Ameican Mineralooist Vol. 57, pp. 962-9850972\
CATION DETERMINATIVE CURVES FoR Mg_Fe_Mn OLIVINES FROM VIBRATIONAL SPECTRA1
RocnrnG. BunNs ANDtr'RANK E. HucerNs,Department ol Earth and Planetarg Sciences, M ass achus ett s I nstitute oI T echnolo gg, Cambridge, M assachusetts02 I Sg
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'Paper presented at the lgz0 Annual Meetings of the Geologioar society of America, Milwaukee, Abstr., p. 5ll-Bl?. 967 968 BUNNSAND HUGGINS
Early studiesof the infrared spectraof olivines (Lehmann,Dutz' that and Koltermann,1961 ; Duke and'stephens,1964) have-shown peak maxima are compositiondependent' Duke and Stephens(1964) suggestedfrom measurementsdown to 400 cm-l that infrared spectra .orrld b. usedas determinativecurves for olivines.we have extended the spectralrange to 200 cm-1and have derived equationsof cation compositiondeterminative curves for the Mg-Fe, Fe-Mn, and Mg-Mn olivine binary solid-solutionseries, and have constructeda determi- native grid for ternary Mg-Fe-Mn olivines' ExronrlrpNter, MPruoos The chemical analyses of the minerals used in the present study are sum- and marized in Table 1. specimens 1-11 belong to the forsterite-fayalite series, the specimens 11-15 conform closely to the fa.yalite-tephroite series, while and 1' tephroite-forsterite series is represented only by specimens 15, 16' 17' (specimen19), Data are also included for roepperite (specimen 18), monticellite (specimens1-18) and willemite (specimen20). The compositionsof the olivines are plotted oo u triuogrrlar diagram for the MpSiOa Fe"SiOn, and Mn'SiO' pseudobinary components in Figure 1-. This figure demonstrates the restricted nature of olivine minerals. Most of the spectra were measured over the range 2000-200cm-' oi a Perkin- Elmer model 225 recording spectrophotometer using powdered olivine specimens that in pressed cesium iodide discs. The precision of this instrument is zuch -F preparation of certain peak maxima may be read to 0'5 cm-' unit' Sample (Burns and silicat'e minerals for irrfrared, measurements is described elsewhere Prentice. 1968:Bancroft and Bums, 196,9)'
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Frq. 1. Compositions of the olivines used fOr infrared measurements. DETERMINATION OF OLIVINES FROM SPECTRA 969
Relationships between olivine composition (X) and frequency (y) of eash peak maximum in the infrared spectrum (in cm-t units) were computed by a least squares method, using the CURFIT 2 ALGOL program on file at the Oxford University Computing Laboratory, England. This progra^rn enables a series of polynomials up to degree n ta be computed, provided there are (n * 2) or more points, together with two statistical error estimates: (l) sum of squares of residuals 2(lz.t" - o",t"l') for all points of coordinates (X, r) for each poly- nomial having the form
v = c(n,O)* c(n,l)X + ... * c(n,n) Y and (2) standard deviations d(n, q) for the correspondingcoefficients c(n; q). The best-fit polynomial relating peak maxima to olivine composition was taken to be that for which the ratio residual (n): residual (n * l) did not exceed2:1. Rnsur,rs The spectraof minerals with the olivine structure are remarkably similar in the region 1000-550cm-1. This is illustrated by Figure 2, in which the spectraof the olivines forsterite,fayalite, tephroite,and monticelliteare comparedwith that of willemite which doesnot have the olivine structure.Five peaksmay be distinguishedin this