Miissbauer Spectra of Synthetic Hedenbergite-Ferrosilite Pyroxenes'

Amefican Min.eralogist, Volume 58, pages 850-868, 1973

MiissbauerSpectra of Synthetic Hedenbergite-ferrosilitePyroxenes'

ERrc Dowry,

U. S. Geological Suruey, Washington, D. C.

D. H. LrNnsrEys

Carnegie Institution ol Washington, llashington, D. C.

Abstract

The hedenbergite-ferrosiliteseries may be taken as representativein some respects of other sections across the common pyroxens quadrilateral. Data are reported for eight clinopyroxenes synthesized at a temperature above the augite-pigeonitesolvus, plus two orthopyroxenesnear ferrosilite in composition.Clinopyroxenes less calcic than about Fse,Wor were found to have the pigeonite structure (p21/c) on quenching. The assignmentof doublets and the interpretation of area ratios in the Miron cations in site Ml. These four types arise from random distribution of calcium and iron in M2. Overlap of some of these doublets with the M2 doublet causesthe area anomaly (overestimation of M2 area) previously noted when only two doublets are fitted. This overlap apparently also influences area ratios of liquid-nitrogen temperature spectra of high-calcium pyroxenes, but in these spectra, it does not seem to be possible to fit all the different Ml doublets, owing to their close superposition.This makes it questionablewhether very accurate site distributions for high-calcium clinopyroxenescan be obtained from Mtissbauer spectra,even at liquid-nitrogen temperature. The quadrupole splitting of both M sites can be rationalized with Ingalls' crystal-field model. The Ml site, becauseof its low distortion, is very sensitive to small changes in its environment, hence the several doublets for different next-nearest-neighborconfigurations. Variation in quadrupole splitting of the distorted M2 site, though less pronounced than that of Ml, probably representslarger structural variations, becauseat high distortion, quadrupole splitting is less sensitive to small changes. The curve of M2 quadrupole splitting versus composition resemblesin its shape the augite-pigeonitemiscibility gap, providing a possible illustration of the crystal-chemicalbasis for thrs gap.

Inhoduction relations obtained with as many different experi- The notorious complexity of the phase relations mental techniques as possible. We report here a and crystal chemistry of the pyroxenes suggeststhat reconnaissancestudy of a series of synthetic pyrox- there may be a great deal of information about enes by Mrissbauer resonancespectroscopy of iron. geologic processes in pyroxene assemblages.This The principal emphasis of most previous Mcjss- complexity also makes it desirable to have informa- bauer work on pyroxenes has been the measurement tion about pyroxene crystal chemistry and phase of order-disorder relations of iron and magnesium over the two nonequivalent metal sites, Ml and M2. 'P"blt."tt.n authorizedby the Director,U.S. Geological For some compositions, order-disorder may be con- Survey. sidered independently of the other problems of the ePresent address:Department of Geologyand Institute crystal chemistry of pyroxenes. Study of this sort of Meteoritics,The Universityof New Mexico,Albuquerque, began with orthopyroxenes (space grovp Pbcq), NewMexico 87131. sPresent address: Department of Earth and Space since they may be regarded as essentially a solid Sciences,State University of New York, Stony Brook, solution of enstatite (MgSiOr) and ferrosilite New York 11790. (FeSiOa). The first work was by X-ray diffraction 850 MOSSBAUERSPECTRA OF SYNTHETIC PYROXENES

(Ghose, 1965), but emphasishas shifted where 20 kbar should be representativeof more magresian possible to Mdssbauer spectroscopybecause of sectionsof the pyroxenequadrilateral at lower pres- greaterprecision and rapidity (e.9.,Virgo and Haf- sures. ner, 1968, 1969,1970;Dundon and Hafner, 1971; A room-temperatureMijssbauer study of a series Saxenaand Ghose, 1970, 197 l) . of clinopyroxeneson the join hedenbergite-ferrosilite Somework in the samevein has also been done was reportedby Dundon and Lindsley (1967), and on clinopyroxenes,augite (spacegroup C2/c) and preliminary results for the present study at liquid pigeonite(P2r/c), especiallysince the return of the nitrogentemperature (90"K) were given by Dowty lunar samples(Bancroft and Burns, 1967a;Hafner and Lindsley (1970). More extensivework, in- andVirgo, 1970;Hafner et al, 197l) . Interpretation cluding particularly room temperature spectra, has of Mcissbauerspectra of clinopyroxenes,however, is shown that some suggestionsmade in the latter re- somewhatmore complicatedthan that of orthopy- port were probablyunwarranted; this report should roxenes, since clinopyroxenesoften consist of an be consideredas supersedingthe earlier work. exsolutionintergrowth of two phases.Clinopyroxenes also containconsiderably more calcium than ortho- Experimental pyroxenesas well as somewhatlarger quantities of Synthesis minor elements such as aluminum, titanium and manganese.AIso, certain technicalpoints have not Pyroxenesused in this study were synthesized yet been establishedconclusively for clinopyroxene from mixturesof Fe-sponge,Fe2O3, quartz (from Lis- spectra,particularly the assignmentof peaks and bon, Maryland) or SiO2-glass,and (exceptfor pure the relative rates of absorption, or recoil free frac- FeSiOs) CaSiOepreviously made from CaCOgand tions, of the two sites.One objectiveof the present quafiz. (Details of the starting chemicalsand weigh- study, concernedwith a seriesof magnesium-free ing procedure have been given by Lindsley and pyroxeneson the join hedenbergite(CaFeSizOo)- Munoz, 1969,p.320).In mostcases these starting ferrosilite (FeSiO.3),was to provide some back- materialswere initially reactedin evacuatedsilica- ground for general clinopyroxenestudy in the form glasstubes at 900-950"C to mixtures of fayalitic of assignmentof peaksin the spectra,and interpreta- olivine, silica, and (for all but the most iron-rich tion of the area ratios of the peaksfor the two sites. compo,sitions) calcium-rich metasilicate. Approxi- A second objective was to try to provide some mately 0.7 g of the pre-reactedmixes were then crystal chemical information which might not be sealedinto silver capsules(12.7 mm long by 6.35 obtainable with other methods, through study of mm outer diameter) togetherwith 20 mg distilled the hyperfineparameters, quadrupole splitting, and H2O, and 1,to 2 mg excesssilica glassto saturate isomershift. the vapor phase.Initial attemptsto synthesizeiron- The choice of the join hedenbergite-ferrosiiite rich pyroxenesyielded products with severalpercent over similar but more magnesiansections in the magnetite,presumably caused by the difiusion of pyroxene quadrilateral (diopside-hedenbergite-fer-hydrogenthrough the silver capsules.Addition of rosilite-enstatite)is advantageousfor severalreasons. trace amountsof acetoneto the starting materials First, subsolidusphase relations on this join are com- inhibited this oxidation.Each capsulewas then re- parativelywell known, whereaslittle work has been acted for approximately2 hours at 20 kbar and done in the interior of the pyroxenequadrilateral. 950'C in piston-and-cylinderapparatus. Two of'the Second,restriction to two kinds of cations,Fe and pyroxenes,FSaz.s and FS1s,s,wero synthesizedby Ca, reducesambiguity in the interpretationof Mciss- repeatedruns in smaller (-0.01 g capacity) cap- bauer area ratios. Third, the relatively high iron sules. content facilitatesMcissbauer study. Our pyroxenes Other than pyroxene,the run productswere pri- were all made at 20 kbar, not becausewe wanted marily fayalite and silica, and occasionally very to study high-pressurephases, but becausethis sup- minor amountsof magnetite.Products were ground pressesfields of pyroxenoid and of fayalite plus and rerun until the content of unreacted fayalite silica, which would have interfered with synthesisof plus silica was judged by microscope examination a completeseries of pyroxenesat lower pressure.In to be well under I per cent. Microprobe examination respect to many of the crystal-chemicalproperties of pyroxenes synthesizedunder similar conditions here of interest,the hedenbergite-ferrosilitejoin at hasshown that compositionalvariations are less than E52 E. DOWTY, AND D. H. LINDSLEY

