pyroxene thermometryl - university of arizona
TRANSCRIPT
American Mineralogist, Volume 68, pages 477493, 1983
Pyroxene thermometryl
DoNaro H. LrNosr-py
Department of Earth and Space SciencesState University of New York, Stony Brook, New York, 11794
Abstract
Experimentally determined Ca-Mg-Fe pyroxene phase relations at E00-1200'C and fromless than one atmosphere up to 15 kbar are combined with calculated phase equilibria forthe diopside-enstatite and hedenbergite-ferrosilite joins to produce a graphical two-pyroxene thermometer applicable to a wide variety of rocks from the earth, moon, andmeteorites. Samples with appreciable contents of "others" components require specialprojection onto the Di-En-Hd-Fs pyroxene quadrilateral; Wo, En, and Fs components asnormally calculated will not yield correct temperatures. The projection approximates theactivities of those components in natural pyroxenes but is largely empirical, and may not beappropriate for large contents ofnonquadrilateral components. Therefore, the thermome-ter should be used only for pyroxenes having Wo + En + Fs > N%.The effects of pressureare <E'C/kbar; graphs are presented for relations at one atmosphere and at 5, 10, and 15kbar, along with approximate formulas for interpolating between these pressures. Theoccunence of granule exsolution-the coalescence of exsolved pyroxene, with possiblemigration to grain boundaries-can complicate the use of the thermometer for slowlycooled rocks. The primary pyroxene compositions must be reconstructed from texturalevidence before correct igneous or peak-metamorphic temperatures can be inferred.
The experimental data and inferred temperatures for three-pyroxene assemblages permitcalibration of an improved pigeonite thermometer.
Introduction
Petrologists have long recognized the potential ofcoex-isting high-Ca and low-Ca pyroxenes to yield thermomet-ric information for a wide variety of rocks (Table l; Fig.l). In particular, the Ca content of high-Ca pyroxene(augite) decreases with increasing temperature, while thatof the low-Ca phase (orthopyroxene or pigeonite) in-creases. Although there may also be thermometric infor-mation in the distribution of Mg and Fe between the high-Ca and low-Ca pyroxenes (see, for example, Kretz, 1982)this paper is concerned only with Ca partitioning, in partbecause there are more experimental data available forthe Ca contents than for the Mg-Fe distributions ofcoexisting pyroxenes. The two-pyroxene thermometerpresented here yields temperatures offormation for manyrocks from the moon, earth, and meteorites.
Previous two-pyroxe ne thermometers
Most two-pyroxene thermometers have been designedfor pyroxene pairs whose compositions plot near the Di-En-Hd-Fs quadrilateral (Fig. lFthat is, Wo + En * Fs
rPresidential Address, Mineralogical Society of America. De-livered at the 63rd Annual Meeting of the Society, October 19,t9E2.
0003--(M)vE3/0506-.&77$02.00 477
usually total X)Vo or more. With but few exceptions, thethermometers involve at least two steps: projection ontothe quadrilateral, followed by application of relations inthe quadrilateral (or a part thereof) to obtain tempera-tures. A successful thermometer must accomplish boththese steps adequately. This paper will show that only thetwo-pyroxene thermometers of Kretz (1982; Ca reaction),Lindsley and Andersen (19E3), and Ross and Huebner(1975) are successful over a wide range of temperaturesand pyroxene compositions, although the Ross-Huebnerthermometer tends to underestimate temperatures forsome igneous pyroxenes by approximately 50"C.
The most frequently used thermometers project thequadrilateral compositions to the Di-En (Fe-free)join andemploy either a phase diagram or solution model for thatjoin to yield temperatures. This approach was pioneeredby Boyd (e.9., Davis and Boyd, 1966; Boyd, 1969; Boyd,1973), who used simple projections ofFe-poor pyroxenesonto the Di-En phase diagram. Following Boyd, almostall two-pyroxene thermometers have treated the effects ofpressure as negligible. A major step forward was made byWood and Banno (1973), who developed a simple solutionmodel for the Di-En join and presented an analyticalexpression for temperature based on the estimated en-thalpy of the reaction orthoenstatite = clinoenstatite(Opn = CEn). Wells (1977) revised this thermometer on
478 LINDSLEY : PYROXENE THERMOMETRY
Table l. Pyroxenes as geothermometers
A. One-Pyroxene Thernometers:
Ca content of Augi te or Orthopyroxene- minirnun T
Pigeoni te - mininun TProtopyroxene - minimum T
B. l lwo-Pyroxene Thermometers:
Ca contents of c.Qeffi€l.iDC augite-or thopyroxene i augi te-Pigeoni tetp igeoni te-or thopyroxene PairsOrientat ion of t r ro-pyroxene t ie l ines:9 .9 . , d i s t r i bu t i on o f Mg and Fe be -tween augi te and or thopyroxene
C. Three-Pyroxene Thernometer :
1 . Aug i te + p igeon i te + o r thopyroxenecan coex is t a t on ly one T fo r ag i v e n p r e s s u r e a n d F e l ( F e + M g ) ta f fec ted by 'o thers ' conponents
D. Re la ted thernometer :
I . Hedenberg i te - fe r robu6tan i te re la -t ions (Skaergaard)
the basis of newer, reversed experimental data on the Di-En join. Both of these thermometers continue in wideuse, although their assumptions of ideal mixing in clino-pyroxene and a large reaction enthalpy for OEn : CEnare seriously in error (Holland et al., 1979; Lindsley eral., l98l; Davidson et al., 1982). At high temperatures,the errors introduced by these assumptions tend to beself-cancelling; for metamorphic pyroxenes the tempera-tures are 100"C or more too high. In view of the recentimprovements in solution models of the Di-En join, useof these thermometers is an anachronism that should beavoided. Saxena and Nehru (1975), Saxena (1976), Mer-cier (1976), and Kretz (1982) also presented thermometersthat involve projection to the Di-En join. Saxena andNehru made the important point that both the clinopyrox-ene and orthopyroxene series must be treated as distinct,nonideal solutions. Mercier emphasized that each pyrox-ene of a pyroxene pair contains thermometric informa-tion, and he also advocated inclusion of the efects ofpressure. Kretz' thermometer is the most successful,probably because his projection to the Di-En join in-volved a careful evaluation of both igneous and metamor-phic pyroxenes.
Other workers have attempted to use phase relationswithin the quadrilateral, natural occurrences, or a combi-nation of both to determine temperatures. The three-pyroxene (augite + pigeonite * orthopyroxene) ther-mometer of Ishii (1975) was based mainly on observedtemperatures of two erupting lavas. The pyroxenes ofthese lavas are rather similar in composition, so theefective calibration is limited to X [: Fe/(Fe+Mg)]values near 0.25 to 0.35. Ross and Huebner (1979) andPodpora and Lindsley (1979) also presented thermome-ters based on the minimum stability of pigeonite. Buteach of these thermometers is appropriate over only alimited range of X values (Lindsley and Andersen, 1983);
the Ishii and Ross-Huebner curyes seem to be better fornatural samples having X from 0.3 to 0.5, whereas thePodpora-Lindsley curve is preferred for Fe-rich samples.Ishii (1981) attempted to extend his thermometer to two-pyroxene assemblages by adopting the Wood-Bannoformalism for augite-orthopyroxene as well as augite-pigeonite equilibria, but this approach also leads to unac'ceptably high enthalpies for the OEn-CEn reaction. Fur-thermore, his assumption of a large reaction enthalpy forthe augite * pigeonite pair is inappropriate because theseclinopyroxenes appear to obey the same equation ofstateat high temperatures (Lindsley et al., l98l). AccordinglyI recommend that this thermometer not be used.