region, the positionsof which changewith cation content of the olivine. An additional seven or eight peaks may be recognizedin the region below 550 cm-1,the relative intensitiesand positionsof which may vary with olivine composition. The spectra of the forsterite-fayalite series (except specimen8, which containsappreciable Mn) are illustrated in Figure 3 and the positionsof the peak maxima are summarizedin Table 2. Thirteen peaks or prominent shoulderscould be identified in the spectrum of forsterite (specimen1). Most of the peaks could be traced across the forsterite-fayalite series.Such sets of peaks are here labelled bands1 to 13. All of the bands on the forsterite-fayaliteseries show a shift of peak maxima to lower frequencieswith increasingiron content.How- ever,the compositionalvariations of the individual bandsdiffer, with the result that there are alsonotable changesof relative intensity and breadthof the band envelopesacross the seriescaused by the merging and divergenceof neighboringbands. For example,bands 6 and 7 appearto divergewith increasingiron content,so that band 6, which starts as a prominentshoulder in the spectrumof specimen1 becomes a distinct peak in the spectraof specimens5 to 11. The spectraof the fayalite-tephroiteseries are illustrated in Figure 4. The sameseries of bandsfound for the fosterite-fayaliteseries are remarkably uniform acrossthe fayalite-tephroite series.The peak maxima data summarizedin Table 3 show that the compositional 'D6 +d€do6rNddo
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oooooo !HAJ ;c: e NNoo06a6a@a o o N No o o o o ! ! .4iHOOCOdd!oObcd-i @H Tanr,n 1, coNr. 1. Forsterite; Webster, North Carolina; analysts: J. Carpenter, D. G. W. Smith (microprobe). 2. Chrysolite; Jan Mayan Island, Arctic Ocean (Berkeley 12489); analyst: D. G. W. Smith (microprobe). 3. Chrysolite; Skaergaard intrusion, East Greenland (Oxford 45Zi); analyst: D. G. W. Smith (microprobe). 4. Hyalosiderite; Skaergaard intrusion, East Greenland (Oxford 5107); analyst: D. G. W. Smith (microprobe). 5. Eyalosiderite; Skaergaard intrusion, East Greenland (Oxford 5111); analyst: D. G. W. Smith (microprobe). 6. Hyalosiderite; Skaergaard intrusion, East Greenland (Oxford 4077); analyst: J. V. Srnith (1966). 7. Hyalosiderite; Lydenburg, Transvaal, South Africa (Cambridge 54087); analyst: D. G. W. Smitb (miooprobe). 8. Hortonolite; location unknown (Berkeley 12494); analyst: D. G. W. Smith (microprobe). 9. Ferrohortonolite; Skaergaard intrusion, East Greenland (Oxford 5181); analyst: D. G. W. Smith (microprobe). 10. Ferrohorionolite; Skaergaard intmsion, East Greenland (Oxford 4147); analyst: D. G. W'. Smith (microprobe). 11. Fayalite; Rockport, Massachusetts (USNM R9517); analyst: D. G. W. Smith (microprobe). 12. Knebelite; Schysshyttan,Sweden (Berkeley l%lll); analyst: D. C. Harris (microprobe). 13. Knebelite; Dannemora, Sweden; analyst: G. E. Brown, personal communi- . cation (microprobe). 14. Manganknebelite; Broken llill, Australia; analyst: D. C. Harris (micro- probe). 15. Tephroite; Clark's Peninsula, Wilkes Land, Antarctica; Mason (1959). 16. Picrotephroite; Sterling, New Jersey, U.S.A. (Ilarva.rd 105490); analyst: Hurlbut (1961). 17. Picrotephroite; Franklin, New Jersey, U.S.A. (Harvard 85551); analyst: Hurlbut (1961). 18. Roepperite; Franklin, New Jersey, U,S.A. (Harvard Bauer Collection); analyst: D. C. Harris (microprobe). 19. Monticellite; Crestmore, California, U.S.A. (BM 1960, 334); ana.lyst: Moehlman and Gonyer (1934). 