THE CRYSTAL CHEMISTRY OF.THE AMPHIBOLES

TABLE 25. PREDICTIVE EqUATIONS FOR n'At tN'tHE pnna A}|PHIB0LES

AlTor _ _26.368 + .l6.zs2<<T_o>>

T1A Al = -13.146 + 8.126<TlA-0> I2A A1 = - '13.175 + 8.126<T2A-0>

T IB A ] = -13 .157 + 8 .126<T18-0>T2B A1 = -13.257 + 8.126<T28-0>

227

A1 = LuAl p. f .u . /4.0

were assigned by assuming linearity betweenholmquistite[3l] and gedrite[33] in Figure 41,with the exception of T2A, for which gedrite[32]was assumed to have zero Al occupancy. Thesite occupancies assigned for anthophyllitel23]and gedrite[32] are supported by the fact that thetotal site-chemistry agrees with the correspond-ing values derived from the chemical analysis(anthophyllite[23]) and estimated from the re-fined value of the A-site Na Gedrite[32]). Inview of the limited data-set, regression analyseswere not performed; preliminary working-curves(Fig. al) were derived by shifting the monoclinicamphibole curves down to correspond to theorthorhombic data to give the equations listedin Table 25.

All the methods outlined above have dependedon ionic size as a criterion for the detectionof AllSi ordering. Howsver, the bond-strengthcurves of Brown & Shannon (1973) may be usedto assign site occupancies, and good agreementwith the results of neutron diffraction experi-ments were obtained for sanidine @rown &Shannon 1973, p.277). As a part of this study,this approach was tried for the amphiboles ofAppendices B and C, with the total amount oftetrahedral Al indicated by the chemical analysisas a check on the total tetrahedral Al indicatedby the bond-valence calculations. Using theuniversal curves of Brown & Shannon (19:73),the agreement.was found to be poor; the tetra-hedral Al was overestimzted le.g,, obs = 0.34,calc = 0.62 atoms p.f.u. for manganoan ferro-actinolite(37); obs = 2.73, cals = 3.57 atomsp.f.u. for subsilicic titanian magnesian hastings-ite(58)l and in synthetic nonaluminous amphi-boles, up to 0.38 Al p.f.u. [fluor-richterite(34)lwas calculated. Results were improved some-what by the use of the "co-ordination corrected"curves of Brown & Shannon (1973). However,co-ordination numbers are sometimes difficultto decide convincingly, particularly when thenext-nearest-neighbor cations are positionallydisordered, the site is only partly occupied andthe bonding contacts are at the margin ofsignificance. In view of the reasonably satisfac-tory natwe of the bond length ys. oscupancy

curves given above, this approach was notpursued further.

Stereochemisty of the double chain

As was shown in the previous section onmodel structures, increasing substitution of Alat the tetrahedral sites is accompanied by in-creased rotation of the tetrahedra of the doublechain toward an O-rotated configuration inorder to maintain linkage between the tetra-hedral chain and octahedral strip parts of thestructure. Substitution of Al at the tetrahedralsites is accompanied by balancing substitutionsin other parts of the stmcture. The combinationof these substitutions must be accompanied bystereochemical adjustments that allow the bond-valence requirements of the anions to be satis-fied. The way in which this is done is apparentfrom the bond-valence tables for selectedamphiboles shown in Table 26. The discussionon bondJength variations in nonJ'Al amphibolesemphasized the role of the O(4) anion; it isapparent from Table 26 that the same bond-valence constraints are operative in the u"Al

amphiboles. Bond valences to the O(4) anionmust be maintained at high values; thus i'Al

will tend to avoid sites bonded to O(4) andorder at sites not bonded to O(4). This is thecase in the amphiboles of Table 26, where itcan be seen that the bond valence of theT(2)-O(4) bond is the largest in the structure ofeach amphibole. The decrease in bond valencecontributed to the anions co-ordinating theT(l) site is compensated for by the substitutionof higher-valence cations at the, other sitesco-ordinated to these anions, and also by astrengthening of the M(a)-O(br) bonds that ispromoted by the increased O-rotation of thedor"rble chain described above.

TUE OcTIHTDRAL STRrp

Sandwiched between opposing tetrahedraldouble-chains is the octahedral strip, an arrayof pseudo-octahedrally co-ordinated cation sitesthat are occupied by the C-type cations of theformula unit. This is the most compliant part ofthe anrphibole structure, accepting cations that

o

oo

@o@

o

THE CANADIAN MINERALOGIST

Il @ F o < a o ol F @ $ o O O A

r l N O O @ - F O-1 .

t ; l - - F F N N N

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r l o o oo l

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ui lcE I O N

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l @ - @o t s * aP l .r l o A O

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228

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&oL

uJ@

F

uzuJ

z

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d

E

@N

UJ@F

THE CRYSTAL CHEMISTRY OF THE AMPHIBOLES 229

zation of ordering and stereochemistry in theoctahedral strip in the past ten years is leadingto increased understanding of chemical sub-stitutions in amphiboles.

The C2/m amphiboles

There are three unique sites with pseudo-octahedral co-ordination in this sructure type,the M(l), M(2) and M(3) sires. The M(1) sitehas point-symmetry 2 and is co-ordinated byfour oxygen atoms and two O(3) anions thatmay be OH-, F-, Cl- or O'-, with the O(3)anions arranged in a crs configuration. TheM(l) octahedron shares five edges with thesurrounding octahedra and one edge with theM(4) polyhedron. The M(2) site has poinr-symmetry 2 and is co-ordinated by six oxygenatoms; the M(2) octahedron shares three edgeswith neighboring octahedra and one edge witheach of the two adjacent M(4) polyhedra. TheM(3) site has point-symmetry 2/m and is co-ordinated by four oxygen atoms and two O(3)anions, the latter being arranged in a transconfiguration. The M(3) octahedron shares sixedges with the adjacent octahedra.

oA

vary,in valence from *l(Li) to *4(Ti) andin sge from -0.535(Al) to -0.g3 A (Mn,*),and having a variable anion substitution [at theO(3) sitel than cair involve O"-, OH-, F and Cl.There are at least three unique pseudo-octa-hedrally co-ordinated sites in each of thedifferent amphibole structure-types. The signif-icant differences in ligancy and local environ-ment ensure considerable and complex cationordering at these sites, a detailed knowledgeof which is essential to the understanding oftheir crystal chemistry, physical properties andphase relations. The stereochemical details ofthis part of the structure are thus of primaryimportance in the interpretation of cationordering patterns and frequently in the actualderivation of complete site-ordering patterns inthe more complex chemical variants. Indeed,most recent work of Ungaretti (1980) andUngaretti et al. (1981) has indicated that accu-rate chemical compositions (including Fee*./Fer*ratios and even Li contents) and detailedpatterns of ordering can be derived from high-quality X-ray data used in conjunction withdetailed crystal-chemical analysis. Thus, theconsiderable effort expended on the characteri-

. o o - o H

" Foulty onolyses ?

