THE AMERTCAN MINDRALOGISI, VOL 55, SEPTEMBER-OCTOBER' 1970
STEREOCHEMISTRY AND ORDERING IN THE TETRAHEDRAL PORTiON OF SILICATES
G. E. BnowNl aND G. V. Grses, Departmentof GeologicalScieruces, Virginia PolytechnicInstitute ortd State Llniaersity, Blocksbwrg,Virginia 24061
ABSi RAcr
The depentlence of si-o(br) and Si-o(nbr) bonrl lengths on Si-o si angle and average electronegativity,v, oI non-tetrahedral cations has been examined for four c2/rn anphi- boles and a number of other silicates with both bridging, O(br), and non-bridging, O(nbr), oxvgens. When both 1 and Si O-Si angle are large, the mean Si O(nbr) bond lengths,
INrnotucrroN Since Pauling proposedhis classicset of semi-empiricalrules for pre- dicting stableconfigurations of atoms in complexionic crystals(Pauling, 1929), the cr)rstal structures of a large number of silicates have been studied and found to agreewith them remarkably well. The rules were developed to predict cation-anion distancesand cation coordination polyhedra in addition to explaining the distortions and polymerization of thesepolyhedra basedon the assumptionthat ions tend to adopt posi- tions such that the potential energy of the resulting configuration is minimized. Although the radius sum of two bonded ions gives a reason- able estimateof mean cation-aniondistance, it fails to predict variations in ind.ividual bond lengths other than those associatedwith shared poly- hedral elements.In an attempt to circumventthis problemand to explain individual bond leneth variations in monoclinic metaboric acid,
1 Present address:Department of Earth and SpaceSciences, S U N.Y. at Stony Brook, Stony Brook, L I., Ne'lv York, 11790. 1587 1588 G. E. BROWN AND G. V. GIBBS
Zachariasen (1963) modified Pauling's second rule of local varence neu- tralization by quantitatively relating charge balance to interatomic dis- tance such that bond strength is uniquely determined by interatomic distance.l The Pauling-Zachariasenmethod has since been appried with some successto datolite (Pant and Cruickshank, 1967), zoisite and clinozoisite(Dollase, 1968),a-NasSizOr (pant and Cruickshank, 196g), 0-NazSizOr(Pant, 1968), eight clinopyroxenes (Clark, Appleman and Papike, 1969) and asbecasite, taramellite, kauskopfite, meliphanite, leucophanite, aminoffite, macdonaldite, bavenite and neptunite (Coda, 1969). rn the datolite study Pant and cruickshank discussedthe method and concluded that its successis independent of whether the nature of the bonding is ionic, covalent or a mixture. rrowever, one possible mechanismfor charge balance, in addition to ionic and o-covalent bond- ing is discussed'byCoulson and Dingle (1963) in a study of B-O bond lengths in a number of planar boron-oxygen compounds including mono- clinic metaboric acid. They,carried out standard Htickel-type molecular- orbital calculations on these compounds and found that a zr-bonding model'can account fbr the variation of B-o bond lengths, neglecting the perturbating efiectof'other cations(see also Svanson,1969). pant (196g) has indicated'that zr-boridingmay also be part of the mechanism where- by local valence neutralization is achievedin the tetrahedral portion of a silicate structure. The importance of zr-bondingin the silicates has been discussedin detail by cruickshank (1961) who formariz ed,a d,-pzr-bonding model for ?Oo"- ions (T= Si; P, S, CI) of ?6 or approxim ate Ta symmetry by showing that only two dr-orbitals (d.", and.d,*r_oz) on I can form strong d-2 zr-bondswith the pzr-oribtalson oxygen anions assuming that the tetrahedral a-bonds are formed from s13hybrid orbitals at ?.2,sThe predictionsof bond length and bond angle variations for structurescon- I In a similar but qualitative fashion, Bauer (1962) has discussed a correlation between H-o bond lengths and the sum of the electrostatic bond strengths to oxygen in several hydrous sulfates. 2 Although the point group s).rnmetries of the majority of Sior and Alor tetrahedral groups in solids are lower thanTa sy.rnmetry, e.g., C"in the olivines and c1 in the amphiboles and pyroxenes, the bonding assignments based on ?d symmetry are probably good approxi. mations. This assumption can be made because the deviations frorn Ta symmetry are usually small (-+5" from the ideal tetrahedral angle and at most -+0.05A from the mean ?