20. Willemite; Belgium (Oxford Museum); unanalysed. variations of all bands for the fayalite-tephroiteseries are smaller than those for the forsterite-fayaliteseries (Table 2). In the forsterite-tephroiteseries the poor representationof speci- menshaving compositionsbetween 10 and 50 percentMnzSiO+ makes it difficult to correlatebands unambiguouslyacross the seriesat low frequencies.This region of the infrared spectrais illustrated in Fig- ure 5 and the peak maximadata are summarizedin Table 3. The spec- 972 BURNS AND HUGGINS mg2sl04 (rl, to25l04 (*||] z = t123l04 I (rlt, a 2 a C.tla!lOa (/19) ln25l O4 (*20) ,lrrrrl looo aoo 600 aoo 200 Gn'r Frc. 2. Comparative infrared spectra of willemite and the olivines forsterite, faYaliLe, tephroite, aud monticellite. DETERMINATION OF OLIVINES FROM SPECTRA 973 -T--r--l-,-Trooo 90() 80() 400 300 #4 *6 #7 o E o : E c E lrl'l l'lrl rooo 90() 800 6()() 50() 4()(, 3()() cm-l Fra. 3. rnfrared spectra of Mg-Fe olivines of the forsterite-fayalite series. 974 BURNS AND HUGGINS 60() 500 400 300 20() #lt #.12 o I c o lb t E UI tr o L F 9N !! cc oo !! lrlrlLlrl 600 500 40(, 300 2oo cm-l Frc. 4. Infrared spectra of Fe-Mn olivinee of the faya,lite-tephroite series. DETERMINATION OF OLIVINES FRCIM SPECTRA w5 Table 2. Peak naxima in the infrareil spectra ol olivines of the f,orsterite - fayalite series Specinen No. L23 4567 891011 Banal 1 982 9 84 980 967 913 968 965 961 958 950 945 2 954 951 945 935 940 939 935 927 926 919 9r4 3 885 885 885 882 882 880 881 874 877 A76 472 838 838 836 834 835 834 833 830 830 a29 427 505 604 597 588 588 585 583 573 57r 568 558 5 s s 510 513 508 5r0 510 506 506 504 496 A90 49L 492 487 482 482 450 472 I 469 s 465 ssss s 408 s s 9 4r5 413 406 394 396 392 390 377 377 366 356 10 399s s s 1I Jt6 3t5 S t2 352 350 348 349 334 338 327 304 I3 294 294 288 284 282 28o s 266 s s 253 :es a proninent shoulder or tra appear to conform with trends in the forsterite-fayalite and fayalite-tephroite series, as most bands (in the forsterite-tephroite series) move to lower frequencies with increasing manganese content' Table 3, Peak mdina in the infrared sPectra of mnganiferous olivines. Specinen No. 1r L2 13 14 ra 18 19 20 Band 1 945 944 945 944 944 965 973 985.4 958 970 97s 914 913 912 9r2 909 924 933 957.3 918 9il8 93r 472 872 870 868 860 871 872 886.9 871 879 900 a27 825 A23 a2l arg a22 827 s39.3 824 829 859 5 564 580 588 611.0 572 595 513 506 504 505 504 505 504 s07 508 513 577 7 472 475 477 478 48I s 485 508,7 480 475 459 8 4t2 440 410 438 394 9 J>b J5) 35t J)Z 348 362 374 420.6 3s8 379 T2 304 3rI 305 297 290 3r9 335 307 303 2L7 1"3 253 250 250 24L 240 265 Extrapolated to 10oB Mq2sio4 using linear equations in table'l denotes a proninent shoultler or inilexion In specinen 16, an additional peak occurs at 294 m-l In specimen L7, an additionaL peak occurs aL '115 m-r In wiltenite (specinen 20)' bands I0 and.11 occur at 266 and 227 m-I BURNSAND HUGGINS 6()() 5()0 400 300 o I tr o + = E c| E g L F ! c o ! 