kornerupine: chemical crystallography, comparative crystallography… · 2007-08-29 · american...

American Mineralogist, Volume 74, pages 642455, 1989

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

P.lur. BnrnN MoonnDepartment of Geophysical Sciences, The University of Chicago, Chicago, Illinois 60637, U.S.A.

Pnlorp K. SnN Gup'rlDepartment of Geology, Memphis State University, Memphis, Tennessee 38152, U.S.A.

Er-rrnn O. Scrrr-nvrppnDepartment of Chemistry, University of Missouri, Columbia, Missouri 6521 I, U.S.A.

Ansrru.cr

Kornerupine from Mautia Hill, Tanzania, orthorhombic holosymmetic, a: 16.041(3),b : 13.746(2), c : 6.7 l5(D A, space group Cmcm, Z : 4, formula from refined structureMg3 ,8Fe3j8Al5 47Si4 r rB0 43Or, ,o(OH)o ,u, has been refined to R : 0.027 for 1807 independentreflections.

One partly occupied site [X] with distorted cubic coordination by oxygen, five octahe-dral sites [M(IFM(5)], three tetrahedral sites [T(1FT(3)], and ten oxygen atoms [O(lFO(10)l occur in the asymmetric unit of structure. Several earlier suggestions were verified:the X site population is partly occupied and refined to 0.374Mg + 0.626E; all B is se-questered at T(3) : 0.572Si + 0.4288, and the distorted M(4) site sequesters reportedFe3*, 0.8104,1 * 0.190Fe3+. In addition, anisotropic thermal-vibration parameters U,, haveaverage diferences of 25o/o between pairs of 18 fully occupied sites in this structure and intwo earlier well-refined structures. O(10) is bonded in part to a H atom that is believed toform a hydrogen bond O-H( I 0) . . O(9) with an O( l0)-O(9) length of 2.7 63 A, a reasonablecoupled relation to X being X?jar,(OH)a.

By analogy with [P4] - [P4O6] - [PoO,o], it is believed that generalized kornerupine,M4oTroO88, which has a cation pseudorepeat of a/5 or M8T4O'76, is a dilated version ofthe intermetallic Nirln, as is also asserted for the olivine structure type. The model basedon .r-.t, s-p, and p-p bond strengths suggested by Pauling and the [Po] - [PoOu] - [PoO,o]structure sequence appear to explain not only the relation to Nirln but also the locationof oxygen sites in that structure type, of which many alternative anion loci are structurallypossible. Thus, kornerupine and sinhalite (olivine), which occur in similar parageneses,are different ways of stufrng interstitial oxygen between cations of similar arrangement.

INrnooucrroN attendant parameters to be varied is R, the "R factor,""reliability index," "discrepancy index," "residual," etc.

Contemporary crystal-structure analysis is rarely an end In contemporary refinements, R usually ranges from 0.04in itself. Beyond solution and characteization of novel to 0.06, and exceptional cases will provide R :0.015-

structure types, comparative relations are often sought 0.04. R : 0.00 is clearly impossible, as a perfect X-raywithin 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 areportant parameters include the linear atomic-absorption many experiments that fall in this region, and when theycoefficient, p, the anisotropic thermal-vibration ellipsoids are reported, a good explanation for this high value isfor the independent atomic sites, the site population for expected from the investigator(s). Typical examples areeach of these independent sites, mosaicity, secondary ex- found in crystals with large p (say >300 cm ') and thosetinction, and the refined atomic coordinates themselves. having cations with associated lone electron pairs andEven if all of these conditions are known to perfection, a consequent difficulty of crystal measurement in prepara-perfect refinement still cannot exist because of uncertain- tion for absorption correction. The other examples areties inherent in the selected scattering factors and the found in crystals that are composed not of one singlet butchoice 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 severe lineage or twin-conventional test of the quality of the data set and all the ning, but these can 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 arecalled "averaged structures."

Kornerupine poses many such hurdles. With 19 inde-pendent atoms in the asymmetric unit, 9 of these arecations; most of the cation sites in turn involve solidsolution of two or more ionic species, and one site is onlypartially occupied. At least six chemical components oc-cur for natural kornerupine. In its favor, however, ishardness (7 on Mohs scale) and low linear absorptioncoefficient, p x 14.3 cm-' (Mo.Ka). Experience suggeststhat substances of superior hardness usually afford su-perior diffracta and superior subsequent refinement es-pecially of the anisotropic thermal-vibration parameters,all probably a result of rather uniform distribution ofchemical bonds with relatively high bond strength. Wewould immediately anticipate relatively low average root-mean-square thermal-vibration amplitudes in such cases.

Three previous kornerupine structure studies were re-ported. The first, by Moore and Bennett (1968), revealedthe broad features of the structure and resulted in R :0. 11 for 1047 independent data. An end-member com-position was proposed: MgrAluOo(OH)[SirO?] (Al,Si)r-Sio,ol. Four formula units made up the structure cell witha: 16.100, b: 13.767, c: 6.735 A, space group Cmcm.This material was from Mautia Hill, Tanzartia, the localitythat formed the basis of McKie's (1965) detailed chemicaland cell results on the species. The excellent crystals fromthat locality were precisely those used toward the resultsin our present investigation. It wasn't that the earlier workof Moore and Bennett was wrong (the R index was aperfectly adequate "state of the art" result over 20 yearsago), but ilwas wanting in certain respects especially forthose investigators interested in B metasomatism in min-erals of granulite facies. In this case, no recovery of onelarge, partly occupied site and the disregard of B parti-tioning in the crystal structure were shortcomings. Thesecond study, by Moore and Araki (1979), defined thepartly occupied site and the preferential sequestering ofB at one tetrahedral site. The crystal, a synthetic B-richkornerupine, gave R : 0.052 for l44l independent re-flections, with formula-unit composition Mg,,rAlr rdi, nr-Bo jTO2oer(OH)ros. a: 16.016, b : 13.758, c : 6.720 A,space group Cmcm. A third investigation, by Finger andHazet (1980), yielded R : 0.058. These results were ofsufficiently precise quality (M-O, T-O = +0.003 A) ttratwe considered it possible to probe the general kornerupinestructure type further through comparison of site parti-tioning, anisotropic thermal-vibration parameters, andatomic coordinates with a superior refinement of the Mau-tia Hill kornerupine.

The results are most gratifying. It is shown that com-parison ofthe thermal-vibration parameters between syn-thetic and natural crystals presents adequate concord andthat minor components are well partitioned with 83+ -T(3) and Fe3+ - M(4), confirming the provisional con-clusions announced in the Moore-Araki study. Finally, R: 0.027 for 1807 independent reflections, a good valuefor such a complex structure.

TABLE 1. Experimental details for Mautia Hill kornerupine

(A) Crystal cell dataa (A)b (A)c (A)v(4")Space groupzFormula (a) McKie 1965

(b) from structure

p""," (g cm+) (a)(b)

Specific Aravity (McKie, 1965)p (cmi) (b)

Crystal size (pm)DiffractometerMonochromatorRadiationScan type20 rcngeScan width

Variable horizontal width (tv)Maximum scan time (s)Orientation monitors

Intensity monitors

Independent reflections

1 6.041(3)13.746(2)6.715(2)

1 480.6(1 )Cmcm

4Nao 01 Mg3 6sTio 02Fqj7Al6 s6Si3 71 Bo 41-

or 75(oH)or3Mgs esFeS:BAl5 1?Si4,1 Bo €O21 24-

(OH)o^3.3373.2883.297

14.3

(B) Intensily measurements1 4 0 x 1 6 0 x 3 0 0Enraf-Nonius cAD-4GraohiteMoKa0-20u,c-/ o-A: 0.70. B : 0.35. where A0 :

(A + Btan d)w h e r e 4 : 4 . 0 , w : A + t a n d90three orientation standards checked

every 200 reflections; 25 reflec-tions used for cell dimensions

every 7200 s of X-ray exposure (de-cay <1Y")

1807. above 2o. used in refinement

H

(C) Refinement of the structureo.0270.049

KonNnnupIltE: ExpERIMENTAL DETATLS

Pale pink crystals of kornerupine from Mautia Hill,supplied by D. McKie over 20 years ago toward the orig-inal structure study, provided the same batch from whichour clear crystal was selected. The data reported here areconsidered superior in every respect to the initial structurestudy of Moore and Bennett (1968). An outline of theexperimental procedure is given in Table l. Twenty-fivehigh-angle reflections defined the orientation matrix thatprovided the crystal cell data. The cell edges are each about0.30/o smaller than those reported by McKie, who usedback-reflection photographs, Si internal standard, andCuKa radiation. The data from our prismatic crystal werecoffected for absorption anisotropy by ry' scan, a minimalcorrection owing to the low linear atomic-absorption coef-ficient of p : 14.3 cm-r for MoKa radiation.