-O bond length; see Fig. 7). Also, because spg and slr hybrids belong to the same representations of the ?a point group, the o-orbitals on ? very probably consist of a mix- ture of both of these hybrids (Cotton, 1963). sNote added in proof. Recent db initio molecular orbital calculations by D. w. J. Cruickshank (per.sonal communication) for tetrahedral SiO{4- show that ail fne of. tjne 3d orbitals on silicon are essential to describe the Si-o bonds in the ion. However, the three orbitals of the 12bases set have slightly larger overlap populations than the two of the e bases set. Nevertheless, this result does not alter the predictions enumerated by Brown, ORDERING IN THE TETRAHEDRAL OF SILICATES 1589 taining ?Oa groups based on Cruickshank's proposal are discussedby Cruickshank (1961) and outlined by Brown, Gibbs and Ribbe (1969a)' Noll (1963)has extendedCruickshank's ideas to include the perturbat- ing effect of non-tetrahedral cations on the Si-O bonds in silicates con- taining both bridging, O(br), and non-bridging oxygens O(nbr)' and has cited data indicating that the differencesin Si-O(br) and Si-O(nbr) bond lengths are dependent on the electronegativity of the non-tetra- hedral cations bonded to o(nbr). others have also discussedthe effect of non-tetrahedral cations of varying electronegativity on Si-O(br) and Si-O(nbr) bond lengths in selectedsingle-chain (McDonald and Cruick- shank, 1967a) and double-chain silicates (Brown and Gibbs, 1969b; 1e70). The present study is an extension of earlier work on the role of zr- bonding in the framework and double-chain silicates and embodies the substanceof a paper (Brown and Gibbs, 1970)presented at the Amphi- bole-Pyroxene Symposium held at the virginia Polytechnic Institute at Blacksburg, Virginia in September 1969. The purpose of the study is to present further correlations between Si-O bond length and electro- negativity of non-tetrahedral cations in the C2/m amphiboles discussed earlier and between Si-O bond length and Si-O-Si and O-Si-O anglesin structures containing both bridging and non-bridging oxygens. Similar correlations are given for the P-O bond in phosphates.A mechanism for the ordering of Si and Al, Be, B or Mg in the tetrahedral portions of framework silicatesis proposed based on the relative bond orderst of the Z-O bonds. The ordering of these cations is also examined in the non- framework silicates and the role of OH and F in the ordering processis discussed.
DnpnNrBNcn ol Si-O(br) exo Si-O(nbr) BoNn LBNcrrrs on Si-O-Si ANcr.B ANDELEcrRoNEGATrvrrY oF NoN-TETRAHEDRALCerroNs The stereochemistry of polymerized SiOna-tetrahedral ions in many silicatesis consistentwith cruickshank's (1961) hypothesis of zr-bonding: (1) the Si-O(nbr) bonds are usually shorter than Si-O(br) bonds (c',f' Coda, 1968), (2) the lengths of the Si-O(br) bonds are usually.related to the Si-O-Si angle, the shortest bonds being associatedwith widest angles (Cannillo, Rossi,Ungaretti, 1968;Brown, Gibbs and Ribbe, 1969a)and
Gibbs and Ribbe (1969a) on page 1045 where it was assumed after Cruickshank (1961) that onfy the orbitals of the e basis set form strong d-p r-bonds with the 1-orbitals on oxygen. Cruickshank,s calculations also show that the residual charge on Si is not 4* as predicted by the ionic model but is close to zero in agreement with Pauling's electro- neutrality principle. r Bond order can be defined as the average number of electron pairs per bond. 1590 G. E. BROWN AND G. V. GIBBS
O TREMOLITE
O IUN CUMMINGTONITE
A GLAUCOPHANE
O GRUNERITE
xl
Frc. 1. Difierence, A(i.1), between averageSi O(br) and Si-O(nbr) bond lengths for the Si(1) tetrahedron plotted against the average electronegativity, i, of non-tetrahedral cations bonded to O(nbr) for four C2/m amphiboles.r,r,'ithvacant A-sites:
tremolite CazMgsSLOz(OH)z papike, Ross and Clark (1969) Mn-cummingtonite Cao 2Mn2Mg4 rFeo giaOzz(OH)z Papike, Ross and Clark (1969) glaucophane NazMgz rAlr oFeSisOu(OH)z Papike and Clark (1968) grunerite Fe2FeazMgo sSisOz(OH)z Finger (1969) ^(7,1)= [si(1)-o(7)]-tsi(1)-o(1)l a(5,1)= [Si(1)-o(s)]-tsi(1)-o(1)l A(6,1)= [Si(1)o(6)1-lsi(1)-o(1)]
Allred and Rochow electronegativity values for elements in various oxidatr'on states .l\'ere taken from Table 2.9, Douglas and McDaniel (1965).