600 soo 400 300 Gm-l Jto. 5. Infrared spectraof Mg-Mn olivinesof the forsterite-tephroite DETENMINATION OF OLIVINES FROM SPECTRA 977 The infrared spectrum of the zincian olivine roepperite (specimen 18) is comparableto those of Fe-Mn olivines and bears no resem- blances to the spectrum of willemite containing tetrahedral Zn2* (Figure 2). However,the band maxima for roepperite(specimen 18) summarizedin Table 3 are displacedto lower frequenciesthan those for an Fe-Mn olivine (specimen13) of similar Fe/Mn ratio. Dornnurner:rvp Cunvss Fnorvrrnn Ixrn.tnnn Sppcrnl F orst erite- F ayalit e Series The infrared spectra ciearly demonstratecompositional variations of peak maxima in each of the binary olivine series,indicating that they form the basis of cation compositiondeterminative curves. Best fitting polynomialswere computedby the CURFIT programfor eight bandsin the infrared spectraof ten Mg-Fe olivines.The polynomials of best fit for all bands in this serieswere found to be linear equa- tions, and are summarizedin Tabte 4. Thesedata relate the Mg2SiOr component in an olivine (X) to peak maxima in the infrared spectra (v). The sum of the squaresof residuals,I(lror" - voa.l2)t are also given togetherwith the standarddeviations d(n, q) in paren- thesesbelow each coefficient c(n, q). Table 4. Best-fit polynonials relating i.r. -peak rnaxina to ofiYine conposition in the forsterite-fayalite Band in Equation of best-fitting --, Resiilual 12. i.r. spectru poiynonial (x = c MSZsioe) t(lvobs-e".1"1-,1 1 v=943.19 +0,439X JU. JC (r.48) (0.24) 2 v=912.'lI +0.433X (1.3s) (0.22) 3 v = 8'72.A3+ 0.144X 5.34 (0.55) (0.09) 4 v=A26.7a+0.L24X 1 10 (0.26') (0.04) 5 v=557.13+0.517X 5.84 (0,s8) (0.r0 ) 7 v = 4-1I.54 + 0.346X (1.38) (0.23) 9 v = 356.01.+ 0.645 23.97 (r. 17) (0.19 ) / 1+r+1+/ | = 4942.B0 + 2.646X 86.21 +5+7+9) (3.66 ) (0.s9 ) (4-s) v=269.64-0.393X (0.94) (0,15) BUNNS AND HUGGINS Any of the equations in Table 4 could be used as an olivine cation composition determinative curve. However, certain bands are pre- ferable to others. Bands 4 and 5 are consideredto be the most suitable ones for determinative curyes in the forsterite-fayalite series (Burns and Huggins, 1970) because they are sharp, relatively free from overlap with neighboring bands, and also show an adequate frequency range between end member compositions. Other determinative curves may be computed from the peak maxima data summarized,in Table 2. For example, the sum of the seven bands included in Table 4 has a large range (200 cm-1) but has a large cumulative error arising from any error in spectra alignment. calibra- tion errors are reduced in determinative curves derived from the dif- ference of bands 4 and 5, for example. Sueh difference polynomials eliminate alignment errors and problems of standardization between different infrared spectrometers. For example, we also computed best-fit polynomials for bands 4, 5, und (4-5) from the data of Lyon (1962) and Duke and Stephens (196a). When compared with the polynomials in Table 4, signifi.cant differences are found between the three sets of linear equations for bands 4 and 5, but there is good agreement between the sets of coefficientsfor band (tt-5). F ag alit e- T ephr oit e Series A selection of polynomials computed from the infrared spectra of Fe-Mn olivines is presented in Table 5. They give the MnBSiO+com- ponent in the olivine (X) as a function of peak maxima (r). The peak maxima show zero, small positive, or small negative composi- tional variations. Because of the small compositional variations, deter- minative curves for this series based on individual bands h'ave limited accuracy. A more accurate determinative curYe is represented by the equation for the difference band (4-7) since the gradient of band 4 is positive and is negative for band 7. This equation is also free of speetrometer alignment errors. F or st erite- T ephr oit e Serie s