Evaluation of thermobarometers for garnet peridotites

001&7037/84/$3.00

Gaxhimim n Cavnochimica Acta Vol. 40. pp. 15-27 Q Perpmon Rem Ltd.1984. Printed in U.S.A.

+ .oo

Evaluation of thermobarometers for garnet peridotites A. A. FINNERTY* Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109

and F. R. BDYD Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC 20008 (Received August 20, 1982; accepted in revisedform September 22, 1983) Abstract-The accuracy and precision of a large number of combinations of geothermometers and geobarometers for garnet lherzolites have been evaluated with a suite of wellcquilibrated xenoliths from kimberhtes of northern Lesotho. Accuracy was tested by comparison of P-T estimates for a diamondbearing and a graphite-bearing xenolith with the experimentally determined diamond-graphite univariant curve and by comparison ofP-Tcstimates for phlogopite-bearing xenoliths to the high-temperature stability limit of phlogopite (EGGLER and WENDLANDT, 1979). Precision was evaluated by measuring the scatter of P-T estimates for each of four xenoliths from a wide range of P and T when many point analyses of the constituent minerals are used for P-T estimation. A thermobarometer composed of the uncorrected diopsidecnstatite miscibility gap of LINDSLEY and DIXON (1976), combined with the uncorrected isopleths for aluminum in enstatite coexisting with pyrope of MACGREGOR (1974), is most satisfactory. Correction schemes such as those of WELLS (1977) and WOOD (1974) will ultimate!y provide a better means of P-T estimation, but at the present stage of development they serve to decrease precision without a demonstrable increase in accuracy. Thermometers based on Fe2+/Mg exchange reactions are imprecise because of variable and unknown Fe2+/Fe3* rn minerals and xenoliths. The inflection observed in the northern Lesotho paleogeotherm cannot be an artifact of the method of temperature estimation. be used in thermobarometric calculations. There is no reason to accept an average temperature derived from multiple thermometers as any more accurate than an estimate made with one thermometer, and indeed the opposite is probably true. In order to conduct a meaningful comparison of geothermometers and geobarometers, a computer program (TEMPEST) has been written to solve for a large number of combinations of thermometers and barometers. Published equations, or equations derived from least-squares fits to published data, for geotherby the five “best” thermometers

INTRODUCIION A PLETHORA of new or modified

geothermometers

rocks have been suggested during the last decade. Uncertainty exists as to which (if any) techniques are accurate, inasmuch as temperature and pressure estimates obtained by different methods on the same rock may disagree by hundreds of degrees and tens of kilobars. It is important to resolve these conflicts so that constraints can be placed on upper mantle petrology, stratigraphy, and thermal state. CARSWELL and GIBB ( 1980) have attempted a comprehensive comparison of many thermometers. They used the average of temperatures derived for each individual rock as a reference, selected five thermometers that consistently gave results closest to the average, and recommended that the average temperature given and geobarometers

for ultramafic

+ Present address: Department of Geology, University of California, Davis, CA 956 16. ’ SeeNAPS document No. 04132 for 36 pages of supplementary material. Order from ASK/NAPS, Microfiche Publications, P.O. Box 35 13, Grand Central Station, New York, NY 10163. Remit in advance $4.00 for microfiche copy or for photocopy, $7.75 up to 20 pages plus S.30 for each additional page. All orders must be prepaid. Institutions and Organizations may order by purchase order. However, there is a billing and handling charge for this service ofS 15.Foreign orders add $4.50 for postage and handling, for the first 20 pages, and $1.00 for additional IO pages of material. 61.50 for postage of any microfiche orders. * Mineral analysesfor most xenoliths are repotted in NIXON and BOYD ( 1973); more detailed analysesof PHN 1569, PHN 1591, FRB I, and PHN 1611 are presented in BOY0 and FINGER (1975). Analyses for diamond-bearing BD 2125 are taken from DAWSON and SMITH (1975).

mometers

and geobarometers

are solved

simulta-

neously, wjth input data consisting ofchemical analyses (expressed as oxides) of coexisting minerals within each rock. Where deemed necessary, details on the formulations and equations used in this program are given in the Appendix. Twenty-one versions of thermometers and six garnet-field barometers are at present calculated with TEMPEST, and the program is being continually updated to add new thermometers and barometers as they become available.’ APPROACH A suite of garnet Ihetzolite xenoliths from kimberlitcs of northern Lesotho, South Africa, that appear chemically equilibrated by criteria discussed below was used for estimation of pressure (p) and temperature (T) by a large combination of thermometers and barometers. The P-Testimates obtained were tested for concordance with critical heterogeneous mineral reactions determined in the laboratory.