(3) the tetrahedral anglesusually decreasein the order O(nbr)-Si-O(nbr) ) O(nbr)-Si-O(br) > O(br)-Si-O(br) (McDonald and Cruickshank, 1967a;Gibbs, 1969).The fact that Si-O(nbr) bonds are usually shorter than Si-O(br) bonds has been convincing evidencein support of Cruick- shank'shypothesis. IIowever, McDonald and Cruickshank(1967a) recog- nized that as the non-tetrahedral cations becomemore electronegativein the series of compounds sodium metasilicate (NazSiO3),wollastonite (CaSiOa), bustamite (CaMnSizOo),rhodonite (Mno.roCao.roXo.o+SiOe) and stokesite(CaSnSiaOs.zIJzO), the difierencesbetween the Si-O(br) and Si-o(nbr) bond lengths decrease.Paralleling this decreasethey also noted a concomitantwidening of the mean Si-O-Si anslefrom about 134o ORDERING IN THE TETRAHEDRAL OF SILICATES 1591
r6 r8
Frc. 2. Difference, A(i,2), between average si-o(br) and (si-o(nbr) bond lengths for the. Si(2) tetrahedron plotted aginst the average electronegativity, [, of non-tetrahedral cations bonded to o(nbr) for the four c2/m amphibores described in the caption of Fig. 1. ^(s,2): tsi(2)-o(s)l_tsi(2)_o(2)l ^(6,2): [Si(2)-o(6)]_tsi(2)_o(2)l ^(s,4): lsi(2)o(s)l_tsi(2)_o(4)l ^(6,4): [si(2)-O(6)]-lsi(2)_o(4)l for sodium metasilicateto 147" for stokesite.The correlation between 1592 G. E. BROTI.NAND G. V. GIBBS
that ite. Similar trends exist for the Si(2) tetrahedron (Fig' 2) except the A(5, 4) and 4(6, 4) are positive in these four amphiboles reflecting highly underbonded nature of O( ) and its high residual electron density, under- a,ir.L Brown and Gibbs, 1969b).The O(2) oxygen is only slightly o(1) bonded resulting in A(i, 2) values intermediate between those for and O(4). TheSi_o_Sianglesinthesefouramphibolesarefairlyconstantrang- ing within about i 5o of the mean value of 141o.Therefore, the variation the io"A1i,j) should be virtually independent of Si-O-Si angle' However' in a a.p.Jir,." of A=t(Si-O(br))l-[(Si-O(nbr))] on Si-O-Si angle Figure number of silicates containing both O(br) and O(nbr) is shown in A' 3, indicating that angle also plays a significant role in determining -170o; data The A'talue is negative for angles greater than the two points at 180", *hi.h ,"pr.sent thortveitite (SczSizOr)(Cruickshank' (SrVSizOz) ,t oL, |OOZ;Prewitt, personal communication) and haradaite (Si-O(nbr)) bonds in these (Takeuchi and Joswig, 1967), show that the which structures u." ui long or longer than the (Si-O(br) ) bonds, a result the is apparently at variance with the expected stereochemistry of on A is SirO;; ion (Cruickshank, 1961)' The effect of Si-O-Si angle and evidently as important as the efiect of the non-tetrahedral cations hara- explains, in pari, the Si-O bond lengths in both thortveitite and (Si-O(nbr)) duit". In facl, when both f, and Si-O-Si angle are large, the is bonds should be longer than the (Si-O(br)) bonds; however, when i than or small, (_1.g or lessj the (si-o(nbr)) bonds should be shorter result equal'to the (Si-O(br)) bonds, irrespective of angle' The same The should be true when the si-o-si angle is narrow, irrespective of i. that correlation coefficient for the data in Figure 3 (-0.67) indicates in terms of a only about 45 percent of the variation in A can be explained below linear dependenceon si-o-si angle; the scatter of data above and to the the regressionline near 140" can be related,,with a few exceptions, values u.r".ut. electronegativity of the non-tetrahedral cationsl those plottiig above the line are from structures containing relatively electro- factors poritirrl cations in comparison to those below' Certainly, other (2) the s,rchus (1) the isovaleni hybridization of the orbitals on oxygen' forma- number of lone pair orbitals on oxygenr available f or d-p zr-bond equally tion, and (3) geometrical and electrostatic effects must play an importantroteinttrevariationofSi-o(br)andSi-o(nbr)bondlengths. In fact, the correlation between (Si-O) and the mean coordination Shannon number of the oxygens bonded to Si (Gibbs and Brown, 1968;
oxygens, r -0, -1 and, -2 in silicates containing four-, three- alld two-coordinated respectivelY. ORDERING IN THE TETRAHEDRAL OF SILICATES 1593
