American Mineralogist, Volume 74, pages642455, 1989

Kornerupine: Chemical crystallography,comparative crystallography, and its cation relation to olivine and to Ni,In intermetallic

P.lur. BnrnN Moonn Department of GeophysicalSciences, The University of Chicago, Chicago,Illinois 60637, U.S.A. Pnlorp K. SnN Gup'rl Department of Geology, Memphis State University, Memphis, Tennessee38152, U.S.A. Er-rrnn O. Scrrr-nvrppn Department of Chemistry, University of Missouri, Columbia, Missouri 6521I, U.S.A.

Ansrru.cr Kornerupinefrom Mautia Hill, Tanzania,orthorhombic holosymmetic, a: 16.041(3), b : 13.746(2),c : 6.7 l5(D A, spacegroup Cmcm, Z : 4, formula from refined structure Mg3,8Fe3j8Al5 47Si4 rrB0 43Or, ,o(OH)o ,u, has been refined to R : 0.027for 1807independent reflections. One partly occupied site [X] with distorted cubic coordination by oxygen, five octahe- dral sites [M(IFM(5)], three tetrahedralsites [T(1FT(3)], and ten oxygenatoms [O(lF O(10)l occur in the asymmetric unit of structure. Severalearlier suggestionswere verified: the X site population is partly occupied and refined to 0.374Mg + 0.626E; all B is se- questeredat T(3) : 0.572Si + 0.4288, and the distorted M(4) site sequestersreported Fe3*, 0.8104,1* 0.190Fe3+.In addition, anisotropic thermal-vibration parametersU,, have averagediferences of 25o/obetween pairs of 18 fully occupied sitesin this structure and in two earlier well-refined structures.O(10) is bonded in part to a H atom that is believed to form a hydrogenbond O-H( I 0) . .O(9) with an O( l0)-O(9) length of 2.763 A, a reasonable coupled relation to X being X?jar,(OH)a. By analogy with [P4] - [P4O6] - [PoO,o],it is believed that generalizedkornerupine, M4oTroO88,which has a cation pseudorepeatof a/5 or M8T4O'76,is a dilated version of the intermetallic Nirln, as is also assertedfor the olivine structure type. The model based on .r-.t,s-p, and p-p bond strengthssuggested by Pauling and the [Po] - [PoOu]- [PoO,o] structure sequenceappear to explain not only the relation to Nirln but also the location of oxygen sitesin that structure type, of which many alternative anion loci are structurally possible. Thus, kornerupine and sinhalite (olivine), which occur in similar parageneses, are different ways of stufrng interstitial oxygen betweencations of similar arrangement.

INrnooucrroN attendant parametersto be varied is R, the "R factor," "reliability index," "discrepancy index," "residual," etc. Contemporarycrystal-structure analysis is rarely an end In contemporary refinements,R usually rangesfrom 0.04 in itself. Beyond solution and characteization of novel to 0.06, and exceptional caseswill provide R :0.015- structure types, comparative relations are often sought 0.04. R : 0.00 is clearly impossible, as a perfect X-ray within a composition series.Usually the quality of a re- diffraction experiment cannot exist with the limiting cri- finement hinges on the quality of the crystal. Most im- teria outlined above. What about R > 0.06? There are portant parametersinclude the linear atomic-absorption many experimentsthat fall in this region, and when they coefficient,p, the anisotropic thermal-vibration ellipsoids are reported, a good explanation for this high value is for the independent atomic sites, the site population for expected from the investigator(s).Typical examples are each of theseindependent sites,mosaicity, secondaryex- found in crystalswith large p (say >300 cm ') and those tinction, and the refined atomic coordinates themselves. having cations with associatedlone electron pairs and Even if all of these conditions are known to perfection, a consequentdifficulty of crystal measurementin prepara- perfect refinement still cannot exist becauseof uncertain- tion for absorption correction. The other examples are ties inherent in the selected scattering factors and the found in crystalsthat are composednot of one singlet but choice of fully ionized or neutral atoms. The data set is of two or more individuals each with a different but re- limited by the X-radiation brought upon the crystal. The lated structure. Yet others display severelineage or twin- conventional test of the quality of the data set and all the ning, but thesecan be easily tested. These are very com- 0003-004x/89/0s0H642$02.00 642 MOORE ET AL.: CRYSTAL CHEMISTRY OF KORNERUPINE 643 mon phenomena,and such structure solutions usually are TABLE1. Experimentaldetails for Mautia Hillkornerupine called "averaged structures." (A) Crystal cell data Kornerupine posesmany such hurdles. With 19 inde- a (A) 16.041(3) pendent atoms in the asymmetric unit, 9 of these are b (A) 13.746(2) cations; most of the cation sites in turn involve solid c (A) 6.715(2) v(4") 1480.6(1 ) solution of two or more ionic species,and one site is only Spacegroup Cmcm partially occupied. At least six chemical components oc- z 4 (a) Nao Mg3 Bo cur for natural kornerupine. In its favor, however, is Formula McKie1965 01 6sTio02Fqj7Al6 s6Si371 41- or 75(oH)or3 hardness (7 on Mohs scale) and low linear absorption (b) from structure Mgs esFeS:BAl51?Si4,1 Bo €O21 24- coefficient, p x 14.3 cm-' (Mo.Ka). Experiencesuggests (OH)o^ p"","(g cm+) (a) 3.337 that substancesof superior hardness usually afford su- (b) 3.288 perior diffracta and superior subsequentrefinement es- SpecificAravity (McKie, 1965) 3.297 pecially of the anisotropic thermal-vibration parameters, p (cmi) (b) 14.3 all probably a result of rather uniform distribution of (B) Intensily measurements Crystal size (pm) 140x160x300 chemical bonds with relatively high bond strength. We Diffractometer Enraf-NoniuscAD-4 would immediately anticipate relatively low averageroot- Monochromator Graohite mean-squarethermal-vibration amplitudes in Radiation MoKa such cases. Scan type 0-20 Three previous kornerupine structure studies were re- 20 rcnge u,c-/ o- ported.The first, by Moore and Bennett(1968), revealed Scan width A: 0.70.B : 0.35.where A0 : : (A + Btan d) the broad features of the structure and resulted in R Variable horizontalwidth (tv) where4:4.0,w:A+tand 0. 11 for 1047 independentdata. An end-membercom- Maximumscan time (s) 90 position was proposed:MgrAluOo(OH)[SirO?] (Al,Si)r- Orientationmonitors three orientation standards checked every 200 reflections;25 reflec- Sio,ol. Four formula units made up the structure cell with tions used for cell dimensions a: 16.100,b: 13.767,c: 6.735A, spacegroup Cmcm. Intensitymonitors every 7200 s of X-ray exposure (de- This material wasfrom Mautia Hill, Tanzartia, locality cay <1Y") the Independentreflections 1807. above 2o. used in refinement that formed the basisof McKie's (1965)detailed chemical (C) Refinement of the structure and cell resultson the species.The excellentcrystals from H o.027 that locality were precisely those used toward the results 0.049 in our presentinvestigation. It wasn't that the earlier work of Moore and Bennett was wrong (the R index was a perfectly adequate"state of the art" result over 20 years ago), but ilwas wanting in certain respectsespecially for KonNnnupIltE: ExpERIMENTAL DETATLS those investigatorsinterested in B metasomatismin min- Pale pink crystals of kornerupine from Mautia Hill, erals of granulite facies. In this case,no recovery of one supplied by D. McKie over 20 yearsago toward the orig- large, partly occupied site and the disregard of B parti- inal structure study, provided the samebatch from which tioning in the crystal structure were shortcomings. The our clear crystal was selected.The data reported here are second study, by Moore and Araki (1979), defined the consideredsuperior in every respectto the initial structure partly occupied site and the preferential sequesteringof study of Moore and Bennett (1968). An outline of the B at one tetrahedral site. The crystal, a synthetic B-rich experimental procedure is given in Table l. Twenty-five kornerupine, gave R : 0.052 for l44l independent re- high-anglereflections defined the orientation matrix that flections,with formula-unit composition Mg,,rAlr rdi, nr- provided the crystalcell data. The cell edgesare each about BojTO2oer(OH)ros. a: 16.016, b : 13.758,c: 6.720A, 0.30/osmaller than those reported by McKie, who used spacegroup Cmcm. A third investigation, by Finger and back-reflection photographs, Si internal standard, and Hazet (1980),yielded R : 0.058. Theseresults were of CuKa radiation. The data from our prismatic crystal were sufficiently precisequality (M-O, T-O = +0.003 A) ttrat coffected for absorption anisotropy by ry'scan, a minimal we consideredit possibleto probe the generalkornerupine correction owing to the low linear atomic-absorptioncoef- structure type further through comparison of site parti- ficient of p : 14.3 cm-r for MoKa radiation. tioning, anisotropic thermal-vibration parameters, and The 1807independent F. valueswere put toward struc- atomic coordinateswith a superiorrefinement of the Mau- ture refinement, beginning with the proposed atom co- tia Hill kornerupine. ordinates of Moore and Araki (1979) for a synthetic crys- The results are most gratifying. It is shown that com- tal. Neutral-atom scattering factors and real and imaginary parison ofthe thermal-vibration parametersbetween syn- dispersion coffections were taken from Ibers and Ham- thetic and natural crystalspresents adequate concord and ilton (1974). Refinementminimized 2 w(lF"l - 14lX that minor components are well partitioned with 83+ - where w-t : unit weight. The conventional R index men- T(3) and Fe3+ - M(4), confirming the provisional con- tioned throughoutthis paper is R : >llF"l - lF"ll/ clusions announcedin the Moore-Araki study. Finally, R > l.F. | . Refinementemployed the full-matrix procedureof : 0.027 for 1807 independentreflections, a good value least-squareswith the program sHELx76.Throughout this for such a complex structure. study, there was no need to challenge centrosymmetric 644 MOORE ET AL.: CRYSTAL CHEMISTRY OF KORNERUPINE