The 1807 independent F. values were put toward struc-ture refinement, beginning with the proposed atom co-ordinates of Moore and Araki (1979) for a synthetic crys-tal. Neutral-atom scattering factors and real and imaginarydispersion coffections were taken from Ibers and Ham-ilton (1974). Refinement minimized 2 w(lF"l - 14lXwhere w-t : unit weight. The conventional R index men-tioned throughout this paper is R : >llF"l - lF"l l/> l.F. | . Refinement employed the full-matrix procedure ofleast-squares with the program sHELx76. Throughout thisstudy, there was no need to challenge centrosymmetric

644

TABLE 2. Kornerupine: Atomic coordinate parameters

MOORE ET AL.: CRYSTAL CHEMISTRY OF KORNERUPINE

Notei Cations of kornerupine and olivine compared with Nirln. A : scat-tering factor, M : equipoint rank. Standard errors in parentheses refer tothe last digit.

. (a) Site population refined to 0.374(4)Mg + 0.626!. (b) Site populationrefined to 0.810(4)Al + 0.190Fe. (c) Site population refined to 0.766(5)Si+ 0.234A1. (d) Site population refined to 0.572(1)Si + 0.4288.

Cmcm. Finally, secondary extinction correction (Z,achar-iasen, 1968) was applied for this hard crystal, which yield-ed a small correction, the maximum being2.60/o of l.F. lfor the (0 2 2) reflection.

At one point, we concluded that the structure had beenfully refined at R : 0.034 and proceeded to draft up thiscommunication. However, it became very clear that oneatom was misbehaving, namely M(4) with B"o:0.12 42.This unreasonably low value was at least three timessmaller than any other value in the asymmetric unit. Sincewe applied the neutral scattering factors for atoms as listedin Table 2 and used Al for M(4), we were forced to con-clude that a heavier atom was preferentially sequesteredat this site, and we placed all Fe3* reported by Scoon inMcKie (1965) here.

Atomic coordinates for all 19 asymmetric atoms in kor-nerupine are given in Table 2, and the cations are com-

pared with the perfect model for Nirln. A similar com-parison is appended for olivine cations, and this becomesa "working table" later on. The values are from Birle etal. (1968) for forsterite. The anisotropic thermal-vibrationparameters and equivalent isotropic thermal vibrationsappear in Table 3. This table is also discussed in somedetail (see below). Bond distances and angles are offeredin Table 4. These values are within M-O, T-O = 0.03 Aand T(3fO(7) - 0.0S A of the earlier Mautia Hill study.Table 51 lists the observed and calculated structure factorsofthe present study.

KonxrnuprNE: CHEMTCAL cRysrALLocRApHy

Since kornerupine's essential details have been coveredin the earlier work, only the salient features will be cur-sorily presented. With three superior refinements, somecomparative crystallography is in order.

Formula. Two formulae can be offered for Mautia Hillkornerupine, the first based on the analysis of Scoon inMcKie (1965), the second computed from the refined crys-tal structure. Individual site populations were estimatedin three ways: fractional site occupancy, as for X, by vary-ing the site-population parameter; use of more than onescattering curve in a complementary fashion, as for M(4),T(2), and T(3); and later calculation based on average M-O, T-O bond distances, assuming a linear relationshipamong lorMg-rarO (2. l0 A), t6lFe3+-r4ro (2.02 A), t6lAl-t41c)(1.91 A), t4rAF4lO (1.77 A), and t4rsir4lo (1.64 A) fromthe tables of effective ionic radii (based on t6ro2- r: 1.40A1 of Shannon and Prewitt(1969). The final assignmentsare X : MgorrEour, M(l) : Mg,oo, M(2) : MgonrAloor,M(3): MgoorAlonr, M(4): MgrrFefr-frAlo56, M(5): Al,.oo,T(l) : Sir00, T(2) : Alo2rSiorr, and T(3) : 86orSior'. Allatoms for Z : 4 were added up, total oxygens fixed at 22,and the charge imbalance was compensated by substitut-ing appropriate OH for O'? . The formulae are

Na" o,Mg, urTio orFefrjrAlu 36Si3 7rB0 4ro2r rr(OH)o r. (a)MBrn, FeljrAlrorSio,,BoorOr,ro(OH)oru, (b)

where (a) is from McKie (1965) and (b) is from this study.Densities were calculated for these two formulae and arelisted in Table l. They are within 1.50/o of each other, andwithin l0lo of the measured value. Site-population refine-ments for Fe3+ and B are in good accord with the chemicalanalysis of Scoon. Our Mg and Si totals are high and ourAl total is low, but site assignments based on average bonddistances are only approximate, as variations occur amongstructure types. As a point of fact, we have observed sim-ilar relations for other stnrctures and conclude that morestructure study on Mg-Al-Si solutions is in order.

This study confirms two conclusions announced in thestudy of Moore and Araki (1979) on synthetic B-rich kor-

I A copy of Table 5 may be ordered as Document AM-89-404from the Business Office, Mineralogical Society ofAmerica,1625I Street, N.W., Suite 4 14, Washington, D.C. 20006, U.S.A. Pleaseremit $5.00 in advance for the microfiche.

Az { l ' )

XN(1 )M( l )N(2)

M(2)N(2)

M(3)N(1 )M(4)N(2)

M(5)N(1 )r (1)t n

r(2')t n

r(3)t nMean

o(1)o(2)o(3)o(4)o(5)o(6)o(7)o(8)o(e)o(10)

M(1 )N(1 )

M(2)N(2)T

t nMean

44

8R

44

88

I8

8I

8I

8n

44

00

00

00

00 0 .12

Mg

Mg

AI

AI

0.12176(5) 0 14031(5)1 /10 1 /61t2 0 14s63(7)5/10 1/6

0.21536(4) 02110 0

0.31366(3) 0.14182(4)3/1 0 116

0.40756(4) 04t10 0

o.40202(3) 0.35299(4)4t10 1t3

o.17842(4) 0.33375(4)2110 1t3

0 0.34253(8)0 1/3

0.2240(1) 0.0448(1)0.40367(8) 0.0460(1)0.40283(9) 0.2355(1)0.13818(6) 0.09959(7)0.2338(1) 0.2358(1)0.31671(6) 0.09479(7)0.0824(1) 0.2821(1)

1t2 0.0885(1)0 0.1128(2)0 0.0882(2)

Olivine0 00 00.4897 0.2226

1t2 116-0.0731 0.4057

0 1/3

0 0 01t4114 0.501t41t4 0.29

0.25114114 0.41

I88

1 68

1 6II44

M g 44

M g 44

si 44

1 t 4114 0.271 t 4114 0.351t4114 0 .13

0.261 1 41 t 41 1 4

-0.0515(2)1 t4

-0.0471(2)1 t 4

- 0.0541(2)-1 t4

1 t4

00 0.00

3t4314 0.57314314 0.82

0.46


Tler-e 3, Kornerupine: Anisotropic thermal-vibration parameters ( x 1 03)

645

B* (A1U""u,aUr"U""ur.uu

XM(1 )M(2)M(3)M(4)M(5)r(1)r(21r(3)

64.1(31 )11 .9 (3 )3 9(4)7.0(3)7 6(3)5.e(3)4.2(3)

16.0(4)3.6(4)

8.3(5)7.2(5)8.e(5)

10.6(4)21.9(8)7.2(4)

14.6(6)5.3(5)4.8(8)8.3(8)

16.2(14)8.6(3)4.5(5)6.1(2)7.7(2)5.6(2)5.2(215.6(2)6.7(4\

6.e(5)6.2(6)6.1(5)s.7(4)

13.5(7)8.4(4)

15.8(7)5.8(5)

12.8(s)13 .1 (6 )

13.8(1 6)6.6(3)

11.0(4)2.5(2)e.4(2)3.4(3)4.0(213.5(2)3.2(4)

3.3(5)3.s(5)

11 .1(6)4.2(41

10.3(7)7.2(4)8.5(6)s.6(5)

22.6(11)17.7(11)

02.2(2100

-0.3(1)01 .0(1)

- 1 .6(2)0

0.3(4)-0.8(3)

1.7(4)4.1(3)

-0.1(6)0.7(3)

-8.6(6)000

000000000

000

- 1 .s(3)0

-0.4(3)0000

- 0.2(13)00

-o.7(2)0

-0.6(2)000

0000.5(3)0

-0.0(3)00.6(1)00

2.48(10)0.71(2)0.51(2)0 .41(1)0.65(1 )0.39(1 )0 35(1)0.66(1 )0.36(2)

0.49(3)0.44(3)0.69(2)0.64(2)1.20(3)0.60(2)1.02(3)0.54(2)1.06(4)1.03(4)

o(1)o(2)o(3)o(4)o(s)o(6)o(7)o(8)o(s)o(10)

Note: The U, are coefficients in the expression exp[-(qrh, + Unk2 + Usl2 + 2uphk + 2UBhl + 24skl)]. The equivalent isotropic thermal parameterisA*:(8/3)r 'z(4 1+ U22+ Us).

nerupine, that 83* is sequestered in the T(3) site and thatFe3+ goes into the M(4) site. In addition, comparison withFinger and Hazen (1980) shows other substitutions by Feare possible.

