THE CANADIAN fiilNERALOGIST

THE CANADIAN fiilNERALOGIST Journal of the MineralogicalAssociationof Ganada Volume 2l

May 1983

Part 2

Canadian Mineralogist Vol. 21; pt.2, 173-48O.

THE CRYSTALCHEMISTRY OF THEAMPHIBOLES F. C. HAWTHORNE Departmenlol Earth Sciences,University of Manitoba, Winnipeg,Monitoba R3T 2N2

Keyv'ords: amphiboles, crystal chemistry, review, structure. spectroscopy.

ABSTRACT

Much experi,mentalwork on the erystallography and crystal cLemistry of the amphiboles has appearedsince the studies of Warren (1929, 1930) and Warren & Modell (1930b). Crystal-structure refinement and absorption spectroscopyhave played a major rolo, particularly in the past twenty years. Over 70 crystal structures bave been refined, and *120 amphiboles have been characterized by Mihsbauer sp€ctroscopy.Thore has been considerable work in infrared-absorption spectroscopy,and electronic-absorptionslrectroscopyis becoming increasingly important. Scattered through the scientific literature is much miscellaneousexperimental work on amphiboles: X-ray photoelectron spectros coly, diffuse'reflectauce spestroscopy, Raman spectroscopy,nuclear magnetic-resonancespectrosqlectroscopy, neutfon copy, electron-spin-resonance i,nelastic-scattering spectroscopy,oxidationdehydroxylation studieo, measurementof elastic, magnetic and electrical propefiies, characterization cf deformational behavior. This information has been assembledhere, and all derivative data have been recalculated to remove (numerous) misprints and errors in the original publications. In addition, these data have been criticaly assessedas to quality and significance.The result is a consistent data-set tbat may form the basis for further studies. Amphiboles belong to five principal strusturetypes, with qrace groups C2/m, P2/a, Hh/m, Pnmo, arrd Pnmn, bat the C2/m ad Pnma stnrctures are by far the most common. The M(4) site is of major importance in amphibole crystal chemistry. Tho large X cation that occupies M(4) is the primary feature on which the current nomenclature of the amphiboles is based; amphiboles with differing' M(4) occupancies are generally immisciblg and thus the resulting classification is natural and convenient. Compositional variation in the amphiboloscan generally be correlated with structural variations; such correlations are useful to derive cry*allochemical information where the experimontaldata give ambiguousresults.

Sour"rane La cristallographie et la cristallochimie des amphiboles ont fait I'objet de nombreux travaux expdrimentaux depuis les d6couvertesde Warren (1929, 1930) et de Warren & Modell (1930b). Parmi ceux-ci, l'affinement de la structure cristalline et l'6tude du spectred'absorptionont jou6 un r6le important, surtout au cours des vingt derniEres ann6es. Plus de 70 affinements ont 6t6 r6alis6s, et environ tZO 6chantillons d'amphibole ont 6t6 caract6ri€s par spectroscopieMiissbauer. On note de grands progrls en spectroscopie par atrsorption infrarouge e! de plus en plus, par absorption 6lectronique.On trouve aussi, 6parpill6s dans la litt6rature scientifique, nombre de r6sultats expdrimentaux sur les amphiboles: d'une part, 6tud€s spectroscopiquesde divers types (photo6lecffons rayons X, r€flectance diffuse, Raman, r6sonance nucl6aire magn6tique, r6sonance de spin 6lectronique, dispersion in6lastique des neutrons) et, d'autre part: 6tudes d'oxydation et de d6shydroxylation, mensuration des propri6t6s 6lastiques, magn6tiques et 6lectrigues, comportement sous contrainte. On prdsenteici toutes ces donn6es rassembl6es,tous calculs v6rifi6s pour 6liminer de nombreusesfautes d'impression et erreurs des m6moires ori.iginaux. De plus, on a 6valu6 de fagon critique la qualit6 et la port6e de ces donn6es.Il en r6sulte une collection coh6rente de donu6es qui peut servir de point de d6part, aux travaux futurs. I*s amphiboles se r6partissenten cinq types de structure prinpipaux, de groupes spatiavx C2/m, Y2/a, Y\/rn, Pnma et Pnmn, parmi lesquels C2/m et Pnma pr6dominent. La posilion M(4) posslde une girande importance dans la cristallochimie des amphiboles: le cation X (de grande taille) qui en occupe les sites d6termine largement, en fait, la nomenclatureactuelle. Deux amphiboles qui diffdrent par la composition cationique des

t73

174

THE CANADIAN MINERALOGIST

sites M(4) sont g6n6ralement immiscibles; la classification fond6e sur M(4) est donc naturelle et commode. En g6n€ral, on parvient i 6tablir une corr6lation entre variations de cbmposition et variations structurelles. Ces corr6lations peuvent fournir pour de I'information cristallochimique lever I'ambiguit6 des r6sultats d'exp6riences. (Iraduit

par la R6daction)

Mots-clAs: amphiboles, cristallochimie, revue, structure, spectroscopie.

INrnouucrroN The amphiboles are the most complex group of rock-forming minerals, exhibiting wide chemical variation and a bewildering variety of paragene$es. They are common constituents across ttre complete range of igneous rocks, from acid (Borley 1963, Lyons 1976) to ultrabasic (Onuki 1964). In sedimentary rocks, amphiboles occur both as detrital (Blatt et al. 1972, Pettijohn 1975) and authigenic phases (Milton & Eugster 1959, Milton et al. 1974). In nietamorphic rocks, amphiboles are important constituents from very low grade to high grade and over a wide variety of rock compositions. Changes in amphibole composition with increasing grade of metamorphism in specific areas are well documented (Compton 1958, Engel & Engel 1962, Binns 1965, Fabries 1968, Hietanen 1974) but the effects of bulk-rock composition are not well understood. The occurrence of amphibole in mafic and ultramafic nodules in calc-alkaline and basaltic rocks led to the suggestion that amphibole is a mantle phase (Green & Ringwood 1963), and the principal source of KgO (Oxburgh 1964, , Hart & Aldrich 1967). Although not common, amphiboles are also found in meteorites; these are usually fluor-richterite (Olsen 1967, Olsen et al. 1973, Graham et al. 1976), but hydroxyamphiboles (kaersutite) have recently been found (Floran et al. 1978). The discovery of amphiboles in lunar rock (Gay et al. 1970, Dence et al. l97l) completes the list of paragenese$ of these minerals. The occurrence of fluorrichterite parallels its fairly common occurrence in meteorites, but the discovery of tschermakite as a possible hydroxyl-bearing lunar phase is intriguing. The amphibole structure is one of great chemical compliance (Ernst 1968), and the wide chemical variations within this group may be seen as arising from the general geometry of the structure. In each structure-type, several crystallographically unique sites occur; these sitesmay accommodatecations of formal charge