3 per cent CaSiOs. Incomplete reaction would tend the full width at half height. Flowever, experimental to make the pyroxenes slightly more calcic than their lines are usually more or less nonideal. In fitting the nominal composition, but the average composition synthetic pyroxenes, a Gaussian component was is probably within one-half percent of the nominal added in some cases,in order to take better account value. of several types of nonideality of line shape. Line broadening caused by essentially random factors, Mdssbauer such as inhornogeneities in composition, chemical Samples were fine-ground and mounted in one- disorder over some sites, temperature variations, inch diameter disks of Buehler transoptic plastic. crystalline defects, e/c, should lead to a Gaussian Spectra were taken on a 200 channel, constant- "smearing" of the line. The true line shape in this acceleration"flyback" spectrometer (DeVoe, 1967). case would probably be closely approximated by a Velocity increment per.channel was usually about combination of Gaussian and Lorentzian shapes.A 0.04 mm/sec. Concentrationsof iron in the absorbers line shape of this kind, called the Voigt profile, is and background counts recorded for each spectrum well known in spectroscopy (see, for example, are given in Tables 3 and 8. The resonance effect at Posener, 1959). An exact evaluation of this line the peaks assigned to the Ml doublet was in the shape calls for solving an integral at each wavelength neighborhood of 10 to 12 percent at liquid nitrogen or data point. We have not yet been able to adapt an temperature for the absorbers with the greatest accurate method for approximating the integral to concentration of iron, and correspondingly less for rapid least-squaresanalysis, and we have therefore those with smaller concentrations. A metallic iron adopted a simple sum of Lorentzian and Gaussian foil with concentration 18 mg/cmz of natural iron terms to describe the line shape. The line shape we was used for calibration. All I.S. (isomer shift) used for the final fits, following suggestionsby W. values are reported relative to iron = 0.0 mm/sec. A. Dollase (personal communication) is: Liquid-nitrogen temperature spectra were taken in moving-source geometry in a styrofoam-insulated c\x):2Af t-u cryostat (DeVoe, rl7;.1,_;;1 1967), using a source consisting + o\-F-i of Co'? in metallic chromium; the source was at L{t / room temperature. The widths of the inner two lines of the metallic iron calibration spectrum measured at ia (l) room temperature were 0.30 mm/sec with this source and geometry. Absorber temperature in the liquid-nitrogen cryostat is assumed to be 90.K where o is the fraction of the area accounted for (DeVoe, 1967). Room temperature (294K -+I") by the Gaussianpart of the line. There are thus four spectra were taken in moving absorber geometry, parameters to be simultaneously varied for each using a source of Co'? in metallic palladium. With peak, A, x,, I and ,a, instead of three as in the case this source the widths of the inner two lines of the o{ pure Lorentzian lines. iron spectrum were 0.25 mm/sec. Such a line shape is only an approximation, but Theoretical line shapes were fitted to the data it has been found to be very useful with respect to with a Fortran program on the IsN{ 360/65 com- reducing the residual chi-square, and it is doubtful puter, using an adaptation of the metric minimization if a more accurate approximation is justifiable in procedureof Davidon (1959). Chi-square,the usual many cases of mineralogical Mrissbauer spectros- residual, was minimized. copy. We did attempt to approximate the integral Ideally, line shapes are given by the Lorentzian (Voigt profile) numerically by means of a small formula, in which the absorption at each channel (5 to 7) number of Lorentzian peaks having a due to each peak is given by Gaussian distribution, but the computing time was ,l increased, while the residual was not significantly l(x):-f ,r, reduced compared to the fits using the line shape ,'.rit+4(*-*"1,( given in equation (1) above. \ r /) Almost invariably, the use of the partially Gaus- where x is channel number, I is the area, xo is the sian line shapehas been found to reduce the residual location in channel number of the peak, and I is of fits in far greater proportion than would be ex- MASSBAUER SPECTRA OF SYNTHETIC PYROXENES pectedsolely from the additional adjustmentparam- doublet, and perhapstwo to three times thesevalues eter. In many spectra of chemically complex or in- for the multi-doubletmodels. homogeneouscompounds, there is a particular kind of "misfit" when I-orentzian lines are assumed-the PhaseComposition of the Pyroxenes fit generally overestimatesthe absorption in the Since exsolution and domain structuresare corn- region of the precise center of the tails and at the mon in clinopyroxenes,we have tried to characterize peak, while underestimatesthe absorption just it the material closely insofar as possible by single- to either side the peak center. This kind of misfit of crystal X-ray study. C. W. Burnham and Y. Ohashi, is "cured?'when term is added. a Gaussian who are presently carrying out independentdiftrac- There real dangers, in the use are however, of tion investigationsof some of the material synthe- the Gaussianterm. principal seemsto be The one sizedin this and previousstudies, have supplemented that it also reducesthe residual when rpn-random our resultsin this respect. deviationsfrom involved. I-orentzian shapeare The Ten pyroxenes (Table 1) were synthesizedat present work gives an example of a case in which 950" C and.20 kbar. Although there is a changeof several non-randomly peaks distinct, distributed ap- symmetry in the series, from C2/c (diopside or pear to be a more correct descriptionof the spectra hedenbergitestructure) in the more calcic composi- than partially singlel-arcntzian or Gaussianlines. tions to P2r/c (clino-enstatiteor pigeonitestructure) in the less calcic ones, no definite evidence was Erros of MdssbauerMeasurements found for the existenceof an augite-pigeonitesolvus. X-ray powder photographs, taken on the Hiigg- The estimatedstandard deviations for the param- Guinier camera, and powder diffractogramsof the eters derived from our least-squaresfits are given in composition in the critical region FszoWogoto parenthesesin the tables. Some cautionary words FssoWoro,showed no splitting of lines which could about these errors are in order, however. They ap- be ascribedto the presenceof two pyroxenes.Some ply for the most part only to the lack of precision of the lines were fairly broad, but this was char- introduced by counting statisticsin each spectrum acteristic of most specimensand can probably be (and also in the calibration spectrum, in the case ascribedto the compositionalinhomogeneities of 3 of hyperfine parametersand widths). It is unlikely, percent or less expected in such syntheses (see for example,that errors introduced by velocity drift above). Thesefindings are consistentwith the hypo- in the spectrometerand other instrumentalerrors are thesisof Lindsley and Munoz (1969) that the clino- fully accountedfor, and of course,error in composi- pyroxene solvus on this join is occludedmetastably tion introduced during synthesisis not considered within the orthopyroxene-clinopyroxenefield at at all. Also, the errors apply only to the particular temperaturesbelow 950"C. The previous finding parameter spaceassumed for the fit, that is, if dif- that Fh/c pyroxenes invert to C2/c at high tem- ferent numbersof peaks are assumed,very different parameterswith non-overlappingerrors are obtained. A specialcase occurs when the number of parameters T,lerE, 1. Symmetries of Synthetic Pyroxenes is atmostequal to the number of channelswhich give Fs Opttcal X-ray X-ray useful information; at this point, the assumptions Content Dethod g!oup which underlie the derivation of errors from least squaresfits begin to break down. 50 nonocli.nic We may be ap- 60 proachingthis 70 casein the multi-doublet fits to room- czl c 80 2 crvstals c2lc temperaturespectra discussed below. 2 crvstals P2,/c* (4 crystals) Without extensivereplication of all steps in the 85 87.5 izlti experiment, including synthesis,absorber prepara- 90 Fz!ti Gulnter 98 orthorhonbic tion, and sample and calibration spectral runs, an 100 accurateestimate of the precision is impossible.We t. ohashi, personal coffiunlcation. The crystals of Psanwo16 sere taken believe,however, that the hyperfine parametersand f.on a special run made for the sole purpose of obtatnlig l:rge ctystals' fre charge was seeded ulth sevelal crystals frm a prevtous !un. fre widths are reproducible to about 0.02 mm/sec, 1ar8e crystals thus obtained ni8ht be expected to be son$hat lnhonogeneous, and the presence of boch symetrtes does not necessarlly lndlcate the and the fractional areasto about 0.01 to 0.02 for exlstence of a tvo-cllnopyroxene fleld at the nomlnal cobposltlon. **c.w. gurnnam, simpler spectral models, i.e., one MI and one M2 personal comunication. E, DOWTY. AND D. H. LINDSLEY

