American Mineralogist, Volume 59, pages 79-85, 1974

The GrystalStructure of Danburite:A Gomparison with Anorthite,Albite, and Reedmergnerite

MrcHnBrW. Pnrrrrps,G.V.Glnns, eNn P. H. RInnp Department of GeologicalSciences, Virginia PolytechnicInstitute and Stote Uniuersity,Blacksburg, Virginia 24061

Abstract

The crystal structure of danburite (CaB,Si.O"; a - 8.038 A; b - 8.752 A; c - 7.730 A; spacegroup Pnam) has been refined to an unweightedresidual of R - 0.021 using 1076 non- zero structure amplitudes. It consists of a tetrahedral framework of ordered B"O" and Si"Or groups which accommodatesCa in irregular coordination ((Ca'*-O) - 2.585 A; (CavII-O) = 2.461 A). A 7-fold coordination model appearsto be more consistentwith structurally similar anorthite, reedmergrrerite, and albite as evinced by the linear relationship between the mean Na/Ca-O bond lengths and the mean isotropic temperature factors of Na and Ca in these structures.The mean T-O bond length is 1.474 A for the B-containing tetrahedron and 1.617 A for the Si-containing tetrahedron, both of which are somewhat longer than those in re- edmergnerite(NaBSLOo). The trends observed between tetrahedral bond lengths, coordination number and Mulliken bond overlap populations for Si-O-+Al and Al-O-+Si bonds in anorthite are similar to those observed for Si-O+B and B-O"+Si bonds in danburite; shorter bonds with larger overlap populations and smaller coordination numbers are involved in wider tetrahedral angles,

Introduction tion of bondingin thesestructures directed toward a The crystalstructure of danburite,CaBzSizOs, was rationalizationof their topologiesand the stericde- (cl determinedby Dunbar andMachatschki ( 1931) who tails and distribution of the tetrahedralatoms describedit as a frameworkof corner-sharingSi2O7 Ribbe, Phillips, and Gibbs, 1973; Gibbs, Louisna- and B2O7groups with the Ca atomscoordinated by than,Ribbe, and Phillips,1973). eight oxygens.Because they had beenunable to de- ExperimentalProcedure termine the positions of the boron ato,msprecisely, Johansson(1959) refinedthe structureusing 538 A smallcleavage fragment (0.10 x 0.t7 x 0.23 intensitiesmeasured by film methodsin a partial mm) was taken frorn a large danburitecrystal from three-dimensionalleast-squares synthesis. His refine- SanLuis Potosi,Mexico. The specimenis part of the ment confirmed the structure and yielded bond C. A. Michael Collectionof Gems and Minerals at lengthswith e.s.d.'s< 0.02A. ConcurrentlyBakakin, V.P.I.S.U. Single crystal photographswere consis- Kravchenko,and Belov (1959) completeda similar tent with Bakakin,Kravchenko and Belov's(1959) analysiswith poorer results.A study of the nuclear choiceof spacegroup Pnam. They statethat a sta- magneticresonance spectrum of 118established that tistical test of intensitiesindicated that danburiteis B-Si order persistsin danburiteup to its decom- centrosymmetric.Counter diffractometermeasure- positiontemperature (Brun and Ghose,1964). mentsof 40 alongthe axial zoneswere used to de- This studywas undertaken to determinemore pre- terminethe unit celldimensions: a = 8.038(3); b = ciselythe bondlengths and anglesof danburite(Phil- 8.752(5) ; c = 7.730(3) 4.. lips, Ribbe, and Gibbs, l97l) for comparisonwith Intensity data were collectedon a Picker auto- topologicallysimilar paracelsian(BaAlzSi:Oa) and mated four-circle diffractometer,using Nb-filtered hurlbutite (CaBe2PpO6)and with structurallysimi- Mo radiation and a scintillationcounter. A com- lar feldspars:anorthite (CaAl:SigOs)and its hexa- puter programwritten by C. T. Prewitt was usedto gonal polymorph; celsian (BaAl2Si2Os);synthetic correct the intensity data for backgroundand Lo- SrAl2SisOs;albite (NaAlSi3Os); and reedmergnerite rentz-polarizationeffects and to convert to lRr,"l. (NaBSi3Os).This is part of an extensiveinvestiga- Absorption and extinctioncorrections were consid- 79 80 PHILLIPS, GIBBS, AND RIBBE