+ O(3)= F2 . l o

tII

o <

3

-,ir':

,f'

Frc. 42. Variation in grand <M-O> with mean ionic radius of the consti-tuent cations f.or the C2/m amphiboles. The regression line was calculatedfor hydroxy-amphiboles only, using data where the e.s.d. of the individualbondJengths is less than 0.01 A; data deviating significantly from the linewere omitted from the regression anatysis as the chemical compositionof those specimens is suspect.

230 THE CANADIAN MINERALOGIST

In many groups of isomorphous structures,the variation in mean bond-lengths of cationpolyhedra may be related to the mean ionicradius of the cations occupying the sites. Thusthe variations in the mean octahedral bond-lengths in garnet (Novak & Gibbs 1970,Hawthorne 1981c), olivine (Brown 1978) andpyroxene (Hawthorne & Grundy 1974, 1977c,Ribbe & Prunier 1977, Cameron & Papike 1981)are linear functions of the variation in radiusof the constituent cation. Where this relation-ship is well characterized, it is extremely usefulin deriving complete site-occupancies in caseswhere the results of a site-occupancy refinementdo not give a unique solution, or to check outthe consistency of the derived site-occupanciesand the mean bond-lengths. The variation ingrand mean bond-length as a function of grandmean ionic radius for the M(l), M(2) and M(3)sites in the C2/ m amphiboles is shown inFigure 42. A linear relationship is reasonablywell developed, being described by the equation<M-O> - r.527 *O.764(17)<r>.

Some of the scatter in this figure is due tovariation at the O(3) anion position, as the

data for the fluor-amphiboles indicate [r(nonF) -

1.30 A; r(t{OH) - 1,34 Al. However, some ofthe scatter seems to be due to bad or unrepre-sentative chemical analyses. For example, con-sider potassium arfvedsonite(66); the assignedsite-populations (Appendix B3) indicate a meanradius of the constituent cations of 0.779 Athat suggests a (M-O> of.2.122 A and is notcompatible with the observed value of 2.098 A.Other questionable structures are also indicatedin Figure 42, and discussed in detail inAppendix 83. Hence this relationship is a usefulcheck on the compositional data for the crystal.Inclusion of the ionic radius of the O(3) anioninto the above equation gives the relation<M-O> - 1.017 + 0.817(13) <r> * 0.354(37)rot.r. This may also be used to indicate thepresence of F if one has confidence in thechemical data.

The grand <M-O> bond-length can also becalculated by summing the relevant cation andanion radii; a comparison of the values obtainedwith the observed data is given in Figure 43.There is a systematic deviation from the idealhard-sphere model; the calculated values are

. O (3)= OH

* O(3)= F

2 . O 5 o 2 . l o(M-O2ot. ! , -

Frc. 43. Comparison of the grand <M-O> with the conesponding sumof the constituent cation and anion radii for the C2/m amphiboles.

THE CRYSTAL CHEMISTRY OF THE AMP'HIBOLES 231

less than the ideal values at larger ionic radii,but the reason for this is not clear. Similarbehavior is also exhibited by the pyroxenesand the garnets (Hawthorne l98lc). The fluor-amphiboles also deviate from the general trendof Figure 43; again, the reason is not clear.

In a refinement of the structure of magnesio-riebeckite(3), Whittaker (1949) found that<M(2)-O> was significantly less than<M(l)-O> and qM(3)-.o), indicating thatAl was strongly ordered in this site and showingfor the first time that the mean bond-lengths

in amphiboles were sensitive to cation site-occupancy. The same argument was later usedby Papike & Clark (1968) to show a similarscheme of ordering in glaucophane. Robinson(1971) and Robinson et al. (1973) showed that<M-O> could be related to the mean ionicradius of the constituent cations in a series offour clinoamphiboles and one fassaitic clino-pyroxene, assuming that the Fe at the M(2)site in the hornblendes was Fe'*. As the ligancyand local environment of the three octahedrallyco-ordinated M sites differ considerably among

_ tt .

2 . t o

2 .05

o <

{ z.oo6

I

9 r.e5

FIc.44. Variation in individual <M-O> with mean ionic radius of the constituent cations for the C2/ntamphiboles (modified after Hawthorne 1978a), Also shown is a comparison of the observed meanbond-lengths at the octahedrally co-ordinated [{ sites with the corresponding values calculated from theregression equations of Table 27.

2 . t otIII z.osI

o<

AI 2 .OOs

o<

6t

= g

o<

6III

(trr,e)i

o.72 0.74 0.76 0.78

(ure)A (M-O "or"

A -

232 THE CANADIAN MINERALOGIST

TABLE 27. REGRESSI0N ANALYSIS RESULTS FoR C2lm AI'IPHIBoLES

Dependent Independentv a r i a b l e v a r i a b l e c n R o I t l r 2. to

<M( I )-0>

<|t t( 2)-o>

<M( 3)-0>

<M-0>

"lr( r )"o(:)rufr t

"tl(:)"o(:)

26.39

8.50

97.08

1 6 . 3 4

9.08

43.68

64.40

9.46'18 .08

7.06

5.43

2.O9

<r><M-0>

"o( g)

"u(:)<M(3) -0> rO( : )

"m(z)

0.82( 3)0.877 0.46(5) 0.96r o.oo4

1.488 0.e27(8) 0.997 0.004

0.73(4)0.387 0.87(o) 0.925 0,007

1.527 0.76(2) 0.983 0.004

0.82( 1 )1 .0 t 7 0.35( 4) 0.993 0.002

0.6e( 4)0.773 0.64(9) 0.949 0.006

-0.07( 1 )

o {

6z.oe1I

2.O7' l t l - va lues are ca lcu la ted fo r tJ |e nu l l hypothes is Ho:m = 0 .0

themselves, it is best to examine such relation-ships separately for each site. This was origin-ally done by Hawthorne (1978a) for a series ofnineteen C2/ m amphiboles, and has' been ex-tended here for the much larger data-set nowavailable. Figure 44 shows the mean bond-length - ionic radius ralationships for -70amphibole structures; less precise strlcturesfrom Appendix B were omitted from this study.The relationship for the M(2) site is welldeveloped and similar to those developed inprevious studies. For the M(l) and M(3) sites,there is considerable scatter in these relation-ships; much of this stems from the variableoccupancy of the O(3) site by OH-, F-, Cl-and O!-. Inclusion of the mean ionic radiusof the O(3) anion as an independent variablein a stepwise linear-regression analysis indicatesthat this factor contributes significantly tovariations in the mean bondJengths at the M(1)and M(3) sites; the results of this analysis aresummarized in Table 27, and a comparison ofthe observed and calculated mean bond-lengthsis given in Figure 44. As is apparent in Figure44, significant scatter still exists, particularlyin the relationship for the M(3) site. Hawthorne(1978a) has shown that octahedral distortiondoes not significantly contribute to mean bond-length variations in the clinoamphiboles andsuggested that this scatter may result from in-correct assignment of site populations of suchcations as Mn, Fe2*, Fe"*, Ti8+ and Tio* andsuch anions as OH, F, Cl and O'-. However,the results of Ungaretti et al. (1981) suggestsome kind of inductive effect of other cationson the <M-O> bond-lengths. Figure 45suggests that this is the case, <M(3FO> beingsignificantly affected by the mean size of the