* 1 to *4 and ionic radius 0.25 to 1.6 A. Inspection of proposed average compositions of the crust (Holmes 1965, Ringwood 1969) shows that all major cations fall within this range, reflecting the ubiquity of these minerals. Despite the complexity of the amphiboles, they have been the object of considerable attention in the past hundred years. Schaller (1916) was first to derive the formula of tremolite when he recognized that hydroxyl is an essential constituent of that mineral. Tschermak (1872) recognized that there is a strong relationship between the chemistry, physical properties and paragenesis of the pyroxenes and the amphiboles. Warren (1929) and Warren & Modell (1930b) showed that this relationship also extended to the unit-cell dimensions and diffraction patterns, and solved the structures of tremolite and antfrophyllite by analogy with the known structures of diopside (Warren & Bragg 1928) and enstatite (Warren & Modell 1930a). Warren (1930) and Kunitz (1930) showed the structural and chemical homology of the amphiboles, emphasizing the importance of both homovalent and heterovalent substitutions to the chemistry of this group. The considerable effort expended on the structural chemistry of the amphiboles in the past fifteen years has been aided by extensive automation of equipment in the fields of X-ray diffraction and mineral analysis, and by the application of spectroscopictechniques to problems in amphibole chemistry. The resulting proliferation of structural and chemical data has led to an increase in our understanding of the complexity of these minerals. The structural details of a considerable number of natural (and synthetic) amphiboles have now been fairly well characterized, and a general survey of the results is presented here. Structural, chemical and spectroscopic data are listed and cross-correlated in a series of appendices.In the numbering system used, [ ] and ( ), respectively, denote orthorhombic and monoclinic amphiboles for which crystal-structure data are available: { } and ( ) denote amphiboles characterized by Miissbauer and infrared spectroscopy,respectively; the keys to this system are found in Appendices A-E -> { } and O, AppendicesF and G + { }, Appendix G -> < >. All isomer shifts have been normalized relative to that of metallic iron. A synopsis of the information presented here is given by Hafihorne (l98la, b); however, it should be stressed that the latter articles are instructional and do not incorporate the amount of critical assessmenteiven here.

THE CRYSTAL CHEMISTRY OF THE AMPHIBOLES

Cr,essrrrc.etroNAND NonanNcretunp The information contained in this section is taken from the report of the I.M.A. Subcommittee on Amphiboles ([rake 1978), the addendurn to this report (Leake & Hey 1979) and kake (rers. comm.). A standard amphibole formula may be written as: Ao-rBzCsT8O22(OH,F,Cl) 2 where A : Na,K; B : NaIi,Ca,Mn,Fe2+, Mg; C : Mg,Fe2+,Mn,A1,Fe3+,Ti,Li,and T : Si,Al. The assignment of cations given above is by no means comprehensive, and a more detailed examination of group and site occupancieswill be given in a later section. The classification of the amphiboles is based largely on crystal chemistry, having as its basis the chemical contents of the fornula unit calculated to 24(O,OH,F,CI), where possible. A large number of amphiboles are now routinely analyzed by electron microprobe, and the Fes+lFe3+ ratio is not derived experimentally. There are general techniqueswhereby this ratio may be calculated; these are examined more closely in the next section. Leake & Hey (1979) suggestedcalculating the fonhula on the basis of thirteen cations excluding Ca, Na and K, and then adjusting the Fe'z*/Fee+ ratio to bring O + OH to 24 or O to 23. In this classification, principal stoichiometries are identified by generally well-established names, with prefixes and adjectival modifiers to indicate the presenceof substantial substitutions by ions that are not essential'constituents of the end members. Prefixes are an inseparable part of the name and should be attached by a hyphen; consequently, an amphibole should be indexed, under (the initial letter of) the prefix, with perhaps a cross-referenceunder the species name. Adjectival modifiers are not an essential part of the amphibole name, but are simple adjectives ending in -ian or -oan according to the valency of the substituting ion- They denote minor substitutions and are not an essential part of the amphibole name; consequently, they are not used in the first stage of indexing, and the amphibole should be indexed under its speciesname. Prefixes and adjectival modifiers of general application are listed in Table 1, together with . the limits and restrictions on their use. A$ditional adjectivesmay be approved as needed Q.s., nickeloan, cuprian). A few prefixes must be defined differently in the different amphibole groups; these will be given later. The prefixes magnesio-, ferro-, alumino- and ferri-

TABLEI.

t75

PREFIXES AI{DADJECTIVAT IIODIFIERS FORTHEAI.IPHIBOLES

Prefires s€e Tables 2, 3 and 4, also text whenCl:1.00* ({42 Cl) whs Crzl.oo (*9X Cr2\) whenFe32l'00 1"Sf rir6r) except ln alkall anphJboles and hastlngslte ferrcsee Tables 2, 3 and 4, also text fluorwhenF:1.00 (r2U F) Itydrowhen0H:3.00 (r3% Hrl\ mnganese- whenMn:I.00 ("10%ilno) except ln end-mmbers containlng l,4n nagneslo- see Tables 2, 3 and 4, also text oxywhen (oH+FiCs)is confimed as O.5O ; T i < O . 5 0 ; F e 3 +< A l v l

t.o

PA@StTrC

t

I

Me Mg+Fe2+

I

STLICIC

o.7 o.5 o.3

ENN ?ABN11IC

SILICIC

MIGBDENIlE

PARNIIE

ssG

EDE!ITIC HONBLME

PA(CASI1lC

rEUO-'ArcAS

lIE

HOf\BLENDE

o.o

'rf,::.:

MRrcN

UOIXBLEND!