TABLE2. Kornerupine:Atomic coordinateparameters pared with the perfect model for Nirln. A similar com- parison is appendedfor olivine cations, and this becomes A z{l') a "working table" later on. The values are from Birle et al. (1968)for forsterite.The anisotropicthermal-vibration X 4 0 0 N(1) 4 0 0 000 parameters and equivalent isotropic thermal vibrations M(l) Mg 8 0.12176(5)0 14031(5) 1t4 appear in Table 3. This table is also discussedin some N(2) R 1/10 1/6 114 0.50 detail (seebelow). Bond distancesand anglesare offered M(2) Mg 4 1t2 0 14s63(7) 1t4 in Table 4. Thesevalues are within M-O, T-O = 0.03 A N(2) 4 5/10 1/6 1t4 0.29 and T(3fO(7) - 0.0SA of the earlierMautia Hill study. M(3) AI 8 0.21536(4) 0 0 Table 51lists the observedand calculatedstructure factors N(1) 8 2110 0 0 0.25 M(4) I 0.31366(3) 0.14182(4) 114 ofthe presentstudy. N(2) 8 3/10 116 114 0.41 M(5) AI 8 0.40756(4) 0 0 KonxrnuprNE: CHEMTCALcRysrALLocRApHy N(1) I 4t10 0 0 0.12 Sincekornerupine's essentialdetails have been covered r(1) 8 o.40202(3) 0.35299(4) 1t4 in the earlier work, only the salient featureswill be cur- tn I 4t10 1t3 114 0.27 sorily presented.With three superior refinements, some r(2') 8 o.17842(4) 0.33375(4) 1t4 tn n 2110 1t3 114 0.35 comparative crystallographyis in order. r(3) 4 0 0.34253(8) 1t4 Formula. Two formulae can be offered for Mautia Hill tn 4 0 1/3 114 0.13 kornerupine, the first based on the analysis of Scoon in Mean 0.26 McKie (1965),the secondcomputed from therefined crys- o(1) I 0.2240(1) 0.0448(1) 114 structure. Individual site populations were estimated o(2) 8 0.40367(8) 0.0460(1) 1t4 tal o(3) 8 0.40283(9) 0.2355(1) 114 in three ways: fractional site occupancy,as for X, by vary- o(4) 16 0.13818(6) 0.09959(7)-0.0515(2) ing the site-population parameter; use of more than one o(5) 8 0.2338(1) 0.2358(1) 1t4 o(6) 16 0.31671(6) 0.09479(7)-0.0471(2) scatteringcurve in a complementary fashion, as for M(4), o(7) I 0.0824(1) 0.2821(1) 1t4 T(2), and T(3); and later calculation basedon averageM- o(8) I 1t2 0.0885(1) - 0.0541(2) -1t4 O, T-O bond distances, assuming a linear relationship o(e) 4 0 0.1128(2) lorMg-rarO t6lFe3+-r4ro t6lAl-t41c) o(10) 4 0 0.0882(2) 1t4 among (2.l0 A), (2.02A), t4rAF4lO t4rsir4lo Olivine (1.91A), (1.77A), and (1.64A) from M(1) Mg4 00 0 the tablesof effectiveionic radii (basedon t6ro2-r: 1.40 N(1) 4 00 0 0.00 A1 of Shannonand Prewitt(1969). The final assignments M(2) Mg4 0.4897 0.2226 3t4 are X : MgorrEour,M(l) : Mg,oo,M(2) : MgonrAloor, N(2) 4 1t2 116 314 0.57 T -0.0731 M(3): MgoorAlonr,M(4): MgrrFefr-frAlo56,M(5): Al,.oo, si 4 0.4057 314 : : : tn 4 0 1/3 314 0.82 T(l) Sir00,T(2) Alo2rSiorr,and T(3) 86orSior'.All Mean 0.46 atoms for Z : 4 were added up, total oxygensfixed at 22, NoteiCations of kornerupineand olivinecompared with Nirln.A : scat- and the chargeimbalance was compensatedby substitut- tering factor, M : equipoint rank. Standard errors in parenthesesrefer to ing appropriate OH for O'? . The formulae are the last digit. . (a) Site populationrefined to 0.374(4)Mg+ 0.626!. (b) Site population refinedto 0.810(4)Al+ 0.190Fe.(c) Site populationrefined to 0.766(5)Si Na" o,Mg,urTio orFefrjrAlu 36Si3 7rB0 4ro2r rr(OH)o r. (a) + 0.234A1.(d) Site populationrefined to 0.572(1)Si+ 0.4288. MBrn, FeljrAlrorSio,,BoorOr,ro(OH)oru,(b)

where (a) is from McKie (1965) and (b) is from this study. Cmcm. Finally, secondaryextinction correction (Z,achar- Densities were calculatedfor thesetwo formulae and are iasen,1968) was applied for this hard crystal,which yield- listed in Table l. They are within 1.50/oof eachother, and ed a small correction, the maximum being2.60/oof l.F. l within l0loof the measuredvalue. Site-population refine- for the (0 2 2) reflection. ments for Fe3+and B are in good accordwith the chemical At one point, we concluded that the structure had been analysisof Scoon.Our Mg and Si totals are high and our fully refined at R : 0.034 and proceededto draft up this Al total is low, but site assignmentsbased on averagebond communication. However, it becamevery clear that one distancesare only approximate,as variations occur among atom was misbehaving,namely M(4) with B"o:0.12 42. structure types.As a point of fact, we have observedsim- This unreasonably low value was at least three times ilar relations for other stnrcturesand concludethat more smaller than any other value in the asymmetric unit. Since structure study on Mg-Al-Si solutions is in order. we applied the neutral scatteringfactors for atoms aslisted This study confirms two conclusionsannounced in the in Table 2 and used Al for M(4), we were forced to con- study of Moore and Araki (1979) on synthetic B-rich kor- clude that a heavier atom was preferentially sequestered at this site, and we placed all Fe3* reported by Scoon in I Document AM-89-404 McKie (1965)here. A copy of Table 5 may be ordered as from the BusinessOffice, Mineralogical SocietyofAmerica,1625 Atomic coordinatesfor all 19 asymmetric atoms in kor- I Street,N.W., Suite4 14,Washington, D.C. 20006,U.S.A. Please nerupine are given in Table 2, and the cations are com- remit $5.00 in advance for the microfiche. MOORE ET AL.: CRYSTAL CHEMISTRY OF KORNERUPINE 645

Tler-e3, Kornerupine:Anisotropic thermal-vibration parameters ( x 103)

uu ur. U"" Ur" u,a U"" B* (A1 - X 64.1(31) 16.2(14) 13.8(16) 0 0 0.2(13) 2.48(10) M(1) 11.9(3) 8.6(3) 6.6(3) 2.2(21 0 0 0.71(2) M(2) 3 9(4) 4.5(5) 11.0(4) 0 0 0 0.51(2) M(3) 7.0(3) 6.1(2) 2.5(2) 0 0 -o.7(2) 0.41(1) M(4) 7 6(3) 7.7(2) e.4(2) -0.3(1) 0 0 0.65(1) M(5) 5.e(3) 5.6(2) 3.4(3) 0 0 -0.6(2) 0.39(1) r(1) 4.2(3) 5.2(21 4.0(21 1.0(1) 0 0 0 35(1) r(21 16.0(4) 5.6(2) 3.5(2) - 1.6(2) 0 0 0.66(1) r(3) 3.6(4) 6.7(4\ 3.2(4) 0 0 0 0.36(2) o(1) 8.3(5) 6.e(5) 3.3(5) 0.3(4) 0 0 0.49(3) o(2) 7.2(5) 6.2(6) 3.s(5) -0.8(3) 0 0 0.44(3) o(3) 8.e(5) 6.1(5) 11.1(6) 1.7(4) 0 0 0.69(2) o(4) 10.6(4) s.7(4) 4.2(41 4.1(3) - 1.s(3) 0.5(3) 0.64(2) o(s) 21.9(8) 13.5(7) 10.3(7) -0.1(6) 0 0 1.20(3) o(6) 7.2(4) 8.4(4) 7.2(4) 0.7(3) -0.4(3) -0.0(3) 0.60(2) o(7) 14.6(6) 15.8(7) 8.5(6) -8.6(6) 0 0 1.02(3) o(8) 5.3(5) 5.8(5) s.6(5) 0 0 0.6(1) 0.54(2) o(s) 4.8(8) 12.8(s) 22.6(11) 0 0 0 1.06(4) o(10) 8.3(8) 13.1(6) 17.7(11) 0 0 0 1.03(4)