0.08 ooo € o E o^d 5 0.06 \ c \E o 'cz| 0.04 \\ o tVr ta' I o.o2 o r,^.-1 oo t e o.oo o I 160 lScr si-0-si Frc. 3. Variation of A=[(Si-O(br)>]-[ o.t4 F t -o c o.t2 o o.to o_I ,V, I o F c ! o 8:o4 )ad. 11 O.O2 \ o.oo t20" t400 1600 t800 P-O-P Frc.4. VariationofA=[(P-O(br)>]-[ ]withP-O-Pangleforthefollow- ing phosphates: B-Mg2P2O7(Calvo, 1965a); F-ZnzPzOz(Calvo, f965b); a-MgzPzOz(Calvo, 1967);a-CazPzoT(Calvo, 1968);NarPzor.l0Hzo (Cruickshank, 1964a);NasProro (Cruick- shank, 1964b); (RbPOr)- (Cruickshank, 1964e); NazHzPrOu (Jarchow, 1964); (NaPOa)" (McAdam et a1,.,1968); NarPrOrz.4HzO (Ondik, 1964); a-CuzPrOz (Robertson and Calvo, 1967); p-CuzPzOT(Robertson and Calvo, 1968). the Si-O-Si angle (Brown, Gibbs, Ribbe, 1969b). Cannillo, Rossi and Ungaretti (1968) have prepared a similar plot except theirs correlates the averageSi-O(br) length to Si-O-Si angle for two tlpes of tetrahedra: those with bridging oxygens only and those with both bridging and non- bridging oxygens.Figure 5 shows that in silicatescontaining both O(nbr) and O(br), (Si-O(br)) dependsin part on the Si-O-Si angle,the shortest onesbeing associated with the widestangle. Such a correlationis expected if some degree of d-orbital participation (Cruickshank, 1961; Lazarev, 1964; Cotton and Wilkinson, 1966; Mitchell, 1969) is important in determining the variation of Si-O bond lengths and the steric details of the tetrahedral portion of a silicate. The increasein Si-O-Si angle with the shorteningof Si-O bond length may be considereda means of (1) maximizing the zr-orbital overlap, (2) minimizing the resulting repulsions between the increasedelectron density in the partial double bonds, (3) minimizing the repulsions between the positive charges on the Si ions (Mitchell, 1969) and (4) increasingthe fraction of s-characterin the ORDERING IN TIIE TD,TRAHEDRAL OF SILICATES 1595 E r.680 o r.660 I 640 -o O I |.620 (t') I 600 1.580 120. I 60' | 80' si-0-si Frc. 5. Variation of mean Si-O(br) bond length i,r'ith Si-O-Si angle for a number of silicates containing both bridging and non-bridging oxygens. Data from the structures listed in the caption of Fig. 3 u'ere used. Si-O bonds (Fyfe, 1954).Brown, Gibbs and Ribbe (1969a)have made similar correlationsbetween the Si-O(br) bond lengths and Si-O-Si angles in the framework silicates which contain only bridging ox_vgens. The slope of the regressionline in Figure 5 is statistically identical to that found for the same correlation with the data from the SiO2poly- morphs; however, its intercept is -0.035 A greater than that for the SiO2polymorphs for a given Si-O-Si angle"This increasein averageSi-O bond Iength can be attributed, in part, to the perturbating effect of the non-tetrahedralcations on the Si-O bond, to the absenceof O(nbr) and to the constant coordinationnumber of O(br) in the SiOzpolymorphs. The variation of (P-O(br)) bond length versus P-O-P angle from structurescontaining both O(br) and O(nbr) is shownin Figure 6 and is similar to the variation shown in Figure 5 for the silicates.The slopesof the regressionlines in Figures 5 and 6 are identical (-0.001, a:0.003) resulting in a constant difference of -0.05 A o.ner the entire range of f-O-T angles.This differenceis the same as that between the Si-O (1.76 A) and the P-O (1.71 A) single-bondvalues predicted using the Schomaker-Stevenson(1941) equation and implies similar degreesof d-orbital participation in the Si-O(br) and P-O(br) bonds. Gillespieand Robinson (196$.;however, suggest that Si-O(br) bonds are generallyof higher bond order than P-O(br) bonds. 1596 G. D. BROWN AND G. V. GIBBS r.640 o o t.620 o@ o r.600 c _o t.580 o I o_ 1.560 r.540 r.520 1200 160" P-O-P Frc. 6, Variation of mean P-O(br) bond length with P-O-P angle for a number of phosphates containing bath bridging and non-bridging oxygens. Data from the structures Iisted in the caption of Fig. 4 were used. Additional data points are from: (NHa)r PrOr: (Cruickshank, 1964c); PzOs (Cruickshank, 1964d); PrOs (Beagley et al",1967) V.rnrarroN or Z-O(br) eNl Z-O(nbr) BoNl LnNcrHS wrrH O-f-O ANcr-B In a comparative study of the tetrahedral distortions in chlorates, sulfates,phosphates and silicates,McDonald and Cruickshank (1967a) have correlated (?