peratures(Smyth, 1969) suggeststhat the lesscalcic clinopyroxenes(Bancroft, Maddock, and Burns, clinopyroxenesmay actually have formed with C2/c 1967;Dundon and Lindsley,1967; Matsui, Maeda, symmetry,as part of a completeclinopyroxene sedes, and Syono, 1970). Williams et al (1971) found and that they invertedto P2r/c on cooling. these anomaliesto be generallypresent in natural A domain structureof someP21/c pyroxeneshas and synthetic C2/c pyroxenes, and attempted to been inferred from the diffusenessof the h + k explain them by postulating a domain structure odd reflections (Morimoto and Tokonami, 1969; whereby two distinct phases,differing primarily in Clark et al, l97l), and corresponding domain calciumcontent, and thereforetwo doubletsfor each boundarieshave been observedin electronmicro- site would be expected.They suggestedthat the M2 graphs (e.9., Christie et al, I97l). None of our doubletsfor the two phaseswere essentiallycoin- P21/c pyraxeneswhich had grains large enough for cident, while the Ml doublets were separatedat single-crystalstudy appearedto have diffuse h + k room temperature.If one of the Ml doubletswere odd reflections(Y. Ohashi, personal communica- closeto the M2 doublets,fitting only two doubletsto tion). There is hence no evidencefor Morimoto- the spectrummight tend to augmentthe areaof the type domains. M2 doubletsat the expenseof Ml. Williams et aI Thus all our pyroxenes seem to be single-phase (1971) were able to obtain Ml/M2 area ratios specimens,with no exsolution,and no apparentdo- which agree with those from the liquid-nitrogen main structure.It is important to point out, however, temperaturespectra by fitting two Ml. doublets.At that most of thesecompositions are only stable at liquid nitrogen temperature,according to this hy- high temperature,and thosewithin the broad ortho- pothesis,the Ml doubletsbecome more similar to pyroxene-clinopyroxene solubility gap found by each other, while both are resolvedmore distinctly Lindsleyand Munoz (1969) are metastableat room from the M2 absorption. temperature with respect to two pyroxenes. (Of Like Williamset al (1971), we supposethat more course,at low pressurethe more iron rich ones are than one doublet is necessaryto describethe Ml alsometastable with respectto fayaliteplus quartz.) absorption.Ifowever, we proposean explanationfor this which is somewhat different and more satis- Assignmentand Area Ratios of MiissbauerPeaks factory in certain respects than the domain hypothesis.Our hypothesisinvolves variation in next- Room T emperatureSpectra nearest-neighborconfigtrations of the Ml site, due In the pyroxene structure, there are two metal to purely random distribution of iron and calcium sites,M1 and M2. Ml is occupiedin both heden- in the M2 site. Although next-nearest-neighborin- bergite and ferrosilite by ferrous iron, while M2 is fluencehas been considered as a causeof variationof occupiedin hedenbergiteby calcium, and in fer- hyperfine parametersin silicates (Bancroft, Mad- rosilite by ferrous iron. Ferrous iron in eachof these dock, and Burns, 1967), it has not generallybeen sites would normally be expectedto give rise to a thought to be sufrcient to cause actual splitting of doublet, and often two apparentdoublets can be the doublets.However, it will be shown in the next distinguishedby eye in the spectra.In orthopyrox- sectionthat quadrupolesplitting of iron in the pyroxenes,the two outerpeaks have been assigned to iron eneM'J. site, because of the low distortionof this site, in Ml, and the two inner peaksto iron in M2. We is extraordinarilysensitive to small changesin the have found this assigrment to be correct also for environment,more so than iron in most silicatesites. the hedenbergite-ferrosiliteseries at both roorn and Each MI octahedron in pyroxene shares edges liquid-nitrogentemperatures. Recent work (Williams with threeM2 polyhedra.As the compositionchanges et al, l97l) has also confirmedthis assignmentfor through the series hedenbergite-ferrosilite,the oc- certainnatural sub-calcicpyroxenes. cupancy of the M2 site changesfrom all calcium to However,in previouswork and the presentstudy, all iron. The Ml octahedronalso sharesedges with anomalieshave been found in the relative areasof other Ml octahedra,but Ml is always occupiedby the peaks in room temperature spectra o,f some iron. Thus, four basically different types of next- clinopyroxeneswhen the above assignmentis fol- nearest-neighborconfiguration may be distinguished lowed. Often, one or both of the peaks for M2 seem for the Ml site, according to whether the three far too intense. This is one reason why alternate adjacentM2 sitesare occupiedby: (1) three iron assignmentschemes have been proposed for some atoms; (2) two iron atoms and one calcium ato'm; MASSBAUER SPECTRA OF SYNTHETIC PYROXENES 855

(3) one iron atom and two calcium atoms; and Trsrn 2. Expected Relative Iron Occupancies for the M2 (4) three calcium atoms. The probabilities of each Site and Four Next-Nearest-Neighbor Configurations of the Ml Site in Hedenbergite-FerrosilitePyroxenes of theseconfigurations, assumingrandom distribution of cations in M2, are easily worked out for each ul* composition, and the resultant expected fractional FS (1) Contenl lle, oca areas, with the expected fractional area of the M2 site, are shown in Table 2. 50 1.0 60 0.007 0.080 a. i20 427 0.167 T\e M2 polyhedra share corners, but not edges, 70 .446 246 308 .154 -286 t5 .083 .250 .250 .08:] ,333 with other M2 polyhedra. Furthermore, as will be 80 .135 270 .180 .040 ,375 85 2A2 .2s9 .1ff .016 ,4t2 shown in the next section, quadrupole splitting of 8t .5 24I . 080 .009 429 90 .285 ,2IL .053 .004 .444 the M2 site is not nearly so sensitiveto small changes 98 .056 .002 - '490 in the environment as that of Ml. Thercfore, only a 100 .500 - .500 single doublet is expectedfot M2. In attempting to fit theoretical line shapes to the room temperature spectra, we have considered four hypotheses: (1) that the absorption for each site consistsof a single doublet, with lines of Lorentzian or near Lorentzian shape; (2) that each site is represented by a doublet with lines of partially Gaussian square was usually reduced in these fits (Table 3). shape, that is, lines which have been broadened by When the peaks were unconstrained (using either essentiallyrandom factors; (3) that the M2 absorp- pure Lorentzian or partially Gaussian lines), match- tion is adequately represented by a single doublet, ups of peaks into doublets were not obvious from but that the Ml absorption is split into two doublets their areas, and if peaks were assignedto doublets becauseof the presenceof domains as suggestedby on the basis of the conventional assignment, which Williams et al (1971); G) that the M2 absorption assumesthe two M1 doublets to have similar isomer is adequately represented by one doublet, but that shifts, no systematic patterns were discerned in the Ihe Ml absorption is split into up to four doublets, relative areas of the two Ml doublets. Also. for becauseof next-nearest-neighboreffects, as explained many of the spectra, the resultant MZ/MI arca above. Chi-square values for the four types of fit are ratios did not agree well with those expected. Fits given in Table 3. were tried with heights and widths of the two peaks (1) When four Lorentzian lines (two doublets) of each doublet constrained to be equal, but in this were fitted, with no constraints, the M2/Ml arca case, the locations of the Ml peaks sometimes ratios obtained were 4nsrn2l6us-the M2 area was migrated in such a way that the isomer shifts of the larger than predicted, and this anomaly increased two Ml doublets were not nearly the same (in with calcium content (Table 4). Our spectra are other words, the locations of two of the Ml peaks very similar in this respect to those of Dundon and which were close together would be interchanged). Lindsley (1967), provided we assign their peaks so that the M2 doublet inside is the Ml doublet. These Tesrn 3. Data Collection Information and ChiSquare area ratios are quite unacceptable, and indicate that Values for Room Temperature Spectra of Synthetic this description of the spectrum is inadequate. Fur- Hedenbergite-FerrosilitePyroxenes thermore, values of chi-square for these fits are very high (Table 3). Chi- s qua r€ Iron Bkgd. (2) Addition of a Gaussian component to the c ts. n e/cn'2 x 105 fitted lines reduced chi-square values, but the anomalies in area ratios persisted (Table 4). We 50 3.7 177 714 2 tentatively 60 5.6 388 208 2tq I7q conclude from this that the perturbing lo ]. IJ 6.9 3II 1-53 l3q 757 4 influences on the M1 15 1() 5,4 237 116 r27 5 doublet are not random. 80 7.3 5,7 639 235 1i4 1q2 4 (3) Several attempts to fit two Ml doublets and 85 6.7 563 204 300 254 4 87 5 2.6 6.5 135 101 121 127 one M2 doublet were unsuccessful with respect to 90 8.7 5.6 448 2i5 252 i49 3 98 1-9 5.fl 217 173 r76 obtaining reasonable and systematic area ratios, 100 3.2 7.5 r49 2 quadrupole splitting, and isorner shift, although chi- 855 E. DOWTY. AND D. H. LINDSLEY

Tau,E 4. Area Ratios and McissbauerParameters (mm/sec) for Two-Doublet Fits to Room Temperature Spectra of Synthetic Hedenbergite-Ferrosilite Pyroxenes

Mr M2 - M2 Area Wldths Widths

Content Expected Lorent, Gauss. QSISLHqSIS

50 0.0 2,222(2) 1.188(2) o.294(5) 0,297(5) 60 .167 0.436(17) 0.251(3) 2.36O(s) 1.187(2) .477(LL) .475(8) 1.909(10) r.138(s) 0,349(13) 0.412(9) 70 .286 .45s(7) .473(9) 2.573(7) 1.183(4) .408(11) .39s(7) r.862(7) 1.140(4) .332(11) .422(6) 75 .333 .466(15) .5r2(9) 2.s7O(6) 1.163(3) .338(r2) .392(6) L.823(7) 1.10s(4) ,369(9) .37s(6) 80 .37s ,456(7) .496(4) 2,545(3) r.177 (2) .359(7) .3e4(5) 1.763(3) 1.116(2) .322(6) .372(5)

85 .4r2 .s72(7) .537(3) 2.s2O(3) 1.180(2) .339(5) .3s6(s) 1.7e8(3) L.Lr4(2) .326(4' .396(5) .429 .509(11) ,s76(4) 2.538(7) r.169(3) .334(5) .348(s) 1.844(6) r.1r7(3) ,330(5) .355(5) 90 .444 .523(8) .s4s(4) 2,547(3) r,L76(2) .32r(5) .323(4) 1.887(3) 1.72s(2) .315(4) .376(6) 98 .490 .480(8) .478(3) 2.488(3) 1.179(1) .313(4) .28s(4) 1.910(3) L.r2s(2) .281(4) .289(4) r00 .500 ,4s1(9) .434(8) 2.490(5) 1.182(3) .296(10) .264(6) 1.906(4) 1 11A/t\ 'q4lO\ '14l(\

QuadruPole spliEtlng (qs), isoBer shlft (IS), and full wldths at half-heLght (lou and blgh velocity) are flon pattlally Gaussian fics. Figures in parenrhese6 represent e6tl@ted standard deviation fron rhe least-squares fits, io tems of the Ieast units ciEed.