Note: The U, are coefficientsin the expressionexp[-(qrh, + Unk2 + Usl2 + 2uphk + 2UBhl + 24skl)]. The equivalentisotropic thermal parameter isA*:(8/3)r'z(4 1+ U22+ Us). nerupine, that 83* is sequesteredin the T(3) site and that consistentwith the present refinement." The Moore and Fe3+goes into the M(4) site. In addition, comparison with Araki sample was a synthetic crystal in the systemMgO- Fingerand Hazen(1980) shows other substitutionsby Fe AlrO3-BrO,-SiOr-HrO,but a variety of other analysesfor are possible. natural kornerupine was discussedin that paper.Actually, Thermal vibration. Isotropic and anisotropic thermal- Moore and Araki (p. 335) declared, "Finally, it is quite vibration effectsare difficult to appraise,even in contem- likely that Fe2+reported in chemical analysesoccurs in porary structural refinements. Rather high correlations 4-coordination at the X-position with Fe3+dissolved in among variable parameters such as atomic coordinates the M(4) position. These two distorted sites seem to ac- with at least one degree of freedom, the linear atomic- count for the pleochroism observed for iron-containing absorption coemcient,the anisotropy of the crystal shape, kornerupines." In this study, only the crystals of Finger and crystal mosaicity-all are coupled to some degreeto and Hazen and our presentone from Mautia Hill contain the at most six independentanisotropic thermal-vibration substantial Fe. It is desirable to outline the partitioning parameters.Minerals, which often have a large pr com- of "heavy" Fe among the sites on the basis of refined pared with organic crystals,are palticularly problematic. fractionaloccupancies: M( I ), 0.3 6Fe; M(2), 0.30Fe; M(4), For this reason, it is common practice to accept aniso- 0. l2Fe; and X, 0.07Fe according to Finger and Hazen or tropic thermal-vibration parametersin mineral structures M(4), 0. l9Fe according to this study. as "sponges" that absorb the errors arising earlier among McKie (1965) reported FerO, 3.980/oand FeO nil for the other variable parameters,particularly those arising the Mautia Hill material used in this study. Since the from crystal size and crystal shape and from the linear largestsites are X, M(l), and M(2), Fe2* is believedto atomic-absorption coefficient. enter into these, with Fe3+ partitioning into the much For reasonably well-refined structures of a complex smaller and also more distorted M(4) site; that is X, M(1), mineral, it is desirableto compare the thermal-vibration M(2) t (Mg'z+,Fe2+),and M(4) E (A13+,Fe3+).It would parametersamong refined structures.Three such studies appearthat the conditions of formation for the Finger and have beenselected: this study, the earlier Moore and Araki Hazen (1980) kornerupine were those of relatively lower (1979)investigation, and the resultsofFinger and Hazen oxygen fugacity than those for formation of the Mautia (1980). Although Finger and Hazen reported crystal data Hill material. for a high-Fe kornerupine from Rangeleyquadrangle in Comparisonof individual U,'(i: I to 3) and of B.owas Maine including average electron-microprobe composi- performed in the following manner. It was askedwhether tion, atomic coordinatesand equivalent isotropic thermal individual values from Moore and Araki (1979) and Fin- parameters-8"o, cation occupancies,and polyhedral mean ger and Hazen (1980) were relatively greateror lessthan bond lengths, we were anxious to obtain their original those from this study, which was used as the reference. reflned Uuset. We thank L. W. Finger for providing these We should suspectsome significant departuresowing to data. We note a small (+100/o)difference between our different proceduresofdata collection and reduction and computed .B"ofrom U,,(i : I to 3) of this output and the to deduced site partitionings. As X is only a partly oc- result reported in Finger and Hazen. But of more concern cupied site, it was excludedfrom comparison.The values is their statementon p. 373, "Moore and Araki also as- for M(lfM(5), T(1FT(3), and O(llO(10) werecalculat- sumed that there was no iron in M(4), an assumption not ed asd ffi r enc e, A, expressedin percent.Setting W to equal 646 MOORE ET AL.: CRYSTAL CHEMISTRY OF KORNERUPINE

TABLE4. Kornerupine:Polyhedral interatomic distances (A) and angles(")

M(l) M(3) 1 M(1)-o(7) 2.049 2 M(3)-O(1) 1.794 1M(1Fo(l0) 2.080 2 M(3)-O(4) 1.878 1M(1FO(1) 2.101 2 M(3)-O(6) 2.107 2 M(1Fo(4) 2.117 Mean 1.926 1 M(1)-O(5) 2.225 2 o(1)-o(4)-' 2.561 88.45 Mean 2.115 2 o(1)-0(6)-- 2.58'l 82.43 1o(5Fo(7)' 2.511 71.81 1 0(6)-0(6)(3)'' 2.682 79.03 2 o(1)-O(4)" 2.561 74.79 2 O(1)-O(4)(3) 2.759 97.42 1O(1)-O(5).. 2.630 74.82 2 O(1)-O(6)F) 2.784 90.69 1O(7)-O(10) 2.974 92.16 1 o(4)-o(4)€' 2.824 97.51 2 o(4)-O(10) 3.006 91.48 2 0(4)-0(6) 2.865 91.73 2 o(4)-o(5) 3.155 93.18 Mean 2.717 89.83 2 o(4)-o(7) 3.346 106.86 1o(1Fo(10) 3.642 121.20 M(4) Mean 2.991 91.05 1 M(4)-O(5) 1.820 1 M(4)-o(3) 1.925 M(2) 1 M(4)-O(2) 1.954 2 M(2Fo(3) 1.989 1 M(4)-o(1) 1.961 2M(2)-O(21 2.064 2 M(4)-o(6) 2.098 2 M(2)-o(8) 2.188 Mean 1.976 Mean 2.080 2 0(2)-0(6)"- 2.525 77.O0 2 o(2Fo(3)-' 2.604 79.94 2 o(1)-0(6)-- 2.581 78.90 4 o(2)-o(8)-. 2.626 76.23 1O(2)-O(3r. 2.604 84.36 1O(2)-O(2)(4) 3.090 96.93 1O(1)-O(5)" 2.630 88.08 1 O(3)-O(3)4) 3.117 103.20 1o(3)-o(5) 2.712 92.77 4 o(3)-o(8) 3.268 102.89 1O(1)-o(2) 2.882 94.79 Mean 2.916 89.71 2 0(5)-0(6) 3.083 103.61 M(5) 2 0(3)-0(6) 3.103 100.88 2 M(5FO(2) 1.795 Mean 2.784 90.06 2 M(5Fo(8) 1.952 r(21 2 M(5)-0(6) 1.980 1r(2FO(5) 1.612 Mean 1.909 2 r(2FO(6Xo) 1.681 2 0(2)-0(6)-. 2.525 83.79 1 r(2)-o(7) 1.697 1o(8)-O(8)o* 2.539 81.13 Mean 1.668 2 o(2)-o(8)-- 2.626 88.90 1 o(s)-o(7)'. 2.511 98.66 1 0(6)-0(6)(E-' 2.682 85.23 2 O(6)t1o-9171 2.709 106.63 2 O(2)-O(8)€) 2.746 94.13 1 0(6Ir0)-0(611') 2.725 108.30 2 o(2FO(6)€' 2.748 93.27 2 O(5)-O(6)no) 2.817 117.58 2 0(6)-0(8) 2 942 96.85 Mean 2.715 109.23 Mean 2.700 90.02 r(3) r(1) 2 r(3)-o(7) 1.561 1r(1)-O(3) 1.615 2 T(3)-O(8)t1o) 1.621 2 T(1)-O(4)(io) 1.618 Mean 1.591 1 T(1)-0(9)00) 1.640 4 O(7)-O(8)00) 2.577 108.15 Mean 1.623 1 O(8)ro)-O(8I1i) 2.631 108.50 2 O(4)(10)-O(9)oo) 2.593 105.47 1 0(7)-0(7)(1) 2.644 114.72 1 O(3)-O(9)oo) 2.603 106,20 Mean 2.597 109.30 1 O(4I1oLO(4)0') 2.666 110.95 2 O(3FO(4)00) 2.71'l 113.98 x Mean 2.646 109.34 2 x-o(10) 2.O71 2 x-o(s) 2.286 4 x-o(4) 2.628 Mean 2.403 Note; Under each atom heading are listed (X,M,TFO bond distances and angles. Errors: M-O < 0.002 A, O-O' < O.OO3A, angles O-M, T-O, -y, -z; -x,y, 0,09'. Equivalentpoints are referredto Table2 and appearas superscripts:(3) x, (41 z; (1OlYz- x,lz - y, -zi i1)V2 - x,V2 - v, V2+2. 'Shared edge betweenM and T polyhedra. .'Shared edge betweenM and M'polyhedra. the value in Moore and Araki or Finger and Hazen and a consequenceof smaller thermal motion for the cations I to equal the value obtained in this study, and of more variegatedsolid solution in thesecation po- sitions. The greatestdeviants, + | 56.2o/o for T(3) A: l(W- r)/Tl x 100. of Moore and Araki (1979) and *l4l.0o/o for M(2) of Finger and Mean values and their extrema are tabulated in Table 6. Hazen (1980) arise in part from the arithmetic involvedl For three kornerupines from three different sources(two since the [l, individual values employed the relatively natural minerals, one synthetic), the similarities rather small values in this study as the divisor, such differences than the differencesare surprising.The mean value of lA I appear exaggerated,at least in the condensedmanner by for all U,, of the 8-cation and lO-anion unique positions which we expressthem. is a little over 25o/ofor cations and a little under l7olofor The averageB"o are also listed. The match is remarkably anions. Cations usually give larger A values than anions, close, within 20o/ofor cations and 3o/ofor anions. These MOORE ET AL.: CRYSTAL CHEMISTRY OF KORNERUPINE 647