Thermal vibration. Isotropic and anisotropic thermal-vibration effects are difficult to appraise, even in contem-porary structural refinements. Rather high correlationsamong variable parameters such as atomic coordinateswith at least one degree of freedom, the linear atomic-absorption coemcient, the anisotropy of the crystal shape,and crystal mosaicity-all are coupled to some degree tothe at most six independent anisotropic thermal-vibrationparameters. Minerals, which often have a large pr com-pared with organic crystals, are palticularly problematic.For this reason, it is common practice to accept aniso-tropic thermal-vibration parameters in mineral structuresas "sponges" that absorb the errors arising earlier amongthe other variable parameters, particularly those arisingfrom crystal size and crystal shape and from the linearatomic-absorption coefficient.

For reasonably well-refined structures of a complexmineral, it is desirable to compare the thermal-vibrationparameters among refined structures. Three such studieshave been selected: this study, the earlier Moore and Araki(1979) investigation, and the results ofFinger and Hazen(1980). Although Finger and Hazen reported crystal datafor a high-Fe kornerupine from Rangeley quadrangle inMaine including average electron-microprobe composi-tion, atomic coordinates and equivalent isotropic thermalparameters -8"o, cation occupancies, and polyhedral meanbond lengths, we were anxious to obtain their originalreflned Uu set. We thank L. W. Finger for providing thesedata. We note a small (+100/o) difference between ourcomputed .B"o from U,, (i : I to 3) of this output and theresult reported in Finger and Hazen. But of more concernis their statement on p. 373, "Moore and Araki also as-sumed that there was no iron in M(4), an assumption not

consistent with the present refinement." The Moore andAraki sample was a synthetic crystal in the system MgO-AlrO3-BrO,-SiOr-HrO, but a variety of other analyses fornatural kornerupine was discussed in that paper. Actually,Moore and Araki (p. 335) declared, "Finally, it is quitelikely that Fe2+ reported in chemical analyses occurs in4-coordination at the X-position with Fe3+ dissolved inthe M(4) position. These two distorted sites seem to ac-count for the pleochroism observed for iron-containingkornerupines." In this study, only the crystals of Fingerand Hazen and our present one from Mautia Hill containsubstantial Fe. It is desirable to outline the partitioningof "heavy" Fe among the sites on the basis of refinedfractional occupancies: M( I ), 0. 3 6Fe; M(2), 0. 30Fe; M(4),0. l2Fe; and X, 0.07Fe according to Finger and Hazen orM(4), 0. l9Fe according to this study.

McKie (1965) reported FerO, 3.980/o and FeO nil forthe Mautia Hill material used in this study. Since thelargest sites are X, M(l), and M(2), Fe2* is believed toenter into these, with Fe3+ partitioning into the muchsmaller and also more distorted M(4) site; that is X, M(1),M(2) t (Mg'z+,Fe2+), and M(4) E (A13+,Fe3+). It wouldappear that the conditions of formation for the Finger andHazen (1980) kornerupine were those of relatively loweroxygen fugacity than those for formation of the MautiaHill material.

Comparison of individual U,'(i: I to 3) and of B.o wasperformed in the following manner. It was asked whetherindividual values from Moore and Araki (1979) and Fin-ger and Hazen (1980) were relatively greater or less thanthose from this study, which was used as the reference.We should suspect some significant departures owing todifferent procedures ofdata collection and reduction andto deduced site partitionings. As X is only a partly oc-cupied site, it was excluded from comparison. The valuesfor M(lfM(5), T(1FT(3), and O(llO(10) were calculat-ed as d ffi r e nc e, A, expressed in percent. Setting W to equal

646 MOORE ET AL.: CRYSTAL CHEMISTRY OF KORNERUPINE

TABLE 4. Kornerupine: Polyhedral interatomic distances (A) and angles (")

1 M(1)-o(7)1M(1Fo( l0 )1 M ( 1 F O ( 1 )2 M(1Fo(4)1 M(1)-O(5)

Mean1o(5Fo(7)'2 o(1)-O(4)"1O(1)-O(5)..1O(7)-O(10)2 o(4)-O(10)2 o(4)-o(5)2 o(4)-o(7)1o(1Fo(10)

Mean

2 M(2Fo(3)2M(2)-O(212 M(2)-o(8)

Mean2 o(2Fo(3)-'4 o(2)-o(8)-.1O(2)-O(2)(4)1 O(3)-O(3)4)4 o(3)-o(8)

Mean

2 M(5FO(2)2 M(5Fo(8)2 M(5)-0(6)

Mean2 0(2)-0(6)-.1o(8)-O(8)o*2 o(2)-o(8)--1 0(6)-0(6)(E-'2 O(2)-O(8)€)2 o(2FO(6)€'2 0(6)-0(8)

Mean

1r(1)-O(3)2 T(1)-O(4)(io)1 T(1)-0(9)00)

Mean2 O(4)(10)-O(9)oo)1 O(3)-O(9)oo)1 O(4I1oLO(4)0')2 O(3FO(4)00)

Mean

2 M(3)-O(1)2 M(3)-O(4)2 M(3)-O(6)

Mean2 o(1)-o(4)-'2 o(1)-0(6)--1 0(6)-0(6)(3)''2 O(1)-O(4)(3)2 O(1)-O(6)F)1 o(4)-o(4)€'2 0(4)-0(6)

Mean

1 M(4)-O(5)1 M(4)-o(3)1 M(4)-O(2)1 M(4)-o(1)2 M(4)-o(6)

Mean2 0(2)-0(6)"-2 o(1)-0(6)--1O(2)-O(3r.1O(1)-O(5)"1o(3)-o(5)1O(1)-o(2)2 0(5)-0(6)2 0(3)-0(6)

Mean

1r(2FO(5)2 r(2FO(6Xo)1 r(2)-o(7)

Mean1 o(s)-o(7)'.2 O(6)t1o-91711 0(6Ir0)-0(611')2 O(5)-O(6)no)

Mean

2 r(3)-o(7)2 T(3)-O(8)t1o)

Mean4 O(7)-O(8)00)1 O(8)ro)-O(8I1i)1 0(7)-0(7)(1)

Mean

2 x-o(1 0)2 x-o(s)4 x-o(4)

Mean

M(l )2.0492.0802.1012.1172.2252.1152.5112.5612.6302.9743.0063.1553.3463.6422.991

M(2)1.9892.0642.1882.0802.6042.6263.0903.1 173.2682.916

M(5)1.7951.9521.9801.9092.5252.5392.6262.6822.7462.7482 9422.700

r (1)1 .6151 . 6 1 81.6401.6232.5932.6032.6662.71'l2.646

71.8174.7974.8292.1 691.4893.1 8

106.86121.2091.05

M(3)1.7941.8782.1071.9262.5612.58'l2.6822.7592.7842.8242.8652.717

M(4)1.8201.9251.9541.9612.0981.9762.5252.5812.6042.6302.7122.8823.0833.1032.784

r(211.6121.6811.6971.6682.5112.7092.7252.8172.715

r(3)1.5611.6211.5912.5772.6312.6442.597

x2.O712.2862.6282.403

88.4582.4379.0397.4290.6997.5191.7389.83

77.O078.9084.3688.0892.7794.79

103.61100.8890.06

98.66106.63108.301 17.58109.23

108 .15108.50114.72109.30

79.9476.2396.93

103.20102.8989.71

83.798 1 . 1 388.9085.2394.1 393.2796.8590.02

105.47106,201 10.951 13.98109.34

Note; Under each atom heading are listed (X,M,TFO bond distances and angles. Errors: M-O < 0.002 A, O-O' < O.OO3 A, angles O-M, T-O,0,09'. Equivalent points are referred to Table 2 and appear as superscripts: (3) x, -y, -z; (41 -x,y, z; (1OlYz - x,lz - y, -zi i1)V2 - x,V2 -V 2 + 2 .