'EUG

lrcEDilIT!

o,

PNCNIE

IONBLND!

gON!LNDE

DSIE

( N o+Ko>O.sOfi < O.5O ; Fe3lAl

r.o

I

EDENITIC EDINIIE

uoEsl0EDENITIC

SILICIC EDSITE

IO&\BLNDE

DNII!

tsatN6lTIc

UCNESIESSTINCSIE

HONALNDE MESTN NCNESIN

SSTINCSITE

UONALNDE

rERRG STLICIC

ERRGEDlNITE

tDE!_lTlC

usTlN6rlrc

ERGIDENIlE

SORNB!ONDE

o.o

HNT!NC3IT

IONBIEME

Ti > O.50

t

uft."' o.o 7.5O

7.25 *

Si -

650

6.25

Frc. 2. The nomenclature of the calcic amphiboles lmodified from Leake 1978)].

percentagesof the oxides or elements present. was given by Hey (1939). A chemical analysis To calsulate the contents of the unit cell from provides the ratios of the chemical constituents this information is not a sfiaightforward matter; in the structure, and calculation of the unita useful discrusion of the inherent problems cell contents requires normalization to some

THE CRYSTAL CHEMISTRY OF THE AMPHIBOLES

t79

( N q +K L . o .s O

l''

III{CHITE

BARROISITE

Mg

M;:Gi"o'5 FERROI,III{CHIlE

FERRO-BARROISITE

o.o 8.O

7.5

6.5 Si p.f.u. ---+

6.O

(No+Kl >O.50

l''

I

RICHTERITE IIIAGNES I O-KATOPHOR ITE

Mg

|4ACNESt0TAMIIITE

uffi'o's FERRORICHTERITE

KATOPHORIIE

TARATIIIE

o.o 8.O 7.5 +--si

6.s

6.0

p.f.u._..+

Ftc. 3. The nomenclatureof the sodic-calcicamphiboles[after Leake (197g)].

standard basis that is characteristic of the structure. This may be done in two ways. If the density and unit-cell volume are known. the analytical ratios may be scaled by these values to give the empirical unit-cell contents (Hey 1939) that are based entirely on experimental measurements.The difficulties associated with obtaining a good value for the density (purity of sample, presenceof fluid inclusions, occluded space and adsorbed species) usually preclude this method. The alternative method is to scale the ratios to some basis that relates to the crystal structure; this is called the unit.cell contents (Hey 1939). This second method is by far the most common method of amphibole recalculation.

Thc chemical complexity of the amphiboles has given rise to numerousdifferent normalization schemes. We will first examine those schemes that do not involve any adjustment of the Fe'i'lFc'- ratio. 24 (O,OH,F) This method, which assumesthat the total anion content of the formula unit is twentyfour, was introduced by Warren (1929, 1930) following the solution of the amphibole crystal, structure, There is no direct evidence to suggest anion vacancies in amphiboles themselves. Polysomatic intergrowths may give rise to anion vacancies, particularly at their terminations,

180

THE CANADIAN MINERALOGIST

( N o + K ) A> O . 5 0

0.o ARFVEDSOI{I]E FERRO-ECKERIIANI{ITE (KozuLrre rr lln. >2,5)

Mg

u[P;'o's

II +

ECKERI{ANNITE

t.o o.o

f'IAGNES I O-ARFVEDSON I TE

t.o

o.5 p"t+/(f ettAtvr )-

( N o + K ) o< O . 5 0

II

0.o FERRO-

I

Mg Mg + Fe

RIEBECKITE

6LAUCOPHANE a'r R 2'v'e

II

CROSS I TE

GI.AUC()PHAI{E

IIAGNESIO_ RIEBECKITE

* l.o

o.o

o.3 -

o.7

r.o

F es + / l f e 3 + 4 4 1 v 1 ) -

Frc. 4. The nomenclature of the alkali amphiboles [modified from l-eake (1978)1.

and also affect cation stoichiometry, but this for oxy-amphiboles. This point is illustrated has not yet been shown to be of widespread in Table 6, which shows the cell contents significance. Thus in principle, this is the best calculated by both the 24(O,OH,F) and 23(O) methods for potassian oxy-kaersutite(55). In method of amphibole recalculation. the 23(O) calculation, the sum of the C-type 23(Ot cations (XC) is significantly less than the ideal This method was introduced by Miyashiro value, which is equal to or greater than 5.0. (1957) and others in order to compensate for The reason for this is quite simple. In a normal poorly determined H,O(+) and lack of F and amphibole, each hydrogen is associated with Cl analyses.Because most amphiboles are now an oxygen; in an oxy-amphibole, the hydrogen analyzed by electron microprobe, this is the is not present and the oxygen is now aisociated method most commonly used to calculate unit- with a (probably trivalent or tetravalent) cation. cell contents. This calculation assumbs that Thus, thi assumptionin an oxy-amphibolethat there are two (OH,F) per formula unit and, as there is (OH)' in the formula unit introduces indicated by Phillips (1963), is unsatisfactory an excess of oxygen into the normalization

THE

CRYSTAL

CHEMISTRY

OF THE

AMPHIBOLES

181

TABLE6. UNIT.CELL CONTENTS FOR 24(O,OH,F) in half the unit cell and (ii) errors in HsO(*) and F are compensatedby errors in PoTASS rAN oXY-MERSUTTTE( 55). wt. Vo of reported metal oxides. The second CALCULATED ONTHEBASES OF is based on the observation that 2 4 ( 0 , 0 H , F )A N D2 3 ( 0 ) ,R E S P E C T I V E Lpremise Y