C'f course, we cannot claim to have exhaustedall are shown in Table 2, the middle two could be the possibilitiesfor starting parametersin this type broken down even further, according to which of of fit, and the experiment is not completely con- the adjacentM2 polyhedra, only two of which are clusive for this reason. The domain hypothesis at equivalent to each other by the point symmetry of present does not furnish a priori prediction of rela- the Ml site, is occupiedby the singleiron or calcium tive areasof the two Ml doubletsor their parameters, atom. so that there is no other way than trial and effor to Of course,we cannot claim that theseare the only try to fit doubletsin this hypothesis. correct or the optimum doubletswhich could be fitted (4) In fitting multiple doublets according to the to the data. The number of data points in eachspec- next-nearest-neighborhypothesis, starting peak pa- trum which actually give useful information is small rameterswere derivedusing the predictedareas given enough,and the number of fitted parametersis large in Table 2, and it was assumedthat the severalM\ enough, so that fitting this many doublets is prob- doublets for each spectrum had nearly the same ably near marginal in a purely statisticalsense. I{ow- isomer shift. A next-nearest-neighborconfiguration ever, the limits of the particular data used in this was neglectedif its predicted area was less than 6 case, and of the technique in general, must be ac- percent of the total absorption.Pure Lorentzian line cepted. It might be possibleto obtain a statistically shapeswere used, and both heights and widths of more valid test of the hypothesisby taking spectra the two peaksof eachdoublet were constrainedto be with more channelsfor much longer counting times, equal, in order to keep to a minimum the number of but we suspectthat with the peaks being as close variable parameters.Some representative spectra are together as postulated, the limit of instrumental shownin Figure 1. resolution would be reached before a statistically The results of this processappeared to be satis- valid distinction between hypotheses(3) and (a) factory, keeping in mind the limitations of the data. could be made. The line widths and isomer shifts were reasonable, The next-nearest-neighborhypothesis is so far and the quadrupolesplitting for the various Ml con- consistentwith all observations,but the samecannot figurations fell into a remarkably consistentpattern be said of any of the other three hypothesescon- (Tables 6 and 7, Figure 5). Some of these aspects sideredabove. The first two hypothesescan be ruled will be discussedin more detail below. Chi-square out becausethey give unsatisfactoryarea ratios. The for thesefits was as low as that for any of the other domain hypothesisappears to have several serious types of fits (Table 3). Final fractional areaswere deficiencies. (a) Although some satisfactory area in most caseswithin a few percent of the predicted ratios (satisfactory by comparison with liquid- values (Table 5). Better agreementis hardly to be nitrogen temperaturespectra) and hyperfineparam- expected,considering that as much as 6 percent of eters were obtained for some natural and synthetic the predicted area was deliberately neglected in pyroxenes (Williams et al, 1971.), we have been sorne cases,and that the heights and widths were unable to obtain confirmation of reasonable area constrained.Also, although only four configurations ratios and Mdssbauer parameters for the heden- MASSBAUER SPECTRA OF SYNTHETIC PYROXENES 857

bergite-ferrosiliteseries. (b) If a domain structure doublets (domain hypothesis)were tried. This is not actually existedin C2/c pyroxenes,we would expect surprising if we consider that the Ml. doublets are its detection in at least some specimensby other very nearly superimposed.The information in the techniques.However, there have been no reports of spectrauseful for fitting more than one Ml doublet detectionof domain structure in CZ/c pyroxenesby would be even less than in the room temperature X-ray or electrondiffraction, or electronmicroscopy. (c) The fact that the pyroxeneswhich are supposed to have domain structuregive normal, sharp diffraction photographsputs very severelimitations on the nature of the domains.In the C2/c pyroxenes,this requires either that one of the two types has individual domains so small that its diffraction effects =2. t! are too diftuse to be observed,or that the two types o G have exactly the samesymmetry and lattice constants U -otherwise we would see two diffraction patterns. -iu. The first alternativeimplies that the relative volume CI F of the type with small individual domains should H6. C' o also be small in relation to the volume of the other @ type, barring a rather peculiar and unlikely size dis- G tribution of domains. Ilowever, the results of Wil- liams e/ al (1971) in somecases show comparable areasfor the doublets attributed to the two types of "domains". which seemsto rule out this alternative. The secondalternative implies, in efiect, a miscibility 1.0 2.o gap within the C2/c field, and we would therefore YELoCtTY,ilHlSEC predict that some C2/c pyroxenes,those lying out- side the gap, would have no dornain structure and no area anomaly. All of our C2/c pyroxenesshow an atea anomaly.Furthermore, oul P21fc pyroxenes also show area anomalies,which would seem to require a differenttype of domainstructure. -F lr, .J Liquid-nitro,gen temperatures pectra G H2. In liquid-nitrogen temperature spectra, the Ml - peaks becornemore cleady separatedfrom the M2 I F peaks, G becauseof a greaterincrease of Ml quadru- G o pole g, splitting with decreasingtemperature (see be- @ low). At the sametime, it must be presumedthat Gl. the doublets for the various Ml configurationsbe- come more alike, becausein two-doublet fits, the area ratios are much closer to the predicted values (Table 9, Figure7). This is presumedin the domain -t.o o.0 t.o 2.o 3.o hypothesis(Williams et al, l97l) as well as in the next-nearest-neighborhypothesis. A probablereason VELOCITY,rrlsEc for the greatersimilarity of. the Ml doublets at low Frc. 1. (a) Room temperature spectrum of FssoWoa, temperaturewill be discussedin the next section. fitted with two partially Gaussian doublets. The fit is We werenot successfulin attemptingto fit multiple visually good, but gives an M2 relative area that is about Ml doublets to the liquid-nitrogen temperature 20 percent too high. (b) fitted with spectra. Room temperature spectrum of FsrcWoso, The final relative areas of the various M1 one M2 and three Ml doublets. From center outward in doublets for such fits appeared to be essentially either direction, the peaks are assigned to: M2, Ml(4), random. The result was the same when onlv two Ml(3), and Ml(2) (seeTable 2). 858 E, DOWTY, AND D. H. LINDSLEY

Tlnt-B 5. Measured Relative Areas for Multi-Doublet Fits spectra, namely, overlap due to splitting of MI to Room Temperature Spectra of Synthetic Hedenbergite- absorption.Indeed, it would be fortuitous if such a Ferrosilite Pvroxenes causewere presentat room temperaturebut completely absent at liquid-nitrogen temperature.How-

Content (2) (3) ever, in view of the practical implications of such a causeof bias on the measurementsof cation distribu- 50 - 1.000 60 - 0.0s1(1) 0.314(3) .436(2) o.2oo(2) tion, a discussionof certainalternate possible causes 70 - .228(7) .308(2) .162(1) .302(2) 0.0783(6) .247(2) .263(2) .083(6) .331(2) of the bias at liquid-nitrogentemperature is in order, .194(r) - .366(2) 80 .1129(B) .328(2) might or for if 85 .170(1) .2t-4(2) . 17e(1) - .436(2\ since a bias be avoided compensated 87.5 .267(2) .273(2) .0808(6) - .380(2) some of these alternatehypotheses were correct. 90 .270(2) ,294 (2) .436(2) 98 ,520(8)t* .480(8r* ( 1) It waspreviously suggested that somecalcium 100 . s43(e)"x .457Of* waspresent in Ml (Dowty and Lindsley,1970), but *Dirid.d as in Table 2. this now seems unlikely, in view of the larger **values fron Table 4. anomaliessubsequently verified in the room tempera- Iigures in parentheses represent esEimated slandard deviation fron the leasE-squares fits, interms of leasE uni!s ciEed' ture spectra,which definitely require another explanation. Also, X-ray refinementsof synthetic hedenbergite(Veblen and Burnham, 1969) and FsesWo'rr spectra, and the operation is certainly unjustifiable (Y. Ohashi,personal communication) gave no indi- statistically. cationof calciuminMl. Although the area ratios for two-doublet liquid- (2) Systematicerror in compositionor contamina- nitrogen temperature fits are much improved over tion introduced in synthesisare not likely causesof thosefor room temperature,there is still a significant the bias, becauseall effects of this type (of which difference between measured and predicted values we are aware) would lead to a bias in the opposite (Fig. 7). We have taken our "final" arearatios for direction.Incomplete reaction at 20 kbar leads to liquid-nitrogen spectra from partially Gaussianfits, the assemblagepyroxene plus fayalite plus silica, and which give much lower values of chi-square than the pyroxene is more calcic than the nominal com- pure Lorentzian fits. Tlie area ratio anomalyusually position of the run. The Mtjssbauerabsorptions for seemsslightly less for pure Lorentzian fits, but is iron in fayalite overlap with the pyroxeneMl doublet neverthelesssignificant at all compositions. Thus, and not with M2. Therefore. if reaction were in- there is clearly a bias with respectto Ml/M2 area complete, we would expect a "double" enhance- ratios in our spectra,at liquid nitrogen temperature. ment of Ml. at the expenseof M2. It seemsmost reasonableto supposethat the cause (3) Cause of the bias through differencesin of the bias is the same as that for room-temperature recoil-freefractions for the two sites would indicate