'Shared edge between M and T polyhedra..'Shared edge between M and M'polyhedra.

v,

the value in Moore and Araki or Finger and Hazen andI to equal the value obtained in this study,

A: l (W - r ) /T l x 100.Mean values and their extrema are tabulated in Table 6.For three kornerupines from three different sources (twonatural minerals, one synthetic), the similarities ratherthan the differences are surprising. The mean value of lA Ifor all U,, of the 8-cation and lO-anion unique positionsis a little over 25o/o for cations and a little under l7olo foranions. Cations usually give larger A values than anions,

a consequence of smaller thermal motion for the cationsand of more variegated solid solution in these cation po-sitions. The greatest deviants, + | 5 6.2o/o for T(3) of Mooreand Araki (1979) and *l4l.0o/o for M(2) of Finger andHazen (1980) arise in part from the arithmetic involvedlsince the [l, individual values employed the relativelysmall values in this study as the divisor, such differencesappear exaggerated, at least in the condensed manner bywhich we express them.

The average B"o are also listed. The match is remarkablyclose, within 20o/o for cations and 3o/o for anions. These


Traue 6. Refined kornerupines: Differences in thermal parameters

aq, (, : 1 to 3) A8*

647

Extrema

20.823.0

22.228.6

MAFH

MAFH

MAFH

30.232.1

15.925.9

A. M(1FM(5) and T(1)-r(3)-16.2tor T(2) to +156.2 for T(3)-32.5 for M(4) to +141.0 for M(2)

B. o(1)-o(10)-27.5 tor O(10) to +69 0 for O(4)-40.5 for O(7) to +88.1 for O(4)

-0.0 for M(3) to +88.9 for T(3)-23.1 tor M(4) to +72.5 for M(2)

-21 .3 tot O(1 0) to + 14.1 for O(4)-20.6 for O(7)ro +22.7 lot O(21

9.415 .6

C. Mean of lAl for M(1)-M(5), T(1)-T(3), and O(1)-O(10)14.518 .9

M(1FM(5) r(1Fr(3) o(1FO(10)

D. Mean B* (A')0.46U.JY

0.47

Note: All calculations refer 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 asymmetric unit. Mean values of the difference magnitudes'

lA | , and individual extreme points are also given in percent. These values are given for 4 (, : 1 to 3) and 8q. Part D lists the mean equivalent isotropic

TSMAFH

0.530.590.61

i 7'l

0.770.79

thermal parameters.* References: MA-Moore and Araki (1979); FH-Finger and Hazen (1980); Ts-this study.

similar results from three independent studies underlinethe importance of assessing thermal-vibration parametersin evaluating the "correctness" of a structure.

When a structure is accurately known, it is desirable tocalculate individual deviations from bond-distance av-erages and compare them with deviations in electrostaticneutrality. The simple Pauling model was adopted, mainlybecause it does not masquerade deviations but proceedsdirectly from formal charges, coordination numbers, andindividual distance deviations calculated directly fromTable 4. Individual bond strengths, s, were calculated fora purely ionic model and from the cation-site populationsand coordination numbers discussed earlier. Calculateddeviations from po : 2.00 for 02 and individual distancedeviations are listed in Table 7. Only O(10) has attachedH and the O-H bond was given s : 5/6 suggested by Baur(1970). The centroid ofthe H atom could not be locatedin our difference synthesis. However, it was postulated byMoore and Araki (1979) thata series X7,+tr"OH--X1*62existed. This can now be tested to some degree.

Thirty-six entries occur in Table 7, and of these, sixviolate the expected bond length-bond strength relation-ships. In other words, 830/o of the values are in concord.Five of the six values involve X and M(l), the two mostdistorted polyhedra in the structure. The violations in-volve the anions O(4), O(5), O(7), and O(9) of which O(7)and O(9) have undersaturated values for these entries. TheO(4), O(5), and O(7) are eliminated as they involve sharededges with other fully populated polyhedra, that is, theirdistances are too long, owing to cation-cation repulsioneffects. The O-H(10)" O(9) distance of 2.763(3) A cor-responds to a shared edge between two XO(4).O(9)rO(10),distorted cubes. If a successive pair of such cubes hasunoccupied X, the O-H( l0) ' ' ' O(9) hydrogen bond is pos-

sible. The increase in X occupancy would tequite a de'crease in H content, suggested earlier by the postulatedX?,*tr%OH--X?"O'- series. However, the left side of theequation is not balanced, and quantitative presence ofhydroxyl groups would not be possible in this model owingto shared edges with occupied cubes. A more reasonable

TABLE 7. Kornerupine: Electrostatic valence balance of cations and anions

Cations

Anions M(1 ) M(2) M(3) M(4) M(5) LPor(3)r(2)r(1)

o(1)o(2)o(3)o(4) + 0.22o(5)o(6)o(7)o(8)o(9) - 0.11o(10) -0.33, -0.33

-0.01

+0.00+ 0 . 1 1

- 0.07

-0.03, -0.03

-0 .13 , -0 .13

-0.05

+ 0 1 8

-0 03-0 .11

+ 0 . 1 4

-0.01-o .02 - 0 .11 , -0 .11-0.05 -0.01

-0'00-0 .15+0.12 +0.07

+0 04, +0.04+0.01 , +0 .01

-0.06+0.02+0.03

-0.17-0.17-0 .17-0.07-0.23+o.44+0.17+0.23+0.19-0.32

-0.03+0.03

Nofej Bond length-bond strength contradictions are in italics. Entries are individual deviations from polyhedral averages (Table 4).


Trele 8, Comparison of Ni2ln, olivine, and kornerupine

Ni, lnOlivineKornerupine

ao(N) :4 .18a(n : 4 .76a(K): als : 3.21

4 (N) :7 .24b(n:10.22D(K) : 13.75

cD(N) : 5.13c(F) : 5.99c(K): 6.72

CmcmPbnmCmcm

A/ofe.'Values are in angstroms.

series on the left side would be Xfl,+tr*OHu,. This stoi-chiometry appears to fit our refined structure fairly well.

Finally, bond distances in Table 4 can be addressed.The polyhedral distortions resulting from shared edgesare in perfect agreement with predicted results, the soleT(2F8[;FM(I) tetrahedral-octahedral shared edge beingthe shortest for all the polyhedra.

KonNnnuprNB: SrnucruRAl pRTNCIpLES

Since Moore and Bennett (1968) first reported the crys-tal structure of kornerupine, Moore and Araki (1979) re-fined data from a B-rich synthetic crystal, and Finger andHazen (1980) refined a Fe-rich member, but little insighthas been gained on the crystal-chemical principles of thiscomplex structure type. This is especially embarrassingsince the structure type has been turning up in many ter-ranes of granulite facies. All attempts to derive its struc-ture from hexagonal and/or cubic dense-packed oxide an-ions have failed. Both the first and second structure studiesstressed principles of anion close-packing in sections ofthe crystal structure, from a projection along [001] in thefirst study and along [010] in the second. Yet the packingefrciency of 16.8 A, per 02 , when compared with4yQ. f : 15.52 A: for the "classic" Paulins 02- radius r: 1.40 A, suggested a dense-packed structuie. Such pack-ing, however, does not necessarily imply cubic or hex-agonal close-packing: many very dense-packed structuretypes (glaserite, K.NaSrOs; or garnet, MgrAlrSi.O,r, forexample) do not belong to these simple packing principles.For such structures, we have had considerable successthrough seeking out analogies between cations in the oxy-salts and atomic positions in intermetallics. This ap-proach largely stems from the penetrating study ofO'Keeffeand Hyde (1985), where they discussed isopunctal rela-tionships comparing cations in garnet with Cr3Si, cationsin olivine with Nirln, the apatite structure type with MnrSi,and many other analogies. Incidentally, glaserite's cationscan be directly related by comparing the cations of(K.NaSr)O, to Nioln, and those of the lAngbanite mon-strosity with americium, .ch.!

