ( 1 )

94 .6 (2 )

94 . 5 ( 2 )

95 .0 (2 )

L 3 7 . 6 ( 2 )

L36 .2 (2 )

r 3 2 . O ( 2 )

1r5 . 0 (1)

2.L24 (4)

2.L24 (4)

2 .135 (4)

2.L28 (2)

L 2 7 . 4 ( r )

1 3 2 . 6 ( 1 )128 ,3 (1)

r29 .4(L)

9 s . 0 ( 1 )e4 .5(1)9 s . 2 ( 1 )

137 . s (1 )

137 . 0 (r.)

131. 9 (1)

r l s . 2 ( 1 )

2.Lro(2)2.Lro(2)2.LLg (2 )

2 . L L z ( L )

tzl1 2 l

t2'l

a2ll2ll 2 I

I2lI2lt2l

t2lt2lI2l

L 2 7 . L

r32.9

L28.9

L29.6

94 .9

94,3

9 5 . 0

137 . 8

136 .5

T3L.7

115 . 0

2 .L20

2.tzL

2.L32

2.L24

L28.7 (2) L28.7 <3)

L33 .2 (2 ) 133 .4 (3 )

L29 .4 (2 ) t 29 .5 (3 )

130 .4 (1 ) 130 .5 (1 )

94 .4 (2 ) e4 .L (2 )

94 . r ( 2 ) e3 .e (2 )

94 .1 ( z ) 94 .e (2 )

L36 ,6 (2 ) 136 .9 (3 )

136 .0 (2 ) 136 .0 (3 )

1 3 1 . 1 ( 2 ) 1 3 1 . 2 ( 3 )

114 .4 (1 ) 114 .5 (1 )

2.Ls3<4) 2.L6L(5 '

2 .L54 (4 ) 2 .L62 (5 )

2 .L56 (3 ) 2 .L73 (5 )

2 .158 (1 ) 2 .165 (3 )

SitruLated ecpansion by DLS. See text.

Aften heating.

to expand at temperatures greater than 400o, whereasLee and Pentecost find that c continues to contract atleast to 1000"C. However, when Lee and Pentecostannealed their hexagonal specimen to produce anorthorhombic polymorph (with a greater degree ofAllSi order), they discovered that the contractionalong c was increased over that of the hexagonalpolymorph. Because the degree of AllSi ordering inindialite is probably variable (Meagher and Gibbs,

1977), and because the contraction properties in the cdirection apparently depend on thermal history,structural state. and channel constituents, we believethat the differences in the curves determined by Fis-cher et al. and Lee and Pentecost are real and repre-sent measurements on hexagonal polymorphs withdifferent structural states.

Structure

The crystal structure of cordierite is described byTakane and Takeuchi (1936), Bystrdm (1942), Gibbs(1966), Cohen et al. (1977), and Meagher and Gibbs(1977), and consists of a framework of four- and six-membered rings of tetrahedra. The six-memberedrings, made up of T, tetrahedra, lie in planes per-pendicular to c (Fig. 2). The four-membered rings,consisting of alternating Tr and T, tetrahedra, arelinked into chains parallelling c which are furthercrosslinked to form the tetrahedral framework (seeFig. 3). A neutron site refinement by Cohen et al.(1977) has shown White Well cordierite to be com-pletely ordered (tr6 : tzl : tz3 :0.0 and trl : tz6 =1.0 where t,y represents the probability of finding anAl atom in T"y) within the experimental error. The Matoms (M : Mg,Fe) in cordierite reside within theframework in somewhat flattened octahedra thatshare two edges with AlOo tetrahedra and one with a

o 3 0- White Well cordierile (lhis study)----_ indiolilc {be ond Prdecod)

- - indiolile {Fl*haiEvona,ond G.igar)Izo o20ozfi l oroJ

E o *l!IF

o 200 400 600 800

TEMPERATURE (CCI

Fig. l. Axial expansion ([(X, - Xu)/Xrr].100 where X is a, D orc) ur. temperature for two synthetic indialites and the White Wellcordierite. The brackets for the White Well data are drawn at * I o.