0.60 o 0.65 o.7o(.*,r) A...............*

Frc. 45. Variation in (M(3I-O) as a function ofthe mean ionic radius of the constituent M(2)cations for values oJ rM(3) in the range 0.72-0.73A for the C2llr amphiboles.

constituent M(2) cation. Multiple regressionanalysis (lable 27) shows (M(3)-O) to besignificantly affected by 1r)m<zt. Howevero<M(l)-O> and <M(2rc> are dependentonly on their constituent cation and anion radii.Hawthorne (1979) has further examined therelationship for the M(2) site and concludedthat either this relationship is nonlinear at smallmean cation-radius values or the assignedsite-populations for some amphiboles where0.58(ru,z,(0.68 are incorrect; the latter is adistinct possibility, as the majority of the amphi-boles in this class do not have experimentallydetermined Fe"*/Fe'* ratios, and all Fe*(:Fe'*+Fe3**Mn) at M(2) was assumed tobeFe3*. The results of the current study indicatea linear relationship for the M(2) site, support-ing the contention that some of the site occtl-pancies are incorrect.

Hawthorne (1978a) has noted some unusualfeatures in the mean bond-length - ionic radiusrelationships outlined above. They do not con-form to a hard-sphere model ((M-O)=r".uoo* r..ro,) particularly well. For the M(1) andM(3) octahedra, the slopes of the relationshipsare -1.0, but the actual mean bond-lengthsare nO.O2 A less than values forecast from thesum of the relevant ionic radii. For the M(2)octahedron, the slope of the relationship (-0.74)

THE CRYSTAL CHEMISTRY OF THE AMPI{IBOLES 233

is less than the ideal value of 1.0. This suggeststhat the M(2) site is held open for small cationsand compressed for large cations (Ifawthorne1978a). This is quite reasonable in terms ofthe rest of the octahedral strip. The c repeatof the M(1FM(3FM(1FM(3FM(I) chain hasto be equal to the c repear of the M(IFM(2FM(l)-M(2FM(l) chain; consequently, when. agreat disparity exists between the sizes of theM(2) and M(3) cations, as is present if consider-able Al occupies the M(2) site, the M(2) octa-hedron is held open by this requirement. As thesize of the M(2) cation increases, this effectdecreases as the size difference between theM(2) and M(3) cations decreases. If this is so,one might expect higher pressures to favorsmaller cations at the M(2) site. This seemsto be the case; prograde metamorphism leadsto compositionaf changes in this direction, andamphiboles with high dAl contents, such astschermakite and glaucophane, are characteristicof high-pressure environmenls.

A somewhat different approach to meanbond-length variations in amphiboles has beentaken by Litvin er al, (1972a) and Ungarettiet al. (1978), who proposed ideal mean bond-Iengths for complete occupansy of an octa-hedral site by a specific cation. These values(Table 28) were subsequently used togetherwith other structure-refinement results for

Grunerl te(22)

G1 aucophane(26)

Trenolite(30)

Fl uor-fl chterl te( 34)Fl uor-tremol i te( 36)

Potassian pargasite(39)

T i rod i te (41 )tlagnes I o-ho rnb I ende( 42)Hast ingsi te(44)

Ferro- tschermak.t te( 54)

TABLE 28. IDEAL <lir-o> DISTANCES (8) pOn COnplErgoccuPANcy 0F M(I ,2,3) SrTES By A STNGLE CATI0N

I

A l I . 9 0

Fe- 2.03

t t -

Mg 2.07

F.2+ 2,14

Mn2+

LI

- 1.929- Z , U J I

- . l . 960

2.078 2.078 2.083

2 .119 2 .119 2 .125

L114 LcRl 1-r,L

2.014 2,022 2.027

1.982 l 989 1.998

2.035 2.0$ 2.045

2.075 2.084 2.082

2.124 2.134 2.126

2.16s 2. ' t75 2.163

2 .109 ? .117 2 .112

lL i t r i n ( t gz : ) ; zUnga re t t i e t a l . ( 1981 ) ; 3ca l cu ta tedfrom the curves of Table 27 with 0(3) = 0H.

assignment of cation occupancy in amphiboles.A comparison of the values used by theseauthors with values derived from the regressionrelationships of Table 27 is shown in Table 28.There is fairly good agreement between thevalues, although significant differences dooccur. These differences probably arise fromthe fact that the values of lJngaretti et al.(1978) were derived specifically from data onempty A-site alkali amphiboles, whereas thevalues derived here are derived from data onall amphiboles. There is almost certainly somevariation in these values with amphibole type(c/. Fig. 45), and thus some difference is norrunexpected.

IABLE 29. PotYHEpRoN-p[sToRTrqN pARfMETERS rN sElEcrrp czln MpHtBoLEs

Tf l ) + f (21 ̂ M( l ) . M(2) = r ,4(3) =L o ' a a z L o z t o 2 t o 2

0.29 0.8 0.78 15.8 2.25 36.0 2.79 43.2 0.11 60.90.05 0.6 1.88 17.4 0.21 69.5 15.77 35.0 0.34 85.00 .54 5 .0 4 .14 ' 19 .9 0 .15 35 .6 5 .52 22 .9 o .O9 43 .62.06 14.3 s.60 22.4 0.62 43.1 12.54 33.1 0.97 43.30.38 6.2 3,45 19.3 0.01 46.9 5.76 21,9 1.03 47.90 .59 6 .6 1 ,42 19 .1 1 .25 50 .5 5 .98 24 .3 o .O l 75 .70.13 1.6 2.66 21.0 0.92 32,7 4.65 25.1 o.07 43.50 .97 4 .7 1 .79 12 .3 0 .90 47 .5 5 .89 25 .1 0 .07 70 .92 .32 5 .5 3 .36 5 .0 1 .26 42 .5 7 .37 33 .5 t . t 8 75 .40 .63 4 .8 0 .61 17 .0 4 .00 57 .3 5 .00 19 .6 0 .33 106 .0

Potass ian oxy-kae*u t l te (55) 0 .29 S.S l . l6 lg .9 .14 .35

47 .9 t ,06 31 .2 O,0S 56,8Subs i l i c ic t i tan iannagn€s lan t ras t ing i l te (sa) 0 '3 . l 4 '6 - 0 .78 l7 . l 3 .59 65 .0 6 .87 23 .4 o '08 107.9

Potass ian fe rd- ta rmi te (F9) O.ZS 3 .6 1 .53 .13 .8

2 .45 45 .B a .SS Za. i O.08 g2 .3Sodli l f luor-

c t tno t ro i rnqu is t r te (Oe) 9 .74 14 .1 10 .78 12 .9 3 .43 84 .5 9 .31 32 .6 5 .37 93 .6

Potassiurn-arfvedsonite(67) L05 ]L4 S.E4 21.4 O.gt 44.6 17.?7 44,5 0.60 67.6FIuor-riebeckite(68) O.OZ 4.4 2.OZ 12.7 0.2g 47.9

.15.48 39.1 O.26 68.7

Fer rc -g laucophane(69) 0 .06 0 .7 Z .O4 . t4 .g

0 .39 70 .5 14 .36 31 ,g 1 .14 97 .4

n ^^ = { . i t l I ( r , i -h ) / r r l ' l n }x lou , where a i = ind iv idua l bond- length , sm E rean bond- length ,

n = nrcnber of bonds tn coordinailon polyhedron; o2 = .!-rcr-urr2l(n-l), where oi . indl-i = l

vidual bond-angle, Om = ideal bond-angle, n - number of bond angles in coordination po.ly-hedron.