The Ross and Huebner graphical thermometer (1975)was based on unreversed experimental data at hightemperatures (mainly above 1000"C) and on petrologicintuition at lower temperatures. Topologically their dia-gram is closely similar to the one-atmosphere diagrampresented here. The two thermometers give virtuallyidentical temperatures for metamorphic pyroxenes. Kretz(1982) derived two two-pyroxene thermometers, onebased on the distribution of Mg and Fe and the other onthe partitioning of Ca between augite and low-Ca pyrox-ene. Kretz' Mg-Fe thermometer greatly overestimatestemperatures for some experimentally equilibrated py-roxenes (Lindsley and Andersen, 1983). In contrast, hisCa thermometer gives results that are closely similar tothose of the thermometer presented here and by Lindsleyand Andersen (19E3).
Attempts to use phase-equilibrium data for quadrilater-al pyroxenes (Lindsley et al. 1974; Lindsley, 1980) to
Fig. |. schematic representation of pyroxene relations in theDi-En-Hd-Fs quadrilateral (at some arbitrary pressure andtemperature), showing the two- and three-pyroxene assemblagesthat can be used for geothermometry. A, augite +orthopyroxene; B, augite + orthopyroxene + pigeonite; C,augite * pigeonite. The CaSiO3 (Wo) content of each pyroxeneyields an independent estimate of temperature. The augite *pigeonite field (C) ends at a consolute point, to the right ofwhichthere is a coqtinuous clinopyroxene field because pigeonite athigh temperature has the same space group as augite. At lowpressures this continuous clinopyroxene field is metastable withrespect to melting and/or to the assemblage augite + olivine +silica. Depending on pressure and temperature, other portions ofthe diagram may be metastable with respect to protopyroxene,pyroxenoid, or olivine + liquid. Relations near Fs are omitted.
l .
2 .3 .
l .
LINDSLEY : PYROXENE THERMOMETRY 479
extract thermometric information from complex naturalpyroxenes have not been very successful, at least in partbecause the efects of nonquadrilateral components in thelatter were not accounted for. For example, Figure 2shows the trend for Mg-rich Skaergaard augites (Brown,1957) superimposed on the 900'C, I kbar, augite solvus(stippled area) of Turnock and Lindsley (1981). Not onlyare the apparent temperatures unreasonably low, but alsoit appears that temperature increased with increasingFe/(Fe+Mg)! Possible causes of these discrepancies are:(l) natural pyroxenes require a special projection onto thequadrilateral to provide a realistic estimate of the activi-ties of Wo, En, and Fs; and (2) the Mg-rich Skaergaardaugites have reequilibrated to subsolidus temperatures(Lindsley and Andersen, 1983). A successful thermome-ter must be based both on experimental data of highquality and on an understanding of the effects of thenonquadrilateral components. Lindsley and Andersen(1983) derived a (mainly empirical) projection schemethat approximates the activities of Wo, En, and Fs innatural pyroxenes, thereby permitting the use of quadri-Iateral phase relations for thermometry. The presentpaper is an expansion of their work.
The new two-pyroxene thermometer
The approach to the present graphical two-pyroxenethermometer is twofold: (l) Determination of phase equi-libria for pure Ca-Mg-Fe pyroxenes over a wide range ofpressures and temperatures, since these relations containthe basic thermometric information. (2) Assessment ofthe efects of nonquadrilateral components on the activi-ties of the Wo, En, and Fs components. The first part isvirtually complete; the second is really just beginning.Additional data on the effects of the nonquadrilateralcomponents will surely require modifications of the pro-jection scheme, but the graphs themselves are expectedto need little if any change. Thermodynamic solutionmodels now being developed for quadrilateral pyroxeneswill ultimately permit direct calculation of temperaturesfrom compositions of coexisting pyroxenes, but thegraphical thermometers should be useful in the meantime.
Experimental calibration
Details of the low-pressure ((one atmosphere to 2kbar) experiments are given by Turnock and Lindsley(1981) and by Lindsley and Andersen (1983). This paperpresents data for experiments at 15 kbar.
Starting materials
Starting materials for the phase-equilibrium experi-ments were prepared following the methods of Turnocket al. (1973), and were characterized by means of X-raydiffraction, electron probe microanalysis, and opticalexamination. Approximately one-half of the phases weresynthesized by Turnock at one atmosphere in a gas-mixing furnace; most of the others were synthesized
Skoergoord Pyroxenes
En FsFig. 2. The Mg-rich augite trend from the Skaergaard intrusion
(Brown, 1957; dots and heavy line), superimposed on the 900"C,I kbar augite solvus (stippled band) of Turnock and Lindsley(lgEl). Both the apparent temperatures of the augites and theapparent increase in temperature with increasing Fe are contraryto petrologic expectation. Temperatures on the Di-En join arecalculated from Lindsley et al.,1981.
hydrothermally at 15-20 kbar, 950-1000'C. Phases withintermediate Ca contents (20-30 moleVo Wo) served asstarting materials for exsolving experiments; traceamounts (<<l%) of orthopyroxene were added to some toprovide seeds for the growth of orthopyroxene. Finelyground mechanical mixtures of high-Ca and low-Ca py-roxenes served as starting materials for dissolving experi-ments. Details of each starting material are given in Table2.
Table 2. Starting materials
Index
P H A S E ( S )Aug (Cpx) * Loe-Ca*rW o X W o X
Bulk Conp.l { o x
A 3 0 0 . 1 0B 3 0 0 . 1 0c 3 0 0 . 1 0D 2 0 0 . 2 0E 2 5 0 . 2 0F 2 5 0 . 2 0
G 3 0 0 . 3 0H 3 0 0 . 3 0r 2 8 . 5 0 . 3 0J 3 0 0 . 3 0
K 2 5 0 . 4 0L 2 5 0 . 4 0x 3 0 0 . 5 0N 3 0 0 . 5 0o 2 s 0 . 5 0
P 2 0 0 . 6 0R 2 5 0 . 5 0s 3 0 0 . 6 0T 2 0 0 . 5 0u 2 5 0 . 6 0v 2 0 0 . 6 0
w 2 0 0 . 7 5x 2 5 0 . 7 5v 2 0 0 . 7 5z 2 5 0 . 7 5
A A 2 5 0 . 7 sB B 2 5 0 . 7 5c c 2 5 0 . 7 5
D D 2 5 0 . 8 5E E 2 5 0 . 8 5F F 2 5 0 . 8 5G G 2 5 0 . 8 5H H 2 5 0 . 8 5
(zoned in Ho)0 . 2 0 0 0 . 0 2 5 ( O )
0 . 0 0 0 . 2 0 ( o )(zoned in wo3 l5 -2?)