Taele 6. Hyperfine Pa.rameters(mm/sec) for Multi-Doublet Fits to Room Temperature Spectra of Synthetic Hedenbergite-FerrosilitePyroxenes

Ml*

(4) Fs ConEent IS Qs IS

50 2.222(2)** 1 ,188(2 ) ** 60 2.762 (L) 1.191(5) 2.491(7) 1.101(3) 2.18s(6) 1.184(3) 1.83 3 (8) L.L52(4) 70 2.729(6) r.178(3) 2.43L(6) 1.191(3) 2.069(9) 1.18s(s) L.787(6) r 120/?\ 15 2,586(3) 1.ls6(1) 2.642(t) 1.183(6) 2.289(L) 1.175(6) 2.047(2) 1.142 (1) L,7 40 (6) 1 .11r.(3) 80 z. I J6\) ) 1.r.83(3) 2.5L2(3) 1.187(2) 2.rr9(7) 1.18r(4) 1 . 719(3) 1.115(2)

85 2.690(4) L.L82(2) 2.442(4) 1.1e3(2) 2.L0L(7) L.Le4(4' L.7s4(3) r.,114(2) 87.5 2.616(10) 1.179(s) 2.343 (13) r.2L2(6) 2.0(1) L.2L9(6) 1.811(3) I .116(1) 90 2.619(3) 1.180(2) 2.295(5) '''::"' 1.852 (3) L.L29(2) 98 2.488(3)** 1 17Ar1\** 1 . 910(3) ** r 1tq rr\** 100 2.490(5)** 1. 182 (3) ** __ :: 1.906(4)** 1.130(2 )**

*Dtvlded as in Table 2. **Values fron Table 4. QS is quadrupole spllttlng, IS ts lsoEer shlft. Values in parentheses represent estL@ted standard deviatlon froE the least-squares flts, ln tems of least unlts clted. MASSBAUER SPECTRA OF SYNTHETIC PYROXENES 859

a larger thermal motion for Ml than for M2 iron, Tesrp 7. Widths (mm/sec) for Multi-Doublet Fits to Room which would conflict with relative temperaturefac- Temperature Spectra of Synthetic Hedenbergite-Ferrosilite tors measuredby X-ray diffraction. Our measure- Pvroxenes ments for orthoferrosilite, the only cornpositionfor which the recoil-free fractions can be compared Fs Conlen E (l) unambiguously,indicate no difference between the two sites within the error of measurement(Tables 50 0 296x* 60 0.127(r0) 0.308(7) .302(3) 0.278(1) 4 and9). 70 .255(r) .309(3) .278(3) .296(3) 75 0.2s1(3) .2s9(6) .326(3) .267(3) ,272(3> (4) Some bias might be expectedbecause of 80 . r97 (2) .287(3) .309(3) - .282(3) 85 .208(2) .218(3) .277(3) - .305(3) saturation effect, 1.e.,the fact that the increase in 475 .269(3) .318(3) .287(3) - ,29r(3) 90 ,231(2) '313(3) area of a peak drops off nonlinearly with increasing 98 .299** 100 .280** : : ';iili' iron concentration,when the concentrationis relatively high. This would effectivelyreduce the area of Ml more than M2, becausethe Ml iron concentra- **Average fron TabIe 4, I{ldths of the two peaks of a doublet constrained ro be equal, cxcept for tion is alwaysgreater (exceptfor Fs16). However, values from Table 4. Iigures in ,parentheses represent estinated sEandard deviation fron rhe least-squa.es fits, in of this effect should be related to total iron content in tems least units clted. the absorber,and thereseems to be no correlationof the anornaly with iron concentration in our ab- are only qualitative,or at most, accuratein a relative sorbers.Absorbers of two compositions,Fs6eWoas sense, then some relationships may be developed and Fs7,eWo36,wers prepared with especially low which apply to a significantrange of site configura- iron concentrations,and were run with the palladium tions. Ingalls (1964) has derived a set of relation- source, as a test for saturation effects and for any ships for distorted octahedral sites which we will efiects of the use of the chromium source in the attempt to use to interpret relative variations in the originalspectra (the Cr sourcehas a relativelybroad quadrupole splitting of synthetic hedenbergite-fer- line). The anomaly not was significantlyreduced for rosilite pyroxenes. these spectra.(These spectraare marked with an asteriskin Table9). We concludethat the bias in liquid-nitrogen tem- Tael-n 8. Data Collection Information and Chi-square perature spectraprobably is causedby the same Values for Liquid-Nitrogen Temperature Spectra of Synthetic Hedenbergite-Ferrosilite Pyroxenes phenomenonas the biasin room temperaturespectra, and is therefore essentiallyunavoidable in measure- Iron background Chi-square ments of calcium-bearingpyroxenes. The implications of this and another possiblecause of bias will Content ng/cm x 106 T.orentz. Gauss. be discussedin the concludingsection. 50 (1) 0.68 ozo 539 (t\ 3,7 .fo IIOJ 114s QuadrupoleSptitting (3) 3,7 .z) zcl 232 The existence of two peaks in the M,tjssbauer 60 (1) 4,O .78 710 372 (2) r.f 787 4ro spectrumfor each site is due to a non-cubic charge 70 (1) J. O .86 tzL 262 distribution around the iron nucleus,and the separa- (2) 3.8 ,78 480 283 (3) tion of the two peaks, quadrupole splitting, is de- r. oo o)z 409 pendent on 7s (1) 7.O 464 259 the degree of distortion of the charge (2) 7.0 0Jz 383 from cubic symmetry. The quadrupole splitting can 80 (1) 7.3 .66 433 260 in principle be calculated if the crystal structure is <2) 7,3 .68 /oo JI/ known, but the computationsare exceedinglycom- 8s (1) .68 734 plex for low site symmetry, and there 87.s (1) 2,6 L,27 309 zJ) are several (2) 2.6 r. )o 388 244 factors entering into the calculation which are not 90 (1) 1,29 535 302 perfectly known and are dfficult to measureinde- 98 (1) 70 436 385 pendently. It is not always possible, therefore, to (2) 70 .JO 504 428 attain absolute accuracy. If some simplifying as- r-00(1) ,43 432 360 (2) 3.2 1.18 2]-'5 sumptionsare made about the geometryof the site, (3) 3.2 . DJ 382 JZU however, and if we are satisfiedwith results which 860 E. DOWTY, AND D, H. LINDSLEY

Trsrn 9. Area Ratios and McissbauerParameters (mm/sec) for Fits to Liquid-Nitrogen Temperature Spectra of Synthetic Hedenbergite-Ferrosilitefuroxenes

l,l2 area Widths Wldths Fs Content Expected Lorentz. Gauss. LH

50 (r) 0.0 2.735(2) 1.300(2) 0.446(s) o'4s2(4) (2) 0.c 2.764(2) 1.308(2) .409(6) .377(4) (3)* O.O 2.778(3) 1.306(2) ,327(s) -314(6) 0.3r4(8) 0.454(9) 60 (1) 0.167 0.184(12) o.21-4(4) 2.873(2) 1,.3o9<2) .460(4) .425(4) 1.90s(6) 1.270(3) 1.24r(3) .313(7) .400(6) e)* .i-67 .189 ( 7) .237(3) 2.876(2) 1.301(1) .374(4) .379(4) r.942(6) (9) .425(6) (1) .286 .308(8) .323(3) 2.s63(3) 1.300(2) .416(6) -42r(5) 1.871(6) L.234(3) . 381 70 .472(7) (2). .286 .302(9) .341(6) 2.s7o(3) L.297(2) .441(6) '423(5) r.884(6) L,242(3) .3ss(6) .341(5) .376(5) (3)- .286 .310(4) .348(3) 2.956(2) r.299(2) .370(4) .384(4) r.862(4) r.222(2) .s30(10) .s36(7) (1) .333 .381(s) .38s(3) 2,987(4) r.288(2) .534(7) .526(6) 1.836(6) 1.217(3) 7s .478(5) (2) .333 .342(e) .378(4) 2.99o(2) r.295(2) .4s9(6) .454(6) r.832(4) L232(2) .369(s) .426(6) . s12(8) (1) .37s .395(7) .420(3) 3.018(3) 1-.291'(2) .48r(6) .4s5(s) 1.810(4) L.222(3) e0 (2) .441(s) (2) .37s .383(5) .415(3) 3.024(2) r.294(L) .436(s) .430(4) 1. 801(3) r.225 .384(s) ,4L2(5) .504(5) 85 (1) .4r2 .438(10) .4ss(4) 3.o04(2) r.28s(2) .458(s) .448(s) 1.80s(3) r.22r(2) .507(7) (l-) .t+29 .4s1(r4) .444(4) 3.06s(3) 1.305(2) .382(6) .391(5) 1.e14(4) r.25L(2) .39e(s) 87.5 (s) .s2s(7 (2) .429 .442(7) .438(4) 3.OsO(4) 1.300(2) .4r4<6) .4r4(6) 1.e07(5) r.243(3) .400 ) .45r(6) ,sL2(6) 90 (1) .444 .sos(12) .471(3) 3.068(3) r.289(2) .453(6) .446(4) 1.966 ( 3) L.236(2) . 3s7(4) .412(6) 98 (1) .490 .s05(8) .s07(3) 3.ro2(2) r.297(2) .361(s) .367(s) 2.005(2) L.2s4(2) . (s) .422(6) (2) .49o .486(7) .523(3) 3.147(3) 1.300(2) .400(s) '401(6) 2.02o(3) r.259(2) 343 . (5) .3?2(s) 100 (1) . s00 .496(13) .486(3) 3.130(2) L.2e1(2) .337(6) -332(4) 2.OoO(2) L.258(2) 334 .322(5) .34e(4) (2) .500 .495(14) .497(3) 3.140(2) 1.309(2) .322(6) .320(s) 2.Oo4(2) r.273(2) .331(6) .406(7) (3) . s00 , 497(8) .540(s) 3.11?(4) 1.304(2) .361(s) '369(6) 2.023(3) L.26L(2)

rTheae apectra eere taken stth a palladiuo aource, the others Flth a chroniu source. quadrupole spll.Etlng (QS), lsouei shlfr (lS) and fu1l rldthB at half height (low and htgh veloc{ty) are fron Partlally Gaussian flts. Flgures ln parentheaes represent estlMted standard devlatlon frou each least-squEres flt' ln tema of the least unll clted.