-O) bond length with non-bonded O ' ' ' O distance in O-T-O linkages and have concluded from the negative slopes of the silicate and phosphate lines that O(nbr) have larger negative electronic charges than O(br). Figure 7 is a revision and modification of their Figure 4 including new data for O-Si-O and O-P-O tetrahedral angles and the addition of a few data for O-AI-O angles taken from structure analysesof sapphirine (Moore, 1969a)and sillimanite (Burnham, 1963)' Gibbs (1969)found that the majority of the tetrahedralangles in proto- amphibole decreasein the order O(nbr)-Si-O(nbr))O(nbr)-Si-O(br) >O(br)-Si-O(br) and argued that this order can be consistentlyinter- preted in terms of Cruickshank's (1961) d-p zr-bondinghypothesis and Gillespie's (1963) Valence Shell Electron-Pair Repulsion Theory' The new data for silicateswith both O(br) and O(nbr) corroboratethis inter- pretation as well as that proposed by McDonald and Cruickshank (1967a). However, these two interpretations are not mutually exclusive becaused-p r-bond formation gives a polarity to the Si-O bond similar ORDERING IN THE TETRAHEDRAL OF SILICATES r.80 ,//. / r.70 € t.60 +o r50 o O(br)-T-O(br) o O(br)-T-O(nbr) o O(nbr)-T-O(nbr) t.40 2.40 2.60 2.80 3.OO o o(A) Frc. 7. variationof meanz-o bondlength with o . . . o nonbondeddistance in o-r- sapphirine(Mgr.sAls.oS\.sOzo) (Moore, 1969a); sillimanite (Alrsirot (Burnham,1963). Data for o-P-o linkagesare the same as thoselisted in the captionsof Fig. 4 andFig. 6 andare encircled with a dashline. to that predicted from electrostatic considerations with the negative charge concentrated in the vicinity of the oxygen atom (Bissey, t967; Mitchell, 1969). The data for phosphatesfollow a similar but much less well-defined trend (correlation coeftcient: -0.31), somewhat at vari- ance with that reported by McDonald and Cruickshank (1967a). Cotton and Wilkinson (1966) have suggestedthat d,-p r-bond, forma- tion between Al, si and o may account for the nearly copranar arrange- ment of one Si- and two Al-cations about each oxygen in tetramethyl- oo'-bistrimethylsilyl-cyclodialumoxane. More recently, estimates of the d-p zr-overlapintegral (0.18) for the Alor'- tetrahed.ralion together with correlations of Al-o bond lengths with Al-o-si angles and data from X-ray emission studies have led Brown, Gibbs and Ribbe (1969a) to suggest that d.p zr-bondingalso plays an important role in the varia- tion of the Al-o bond lengths in the framework silicates. If these argu- ments can be extended to all structures containing tetrahedral Al, Al-O(br) bonds should be longer, in general, than Al-O(nbr) bonds 1598 G, E, BROWNAND G. V' GIBBS providing the efiectsof i and T-O-T angle on AI-O bond lengths are not iignificant. The curve constructed for the small number of data in Figure 7 for AIOa tetrahedra with both O(br) and O(nbr) is roughly horizontal' This indicates that the Al-o(nbr) bonds in sapphirine and sillimanite are not shorter or of higher bond order, on the average,than the Al-O(br) bonds. If the efiects of the AI-O-Si angle and ! are ignored, the Si-O bond Iengths in sillimanite (Burnham, 1963) also appear to be at vari- ance with double bonding; the Si-O(nbr) bond (1.629 A) is longer than Al-O" and Al-Oa, respectively, is predictable and not at variance with the hypothesis of double bonding. In other words, when i and Z-O-? ungle a.e both Iarge (?:Al, Si), the (f-O(nbr)) bonds are expectedto be longer than (?-O(br)) bonds; but when i is large and the angle is ,rurro*, the (?-O(nbr)) bonds are expected to be shorter than or equal to the (r-O(br))) bonds. TBrnauBpnAL ORDERTNcrN Srrrcarns The well-known Al-avoidance rule (Loewenstein, 1954), which Gold- smith and Laves (1955) explained in terms of Pauling's rule of local va- Ienceneutralization, is usually invoked to explain the observed distribu- tions of tetrahedral Al and Si and the almost total absenceof tetrahedral AI-O(br)-At linkages in silicates.As discussedabove, valence neutraliza- tion is believed to be achieved by some means of charge transfer from anion to cation, whether it is by ionic or covalent bonding, or more probably, by a mixture of the two, including a degree of electron de- localization associatedwith double bonding. If double bonding is sig- nifi.cant in the tetrahedral portion of a silicate, valence neutralization involving Si-O, Al-O, Mg-O, B-O or Be-O bonds, as well as the distribu- tion of these'cations, should.depend, in part, on their bond orders' Be- cause a difference exists between the predicted zr-bond orders for the 1 In casesof significant Iocal charge imbalance at oxygen in structures containing O(br), and I-O-? e.g., the highly underbonded nature of O" in sillimanite, ?