0 . 2 0 0 0 . 2 0 ( o )0 . 0 0 0 . 3 0 ( 0 )
0 . 3 0 0 0 . 3 0 ( o )0 , 0 0 0 . 5 0 ( 0 )0 . 0 { 0 . 5 0 ( P )
0 . 5 0 0 0 . 3 0 ( o )0 . 3 0 0 0 . 5 0 ( o )
0 . 5 0 4 0 . s 0 ( P )0 . 3 0 0 0 . 6 0 ( o )
0 . 5 0 0 0 . 6 0 ( O ,0 . 5 0 l 0 0 . 6 0 ( P )0 . 3 0 5 0 . 7 5 ( O )
0 . 7 5 0 0 . 7 5 ( O )0 . 7 5 0 0 . 7 5 ( O )0 . 7 5 I 0 0 . 7 5 ( P )0 . 5 0 I 0 0 . 8 5 ( P )0 . 6 0 0 0 . 8 0 ( o )
0 . 8 5 0 0 . 8 5 ( O )0 . 7 5 0 0 . 9 2 ( O )0 . 8 5 r 5 0 . 8 5 ( P )0 . 7 5 1 s 0 . 9 2 ( P )
cpx5 04 6 . 2cpx5 05 0
cpx5 05 0
4 04 0cPx5 05 0
cPxcpxcpx4 0i l 0
4 0
cpxcpxi l 5
5 0t 54 05 0
cpx{ 5{53 53 5
l {o ia mo le percent CaSiOr . X - Fe / (Fe + U9) .rcpx neans Eingle phaae {zoned in sone caseg)**Low-Ca phase ia ortbopyroxene (O) or
c l inopyroxene (P) .
o a i
480 LI N D S LEY : P YROX ENE THERMO M ETRY
Experiments at 15 kbar
The experiments at 15 kbar expand the range of thosereported by Lindsley et al. (1974). Each experimentcontained the de sired pyroxene (or mechanical mixture ofpyroxenes) sealed in a silver capsule with approximatelyl0 wt.Vo water, 3-5 wt.Zo excess SiO2 to saturate thevapor phase, and a trace (<l wt.%) of oxalic acid toinhibit oxidation. Most of the points are bracketed bytriplets of experiments: (l) exsolving experiments fromsingle-phase clinopyroxenes of intermediate Wo content,(2) dissolving experiments with mechanical mixtures ofhigh-Ca and low-Ca pyroxenes having the same X values,and (3) dissolving experiments with mechanical mixturesof Ca-rich, Mg-rich augites and Ca-poor, Mg-poor ortho-pyroxenes (or pigeonites). Such triplets bracket the distri-bution of Mg and Fe as well as of Ca between thecoexisting phases. The furnace assemblies and experi-mental procedures are similar to those described byLindsley (1981). The redox conditions of the experimentswere sufficiently low to prevent formation of magnetite;however, Mrissbauer measurements to detect possibleferric iron in the run products have not been made.
Analytical techniques
The products of each experiment were examined underthe petrographic microscope and by powder X-ray dif-
Fig. 3. A portion of the pyroxene quadrilateral, showingmicroprobe analyses, and Wo contents from X-ray determinativecurves, of the products of a dissolving experiment at 990'C, 15kbar. Filled circles show the starting phases; + b.c. shows thebulk composition of the experiment. Small open circles aremicroprobe analyses ofindividual product crystals. Wo contentsdetermined by both methods are in close agreement for thepigeonites (P). However, the augites (A) show an apparentspread in Wo content that is considered to reflect bothincomplete reaction and grain overlap with pigeonites. The datasymbols (arrowheads) are drawn so as to be compatible withboth the microprobe and the X-ray data.
fraction. Wo contents of clinopyroxenes were estimatedfrom X-ray data using determinative curves (calculatedfrom the data ofTurnock et al. 1973) for the (220), (221),(310), (3lT), (002), (2ll), and (3ll) reflections. Ifthe X-ray results indicated that pairs or triplets of exsolving anddissolving experiments had come substantially to equilib-rium (as shown by closely similar patterns for the runs),the samples were mounted in epoxy and polished forelectron microprobe analysis. The microprobe used wasthe Stony Brook ^lnr--eMx automated system, with theBence-Albee and Albee-Ray colTection schemes. Oper-ating conditions were 15 kV, beam integration, beamcurrent of 0.17 to 0.18 microamps, specimen current of0.015 microamps on brass, and minimum spot size (ap-prox. one square micron). Standards were Y6 diopsideand a synthetic orthopyroxene WoaEn2aFs72. Microprobeanalysis offine-grained and often zoned run products canlead in some cases to ambiguous results (see, for exam-ple, discussions by Lindsley and Dixon, 1976, and Tur-nock and Lindsley, 1981). The compositions listed in thedata table and plotted in the figures represent interpreta-tions of data that involved varying amounts of composi-tional zoning and grain overlap. Usually, however, thecombination of microprobe and X-ray diffraction datapermits a unique interpretation of the results. The resultsreported here for some 15 kbar experiments show some-what different Wo contents from those illustrated byLindsley (1980), mainly because greater weight has beenassigned to the Ca contents indicated by the X-raydifiraction data. Figure 3 illustrates the logic in thisdecision. Microprobe analysis of the product augitesyields a range of apparent Wo contents. In contrast, theX-ray diffraction peaks are all sharp and indicate that theaugite is Wo3o=r, with X in the range 0.52-0.62. Accord-ingly, the run symbol (an arrowhead pointing away fromthe starting augite) for augite is plotted at Wo34, X : 0.57,where the X-ray and probe plots intersect. I interpret themore calcic probe points as representing incompletereaction, and the less calcic ones as resulting from grainoverlap with pigeonite; note that the latter fall on a mixingline between Wo3a and the product pigeonite. Figure l2c(mislabeled l2a) of Lindsley (1980) had accepted thecluster of probe analyses at Wo2g-2e as representing thecomposition of the product augite of this experiment, andaccordingly the augite solvus was drawn at a lower Wocontent than shown in the present paper. The experimen-tal results at 15 kbar are summarized in Table 3.
Construction of the two-pyroxene thermometer
The two-pyroxene thermometer for the quadrilateralhas been constructed on the basis of (l) phase equilibriaat and near one atmosphere, including calculated phasediagrams for the Di-En and Hd-Fs joins; (2) estimates ofthe temperature of the consolute point for augite-pigeon-ite as a function of X; (3) the minimum stability ofpigeonite, also as a function of X; and (4) the effects ofpressure.
LINDSLEY : PYROXENE THERMOMETRY
Table 3. Hydrothermal experiments at 15 kbar
S t a l t . D r r a t i m R U NUtl- T, oC d h X-ray
P R O D U C T S T
AUg IGqa** Aug O
482 LIN DSLEY : PYROXENE THERMOMETRY
Fig. 6. Ca-Mg-Fe pyroxene phase relations at and near one atmosphere. Data symbols are arrowheads pointing the directions fromwhich equilibrium was approached: V symbols are based on microprobe analyses, sometimes augmented by X-ray diffraction data(see Fig. 3). Open triangles give Wo contents based on X-ray diffraction only. In this and the following diagrams, the phase
boundaries shown are constrained to be consistent with experiments at other temperatures as well as with the data points shown.Boundaries dashed where approximately located. Q : quartz; S means a silica polymorph, probably tridymite but possibly
cristobalite. a. E0ffC and I to 2 kbar. b. 900oC and l kbar; light lines show the boundaries ofTurnock and Lindsley (l9El), heavy linesthe revised boundaries drawn to be mutually consistent with isotherms at lower and higher temperatures. c. 1000'C and P < oneatmosphere; line weights as in Figure 6b. d. I100"C and P < one atmosphere. Pyroxene symbols as in Figure 6a. Other symbols are:filled triangle, ferrobustamite; triangle with dot, ferrobustamite + olivine + silica; circle, augite + olivine + silica. e. Pyroxenerclations at 1200'C and P < one atmosphere. Symbols as in Figures 6a and 6d; Liq is liquid. Assemblages with olivine (Ol) and either
Q or S constitute the "forbidden zone" within which pyroxenes are not stable at low pressures.
for constructing the stable portions of the two-clinopyr-oxene field. Both the binary solution models and experi-mental data at 15 kbar suggest that the consolute line isvirtually unafiected by pressure.