234 THE CANADIAN MINERALOGIST

C o l i o n c h o r g e o t M ( 4 ) 3 i l e -

Ftc. 46. Variation in polyhedral distortion A of the M(2) polyhedron asa function of the mean formal cation charge at the M(4) site in the C2lnramphiboles [after Hawthorne (1976)1.

III

;o

T;

2.Ol ql .o

The recent development of bond-valence'bond-length relationships (Badr 197A, D7l,Donnay & Allmann 1970, Brown & Shannon1973, Brown & Wu 1976, Pyatenko 1973,Ferguson 1974) has indicated that bond-valencerequirements are a major factor in controllingbondJength variations in inorganic structures.Amphiboles exhibit considerable deviationsfrom Pauling's second rule (Pauling 1960) fora formal bond-streqgth model, and thus bond-valence requirements should have an extremelystrong effect on bond-length variations inamphiboles. Tables 19 and 26 show empiricalbond-valence tables for selected amphiboles, inwhich it can be seen that the bond-length varia-tions observed tend to minimize the deviationsfrom ideality in the bond-valence sums aroundthe anions. As we saw when examining thetetrahedral double-chain, this is particularlysignificant with respect to cations co-ordinatingthe O(4) anion, all of whish show extremelyshort bonds to O(4). In order to maintain meanbond-lengths in accord with the size of theconstituent cationso there is a consomitantlengthening of the other bonds to these cations,resulting in extremely distorted cation-sites.This is evident from Table 29, which lists somedistortional parameters for the cation polyhedrain selected amphibole structures. Also in accordwith this argument h the correlation betweenthe dispersion of the M(2)-O bondJenghs andthe mean charge of the M(4) cations (Fig. a6).

Hawthorne (1978a) has also examined bond-length variations in the octahedra of the.

clinoamphiboles using the methods of Baur(1970, l97l). Sample calculations for tremolite(30), glaucophane(26) and pargasite(38) areshown in Table 30. For a priori prediction ofdistances, the calculated bond-lengths at theM(l) and M(3) sites are generally larger thanthe observed values, in agreement with the factthat the observed mean bondJengths are signif-icantly less than the sum of the constituentionic radii. Conversely, the calculated bond-lengths for the M(2) octahedron are small andthe amount of deviation from the observedvalues appears to be correlated with the meanionic radius of the constituent M(2) cations.This behavior is directly analogous to the meanbond-length - mean constituent-cation radiusrelationships outlined earlier. A more accurateprediction of bond lengths can be made ifBaur's relationships are used to forecast thedeviation of individual bondJenglhs from amean value predicted from the regressionrelationships of. Table 27. As indicated inTable 30, this does produce an improvementover the a priori values, but discrepancies be-tween observed and calculated values are stilllarge. This is not surprising, as bond-valencerequirements do not provide sufficient con-straints to exactly define the structure. Addi-tional features such as cation-cation repulsionand intermodule linkage requirements will alsohave an effect on bondJength variations, aneffect that is not recognized in the bond-valencemodels.

It has been suggested (Pauling 196O) that

TABLE 30. BorlD LENGIIIS FoR SELECTED Ar4pHrBoLEs CALCULATED By cation_cation repulsive interaitions are muchTHE METHoD 0F BAUR (1970, ]971)stronger than anion-anion repulsive interactionspx apx dcatc d;alc dobs ^d' ^d' and that, as a result, edges shared between

Tremli te(30)

! ! f l ) -g( t ) 2.00 +0.027 2.090 2.078 2.064 _0.026 _0.014I l l l -g(2) 1.92 -0.053 2.080 2.069 2.078 _0.002 +0.00eM(D-0(3)

?..8?t *o.or,

?W tffi u.qqt +o.ooi +0.005

THE CRYSTAL CHEMISTRY OF THE AMPI{IBOLES

2.133 +0.043 +0.0362.083 +0.003 -0.0042.014 -0.026 -0.033Tn772.070 -0.020 +0.004?.057 -0.033 -0.009uI66'

235

polyhedra are shorter and subtend smallerangles at the cation than unshared edges. In theoctaliedral strip of the clinoamphibole structure,the M(l), M(2) and M(3) octahedra share six,five and six edges, respectively, with adjacentcation polyhedra, suggesting that cation-cationrepulsion should play an important role inbond-angle distortion. As indicated in Figure 47,this appears to be the case. For the M(1) andM(3) octahedra, the separation of the edgesand angles into two populations correspondingto shared and unshared elements, together withthe marked linear correlations exhibited.suggest that cation-cation repulsion is of primeimportance. For the M(2) octahedron, althoughthere is a tendency for the data to separate outinto two populations corresponding to sharedand unshared elements, considerable overlapoccurs and the linear correlation is far lessmarked than for the M(1) and M(3) octahedra.Hawthorne (1978a) has proposed that a con-siderable amount of the angular distortion ofthe M(2) octahedron is a direct result of theO(4) bond-valence requirements. To assess themagnitude of this effect, the bond angles werecalculated for a holosymmetric octahedron withthe observed bond-lengths of tremolite(30),fluor-richterite(34) and fluor-tremolite(36). Theresults are given in Table 31, where they arecompared with the observed values. It isapparent that the anion bond-valence require-ments have a considerable effect on the bond-

M(2)-0( l ) 2.00 +0.167 2.090 2,0s7M(2)-0(2) 1,92 +0.087 2.080 2.087M(2)-0(4) 1.58 -0.253 2.040 2,047

r,tean T:833 12.-n6 z_on-M(3 ) -0 ( l ) 2 . 0o 0 .000 2 .0e0 2 .066M(3)-0(3) 2,00 0.000 2.090 2.066

lilean ZTil 7:6qE Z:d66

r ' t( l )-o(t)M( I ) -0(2)r,r( r )-0(3)

lilean

Gl aucophane( 26)2. '17 +0. '127 2,126 2.106 z,OtB1.96 -0.083 2.095 2.075 2.082

*8Fg -o'on' ?i8+ ?f# #+-0.047 -0.028-0.013 +0,007-0.001 +0.01 9

+0.056 +0.016+0.057 +0.017+0.009 -0.031

!(?)-q(t) 2.17 +0.2s0 1.959 2.003 2.038 +0.079 +0.03514(?) -S(?) 1 .e6 +0.040 ' t .eoe t ,gss t .ea3 *o .o iq -o .o torir(2)-0(4)

l,0L -o.zso

+#g +€i* ffi +o.ore -o.ozs

I ( 9 ) -S ( l ) 2 ' 17 +0 .057 2 .139 2 . t 04 2 .103 -0 .036 -0 .00 rM(3)-0(3) zr,?gs