-O bonds shorten angles widen lo contribute to valence neutralization. On the other hand, for highly over- booded o*ygens, e.g., 06 in sillimanite, ?-O bonds lengthen and ?-O-I angles close' ORDIJRINGIN TI]IJ TETRAI]EDRAL OF SILICATES 1599 Si-O (0.32),Al-O (0.18),Mg-O (0.08),B-O (0.0) and Be-O (0.0) bonds in tetrahedral ions, a mechanismfor tetrahedral ordering based on the relative bond orders of the ?-O bonds is proposed. Recalling that Z-O(br) bonds in T-O-T linkages with wide anglesare usually of higher bond order than those involved in narrow angles and that Al, B, Be and Mg have lower "zr-bondingpotentials" in tetrahedral coordination than Si, the following proposal concerning tetrahedral site preferencein framework silicatescan be made: Si should prefer those tetrahedral sites involved in the widest averageT-O-T anglesand Al, B, Be or Mg thoseinvolved in the narrowestaverage T-O-T angles. This proposal is examined below for a number of silicates anC appears to apply to the framework but not to the non-framework silicatesin general. The ordering of Al and Si in the framework silicate low albite (Ribbe, Megaw and Taylor, 1969)has been discussed(Brown, Gibbs and Ribbe, 1969b; Stewart and Ribbe, 1969) in terms of the proposal,and it was pointed out that AI, with lower predicted "zr-bonding potential" than Si, prefers the Zr(0) site, in part, becausethe average ?'(0)-O-? angle is 3 to 10o smaller than the average T-O-T angles to the lr(m). Iz(0) and T2(m) tetrahedral sites. In disorderedhigh albite (Ribbe et a1,.,1969) the average T-O-T anglesto the T1(m), fr(0) and,Tz(m) tetrahedra are all slightly smaller than those in ordered low albite, whereasthe average Z1(0)-O-" angle is larger. Therefore, it appears that upon ordering the structure adopts a configuration which tends to optimize the overlap of dr- and pzr-orbitalson ? and O, respectively, with wider Z-O-? angles being formed at the Si-rich sites. Ideally, we would also expect the angle at the Al-rich site to widen with ordering. However, this does not take place, possibly becausethe change of angle for the Al-rich site will have less effect in altering the potential energy of the structure than cor- responding changesin angle at the Si-rich sites. Becauseof the precedingobservations, llable 1 was prepared including data from eight additional, precisely determined framework structures containing Si and Al, B, Mg or Be in tetrahedral coordination.In each casethe average T-O-T angles to the Si-rich tetrahedra are widest with the possibleexception of maximum microcline where the average T-O-T angles to the Si-rich sites is only 0.3o wider than that to the Al-rich site. However,tetrahedral Al in Iow albite, osumilite,low-cordierite, laumont- ite and natrolite, tetrahedral B in reedmergnerite,tetrahedral Be in beryl and tetrahedral Mg and Al in Mg-rich cordierite all prefer those sites in- volved in the narrowest averageT-O-T angles,agreeing with the smaller predicted degreeof dzr-orbital participation of Al and Mg relative to Si ,1600 G. E. BROWN AND G. V. GIBBS Tesr,B f : Awnecr ?