"neither low nor high X(OH,F) is reflected in correspondingly low or high total reported Ana'lys is 2 4 ( 0 , 0 H , F2) 3 ( o ) oxides". This is illustrated in Figure 5, which shows the relationship between total oxide si 02 39.90 si 5 . 8 7 8 5 . 6 9 7 wt.Vo and (OH,F,CI) content for 1O59 amphiconclusions may be drawn from Ti02 4.65 At 2 . 1 2 2 2 . 3 0 3 boles. Various Figure 5: (a) the scatter abott lMVo may be A 1 2 0 3 1 4 . 3 5 ET g=!gq 8.!qq random error in all components; variations in (OH, F, Cl) may be real (strongly adsorbed 'l Fer0, 9.60 At 0 .3 7 0 0 . 1 3 HzO, presence of fluid inclusions, excessstruc?r . | . 0 6 0 . | . 0 3 2 tural OH, oxidation during sample preparation, FeO 0.04 Fe"' deficient structural OH); (b) errors in H,O(+) )+ MnO 0 . 0 8 F e - ' 0 . 0 0 4 0 . 0 0 4 and F are compensatedby errors in wt. Eo of. reported metal oxides. The skewed distribution MgO 14.52 Mg 3 . I B B 3 . 0 9 0 of (OH,F"CI) suggestseither that at least some CaO 12.14 Mn 0 . 0 0 9 0 . 0 1 0 of the (OH,F,CI) variation is real or that there is a systematic bias to low values associated Naro I .90 Ti 0 . 5 ' l5 0 . 4 9 9 with the experimental method for HzO determination. conclusions (a) and (b) Kzo 2 . 3 1 rc 5-_Ug.!.148 are equallyAlthough likely just from a considerationof tro* Figure 5, I incline toward (a) as the more 0.48 xc-5 0.146 reasonable. The errors of conclusion (b) are Hzo 0.02 Ca r . 9 1 6 l B 5 7 not random; they would have to be associated F 0 . 1 2 Na 0 . 1 4 3 with the specific analytical methods used and would be the same lor all analyses; thuso a T00.Tf X B compositional dependence of (OH,F,CI) would -0 = F 0 . 0 6 Na 0 . 5 4 3 0 . 3 8 3 be apparent. In iron-rich amphiboles, lowtemperature dehydroxylation by oxidation I 00.05 K 0 . 4 3 4 0 . 4 2 1 during HeO analysiscan give rise to low HrO(+) XA 0 . 9 7 7 0 . 8 0 4 determinations (unless evolved H, is measured also); however, FerO, is not determined on the same aliquot of sample, and thus the compensating error is not measured. Premise (ii) of Borg (1967a) is thus of questionable procedure, giving rise to lower cation-totals; general validity; as the ". . compensatingand the method of assigning cations to their groups compounded errors of opposite sign" are the then leads to totals that are norrnally considered result of these compensating errors in metallic unacceptable. oxides, the conclusions are not of general Borg (1967a) discussed in some detail the applicability, unlessit can be shown that prempros and cons of 23(O) and 24(O,OH,F) ise (ii) is correct. calculations, and concluded that "for chemical The crucial assumptionin the 23(O) calculaanalyses with inaccurately reported HzO(*) or tion is that (OH, F, Cl) equals 2 in the formuia F. calculation of an amphibole formula on the unit. Whether or not this assumptionis usually basis of 23(O) after discarding the reported valid is still not known. This point is discussed HrO(+) is, in most cctses,(N unsatisfactory as in more detail in the section on the O(3) site. a standard calculation including H:O(*) based The .cynic might ask: if numerous determinaon 24(O,OH,F). The sum of the cations in tions of HzO have not clarified the role of (OH) X, Y and Z groups most closely approaches in this regard, why go to the trouble of analyztheoretical values in a 23(O) calculation, but ing for it? Hopefully, more precise analytical only by virtue of compensating and com- techniquesmay eventually resolvethis question. pounded errors of opposite sign". The argu8rs, ments developed by Borg (1967a) are based on two explicily stated premises: (i) there are This method has generally been 'used when

m-od 2;000

182

THE CANADIAN

MINERALOGIST

o < to.

2.m

l.@

(ol,

3.OO

F. cl )

Ftc. 5, Total oxide wt. Vo versus (OH, F, Cl) p.f.u. for lhe superior and moderate analysesof Leake (1968) From Borg (1967a)1.

the calculated Si content exceeds8 atoms p.f.u.; there seemsto be no justification at all for this method.

81si+ AA This method has been used when the cal.

culated (Si + Al) content is significantly less than 8 atoms p.f.u.; there seems to be no justification for this method. Some high-quality analyses do show (Si + Al) less than 8.O (unpublished work by the author and others), but the structural details of this are not at all clear, and renormalizing to 8(Si + Al) simply ignores this problem. Similar problems have been noted in biotite by De Pieri (198O). 13 cations

I I

3ro t! f

o

lrJ G t!

5.4

5.O 4.6 C O C C U P A N C+Y

4.2

Ftc. 6. Frequency diagram for the sum of. C-type cations in amphiboles of the eckermannite - arfvedsonite and magnesio-katophorite - katophorite series [from Hafihorne (1976)1.

This method is based on the assumption that the sum (Si+Al+Ti+Fe2+ + Fe3++Mn*Mg) is equal to thirteen; thus these cations (types C and T) do not occupy the M(4) site(s), and B-type cations or vacanaciesdo not occur at the T(1,2) and M(l,2,3) sites. Experimental studies have shown that these assumptions are not necessarily true. X-ray structure refinements (Ungaretti 1980, Ungaretti et al. 1981, Hawthorne et al. 1980) have shown the presence of smaller divalent cations at the M(4) site in calcic and sodic-calcic amphiboles. Goldman & Rossman(1977a) gave extensivespectroscopic evidence for the presence of Fez* at M(4) in some calcic amphiboles. Similarly, the phase studies of Cameron (1975) on a cummingtonite - actinolite join indicate significant solidsolution of the cummingtonite component in the actinolite phase, requiring Fe'" occupancy of M(4) in actinolite. Thus, the sum (Si*Al-r can commonly exTi+Fe'*+Fe"++Mn+Mg) ceed 13,0. Can this sum be lessthan 13.0?Here the situation is far from clear. It has generally been assumed that Cf+C) cannot be less than

THE CRYSTAL CHEMISTRY OF THF, AMPHIBOLES

thirteen; however, this may not be the case. In a brief study of the eckermannite - arfvedsonite amphiboles, Hawthorne (1976) showed that the sum of the C-type cations in this series is frequently less than 5.O (Fig. 6), with a mean sum of 4.88 atoms p.f.u. It was suggestedthat the presenceof vacancieswas unlikely and that Ca might enter the M(1,2,3) sites; in fact, using the arguments of Hawthorne (1978c), one can show that vacancies at the M(3) site apparently do not cause great structural instability. Leake et al. (1981) have discovered amphiboles with sums of C-type cations going down to -4.2 atoms p.f.u.; it is of interest to examine the structures of these amphiboles to see if the vacancies occur at the M(3) site as predicted by bond-valence arguments. Thus, calculation of amphibole formulae on this basis would not seem to be justified. Neumann (1976) has proposed a slight modification to this calculation to allow for some M(4) occupancy by Mn2*. On the basisof Onuma diagrams (Onuma et al. 1968), she proposed that in amphiboles from mafic and ultramafic rocks, half the Mn be assignedto the M(4) site, whereas in amphiboles from alkaline and silicic rocks, all the Mn be assignedto the M(1,2,3) sites. The objections outlined above still stand.