Traue6. Refinedkornerupines: Differences in thermalparameters aq, (,: 1 to 3) A8* Extrema A. M(1FM(5)and T(1)-r(3) -0.0 MA 30.2 -16.2tor T(2)to +156.2for T(3) 20.8 for M(3)to +88.9 for T(3) -23.1 FH 32.1 -32.5for M(4) to +141.0for M(2) 23.0 tor M(4)to +72.5 for M(2) B. o(1)-o(10) -21 MA 15.9 -27.5 torO(10) to +69 0 for O(4) 9.4 .3 tot O(10) to + 14.1 for O(4) -20.6 FH 25.9 -40.5 for O(7)to +88.1for O(4) 15.6 for O(7)ro +22.7 lot O(21 C. Mean of lAl for M(1)-M(5),T(1)-T(3), and O(1)-O(10) MA 22.2 14.5 FH 28.6 18.9 M(1FM(5) r(1Fr(3) o(1FO(10) D. Mean B* (A') TS 0.53 0.46 i 7'l MA 0.59 U.JY 0.77 FH 0.61 0.47 0.79 Note: All calculationsrefer to values in the present study. part A is for cations, Part B is for anions, and Part C is ior all 18 occupied atoms in the asymmetricunit. Mean values of the differencemagnitudes' : mean equivalentisotropic lA | , and individualextreme points are also given in percent.These valuesare given for 4 (, 1 to 3) and 8q. Part D lists the thermalparameters. * References:MA-Moore and Araki (1979);FH-Finger and Hazen(1980); Ts-this study.

similar results from three independent studies underline Thirty-six entries occur in Table 7, and of these, six the importance of assessingthermal-vibration parameters violate the expectedbond length-bond strength relation- in evaluating the "correctness" of a structure. ships. In other words, 830/oof the values are in concord. When a structure is accuratelyknown, it is desirableto Five of the six values involve X and M(l), the two most calculate individual deviations from bond-distance av- distorted polyhedra in the structure. The violations in- eragesand compare them with deviations in electrostatic volve the anionsO(4), O(5), O(7), and O(9) of which O(7) neutrality. The simple Paulingmodel wasadopted, mainly and O(9) have undersaturatedvalues for theseentries. The becauseit does not masqueradedeviations but proceeds O(4), O(5), and O(7) are eliminated as they involve shared directly from formal charges,coordination numbers, and edgeswith other fully populated polyhedra, that is, their individual distance deviations calculated directly from distancesare too long, owing to cation-cation repulsion Table 4. Individual bond strengths,s, were calculatedfor effects.The O-H(10)" O(9) distanceof 2.763(3)A cor- a purely ionic model and from the cation-sitepopulations respondsto a sharededge between two XO(4).O(9)rO(10), and coordination numbers discussedearlier. Calculated distorted cubes. If a successivepair of such cubes has deviations from po : 2.00 for 02 and individual distance unoccupiedX, the O-H( l0) ' ' ' O(9) hydrogenbond is pos- deviationsare listed in Table 7. Only O(10) has attached sible. The increasein X occupancy would tequite a de' H and the O-H bond was given s : 5/6 suggestedby Baur creasein H content, suggestedearlier by the postulated (1970).The centroid ofthe H atom could not be located X?,*tr%OH--X?"O'- series.However, the left side of the in our differencesynthesis. However, it was postulatedby equation is not balanced, and quantitative presenceof Moore and Araki (1979)thata seriesX7,+tr"OH--X1*62 hydroxyl groupswould not be possiblein this model owing existed. This can now be tested to some degree. to shared edgeswith occupied cubes.A more reasonable

TABLE7. Kornerupine:Electrostatic valence balance of cationsand anions Cations Anions M(1) M(2) M(3) M(4) M(5) r(1) r(2) r(3) LPo o(1) -0.01 -0.13,-0.13 -0.01 -0.17 o(2) -0 03 -o.02 - 0.11,-0.11 -0.17 o(3) -0.11 -0.05 -0.01 -0.17 o(4) + 0.22 +0.00 -0.05 -0'00 -0.07 o(5) + 0.11 -0.15 -0.06 -0.23 o(6) +018 +0.12 +0.07 +0.02 +o.44 o(7) - 0.07 +0.03 -0.03 +0.17 o(8) +0.14 +0 04,+0.04 +0.03 +0.23 o(9) - 0.11 +0.01,+0.01 +0.19 o(10) -0.33,-0.33 -0.03,-0.03 -0.32 Nofej Bond length-bond strength contradictionsare in italics. Entries are individualdeviations from polyhedralaverages (Table 4). 648 MOORE ET AL.: CRYSTAL CHEMISTRY OF KORNERUPINE

Trele 8, Comparisonof Ni2ln,olivine, and kornerupine

Ni,ln ao(N):4.18 4(N):7.24 cD(N): 5.13 Cmcm Olivine a(n: 4.76 b(n:10.22 c(F): 5.99 Pbnm Kornerupine a(K): als : 3.21 D(K): 13.75 c(K): 6.72 Cmcm A/ofe.'Valuesare in angstroms.