In Ingalls' crystal-field model, the quadrupo.le orthorhombic distortion. In silicates,iron-site sym- splitting, A,E, for ferrous iron in near-octahedral co- metriesare commonly monoclinic (as in C2/c pyrox- ordination is given by enes) or triclinic (as in orthopyroxenes).Thus for many applications, the model in this form is an -- AE AE,ranF(A,,,Ar, tr', ot", T) (2\ approximation at best. flowever, the orthorhombic The heart of the model is the "reduction function" parr of the distortionis expected(Gibb, 1968) to be F, whose value is calculated by perturbation theory. subsidiaryto the axial part (tetragonalin this treat- AE6 is the maximum possible value of quadrupole ment), and contributions from distortion of sym- splitting,a a2 is a covalency factor which has a value metry lower than orthorhombic should be even less of 1.0 in perfectly ionic sites and is reduced for more important. covalent bonding, tro is a spin-orbit constant, ? is Mainly for simplicity, we will analyzethe quadru- the absolute temperature, and Ar and A2 ate the two pole splitting as if the distortion of the iron sites in lowest splittings of the crystal-field levels, as shown the, hedenbergite-ferrosiliteseries can be uniquely in Figure 2. In general, the values of 41 and a2 may correlated with the distortion parameter shown in be thought of as increasing with the distortion of the Figure 3, at least with respect to relative variations coordination from perfect octahedral symmetry. within the series.We will show that this simplified Curves of the reduction function F versus a dis- approach yields an interpretation of quadrupole tortion parameter, Lf xoa2, are drawn (Fig. 3) for splitting variation in the series which is essentially the special case A - Ar = A2 (the tetragonal case complete and consistent with all observations.In in Figure 2). This is the simplest case of distortion view of the limitations of the model with respectto even of those treated by Ingalls, who also described the symmetry of the sites, and our limited information about the actual configurationsof the sites,part t AEofor ferrous iron is approximately5.6 mm/sec, for of our apparent successmight well be fortuitous. the formulation given here (Ingalls, 1964). Application of the model to other systemsis not MASSBAUER SPECTRA OF SYNTHETIC PYROXENES 86r

x2-y2

xz, yz / /---_\ --- | -y2, z2 -- tt II a^ a. :_--_. T'Tt II?

Octahedral Tetragonal Orthorhombic (compressed) or lower Ftc' 2. Crystal field levels for various types of six and eight coordination showing the splitting of the lowest levels, A, or Ar and Az. necessarily expected to be as straightforward, nor Iattice term arises from the deviation from cubic the results to be as consistent.Nevertheless, the use- symmetry of the surroundings of the iron atom, fulness of the model in the form used here should particularly the coordination polyhedron. It increases be evident. approximately linearly with the distortion parameter, The use of at least part of the Ingalls model has Af \,sa'. The ualence term arises from asymmetry of been suggestedbefore in the mineralogical literature. the electronic charge on the iron atom itself. Since the For example, Bancroft, Maddock, and Burns (1967) filled inner electron shells all have near-spherical pointed out that the quadrupole splitting of iron symmetry, only the outermost, or valence shell, can sites in many silicatesis inversely correlated with the contribute substantially to the quadrupole splitting. distortion of the coordination polyhedron. Our model In iron, the incomplete part of the valence shell is differs from previous ones by suggesting that some composed of the five d orbitals. When each of the iron sites may lie on the part of the quadrupole d orbitals is equally occupied by electrons, this shell is splitting curves with positive slopes, and in more also spherically symmetric. Thus, in ferric iron, which systematically using the temperature dependence of has five delectrons, each orbital contains one electron. the quadrupole splitting relationships. Thus the valence term is nonexistent and the quad- We might add that Gibb (1968) has extended the rupole splitting is given by the lattice term only. valence-term part of the model to several other rypes Ferrous iron, however, has six d electrons, one extra. of iron configurations,including high-spin tetrahedral In the free ion, this extra electron spends its time and low-spin octahedral ferrous iron coordination, uniformly among the five orbitals, since they are and low-spin octahedral ferric iron. Unfortunately, equally favorable energetically (degenerate). The the lattice term, which we can usually expect to be transition time of the electron among the orbitals is important in structurally complex minerals, was not sufficiently short that the time average of its distri- included in his calculations. bution is spherically symmetric. In perfect octahedral coordination, three of the orbitals (the rr, set) are more Explanation of thc Model favorable than the other two, so the electron spends The function F may be thought of as the sum of two its time among these three. However, these three terms, the lattice term and the valence term. The orbitals together are also spherically symmetric, so 862 E. DOWTY, AND D. H. LINDSLEY

distortion, however, higher temperature becomes inadequate to boost the electron to the next highest level. Therefore, the difference in quadrupole splitting between two given temperatures tends to decrease with increasing distortion, after reaching an z initial maximum. )a AT 90" K The quadrupole splitting, and each of the terms, o The sign is not usually F AT 2940 X may be positive or negative. l / o determinate from powder Mtjssbauer spectra alone, .-' but the particular geometry of the d-orbitals relative IATTICETERMl ./u / the / to the crystal field requires that the signs of lattice and valence terms be opposite to one another. The extra d electron naturally disposesitself in such a way as to counteract the potential of the surround- 40 50 o/::,, ing atoms. To obtain the absolute value of F, shown by the doubly sloped curves in Figure 3, the lattice Ftc. 3. Relation of the reduction function F, to distortion term as plotted in Figure 3 is subtracted from the from perfect octahedral coordination, A/l"a'. Quadrupole is equal to the splitting is approximately 5.6 mm/sec times F times the valence term. The quadrupole splitting covalency factor, an. The reduction function (solid lines) "maximum" quadrupole splitting, aE6, multiplied is the sum of the valence and lattice terms (dashed lines); by F and the covalencyfactor (Eq. 2). the lattice term is shown here with sign reversed. The The value of af xoa'can in principle be estimated darkened segments are intended to represent the variation independently, but, in fact, very few data are pres- with composition of a single next-nearest-neighborconfiguration for the M7 site, for example, any of numbers I ently available to do so. The value of ,\o has been through 4 in Figure 5. After Ingalls (1964). calculated theoretically at about 100 cm-' (Ingalls, 1964\. but this is for tbe free ion. The value of a2 can only be guessedat, and is probably in the neigh- that for both the free ion and perfect octahedral borhood of 0.6 to 0.8 for iron in silicates. The coordination, the quadrupole splitting is zero (a1- values of Ar and 42 coo be obtained from optical though perfect octahedral coordination is seldom spectra, but although a few optical measurementson expected to exist for ferrous iron coordination, be- pyroxenes have in fact been made, these can hardly cause of the Jahn-Teller effect). If the coordination be regarded as definitive with respect to establishing distorts slightly from octahedral symmetry, one of the A1 and 42, ?rrd no measurements are available for lower d orbitals becomesstabilized relative to the other the hedenbergite-ferrosiliteseries specifically (Burns, two, and the electron spends most of its time in this 1970, does give a spectrum of a natural heden- orbital to produce a very strongly asymmetric charge bergite). It will be necessary to take a qualitative distribution. Thus the valence term increases very approach in the present case, "fitting" the quadru- rapidly with distortion to a maximum value cor- pole-splitting data to the model curves. responding to unique occupancy of the lowest energy orbital by the sixth d electron. The Ml site The lattice term is sensitive to temperature only The question arises whether the Ml site is asso- insofar as the locations of other atoms relative to the ciated with a positive or negative slope of the F iron nucleus change with temperature. Normally such curves (Fig. 3). We note that the MI site is very changes are rather slight. The valence term can be little distorted in any pyroxene. Burns (1970) has quite sensitive to temperature because the distribu- inferred that A1 and A2 are probably less than 100 tion of electrons among different energy levels is cm-' in orthopyroxenes. If this is correct, Ml would temperature dependent and given by a Boltzman fall in the region of positive slope, close to the zero function. As thermal energy is infused into the atom, point. The average deviation of the 6 MI-O bond the sixth d electron can spend more time in higher lengths from the mean Ml-O bond length, which is energy orbitals to produce a more symmetric charge an index of distortion, is 0.027 A in hedenbergite distribution and a lower value for the valence term. (data from Veblen and Burnham, 1969), whereas it As the separation between the levels increaseswith varies from 0.040 to 0.048 in the orthopvroxene MOSSBAUERSPECTRA OF SYNTHETIC PYROXENES E63

series (data from Burnham, 1966; Morimoto and 320 Koto, 1969). Quadrupole splitting increasesa great 3 t0 deal between hedenbergite and orthoferrosilite (Fig. E