A general formula can be written for kornerupine, whereM are cations in octahedral and higher coordination byoxide anions, T are tetrahedrally coordinated cations, and@ corresponds to generalized anion. Including the large,partly occupied X site, kornerupine has MooTrofr, for theunit-cell contents. Ifthe cations only are projected alongthe three principal crystallographic axes, a quite diferentpicture from the earlier studies is immediately recogniz-able. All nine cations in the asymmetric unit define three

distinct rods, each made up of three unique cations whenprojected along the I I 00] direction. When the mirror planenormal to the c axis at x : 0 is included, five beads ofcations are created per rod for one cell translation. Eachunique rod is given a symbol: M(a) at x, 0, 0; M(b) at x,l/6,l/4; and T at x, -l/3,l/4.It is noted that the beadsare separated by intervals of approximately x/ 5 along thedirection ofprojection. The separation, A, ofbeads in eachrod in the projection 0-z plane) are within A : 0.0 forM(a), 0.1 for M(b), and 0.3 A for T.

The orthogonalized cell and its atom positions forNirln can be directly related. That is, P6r/mmc, a(h) :4.179, c(h) : 5.131 A llaves and Wallbaum, 1942),2In(r /32/3r /4) ;2 N( l ) (000) ; 2 N(2) ( r /32/33/4) -Cmcm, ao: 4.18, bo: a(h) \ /3 : 7 .24, co : 5 .13 A; 4In(O l/3 r/4); 4 Ni(l) (0 0 0); 4 N(2) (1/2 t/61l4). Thus,we can compare the average cation or metal positions inthe y-z plane: (0.343, l/4), (0.333, 1/4) for T, In; (0, 0),(0, 0) for M(a), Ni(l); and, (0.142, l/4), (0.167, l/4) forM(b), N(2). The displacements in the y-z plane are A :0. 16, 0.00, and 0.40 A, respectively, when computed onthe kornerupine unit cell.

Kornerupine's cations track very nicely on Nirln po-sitions along [00]. Therefore, the comparison amongNirln, olivine, and kornerupine is a very anisotropic re-lation, indeed, as shown in Table 8. Can these relativeanisotropies be explained? From this prelude, a fugue isnow required.

But discussion on correlations among cations or metalsin kornerupine, olivine, and Nirln hardly explains theextreme anisotropy among equivalent cell translations,and the role of the electronegative oxides must also bediscussed. It would be most desirable to seek an inter-metallic cluster or molecule with well-defined geometryand to examine the locations of and distortions createdby oxygen insertion. From this model, which involves afinite cluster, an extension to infinitely extending arraysis possible so long as all atoms in the asymmetric unit canbe counted and so long as the electron count is preserved.

Such a model exists and illustrates the insertion of oxy-gen into an intermetallic, in this case one of the poly-morphs of phosphorus, Po or white phosphorus. Figure Ishows the progression [Po], [PoO6], and [PoO,o], the samesequence as featured in Wells (1975). Errors in distancesreported for these three structure determinations each areabout +0.03 A. In the [Po] tetrahedron, the P-P edge(bond pair) is 2.21 A. This value was esrablished by elec-tron diffraction of a jet of Po vapor (Maxwell et al., 1935).From the model, each vertex is 3-connected, and each Pcontributes three electrons to bond-pair formation and

two electrons to the terminal electron lone pair, ry'. SinceP has five valence electrons (3sr3p3), the package [Pory'o]has six bond pairs and four lone pairs, thus accountingfor all 5 x 4 : 20 valence electrons for [P"].

Now in [PoOu], six oxygens are inserted near the mid-points of the P-P edges. Since the more electronegativeoxygen has six valence electrons (2sr2po), two more elec-trons are required for kwis octet closure. In fact, Lewisoctets constitute a hallmark of twentieth century science,both in crystals and in other condensed states (Lewis.I 9 I 6). Octet closure is achieved by the P-P bond pairs atthe midpoints of the six edges that incorporate the sixoxygens. The P-O distances are 1.65 A, and the P-P dis-tance is expanded to 2.95 A. fnis experiment also em-ployed electron diffraction of jets, reported by Hampsonand Stosick (1938). The terminal positions from the Patoms still remain electron lone pairs, and the moleculecan be expressed as [PoOury'o]. The midpoint of the P-Pdistance was expressed in atomic coordinates for the pur-ported locus ofthe bond pair. The distance d between thismidpoint and the centroid for the adjacent oxygen com-puted to be 0.7 4 A. These distances are shown in Figure I .

Finally, in PoO,o, the four terminal lone pairs completethe octets of four terminal oxygens. Its structure was de-rived from an X-ray diffraction experiment earlier con-ducted by de Decker and MacGillavry ( 1 94 I ), later refinedby Cruickshank (196a) who- reported average distancesfor P-O (bridging) of 1.60 A and for P-O (terminal) of1.40 A. These differences can be easily understood fromPauling's rules, the bridging oxygen being oversaturated(Apo : +0.50 valence units) and the terminal oxygen beingundersaturated (Apo : -0.75 v.u.) by bonded P atoms.The P-P distance of 2J9 A is an average of two inde-pendent but very similar distances. The average distancebetween the midpoint of P-P and the centroid for adjacentoxygen is d : 0.7S A. Thus, the progression lPo*ol -

lPoou'y'.] - [PoO,o] exploits the Lewis octet formationabout the most electronegative species, oxygen. Note thatin the progression in Figure l, the inserted oxygens are atapproximate midpoints of P-P edges and displaced some-what outward from these edges in the tetrahedron. Theexpansion ofP-P is considerable: for PuOu, the P-P di-lation is A: t25o/o, and in P4Or0 it is A : +210lo w'ithrespect to Po. In these calculations and those that follow,the dividend is the difference between the oxysalt and theintermetallic values being compared. The divisor is theoxysalt value, and the quotient is multiplied by 100 androunded off to the nearest whole number. The result isexpressed in linear measure by extracting the cube rootof volume per metal atom, which was derived from thecrystallographic unit cell.

O'Keeffe and Hyde (1985, especially p. 99) discussedlinear and volumetric changes in some detail and stressedthat dilation does not necessarily follow in the progressionM,T, - M"TuQo where M and T are metals and 4 theelectronegative anion, usually O, . They declared, "Al-though there is often a considerable volume increase onforming an inorganic structure from the corresponding

649

Pq Pt 06 P4 0ro

Fig. l. Spoke diagrams for [Po], [PoOu], and [PoO,o]. O : Patoms, X : the oxygen centroids, and {, : the lone pairs ofelectrons. Key distances are given.

alloy 'by (notionally) inserting anions into the latter' . . . ,"exceptions abound. This can be demonstrated in Table 9where examples of well-defined oxysalt-metal pairs havebeen selected from Villars and Calvert (1985) and Donnayand Donnay ( I 963). The seven pairs include binary oxidesin the system MgO-AlrOr-SiOr, which encompasses mostofkornerupine. Note that five oxysalt-metal pairs in Table9 exhibit the same cation or metal eutaxy (: "well-ar-ranged") but two MgO-Mg andAlrOr-Al do not, althoughtheir structures are based on principles of close-packing.We found the most convenient way to relate the pairsinvolves calculations of cell volume per metal for eachpair, then taking the cube root of these values to get alinear expression as percent change, which was earlierdiscussed.

In Table 9, the valence electrons are listed as well, andthe table is arrayed according to increasing electron pop-ulations of the orbitals. A trend immediately becomesobvious. The top three entries with only ns2 valence elec-trons for the metals decrease in volume for Me - MeO.Note that the Ca - CaFr, A : -2o/o compared with Ca- CaO, A,: - 160/o.It is believed that an aliquot of twicethe number of fluoride ions compared with oxide ions forthe isopunctal Ca metals accounts for this difference. Theremaining five pairs increase in volume for Me * MeO.These pairs include additional p- and d-electron popu-lations. This contrast appears easily explained by Pauling(1960, p. ll0): "p bonds are stronger than s bonds" and"it is convenient to call the magnitude of a bond orbitalin its angular dependence the strength ofthe bond orbital,with value I for an s orbital and 1.732 for a p orbital."