HOCHELLA ET AL.: CRYSTAL CHEMISTRY OF CORDIERITES 345

Fig. 2. Onren (Johnson, 1965) drawing of the cordieritestructure viewed down c (from 0c to 7:c). In ordered cordierite, Trland T16 represent Al atoms, while T16, Trl, and Tr3 represent Siatoms. The M octahedra house Mg and Fe.

SiOn tetrahedron. The large cavities, connected toform continuous channels parallel to c, house thewater molecules in hydrous cordierite. The alkaliatoms in alkali-bearing cordierites reside at the cen-ters of the six-membered rings of T, tetrahedra(Meagher, 1967).

I sot ropic temperature faclorsFigure 4a shows the isotropic equivalent temper-

ature factors (B"o) for the cations and oxygens inWhite Well cordierite plotted against temperature. Siatoms in the six-membered ring have lower temper-ature factors than Si atoms occupying T, tetrahedraor Al atoms occupying T, and T, tetrahedra; further-more, the B"o values of the tetrahedrally- coordinatedcations increase at the slowest rate relative to otherB"o values. The temperature factors for the tetrahe-drally-coordinated Al atoms increase slightly fasterthan for the Si atoms. The M cations show the high-

est temperature factor and the greatest rate of in-crease to 775o among cations.

The B"o values for the Dolni Bory cordierite areplotted against temperature in Figure 4b. Despite thelimited amount of data, the temperature-factor varia-tion with temperature for each cation has the samegeneral trend as that observed for the White Wellcordierite. These observations agree well with find-ings for the pyroxenes by Cameron et al. (1973) andfor tremolite by Sueno et al. (1973). Both studiesshow that cations with higher charge and lower coor-dination have smaller temperature factors that in-crease more slowly with increasing temperature thancations with lower charge and higher coordination.

The six non-equivalent oxygens in both cordieritesare clearly separated into two groups on the basis ofB"o values. The three distinct O' oxygens are three-coordinated and have smaller temperature factorswhich increase at a slower rate than those of the threeindependent 02 oxygens in the ring which are onlytwo-coordinated. In general, oxygens with high coor-dination are more restricted in movement and displaysmaller ternperature factors that increase more slowlywith increasing temperature than oxygens with lowercoordination (cl Burnham, 1964;Sueno et al., 1973).

Fig. 3. An Ontee stereopair drawing showing the four-membered rings which are linked into chains paralleling c. Bothsymmetrically distinct chains are shown (the two overlying chainson the left are related by a c glide) and have been highlighted byheavy-lined bonds. Note that the octahedron (single line bonds)shares three edges with tetrahedra. In this figure, a is horizontaland c is vertical.

346 HOCHELLA ET AL.: CRYSTAL CH EM ISTRY O F CO R D I ERITES

Table 7. Polyhedral volumes (A3) us. temperature for White Welland Dolni Bory cordierites

white WelI

Po lyhedra 24 'c a75" c 775" c 24 ' {

Dolnl Bory

zh" c a75" c

o<

@

T1 t

Tt6

Tzl

Tz6

T 1- 2 -

M

2 . 5 8 2 . 5 7 2 . 5 8

2 . L 4 2 . L 3 2 . L 5

2 . L 5 2 . L 6 2 . L 5

2 . 7 0 2 . 7 2 2 . 7 2

2 . L 6 2 . t 6 2 . L 7

tr .79 11.91 12.06

2 . 5 9 2 . 6 1 2 . 6 3

2 . L 3 2 . 1 6 2 . 1 7

2 . L 7 2 . 1 8 2 . L 7

2 . 7 2 2 . 7 3 2 . 7 2

2 , t 6 2 . L 6 2 . r 7

1 -1 .85 L2 .42 L2 .55

- ' -o 200 400

(b) TEMPERATURE (oC)

Fig. 4. (a) Isotropic equivalent temperature factors (B"o) for theWhite Well cordierite plotted as a function of temperature from24" to 775"C. (b) Isotropic equivalent temperature factors (B"o)for the Dolni Bory cordierite plotted as a function oftemperaturefrom24" to 375'C. (The nomenclature of the atoms from a and D isthe same as that in Fig. 2.)