4), which would appear to confirm that MI lies on t{ 9 o the part of the F curves with positive slope. Indeed, z 260 2eog the magnitude of this difference in quadrupole - split- 250 2AO ting compared with the relatively small change in ? R zro 270 distortion seemsto be more consistentwith the posi- oxygen atoms coordinating Ml in response to the close to the strongest of the next-nearest-neighbor peaks, or between the two peaks-weaker strongest 280 next-nearest-neighborpeaks seem to have little in- 'rt'- \ -\. fluence. Thus, given the trends for the individual 270 + -\ \ configurations shown in Figure 5, and the varying u 260 \... to.t. \ .\. _\ populationsof each of these,it may be seenhow the { ^\\ t zso apparent quadrupole splitting of Ml from o two- z \\ \r \ doublet fits to room temperature spectra could show = 21o .\\ a maximum in the middle of the series, as in Figure \>\ d z3o A -.-- \^\'\ 2 --! At liquid-nitrogen : 220 \ temperature, the doublets for o \__ -\\ \ r\ the various M1 configurations are evidently closer ? l0 .--<. \^\ to each other than at room temperature. In Figure 5, '\, 2@ . this would have the effect of drawing together the 50 60 70 80 90 r@ points for each composition and flattening the trend FERROSItI'ECONTENT, AOTE PERCENT for each configuration. This also may be explained FIc. 5. splitting of the Ml site at room tem- by a detailed consideration Quadrupole of the model curves in perature from multi-doublet fits (up to four Ml doublets). Figure 3. Note that the curves for the two tempera- Numbers I through 4 correspondto the next-nearest-neigh- tures have different slopes in the region just on the bor confieurationsin Table 2. 864 E. DOWTY, AND D. H. LINDSLEY differing occupanciesof the three adjacent M2 sites. to be temperature dependent in calcium-poor com- Positional disorder of the oxygen atoms in clino- positions but not in calcium-rich compo'sitions,the pyroxenes with intermediate calcium content has multidoublet fits indicate that the temperature de- been indicated by X-ray refinements (Takeda, in pendence is small, but more or less the same for all preparation). The changesin quadrupole splitting of compositions(Fig.6). each type of next-nearest-neighborconfiguration with The changes in quadrupole splitting of the M2 site composition evidently result from the pervasive through the seriesare undoubtedly related to the way efiects of the calcium/iron ratio throughout the in which the coordination of this site changes from structure. The slopes for some of the configurations six around iron in ferrosilite to eight around calcium in Figure 5 are surprisingly large in comparison with in hedenbergite.The actual atomic positional changes the changesin quadrupole splitting due to changesin of oxygen atoms surrounding M2 have been de- next-nearest-neighborpopulations in the same series, scribed for a partial series of low- to high-calcium and in other mineral series (e.g., olivines; Bancroft, pyroxenes by Takeda (1972; in preparation). The Maddock, and Burns, 1967). This might be con- changes in coordination are chiefly related to dis- sidered anomalous, but the trends seem susceptible placementsof the 03 oxygen atoms. to rationalization on the basis of the model curves The trends shown in Figure 6 seem inconsistent (above). The absenceof comparable trends in other with the idea that the iron cation, which is small in minerals possibly indicates that the Ml site in our relation to calcium, maintains its own type of co- pyroxenes is almost unique in its low distortion and ordination in the series (as suggestedfor iron and consequent high susceptibility to slight structural magnesiumin pigeonite by Morimoto and Tokonami, changes. 1969). If this were true, we would expect a more nearly linear trend, and probably less abrupt change, The M2 site especiallyat the low-calcium end. The fact that there The few optical data indicate that at least one of is a very pronounced change in quadrupole splitting the A's for M2 in pyroxenes is large; the value of almost as soon as calcium enters the structure, and 3000 cm-' determined for orthopyroxenes (Bancroft the fact that there are minima in the curves, suggests and Burns, 1967b; White and Keester, 1967) is that the coordination of Fe changessignificantly even probably exceeded in clinopyroxenes. X-ray results at low concentrations of calcium. The same con- also indicate that M2 is much more distorted than clusion has been reached by Takeda (1972; in prep Ml, even in ferrosilite, where the coordination of aration) on the basis of thermal parameters of the M2 is six. This becomesmore pronounced in henden- oxygen atoms. bergite where the M2 site contains calcium in a In the more calcic pyroxenes of the serieswe may distorted eight-coordination.The quadrupole splitting assumethat the coordination of iron atoms is similar of M2 shows relatively slight temperature depen- to that described by Takeda (1972; in preparation) dence. These considerationsleave no doubt that M2 for iron and magnesium in subcalcic augites. This is falls well out on the F curves in Figure 3 where the a four-plus-four coordination, in which the cavity, slopes are negative. To the extent that the distortion formed by eight oxygen atoms, is similar to that in of the coordination is adequately described by the which the calcium atom is found, but the iron or crystal-field model for octahedral coordination, the maglesium atom is very much to one side so that quadrupole splitting of M2 would tend to decrease the bond distances are normal to only four of the only moderately for a large increase in distortion. oxygen atoms. As pointed out before, an M2 cation is not ap- One of the most interesting aspectsof the quadru- proached as closely by other M2 cations as is an Ml pole spliting curves for M2 in Figure 6 is the fact cation. Since the M2 site is also in a region of distor- that they bear a pronounced resemblance to the tion in which the quadrupole splitting is much less clinopyroxene miscibility gap (as it is known in more sensitive to changes in the environment, the M2 site magnesian compositions) turned upside down. The is probably adequately representedby one doublet. slopes of the quadrupole splitting "solvi" are steep However, overlap of Ml peaks on the M2 doublet on the pigeonite side and more gradual on the C2/c does appear to have an influence on the apparent side, as we expect the real solvi to be, and the locations of the M2 peaks. Whereas with the two- minimum of the curve also coincides approximately doublet fits, the quadrupole splitting of M2 appeared with the change in symmetry observed in X-ray MASSBAUER SPECTRA OF SYNTHETIC PYROXENES 865

photographs. This might be regarded as an illustra- marily to temp€rature variation and cryostat vibra- tion of the crystal-chemical basis for the real misci- tion and are expectedto be less at room temperature. bility gap. The minimum of quadrupole splitting Fortunately, such variation seemsto have little effect probably representsmaximum distortion, and there- on area ratios or hyperfine parameters. fore greatest potential energy of the structure in the Second, the two-doublet fits apparently are not vicinity of the iron atoms at this composition. Other the best model for the spectra, and the meaning of factors being nearly equal, this might cause this line widths for these spectra is therefore questionable. composition to be unstable with respect to composi- Third, some broadening may be caused by com- tions both more and less calcic. The quadrupole positional inhomogeneity. This type of broadening is splitting model is not technically applicable to the difficult to isolate from that due to next-nearest- type of iron coordination found in the more calcic neighbor effects, since the two compositions which pyroxenes (closer to eight than six coordination) but are least likely to be inhomogeneous,Fs5e and Fs16s, the very fact that the trend in quadrupole splitting also do not suffer from next-nearest-neighbor effects. corresponds to the phase relations suggeststhat it These compositions give reasonably narrow lines is at least qualitatively useful in this case. (Tables 4 and9\. For the multi-doublet, room-temperature fits, Isomer Shift widths are also reasonably small (see Table 7), but With the correct assignment of the M2 doublet precision is poor and constraints were used, so that inside the Ml doublet, the isomer shift of MI is these measurements are probably not meaningful 0.04 to 0,08 mm/sec larger than that of M2. The with respect to detection of composition broadening. difference between room and liquid-nitrogen tem- One apparent trend which does emerge is a tend- peratures of about 0. 1 1 mm/sec for both sites may ency for the width of the high velocity peak of the be ascribed to a thermal (second-order Doppler) M2 doublet at liquid-nitrogen temperature to be shift. larger than that of the low-velocity peak (Table 9). In the room temperature spectra, there is no defi- If this is not due to partial overlap of M1 absorption, nite evidencethat the isorner shifts of the various Ml relaxation effects are probably indicated, becausethe doublets (Table 6) are different frorn each other. height of the high-velocity peak is concomitantly re- The total error is somewhat large for these measure- duced, so that the areas of the two peaks are not ments, probably becauseof the approximations made significantly different. Shenoy, Kalvius, and Hafner in the fitting and the near-marginal amount of in- (1969) found that spin-lattice relaxation effects in formation in the data in relation to the number of the orthopyroxene series increase with decreasing fitted parameters. iron content. In our case also, the effect seems to For the M2 doublet, the isomer shift seems to be slightly lower in the middle of the series at both temperatures. If this is real, it may possibly be related