TAILE 1. Observed and Calculated Structure Factors for Danburite*

F(bb3) Ftcalc) h L k.tobs) rtca)c) k \ F(abg) rlcatc) F(abs) Ftcatc)

1 5 2111 2312 e B 2799 257r

r0 5 2313 2315 2 4 2A6! 2654

I 16 29ro ?81)

r0 r 29rr 2979

rz t 2956 29,1e 9 ro 2935 2796

4 rr r0(l rr24 |2 \ )o41 26ol r 9 r05r zass 7 5 r0t6 2916

2 6 1|45 2J\5

rt I 6 tr 3ir9 235? 50 9 I 3 3rl5 2S97

50 s 6 1 t\t1 iz12

14 5 i I l17r rrrT 27 r 6 6 lrss ,3a4 5 r355 15r9 4 4 1 1192 21\J

65 r0 6 5 r?05 Irsl

66 12 0 r 1216 1056

2 1966 r7 33 1 1 | t26r 1215 6L 6 | 9 316s 212A 14 6 1 7 1Jr5 i2S1 l1 73 )4 s5

13 5 0 rr 135? lr01 rr 5 r 12 lr9r r1e7 31 79 30 33 a5 rr I 3 t4r5 lllr

s! 3 1 ro 1164 J625 13 ? 12 5 31 35 lr.6 1 2062 ?2 1t I 1 3 1te| J146 rr s 4 I 1501 1612 29 I r? I 1501 rr4{

50 , 3 6 l514 ]57A ! 109r r1 16 t a rt l561 3291

* The k and / columns are not in their usual order. CRYSTAL STRUCTURE OF DANBURITE 8I ered unnecessary.An anisotropicleast-squares re- Tesrn 3. Interatomic Distancesand Angles and Bond finementwas calculatedwith 1076 structureampli- Overlap Populations (n) in Danburite* tudes, (lF"o"l > 4c-),using the programby Busing, B-o discances (l) n(B-o) o-o dlstances (fr) o-B-o ansles (') Martin, and Levy (1962). The lF"5"lwere weighted T1-01 1.479 0.534 or-o2 2.32r 102.5 accordingto the schemeproposed by Hanson ( 1965) 02 r.498 0.513 01-03 2.419 I10, 7 03 I. 461 0.545 02-o3 2.429 110,4 and the variation of (waF'?)over the entire range of 05 r. 456 0.539 o2-o5 2.372 106.9 iiean 1.474 03-o5 2.406 11r.2 lF"o"l was minimized as suggestedby Cruickshank q.-o n (si-0) o-o distdnces (;.) (1965). The valuesof lF"o"land F*L are given in 4+tqreee=(4) .o:.!:9:_!al_99(') T2 0t 1,617 0.507 or 02 2.612 rlt,l Table 1. Atornic scatteringfactors for neutral atoms D2 r,624 0 549 0r-o3 2.650 110.4 were taken from Cromer (1965). 03 1. 6r.t 0.492 oL-04 2.66tt ltt. I and Waber The 04 1.614 0.514 o2-o3 2.574 105.4 positionalparameters and temperaturefactors (Ta- ileatr I. 6l 7 o2-o4 2.636 109.0 o3-o4 2.63a r09.7 ble 2), interatomicdistances and angles(Table 3), qcrg-{r.9Erres G) --l!ci|l L!:f-l!eleq-() and thermal ellipsoiddata (Table 4) were obtained ca 01- 2.496 t2l Tl-0r-T2 132.4 from the final cycle of the anisotropic refinement 02 2.452 I2) TI-O2-T2 t26.3 03 2.467 l2l T1-O3-T2 128. r 'r2-o4-'r2 which yieldedan unweightedresidual of R = 0.021. 05 2.399 trl 136.a 11-O5-Tl 130.6 02 3.020 t2) Description of the Structure * Estinated standart! errors fot aff distances are O.00lA and aff anqles 0.L". The asymmetricunit of danburite containstwo tetrahedrallycoordinated (7) cations (B and Si), one calcium, and five oxygen atoms. Of the latter BzOz and Si:1O7groups with the Ca atomsin either O(1), O(2), andO(3) arebonded to both Si and 9-fold coordination((Ca-O) = 2.585 A) or 7-fold B, whereasO(4) and O(5) arethe bridgingoxygens coordination((Ca-O) = 2.461 A). The 7-fold co- of the SizOz and B2O7 groups, respectively. The ordination model appearsto be more consistentwith mirror planesnormal ta c at heightsof 0.25 and structurally similar anorthite, reedmergnerite,and 0.75 contain the calcium atoms and the bridging albite as evincedby the strong correlationbetween oxygens,O(4) and O(5). The structurecan be thought of as a continuousframework of alternating Tesrs 4. Thermal Ellipsoid Data for Danburitet'