Tetrahedral and octahedral bond length expansion

Mean T-O bond lengths for individual tetrahedrain both the White Well and the Dolni Bory cordier-ites do not appear to change significantly with tem-perature (Table 6). Moreover, because they are un-changed after heating in White Well cordierite, we

I After heati,ng,

may conclude that the ordered configuration of Aland Si in the tetrahedral framework of low cordieritewas unaffected by our heating experiments. On theother hand, the octahedral M-O bonds show a signif-icant increase in length with increasing temperature.The Mg-O bonds in White Well cordierite increase0.018A on the average when heated from 24" to775"C whereas the Fe-O bonds in the Dolni Borycordierite increase by 0.0074 when heated from 24"to 375'. In the temperature range 24" to 375o, themean Fe-O bond length expansion [-0.007(l)A] isless than the mean Mg-O bond length expansion[-0.011(l)A]. This result agrees with similar resultsobtained by Cameron et al. (1973) and is consistentwith the notion that the Fe-O bond is stronger thanthe Mg-O bond.

Volumes of the AlOo and SiOo tetrahedra showlittle or no change with heating (see Table 7). Incontrast, the MgO. octahedra in the White Well cor-dierite exhibit a volume increase of 0.27As whenheated from 24" to 775". Similarly, the FeOu octa-hedra in the Dolni Bory cordierite show a volumeincrease of 0. l3As when heated to 375'C.

The mean thermal expansion of the octahedron inthe Mg-rich cordierite (12.6 x l0-6oc-1) is signifi-cantly less than that observed for corresponding octa-hedra in periclase (13.9 X l0- 'oC-'), forsterite (14.2X l0-6oc-r) , and diopside (14.4 X l0-6oc-1) (Hazenand Prewitt, 1977). As indicated earlier, the octahe-dron in cordierite is isolated from other octahedraand shares three of its edges with tetrahedra. Sincethe dimensions of these tetrahedra show little or nochange with heating, they act as rigid clamps andconstrain the octahedron in its expansion upon heat-ing. The octahedra in forsterite and diopside shareedges with both tetrahedra and octahedra, whereasthose in periclase share edges only with other octa-

l < rdl

9os-/il(e

-t2,./

, . t t , / t '. /'...r1/t

-4vz'<' --17' y'"Ft

,Y.ti' ---'_'.rqou

i2'7.:-'

TEMPERATURE ('C)

HOCHELLA ET AL..'CRYSTAL CHEMISTRY OF CORDIERITES 347

hedra. Therefore, the mutual expansion of the octa-hedra in these structures should not be as restricted asin cordierite. If this is true, the mean thermal expan-sion of an M-polyhedron depends upon its environ-ment as well as on the strength of the M-O bonds. Infact, when trying to predict the thermal expansion ofa crystalline material from its structure at 24oC, asattempted by Khan (1976), it may be inappropriateto assign a fixed rate of expansion to an M-O bondfrom one structure type to another.

A structural interpretation of the thermal expansion ofcordierite

The anisotropic thermal expansion of the unit cellof the White Well cordierite is related to the ani-sotropic thermal expansion of its Mg-rich octahedronand its accompanying effect on the tetrahedral frame-work. Changes in the thickness of the octahedronmeasured along a and b correlate with changes in thelengths of a and 6, respectively (Fig. 5), whereas the

,--i-Fe-cord ie r i le / ' l ?

-{-' 24"C

/ , t Mg - cord ie r i le

.z4iq"c

octahedral thickness measured along c is unaffectedby the temperature change. This anisotropic expan-sion of the octahedron serves to rotate (-0.2") therigid six-membered rings clockwise and counter-clockwise in alternate layers perpendicular to c (Fig.6). Figure 6 also shows the displacements accom-panying this rotation of each of the tetrahedral cat-ions in the rings. The twisting of the tetrahedralframework attending the rotation is associated with adecrease in selected T-O-M and O-T-O angles,which results in a more efficient packing of the struc-ture and a concomitant contraction of the c cell edge(Fig. 7).