-o.rr, #* ?H&

z.oz -o.o:r +o.ooz

Pargasi te( 38)'1.98 -0.013 2.103 2.086 2.056 -0.047 _0.0302.00 +0.007 2.106 2.089 2.1 'n +0.005 +0.022

i,33a *o'oot

il€g t*B ?'qff -0.00e +0.0081 .98 + . ] 00 2 .0132.00 + .120 2.017'1.66 - .220 1.957t-m T.996

2.053 2.0692.057 2.074'r .997

I .966z:656 Z:ffi

M ( r ) - 0 ( l )M( r )-0(2)r,r( l )-0( 3)

Mean

M(2) -o( r )M(2)-o(2)M( 21.e1 a1

Mean

ao ^ 90 roo(o-t i l ) -o) ' - 80 90 r0o

(o -M(21-o)"_.-8 0 9 0 t 0 0

( o - u ( g ) - o t " -

f1(1)-9( t ) r .e8 -0.007 2.103 2.076 2.076 -0.027 0.000M(3)-0(3) 2.00 +o.ol3 2.106 z.o7s z.oeo -o.ozb +o.dor

Mean ].9ET Z:TIE Znn 7.fr7

lcalculated from tJle relationship d=a+bp.. (Baur 1970) where dis the predicted bond length, p.. is thixsum ot ttre iomitbond.strengths received by the Anion, and a i ld b are empir_

, rcar ry oer lved cons tan ts-calculated from the relatlonshjp d=<d^.->+b^p--, where AD js

the bond strength sm deviation frcm tHB meanxvalue recilvedby the anions in a coordJnation polyhedmn

o o0)-o0) '! oi l1-o(2')o o([ ]oer).o o { r ) - o ( 4 ). O(2.)-o(4')! o ( 2 ' ) - o ( 4 d l '+ o ( 4 ' ) - o ( 4 " 1

/ } r

*uq" . 4 -.".tr

Ftc. 47. Variation in length of the octahedral edges with the correspond.ing angles subtended at the cationfor the octahedrally co.ordinated M sites in a variety of. C2/m imphibbles.

x o( ' ) -o0 ' )i o ( t ' ) - 0 ( l ' ) '. C{ l ' ) -o(3')o o 0 , l - o ( 3 . ) r

3.4

III| 3 . 2

II.;; 3 . o

236 THE CANADIAN MINERALOGIST

TABLE 31. CALCULATED O-X(2)-O ANGLES(o)' IN AMPHIBoLES l l l lH M(l)=M(2)=r(3)rMg*

Fluor- Fluor- Antho- Proto-Tremoli te(30) tremoli te(36) r ichteri te(34) phyl l i tet23l amphibolet20l

obs.

80 .0

92.8

ca lc . obs . ca lc . obs .86 .8 80 .0 86 .5 79 .7

ca l c . obs . ca l c . obs . ca l c .

84 .6 80 .4 86 .9 79 .6 W.7o( r ) -M(2) -o ( r )o( lu)-M(2)-o(?u)o( r u) -M( 2) -o( 2d)o( i )-r ' { (2)-o(4)o( 2u) -f i( 2) -O(4u)o( zu) -M(2) -o(4d)o(4)-M( 2) -o(4)

9 t . 09 0 . 5 )

i 9 3 . 095.6 !o o I

9 2 . 69 0 . 5 1

i 9 l . 99 3 . 3 !v 3 . f ,

9 0 . 3 I! o 1 0

%.41 ' " -

o R n

89.9

9 1 . 4

93.4

89.7

9 t . 6

9 5 . 2

88 .9

94.0 93.4 92.8

92.51188.4 88 .4

8 4 . 3 t93 . I 89 .697.01

) 9 1 . 5 9 1 . 38 6 . 0 !

9 1 . 4 1187.7 87.1

83. 9 l9 0 . 9 8 9 . 5J t . 5 t

,92.0 92.38 6 . 4 l

98.5 95.2

e2 .11 e ' r . e l 90 .2 )$.7f87.e

88.r 83.718i .8

88.3 82.6186.4

87.7

*angles calculated for a holosynrnetric octahedron with the observed M-0 bond lengths.

angle distortions of the M(2) site. This is pre-sumably the reason why the correlation forthe M(2) site exhibited in Figure 47 is less thanfor the M(l) and M(3) sites, where the anionbond-valence requirements are not as extreme.

Fleet (1974) has examined polyhedral dis-tortions in three amphiboles in terms of sation*cation repulsion across shared polyhedral edges.He noted that the M-M distances parallel tothe I axis M(l)-M(l), M(1)-M(4) and M(2)-M(3)l are stretched the most (Cameron & Gibbs1973) and suggested that this must reflect therelative rigidity of the tetrahedral elementparallel to the Z axis. This seems to be mostunlikely; much more important is the fact thatthe tetrahedrir will tilt relative to their mirrorequivalents to encompass expansion in the Ydirection. Hawthorne (1978a) has also examinedsome of the factors that can affect elementsshared between adjacent octahedra. There isconsiderable variation in the size of the octa-hedra in the clinoamphiboles with variation incation occupansy. As polyhedral elements areshared between octahedra' of disparate size,shared elements must adjust accordingly. Pro-minent in this respect is the mean size of thecations occupying the M(2) site; the variance inthe octahedral angle at both the M(1) andM(3) sites is negatively correlated with meanionic radius of the constituent M(2) cations(Fig. 8). Thus the mean ionic radius of theconstituent M(2) cation could have a significanteffect on the CFSE of transition-metal cationsat the M(1) and M(3) sites, and significantlyaffect cation ordering patterns.

The P2Jm amphiboles

There are tluee unique sites with pseudo-octa-hedral co-ordination in this structure-type, theM(1), M(2) and M(3) sites. Both the octahedra

and the way they link together are similar tothe corresponding octahedra in the C2/mamphiboles. However, the point-symmetry ofthe M(l), M(2) and M(3) sites is l, 1 and m,respectively. Our understanding of this structure-type sLlggests that it should be of magnesio-cummingtonite composition. In agreement withthis. nearly all P2'/ m amphiboles reported arerestricted to this compositional range (Rosset al. 1968a, Kisch 1969, R.ice et al, 1974,Yakovleva et al. 1978). This being the case, theoctahedral sites will show virtually completeoccupancy by Mg, and the only octahedralbondJength variations expected in this structure-type will be due to inductive effects of theM(4) cation(s). Thus the octahedral strip elementof tirodite P2t/ m(27) should be fairly repre-sentative of all compositional variations in thisstructure-type.