Tnsrn 2. Positional Parametersand Temperature R.l'1.s. Factors for Danburite's Atom Ellipsoid displacement Angles to crystal axes (degrees) axis tll x y-z

I'osicional parameters 0.068(1) 82(3) 8(3) 90 Atom jJ(82) xgz . 073(1) 90 90 180 .077(1) 8 (3) 98(3) 90 Ca 0.38s4(1) 0.0765(1) r/4 0.42(r) TI .060(3) r14(39) 24(39) 91(r 4) TI .2s90(1) .4r92(r) .4zoL(r) .31(1) .063(3) 155(38) 114(39) 81(19) T2 .0s33(r) .L924(r) -.0ss8(1) .25(1) .069(3) 82(18) 85(14) 9(19)

T2 .0s2(r) 89(6) 19(7) 7r(7) ol .re30(1) ,.0680(r) -.0032(1) .s6 (1) (1) -.0433 .0s7 48(23) i6(13) 135(19) o2 .r263 (r) .36s0(1) (r) .4e(1) .060(1) 41( 21) 103(7) s1(19) o3 .3998(r) .3r3s(1) .078r(1) .47(r) o4 .sr36 (1) .6636(1) r/4 .60(2) .066(2) 1r2(5) 23(4) 82(4) 05 .1818(1) . 4282(L) r/4 .54(2) .082(2) 137(4) 101(s) 131(4) , ro2 (2) 12s(3) 1r0(2) 42(3)

Anisotropic temPerature factors (x 10q) .o62(2) 63(s) Atom ^ s6(4) 46(7) 611 6zz B:: Btz Br: Bzz 67(5) r35(7) 54(5) .094(2) 43(3) 98(3) 132(3) Ca 18(1) 12(1) 18(r) -r (r) 0 0 r1 12(t) e(1) 16(1) o3 .070(2) 42(rr) 101(1i) 130(18) 0(1) 0(1) 0(1) .074(2) 7r(17) 138(9) 54(17) 12 r0(r) 7(r) 1r(1) 0(1) 0(1) .1(r) .086(2) s4(5) 50(6) 6r(s)

or 23(1) 13(1) 29(r) 4(1).-s(1) 4(1) .066(3) 90 900 02 2r(1) 12(1) 22(r) -3(r) -7(1) -r(1) .086(2) 46(5) 136(5) 90 (2) 03 18(r) 16(r) re(1) 2(1) 3(1) 2(r) .104 44(5) 46(5) 90 04 28(r) 23(r) 14(1) s(1) o 0 o5 .066(3) 90 90 0 os r8(r) 26(L) 14(1) 3(1) 0 0 .016 (2) 167(4) t7 (4) 90 , ro2(2) 17(4) 13(4) 90 * Estiilated standard errors are in parentheses and * Escinated standard eirors are in parenfheses and refer to the Iast decimal pLace. refer to the last decimal place. 82 PHILLIPS, GIBBS, AND RIBBE