A distance least-squares ( DLS ) refinement (Meierand Villiger, 1969) of the White Well cordierite struc-ture was undertaken to learn whether the results ofsuch a regression are consistent with our assertionthat the thermal expansion of the octahedron is thedriving force behind the thermal expansion of cor-dierite. The T-O bond lengths, the nearest-neighborO...O separations, and the unit-cell edges used inthe calculation were initialized at the values measuredat 24o, and the M-O bond lengths were initialized atthe values measured at775"C.In the refinement, eachof the T-O and M-O bonds was assigned a weight of

Fig. 6. Rotation of the six-membered rings in the White Wellcordierite. The open circles represent the tetrahedral cations in thering, the dotted circles the O, oxygens, and the solid circles theoctahedral cations (96 percent Mg). The vectors radiating from theoctahedral cation represent the expanding Mg-O bonds. Asshown, the upper six-membered rings rotate in a clockwisedirection upon heating whereas the lower ones rotate in acounterclockwise direction. The three independent tetrahedral ringsites are labeled together with the distance (in A) that these cationsare displaced about the ring over the temperature range 24o to775"C.

t 7 2 4

o{v 1 7 . 1 6s

t7 .o8

3 . 2 6 3.30 3 .34

/ o ( A )3.38

re -coroierit . Su"'24cC

775"C3750C / '

?o7* Ms- cordierile

2.44 2 .48 2 .52

/ b ( A )

Fig. 5. The a and b cell edges us. the thickness of the Moctahedron measured along a,t", and along b,tr, for the White Well(Mg) and Dolni Bory (Fe) cordierites at various temperatures. Therefationships between a and t" and b and 16 are similar for bothcordierites and seem to be continuous from the Mg- to the Fe-cordierite. The brackets are drawn at *lo.

o{

a - 7 6

t-;' //.,

348 HOCHELLA ET AL.: CRYSTAL CHEMISTRY OF CARDIERITES

ol

9 . 3 7

9 . 3 5

9.37

9 . 3 5

9.37

Pd5750C

7750C

106.0 to7.o lo8.o

tO t l -Tz l -Os16 ( " )

the White Well cordierite. This greater thickness con-forms with the larger a and b cell dimensions of theDolni Bory cordierite. Changes in the thickness of theoctahedron measured along a and b correlate linearlywith changes in the cell dimensions of both DolniBory and White Well cordierites with increasing tem-perature (Fig. 5). Despite the larger volume of the Fe-octahedron, the c cell dimension of the Dolni Borycordierite is 0.054 shorter than that measured for theWhite Well cordierite. However. the thickness of theFe-rich octahedron along c is 0.025A less than that ofthe Mg-rich octahedron. This difference in octahedralthickness along c precisely accounts for the 0.054difference in the c cell dimension between the twocordierites (there are two octahedra along each trans-lational repeat in the c direction). Unlike those of theWhite Well cordierite, both the thickness of the oc-tahedron and the c cell dimension of the Dolni Borycordierite increase with rising temperature. AIso,there is no evidence of a rotation of the six-memberedrings associated with expansion of the octahedron upto 375oC in the Dolni Bory cordierite.

The efects of heating on channel constituents

The loosely-bound channel constituents in cordier-ite undergo large anisotropic vibrations and posi-tional changes upon heating, as shown in the Apmaps at each temperature of refinement for the WhiteWell cordierite (Figs. 8a-d). The peak ascribed to thealkali and Fe atoms at 0,0,0 is elongated parallel tothe channel axis, c, at 375o, while the Ow (oxygenassociated with the water molecule) peak at0,0,l/4isa single peak elongated further along a than the samepeak at 24'C. AL775"C in the White Well cordierite,the Ow peak is absent. It reappears in the 24o (afterheating) Ap map as a single peak, less than half thesize of the original Ow peak, and is no longer elon-gated parallel to a. The absence ofthe peak at 775' isprobably due to high-temperature factors and seem-ingly complete disorder of water molecules within thecavity. The Ow peak also vanishes in the Dolni Borycordierite in the Ap map computed from the 375oCdata. On the other hand, the peak ascribed to alkaliions centering the six-membered ring has enlarged inthe 775'C Ap map for the White Well cordierite.Also, the 24" (after heating) Ap map for White Wellcordierite shows that there is (l) more electron den-sity at 0,0,0 than in the unheated sample, (2) lesselectron density at 0,0,1/4, and (3) an overall sub-stantial drop in the original amount of channel con-stituents. It seems reasonable to suggest that some ofthe channel constituents have been driven out of the

rol

240C1

3750C?40C

7750C

tos.o 106.0L O 1 6 - T z 6 - O 1 6 6 ( o )

ol>1lr-

r 7750C9 . 3

r36 .0 r37.0 r38.OLr23-Ot3 -M(" )