In tirodite P2t/m(27), the octahedral sitesare completely occupied by Mg, and the meanbond-lengths are not significantly different fromthose forecast from the curves of Table 27 forthe C2/ m amphiboles. Table 32 compares theindividual bond-lengths in tremolite(30) withthe corresponding mean values in tiroditeP2r/ m(27). The only significant difference isin the M(l)-O(2) bond, which is 0.030(4) Alonger in the P2r/ m structure. This may beinterpreted as an inductive effect due to thechange in the M(4) cation. The bonding radiusof (Mg, Fe) is much smaller than that of Ca,and thus the interaction between the M(4)cation(s) and the chain-bridging anions will bemuch weaker in Fe-Mg-Mn amphiboles. Inorder to satisfy the bond-valence requirementsof the M(4) cation(s), the bonding to the non-bridging anions O(2) and O(4) will have to bestronger in tirodite Y2t/ mQ7) than in tremolite.In order to accommodate this, the M(1)-O(2)bonds are longer in tirodite P2'/ mQ7) than in

T}IE CRYSTAL CHEMISTRY OF THE AMP}TIBOLES

0.60 o o.7o(r, r.r) (A) -

0 . 6 0 0.70<rM(2)> (A)

Frc.48. Variation of the variance o2 in the octahedral angle for M(l) andM(3) wilh the mean ionic radius of the'M(2) cations f.or C2/m amphi-boles (after Hawthorne 1978a). Open circles denote additional data fronlless precise structures.

237

II=

s t

bUJc,

3aEgLr.l-t(9z

240ocl

;

II roo

o' ; r

oUJ

ieosUJ(,zo 6 0zdt

lO

;

tremolite(30). Examination of the differencesbetween the M-O(A) and M-O(B) bonds (fable32) shows that the only significant differencesoccur for the O(2A) and O(2B) anions. Thisreinforces the above conclusion that the induc-tive effect of the M(4) cation affects the octa-hedral strip through the O(2A) and O(2B)anions.

All elements shared between adjacent octa-hedra are greater than all unshared elements,indicating the influence of cation*cation repul'sion. In addition, this amphibole agrees withthe correlations developed for the C2/mamphiboles (Hawthorne 1978a), indicating thatpacking considerations and bond-valence re-quirements significantly affect interbond angles

238 THE CANADIAN MINERALOGIST

TABLE 32. COMPARISON OF M-O BOND LENGfiSIN TIR0DITE p2.,n(z-7) AND TREM0LITE(30)

ti rodi teP2./n(d)

(avdraged) tremol i te(30) di f f .

M ( r ) - 0 ( r ) 2 . 0 5 8 ( 5 ) A 2 . 0 6 4 ( 4 4 0 . 0 0 6 ( 6 ) IM( I ) -0 (2) 2 .108(4) 2 .078(2) 0 . .030(4)M(r ) -0 (3) 2 .076(4) 2 .083(2) 0 .007(4)

and the amount of structural relaxation due tocation-cation repulsion.

The P2/a amphiboles

There are five unique sites with pseudo-octa-hedral co-ordination in this structure-type, theM(l)A, M(l)B, M(2)A, M(2)B and M(3) sites.The M(l)A and M(l)B sites have point-sym-metry 2 and are co-ordinated by four oxygenatoms and two O(3) anions that are OH in theonly representative of this structure-type found(Moore 1968a, b, 1969); the O(3) anions arearranged in a cis configuration. The M(2)Aand M(2)B sites have point-symmetry 2 andare co-ordinated by six oxygen atoms. TheM(3) site has point-symmetry 2 and is co-ordinated by four oxygen atoms and two O(3)anions arranged in a trans configuration. Theedge-sharing characteristics of these octahedraare similar to those found in the C2/ m amphi-bole structure.

Joesmithite (Moore 1969) is the only amphi-bole of this structure-type that is known. Poly-hedral distortions, aside from effects of localelectroneutrality, result largely from cation-cation repulsion effects. Shared edges betweenoctahedra are the shortest distances for eachof the polyhedra, and subtend the smallestangles at the central cation.

The Pnma amphiboles

There are four unique sites with pseudo-octahedral co-ordination in this structure-type,the Ml, M2, M3 and M4 sites. However, theM4 site will not be regarded as part of theoctahedral strip, and discussion of it will bedeferred until later. The Ml site has point-symmetry 1 and is co-ordinated by four oxygen

atoms and two 03 anions that may be OH-,F-, or O'-, with the 03 anions arranged in acls configuration. The Ml octahedron $haresfive edges with the surrounding octahedra ofthe strip and one edge with the M4 octahedron.The M2 site has point-symmetry I and isco-ordinated by six oxygen atoms; the M2octahedron shares three edges with neighboringoctahedra of the strip and two edges with theadjacent M4 octahedra. The M3 site haspoint-symmetry m and is co-ordinated by fouroxygen atoms and two 03 anions, the latterbeing arranged in a tans configuration. The M3octahedron shares six edges with the adjacentoctahedra of the strip. For the octahedral stripderived from the cations of the asymmetricunit, anions with x>0 are B-type anions whereasanions with r(0 are A-type anions (notecorrespondence with u-d nomenclature of themonoclinic amphiboles).

The relationship between grand mean octa-hedral bond-length and grand mean sonstituent-cation radius for the M l. M2 and M3 sitesis' shown in Figure 49. The values for antho-phyllitel23], holrhquistite[31] and gedrirel32]are linear, forming a trend that is approximatelyparallel to the corresponding relationship forthe C2/ m amphiboles. However, the value forgedrite[33] deviates by almost 0.Ol A in <r2,indicating that the bulk.chemistry of the sampleis not compatible with the structure-refinementresults. This is discussed in more detail inAppendix B3. Linear regression on the remain-ing three values gives the following relationship:<M-O> - 1.484+0.823<r> R = 0.99.

2.O8

o <

.6. 2'06I

2.O4

Ftc. 49. Variation in grand <M-O> with meanionic radius of the constituent cations for thePnma amphiboles; gedrite[33], denoted by theopen circle, was omitted from the regressionanalysis.

M ( 2 ) - 0 ( 1 ) 2 . 1 3 e ( 4 ) 2 . 1 3 3 ( 2 ) 0 . 0 0 6 ( 4 )M(2 ) -0 (2 ) 2 .081 ( s ) 2 .083 (2 ) 0 .002 (6 )M ( 2 ) - 0 ( 4 ) 2 . 0 t 4 ( 5 ) 2 . 0 1 4 ( 2 ) 0 . 0 0 0 ( 6 )M ( 3 ) - 0 ( l ) 2 . 0 8 0 ( 5 ) 2 . 0 7 0 ( 2 ) 0 . 0 1 0 ( 6 )M(3 ) -0 (3 ) 2 .060 (B ) 2 .057 (3 ) 0 .003 (e )

THE CRYSTAL CHEMISTRY OF THE AMPHIBOLES 239

The utility of this relationship is apparentimmediately in its indication of the unsatis-factory nature of the chemical analysis ofgedrite[33].