Only four analysed specimens were aYailable for the Mg-Mn olivine series. One of these specimens contained about 7 percent Fe2SiOa and peak maxima for the end-member MpSiO+ component were obtained by extrapolating the linear equations in Table 4 t'o zerc FezSiOr. Because of the limiied number of samples, only polynomials up to degree two are included in Table 5 as expressions relating MgzSiO+ component (X) to peak maxima (v). On the basis of standard deviation and residual data, the most suitable equation for Mg-Mn DETERMINATION OF OLIVINES FROM SPECTRA W9 Table 5. Best-fit polynonr-ials relating i.r. peak naxirna to olivine cornposition for manganiferous olivines. Band in Equation of Best- Residual i,r. spectrum tittinq porynonlial I(luol"-u.ut"lt) Fayalite - Tephroite Series (x mole I Mn2si04) L v = 944.40 r.20 (0.24) 2 | = 909.49 + 0.049 L.32 (o.ss) (0.009) 3 v=859,45+0.308X-0.0018X2 0.69 (0.62) (0.028) (o.oo3) 4 v=817.88+0.096x 0.07 (0.13) (o.o02) 5 v=564.88-0.050X 13.65 (1.78) (o.o2e) 6 v = 504.80 2. 80 (0.37) 7 v=481.30-0.092X 4.73 (0.4r) (o.oo7) 9 v=348.49+0.084x 1.72 (0.80) (0.013) (4-7) v = 336.58 + 0.188x 0.50 (0.34) (0.006) FdrqfarifF - 'lorrhrnifa scries fx mole ? l4q^Sio,) "^ "'--- "--z 4' 1 v=943.00+0.921X-0.0050X2 8.3I (3.00) (0.ls4) (0.0014) 2 | = 908.19 + 0. 524X-,0.OO13X2 2.28 (1.s7) (o.o8r) (o.o0o7) 3 v=861.35+0.285x 15.36 (2.1s) (0.038) 4 v=8J.7.07+O.22Ox 0.58 (0.421 (o.oo7) 5 v=563.34+0.645-0.0017x2 4.82 (2.281 (0.117) (o.oo11) 9 v=347.38+0.489+0.O024X2 r.66 (1.34) (0. 06e) (0.0006) (2-4) ! = 90.70 r- 0.43ttx - 0.0015x2 3.93 (2.06) (0.r06) (0.0010) olivine determinativecurves are consideredto be those for band 4 and the differenceband (2-4). Determinatiue Grid Jor Mg-Fe-Mn Oliuines SinceMg'*, Fe2*,and Mn2* ate the three principal cationsin most 980 BURNSAND HUGGINS olivine minerals, it is theoretically possibleto estimatethe relative proportionsof these cations from the positionsof any two bands in an infrared spectrum.This suggeststhat a triangular diagrammay be constructedfrom the infrared data to form a cation composition determinative grid for Mg-Fe-Mn olivines. Figure 6 showsthe determinativegrid constructedfrom bands4 and 5 in the infrared spectra.The choiceof band 5 as the secondband was basedon the manner in which the band 4 and band 5 contours cross.Band 1 could also be usedin place of band 5, but the accuracy of estimatingthe peak maxima of band 1 is considerablylower. The contours have been drawn as straight lines in Figure 6. Although this is true for band 4 in all three binary series,it is not strictly correct for band 5 since in the forsterite-tephroiteseries the best- fitting polynomial of this band is a quadratic equation. Drscussrom Assessmentof the Infrared,Oliuine CompositionDeterminatiue Cwues Analysesof four of the Mg-Fe olivineswere not availableinitially. Their compositionswere estimatedby the linear equationsgiven in MSrSiOn (' S9O b oQ {15 .e| seo +b 7S a6 57o 65 62 560 Fe25i 04 lln2S i 04 Frc. 6. Compositiondeterminative grid for Mg-Fe-Mn olivines. DETERMINATION OF OLIVINES FROM SPECTRA 981 Table 4 and also by the determinativemethods of Yoder and Sahama (1957) and Louisnathanand Smith (1968) basedon X-ray data. The MgzSiOacomponents of the unanalysedolivines estimated by each of thesedeterminative methods are summarizedin Table 6, to- gether with values ultimately obtained from microprobeanalyses. The data in Table 6 showthat olivine compositionsin the