-O-? Arcrns lon Sr-Rrcs axo Ar,-, B-, Mc- on Br-Rrcn Tntn.tnronl, rN Nrrr FRAMEwoRKSrr,tc.tros. Low albite l4l .7" 136.00 Ribbe, el al. (1969) Reedmergnerite 140.2" 136.0o' Appleman and Clark (1965) Maximum microcline 141.90 l4l.6" Finney and Bailey (1964) Osumilite 150.10 125.00 Brown and Gibbs (1969a) Beryl 168.3' 127.0"b Gibbs, Breck and Meagher (1968) Low-cordierite 145.30 139.7" Gibbs (1966) Mg-rich cordierite 151.60 129.0o" Meagher and Gibbs (1967) Natrolite 145.2" 142.20 Meier (1960) Laumontite 140.30 136.4" Schrammand Fischer (1970) ' B-rich tetrahedra b Be-rich tetrahedra " Mg, Al-rich tetrahedra and the negligible degreesof dzr-orbital participation expectedfor the B and Be atoms. The proposal cannot be verified for those framework sili- cates like anorthite which consist of a perfect alternation of Al-rich and Si-rich tetrahedra (Megaw, Kempster and Radoslovich, 1962) because the T-O-T angles at the Al-rich sites must perforce equal those at the Si-rich sites on the average. The proposal is also consistent with the distribution of Al and Si in the rare, non-framework silicate zunyite (Pauling, 1933; Kamb, 1960) where Si is ordered into a lrOro group consisting of four peripheral tetra- hedra with three O(nbr) and one O(br) and a central tetrahedron with four O(br) and where Al is ordered into an isolated tetrahedron with four O(nbr). The ?a point symmetry of the TsOrogroup requires that the T-O-T angle equals 180o permitting maximum d-p r-overlap' This example suggests that T-O-T angle may play a role in tetrahedral ordering in silicates containing both O(br) and O(nbr). Ilowever, Zagal'skaya and Belov (1962) question the Pauling-Kamb distribution and suggestthat Al occupiesthe central tetrahedron in the TsOroErouP with Si occupying the isolated tetrahedron. The Zagal'skaya-Belov distribution results in severe charge imbalances and violates the pro- posal on tetrahedral ordering. Nevertheless,because the estimated bond length and angle errors are relatively large (Kamb, 1960) and because the Si-O(br) bonds are somewhat longer than expected for a straight Si-O-Si angle and a relatively large i, a study of F- and OH-containing ORDERINGIN THE TETRAIIEDRAL OF SILICATES 1601 zunyites is currently underway at VPI to clarify the AI/Si distribution as well as to establish the steric effectsinduced by replacing OH by F. Papike, Ross and Clark (1969) have refined the structure of the Kakanui hornblende and have reported the following Al/Si occupancies estimated from a Smith-Bailey type plot (Smith and Bailey, 1963) for the ?(1) and,T(2) sites in the double chain: f(1) (0.34 Al, 0.66 Si), fQ) (0.16 Al, 0.84 Si). In this laboratory K. Robinson (pers.commun.) has since undertaken a site refinement for the Kakanui hornblende as well as for pargasite and kaersutite and has found that the ?(2) site in each contains only Si whereasthe site contains equal amounts of both Al and Si. However, these distributions"(1) are not consistent with the proposal on tetrahedral ordering becausethe average T-O-T angle to the Al-rich site is 0.2 to 1.0olarger than that to the Si-rich site. In view of this observation, additional factors such as local charge balance and the number of available lone pairs on oxygen must be operative in con- trolling the preferenceof Al for the ?(1) site. Gibbs (1969) has explained the distribution of AI and Si in these minerals in terms of the under- bonded nature of O(a) and the suggestionthat a relatively strong zr-bond forms between Si(2) and O(4). Further examination shows that because all other oxygensare effectively four-coordinated and probably lack lone pairs, O(4) is the only oxygen in these hornblendes which may have a lone pair orbital available for strong r-bond formation. Accordingly, becauseSi has a higher "zr-bonding potential" than Al, Si probably pre- fers the T(2) site in order to take advantage of this lone pair in spite of the slightly wider average T-O-T angle to the T(2) site. The ordering of Be and Si in the Be-containing amphibole, joesmithite, (Moore, 1969) can be rationalized in a similar fashion as pointed out in part by Moore. The general lack of Al/Si ordering in the layer silicates has been dis- cussedby Bailey (1967) who concludesthat tetrahedral ordering is more difficult for a layer silicate than for a coexisting phase such as microcline or low albite. However, one excdption is 3I muscovite (Giiven and Burnham, 1967) where partial ordering of AI and Si is indicated by the mean ?