Fig. 7. The length of the c cell edge us. one T-O-M and two O-T-O angles at various temperatures for the White Well cordierite.These angles are oriented such that their change directly affects c.Their decrease is apparently related to the expansion of theoctahedral bonds and slight rotation of the rings. Error bars aredrawn at ilo. (24'C* is after heating.)

l.0, and each O. . .O separation was given a weight of0.25. More than 40 cycles of refinement were calcu-lated in which the positional parameters of the atomsin the asymmetric unit and the cell-edge lengths weresimultaneously varied. The resulting cell edges (a :17.143, b = 9.758, c : 9.348A) agree within about 4parts in 10,000 with those observed at 775"C la :r7.149(2), b : 9.7 59(r), c : 9.352(r)Al. In addition,as the refined T-O and M-O bond lengths are within0.001A of the starting values, the results of the DISrefinement indicate that the anisotropic thermal ex-pansion of the unit cell of cordierite is principallycontrolled by the thermal expansion properties of theoctahedron, as concluded above on the basis of ob-served structural change with increasing temperature.

As shown in Figure 5, the thickness of the octahe-dron in the Dolni Bory cordierite measured along aand b is significantly greater than that measured for

iQ

^

it

D

f',

HOCHELLA ET AL.: CRYSTAL CHEMISTRY OF CORDIERITES 349

- o t 5 -o 09

z o o o

- o r 2

- o 2 4

b

o t 2

zo oo

- o r 2

- o 2 4

- 0 1 5 - 0 0 9 - o 0 3 0 0 3 0 0 9 0 t 5

c X d

Fig. 8. X-ray Ap maps of the White Well cordierite showing thepeaks asffibed to channel constituents at (a) 24",. (b) 375", (c)775", and (d) 24"C (after heating). All sections are the (010) planeat y : g. Solid contours are positive; dashed contours are negative.The zero contour is omitted, and the contour interval is 0.20e-lAsfor each map.

structure, while some of the remaining HrO mole-cules have taken up positions centering the six-mem-bered rings.

The state of the White Well cordierite after heating

The a and D cell edges of the White Well cordieritedo not return to their original lengths after cooling to24"C (Table 2). Observations such as these are usu-ally attributed to a change in structural state withheating (see, e.g., Karkhanavala and Hummel, 1953;Levien and Papike, 1976). However, this is not thecase for the White Well cordierite because its com-pletely ordered structure did not disorder at all dur-ing data collection at high temperatures. A possibleexplanation in this case is that changes in amount andperhaps position of channel constituents with heatingand cooling cause a and b to increase. It is not clear,though, how these changes might affect the AloSiuO*framework, if at all (see Langer and Schreyer, 1976;Stout, 1976). Another more plausible explanation isthat some of the iron in the framework was used toform secondary hematite, and as a result some of theoctahedra were left empty. Octahedral vacancies takeup more space than filled octahedra, and a and b

would be appropriately larger (see Table 7 and Fig.5). This hypothesis is supported by our observationof powder rings with d spacings corresponding to the104, ll0, 024,116,2l4 and 300 spacings of hematitein the precession photographs of heated White Wellcordierite. However. if octahedral vacancies existedin the framework after heating, one would expect theisotropic temperature factors of the octahedra to beless after heating than before; this is not the case(Table 4). The observed differences in a and b dimen-sions of the White Well cordierite before and afterheating are probably due to a combination of theabove factors.