3. Minimum stability of pigeonite. The plot for theminimum stability of pigeonite in Figure 8 is adapted fromPodpora and Lindsley (1979) and Lindsley and Andersen(19E3), with the efects of pressure added from Lindsleyet al. (1981), Lindsley (1981), and the present results. It isemphasized that Figure 8 applies to the stability of
pigeonite in the pure Ca-Mg-Fe system. The results ofIshii (1975) and of Ross and Huebner (1979) are probablymore germane to Mg-rich natural pyroxenes, becausethese tend to contain appreciable amounts of non-quadri-lateral components, which, being more abundant in augiteand orthopyroxene, stabilize that assemblage relative topigeonite. As a result, for fixed X the minimum tempera-ture for pigeonite is raised. For a fixed temperature, thethree-pyroxene triangles are displaced towards slightlyhigh X-values. For consistency, the graphical thermome-
9000cHydrolh
I kbor- - - - - - - r L i q
-------'72;x,
X = F e l ( F e + M g ) +
2 4 6
Fig. 7. Variation with X (=Fe2*/(Fe2*+Mg)) of the consolutetemperature for augite * pigeonite. The arrows indicateminimum X values for the consolute temperatures at ll00o and1200"C as estimated from Figures 6d and 6e.
ter is drawn according to the results for the pure Ca-Mg-Fe system; however, readers should be aware that the12fi)o and I100"C three-pyroxene triangles as drawn mayneed to be shifted a few mole percent to the right (and theorthopyroxene and augite solvi extrapolated accordingly)for applications of the thermometer to Mg-rich naturalpyroxenes. The need for this shift will be illustrated bysome of the applications to natural pyroxenes presentedin a later section of this paper, along with a best estimateof the minimum stability of natural pigeonites.
4. Effects of pressure. Increasing pressure has threemain effects on pyroxene equilibria: (l) the augite-ortho-pyroxene field widens at a given temperature; (2) thethree-pyroxene triangles for each temperature becomemore Fe-rich; and (3) the "forbidden zone" becomessmaller, disappearing at around ll.5 kbar. The pressureeffect on augite--orthopyroxene equilibria can be approxi-mated by means of a simple interpolation between the Di-En and Hd-Fs joins, which leads to the estimated pres-sure corrections for the orthopyroxene and augite iso-therms:
augite: Tp = T + (P - P")1.63 - 2.104X+ T(0.0027 + 0.0013x)l
orthopyroxene: 7p = T + (P - f")t0.33 - 0.98X+ r(0.002 + 0.0075x)l
where Tp is the corrected temperature for pressure P (inkbar) and T is the apparent temperature indicated by thethermometer for pressure P". For example, at an apparentT of 1000.C and X = 0.50, the temperature for augiteincreases by 3.9'Clkbar and that for orthopyroxene by5.5"C/kbar. However, the pressure correction must van-ish in the vicinity ofthree-pyroxene (augite + pigeonite +orthopyroxene) assemblages, because augite-pigeoniteequilibria are nearly independent of pressure; excessvolumes of the clinopyroxenes are very small (Turnock elal., 1973; Lindsley et al., l98l; Lindsley, l98l).
Superimposed, the isothermal diagrams (Figs. 6a-e)constitute a graphical two-pyroxene thermometer for lowpressures (Fig. 9a). Isotherms below 800"C and above1200"C are extrapolations from the Di-En and Hd-Fs
LI N DS LEY : P YROXEN E THERM O METRY ,|83
joins, drawn to be consistent with the experimentallydetermined isotherms. The diagram omits most pigeon-ite.orthopyroxene relations (which are poorly con-strained), melting, and the stability fields for protopyrox-ene and ferrobustamite. Within the "forbidden zone" athigh X values, the diagram shows the metastable pyrox-ene relations within that zone (rather than the stableassemblages olivine + silica + augite or ferrobustamite)so as to facilitate the interpretation of pyroxenes that mayform or persist in this region.
The effects of pressure can then be used to extrapolateFigure 9a to higher pressures. Graphical thermometersfor pressures of 5, 10, and 15 kbar (Figs. 9b{) have beenconstructed by applying the pressure dependence ofpyroxene equilibria in the Di-En and Hd-Fs binaries aswell as the pressure effect on the minimum stability ofpigeonite (Fig. 8) and the boundary of the "forbiddenzon€" (L indsley and Grover , l9E0; Bohlen andBoettcher, l98l) to the one atmosphere relations inFigure 9a. Figures 10a-c compare the extrapolated 8(X)',900o, and 1000"C isotherms in Figure 9d with the phaserelations determined experimentally at l5 kbar for8l0t 10", 905110", and 990-r l0'C (Table 3). For the mostpart the agreement is very good, although a number ofthedissolving experiments at 810= l0"C yield augite composi-tions that are slightly less calcic than the extrapolationwould suggest. The extrapolated values are retained sothat the thermometer will remain consistent with theresults at higher temperatures and at lower pressures.The 12fi)'C isotherm in Figure 9d is mainly consistentwith the l5-kbar data of Mori (1978); his results suggestthat the pigeonite ofthe three-pyroxene triangle is slightlymore calcic than is shown in Figure 9d, but they do notconstrain it.
Fig. 8. The temperature of minimum stability for pure Ca-Mg-Fe pigeonite, relative to augite + orthopyroxene, as a function ofX, for five pressures; curves are labelled in kbar. Note that thecurves give only the X value of the pigeonite that coexists withaugite and orthopyroxene; the augite and orthopyroxene aneslightly more magnesian, as expressed by the widths of the three-pyroxene triangles in Figure 6. In contrast, the plot ofRoss andHuebner (1979) shows the X value of the orthopyroxene thatcoexists with the pigeonite. The lines are dashed below 825"C toemphasize that Mn-poor pigeonites are not stable.
X=Fel(Fq+Mg).+ - i-
.2 .4 .6
484
1
LIN DSLEY : PYROXENE THERMOMETRY
otm
mole-- Polythermol
7"l l
LOne
1 0 0
Fig. 9. Polythermal orthopyroxene * augite, orthopyroxene + augite + pigeonite, and pigeonite t augite relations, contoured at100'C intervals for use in geothermometry. At various combinations of temperature and composition, the phase relations shown heremay be metastable with respect to liquid, protopyroxene, ferrobustamite, olivine + silica, or combinations thereof. Compositions ofmost natural pyroxene pairs must be projected according to the scheme outlined in the text before they are plotted on these diagrams.Use of raw Wo-En-Fs data for all but very pure natural pyroxenes will yield incorrect temperatures and will not be tolerated. a.Relations at low pressure (P < 2 kbar). The 1300'C contour and those below 800'C are extrapolated from the Di-En and Hd-Fsdiagrams (Figs. 4 and 5) so as to be compatible with the experimentally determined isotherms. b. Relations at 5 kbar. c. Relations atl0 kbar. d. Relations at l5 kbar. Figures 9b-d derived by extrapolation as described in the text. The short-dash curve in Figures 9a<is the boundary of the "forbidden zone"; pyroxene relations to the right of that curve are metastable with respect to augite * olivinef silica.