Since kornerupine is constructed principally of AlrO,and SiO, components with somewhat less MgO, it followsthat the kornerupine cell will expqnd with addition ofelectronegative oxide ions relative to its chemical equiv-alent of the Nirln intermetallic.

The [P.] cluster model above was applied directly tothe complex kornerupine crystal structure. In every re-spect, the same calculations were performed. This re-quired taking all the countable cation-cation positions, todetermine the midpoints of their connections and to cal-culate the distance between each midpoint with respectto its adjacent oxide centroid. The midpoint is suggestedby the [P"Oury'o] and [PoO,o] molecules where d - 0.76 Aoccurs on the average between adjacent oxide centroid



1 .

Tlar-e 9. Kornerupine components and some oxysalt-metal re-lations

To make sure all cations and anions were represented,graphs (of which there are many choices) from Figure 2were constructed. The collection used here for kornerup-ine includes two chain segments: -M(5)-O(2FM(5FO(6F

r(2)-o(5)-M(4)- and -M(l)-o(10)-M(l)-o(7)-r(3)-

o(8FM(2)-o(3Fr( I )-o(eFr( 1 )-o(4FM(3Fo( I FM(3F. Since all anions are listed, the formation of Lewis octetscan be achieved. Clearly, many other combinations canbe written, as each anion is either three-coordinated orfour-coordinated by cations, but this doesn't matter sincewe are only required to seek out bond pairs associatedwith anions for potential Lewis octet closure. Segmentsof these chains occur in Table 10, compared with the Nirlnintermetallic, and the distance d between cation-cationedge midpoint and oxide centroid is entered. The rangeis d : O.2l A for O(5) to 0.96 A for 0(6) with a mean of0.68 A for all oxygens. For olivine, the range is 0.88 Afor O(3) to 0.99 A for O(l) with a mean of 0.93 A. It isobvious that kornerupine more closely mimics the Nirlnarrangement than does olivine, as shown by a model forthe 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 seen that themean is 0.26 L for kornerupine (range 0.00 to 0.50 A)and 0.46 A for olivine (range 0.00 to 0.82 A). Yet again,kornerupine, even with its relatively large number of at-oms in the asymmetric unit, shows the best correspon-dence with the intermetallic. The space groups of the latterpair are the same, Cmcm. Note that a nearly regular sub-cell occurs for kornerupine with q(N x a/5(K) that wasautomatically included in calculating the cation (metal)positions between these two structures.

The X cation in kornerupine and the M(l) cation inolivine are the only atoms not represented for these struc-tures in Table 10. Attempts were made to find reasonablegraphical connections, but these were either too long, orthe ensuing d values were too large. It appeared that Xand M(l) played somewhat different roles in the structuresthan in corresponding Nirln. It is interesting to note thatthese sites play anomalous roles in the structures: X isonly partially occupied in kornerupine, and M(l) in oli-vine, which experiences similar disorder, is the basis ofomission derivative structures such as sarcopside, heter-osite, and laihunite.

Kornerupine, olivine, and Nirln: Similarities and cellanisotropies. Emphasis in Tables 2,9 , and I 0 and in Figure2 has been placed on the similarities of cation positionsamong these three structure types. For example, in Table2, it is seen that X, M(IFM(5), and T(1fT(3) in korne-rupine and M(l), M(2), and T in olivine (forsterite) cor-respond to N(l), N(2), and In in Nirln. The relation X,M- Ni and T - In is hardly an accident! If such a corre-spondence occurs, then why do the cell shapes markedlydiffer? As before, for proper comparison, the a axis ofkornerupine must be partitioned into its subcell a' : a/5.Figure 2 presents the general relationships among the cat-ions and their correspondence in these structures. For

MgO-MgMgo

'CaO-'Ca.CaO

*CaF,-*Ca

*CaF,

V2Al2O3-Al

Y2AI2Oo-sio,--si

-sio,.CoO--Co

Fn€mvs. ftJmmc

Fnfmvs. FnEm

Fnlsmvs. FnBm

R3cvs. FnBm

FdSmvs. Fd3m

FnEm vs. Fntsm

FnBm vs. FnBm

3sf

4s

4e

3se3p

3*3e

3clt4*

-7o/o

-160/ "

-2%

!8o/o

I24o/"

-116o/o

e

b

7 .

.CoO-Nio--Ni

3do4* -116o/o

Note; Starred metals are in isopunctal relationship. Col. A: oxysalt andmetal pairs used in volumetric calculations. Col. B: space groups of oxysaltvs. metal. Col. C: valence electrons for metal. Col. D: linear chanoe orcube root of volume per metal (A3, based on unit cell) for oxysalt-iletalpairs. Nos. 1,4, and 5 from Villars and Calvert (1985); 2, 3, 6, and 7 arefrom Donnay and Donnay (1963).

and the P-P centroid. Calculations that ensue always takethe midpoint of two adjacent cations as the locus of thebond pair.

But kornerupine is an extended three-dimensionalstructure. How are the cations counted? Unconventionaldiagrams in Figure 2 are presented for both kornerupineand olivine where emphasis is placed on cation coordi-nation about anions. Note that O(l), O(2), O(4), 0(6),O(8), O(9), and O(10) are each four-coordinated and de-fine rather distorted tetrahedra and O(3), O(5), and O(7)are each three-coordinated by cations that define distortedtriangles. The olivine map also reveals four-coordinationofcations about anions, in each case three octahedral (M: Mg) and one tetrahedral (T : Si) cation. In both cases,the maps appear rather cumbrous, but much informationis given in them: they are more extended equivalents ofthe [P4] sequence. Since Pbnm (olivine) c Cmcm (kor-nerupine), both structures were projected along the z di-rection, the shortest translation in kornerupine. Only an-ions within 0 = z < 7z are shown in order to minimizeredundancy and congestion. The olivine and Nirln cellswere scaled to conform with kornerupine for purposes ofcomparison. Heights in z are given as fractional coordi-nates. Anions are shown as filled squares, and cations assolid disks; the scaled N(l), N(2), and In centroids forthe Nirln intermetallic are shown as crosses. Dashed linesin Figure 2 have the same connotation as those for the[Po] series in Figure l, that is, a dash between the cationpair, and a dash from the adjacent anion to this pair. Inaddition to many of the d values (the distance betweencation-cation midpoint and adjacent anion) in the figures,cation deviations between oxysalt and intermetallic aregiven in angstroms, as are the d values between oxidecentroids and cation-cation midpoints listed in Table 10.

'Nio


M(5)0,liz

'l'n

lzr)0.64

b-

b--x=3

6 5 1

Y=VzI11/q

IFT

'=+ r:::l

m ]-0,1/zl0,t/q

b -, M(3)0,h.

Y : : - +^ s Ni(r)o.ti

D _

b-t=o qrl,?,lif

b-

b -

x=5!!llr;l;l;t

+ t f alnlq

Vq

1 o}l(ZlleNil2lt/c

oI Vq'rn'/o

, .MQ l l+-Nilzlyo

e M(5)0.x= f

-Hirl i

Ml4l1c'+Hi(z),rn Tll,t#

' l n 1 4a'

. T ( Z l y 4Mfi)y4

a+ N i (2 )%

*=+'!L *J,?;,%',u, 'n*"r,,,* J

,Ni (t )0,r/zrttt(s)0,%

d;lli3:11:

+iltlli:ii* t'vl'ln%

Fig. 2. Spoke diagrams of kornerupine on left and olivinescaled to kornerupine cell on right. Cell origins and outlines ofprojection along [00 1] are designated by arrows and right angles.Most atoms are 0 < z < t/2. Heights in fractional coordinates,cations as circles, anions as squares, Nirln as crosses, translationsin x on left. Some symmetry elements are shown. Dashed lines

have same connotation as in Fig. l. Displacements in A frommidpoints of cation pair to nearest anion are given under thatanion. The lower portions of both maps show cation and Nirlncentroids only. This is a map of cations about anions. Note three-coordination for O(3), O(5), and O(7), and four-coordination foro(l), o(2), o(4), 0(6), o(8), o(9), and o(10).

4

iij:ii'/

?11/+Zlslq

0(3)?r M

convenience, set r,, i: I to 3, as the unit-cell translationsa (or a/5 in kornerupine), b, and c. The orthohexagonalcell for Nirln has been already defined. Its contents are4Nirln, and the cell translations and axial ratios are listedin Table I l.