183

substitutions or make results of poor analyses look acceptable. Formulae should be calculated on the basis of 24(O,OH,D, or 23(O) in the absence of HzO analyses; note that the latter tacitly assumesthe presence of two (OH,F,CI) in the unit formula. Calculation ol Feg+/ FE+ ratios

Most amphiboles are now analyzed by electron microprobe, which cannot practically distinguish between valence states of an element. This is of particular importance with regard to Fe, as the role of this element in the amphibole structure is strongly a function of its valence state, and the oxidation ratio strongly affects the recalculation procedure of the unit-cell content. The possible range of cell contents can be derived by performing the calculation twice, with the iron as FeO and Fe2Oa,respectively. It is generally desirable to obtain more accurate estimates than these extremum values. For some amphibole types, an estimation based on experience can be quite accurate; for example, Fet*/Fet* is approximately equal to 0 for monoclinic Fe-Mn-Mg amphiboles. However, most amphiboles are not this amenable, and other methods have been developed to try and obtain this ratio. I5 cations When the unit-cell contents of an amphibole The assumptions in this model concern the are calculated, either the calculation is based behavior of Na (and K). Calculations are on a fixed number of anions in the formula unit performed normalizing the sum of the [24(O,OH,F) or 23(O)] with the number of (B+C+T) cations to 15.0, either including cations necessary for electroneutrality, or it is or excluding Na. As Na may occupy both the based on a fixed number of cations per formula M(4) and A sites in most varieties of amphibole, unit with the necessarynumber of anions reneither assumption is particularly appropriate. quired for electroneutrality. If we wish to Such methods may be adequate for Fe,Mn-Mg calculatethe Fe3*/Fe'z+ratio, it is necessaryto amphiboles wlrere Na contents are very low; normalize the anions to a fixed number and however, the demonstrated A-site occupancy normalize the cations to a fixed number, and of Na in gedrite and M.(4)-site occupancy of then adjustthe Fes+/Fe2+ratio to obtain electroNa in synthetic sodian magnesio-cummingtonite neutrality. All of the schemes used in the NaMgNaMg'SieOr:(OH): does cast doubt upon literature are based on these constraints; it is this method even in these circumstances. irrelevant to note which conditionsare assumed and which are adjusted, as the end product is 16 cations the same. Becauseof the limitations concerning This is the maximum number of cations the renormalization based on fixed cation-contents. amphibole structure can accommodate; the tlese calculations only provide limiting bounds; presenceof vacancies at the A site is common in fact, if vacancies occur at the M(l,2,3) in all amphibole groups, indicating that this is sites. even this is not the case. not a suitable basis for recalculation. This method was first used by Stout (1972), who calculated the md(imum Fe'+/Fe'* ratio based on 13 cations (see above) and the miniGenercl comments mum Fe8+/Fez+ ratio based on 15 cations Normalization of amphibole formulae on the (excluding Na) for a B(a) anion basis. The basis of fixed cation numbers is usuallv not method was also used by Papike et al. (1.974), valid; these methods often obscure certain who calculated an Feu+content from the charse-

184

THE CANADIAN MINERALOGIST

TABLE7. UNIT-CELLCOMENTS FORANAMPHIBOLE OF BINNS(1965), CALCULATED USING THEMETHOD OF ESTIMATING THEIINIMUMANDMAXIMUM BOUNDS OF THEFez'ANDFerr C0NTENTS Analysi s si02 A1203 Ti02 Fer0, FeO Mno MSo Cao Na20 Kzo HzO F

40.85 14.45 0.65 5.59 18.53 0.35 s.]l 10.86 I.48 6l .0. 1.62 0.00

Min. si A1 tT

M a x . 2 3 ( 0 )2 4 ( 0 , 0 H , F )

6 . 2 8 6 .r 8 6 , 2 0 6 . 2 5 1.7? 1,82 1.80

2(OH,F,CI); deviation from this condition will further affect the Fet*/Fe'* ratios and calculations of the unit-cell content, THe AvrpnrsolE CRySTALSTRUcTUREs

The basic amphibole structure was first characterizedby Warren (1929) when he solved the crystal structure of tremolite. Evidence of structural unity throughout the minerals of the A1 0.89 0.75 0.79 0.86 amphibole group was provided by Warren Ti 0.08 0.07 0.07 0.08 (1930) in a general survey of the structure and Fe-' 0.12 0.86 0.64 0.64 chemistry of the monoclinic amphiboles, and FeZ+ z.g1 2 . 1 2 2 . 3 5 2 . 3 7 by Warren & Modell (1930b) in their solution Mn 0.05 0.05 0.05 0.05 to the crystal structure of anthophyllite. Mg 1.17 l.t5 l.t6 1.17 Tschermak (1872) had recognized that there was a strong relationship between the chemistry. rc 5_4 l.!q !=_qg. !=l_q. physical properties and paragenesis of the pyroxenes and the amphiboles.Wanen (1929) xc-5 0.21 0.06 0.t6 and Warren & Modell (1930b) showedthat this Ca 1.79 1.76 1.77 1.78 relationship also extended to the unit-cell Na 0 . 2 4 0 . 1 7 0 .0 6 dimensions (Fig. 8) and diffraction patterns, EB ?..Q.Q. ?roo- ?.!!. ?..Q!. and used this relationship to solve the structures of tremolite and anthophyllite by analogy with Na 0 . 4 4 0 .1 9 0 . 2 6 0 . 3 8 the known structures of diopside (lVarren & K 0.12 0.12 0.12 0.12 Bragg 1928) and enstatite (Warren & Modell 1930a). Warren (1930) noted the striking rA 0.56 0.3] 0.38 0.50 similarity of the iOl reflections in tremolite and diopside, and, coupled with the similarity of the unit-cell dimensions in this projection, balance equation, Fe3+-iuAl*Not'rG'-(.Na,K)o concluded that on the (010) projection, the -"1A1-2Tf*, repeated the normalization pro- tremolite and diopside structures were practicedure and calculated a new Fe3* content. cally identical. Thus. the tremolite structure iterating this procedure until there was no was conslructed by incorporation within the change in the derived Fent/Fe'* ratio. An tremolite unit-cell of "blocks of the diopside example is given in Table 7. It has been structure" and "reflexion planes". Warren suggestedthat the halfway point between mini- found that there were only two possiblerelative mum and maximum Fe3" contents be taken positions of the "diopside blocks" and the as an estimate of the actual Fe3+ content. This mirror planes that generated a feasonable premise was tested for calcis and subcalcic structural arrangement; as only one of these amphiboles on the supsrior analyses from the arrangementswas commensuratewith the meacompilation of Leake (1968); the results are sured D parameter of the tremolite unit-cell, shown in Figure 7, where it can be seen that the essential features of the tremolite structure there is (unfortunately) no significant correlation were determined.The remaining atoms (2 Mg) between the observed and calculated values. were located by symmetry and bond-valence This is really not surprising if we consider the arguments, as were the presence and position constraints used in the calculations; the actual of the hydroxyl group in the structure. Strucvalues of the bounds will be functions of such ture-factor calculations confirmed the derived factors as the amount of Fe-Mn-Mg amphi- atomic arrangement. bole substitution in calcic amphibole and the The essential feature of the amphibole strucamount of alkali amphibole substitution in ture (Fig. l l) is a double chain of corner-linked calcic amphibole, factors that are a function tetrahedra that extends infinitely in one direcof bulk-rock chemistry and environment. Perhaps tion and has the general stoichiometry Cf"Olt-. a detailed correlation between these calculations The direction of infinite polymerization of the and the specific paragenesisof each amphibole double-chain unit defines the Z axis of the could lead to a better estimate. It is implicit amphibole cell in the normal orientation. The in these methods that the formula unit contains actual value of the repeat distance in the Z !.!q.