series on the left side would be Xfl,+tr*OHu,.This stoi- distinct rods, each made up of three unique cations when chiometry appearsto fit our refined structure fairly well. projectedalong the I I 00] direction. When the mirror plane Finally, bond distances in Table 4 can be addressed. normal to the c axis at x : 0 is included, five beads of The polyhedral distortions resulting from shared edges cations are created per rod for one cell translation. Each are in perfect agreementwith predicted results, the sole unique rod is given a symbol: M(a) at x, 0, 0; M(b) at x, T(2F8[;FM(I) tetrahedral-octahedralshared edge being l/6,l/4; and T at x, -l/3,l/4.Itis notedthat the beads the shortest for all the polyhedra. are separatedby intervals of approximately x/ 5 along the direction ofprojection. The separation,A, ofbeads in each rod in the projection plane) are within A : 0.0 for KonNnnuprNB: pRTNCIpLES 0-z SrnucruRAl M(a), 0.1 for M(b), and 0.3 A for T. SinceMoore and Bennett (1968) first reported the crys- The orthogonalized cell and its atom positions for tal structure of kornerupine, Moore and Araki (1979) re- Nirln can be directly related. That is, P6r/mmc, a(h) : fined data from a B-rich synthetic crystal, and Finger and 4.179, c(h) : 5.131 A llaves and Wallbaum, 1942), Hazen (1980) refined a Fe-rich member, but little insight 2In(r/32/3r/4);2 N(l) (000); 2 N(2) (r/32/33/4) - has been gained on the crystal-chemicalprinciples of this Cmcm,ao: 4.18,bo: a(h)\/3 : 7.24,co : 5.13A; 4 complex structure type. This is especially embarrassing In(Ol/3 r/4); 4 Ni(l) (00 0); 4 N(2) (1/2 t/61l4). Thus, since the structure type has been turning up in many ter- we can compare the averagecation or metal positions in ranes of granulite facies.All attempts to derive its struc- the y-z plane:(0.343, l/4), (0.333,1/4) for T, In; (0, 0), ture from hexagonaland/or cubic dense-packedoxide an- (0, 0) for M(a), Ni(l); and,(0.142, l/4), (0.167, l/4) for ions have failed. Both the first and secondstructure studies M(b), N(2). The displacementsin the y-z plane are A : stressedprinciples of anion close-packingin sectionsof 0. 16, 0.00, and 0.40 A, respectively,when computedon the crystal structure, from a projection along [001] in the the kornerupine unit cell. first study and along [010] in the second.Yet the packing Kornerupine's cations track very nicely on Nirln po- efrciency of 16.8 A, per 02 , when compared with sitions along [00]. Therefore, the comparison among 4yQ. f : 15.52A: for the "classic" Paulins 02- radius r Nirln, olivine, and kornerupine is a very anisotropic re- : 1.40 A, suggesteda dense-packedstructuie. Such pack- lation, indeed, as shown in Table 8. Can these relative ing, however, does not necessarilyimply cubic or hex- anisotropies be explained?From this prelude, a fugue is agonal close-packing:many very dense-packedstructure now required. types (glaserite,K.NaSrOs; or garnet,MgrAlrSi.O,r, for But discussionon correlationsamong cations or metals example)do not belongto thesesimple packingprinciples. in kornerupine, olivine, and Nirln hardly explains the For such structures, we have had considerable success extreme anisotropy among equivalent cell translations, through seekingout analogiesbetween cations in the oxy- and the role of the electronegativeoxides must also be salts and atomic positions in intermetallics. This ap- discussed.It would be most desirable to seek an inter- proachlargely stems from the penetratingstudy ofO'Keeffe metallic cluster or molecule with well-defined geometry and Hyde (1985),where they discussedisopunctal rela- and to examine the locations of and distortions created tionships comparing cations in garnet with Cr3Si,cations by oxygen insertion. From this model, which involves a in olivine with Nirln, the apatitestructure type with MnrSi, finite cluster, an extension to infinitely extending arrays and many other analogies.Incidentally, glaserite'scations is possibleso long as all atoms in the asymmetric unit can can be directly related by comparing the cations of be countedand so long as the electroncount is preserved. (K.NaSr)O, to Nioln, and those of the lAngbanitemon- Such a model exists and illustrates the insertion of oxy- strositywith americium, .ch.! gen into an intermetallic, in this case one of the poly- A generalformula canbe written for kornerupine,where morphs of phosphorus,Po or white phosphorus.Figure I M are cations in octahedral and higher coordination by showsthe progression[Po], [PoO6], and [PoO,o],the same oxide anions, T are tetrahedrally coordinated cations,and sequenceas featured in Wells (1975). Errors in distances @corresponds to generalizedanion. Including the large, reported for thesethree structure determinations eachare partly occupied X site, kornerupine has MooTrofr,for the about +0.03 A. In the [Po] tetrahedron, the P-P edge unit-cell contents. Ifthe cations only are projected along (bond pair) is 2.21 A. This value was esrablishedby elec- the three principal crystallographicaxes, a quite diferent tron diffractionof a jet of Povapor (Maxwellet al., 1935). picture from the earlier studies is immediately recogniz- From the model, each vertex is 3-connected,and each P able. All nine cations in the asymmetric unit define three contributes three electrons to bond-pair formation and MOORE ET AL.: CRYSTAL CHEMISTRY OF KORNERUPINE 649

two electronsto the terminal electron lone pair, ry'.Since P has five valence electrons (3sr3p3),the package[Pory'o] has six bond pairs and four lone pairs, thus accounting for all 5 x 4 : 20 valence electronsfor [P"]. Now in [PoOu],six oxygensare inserted near the mid- points of the P-P edges.Since the more electronegative

oxygen has six valenceelectrons (2sr2po), two more elec- Pq Pt 06 P40ro trons are required for kwis octet closure. In fact, Lewis : octets constitute a hallmark of twentieth century science, Fig. l. Spokediagrams for [Po],[PoOu], and [PoO,o]. O P : : both in crystals and in other condensed states (Lewis. atoms,X the oxygencentroids, and {, the lone pairs of electrons.Key distancesare given. I 9 I 6). Octet closure is achievedby the P-P bond pairs at the midpoints of the six edgesthat incorporate the six oxygens.The P-O distancesare 1.65 A, and the P-P dis- 'by tance is expandedto 2.95 A. fnis experimentalso em- alloy (notionally) inserting anions into the latter' . . . ," ployed electron diffraction of jets, reported by Hampson exceptionsabound. This can be demonstratedin Table 9 and Stosick (1938). The terminal positions from the P where examplesof well-defined oxysalt-metal pairs have atoms still remain electron lone pairs, and the molecule beenselected from Villars and Calvert(1985) and Donnay can be expressedas [PoOury'o].The midpoint of the P-P and Donnay ( I 963). The sevenpairs include binary oxides distancewas expressedin atomic coordinatesfor the pur- in the systemMgO-AlrOr-SiOr, which encompassesmost ported locus ofthe bond pair. The distanced betweenthis ofkornerupine. Note that five oxysalt-metalpairs in Table midpoint and the centroid for the adjacent oxygen com- 9 exhibit the same cation or metal eutaxy (: "well-ar- puted to be 0.74 A. Thesedistances are shown in Figure I . ranged")but two MgO-Mg andAlrOr-Al do not, although Finally, in PoO,o,the four terminal lone pairs complete their structuresare based on principles of close-packing. the octets of four terminal oxygens.Its structure was de- We found the most convenient way to relate the pairs rived from an X-ray diffraction experiment earlier con- involves calculations of cell volume per metal for each ducted by de Decker and MacGillavry ( 194 I ), later refined pair, then taking the cube root of these values to get a by Cruickshank (196a) who- reported averagedistances linear expression as percent change, which was earlier for P-O (bridging) of 1.60 A and for P-O (terminal) of discussed. 1.40 A. These differencescan be easily understood from In Table 9, the valenceelectrons are listed as well, and Pauling's rules, the bridging oxygen being oversaturated the table is arrayed according to increasingelectron pop- (Apo: +0.50 valenceunits) and the terminal oxygenbeing ulations of the orbitals. A trend immediately becomes undersaturated(Apo : -0.75 v.u.) by bonded P atoms. obvious. The top three entries with only ns2valence elec- The P-P distance of 2J9 A is an averageof two inde- trons for the metals decreasein volume for Me - MeO. pendent but very similar distances.The averagedistance Note that the Ca - CaFr, A : -2o/o compared with Ca betweenthe midpoint of P-P and the centroid for adjacent - CaO, A,: - 160/o.Itis believedthat an aliquot of twice : oxygen is d 0.7S A. Thus, the progressionlPo*ol - the number of fluoride ions compared with oxide ions for lPoou'y'.] - [PoO,o]exploits the Lewis octet formation the isopunctal Ca metals accountsfor this difference.The about the most electronegativespecies, oxygen. Note that remaining five pairs increasein volume for Me * MeO. in the progressionin Figure l, the inserted oxygensare at These pairs include additional p- and d-electron popu- approximate midpoints of P-P edgesand displacedsome- lations. This contrast appearseasily explainedby Pauling what outward from these edgesin the tetrahedron. The (1960, p. ll0): "p bondsare strongerthan s bonds" and expansionofP-P is considerable:for PuOu,the P-P di- "it is convenient to call the magnitude of a bond orbital lation is A: t25o/o,and in P4Or0it is A : +210low'ith in its angulardependence the strengthofthe bond orbital, respectto Po.In thesecalculations and those that follow, with value I for an s orbital and 1.732 for a p orbital." the dividend is the differencebetween the oxysalt and the Since kornerupine is constructed principally of AlrO, intermetallic values being compared. The divisor is the and SiO, componentswith somewhatless MgO, it follows oxysalt value, and the quotient is multiplied by 100 and that the kornerupine cell will expqnd with addition of rounded off to the nearest whole number. The result is electronegativeoxide ions relative to its chemical equiv- expressedin linear measure by extracting the cube root alent of the Nirln intermetallic. of volume per metal atom, which was derived from the The [P.] cluster model above was applied directly to crystallographicunit cell. the complex kornerupine crystal structure. In every re- O'Keeffeand Hyde (1985, especiallyp. 99) discussed spect, the same calculations were performed. This re- linear and volumetric changesin some detail and stressed quired taking all the countablecation-cation positions, to that dilation doesnot necessarilyfollow in the progression determine the midpoints of their connectionsand to cal- M,T, - M"TuQowhere M and T are metals and 4 the culate the distance between each midpoint with respect electronegativeanion, usually O, . They declared, "Al- to its adjacent oxide centroid. The midpoint is suggested though there is often a considerablevolume increaseon by the [P"Oury'o]and [PoO,o]molecules where d - 0.76 A forming an inorganic structure from the corresponding occurs on the average between adjacent oxide centroid 650 MOORE ET AL.: CRYSTAL CHEMISTRY OF KORNERUPINE