two adjacenttetrahedra have apical oxygen atoms (U) point down (D). ()o 4 gqvll Ab ,zx that point up and two that c Figure 3C is a simplified representationof one of P zeo x Novll ,// .9 these rings in which the oxygen atoms are omitted !, and the U-D notation of Smith and Rinaldi (1962) o Rd I -./ is used to describethe orientation of the tetrahedra. o x/ () / In both feldspar and danburite the 4-membered vAn chain which 2 zso ./ rings are tilted with respectto the axis, c ./ is parallel to a in feldspar and c in danburite. In the o o Db ./ feldspar structure there is also a rotation of succes- = 04 t? 2.4 sive rings within each chain, although in danburite, which hasmirror symmetryperpendicular to the chain tvteong (42 ) axes,no such rotation is possible. Frc. 1. A plot of mean Ca-O distances for danburite Another point of interest is the cation distribution (Db) and anorthite (An), and mean Na-O distancesfor within a given chain. In danburite,the silicon and reedmergnerite (Rd) and albite (Ab) versus the mean boron tetrahedrawithin a 4-memberedring are al- isotropic temperature factors for 7-coordinated Ca and Na. Data for Ab and An from Wainwright and Starkey (1968, ways linked to like tetrahedrain mirror-related rings 1971) and for Rd from Appleman and Clark (1965). directly above and below in the chain, forming Si- O-Si and B-O-B linkages.Similar linkages are not found in the feldspars,even in anorthite and celsian, the mean Na/Ca-O bonds lengths and the mean which have the same Tzr:Ta*ratio as danburite.In isotropic temperature factors of the Na and Ca anorthite, like danburite, there is alternation of T3* atoms (see Fig. 1 ). and Ta*atoms within the layer of 4- and S-membered Figure 2 represents a portion of the structure rings (Figs. 3D, 3E); however, unlike danburite, viewed down c, showing the 4- and 8-membered there is also a perfect alternationbetween tetrahedra rings formed by the alternatingB- and Si-containing of subsequentrings within a chain. Thus Al-O-Al tetrahedra.Similarities between danburite and feld- and Si-O-Si linkages are not present in anorthite. spar structureswere first noted by W. L. Bragg Anorthite-like alternation of unlike tetrahedral cat- (Taylor, 1933). Both contain double-crankshaft ions is alsofound in the chainsof paracelsian(BaAle chains (Figure 3A') which consistof 4-membered SieOs;Louisnathan, Gibbs, and Craig, in prepara- rings of tetrahedra(Fig. 3B). Within these rings, tion), and hurlbutite (CaBe2P2O6;Lindbloom, Gibbs,and Ribbe,in preparation),even though these structuresare topologicallysimilar to danburite (Fig. 3E). Smithand Rinaldi (1962) and Smith (1968) de- scribed a number of possibleframework structures basedon the cross-linkingof double-crankshaftchains composedof UUDD 4-memberedrings. In the feld- spar structure (Fig. 3D) each chain is rotated ap- proximately 180' from the neighboring chains, whereasin danburite(Fig. 3E) successivechains are altemately rotated clockwise and counter-clockwise by approximately90'. In both anorthite and dan- burite the 8-memberedelliptical rings, which result from cross-linking of the double-crankshaftchains, are characterizedby alternationof T3* and T4* tetra- hedral cations. In anorthite there are two types of Fra. 2. A portion of the danburite structure viewed down 8-memberedringS UUUUDDDD (elongateparallel [001] showing the 4- and 8-memberedrings formed by the to c*) and UUDUDDUD (elongateparallel to D*). alternating B- and Si-containing tetrahedra. Mirror planes pai;sthrough O(4), O(5) and the Ca atoms (open circles) In danburite only one sequenceoccurs (UUDUD parallelto (001). DUD). CRYSTAL STRUCTURE OF DANBURITE 83