forsterite- fayalite seriesestimated from the infrared determinativecurves are as closeto the true compositions,if not closer,as the estimatesbased on the d13espacings and cell parameterdata. The accuracyof an infrared determinativecurve may be assessed as follows.An error 8z in peak position will causeai eruorEX in the determinedmole percent X in the olivine. In the generalcase: v L 6v: c@,0)* c(n,1)(X + dX) + ... I c@,n)(X+. aX)" and v : c@,0)I c(n,l)X + .. - | c(n,n)X" Subtractingand ignoring secondorder terms and higher in X gives: *dz : +6X[c(n,1) + . .. * nc(n,n)X"-'] 6,: 6x(#) 6X: 6rf #) Assuming an error of te cm-1 arising from spectrometer alignment and personal reading errors, the error in composition estimated from a linear equation becomes Table 6. Conpositions of Selected olivines estimaLed frorn Determinat.ive Curves (g Mg2Si04) Specimen l4rcroprobe YrsI r -^2 Infrared Bands Nunber 454-5 3 78.9 79 74 75 72 77 74 7A tr 5q ? .10 65 62 61 58 62 5 60.0 6L 69 59 59 61 66 60 L0 20.2 22 1B 24 1 Yoder and sahama (1957) 2 Louienathan and Snith (1968) 982 BURNS AND HUGGINS 6X : +e/c(|,l) while for quadraticequations it is 6X : *e /lc(2,l) + 2c(2,2)Xl This analysis showsthat for bands 4, 5, and (4-5) (the estimated peak positionsof which are in error by a maximum of !1 cm-'), the errors in the MgrSiOacomponents in Table 6 estimatedfrom infrared spectroscopyare about !8, !2, and rB percent,respectively (using the c(1,1) coefficientsin Table4). While it was not possibleto compareresults based on infrared deter- minative curvesfor Fe-Mn olivines,the smaller compositionalvaria- tions of peak maxima in the fayalite-tephroiteseries (and hence,the smaller c(1, 1) coefficients)Iead to larger errors in compositionesti- mates.Thus, errors of 10, 10, and 5 percent are expectedfor bands 4,7, and (4-7). Althoughc (1, 1) and c(2,I) parametersare generally large for the linear and quadraticequations for the forsterite-tephroite seties,the accuracyof the infrared compositiondeterminative curves for Mg-Mn olivines is probably reducedbecause they are basedon few availablespecimens. The usefulnessof the olivine compositiondeterminative grid may be illusterated by the results obtained for specimen8, which is a Mg-Fe olivine with appreciablemanganese content (Table 1). The maxima of bands 4 and 5, 830 and 573 cm-1 respectively,for this specimen(Table 2) are locatedon the determinativegrid in Figure 6 at the composition(Mge.31Fe6.61Mn0.o8)2SiOn. This composition is in good agreementwith the formula derived from the electronmicro- probe analysis, (Mg6313Fee.62aMno our)2SiO+. Euidence Bearing on Cation Ortlering in Oliuine A significant feature of the infrared data is the nonlinear best-fit equationscomputed for many of the determinativecurves of man- ganiferousolivines, which contrastswith the linearity of all best-fit equationsfor Mg-Fe olivines. Since Mn2* ions are enrichedin the olivine M(2) positions(Burns, l97O),this suggeststhat peak-maxima -olivines composition data are not linear whenever appreciable cation ordering occursin the olivine structure. Such non-linearity implies that the vibrational frequenciesare site dependent.If the vibrations were equally influencedby cationsin the M(1) and M(2) positions,then the determinativecurves for man- ganiferousolivines would be linear and reflectonly the bulk chemical DETERMINATION OF OLIVINES FROM SPECTRA 983 composition of the olivine. Equations which are non-linear all have negative c(2, 