8.q9. !.!q

g.qq

184

THE CANADIAN MINERALOGIST

TABLE 7.

UNIT-CELL CONTENTS FOR AN AMPHIBOLE OF

BINNS (1965), CALCULATED USING THE METHOD OF ESTIMATING THE MINIMUM AND MAXIMUM BOUNDS OF

THE Fez+ AND Fe34 CONTENTS Analys is

S102 A1203 T102

Fe2°3

Min.

Max.

6.28

6.18

2(OH,F,Cl); deviation from this condition will further affect the Fe'VFc** ratios and calcula tions of the unit-cell content.

23(0) 24(0,0H,F)

The Amphibole Crystal Structures

40.85

Si

14.45

Al

1.72

1.82

1.80

1.75

0.65

IT

8.00

8.00

8.00

8.00

6.20

6.25

5.59

The basic amphibole structure was first characterized by Warren (1929) when he solved the crystal structure of tremolite. Evidence of structural unity throughout the minerals of the

FeO

18.53

Al

0.89

0.75

0.79

0.86

MnO

0.35

Ti

0.08

0.07

0.07

0.08

MgO

5.11

0.12

0.86

0.64

0.64

CaO

10.86

Fe3+ Fe2+

2.91

2.12

2.35

2.37

by Warren & Modcll (1930b) in their solution

0.05

0.05

0.05

0.05

Na20 K20 H20

1.48

Mn

0.61

Mg

1.17

1.15

1.16

1.17

1.62

EC

5.21

5.00

5.06

5.16

F

0.00 0.06

EC-5

0.21

Ca

1.79

Na

-

£B

(1930) in a general survey of the structure and chemistry of the monoclinic amphiboles, and

0.16

to the crystal structure of anthophyllite. Tschermak (1872) had recognized that there was a strong relationship between the chemistry, physical properties and paragenesis of the pyroxenes and the amphiboles. Warren (1929)

1.76

1.77

1.78

and Warren & Modell (1930b) showed that this

0.24

0.17

0.06

2.00

2.00

2.00

-

2.00

amphibole group was provided by Warren

Na

0.44

0.19

0.26

0.38

K

0.12

0.12

0.12

0.12

EA

0.56

0.31

0.38

0.50

relationship

also

extended

to

the

unit-cell

dimensions (Fig. 8) and diffraction patterns, and used this relationship to solve the structures of tremolite and anthophyllite by analogy with the known structures of diopside (Warren & Bragg 1928) and enstatitc (Warren & Modell

1930a). Warren

(1930) noted the striking

similarity of the hOl reflections in tremolite and

diopside, and. coupled with the similarity of balance equation, Fe»*=i"Al+NaM'"-(Na,K)A

—"Al—2TJ'*, repeated the normalization pro cedure

and calculated

a

new Fe3*

content,

iterating (his procedure until there was no change in the derived Fe*VFe2* ratio. An example is given in Table 7. It has been suggested that the halfway point between mini mum and maximum Fe3* contents be taken as an estimate of the actual Fe3* content. This

premise was tested for calcic and subcalcic amphiboles on the superior analyses from the compilation of Leake (1968); the results are shown in Figure 7, where it can be seen that there is (unfortunately) no significant correlation between

the

observed

and

calculated

values.

This is really not surprising if we consider the constraints used in the calculations; the actual

the unit-cell dimensions in this projection, concluded that on the (010) projection, the tremolite and diopside structures were practi cally identical. Thus, the tremolite structure was constructed by incorporation within the

tremolite unit-cell of "blocks of the diopside structure"

and

"reflexion

planes".

Warren

found that there were only two possible relative positions of the "diopside blocks" and the mirror planes that generated a reasonable structural arrangement; as only one of these arrangements was commensurate with the mea

sured b parameter of the tremolite unit-cell, the essential features of the tremolite structure

were determined. The remaining atoms (2 Mg) were located by symmetry and bond-valence arguments, as were the presence and position of the hydroxy! group in the structure. Struc

values of the bounds will be functions of such

ture-factor calculations confirmed the derived

factors as the amount of Fe-Mn-Mg amphibole substitution in calcic amphibole and the amount of alkali amphibole substitution in calcic amphibole, factors that are a function of bulk-rock chemistry and environment. Perhaps

atomic arrangement.

a detailed correlation between these calculations

The essential feature of the amphibole struc ture (Fig. 11) is a double chain of corner-linked

tetrahedra that extends infinitely in one direc

tion and has the general stoichiometry (T40n)». The direction of infinite polymerization of the

and the specific paragenesis of each amphibole

double-chain

could lead to a better estimate. It is implicit

amphibole cell in the normal orientation. The

in these methods that the formula unit contains

actual value of the repeat distance in the Z

unit defines the Z

axis of the

185

THE CRYSTAL CHEMISTRY OF THE AMPHIBOLES

10.0

5

5.0

O o

0.0

10.0

5.0

0.0

15.0

Fe203 obs. (Wt.%) Fig. 7. Fc3* p.f.u. calculated by the method of Papikc et ul. (1974) com pared with the observed value |b;iscd on a 24(0. OH. F) calculation] for the superior analyses of Leake (1968).

direction is the c dimension of the unit cell and

is dependent on such factors as the type of tetrahedrally co-ordinated cation and the stereo chemistry of the tetrahedra; however, these

factors from

produce the

ideal

only

minor

value of

~5.3

perturbations A

for

an

(SiiOn). chain. It is convenient to recognize two different types of oxygen anions in this double-chain element. The oxygen atoms lie approximately in two planes parallel to the chain direction; all oxygen atoms lying in the

plane containing the linkages between adjacent tctrahedra are called basal oxygen, whereas the oxygen atoms lying in the other plane are called apical oxygen. Oxygen atoms bonded to two tetrahedrally co-ordinated cations are called bridging (linking two TO« tctrahedra together) and here are denoted as O(br), whereas oxygen atoms bonded to one tetrahedrally co-ordinated cation are called nonbridging and here are denoted as O(nbr).