Papike & Ross (1970) and lrusteta &Whittaker (1975) noted that <M2-O> ingedrite[32] and t33l and holmquistitel31],respectively, are smaller than (Ml-O) and<M3-O> due to occupancy of M2 by con-siderable amounts of Al. However, a moresystematic examination of mean octahedralbondJength variation in the orthorhombicamphiboles has not been given until now. Therelevant data are summarized in Table 33 andin Figure 5O, where the possible variation inconstituent-cation radius is shown. Considerfirst the relationship for the M2 site. Theminimum value for holmquistitel31], themaximum value for gedrite[33] and antho-phyllite[23] are collinear. The values for ged-rite[32] assigned from the site occupancy ofPapike & Ross (1970) straddle this trend. Forthe Ml and M3 sites, the values for antho-phyllite are well defined; as a starting approx-imation, the curyes were assumed to passthrough the values for anthophyllite with a slopeof 1.0. The values for each site consistent withthe overall stoichiometry of each amphiboleare marked on each of the graphs (Fig. 50).There seems to be satisfactory agreement, ex-cept for gedrite[33], which shows a low (r)at the M3 site. Note that these curves indicatethat the crystal of gedrite[32] used in thethe structure refinement has Feu* at the M(3)site. The paucity of the data does not reallywarrant linear regression analysis at the presenttime, particularly as some of the site populationsare not that well characterized. However, theequations of the surves derived in Figure 50are: <M(l)-O> - 1362+(ru<o), <M(2)-O) - 1.513+O.782(rurzr) and (M(3)-O)- 1.348+<rM<s)>.

Note that these relationships are similar tothose of the C2/ m amphiboles in that theobserved mean bond-lengths are -O,02 A lessthan the sum of the constituent ionic radii,and the slope of the bond length - ionic radiusrelationship for the M2 site is significantly lessthan the ideal value of 1.0.

Th.e Pnma orthoamphiboles show consider-able deviations from Pauling's second rule(Pauling 196O) for a formal bond-strength model,and thus bond-strength requirements shouldhave an extremely strong effect on bondJengthvariations in orthoamphiboles. Table 22 showsbond-valence tables together with the formalbond-strength sums around the anions. Inspec-

TABLE 33. <M.O> DISTANCES AND RANGE OF POSSIBLECONSTITUENT CATION MDII CONS0NANT IIIITH X-MY SITE

P0PULATI0NS AND CELL C0NTEI{TS FOR THE Pnna AMPHIBOLESU U

<M-0>A .ftminA ."tra"A

Anthophyl 1 i tet2310.7220.7210.722

0.737 0 .7440.538 0 .5480.740 0 .7540.71 I 0 .7270.604 0 .6050 . 7 1 3 0 . 7 2 60.730 0.7400.585 0 .5940.725 0.743

Holmqui sti te[ 3l ]

Gedri tet32l

Gedri te[33]

tion of this table shows that the bond-lengthvariations observed tend to minimize the devia-tions from ideality in the bond-valence sumsaround the anions. As with the C2/ m amphi-boles, this accounts for the cations showingshort bonds to the O4A and O4B anions. Inaddition, where M4 is occupied by a monovalentcation (Li*), the M2 octahedron is much moredistorted than where M4 is occupied by adivalent cation. Examination of the orthorhom-bic amphiboles using the scheme of Baur (1970,l97l) is shown in Table 34. The results arevery similar to those for the C2/ m amphiboles.Bond lengths calculated for the M I and M3octahedra are generally larger than the observedvalues, whereas the deviation between theobserved and calculated bond-lengths for theM2 octahedron is correlated with the meanionic radius of the constituent M2 cation.

Polyhedral distortion seems to be dominantlydue to cation-cation repulsion, locally modifiedby factors specific to the amphibole structure.The distortion of the three octahedra in termsof shared and unshared elements is examinedin Figure 5l; the results are similar to thoseof the C2/m amphiboles. For the Ml and M3octahedra, the data separate out into twopopulations corresponding to shared and un-shared elements. For the M2 octahedron, thereis some overlap between the two populations,and the linear correlation is far less markedthan for the Ml and M3 octahedra. Thearguments put forward by Hawthorne (1978a)for the C2/ m amphiboles should be directlyapplicable to the Pnma amphiboles. Thus theangular distortion of the Ml and M3 octahedronshould be a function of the mean ionic radiusof the constituent MZ cations; Figure 52shows this to be the case. Similarly, the O4Aand O4B bond-valence requirements should

2.084( r )2 .076( r )2.070(2)2 . i0o(3)1 . e 3 2 ( 4 )2 .0e5 ( 4 )2 .oer (4 )r .e86(4)2.057(4)2 . r o r ( 3 )r .97e(3)2 .0e7(4)

MMM

MMM

t'lMM

MMM

240 THE CANADIAN MINERALOGIST

I"3'

3)o../"i

<r>r,(i)-

<r>M'a( i ) .-_

oronrn [sr]- HOLtvrQUlSTlTE [31]

crorrre lszl

o.rrnopnntrrr [z:]

HoLlaoursrrrr Igtl

oronrrr [::]HoLuoursrrrr [:t]

mrrHorHvLrrrr [zr]

oeonrrr llzlcrosrrr [:r]

1.95

0.60 0 .65

t1P-t--

l/ItI

II

.3oO{

f"lr-1 or orrrr [rz]

<r>rr(i) ---.-----*

0.72

Flc. 50. Variation in individual <M-O> with mean ionic radius of theconstituent cations for the Pnnu amphiboles; the possible ranges in meanionic radius of the constituent at each site consonant with the diffraction

THE CRYSTAL CHEMISTRY OF

considerably affect the angular distortion of theM2 octahedron, as seems to be the case foranthophyllitel23], as shown in Table 31.

The Pnmn amphiboles

There are three unique sites with pseudo-octahedral co-ordination in this structure-tytrr€,the Ml, M2 and M3 sites: these are similar tothe analogous sites in the C2/ m amphiboles. Itshould be noted that the M4 site is alsoprobably [6]-co-ordinate, but this polyhedronwill be considered in the section on the M(4)

TABLE 34. BOND LENGTHS (A) FOR SELECTED PNNA AMPHIBOLEScAtcULATED By TllE !!E1l10D 0F BAUR (t970, l97l)

Ml -014tit'l -024Ml-034M]-0 tBMl-028Ml-038Mean

241

obs.

2 .067(e l2 l ? n / o l2.078(9)2 .054( l 0 )2 . r 5 8 ( 8 )? .061 (8 )2.091

2.028( 8)' r . 985 ( r 0 )1.924(9)2.005( 9)2,021 (8)r .951 (8)I .986

THE AMPHIBOLES

Gedri tel 321

M4 = t6l Coordinate^ r l A zPX

, .102 lJB 'n ,+2.165 2,12? ?.1032.000 2,098 2.0792.095 2.112 2.0932.133 2.117 2.0982.000 2.098 2.0792:IB3 ZTIO 2.0-97

M2-0lA 2.102M2-024 2.165M2-04A 1.832M2-01B 2.095M2-028 2.133M2-048 1.800Mean Z:m

M3-0lA ?.102!13-034 2.000M3-0tB 2.095M3-038 2.000l.|ean Z:d66

r. 9982 . 0 t 0I .945I O O 7

2.004r o10

@2 . 1 n2.0972 . 1 1 0?.0972:T6

2.0022.014I .9492 .0012.0081 .943-tr-9862.062?.0482.06'l2.048z:ofr

2.055( 8)2 .01 7 ( 1 5 )2 .0e7 (e )2.023(13)2.057

Icalculated from the relatlonship d.a+btu where d is the predictedrururvPr r r r r ruc l ' J r bond ' length , px i s the sum o f the fomal bond-s t rengths rece ived