The final structuralcomparisons concern the stack- ing of the "layers" shown in Figures 3D and 3E to form the respective feldspar- and danburite-type frameworks. In feldsparsthe S-memberedrings are underlain by rings of the different sequenceand dif- ferent elongation:UUUUDDDD rings alternatewith UUDUDDUD rings along a. In danburite there is only one type of 8-memberedring present; and be- cause there are mirror planes perpendicularto the stacking axis, both sequenceand elongation are the samefor the rings in successivelayers.

Discussionof Bonding in Danburite and Related Compounds In a study of anorthite Megaw, Kempster, and Radoslovich (1962) were first to recognizethe cor- relation betweenthe tetrahedral(7-O) distancesand the coordination number of oxygensinvolved in the Z-O bonds.Fleet, Chandrasekhar,and Megaw (1966) found that in bytownite the Na/Ca-O and the Z-O distancesare also inverselycorrelated. To take into accountboth the coordinationnumber of oxygen, CN(O), and the distances to the bonded non- tetrahedralcations, Phillips, Ribbe, and Gibbs (1972, 1973)introduced the parameter >|/(Ca-O)'z1, where Frc. 3. Schematic representationsof portions of the Ca-O representsthe Ca-oxygenbond length. Since tetrahedralframework: (a) "Jacob's ladder" chain common (after (b) the oxygensin anorthite are bonded to to danburite and the feldspars Taylor, 1933); either 0, I 4-fold tetrahedral ring, and (c) its symbolic representation or 2 calcium atoms, >[/(Ca-O)'?] will have the (after Smith and Rinaldi, 1962). "U" indicates that the values of zero, l/(Ca-O)" or E lt/(Ca,-O)'1, re- tetrahedron points upward and "D" downward. (d) The arrangement of 4-fold rings of tetrahedra in anorthite re- spectively. As expected,this parameter is strongly sulting in the two types of 8-memberedrings (UUUUDDDD correlated with individual tetrahedral bond lengths, elongateparallel to c* and UUDUDDUD elongateparallel giving correlation coefficientsof 0.84 for Al-O and to b+). (e) Similar arrangement in danburite resulting in 0.90 for Si-O distances.Moreover, when the T-O-T only one type of 8-memberedring (UUDUDDUD). angles (linearized by the inverse cosine function, - l/cos Q-O-D) were included in multiple linear bondedcarbon (sp' hybridization).Similar relation- regressionanalyses, the correlation coefficientsin- ships are observedin anorthite, CaAl2Si2Or(Fig. creasedto 0.89 and 0.94, respectively(Ribbe et al, 4b), where shorter Al-O-+Si and Si-O+Al bonds r973). have larger Mulliken bond-overlappopulations on The trends observedbetween bond lengths and the averageas well as smallervalues of CN(O). It coordination number can also be rationalizedin is not surprisingthat in structurallysimilar danburite, terms of overlap integrals, S, and Mulliken bond CaBpSi2Os,the sametrends are found for Si-O+B overlap populations, n. lnterrelationships of bond and B-G>Si linkages(Fig. ab). lengths, coordination number, and overlap integrals In a study of Mulliken bond-overlappopulations for carbon containingcompounds have been estab- in feldsparstructures, Gibbs el aI (1973) found that lishedby Coulson(1951) and arepresented in Fig- n(T-O) valuescalculated assuming constant T-O ure 4a. The largestoverlap integral is calculatedfor distancescorrelate with observedZ-O bond lengths 2-coordinatedbonded carbon (cg hybridization) and O-Z-O and T-O-T anglesfor Al- and Si-con- which indicatestha't bonds involving 2-coordinated taining tetrahedra. The shorter Z-O bonds had atomsshould be shorter than those involving 3-co- larger overlap populationsand were involved with ordinated (sp, hybridization) or 4-coordinated wider O-7-O and T-O-T angles.They also calcu- 84 PHILLPS, GIBBS, AND RIBBE