Tlar-e9. Kornerupinecomponents and someoxysalt-metal re- To make sure all cations and anions were represented, lations graphs (of which there are many choices)from Figure 2 were constructed.The collection used here for kornerup- ine includes two chain segments:-M(5)-O(2FM(5FO(6F MgO-Mg 1. Fn€mvs.ftJmmc 3sf -7o/o r(2)-o(5)-M(4)- and -M(l)-o(10)-M(l)-o(7)-r(3)- Mgo 'CaO-'Ca o(8FM(2)-o(3Fr(I )-o(eFr( 1)-o(4FM(3Fo( I FM(3F .CaO Fnfmvs. FnEm 4s -160/" . Sinceall anions are listed, the formation of Lewis octets *CaF,-*Ca can be achieved. Clearly, many other combinations can e Fnlsmvs.FnBm 4e -2% *CaF, be written, as each anion is either three-coordinated or V2Al2O3-Al but this doesn't matter since R3cvs.FnBm 3se3p !8o/o four-coordinated by cations, Y2AI2Oo -sio,--si we are only required to seek out bond pairs associated -sio, FdSmvs.Fd3m 3*3e I24o/" with anions for potential Lewis octet closure. Segments .CoO--Co of thesechains occur in Table 10,compared with the Nirln -116o/o b .CoO FnEmvs. Fntsm 3clt4* intermetallic, and the distance d between cation-cation -Nio--Ni edge midpoint and oxide centroid is entered. The range 7. FnBmvs. FnBm 3do4* -116o/o 'Nio is d : O.2l A for O(5) to 0.96 A for 0(6) with a mean of Note; Starred metals are in isopunctalrelationship. Col. A: oxysalt and 0.68 A for all oxygens.For olivine, the rangeis 0.88 A metal pairs used in volumetriccalculations. Col. B: space groups of oxysalt for O(3) to 0.99 A for O(l) with a mean of 0.93 A. It is vs. metal.Col. C: valenceelectrons for metal.Col. D: linearchanoe or obvious that kornerupine more closely mimics the Nirln cube root of volume per metal (A3, based on unit cell) for oxysalt-iletal pairs.Nos. 1,4, and 5 from Villarsand Calvert(1985); 2, 3, 6, and 7 are arrangementthan does olivine, as shown by a model for from Donnayand Donnay(1963). the olivine arrangement by O'Keeffe and Hyde (1985). An equally important calculation is the diference, A (A), between ideal and real atomic coordinates for korne- rupine, olivine, and Nirln. In Table 2 it is seenthat the and the P-P centroid. Calculationsthat ensuealways take mean is 0.26 L for kornerupine(range 0.00 to 0.50 A) the midpoint of two adjacent cations as the locus of the and 0.46 A for olivine (range0.00 to 0.82 A). Yet again, bond pair. kornerupine, even with its relatively large number of at- But kornerupine is an extended three-dimensional oms in the asymmetric unit, shows the best correspon- structure. How are the cations counted?Unconventional dencewith the intermetallic. The spacegroups of the latter diagrams in Figure 2 are presentedfor both kornerupine pair are the same,Cmcm. Note that a nearly regular sub- and olivine where emphasis is placed on cation coordi- cell occurs for kornerupine with q(N x a/5(K) that was nation about anions. Note that O(l), O(2), O(4), 0(6), automatically included in calculating the cation (metal) O(8), O(9), and O(10) are each four-coordinated and de- positions between thesetwo structures. fine rather distorted tetrahedra and O(3), O(5), and O(7) The X cation in kornerupine and the M(l) cation in are eachthree-coordinated by cationsthat definedistorted olivine are the only atoms not representedfor thesestruc- triangles.The olivine map also revealsfour-coordination tures in Table 10. Attempts were made to find reasonable ofcations about anions, in eachcase three octahedral(M graphical connections,but these were either too long, or : Mg) and one tetrahedral (T : Si) cation. In both cases, the ensuing d values were too large. It appearedthat X the maps appearrather cumbrous, but much information and M(l) played somewhatdifferent rolesin the structures is given in them: they are more extended equivalents of than in correspondingNirln. It is interesting to note that the [P4] sequence.Since Pbnm (olivine) c Cmcm (kor- these sites play anomalous roles in the structures: X is nerupine), both structureswere projected along the z di- only partially occupied in kornerupine, and M(l) in oli- rection, the shortesttranslation in kornerupine. Only an- vine, which experiencessimilar disorder, is the basis of ions within 0 = z < 7zare shown in order to minimize omission derivative structures such as sarcopside,heter- redundancy and congestion.The olivine and Nirln cells osite, and laihunite. were scaledto conform with kornerupine for purposesof Kornerupine, olivine, and Nirln: Similarities and cell comparison. Heights in z are given as fractional coordi- anisotropies.Emphasis in Tables2,9 , and I 0 and in Figure nates.Anions are shown as filled squares,and cations as 2 has been placed on the similarities of cation positions solid disks; the scaled N(l), N(2), and In centroids for among thesethree structure types. For example,in Table the Nirln intermetallic are shown as crosses.Dashed lines 2, it is seenthat X, M(IFM(5), and T(1fT(3) in korne- in Figure 2 have the same connotation as those for the rupine and M(l), M(2), and T in olivine (forsterite) cor- [Po] seriesin Figure l, that is, a dash between the cation respondto N(l), N(2), and In in Nirln. The relationX,M pair, and a dash from the adjacent anion to this pair. In - Ni and T - In is hardly an accident! If such a corre- addition to many of the d values (the distance between spondenceoccurs, then why do the cell shapesmarkedly cation-cation midpoint and adjacentanion) in the figures, differ? As before, for proper comparison, the a axis of cation deviations between oxysalt and intermetallic are kornerupine must be partitioned into its subcell a' : a/5. given in angstroms, as are the d values between oxide Figure 2 presentsthe generalrelationships among the cat- centroids and cation-cation midpoints listed in Table 10. ions and their correspondencein these structures. For MOORE ET AL.: CRYSTAL CHEMISTRY OF KORNERUPINE 651

M(5)0,liz Y=Vz 4 'l'n 11/q IFT I

?11/+ Zlslq 0(3)?r M lz '=+r:::l r)0.64 b- m ]-0,1/z l0,t/q iij:ii'/ b-- e M(5)0. x= -Hirli x=3 + tfa f lnlq D_ Vq Ml4l1c '+Hi(z),rn 1 o}l(Zlle Nil2lt/c d;lli3:11: b- Tll,t# b- M(3)0,h. oI Vq , 'ln14 qrl,?,lif ^Y:: - + t=o 'rn'/o s a' Ni(r)o.ti . T(Zly4 Mfi)y4 a (t b- ,Ni )0,r/z , .MQll+ + Ni(2)% rttt(s)0,% -Nilzlyo +iltlli:ii b- t'vl *=+'!L *J,?;,%',u,'n*"r,,,* J x=5!!llr;l;l;t *'ln%

Fig. 2. Spoke diagrams of kornerupine on left and olivine have same connotation as in Fig. l. Displacementsin A from scaledto kornerupine cell on right. Cell origins and outlines of midpoints of cation pair to nearestanion are given under that projection along [00 1] are designatedby arrows and right angles. anion. The lower portions of both maps show cation and Nirln Most atoms are 0 < z < t/2.Heights in fractional coordinates, centroidsonly. This is a map of cationsabout anions.Note three- cationsas circles, anions as squares,Nirln as crosses,translations coordination for O(3), O(5), and O(7), and four-coordination for in x on left. Some symmetry elementsare shown. Dashed lines o(l), o(2), o(4), 0(6), o(8), o(9), and o(10).

convenience,set r,, i: I to 3, as the unit-cell translations { 100}, {0 I 0}, {00 I }, or { I l0}, etc.,would leadto marked a (or a/5 in kornerupine), b, and c. The orthohexagonal anisotropy in axial ratios comparedwith the intermetallic; cell for Nirln has been already defined. Its contents are the anisotropy would be particularly pronounced normal 4Nirln, and the cell translations and axial ratios are listed to that layer receiving the extra insertions. Any "isotro- in Table I l. pic" insertion for an orthorhombic intermetallic would It is immediately recognized that the ratios indicate lead to a compound with closely similar axial ratios. extensive cell anisotropy among these compounds. We It is believed that the adjusted axial ratios in Table I I believe that this can be explainedby the rather anisotropic best explain the anisotropy through oxygen insertion and insertion of the oxygenatoms. Recallingthe sequence[Po] bond-pair formation. Through trial and error, the best - [PoOu]- [PoO,o]with a linear increaseof some 25010, axial direction was selected,and the standard ratios were note that in Figure I the oxygen insertions can also be scaled according to the axial ratio for Nirln. These are consideredas insertions oflayers or planesthat lie between listed in parentheses.Here, c for kornerupine and a for but do not anywhereinclude cations. In cubic structures, olivine were set according to Nirln. For kornerupine, we we saw that dilation was uniform in three dimensions. seea decreasein aby about 42o/oand an increasein D by Analogous to the tetrahedral [Po] sequence,such planes about 45010.In olivine, a and c are similar to the Nirln would be parallel to { I I 1} for example. In orthorhombic ratios, but b is increasedby about 24o/o.In kornerupine, crystals, orientation ofadded oxygen layers according to anions O(lp(8) all contribute to laminae betweenX and 652 MOORE ET AL.: CRYSTAL CHEMISTRY OF KORNERUPINE