boundory of"Forbidden
FsEn
o
Estimation of uncertaintie s
Lindsley and Andersen (1983) estimated that the place-ment of the isotherms in Figure 9a is accurate to approxi-mately 20" to 30'C within the experimentally calibrated
range, and similar uncertainties should apply to the 5, 10,and 15 kbar diagrams (Figs. 9b-d), although with largeruncertainties at 8fi)'C and l5 kbar. Errors in compositionprobably introduce additional uncertainties ofat least 20to 30'C. Thus for pyroxenes having low contents of
\,1 \fi- l\ \\i'' --.\\ -\
[; /)l\ $l )\ )' [k".] F"""iF'...'ffi>.; "',i- - - Boo" -
1
LINDSLEY : PYROXENE THERMOMETRY 485
En
Fig. 9 (continued).
nonquadrilateral components, the thermometer probablyis accurate to t50"C. Correction for nonquadrilateralcomponents (see below) will introduce additional uncer-tainties that will generally be proportional to the amountsof those components, although this efect is difrcult toquantify. Lindsley and Andersen suggested that the un-certainty may increase by 5'C for each percentage pointby which the proportion of nonquadrilateral componentsexceeds two mole percent.
Projection to the quadrilateral
Projection scheme
The projection scheme used (Lindsley and Andersen,1983) is based on crystal-chemical considerations, experi-mental data where available, and a statistical study (An-dersen, 1980 and unpublished data) of correlations amongminor constituents in pyroxenes. Only an outline is
486 LINDSLEY: PYROXEN E THERMOMETRY
presented here; the reader is referred to Section 4 ofLindsley and Andersen for details. One calculates cationsper 6 oxygens and assigns Si to the tetrahedral site, andFe3*, Ti, and Cr to the Ml site. Al is apportionedbetween the tetrahedral and Ml sites as outlined below.Ca and Na are restricted to the M2 site. Because the solepurpose of the projection scheme presented here is toobtain mole fractions of Wo, En, and Fs that most closelycorrespond to the bulk activities of those components, itis unnecessary to apportion Fe and Mg between the Mland M2 sites.
Clinopyroxenes. Ferric iron is accepted from the chem-ical analysis where available. In that case tetrahedral and
cFig. 10. Three l5-kbar isotherms from Figure 9d compared
with experimental data obtained at 15 kbar (Table 3). a. The800"C isotherm compared with data obtained at 810-815'C. b.The 900"C isotherm compared with data obtained mainly at 900-915"C. The dashed data symbols locate a three-pyroxene trianglefor 925"C. c. The 1000'C isotherm compared with data obtainedat 980-990'C.
octahedral Al are then inferred from charge-balance con-siderations, through the relation (Papike et al.,1974):
Al(vD + Fe3+(VI) + Cr(VI) + 2Ti4+(VD= A(rv) + Na(M2)
and from the requirement that A(IV) + A(VD : Al(To-tal). If only total Fe is available (as is the case formicroprobe analyses), the sequence is different. Tetrahe-dral Al is taken as 2 - Si, with the remaining Al assignedto the Ml octahedral site. Fe3+ is then calculated from thecharge-balance equation above. However, unless theanalysis (especially for Si) is ofsuperior quality, this stepmay seriously bias the results.
Now calculate the clinopyroxene components in thefollowing sequence:(l) Ac : NaFe3*SizOe = Na or Fe3*, whichever issmaller.(2) Jd = AI(VI) or any remaining Na, whichever issmaller.(3) FeCaTs = remaining Fe3*.(4) CrCaTs = Cr.(5) AlCaTs = remaining A(VI).(6) For augite, "Ca" = Ca; for pigeonite, "Ca" = 2 -
(Fe2*+Mg). Finally, for clinopyroxenes, take Wo =("Ca" + Ac - AlCaTs - FeCaTs - CrCaTs)/2, En = (l- Wo) 0 - n, and Fs : (l - WoXX), where X =
Fez*l(Fe2* + Mg). Plot these Wo, En, and Fs values onFigure 9 to estimate the temperature.
Orthopyroxene. The projection scheme for orthopyrox-ene is slightly different: A(IV) is taken as 2 - Si, andAI(VI) as Al(tot) - A(IV). Ferric iron is then estimatedfrom the charge-balance equation above. R3* is taken as
IA(VD * Cr + Fe3*1, and R2+ as [Mg(l - n + Fe2*(X)].Components are then calculated in the sequence:(l) NaR3*Si2Oo = Na or R3*, whichever is smaller.(2) NaTiAlSiOo : Ti or AI(IV) or any remaining Na,whichever is smallest.(3) R2+TiAl2O6 = the remaining Ti or [AI(IV)]/2, which-ever is smaller,(4) R2*R3+AISiO6 : the remaining R3* or AI(IV); in aperfect analysis these would be equal.(5) Ca, and the remaining Fe2+ and Mg, are then normal-ized to yield Wo + En * Fs = l.Note that the effect of this sequence is to maximize thecontent (and therefore the bulk activity) of Wo in theorthopyroxene. The resulting composition is then plottedon Figure 9 to yield the orthopyroxene temperature.
A program in seslc to process chemical analyses ofpyroxenes as outlined above will be supplied upon re-quest. The program accepts data either as weight percentor as cations per six oxygens.
A word of caution.I should emphasize that this largelyempirical projection scheme is an approximation only.Ordering of Fe and Mg between the Ml and M2 sites ofpyroxenes may introduce additional complexities, espe-cially at metamorphic temperatures. We also need moreand better experimental data on the effects of additional
\
LINDSLEY: PYROXENE THERMOMETRY 487
components on the activities of quadrilateral compo-nents. For example, Suzanne Kay (pers. comm., 1982)has found that the apparent temperatures yielded by thethermometer increase with increasing alumina content:augites (from garnet granulites) with 8 wt.Vo Al2O3 yieldtemperatures in excess of 1000'C. Her results stronglysuggest that the removal of the Tschermak's components(steps 3-5) from the effective Wo content of the augite isan overconection that results in an underestimation ofthe activity of Wo. Experimental evaluation of the effectsof alumina on quadrilateral equilibria is urgently needed.In the meantime, use of the thermometer should berestricted to pyroxenes containing more than 90Vo Wo +En * Fs, and the user should bear in mind that theuncertainties increase with increasing amounts of non-quadrilateral components.
Applications of the two-pyroxene thermometer
Pyroxenes from lavas of known eruption tempera-tures
Probably the most appropriate samples for use ofpyroxene thermometers are lavas with pyroxene pheno-crysts. In at least some cases the phenocrysts may havecrystallized in mutual equilibrium; eruption of the lavaserved to quench the samples and minimize any subsoli-dus re-equilibration. Groundmass pyroxenes, however,seem to have crystallized metastably in many cases andshould be used with caution. Phenocryst (or micropheno-cryst) compositions have been determined for two lavasof known eruption temperature.