( rse r.50 o. b. N X r.+e Or - € xO t.52 x Xx a o x l I co o o o t.46 a o rso fl x t.44 Fz ! r.+e o52 0.54 0.56 foa ilo" |t n(B-O) (o-B-o)3 so o r.+6 Frc. 5. Individual B-O bond lengths versus n(B-O) and ooo oro o20 (O-B-O)" for danburite (B-O+Si, open circles; B-O->B' s( c -c )tr'Ir'EZ- s(c -c)Is filled circles) and for reedmergnerite(B-O-+Si, X's).

lated,n(T-O) for the B-tetrahedronin reedmergner- ite, NaBSi3O6,but correlationswith observedbond Iengths and angleswere not attempted at that time becauseof the paucity of data. These are plotted here in Figures 5a and 5b with similar data for the B-tetrahedronin danburite. The correlationsof ob- t75 servedB-O distanceswith ru(B-O) and the average o I O-B*O angle involving a common B-O bond, (O' t.73 B-O)s, are well developedin the expectedmanner with shorter bonds involving larger overlap popu- ()t! lations and wider tetrahedral angles. z t.7| Itr Ribbe et al (1973) have demonstratedthe im- F t.64 8r L portance of the effect of CN(O) on bond lengthsin o E T-O-T linkagesin the feldspars: Z-O bondsto oxy- o t^ t.62 gens of different coordination numbers should be ro z.! treated as separatepopulations. Correlations of B-O <19t.60 with B-O-Si angle for CN(O) = 4, 3, and 2 in UJ = danburite and reedmergneritewere found to be in- r.58 determinate,because there are only two 4-coordi- nated, four 3-coordinated, and one 2-coordinated t.50 E E- oxygenatoms in thesestructures. \ _ o _ €lo__€i_ Inasmuch as danburite will be included as part of I 1.48 6 - _ __-orr_ an extensive investigation of the crystal chemistry and bondingin MT23rT2a*Orand MTrz*7rs*gecofii- pounds currently underway in our laboratory and in ooo o.ot oo2 003 the Institut fiir Mineralogieat WestfiilischeWilhelms- (n( r- otr'r'El)-(n t r - oEl) Universitzitin Miinster, Germany, and the Istituto di Ftc. 4. (a) The difterences in the overlap integrals, S, Mineralogia e Geochimica at the University in To- for a C-C bond involving a 4-coordinated carbon atom and rino, Italy, further discussionof the structurewill be those involving 4-, 3- and 2-coordinated carbon atoms deferred to a future report. versus C-C bond length. (b) The differencesin the mean populations Mulliken bond overlap for T-O bonds involving Acknowledgments a 4-coordinatedoxygen atom and those involving 4-,3-, and 2-coordinatedoxygen atoms plotted against mean 7-O dis- This study was supportedby NSF grant GA-30864X and tance in A. Anorthite data are connected by solid lines, the Research Division of V.P.I.S.U. The senior author danburite by dashedlines. Roman numerals indicate coordi- received partial support from NASA grant NGR 39-007- nation number. 064-.^. CRYSTAL STRUCTURE OF DANBURITE 85