2) coefficients (Table 5). If linear equations derived from end-member spectra were used as determinative curves, the estimated Mn content of intermediate olivines would be lower than the real values based on quadratic equations. This indicates that the vibrations are influenced more by Mgr* and Fe2*ions in manganiferous olivines, which are known (Burns, 1g70) io be enriched in thti M(1) sites. Further corroborative evidence of. M(l) site oceupancy affect- ing vibrational frequencies stems from the spectra of synthetic 7-CapSiOa, CaMgSiOa, and Mg2SiO+ (Tarte, 1963). Again the posi- tive deviation in'the infrared data of internediate CaMgSiOa correlates with the ordering of Mgr* ions in bheM (l) positions of monticellite. The linearity of the peak-maxima-olivine composition data for the Mg-Fe olivine series indicates that the occupancy of the M(1) posi- tions not only reflects the bulk composition of the olivine but also indicates a nearly random distribution of Mg2* and Fer* ions over the M(1) ana M(2) positions in the olivines used in the present study. Conversely, any significant deviation of the infrared data of a given analysed Mg-Fe olivine from the linear determinative curves presented in Table 4 implies ordering of Mgr* and Fez* ions. Acxwowr,oocunrvrg We wish to thank sincerelyseveral mineralogists who made availablespeci- mensfor this study. Theseinclude: Dr. S. O. Asell. Dr. F. B. Atkins. Dr. G. E. Brown, ProfessorJ. C. Carpenter,Dr. P. G. Embrey, ProfessorG. V. Gibbs, ProfessorC. S. Hurlbut Jr., Dr. B. Mason, ProfessorA. Pabst, and Professor E. A. Vincent. Microprobe analyseswere performedby Dr. R. K. OrNionsand ProfessorD. G. W. Smith (Calsary),and Dr. D. C. Harris (Ottawa).Infor- mation in advance of publication was received from Dr. G. E. Brown and ProfessorG. V. Gibbs.Penny Sha,rpand SueHall assistedin the preparationand editing of the manuscript.Financial asistancefrom NASA Grant No. NGR-22- 009-551is acknowledged. RnnnnnNcrs Acrunnnnc,F. P. (1964)Statistical analysisof X-ray data for olivine. M,i,neral. Mag. 33,742-748. BrNcnorr, G. M., ervo R. G. Burr.rs (196g)Mossbauer and absorptionspectral study of amphibolesof the glaucophane-riebeckiteseries. M,i,neral. Soc. Amer. Spec.Pae. 2, 187-148. Br,oss, F. D. (1952) Relationship between density and compositionin mol. percent for some solid solution senes.Amer. Mi,neral.32, 966-981. BownN,N. L., ewn J. Scrrernpn(1935) The systemMgO-FeO-SiOo. Amcr. J.$ci.. 29, 16t-217. Bunxs, R. G. (1970) Crystal field spectra and evidenceof cation ordering in olivine minerals.Amer. Mi,neral.55, 1608-1682. 984 BI]RNS AND HUGGINS -, ANDF. E. HuccrNs (1970) Cation determinative curves and evidenceof ordering in Mg-Fe-Mn olivines from vibrational spectra' GeoI' Soc' Amer' Ann. IVIeet. Abstr., 5lL-5't2. eNn F. J. PnnNrrcn (1968) Distribution of iron cations in the crocidolite structure. Amer. Minercrl. 53,77V776. Dnnn, W. A., R. A. HowE, aNo J. Zussrrell (1963) Rock-Formi'ng M'inerals' Longmans, Green and Co., Ltd., London. Dur Srtltrr, J. V. (1966) X-ray emission microanalysis of rock-forming *jnerals. II Olivines. J. Geol. 4, L-16. Tenrn, P. (1963) Etude infra-rouge des orthosilicates et des orthogermanates. If. Structures du type olivine et monticellite. Spectroch'im. Acta, 19, 2H7. Younn, II. S,, ano T. G. Sanenra (1957) Olivine X-ray determinative curye, Amer. M'ineral. 42, 475-49L. Maruncript rece'i,ued,June 30, 1911; accepted Jor publicati,on, Decernber 91,1.971.