TABLE10. Kornerupineand olivine: Displacements between cat- TABLE11. Celltranslations and axial ratios ion pairs and adjacentanions t, t, t3 Axial ratio Adjusted axial ratio Displace- Ni,ln(N) 4.18 7.24 5.13 O.577:1:0.7O8 Adjacent cation Distance mentf Korn (K) 3.21 13.75 6.72 0.233:1:0.489 (0.337:1.448:0.708) pairt Nrln atoms (A) (A) Forst (F) 4.76 10.22 5.99 0.466:1:0.586 (0.577:1.238:0.726) Kornerupine o(1) -M(3FM(3)' N(1 2.57 0.73 .M(5FM(5)', )-N(1) o(2) N(1)-N(1 ) 2.57 0.73 o(3) xr(1)-M(2) In-Ni(2) 2.41 0.78 o(4) vT(1)-M(3) In-Ni(1) 2.73 0.64 form laminae between the cations is O(3) in a general xr(2FM(4) o(5) In-Ni(2) 2.4't 0.21 position. The M(2) and Si cations on either side of the o(6) vr(2)-M(5) In-Ni(1) 2.73 0.96 o(7) xT(3)-M(1) In-Ni(2) O(3) laminae parallel to {010} are displaced themselves, -r(3)-M(2) 2.41 0.63 o(8) In-Ni(2)' 2.57 0.94 accountingfor the greaterdifference between atoms in the or(1)-T(1) o(e) In-ln 4.18 0.47 intermetallic and cations in olivine in Table 2. While in o(10) "M(1)-M(1) N(2)-N(2) 4.18 0.71 Mean 0.68 Ni,In, the displacementin the a-b plane is 0.00 A, the - Olivine correspondingM(2FSi in olivine is displaced 1.3 A. o(1) xT-M(2) In-Ni(2) 2.41 0.99 Table l2 summarizesthe chemical crystallographyand o(2) xT_M(2) ln-Ni(2) 2.41 0.91 bond nomenclature for Nirln and a-Fe. Just as it is pro- o(3) .r-M(2) ln-Ni(2)' 2.57 0.88 Mean noe posed that Nirln forms the atomic basis of cation distri- ' butions in kornerupine and olivine, so Nirln is an ordered f Orientations of pairs: tr parallel a, parallel c, X in a-b plane V in a-b-c Dlane. derivative of a-Fe. The element has z : 2, Im3m, a : f The displacement(d) betweencation-pair centroid and adjacentanion. 2.866 A (Donnay and Donnay, 1963).Selecting the hex- agonal cell for a-Fe, a direct comparison can be made as outlined in Table 12. Partitioning Fe into three equiva- M(l)-M(5) cationsto form edge-sharingchains parallel lencesyields the ordering schemecompared with Nirln, given to [00]. This also in Table 12.The maximum differencebetween equivalencesis A : 0.43 A basedon the c axis of Nirln. o With differencesin electronegativitiesand bonding, we \,/\ / believe Nirln can be consideredan orderedpseudoderiva- MM tive structure ofa-Fe. The prefix pseudois used because / \/ \ R32/c and P6r/mmc sharesame cell but not sameclass o relationships. Included in Table 12 are the metal-metal distancesfor sequencedeflnes oxygen insertions where no bonds occur Nirln, the number of equivalent bonds, the planes that in Nirln (the a:4. 18 A translation;see below)! This include them (basedon the orthohexagonalao, bo, co)and wholesaleformation of bond pairs results in M-M = 3.2 a code(1-2, 3-3a,44c,5-5b) for the kinds of bonds.The A. tire big increasealongb is also explained by the anion In[Ni,,] and Ni(2)[InrNiu] define distorted pentacapped insertion.Laminae of O(4), 0(6), O(8), O(9), and O(10) trigonal prisms and Ni(l)[InuNir], a bicapped hexagonal parallel to {010} are inserted nearly betweel,atom bond prism. These bonds are found among the cation-cation pairs and are locatednear y = +(h,3@. Additional lam- distancesin kornerupine and olivine. The 5-5b distances inae of O(3), O(5), and O(7) also parallel to {010} are of ao:4.18 A eachare not bonded.They play a central located near / E +(%). Kornerupine is a particularly in- role in kornerupine as discussedearlier. teresting example where both bond-pair formation and Taken together,the kinds of bonds, their number in the anion-layerinsertion have a ready explanation in the axial olivine, and one-fifth the kornerupine cell (the unit for ratios. This is admittedly a qualitative model, and neither comparison)are asgiven in Table 13.The differencesarise all bond pairs nor all anions were accountedfor. As yet, from bond arrangementsof varying distribution, an "ol- a quantitative model has not been perfected.In such an ivine" stoichiometry of MrTOo o in kornerupine, and the event, many exciting new discoveries will be made, es- appearanceof three-coordination of cations about anions pecially "turning intermetallics into oxysalts." The best O(3), O(5), and O(7) in the latter mineral. display of this remarkable structure is either projection It is now possible to addressthe intriguing question: along [001] or deciphering the diagrams in Moore and can Table 9 serveas a vehicle to comparethe linear change Bennett(1968) and Moore and Araki (1979). for oxysalt-metal pairs associatedwith kornerupine and Olivine posessimilar problems. Its cell parametersand with olivine? An interestingtwist is addedto the problem, axial ratios suggestthat the most anisotropic increaseis for here not single components (such as t/zA7rO.and Al) along b with an increase of about 24o/owith respect to but several components are involved. Several assump- Nirln. Unlike kornerupine, all anions form bond pairs tions are made, some of which were assumedbefore: (l) nearly between the bond pairs in Nirln. In olivine there the single components are based on principles of close- are no additional insertions (as occur for kornerupine) packing, either .c., .fr. or combinations of these.For betweennonbonded regions for Nirln. The only anion to perfect spheres,there is no changein packing efficiency, MOORE ET AL.: CRYSTAL CHEMISTRY OF KORNERUPINE 653

TABLE12. The Nirln and d-Fe intermetallics:Chemical crystallography

Nirln a-Fe ftJmmc ln8m 1*321c) 2 Nirln 2Fe000 a:2.866A a = 4.179 c: 5.131A cla: 1.228 4l: t/2a:4.052 c(h): v€a:4.964 A c(hVa(hl:1.22s ao: 4.179 bo: aVg = 7.238 co: 5.131A ao:4.052 4:7.018 Co:49644 2 ln 1/z 2h Y4 2Fe(a) % % Y6 2 N(1) 0 0 0 2Fe(b) 0 0 0 2 N(2) Vs q 3/q 2 Fe(c) % 2/s % (A) 1 In-Ni(2) 2.41 bo 1 2 In-Ni(2)' 2.41 aoh 2 2 In-Ni(2)" 2.57 e 4In-Ni(l) 2.73 4boh 4 2In-Ni(l)' 2.73 4b 11 pentacappedtrigonal prism 2 N(1)-N(1)', 2.s7 co 3a 1 Ni(2)-ln 2.41 bo 1 2 N(1)-N(2) 2.73 4c 4c 2 Ni(2)-ln' 2.41 aoh 2 4 N(l)-N(2)' 2.73 zodco 4a 2 Ni(2)-ln" 2.57 C e 2 Ni(1)-ln 2.73 Wco 4b 4 N(2)-N(1)', 2.73 aobo% 4a 4 Ni(1Fln 2.73 aboco 4 2 N(2FN(1) 2.73 4.c" 4c 14 bicapped hexagonalprism 11 pentacappedtrigonal prism 2 ln-ln' 4.18 ao 2 N(2)-N(2)', 418 5a 2 N(1)-N(1y 418 5b

Nofe-'ln computed bond distances, axes that includethese bonds and a code (1-5) are included.Nonbonded distances appear at end.