Mihara-yama. Ishii (1975) reported analyses of coexist-ing augite and orthopyroxene phenocrysts in a basaltfrom the 1950-1951 eruption of Mihara-yama Volcano, O-shima Island, Japan. The highest temperature observedduring the eruption was I125'C. Projected onto Figure I l,the compositions of the two augite phenocryst coresindicate 1100 and ll50'C; the orthopyroxene yields1150"C for the temperature of crystallization. Especiallyin view of the possibility that the crystallization tempera-ture of the phenocrysts may have been somewhat higherthan that observed during the eruption, the correspon-dence is excellent. Ishii (1975) used this sample to definethe 1125"C point on his three-pyroxene thermometer,apparently on the assumption that the groundmass pi-geonite was in equilibrium with the phenocrysts. Thisassumption appears to be invalid; ll50'C would seem tobe a better estimate for the temperature at which pigeon-ite would coexist with this augite and orthopyroxene.
Akita-komagatake. Aramaki and Katsura (1973) report-ed compositions of phenocrysts and microphenocrysts ofpyroxenes in an andesite from the 1970-71 eruption ofAkita-komagatake Volcano, northern Honshu. The high-est observed temperature of the erupting lava was1090"C; melting and crystallization experiments suggestan eruption temperature of ll00'C. The Ca contents of
Fig. I I . Compositions of phenocryst augite and orthopyroxene(solid circles) from the 1950.-1951 flow, Mihara-yama Volcano,O-shima, Japan (Ishii, 1975), projected onto part of thethermometer. The highest temperature observed during theeruption was ll25'C; the phenocrysts reflect this or a slightlyhigher, intratelluric temperature. Also shown are compositionsof phenocrysts (solid squares) and microphenocrysts (opensquares) from the 1970-:ll flow, Akita-komagatake Volcano(Aramaki and Katsura, 1973). Eruption temperature of this flowwas 1090-1100"C.
the augite and orthopyroxene phenocrysts (Fig. 11) arecompatible with 1090'C, although the slope of the tie-line,which is more appropriate for an augite-prgeonite pair,raises some question as to whether the phenocrysts werein equilibrium. The microphenocrysts, presumed to haveformed immediately prior to the eruption, form a classicthree-pyroxene triangle. Both the augite and the ortho-pyroxene indicate a temperature at orjust above 1100"C.The pigeonite microphenocrysts are also compatible withthat temperature in view of the likelihood that nonquadri-lateral components shift three-pyroxene triangles to moreiron-rich compositions (Lindsley and Andersen, 1983,Section 3). Ishii (1975) used these samples to define the1090'C point on his three-pyroxene thermometer; theRoss and Huebner pigeonite thermometer (1979) givesll25'c.
Other three-pyroxene assemblages from lavas
The compositions of two reported three-pyroxene as-semblages are plotted in Figure 12. The Funagata pyrox-enes (Ishii, 1981) are all compatible with a temperature of1200"C, in excellent agreement with the temperature ofI195"C as indicated by the minimum stability of pigeonite(Ross and Huebner, 1979). Like the three-micropheno-cryst assemblage from Akita-komagatake, this three-pyroxene triangle also indicates that the triangles for Mg-rich naturals may be displaced to slightly more Fe-richcompositions relative to those for the pure quadrilateralat a given temperature. Ishii (1981) estimated a tempera-ture of 1155"C for Funagata. In contrast, the Weiselberg
Mihoro-yomo,O-shimo r
Observed T=
4EE LINDSLEY : PYROXENE THERMOMETRY
Fig. 12. Compositions of two r€ported three-pyroxeneassemblages projected onto part of the thermometer. F (solidcircles), Funagata (Ishii, l98l). W (solid squares), Weiselberg(Nakamura and Kushiro, 1970a).
samples (Nakamura and Kushiro, 1970a) plot very closeto the pure three-pyroxene triangle for l0(X)oC, and thedata are remarkably consistent with a crystallizationtemperature of 990'C. Note that for this more Fe-richsample, the natural and pure Ca-Mg-Fe three-pyroxenetriangles virtually coincide, confirming that determina-tions of the minimum stability of pigeonite in the quadri-lateral are appropriate for more iron-rich natural samples.Ishii (1981) estimated a temperature of 1039"C for thisassemblage, using his three-pyroxene thermometer(1975). The Ross-Huebner pigeonite thermometer (1979)suggests approximately 1090'C for the Weiselberg pyrox-enes; Lindsley and Andersen (19E3) suggest that tempera-tures from both these thermometers should be consideredas upper limits rather than as actual crystallization tem-peratures for Fe-rich pyroxenes.
Ot he r reporte d t hre e-py roxe ne as semblages. Severalother three-pyroxene assemblages have been described inthe literature [Hakone (Nakamura and Kushiro, 1970b;Ishii, l98l); Ashio (Kuno, 1969; Ishii, l98l)1, but theseappear not to have been in mutual equilibrium (Lindsleyand Andersen, l9E3).
Minimum stability of natural pigeonites-a ther-mometer
A distinct advantage of the present two-pyroxene (orthree-pyroxene) thermometer over earlier thermometersbased simply on the minimum stability of pigeonite (Ishii,1975; Ross and Huebner, 1979; Podpora and Lindsley,1979) is that independent estimates of temperature maybe made from coexisting augite or orthopyroxene or both,as well as from the pigeonite. Nevertheless, there aretimes when a pigeonite thermometer can be very useful;when pigeonite is the only pyroxene to form, for example,such a thermometer gives a minimum value of the crystal-lization temperature. Figure 13 gives a best estimate for
the minimum temperature of stability at low pressures ofnatural pigeonite relative to augite plus orthopyroxene.For Mg-rich pigeonites (0.1 < X < 0.25), the curvecorresponds to that of Ross and Huebner (1979). Place-ment of the curve above that for pure Ca-Mg-Fe pigeon-ites in this region reflects the relative stabilization ofaugite + orthopyroxene by non-quadrilateral componentsand is consistent with the temperature deduced for theFunagata pyroxenes (discussed above). The curve isdashed in this region to emphasize that the actual tem-perature will depend on the amount of "others" in thepigeonite.
More Fe-rich pyroxenes tend to have fewer "others"components, and for them the determinations for theminimum stability of pigeonite in the pure system areappropriate. For example, Vocke (1981) experimentallydetermined the minimum stability for pigeonite (nowinverted) from the metamorphosed Stillwater Iron For-mation; her bracketed temperature of E25t20"C coin-cides with that of Podpora and Lindsley (1979) for purequadrilateral pyroxenes having the same X value. TheWeiselberg pyroxenes (cited above) likewise support thisinterpretation. Accordingly, the curve in Figure 13 usesthe values for pure Ca-Mg-Fe pigeonites forX > 0.5. For0.25 < X < 0.50, the curve is sketched so as to connectthe Ross-Huebner and Podpora-Lindsley curves; itpasses through the temperature inferred for the Akita-komagatake three-pyroxene assemblage. Figure l3should encompass the best features of the Ishii (1975),Ross and Huebner (1979), and Podpora and Lindsley( 1979) pigeonite thermometers.
Fig. 13. Estimated plot (heavy curve) of the X value of naturalpigeonites that coexist with augite * orthopyroxene at lowpressures. Derivation is described in the text. R-H is Ross andHuebner (1979);I is Ishii (1975). The curve labelled (Pure Ca-Mg-Fe) is the 0-kbar curve from Figure 8, and was obtained fromthe data of Podpora and Lindsley (1979) and Lindsley andAndersen (1983). The heavy curve should give the minimumtemperature at which a natural pigeonite of a given X value hascrystallized. It should also yield the crystallization temperatureof a pigeonite that co€xisted with augite plus orthopyroxene, butthat temperature should be checked against the augite andorthopyroxene temperatures obtained from Figure 9a.