The (TiOii). chains are linked together by intermediate-size (0.53-0.83 A) divalent and

trivalent cations that bond to the O(nbr) anions of the chains. Two types of interchain linkage may be recognized. A strip of these divalent and

trivalent

cations

is

intercalated

between

two layers of apical oxygen atoms belonging to double chains that adjoin each other orthogonal to the plane of the basal oxygen atoms. The adjacent double-chains are staggered in the Z direction so that the apical oxygen atoms of adjacent chains assume a pseudo-octahedral arrangement around each of the linking divalent and trivalent cations. In order to complete the co-ordination of the cations in the centre of

this strip, it is necessary to add another anion to the plane of the apical oxygen atoms; this is the monovalent anion in the amphibole formula. Thus these adjacent double-chains arc

tightly bonded together and form a modular unit (an I-beam) that plays an important role in the model structures that will be described

later. The second type of interchain linkage joins these modular units together in a threedimensional array (Fig. 9). The divalent and

186

THE CANADIAN MINERALOGIST

C2/c

Pyroxene

Pbca

Pyroxene

7^'

C2/m Amphibole

Pnma Amphibole

Flo. 8. The relationship between the cells of the pyroxenes and Ihc amphiboles laflcr Warren & Modell (IMOb)J.

trivalent cations at the edges of the I-beam unit link laterally to Ihc nonbridging basal oxygen atoms of adjacent I-beams. These divalent and trivalent cations, together with their co-ordinating anions, define a strip of edge-sharing octahedra that extends infinitely in the Z direction. Thus, an I-beam may also be thought of as a strip of edge-sharing octa hedra

sandwiched

between

two double-chains

of corner-sharing tctrahedra. As described thus far, the structure consists

of C- and T-type cations. Further linkage between the modular units is provided by the

A

and B cations. The B cations are situated

at the margins of the octahedral strips, where they provide additional linkage both within individual I-beams and between adjacent I-beams. The interchain linkage provided by the B-iype cations differs from the second type of interchain linkage described above. The C-typc cations all bond to nonbridg ing anions whereas the B-typc cations bond both to nonbridging and bridging anions. The B cations are surrounded by eight anions, not all of which are necessarily bonded to the central cation; these anions arc arranged in a

187

THE CRYSTAL CHEMISTRY OF THE AMPHIBOLES MS

Ml

M2

M4

Fig. 9. The crystal structure of C2/n> amphibole projected down Z; the shaded areas show the I-beam modules of the structure [after Cameron & Papike (1979)].

distorted square antiprism, the exact configura

notation. This was translated into the standard

tion

form C2/w by later workers, but the unit-cell parameters were still given in the I-ccntred orientation. Current crystallographic conven tion for the monoclinic crystal system defines B as the obtuse angle between the X and Z crystallographic axes. Several later studies

of which

is a

function

of the central

cation and local structural requirements. Between the back-to-back double-chains is a large cavity that is surrounded by twelve bridging oxygen atoms. The A

cations arc situated within this

cavity; the actual position assumed by the A-typc cation and the number and configura

tion of the surrounding anions to which it is bonded arc a function of local stereochemical

requirements, and vary with the chemistry of the amphibole. The A cations thus provide additional linkage between adjacent doublechains orthogonal to the plane of the doublechain. Schematic projections arc shown in Figures 9 and 11.

The original crystal-structure determination for tremolite by Warren (1929) was referred to an I-centred cell and conformed to the early

morphological convention of defining B as the acute angle between the X and the Z axes. Some confusion subsequently arose concerning this point (Whittaker & Zussman 1961). Warren's work was done before the introduction of the

Hermann-Mauguin symbols, and the space group

reported as 2C7-3

reported atomic co-ordinates in an I-centred cell with B obtuse; in these studies, the signs of the z co-ordinates should be reversed.

Here, all crystallographic

information has

been standardized to a C-centred cell with B

obtuse. Maintaining a right-handed set of crystallographic axes with B obtuse, Figure 10 summarizes the relationships between the I- and C-ccntred cells.

Choice of axes

was

(Zussman 1955. Heritsch et al. I960, Hcritsch & Kahler 1960, Heritsch & Reichert 1960)

using the Wyckoff

Principal structure-types

The extensive morphological investigations of the nineteenth century had shown that amphiboles occur in both monoclinic and orthorhombic varieties, and Warren's studies showed

that these were related structures with spacegroup symmetries Cllm and Pnma, respec tively. More detailed work during the past twenty years has unearthed three more struc-

188

THE CANADIAN

MINERALOGIST

aI

=V*c +Cc + 2accccos 8c

a

=«/aj + Cj + 2ajCj cos Sj

°I

CI sin 6, =

1

sin 5

ac sin bc r?

?

Vac *cc * 2accc cos 8c a. sin 3,

=

1

c f &.

+ C|2 + 2ajC[ cos Sj

Fig. 10. The geometrical relationships between the /- and C-centred cells of the clinoamphiboles [modified from Whitlaker & Zussman (1961)).

tural variants with different space-groups. Gibbs et al. (1960) reported the synthesis of protoamphibole, a new orthorhombic amphibole with space-group symmetry Pnmn; Gibbs (1964, 1969) subsequently refined the protoamphibole structure. Deer et at. (1963) postulated the existence of a magnesium-rich Fe-Mg-Mn amphibole with P2,/m symmetry. Bown (1966) subsequently reported such an amphibole, and the structure of a tirodite P2Jm was refined

by Papike et al. (1969). Moore (I968a,b) reported the existence of a peculiar amphibolelike mineral from Langban, Sweden. The unitcell dimensions and space group (P2/a) were found to be compatible with an amphiboletype structure but the chemical composition was not. Subsequent solution and refinement of the structure of this mineral (joesmithite) showed it to be a bona fide amphibole with a beryllosilicate double-chain (Moore 1969).