Zu, or volume per atom. (2) The volumetric differences their small contribution was deemed insignificant, and in types of close-packingamong crystals of same com- this 6.680/oremainder was added to AlrOr. The three- position are negligible.(3) A phasecomposition, whether component "analysis" computed to an olivine-related for- real or hypothetical, involving more than one component mula(5.461x 4)MgurrAl,3,osio67eO400o, theprefix scaling can be evaluatedby a principle of additivity, i.e., the sum it to kornerupine cell contents.The X-ray cell volume is over all componentsin its formula. This implies additivity V : 1480.65A'. That for only the metals (5.461 x of the volumes of each of the componentsin the formula qQ.67 7Nde+ 1.3I 0Al + 0.679Si)from Table9 is I I 14.03 unlt. A', or an intermetallic - oxysalt volume increase of The cell formula for olivine is 4MgrSiOo,the X-ray cell +24.8o/o.The averagelinear inqease is volume V:291.86 A'from Birle et al. (1968)for for- A : (11.398- 10.36'7)/11.3981x 100 : *9.00/0, sterite. In the same manner as deriving Table 9, MgrSi is 8Mg + 4Si: 184.81A, + 80.t0 A3 or 264.91Ar.The a value indeed larger than the corresponding value for volume changefrom intermetallic to oxide is forsterite olivine. The kornerupine value is slightly larger than that for the (7zAlrO,-Al) pair, and the less abundant - 264.9r)/291.86]x r00: +9.2o/o. [(291.86 Mg and Si nearly offset each other. The averagelinear increaseis A : [(6.633- 6.422)/6.633]x 100 : +3.2o/o. This value can be compared with column D in Table 9. Trar-e13. Numberof bondsof varioustypes in olivine and kor- neruptne The valenceelectrons for the metalsare 3J2and 3s2p2,and the small net linear increaseis believed to reflectPauling's Olivine Kornerupine* (1960) estimatesof relative bond strengthsof s and p I 0 0 bonds. Kornerupine with a greater aliquot of p bonds 12 OA would be expected to expand even more than olivine, o 8 8.0 3a A 4.8 when compared with its metal components. 4 24 25.6 To appraisethis effect in kornerupine, the formula de- 4a 32 25.6 rived from Scoonin McKie (1965)was simplified from 4b 4 0 4c 8 0 eight components to the three major components.These 5 0 2.4 three major componentsin the Scoonanalysis add to MgO 5a 0 12.8 + Al,O3 + : 5b 0 2.4 SiO, 93.32o/o,the remaining 6.680/obeing Total 96 9't.2 principally FerO,and BrOr. Good oxysalt-metalpairs could - (the not be obtained for these two components. In addition, Consideringonejifth the kornerupinecell unit for comparison). 654 MOORE ET AL.: CRYSTAL CHEMISTRY OF KORNERUPINE

CoNcr-usroxs er than s bond strengths.An additivity relation was in- linear between M&urr- The individual thermal-vibration parameters for the voked to calculate the difference (modified kornerupine) and its "inter- refined kornerupine in this study and two other refined Al,3,0sio6reoooo Here, A : *9.00/0,a value slightly kornerupines in the literature were compared. Compari- metallic" counterpart. son was basedon the dffirence, A(o/o),between kornerup- larger than the (YzAlrOr-Al) pair. For olivine, a similar : ine in this study (from Mautia Hill) and the other korne- calculation gave A 13.2o/o,reflecting the predominance rupines. of s bonds for Mg metal in MgrSi. Thesecalculations suggestthat relations betweencom- For thermal vibrations, Ae/o) : l(B - A)/AI x 100 plex and their correspondingintermetallics may where B : other kornerupines and A : the kornerupine oxysalts place limitations on which oxysalt structures can in this study, from Mautia Hill. The individual U,,(i : 1 severe and thus may further our understanding of their to 3) values were compared. This gave an estimate of exist structure genealogyby exploiting correspondingisopunc- differencesin which the valuesfor other kornerupinesare tal or near-isopunctalintermetallic phases. relatively less or greater than those for the Mautia Hill Sincethe pioneeringpaper of O'Keeffeand Hyde (1985), kornerupine of this study. The mean IA I of t/, gave25o/o lot work remains to be done. Their study involved for 8 unique cations and l7o/ofor l0 unique anions. The a of mostly relatively simple systems,and questionsofdilation mean lA I of B"ogave 20o/ofor the 8 cations and 3olofor insertion remain in abundance.Although the l0 anions. In addition to reflecting the substitutional due to oxygen tablesofradii for oxidesand fluorides are well established, disorder of different kinds in kornerupine cation sites, analogoustables for nitrides, phosphides,arsenides, stib- theseaverages suggest that thermal parametershave some nides, carbides,silicides, stannides,etc., do not exist. An- physical reality, at least for adequatelyrefined structures. isotropic distortion as a consequenceof insertion of some Note that comparison betweenanion sitesshows remark- electronegativeatoms has barely been examined at all. In able concord. fact, no quantitative rules have appeared regarding cell A novel interpretation ofthe complex kornerupine crys- expansionwhen progressingfrom intermetallic to oxysalt. tal structure suggeststhat its cations are approximately Finally, it is not clear how great distortions can be for isopunctal to the metals for intermetallic Nirln. Six larger intermetallics, and how they should be described.A great cations [X, M(IFM(5)] match up with three Ni(l) and many new intermetallic-oxysaltrelationships have evolved threeNi(2), and threetetrahedral cations [T(1FT(3)] match in the laboratory of the senior author, most involving up with three of the more electronegativeIn. The mean oxysalt structures of considerable complexity such as differenceusing the kornerupine cell is 0.26 A. A similar and fluoborite; CoSn-crandallite, mi- calculation for olivine with two octahedral and one tet- B-CurAs-painite tridatite; Nirln-glaserite, fillowite, a-Car(POo)r, stan- rahedral cation gives a mean differenceusing the olivine fieldite, graftonite, dickinsonite, triploidite, triplite; cell of 0.46 A. It was deemed sensibleto inquire about F e, - dumortierite; CorSi- warwickite. But it is felt the placement of the electronegativeoxide anions in the rZr rP, that before a grcat rush is made in search of structural collection of cations. In the sequencelPor!ol (ry' : electron gold, criteria for relatedness,adjacency, contiguity, and lone pair) - [PoOury'o]- [PoO,o],midpoints of P-P tet- similarity must be evolved first. rahedral edgeswere taken and compared with the oxide -0.8 centroids. The differencebetween the two is A and AcrNowr,nocMENTS suggeststhat oxygen fills its octet by exploiting P-P bond persistentprodding yet pairs. The same was done for kornerupine and olivine, Edward S. Grew, through his and insistencethat more komerupine chemical crystallographywas necessary,perhaps more respectively,both compared with Nirln. Differencesbe- than anyone is responsiblefor the completion ofthis project. The senior tween the ten oxide centroids and the cations correspond- author and ProfessorGrew share a common love for "-ine" minerals: ing to three Ni-Ni, one In-In, and six Ni-In midpoints kornerupine, "prismatine" and sapphirine, even ashcroftine and steen- led to a mean of 0.68 A for kornerupine. In olivine, a strupine! Foundation EAR gave P.B.M. acknowledgesthe National Science Grant 87- similar calculation involving three Ni-In midpoints 07382, and,P.K.S. thanks the Tennesseecomputation facilities at the a mean of 0.93 A. These calculations are summarized in TennesseeEarthquake Information Centerfor useoftheir VAX computer. Table 10. Finally, it was asked how the structures distort when RnrrnrNcns crrED oxides are inserted into corresponding intermetallics. Again Baur, W.H. (1970)Bond length variation and distorted coordination poly- the dffirence, Ae/o) : I(A - B)/Al x 100, where ,4 : hedra in inorganic crystals. Transactions of the American Crystallo- component oxide and B : intermetallic, was calculated graphicAssociation, 6, 129-155. Birle, J.D., Gibbs, G.V., Moore, P.8., and Smith, J.V. (1968) Crystal for major componentsin kornerupine and olivine. These structuresof natural olivines. American Mineralogist, 53,807-824. pairs were arrangedaccording to valenceelectrons on the Cruickshank, D.W.J. (1964) Refinementsof structurescontaining bonds metal. It was observedthat for M - MO, the linear change betweenSi, P, S, or Cl and O or N. V..P4Oro.Acta Crystallographica, is negative-i.e., metal oxides have smaller volumes than 17,677-679 (1941) Die Krystallstruktur isopunctal metals for de Decker, H.C.J., and MacGillavry, C.H. those metals with s bonds only-but des fliichtigen metastabilenPhosphorpentoxyds. Recueil des Travaux positive if s and p bonds are involved. This substantiates Chimiquesdes Pays-Bas, 60, 153-175. Pauling's(1960) statement thatp bond strengthsare great- Donnay, J.D.H., and Donnay, G., Eds. (1963) Crystal data (2nd edition). MOORE ET AL.: CRYSTAL CHEMISTRY OF KORNERUPINE 655

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