Minimum stobil ify of nofurol pigeonites
X= Fe l (Fe+Mg) -
Where pressure can be estimated independently, theapparent temperature from Figure 13 should be increasedby 8.5'C per kbar (Lindsley and Grover, 1980; Lindsleyand Andersen, 1983; Fig. 8 of this paper). Application ofthe pigeonite thermometer to inverted pigeonites in plu-tonic rocks obviously requires a reconstruction of theoriginal composition-especially the X value-of the pri-mary pigeonite.
Pigeonites are not stable at one atmosphere for Xvalues >0.72. Lindsley and Grover (1980) showed thatthe effect of pressure in stabilizing pigeonite (relative toaugite + olivine + quartz) to higher X values is justbalanced by the simultaneous destabilization of pigeoniterelative to Fe-rich augite + orthopyroxene. As a result,E25"C is the lowest temperature at which any Fe-richquadrilateral pigeonite is stable (although approximatelyl0% MnSiO3 component may further stabilize pigeonitedown to 775"C; Bostwick, 1976). The X value of Mn-poorpigeonite coexisting with augite * orthopyroxene +olivine + qtaxtz is a sensitive barometer: P(kbar) =41.07(XeE - 0.28), as revised from Lindsley and Grover(1980). Unfortunately this assemblage is rare.
Pyroxenes from plutonic rocks
Application of this or any two-pyroxene thermometerto plutonic rocks presents certain problems. Most pluton-ic pyroxenes are exsolved. The present compositions ofthe host pyroxene and exsolved lamellae should yield thetemperature at which exsolution (on the scale resolved bythe analytical technique used) effectively ceased. Recom-bination of host and lamellae into original compositions-which ideally yield magmatic or peak-metamorphic tem-peratures-may be tedious but should be straightforward.However, Hodges and Papike (1976), Bohlen and Essene(1978), and Lindsley and Andersen (1983) report a moresubtle form of exsolution from some pyroxenes: granuleexsolution, wherein the exsolved material migrates toform discrete grains at or near the edges of the originalhost. Failure to recognize these grains and to incorporatethem into the reconstructed composition of the host mayresult in serious underestimation of the original tempera-ture.
Skaergaard intrusion. Figure'2 shows the incongruitybetween the compositions of Mg-rich Skaergaard augites(as customarily plotted) and experimental data for purequadrilateral pyroxenes. Projection of the Skaergaardaugites by the scheme of Lindsley and Andersen (1983)removes some but not all of the problem: the apparenttemperatures range from 1050'C for the most Mg-richaugite to I100"C for the most Fe-rich augite that coexistswith primary pigeonite. Nevertheless, the apparent in-crease of temperature with crystallization (increasing X)remains. Lindsley and Andersen (1983) present extensivetextural, chemical, and experimental evidence that theMg-rich augites from the Skaergaard have undergonesignificant amounts of granule exsolution, as have the
LINDSLEY : PYROXENE THERMOMETRY 489
30 40 50
Fig. 14. A portion of the pyroxene quadrilateral showingselected isotherms (light curves) from the one-atmospherethermometer (Fig. 9a). Also shown are the analyses of Mg-richSkaergaard pyroxenes (Brown, 1957), projected by the methodof Lindsley and Andersen (1983). The projected analyses andtrends (open symbols and medium-weight lines) are more nearlycompatible with the experimental data than are the raw Wo-En-Fs plots (see Fig. 2), but both the augite (A) and pigeonite (P)trends remain anomalous. The heavy trends and filled datasymbols are inferred primary igneous trends and compositionsfor the augite and pigeonite; the differences are ascribed to near-solidus granule exsolution of augite from primary pigeonite andof pigeonite and/or orthopyroxene from primary augite (seeLindsley and Andersen, 1983).
pigeonites. Figure 14 presents inferred primary trends forMg-rich Skaergaard pyroxenes, superimposed on a por-tion of the two-pyroxene thermometer. The discrepanciesbetween these trends and the measured trends (as pro-jected) are reflections of the probable degree of granuleexsolution. Since the uncorrected augite trends for theBushveld intrusion (Atkins, 1965) and other plutonicigneous bodies are similar to that for the Skaergaard(Brown, 1957), it seems likely that granule exsolutionmay be the rule for such bodies, and that application ofthe two-pyroxene thermometer to them will requirepainstaking reconstruction of primary pyroxene composi-tions. In many cases, unfortunately, unequivocal distinc-tion between primary pyroxenes and exsolved granulesmay not be possible.
Application to granulites. Application of the thermom-eter to granulites has difficulties. For example, Bohlenand Essene (1979) concluded that none of the thermome-ters then in use gave consistent, meaningful temperaturesfor pyroxenes from Adirondack granulites. Sadly, thatconclusion appears to hold for the present thermometeras applied to their data, which are microprobe analyses.With the present thermometer their clinopyroxenes showlower temperatures relative to the Wood-Banno ther-mometer but just as much scatter (from below 5(X)o to880'C), and there is no consistency with the temperaturesinferred from two-feldspar and oxide thermometry. Thereis a tendency for alumina-rich clinopyroxenes to yield
oOuoiroding ,
490 LINDSLEY : PYROXENE THERMOMETRY
Fig. 15. Compositions of coexisting augites andorthopyroxenes from hornblende granulites, Quairading,Australia (Davidson, l!)68), projected onto part of the ther-mometer.
higher temperatures, in agreement with the findings ofSuzanne Kay (pers. comm.). The remaining scatter mayreflect all or some of the following: incomplete resettingof igneous compositions, inadequate re-integration ofexsolved material. or incorrect calculation of ferric iron.In contrast, their orthopyroxenes give temperatures rang-ing from 5fi) to 620"C, with the great majority above550'C. Thus it is very tempting to conclude that theorthopyroxenes have been reset upon cooling from granu-liie grade, with blocking temperatures near 550"C.
Glassley and Sorensen (1980) also presented micro-probe analyses of coexisting pyroxenes from a granuliteterrane. The present thermometer applied to their ortho-pyroxenes gives very consistent temperatures clusteredaround 600"C. Either that represents a blocking tempera-ture for the resetting of orthopyroxene compositions, orthe thermometer is not suitably calibrated for very low-Ca orthopyroxenes. The clinopyroxenes indicate highertemperatures that unfortunately vary with the calculatedferric iron content. If all iron is presumed ferrous, theaugites give temperatures from 580" to 710'C, with mostbetween 630 and 7fi)'C. Calculation of ferric iron assuggested by Lindsley and Andersen (1983) decreases theprojected Wo content; the indicated temperatures rangefrom 680 to 860oC, a much wider spread. It may benecessary to have independent determinations of ferriciron (perhaps by wet-chemical analysis or by Mdssbauerspectroscopy) before the thermometer can be applied tothese rocks.