to the differences in the nature of the bonding ex- 200 pected as the coordination of M2 iron changes through the series from six to four-plus-four. In the ui 1e5 { four-plus-four coordination, the anisotropic nature { of the bonds (all strong bonds 9rco on one side of the F iron atom) implies a greater degree of covalency. 185 The increase in isorner shift at the calcic end of the =

seriesis not readily explicable. 6 :5r8o o Line Widths and Symmetry of the Doublets 175 For a number of reasons,line widths reported are not good estimates of "intrinsic" line widths. First, there are instrumental effects, which are apparent in FERROSILITECONTENT, AtOtE PERCENT the different line widths obtained for duplicate Frc. 6. Quadrupole splitting of the M2 site at room tem- spectra of the same absorber at liquid-nitrogen tem_ perature from multi-doublet fits, and at liquid-nitrogen perature (Table 9). These are probably due pri_ temperature from two-doublet fits. 866 E. DOWTY, AND D. H. LINDSLEY increase with decreasing content of iron in M2, al- clinopyroxenes, and the two-doublet fits probably though we note that Ml is always fully occupied by must be acceptedas the best estimatesof the iron site iron. We attempted fits of the room temperature distribution. If we are to use these estimates, some spectra with the constraints released for the M2 correction is necessary.Our measurements (Fig. 7) doublet only, to find out if the asymmetry is less than provide tentative values for correction factors, but it at low temperature, as predictcd for relaxation. The is quite likely that these would not be applicable to widths and heights of the two M2 peaks did not ap- more complex natural clinopyroxenes. pear to be significantly different, and the values of In the following subsections,we apply the experi- chi-square were not significantly reduced in these mental results and hypotheses discussed above to fits, but again, the comparison may not be mean- specific types of pyroxenes. If the hypotheses pro- ingful becauseof the poor resolution. posed in this work are accepted, it is evident that a If the interpretation of asymmetry as due to re- certain amount of reinterpretation of previous work laxation is correct, the method of estimating site is necessary. occupanciesby using peak heights alone (Virgo and Augites and pigeonites Hafner, 1969) is not strictly valid in pyroxenes with low concentrations of iron in M2; by this method, In common Mg-Fe-Ca pyroxenes, an additional the area of the high-velocity peak of M2 would be source of bias may be present which is distinct from underestimated. However, the bias thus produced that caused by next-nearest-neighbor influence. would be in the opposite senseto that produced by Augites and pigeonites and also orthopyroxenes the splitting of the Ml absorption. commonly consist of intergrowths of one with another, as a result of exsolution from high-tempera- Application to Natural Pyroxenes ture precursors. Since the difference in composition and Other Minerals of the exsolved phases is chiefly in calcium content, our results permit the M6ssbauer parameters of the Accuracy of room temperature measurements members of these intergrowths to be predicted to a of clinopyroxenes first approximation, at least for very iron-rich pyrox- The use of room temperature spectra for deter- enes. We discuss only liquid-nitrogen spectra since, mining iron-site occupancy in orthopyroxenes was as explained above, room-temperature data are not previously shown by Virgo and Hafner ( 1968 ) to be likely to be useful at all for purposes of determining inferior to the use of liquid-nitrogen temperature site occupancies. spectra. This follows solely from the poorer resolu- The quadrupole splitting of M2 shows some variation of Ml from M2 doublets at room temperature. tion with calcium content, but since the shape of the The same applies to clinopyroxenes, in which the curve for M2 quadrupole splitting os temperature anomalies causedby different M1 configurations give resemblesthe clinopyroxenes solvus, the two mem- further reason for not using room temperature spec- bers of a pigeonite-augite intergrowth and possibly tra. We have apparently had some successin fitting also an orthopyroxene-augite intergrowth will have multiple Ml doublets to our spectra, but the simple M2 doubletswhich are fairly closely superposed.On compositions enabled us to predict the population the other hand, the variation of the quadrupole of the different Ml configurations. Such predictions splitting of MI is larger than that of M2 and not re- would be impossible in natural clinopyroxenes, be- lated to the pattern of exsolution. Thus the Ml cause the compositions are much more complex and doublets of the two pyroxenes in an intergrowth may the MI-Mz iron distribution is not known. be rather dissimilar. If only one doublet is fitted for Ml in such an intergrowth, the result may produce a Accuracy ol liquid-nitrogen temperature bias in the same way, and in the same direction, as measurements next-nearest-neighborinfl u ence. Resolution of Ml from M2 is much better at High-calcium pyroxenes (augites) from lunar liquid-nitrogen temperature, but two-doublet fits still rocks have been reported to be more completely overestimate the M2 area in our calcium-bearing ordered with respect to Fe-Mg site distribution than pyroxenes (Fig. 7 ) . Since we had no successin fitting coexisting low-calcium pyroxenes, or than low-cal- multiple M1 doublets in our simple compositions, it cium pyroxenes in rocks with presumably similar is unlikely that such fits would be possible in natural cooling histories (Hafner and Virgo, 1970; Hafner MASSBAUER SPECTRA OF SYNTHETIC PYROXENES 867

et al, l97I). At least part of this apparently greater lrJ order is probably due to overestimation of M2 iron (r IA

occupancy because of either or both kinds of bias. AI Certainly, the apparent excess of M2 cations (iron = ta o plus calcium) which has been indicated from Mtjss- UJ F bauer measurement of some specimens of lunar high- o t? o calcium iron-rich pyroxenes (Hafner et al, l97I) Lu (Dowty E. may be attributed to this bias et al, 1972). o- t.l D iop side-hedenber git e serie s J l F to In a study of natural diopside-hedenbergite pyrox- C) enes, Bancroft, Williams, and Burns (1971) noted 50 60 7d 80 90 roo that in one specimenwith slightly less than the maxi- FERROSILTTECONTENT, MOLE PERCENT mum amount of calcium, there was evidencenot only Frc. for doublets representing Ml and a slight amount of 7. Discrepancy in area ratios of liquid-nitrogen temperature spectra, two-doublet, partially Gaussian fits. The M2 iron, but a third weak doublet which they could dashedline is a least-squaresfit to the data. not identify conclusively. The third doublet could well be due to next-nearest-neighbor configuration ately suspectas being susceptibleto this effect is the type 3, in the nomenclature of Table 2. (Pure calcic and alkali amphiboles,because of the many diopside-hedenbergite should have only a type 4 structuraland chemicalsimilarities between pyrox- doublet, assumingiron and magnesium are essentially enesand amphiboles. interchangeable.) Acknowledgments Omphacites The Miissbauer equipment for this study was furnished Omphacites are sodic pyroxenes which usually through the courtesy of the National Bureau of Standards, have space group P2 and four symmetrically distinct U.S. Department of Commerce, Gaithersburg, Maryland. types of M1 sites, Bancroft, Williams, and Essene We thank J. J. Spijkerman, P. A. Pella, I. C. Travis, N. Debye, and J. R. DeVoe of that laboratory for their (1969) found evidence for four different ferrous personal assistanceat various stages in the project. Charles doublets in natural omphacites and inferred that W. Burnham provided helpful criticism and guidance, and ferrous iron was disordered over all four Ml sites. we thank him and Y. Ohashi for the use of their unpub- The present results suggest that some of these lished results. J. C. Travis also provided guidance on doublets may have been due to next-nearest-neighbor technical points and inspiration for the use of non-Lorentzian line shapes. The final partially Gaussian line shape was effects, and that ferrous iron may be in only two of arrived at through the comments of W. A. Dollase. H. T. the MI sites, as previously inferred from X-ray Evans kindly indexed and refined the Guinier powder data diffraction data (Clark and Papike, 1968). of several specimens. The manuscript has been greatly improved by the criticism of S. S. Hafner, and we thank Other minerals him for correction on several technical points. The writers bear sole responsibility for interpretations and conclusions In iron sites in silicates there seems to be a in this paper. general negative correlation of quadrupole splitting with distortion (Bancroft, Maddock, and Burns, References 1967). This suggeststhat most of these sites lie in a BeNcnorr, G. M., eup R. G. BunNs (1967a) Distribution region of distortion in which next-nearest-neighbor of iron cations in a volcanic pigeonite by Mcissbauer spectroscopy. Lett. 3, influences would not be likely to cause the kind of Earth Planet. Sci. 125-127. AND- (1967b) Interpretationof the electronic splitting found in the Ml site of clinopyroxenes. spectra of iron in pyroxenes.Amer. Mineral. 52, 1278- Nevertheless,the possibility of splitting of this kind 1287. should not be overlooked; the type of low-distortion A. G. Meooocx, eNo R. G. Bunns (1967) Applica- site which is likely to be affected by next-nearest- tions of the Mcissbauereffect to silicate mineralogy: I. Iron silicates of known crystal structure. Geochtm. Cos- neighbor influences will probably show a relatively mochim. Ac ta, 31, 2219-1146. high dependenceof quadrupole splitting or tempera- P. G. L. Wrrrrlvrs, rNo E. J. EsseNe (1969) ture. Mcissbauerspectra of omphacites.Mineral Soc. Amer. Another class of minerals which we may immedi- Spec.Pap.2,59-65. 868 E. DOWTY, AND D. H. LINDSLEY

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