-O bond lengths. In the majority of sheet silicates all tetrahedra are of one basic type: the correspondingbridging and non-bridging oxy- gens for each tetrahedron have nearly identical coordination numbers and in any one sheet structure the average T-O-T angle for each tetra- hedral site is constant. This results in tetrahedral sites of similar "r- bonding potential" and may explain the absenceof ordering in most of these structures. A similar lack of tetrahedral Al/Si ordering is char- acteristic oI the C2/c pyroxenes (Peacor, 1967) becausethere is only one unique T-O-T angle and, as in the sheet silicates, only one unique type of tetrahedron. 1602 G. E. BROWNAND G. V. GIBBS The proposal on tetrahedral ordering was not tested for the melilites (Smith, 1953a; Louisnathan, 1969). YzSiBezOz(Bartram, 1969) or sapphirine (Moore, 1969a) becauseall of the T-O-T angles are not re- ported. Examination of local charge balance and coordination of oxygen in these structures, however, offers no explanation for the observed tetrahedral distributions. The most serious violations of the proposal made for the framework silicatesare found in the non-framework silicates delhayelite (Cannillo, Rossi and Ungaretti, 1969), zussmanite(Lopes- Vieira and Zussman,1969) and bavenite (Cannillo, Coda and Fagnani, 1966) where Si is found in tetrahedra with the smaller average T-O-T angles.These violations indicate that the proposal cannot be extended to include non-framework silicates in general and thaL the effect of T-O-T angle is not the factor controlling tetrahedral ordering in these structures. The Be/Si distribution in leucophanite (Cannillo, Guiseppetti and TazzoIi, 1967) and meliphanite (Negro, Rossi and Ungaretti, 1967) can be related to the presenceof ?OsF tetrahedral ions. Becausethe p- orbitalson fluorinewill be smallerthan thoseon oxygen,the Si(3d)-F(2p) overlapwill be lessthan the Si(3d)-O(2p)overlap, leading to the ordering of Be into the ?OeF tetrahedra and of Si into the ?O+ tetrahedra. ?Os(OH) and ZOr(OH)z tetrahedra also show a stronger _affinity for cations other than Si or Al (for example, Zn in hemimorphite [McDonald and Cruickshank,1967b], Be in aminoffite fcoda, Rossi and Ungaretti, 1967]. epididymite llto, tO+71,euclase [Mrose and Appleman, 1962f and bertrandite [Solovievaand Belov, 1961] and B in datolite [Pant and Cruickshank,1967]), suggesting that the 2-orbitalson the hydroxyl oxygen are reduced in size, leading to smaller d-p r-ovetlap and a loss of double-bond character in the f-O("' H) bonds (Cruickshank, 1961; Cruickshank and Robinson, 1966). The segregationof Be into fOB(OH) tetrahedra in bavenite is consistent with this reasoning. In conclusion. the basic stereochemistry of the tetrahedral portion of a silicate is dictated primarily by the constraints imposed by ionic and o-covalent bonding requirements. Cruickshank's zr-bonding hypothesis representsa refinement of the theory and provides a more flexible frame- work within which the finer structural details can be rationalized. His hypothesis also permits an interpretation of the SiKB X-ray emission (Dodd and Glen, 1969)and L2,3MX-ray fluorescencespectra of Si (IJrch, 1969) for silicate minerals and glassesin terms of qualitative correlation diagrams deduced from (1) symmetry properties of the molecular orbi- tals for a SiOaa-ion with fd symmetry and (2) estimates of relative binding energiesof electronsin the atomic orbitals on oxygen and silicon. On the other hand, Mitchell (1969)has stated that "one cannot . . ex- ORD]'RINGIN THE TLTRAHEDIIAL O1IYLICATES 1603 pect experimentsto establishwhether d-orbitals are 'really' used, any- more than experimentscan show s and p orbitals definitely occur in the bonding of first-row elements." AcKNoWI,EDGMENTS The authors would like to thank Professor D. W. J. Cruickshank of the Chemistry Department at the University of Manchester Institute of Science and Technology, Man- chester, England, M. W. Phillips and ProfessorsF. D. Bloss and P. H. Ribbe of the De- partment of Geological Sciences and Professor J. C. Schug of the Chemistry Department, the Virginia Polytechnic Institute at Blacksburg, Virginia, Dr. J. W. McCauley at the Army Materials and Mechanics Research Center, Watertolvn, Massachusetts and Professor C. T. 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