Figure 15 shows compositions of coexisting augites andorthopyroxene from the hornblende granulites of Quair-ading, Australia (Davidson, 1968), as projected onto thetwo-pyrox€ne thermometer. At first glance, the Quairad-ing pyroxenes seem ideal for application of the thermom-
eter, for ferric iron was determined directly. The augitesindicate temperatures ranging from 690 to 825'C (mean,740-r45"C) and the orthopyroxenes suggest 650 to 730'C(mean, 693-ts28"C). These temperatures should be in-creased by l6-23"C if the pressure of metamorphism isassumed to have been 5 kbar; the low-pressure tempera-tures are given here to facilitate comparison with othertwo-pyroxene thermometers that lack pressure colTec-tions. The Mg-rich augites tend to yield slightly highertemperatures than the rest, although the difference maynot be significant. Although the mean temperatures foraugite and for orthopyroxene are not significantly differ-ent (the uncertainties are one standard deviation of themeans), most of the orthopyroxenes tend to yield slightlylower temperatures than do the coexisting augites. It isunclear whether this difference reflects imprecision in thecalibration of the thermometer (either in the placement ofthe isotherms or in the projection scheme) or whether theorthopyroxenes may have undergone some minor retro-grade reaction that does not appear in the augites. It isalso noteworthy that Davidson's orthopyroxene analysesconsistently show about one-half mole percent more Wothan do the microprobe analyses cited above. StevenBohlen (pers. comm., 1983) has pointed out that only asmall amount of primary augite in the mineral separatecould cause this difference, which colresponds to cd.l(X)oC on the orthopyroxene thermometer. Thus the bet-ter correspondence between orthopyroxene and clinopy-roxene temperatures for Quairading may be fortuitous.Fortunately, minor contamination of the augite separateby primary orthopyroxene should have a much smallereffect on the augite temperatures.
It is noteworthy that despite the close spacing of theorthopyroxene isotherms of the thermometer, the tem-peratures indicated for suites of granulite orthopyroxenesare remarkably consistent. Presumably this is because theanalytical errors in Ca are proportional to the amount ofCa present. Thus, if the dichotomy between wet-chemicaland microprobe analyses can be resolved, the orthopyr-oxenes may eventually yield temperatures as good asthose from the augites.
Ross and Huebner (1975) drew their 750'C isotherm topass through the compositions of the Quairading augites.Kretz used these augites to define the projection path formetamorphic pyroxenes for his Ca thermometer (1982),and assumed that they formed at 730"C. Both of theseassumed values are closely compatible with the tempera-tures yielded by the present thermometer. In contrast,other thermometers yield 863-+35'C (Wood and Banno,1973);893t18"C (Wells, 1977); and 828136'C (Saxena,1976). These temperatures seem unrealistically high forhornblende granulites. For example, Bohlen and Essene(1977) used cpexisting Fe-Ti oxides and coexisting feld-spars to infer temperatures ranging from 650'C (horn-blende granulites) to 790"C (garnet granulites) in theAdirondacks.
LINDSLEY : PYROXENE THERMOMETRY
Summary and conclusionsGraphical thermometers based on equilibria of quadri-
lateral pyroxenes are presented for I atm and for 5, 10,and 15 kbar. The thermometers can be applied to augite-orthopyroxene, augite-pigeonite, and (to a limited extent)pigeonite.+rthopyroxene pairs as well as to three-pyrox-ene assemblages. Each pyroxene of a pair or triplet yieldsan independent estimate of temperature, thereby permit-ting a check for consistency. The thermometer also givesa minimum temperature for the formation of single pyrox-enes, since at or below the temperature of saturation asecond pyroxene would have formed. The diagramsshould be directly applicable to nearly pure (Wo * En *Fs > 98%) pyroxenes. The compositions of less purepyroxenes should be projected onto the quadrilateralfollowing the scheme of Lindsley and Andersen (1983).That correction scheme is largely empirical, because fewexperimental data of high quality are available regardingthe effects of non-quadrilateral components on the com-positions ofcoexisting pyroxenes. The projection must berefined on the basis of additional experiments; for exam-ple, the data of Kay (pers. comm., 1982) suggest that thescheme is not adequate for pyroxenes containing largeamounts of alumina (8 wt.%).It is suggested that applica-tion be limited to pyroxenes in which Wo * En + Fsexceed XlVo. Ultimately, the graphical thermometer willbe replaced by a quadrilateral solution model fitted to thedata, but the graphical approach should be useful in theinterim.
Successful application of the two-pyroxene thermome-ter to slowly cooled rocks will usually require diligentreconstruction of primary pyroxene compositions on thebasis oftextural evidence. In particular, petrologists mustbe alert to the possibility of "granule exsolution"-theexsolution of low-Ca from high-Ca pyroxene (or viceversa) followed by the coalescence of the exsolved mate-rial into discrete grains, many of which may becomeexternal to the original parent grain. In many cases theresulting texture mimics that of primary crystallizationand is therefore easy to overlook. Granule exsolution ismost likely to occur at relatively high temperatures wherediffusion rates are high; exsolution at lower temperaturesgenerally yields the more familiar lamellar texture. Simi-lar combinations of granule and lamellar exsolution arewell known in some sulfides and (driven by oxidation) inFe-Ti oxides. Although the reconstruction of originalcompositions may be tedious, there may be a bonus: infavorable cases it may be possible to determine not onebut two or three temperatures-that of original crystalli-zation, and those for the cessation of granule exsolutionor of lamellar exsolution. or both.
At present it appears that mineral separation and wet-chemical analysis gives more satisfactory results foraugites from granulite terranes than does re-integration ofprimary compositions from microprobe analyses. A di-rect measurement of ferric iron appears essential, since
calculated Fe2O3 depends critically on the quality of the
rest ofthe analysis, especially SiO2. For orthopyroxenesfrom granulites, wet-chemical and microprobe methods
each give very consistent results, but the former gives Wo
contents that are higher by about 0.5 moleVo; these yield
"reasonable" granulite temperatures. The microprobeanalyses, on the other hand, indicate temperatures mainly
of 550 to 600'C, clearly too low for peak-granulite condi-
tions. There are several possible explanations: (l) the
wet-chemical analyses include but the microprobe analy-
ses exclude small exsolved granules ofCa-rich pyroxene;
temperatures indicated by the former are correct and
reflect those of peak metamorphism; (2) the mineral
separates of orthopyroxene were compromised by small
amounts (lVo) of primary (not exsolved) augite, and thus
the temperatures they indicate are fortuitously good; (3)
the microprobe analyses (with lamellae re-integratedwhere present) indicate true orthopyroxene compositionsat granulite grade, and it is the orthopyroxene portion of
the thermometer (or projection scheme) that is incorrect.
Unfortunately, the present data do not permit discrimina-tion among these possibilities.
Also presented is a revised thermometer based on the
minimum stability of pigeonite.
Acknowledgments
I am grateful to many people who have contributed to thiswork over the years. Allan Turnock generously provided manyof his pyroxenes used as starting materials; he and John Groverhelped perform some of the experiments and provided manyhours of stimulating discussions. Discussions with Steve Bohlen,Tim Grove, and Steve Huebner have also been most helpful.Steve Bohlen, Bob Dodd, and John Grover all improved thepaper with their constructive comments. Selena Dixon, HubertKing, and Clara Podpora assisted with the experiments. It is aspecial pleasure to acknowledge the many contributions ofDavidAndersen and Paula Davidson; they have played a major role inmaking this paper possible. In particular, Andersen helpeddevelop the projection scheme and processed the analyses ofhundreds of pairs of natural pyroxenes, and Davidson hascontributed to the assessment of the experimental data and to thethermodynamic modelling of the pure pyroxenes. Work wassupported by xesl grant # NGL-33-015-130 and by NationalScience Foundation, Earth Sciences Section, Grant EAR-E026250. My deep thanks go to them all.
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492 LINDSLEY : PYROXENE THERMOMETRY
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Manuscript received, January 17' 1983;acceptedfor publication, January 24, 1983.