It is immediately recognized that the ratios indicateextensive cell anisotropy among these compounds. Webelieve that this can be explained by the rather anisotropicinsertion of the oxygen atoms. Recalling the sequence [Po]- [PoOu] - [PoO,o] with a linear increase of some 25010,note that in Figure I the oxygen insertions can also beconsidered as insertions oflayers or planes that lie betweenbut do not anywhere include cations. In cubic structures,we saw that dilation was uniform in three dimensions.Analogous to the tetrahedral [Po] sequence, such planeswould be parallel to { I I 1} for example. In orthorhombiccrystals, orientation ofadded oxygen layers according to

{ 100} , {0 I 0}, {00 I }, or { I l0}, etc., would lead to markedanisotropy in axial ratios compared with the intermetallic;the anisotropy would be particularly pronounced normalto that layer receiving the extra insertions. Any "isotro-pic" insertion for an orthorhombic intermetallic wouldlead to a compound with closely similar axial ratios.

It is believed that the adjusted axial ratios in Table I Ibest explain the anisotropy through oxygen insertion andbond-pair formation. Through trial and error, the bestaxial direction was selected, and the standard ratios werescaled according to the axial ratio for Nirln. These arelisted in parentheses. Here, c for kornerupine and a forolivine were set according to Nirln. For kornerupine, wesee a decrease in aby about 42o/o and an increase in D byabout 45010. In olivine, a and c are similar to the Nirlnratios, but b is increased by about 24o/o. In kornerupine,anions O(lp(8) all contribute to laminae between X and

6 5 2

TABLE 10. Kornerupine and olivine: Displacements between cat-ion pairs and adjacent anions


f Orientations of pairs: tr parallel a, ' parallel c, X in a-b plane V ina-b-c Dlane.

f The displacement (d) between cation-pair centroid and adjacent anion.

M(l)-M(5) cations to form edge-sharing chains parallelto [00]. This

o\ , / \ /M M

/ \ / \o

sequence deflnes oxygen insertions where no bonds occurin Nirln (the a:4. 18 A translation; see below)! Thiswholesale formation of bond pairs results in M-M = 3.2A. tire big increase alongb is also explained by the anioninsertion. Laminae of O(4), 0(6), O(8), O(9), and O(10)parallel to {010} are inserted nearly betweel, atom bondpairs and are located near y = +(h,3@. Additional lam-inae of O(3), O(5), and O(7) also parallel to {010} arelocated near / E +(%). Kornerupine is a particularly in-teresting example where both bond-pair formation andanion-layer insertion have a ready explanation in the axialratios. This is admittedly a qualitative model, and neitherall bond pairs nor all anions were accounted for. As yet,a quantitative model has not been perfected. In such anevent, many exciting new discoveries will be made, es-pecially "turning intermetallics into oxysalts." The bestdisplay of this remarkable structure is either projectionalong [001] or deciphering the diagrams in Moore andBennett (1968) and Moore and Araki (1979).

Olivine poses similar problems. Its cell parameters andaxial ratios suggest that the most anisotropic increase isalong b with an increase of about 24o/o with respect toNirln. Unlike kornerupine, all anions form bond pairsnearly between the bond pairs in Nirln. In olivine thereare no additional insertions (as occur for kornerupine)between nonbonded regions for Nirln. The only anion to

TABLE 11. Cell translations and axial ratios

t, t, t3 Axial ratio Adjusted axial ratio

Ni,ln (N)Korn (K)Forst (F)

O.577:1:0.7O80.233:1 :0.489 (0.337:1.448:0.708)0.466: 1 :0.586 (0.577 :1.238:0.726)

form laminae between the cations is O(3) in a generalposition. The M(2) and Si cations on either side of theO(3) laminae parallel to {010} are displaced themselves,accounting for the greater difference between atoms in theintermetallic and cations in olivine in Table 2. While inNi,In, the displacement in the a-b plane is 0.00 A, thecorresponding M(2FSi in olivine is displaced - 1.3 A.

Table l2 summarizes the chemical crystallography andbond nomenclature for Nirln and a-Fe. Just as it is pro-posed that Nirln forms the atomic basis of cation distri-butions in kornerupine and olivine, so Nirln is an orderedderivative of a-Fe. The element has z : 2, Im3m, a :2.866 A (Donnay and Donnay, 1963). Selecting the hex-agonal cell for a-Fe, a direct comparison can be made asoutlined in Table 12. Partitioning Fe into three equiva-lences yields the ordering scheme compared with Nirln,also given in Table 12.The maximum difference betweenequivalences is A : 0.43 A based on the c axis of Nirln.With differences in electronegativities and bonding, webelieve Nirln can be considered an ordered pseudoderiva-tive structure ofa-Fe. The prefix pseudo is used becauseR32/c and P6r/mmc share same cell but not same classrelationships.

Included in Table 12 are the metal-metal distances forNirln, the number of equivalent bonds, the planes thatinclude them (based on the orthohexagonal ao, bo, co) anda code (1-2, 3-3a,44c,5-5b) for the kinds of bonds. TheIn[Ni,,] and Ni(2)[InrNiu] define distorted pentacappedtrigonal prisms and Ni(l)[InuNir], a bicapped hexagonalprism. These bonds are found among the cation-cationdistances in kornerupine and olivine. The 5-5b distancesof ao:4.18 A each are not bonded. They play a centralrole in kornerupine as discussed earlier.

Taken together, the kinds of bonds, their number in theolivine, and one-fifth the kornerupine cell (the unit forcomparison) are as given in Table 13. The differences arisefrom bond arrangements of varying distribution, an "ol-ivine" stoichiometry of MrTOo o in kornerupine, and theappearance of three-coordination of cations about anionsO(3), O(5), and O(7) in the latter mineral.

It is now possible to address the intriguing question:can Table 9 serve as a vehicle to compare the linear changefor oxysalt-metal pairs associated with kornerupine andwith olivine? An interesting twist is added to the problem,for here not single components (such as t/zA7rO. and Al)but several components are involved. Several assump-tions are made, some of which were assumed before: (l)the single components are based on principles of close-packing, either .c., .fr. or combinations of these. Forperfect spheres, there is no change in packing efficiency,

Adjacent cationpairt Nrln atoms

Displace-mentf

(A)

4 .18 7 .24 5 .133.21 13.75 6.724.76 10.22 5.99

Distance(A)

0.990.910.88n o e

o(1)o(2)o(3)o(4)o(5)o(6)o(7)o(8)o(e)o(10)

Mean

-M(3FM(3)'.M(5FM(5)',xr(1)-M(2)vT(1)-M(3)xr(2FM(4)vr(2)-M(5)xT(3)-M(1)-r(3)-M(2)or(1)-T(1)

"M(1)-M(1)

xT-M(2)xT_M(2).r-M(2)

KornerupineN(1 )-N(1 )N(1 )-N(1 )

In-Ni(2)In-Ni(1)In-Ni(2)In-Ni(1)In-Ni(2)In-Ni(2)'In-ln

N(2)-N(2)

OlivineIn-Ni(2)ln-Ni(2)ln-Ni(2)'

2.57 0.732.57 0.732.41 0.782.73 0.642.4't 0.212.73 0.962.41 0.632.57 0.944.18 0.474.18 0.71

0.68

o(1)o(2)o(3)

Mean

2.412.412.57


TABLE 12. The Nirln and d-Fe intermetallics: Chemical crystallography

653

Nir ln a-Feln8m 1*321c)2 F e 0 0 0 a : 2 . 8 6 6 A4l: t /2a:4.052 c(h) : v€a:4.964 A c(hVa(hl:1.22sa o : 4 . 0 5 2 4 : 7 . 0 1 8 C o : 4 9 6 4 42Fe(a) % % Y62Fe(b) 0 0 02 Fe(c) % 2/s %

ftJmmc2 Nir lna = 4 .179 c : 5 .131 Aao : 4.179 bo: aVg =2 ln 1/z2 N (1 ) 02 N(2) Vs

1 In-Ni(2)2 In-Ni(2)'2 In-Ni(2)"4In-Ni( l )2In-Ni( l ) '

2 N(1)-N(1)', 2.s72 N(1)-N(2) 2.734 N(l)-N(2)' 2.732 Ni(1)- ln 2.734 Ni(1Fln 2.73

cla : 1.2287.238 co : 5.131 A

2h

0q

Y403/q

(A)2.412.412.572.732.731 1 pentacapped trigonal prism

1 Ni(2)-ln2 Ni(2)-ln'2 Ni(2)-ln"4 N(2)-N(1)',2 N(2FN(1)

boaoh

4boh

2.41 bo2.41 aoh2.57 C2.73 aobo%2.73 4.c"

1 1 pentacapped trigonal prism

ao

12e

44b

12e

4a4c

5a5b

co 3a4c 4czodco 4aWco 4baboco 4

14 bicapped hexagonal prism

2 ln-ln'2 N(2)-N(2)',2 N(1)-N(1y

4 . 1 84 1 84 1 8

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

Zu, or volume per atom. (2) The volumetric differencesin types of close-packing among crystals of same com-position are negligible. (3) A phase composition, whetherreal or hypothetical, involving more than one componentcan be evaluated by a principle of additivity, i.e., the sumover all components in its formula. This implies additivityof the volumes of each of the components in the formulaunlt.