M4 = t5l Cgordinals M4. [7] Coordinate by the anion, and a and b are empirical' ly derived constants (Baur- r, )/

^:------f,-----T obs. 1970)

Px " Px 2calculated frcm the relationship d=<d-.-> +blpv where Ap" is theMl-01A l.rr5 'rJrl 'r.o8l l.rr5 ,.orl 'r.086 2.062(3) fomal bond-s*enstt rinui'i';i"';5"" i"*tbn-u""iitreigttr stm in aMl-02A 2.051 2.100 2.089 1.947 2,086 2.080 2.112(3\ coordinat ion polyhedronMt-03A 2,000 2.092 2,092 2.000 2.092 z.086 z.oezl l iM l -o tB 1 .995 2 .091 2 .oB I t . 995 z .og t 2 .086 2 .053 i41Ml-028 2.064 2.101 2.090 l .9so 2.086 2.080 2.133(3)Ml-038 2.000 2.092 ?:98? 2.000 2.992 2.086 2.063(3)I'lean 2.0:lg @ @ 1.36T Z-o=90 z:Oe' 2:!=64* site. Only one example of this structure-type

M2-01A r.ee5 2.0er 2.0s4 1.99: ?.ggl ?.9!g ?.l lc(l) has been reported (Gibbs 1962, 1969, Gibbsw-024 2.061 2.099 2.092 1.947 2,086 2.082 2.067(3) "-", ' - ;- i .-r_-, ' :--M2-04A t.tzs i.oig i.osl 1.614 2.044 z.o4o 2.0r0(;J et al. 196O); this was called "protoamphibole"

il!:3i| t'j|i 2'.i3[ |]n l:333 !:331 !:333 |:l:,Ll'rl as it appears.to bear the same rerationship toM2-o4B r.731 2.060 a$r t.av z.oq4 i.oai t.ogti3i tremolite and anthophyll ite as protoenstatiteri'rean r:qa @ re l'EE m74 @ M- (Smith 1969) does to diopside and enstatite. Inil3:3li L:333 i:331 i'.3i3 L:338 i'.331 3'.313 !:3l8tll proroamphibore, the Mr, M2 and M3 sites areil3:3l| 11333 i'.391 Z'.313 1.3?fi 2'.",i1 i:3i3 i:3l3l3l compretery occupied by Me.rabre 35 compares'M";;

i.6ti i"-6i e!tr i5# t:ffi ffi ffi lhq octahedral bond-lengths in protoamphi-

Hotnouistiter3ll bole[20] with those in tremolite(30), fluor-rich-

M4 = r5l coordinate M4. r7l coodtnate terite(34) and fluor-tremolite(36). The (Ml-O)

;,.-:T:;i ;:=r--;r lil"f i;:"ff[:;li'3,'i_:,#i::l]"il'?,"',::1fi: -

ill:S}f 2.1tr2 'r'.ill 3.[[i i'}18 i.ifi i'.tr31 i.iill3l terite(34) and fiuor+rJmorite(36), being armostMr-03A 2.000 z.ls 2.088 ?.999 ?.ltg z,.g?2 ?.Sg!(9) as large as <Ml_O) in tremolite(30). How_ill:3}B 2:lZ3 i'.12i i'.llj i:113 3'.1ii i.li,? 2.ii3l3l ;;.;,-"<r',rr-oj ro. protoamphiborer2ol isM1-038 2.000 2.118 2.0ss z.0oo z.la z.osz z.ogs(aj intermediate between the values for fluor_rich-Mean 2:0aS ZfO ZmO Z.d@ re. -m am0--M2-ojA 2..156 l.eb4 t.e7B z.ts6 .1.e54 .1.e87 z.orrtd terite(34) and. f luor-tremolite(36), and it ist42-ozA z.o:r t.sis i.eai i.et6 i:eii i : iA i.g,i i i i6t diff icult to explain the large <Ml-O> distance;il3:3i| l:i33 l:$ti l:393 l:f33 l:33i l:331 l:3i3[3] <M(2)-o> ii statisticarry identicar in au threen2-0a 2.033 1.e25 1.e4e 1.92q !.gll 1.911 l.g?gitb) f luor-amphibole structures and is equal to theK;3it **'3 ffi i*"3 +€fg ffi +€8t i:#,1 "o.."rponding,distance in tremolite(30).M3-0lA 2.1s6 2.164 2,103 2.1s6 2.164 2.103 e.rorril The stereochemistry of the octahedral stripM3-03A 2.000 2.130 2.06e ?.ggg ?.llg ?.gqg ?.gl7il! is similar to that of the natural amphiboles.ni-o lB 2.1s6 2.164 2,103 2.1s6 2.164 2.103 2.109(e) ' ; " "" . : - ' ' " "

. ; ' - 'M3-038 z.ooo z.j:o 2.oog e.ooo z.uo z.oog i.oiotiil Inspection of the empirical bond-valence tableri'rean zJM rc M. nm Zf,TT 2;095 Z.d for protoamphibolet22l (Table 23) shows that

data and chemical analysis are shown (open circles). The relationshipshown in each graph was derived to obtain the best fit for all three sites,together with the constraint that these relationships should be fairlysimilar to the analogous ones for the C2/m amphiboles.

242

a

3 .

"f"$

90 lo0o_Ml-o (' l-_.

Flc. 51. Variation in length of the octahedral edges with the corresponding angles subtended ar the centralcation for the Ml. M2 and M3 sites in the Pnma amnhiboles.

THE CANADIAN MINERALOGIST

t1 3 0I

.3t .

3" t

II

I

sl

bEo

.F

o

.2!t

c,

E tco

(tq

o-cl

fo

ItIII

d'

b

co;o

.2 60E

gE tg

E'

!,

Eeo3

=

Ftc. 52. Variation of tle variance o2 in the octahedral angle for Ml and M3 with the mean ionic radiusof the constituent M2 cations inthe Pnma amphiboles,

0.60 o o.7or". (A)-.-

the bondJength variations tend to minimize thedeviations of the bond-valence sums from theirideal values. As is evident from Table 31,the M2 octahedron is far more distorted thanthe corresponding octahedra in tremolite(3O)and fluor-tremolite(36), as expected for anamphibole with a high M4 occupancy of mono-valent cations. Polyhedral elements sharedbetween adjacent polyhedra are generally shorter

0.60 0.70o

ro.(A).--..-..-----*

than the unshared elements, presumably as aresult of cation--cation repulsion (Gibbs 1969),and the steric effects of the 04 bond-valencerequirements significantly affect the interbondangles of the M2 octahedron, as shown in Table3 1 .

Tun M(4) Srrr

The M(4) site is situated at the junction of

3 .2

IIIt , 3 . 0

at

"? * 2.8

o-M3-o f)'---------------

0 . 6 0 o