Orientation of the water molecules in the While LTellcordierite

A re-investigation of the water position in thechannels of the White Well cordierite, as located byCohen et al. (1977} has led to a new interpretation ofthe orientation of water molecules, from the X-rayand neutron diffraction data of Cohen (1975). Al-though attempts at refining the Ow (oxygen of thewater molecule) position during the structure refine-ment were unsuccessful, X-ray Ap maps show Ow tobe split into two positions along the x axis at+.0.021,0,1/4 as shown in Figure 9. Newly calculatedneutron Ap maps (see Fig. l0) strongly suggest thatthe plane of the HrO molecule is inclined by -29"from (100) and that the H-H vector is l9o from c.This HrO position is significantly different from thatproposed by Farrell and Newham (1967) and Tsangand Ghose (1972), based on spectroscopic studies.

XFig. 9. X-ray Ap map (24'C) showing the elongated oxygen peak

along the x axis. Section is the (001 ) plane at z = l/4. The contourinterval is 0.20e-lA8, and the zero contour has been omitted.Solid contours are positive, dashed contours are negative.Subtraction of the peak was most complete when electron densitywas added at i0.027 on x.

0 1 6

o 2 4 on

o -

r)Q ^

Uo

"@[(/{.c1@{

c unc

lol

( - l

aif

o

350

oo8 0 r6 o24 032 040

ZFig. 10. Neutron Ap map (24'C) showing the negative scattering

of the hydrogens (zero contour omitted) in the (100) plane at x =

0.01. Solid contours are negative, dashed contours are positive.The Ow peak, that ascribed to the oxygen of the water molecule,has been subtracted. The dimensions of the two symmetry-relatedwater molecules shown are d(Hl-Ow) : 0.994, d(H2-Ow) :

l .0 lA and H l -Ow-H2 : 105.1 'w i th H l a tx :0 .010, y :0 .025,z = 0 .150, H2atx :0 .010,y :0 .078 andz :0 .311and Ow a tx :0 .027, y : 0 , z : l /4 .

Their results show the water molecule to be in the(100) plane with the H-H vector parallel to c, and weshall refer to water in this proposed orientation astype I after the notation of Wood and Nassau (1967)for water orientation in beryl. Goldman et al. (1977)stated that the White Well cordierite. as well as hav-ing type I water, has a small amount of type II water[H-O-H in the (100) plane with the H-H vectorparallel to 61, also based on polarized IR spectra.There are two possible hypotheses for explaining thedifferences between the spectral and crystallographicresults: (l) type I and type II water actually exist inthe White Well cordierite, and our Ap maps show thecombined scattering of both types, resulting in aspace average position, or (2) the actual water posi-tion is as shown in our model, and the spectroscopicdata show the b and c components of the true H-Hvector. Our data are not consistent with hypothesis(l ) and strongly suggest that hypothesis (2) is correct.

Problems arose when we attempted to completelysubtract out the Ow peak using the multiplicity ofHrO from the chemical analysis of the White Wellcordierite (Pryce, 1973). A negative residual was leftat the Ow position on the neutron Ap map, indicatingthat the amount of HzO in the formula is less than(HrO)o.uu. A series of calculations with smalleramounts of Ow showed that 0.36 Ow at *0.027,0,1/4resulted in a negligible residual in the Ap map. To

HOCHELLA ET AL.: CRYSTAL CHEMISTRY OF CORDIERITES

further support the idea that less water is present thanreported by Pryce (1973), the amount of hydrogenneeded to diminish the negative peaks of the neutronAp map shown in Figure l0 is consistent with(HrO)o.ru. However, a thermal gravimetric weight-loss curve for the White Well cordierite (C. W. Hug-gins, 1976, personal communication) suggests thatthe amount of HzO in the formula is correct.

AcknowledgmentsDr. E. P. Meagher is gratefully acknowledged for performing the

DLS calculations and for reviewing the manuscript. Dr. P. H.Ribbe also read the manuscript and offered helpful suggestions.Dr. G. R. Rossman is thanked for several helpful discussions onchannel constituents in cordierites. We thank Sharon Chiang fordrafting the figures and Marie Phillips for her patient typing of themanuscript. This study was supported by NSF grants EAR74-035056-40l (Brown) and EAR77-23114 (Gibbs and Ribbe).

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HOCHELLA ET AL.' CRYSTAL CHEMISTRY OF CORDIERITES 35r

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Manuscript receiued, December 29, 1977;accepted for publicalion, September 12, 1 978.