The cell formula for olivine is 4MgrSiOo, the X-ray cellvolume V:291.86 A'from Birle et al. (1968) for for-sterite. In the same manner as deriving Table 9, MgrSi is8Mg + 4Si : 184.81 A, + 80. t0 A3 or 264.91Ar. Thevolume change from intermetallic to oxide is

[ (291.86 - 264.9r) /291.86] x r00: +9.2o/o.

The average linear increase is

A : [(6.633 - 6.422)/6.633] x 100 : +3.2o/o.

This value can be compared with column D in Table 9.The valence electrons for the metals are 3J2 and 3s2p2, andthe small net linear increase is believed to reflect Pauling's(1960) estimates of relative bond strengths of s and pbonds. Kornerupine with a greater aliquot of p bondswould be expected to expand even more than olivine,when compared with its metal components.

To appraise this effect in kornerupine, the formula de-rived from Scoon in McKie (1965) was simplified fromeight components to the three major components. Thesethree major components in the Scoon analysis add to MgO+ Al,O3 + SiO, : 93.32o/o, the remaining 6.680/o beingprincipally FerO, and BrOr. Good oxysalt-metal pairs couldnot be obtained for these two components. In addition,

their small contribution was deemed insignificant, andthis 6.680/o remainder was added to AlrOr. The three-component "analysis" computed to an olivine-related for-mula(5.461 x 4)MgurrAl, 3,osio67eO400o, theprefix scalingit to kornerupine cell contents. The X-ray cell volume isV : 1480.65 A'. That for only the metals (5.461 xqQ.67 7Nde + 1.3 I 0Al + 0.679Si) from Table 9 is I I 1 4.03A', or an intermetallic - oxysalt volume increase of+24.8o/o. The average linear inqease is

A : (11.398 - 10.36 '7) /11.3981 x 100 : *9.00/0,

a value indeed larger than the corresponding value forforsterite olivine. The kornerupine value is slightly largerthan that for the (7zAlrO,-Al) pair, and the less abundantMg and Si nearly offset each other.

Trar-e 13. Number of bonds of various types in olivine and kor-neruptne

Olivine Kornerupine*

I

o

3a44a4b4c55a5b

Total

01 28A

243248000

96

0O A

8.04.8

25.625.6002.4

12.82.4

9't.2- Considering onejifth the kornerupine cell (the unit for comparison).


CoNcr-usroxs

The individual thermal-vibration parameters for therefined kornerupine in this study and two other refinedkornerupines in the literature were compared. Compari-son was based on the dffirence, A(o/o), between kornerup-ine in this study (from Mautia Hill) and the other korne-rupines.

For thermal vibrations, Ae/o) : l(B - A)/AI x 100where B : other kornerupines and A : the kornerupinein this study, from Mautia Hill. The individual U,, (i : 1to 3) values were compared. This gave an estimate ofdifferences in which the values for other kornerupines arerelatively less or greater than those for the Mautia Hillkornerupine of this study. The mean I A I of t/, gave 25o/ofor 8 unique cations and l7o/o for l0 unique anions. Themean lA I of B"o gave 20o/o for the 8 cations and 3olo forthe l0 anions. In addition to reflecting the substitutionaldisorder of different kinds in kornerupine cation sites,these averages suggest that thermal parameters have somephysical reality, at least for adequately refined structures.Note that comparison between anion sites shows remark-able concord.

A novel interpretation ofthe complex kornerupine crys-tal structure suggests that its cations are approximatelyisopunctal to the metals for intermetallic Nirln. Six largercations [X, M(IFM(5)] match up with three Ni(l) andthree Ni(2), and three tetrahedral cations [T(1FT(3)] matchup with three of the more electronegative In. The meandifference using the kornerupine cell is 0.26 A. A similarcalculation for olivine with two octahedral and one tet-rahedral cation gives a mean difference using the olivinecell of 0.46 A. It was deemed sensible to inquire aboutthe placement of the electronegative oxide anions in thecollection of cations. In the sequence lPor!ol (ry' : electronlone pair) - [PoOury'o] - [PoO,o], midpoints of P-P tet-rahedral edges were taken and compared with the oxidecentroids. The difference between the two is -0.8 A andsuggests that oxygen fills its octet by exploiting P-P bondpairs. The same was done for kornerupine and olivine,respectively, both compared with Nirln. Differences be-tween the ten oxide centroids and the cations correspond-ing to three Ni-Ni, one In-In, and six Ni-In midpointsled to a mean of 0.68 A for kornerupine. In olivine, asimilar calculation involving three Ni-In midpoints gavea mean of 0.93 A. These calculations are summarized inTable 10.

Finally, it was asked how the structures distort whenoxides are inserted into corresponding intermetallics. Againthe dffirence, Ae/o) : I(A - B)/Al x 100, where ,4 :component oxide and B : intermetallic, was calculatedfor major components in kornerupine and olivine. Thesepairs were arranged according to valence electrons on themetal. It was observed that for M - MO, the linear changeis negative-i.e., metal oxides have smaller volumes thanisopunctal metals for those metals with s bonds only-butpositive if s and p bonds are involved. This substantiatesPauling's (1960) statement thatp bond strengths are great-

er than s bond strengths. An additivity relation was in-voked to calculate the linear difference between M&urr-Al,3,0sio6reoooo (modified kornerupine) and its "inter-metallic" counterpart. Here, A : *9.00/0, a value slightlylarger than the (YzAlrOr-Al) pair. For olivine, a similarcalculation gave A : 13.2o/o, reflecting the predominanceof s bonds for Mg metal in MgrSi.

These calculations suggest that relations between com-plex oxysalts and their corresponding intermetallics mayplace severe limitations on which oxysalt structures canexist and thus may further our understanding of theirstructure genealogy by exploiting corresponding isopunc-tal or near-isopunctal intermetallic phases.

Since the pioneering paper of O'Keeffe and Hyde (1985),a lot of work remains to be done. Their study involvedmostly relatively simple systems, and questions ofdilationdue to oxygen insertion remain in abundance. Althoughtables ofradii for oxides and fluorides are well established,analogous tables for nitrides, phosphides, arsenides, stib-nides, carbides, silicides, stannides, etc., do not exist. An-isotropic distortion as a consequence of insertion of someelectronegative atoms has barely been examined at all. Infact, no quantitative rules have appeared regarding cellexpansion when progressing from intermetallic to oxysalt.Finally, it is not clear how great distortions can be forintermetallics, and how they should be described. A greatmany new intermetallic-oxysalt relationships have evolvedin the laboratory of the senior author, most involvingoxysalt structures of considerable complexity such asB-CurAs-painite and fluoborite; CoSn-crandallite, mi-tridatite; Nirln-glaserite, fillowite, a-Car(POo)r, stan-fieldite, graftonite, dickinsonite, triploidite, triplite;F e, rZr rP, - dumortierite; CorSi - warwickite. But it is feltthat before a grcat rush is made in search of structuralgold, criteria for relatedness, adjacency, contiguity, andsimilarity must be evolved first.

AcrNowr,nocMENTS

Edward S. Grew, through his persistent prodding and insistence that yetmore komerupine chemical crystallography was necessary, perhaps morethan anyone is responsible for the completion ofthis project. The seniorauthor and Professor Grew share a common love for "-ine" minerals:kornerupine, "prismatine" and sapphirine, even ashcroftine and steen-strupine!

P.B.M. acknowledges the National Science Foundation Grant EAR 87-07382, and, P.K.S. thanks the Tennessee computation facilities at theTennessee Earthquake Information Center for use oftheir VAX computer.

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