References JoueNssoN,G. (1959) A refinementof the crystal structure AenrueN, D. E., eNo J. R. Crenr (1965) Crystal structure of danburite. Acta Crystallogr. 12, 522-525. of reedmergnerite, a boron albite, and its relation to Mncew, H. D., C. J. E. KpvrpsrpR, ANDE. W. Reoosrovrcn feldspar crystal chemistry. Am. Mineral. 50, 1827-1850. (1962) The structure of anorthite, CaAl,Si,Or. II. Descrip- BexnrN, V. V., V. B. KnevcnexKo, AND N. V, Bnov tion and discussion.Acta Crystallogr. 15, 1017-1035. (1959) The crystalline structure of danburite CaB$LOe PHILLIeS,M. W., P. H. Rrrnr, AND G. V. Grnns (1971) and hurlbutite CaBe.P,Oe.Doklady Akad. Nauk SSSR, Refinement of the crystal structure of danburite [abstr.] 129, tl55-1158. Geol. Soc. Am. Southeastern Sect. 5th Annu. Meet. BnuN, 8., eNo S. Gnose (1964) Nuclear magneticresonance Blacksburg, Va. May 5-8, 1971, Absft. Programs, 3,338. spectrum of "B and B-Si order in danburite, CaB,Si,Oi. (1972) Tetrahedral bond I. Chem.Phys. 40,3031-3033. length variations in anorthite (rev. abstr.). Am. Geophys. BusrNG,W. R., K. O. MenrrN, AND H. A. Lrw (1962) Union, 53rd Annu. Meet. Washington,D.C. April 17-21, A Fortran crystallographic least-squares program. U.,S. 1972Program, p.48. Nat. Tech. Inform. Seru. OnNr-rlr-305. AND_ ( 1973) Tetrahedralbond length Cout-soN, (1951) C. A. Critical survey of the method variations in anorthite. Am. Mineral. 5E, 495499. ionic-homopolar resonance.Proc. Royal Soc. (London), Rrnau, P. H., M. W. Purrrrs, eNo G. V. Grnrs (1973) 4207, 63-73. Tetrahedral bond length variations in feldspars.In, W. S. CRoMER,D. T., rNl J. T. Wessn (1965) Scatteringfactors MacKenzie and J. Zussman, Eds., ProceedtngsNATO computed from relativistic Dirac-Slater wave functions. Adoanced Study Institute on Feldspars. Manchester Uni- Acta Crystallogr. 18, 104-109. versity Press,pp. 26-48. CnurcrsneNr, D. W. J. ( 1965) Errors in least-squares Surnr, J. V. (1968) Further discussion of framework methods. In, J. S. Rollett, Ed., Computing Methods in structures built from four- and eight-membered rings. Crystallography. Pergamon Press, New York, pp. 112- Mineral Mag. 36, 640-642. I 15. AND F. RrN.lrur (1962) Framework structures DUNBAR,C., ANo F. Mecne,rscnxr (1931) S ructure of dan- formed from parallel four- and rings. burite, CaB^Si,O". Z. Kistallogr. 76, 133-146. eight-membered Mineral. Mag. 33, 202-212. Freer, S. G., S. CneNonAsEKHAR,AND H. D. Meae.w (1966) (1933) The structure of bytownite ('body-centered anorthite'). Tevron, W. H. The structure of sanidineand other Acta Crystallo'gr. 21, 782-801. feldspars.Z. Kristallo'gr. 85, 425-442. Gnrs, G. V., S. L LoursNerrrex, P. H. Rrnnn, eNn M. W. WerNwnrcnt, J. E., eNo J. Srenxry (1968) Crystal structure Punrrps (1973) Semiempirical molecular orbital calcu- of a metamorphic low albite (abstr.). GeoI. Soc. Am. lations for the atoms of the tetrahedral framework in Abstr. Programs,2, 37O. anorthite, low albite, maximum microcline and reed- AND_ (1971) A refinement of the structure mergnerite. In, W. S, MacKenzie and J, Zussman, Eds., of anorthite. Z. Kristallogr. 13,3,75-84. Proceedings NATO Aduanced Study Institute on Feld- spars. Manchester lJniversity Press, pp. 49-67. HANsoN,A. W. (1965) The crystal structureof the azulene, Manuscript receioed,July 13, 1973; accepted S-trinitrobenzene complex. Acta Crystallogr. 19, 19-26. lor publication,October 11,1973.