Site nomenclature in amphiboles

In order to facilitate interstructure compa

rison of structural features in the amphiboles.

it is desirable to have a site nomenclature that

differentiates between structure types but main tains some son of congruence for analogous sites

in

different

structures.

There

are also

considerable advantages in a nomenclature that uses only upper-case characters and has no subscripts, superscripts or Greek letters; such a nomenclature is machine-readable and

causes less type-setting problems. A site nomen clature should not involve symbols for chemical

elements; it is confusing to have Fc occupying an Mg(l) site in a structure. Numerous

site-nomenclature

schemes

have

been used in the various amphibole structuretypes. Many of the earlier schemes are undesir

able in that they use symbols of chemical ele ments, subscripts or Roman numerals. The more recent systems of site nomenclature are based on

the scheme whereby the sites occupied by the T cations are denoted as T sites, the sites occupied by the C and B cations arc denoted M sites, the site(s) occupied by the A cations is (are) denoted A sites, and all anion sites are denoted as O sites. This is the basis of the scheme

used here. However,

some changes lo the

THE CRYSTAL CHEMISTRY OF THE AMPHIBOLES

189

schemes of nomenclature used in some studies

symbols. This is consistent with the current

are necessary in order to satisfy the conditions

nomenclature of the Pnma amphiboles (Finger 1970b, Papikc & Ross 1970), which is thus

outlined above. As will be shown later in this

section, there are a large number of possible amphibole

structures

that

could

occur

as

ordered derivatives of currently known struc tures. A completely general site-nomenclature would satisfy the above restrictions for all these possible structures and would have the same type of structure as the nomenclature schemes that have been derived for the pyroxenes (Burnham et al. 1967) and the feldspars (Megaw 1956). Such a scheme would also be extremely cumbersome and is not really necessary unless numerous

additional

structural

varieties

are

discovered. The scheme developed here is not as systematic but is convenient and satisfies the criteria cited above. The site nomenclature

used by Robinson et al. (1973) and Hawthorne & Grundy (1973a, b) is adopted here for the C2/m amphibole structure-type. The site

adopted in the current scheme. The site nomen clature of the Pnmn structure (Gibbs 1969) is changed; the parentheses are not used and the Si(l) and Si(2) sites become the Tl and T2

sites. For the FIJm structure-type, parentheses

TABLE 8.

SITE-NOMENCLATURE SCHEME FOR AMPHIBOLE STRUCTURE-TYPES

P2,/n

C2/n

tetrahedrally coordinated sites

octahedrally coordinated sites

T{1) T(2)

T(1A) T(2A)

T(1B) T(2B)

P2/a

T(1)A TjllB

T(2)A T(2)B

H(l) M(2) M(3)

H(l) M(2) M(3)

H(1)A H(I)B K(2)A H(2)B H(3)

W)

H(4)

H(4)A

Pma

T1A

F«

TIB T2B

T2A

Tl

12

Ml

Ml

K2 H3

K H3

H4

H4

cubic

antiprisnatie

M|4)8

sites

tl2) cavity*

A

non-bridging

can be derived from this nomenclature by changes that correspond to the space-group

0(1) 0(2)

anion sites

0(3

differences of the structures involved. The difference between the monoclinic and ortho

bridging

rhombic amphiboles may be indicated by the presence or absence of parentheses in the site

•the nore complex nomenclature used to describe the positional

nomenclatures for the other structural variants

0(4) anion sites

as

0(7)

A(2)

A

0(1A)

0(1B)

0M1A

0(1)8

0(2A) 0(2B) 0(2)A 0(2)B 0(3A) 0(4A)

0(38) 0(43)

0(5A) 0(58)

0J6A) 0(68) 0(7A)

0(78

0(3)

0(4)A 0(4)B 0(5)A 0(5)B 0(6)A 0(6)B 0(7)

A

A

OIA 02A 03A 04A

01B 028 038 048

OSA OSA 07A

OSB 068 07B

01

02 03 04 OS 06 07

disorder of cations occupying this site is described In the section on the A site.

I 1 C

Fig. 11. The C2/»i amphibole structure projected on lo (100); the space-group symmetry elements are shown.

190

THE CANADIAN

were added

to

the

nomenclature

scheme of

Papike et al. (1969, Fig. 2). The site-nomen clature scheme for the Pl/a structure (Moore 1969) does not resemble that of the other

amphiboles and was completely revised. The site numbering was adjusted to correspond with numbering in the other amphibole structures; for the "pseudo-mirror equivalent" pairs of

MINERALOGIST

is of the type T(l)-T(l), as required by the mirror symmetry of the chain. These charac teristics of the double chain have significant implications regarding the relative ordering of cations over the noncquivalent tetra hedrally co-ordinated sites in the structure. As in apparent from Figure 11, the doublechain element of the structure is not fully

atoms, those with the smaller value of the

extended [O(5)-O(6)-O(5)^=180''l. The ideal

y co-ordinate were labeled by addition of a suffix A, whereas those with the larger value of the y co-ordinate were labeled with the

double-chain configuration is a series of linked hexagonal rings of tetrahedra. Deviations from this ideal hexagonal aspect impose a ditrigonal aspect to the double chains and can be thought of as arising from coupled rotations of the individual tetrahedra around axes defined by their T-O (apical) bonds. This deviation from

suffix

B.

Parentheses

are

used

because this

structure-type is monoclinic; however, in order to distinguish sites in this structure-type from similar sites in the Plt/m structure-type, the parentheses enclose the numbers only in the Pl/a structure-type. The relationship between Plla site-nomenclatures is shown explicitly in Appendix D. The sites of all the various struc ture-types are summarized in Table 8.

the extended configuration varies with amphi bole composition, and is one of the principal mechanisms whereby the double chain maintains dimensions commensurate with the octahedral

strip.

There are three unique sites with pseudoThe C2fm amphibole structure

This is the most common of the amphibole structure-types, suggesting that this must be the most flexible, or chemically compliant, of these structures. A schematic polyhedral repre sentation of this structure-type is shown in Figure 11. There arc three nonbridging anions: O(l), 0(2) and 0(4); of these, 0(1) and 0(2) are apical oxygen atoms and 0(4) is a basal oxygen. There are three bridging anions: 0(5), 0(6) and 0(7); all of these arc basal oxygen atoms,

and 0(5) and 0(6) bridge along the length of the (TiOu)