Rock suite

The garnet lherzolite xenoliths from northern Lesotho2display the widest range in apparent equilibration temperature 15

4 A Fmnerty and F. R. Boyd

lh

of any known set of mantle rocks. Correlated variations m element partition between minerals indicate that mineral chemical compositions of these rocks have not been altered from a state of chemical equilibration that existed before cooling from mantle conditions, in contrast to the suggestion of FRASERand LAWLESS(1978). Alterations of the xenoliths would most likely cause only partial reequilibration, disturbing these correlations. Four representative specimens from throughout the range of equilibration temperatures have been shown to display only minor compositional inhomogeneities within the major minerals, mostly with respect to chromium (BOYDand FINGER,1975) further supporting the notion that each of these rocks has preserved mineral compositions rep resentative of equilibration at a particular value of P and 7’. Compositional variations for a variety of T- and P-sensitive exchange reactions are concordant (Fig. 1). The diopside content of clinopyroxene coexisting with orthopyroxene correlates strongly and with minimal scatter with Ca-Mg exchange between garnet and otthopyroxene (Fig. IA). Similarly the Ca content of olivine, fixed at any P and T by the coexistence of clino- and orthopyroxene (FINNERTYand BOYD, 1978) is closely related to the Ca-Mg exchange (Fig. I B). Two Fe”Mg exchange reactions (Figs, I C and ID) are also correlated with Ca-Mg exchange but show more scatter, probably due to the effects of Fe’+ that is summed with Fe*’ in electron microprobe analyses. The scatter for the gamet-clinopyroxene reaction is greater than that for the garnet-olivine reaction perhaps because Fe)+ may be present in significant amounts in garnet and clinopyroxene but not in olivine. Other reactions, including such unconventional examples as exchange of Na between two pyroxenes, display similar correlations, sup porting the suggestion that these xenoliths are quenched from a state of chemical equilibration 0.50

*

,

’ :: ” c P 0.40+ m 2 0.35.z

Mineralogical

c0nsrrainl.v

Several heterogeneous mineral reactions may be applied to evaluate the P-T conditions of equilibration. Diamondgraphite equilibrium (KENNEDY and KENNEDY, 1976). a strictly univariant reaction if nitrogen solid solution is not significant, is especially useful in constraining pressure estimates. One lhetzolite within the northern Lesotho suite contains primary graphite (PHN l569), and another (BD 2 125) bears diamond (DAWSONand SMITH, 1975). Some hatzburgites from northern Lesotho and other localities contain graphite, and there are additional diamond-bearing xenoliths from the Soviet Union (POKHILENKOet al., 1977), but none of those examined provides a better bracket to the diamondgraphite curve than the two Lesotho Iherzolite samples. There are nine xenoliths within the northern Lesotho suite that contain phlogopite in textural relationships that have been interpreted as primary (BOYD and NIXON, 1975). The high-temperature stability limit of phlogopite can, therefore, also be used as a petrologic constraint, but inasmuch as this reaction is dependent on the composition of the mica and the presence or absence of a coexisting vapor, the constraint is not precise. For natural iron-bearing phlogopite, the ZIVC solidus curve (EGCLER and WENDLANDT,1979) for a kimberlite-like composition in the presence of CO2 t Hz0 is believed to be representative of mica stability. Maguesian

7-7-------

1

0.45 --

These observations contrast with the hypothesis of HAR-IF and FREER (1982) that low diffusion rates in minerals of peridotite xenoliths may cause differences in “blocking” temperatures for different exchange equilibria. Perhaps mechanisms other than intragranular diffusion (e.g., recrystallization) are involved in equilibration of peridotite xenoliths.

l.‘O

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i i

0.30-j

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IO 15 20 25 Xl 35 40

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:

’

’

I

I

(Ca)(Ca + M9))garl(Ca/(Ca+ Mc#ox

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FIG. I. Chemical correlations between minerals from garnet lhetaoiite xenoliths from kimberlites of northern Lesotho. All analyses were determined by ekctron microprobe. ln all taxes, compoaitional data are plotted against the values calculated for the atomic ratio [Ca/(Co + Mg)Y/[Ca/(Ca + M&J’“. (A) atomic [Ca/(Ca + Mg)P’; (B) Ca“” (ppm by weight); (C) (FeO/MgD~/(FeO/Msoyl’*; (D) (FeO/MgO)P’/ (FeO/MgOP”.

17

Garnet peridotite thermobarometers phlogopite is expected to be stable to temperatures about 50°C higher than the ZIVC solidus, but the presence Of small amounts of Fer+ in the natural micas probably lowers the stability by an equivalent amount. The melting of perldotite can also be used as a constraint. NO FTestimates for xenoliths should exceed the temperature of the lherzolite dry solidus because none of the xenoliths displays evidence of partial melting. On the other hand, xenoliths may come from the high-tempemtum side of the ZIVC solidus ifthe mantle from which they are derived is suihciemly low in CO, and HrO so that significant melting does not take Place. The continental geotherm calculated for a 40 mW/m2 surIbce heat Bow above a conductive mantIe (POLLKR and CHAPMAN, 1977) is useful as a geophysical model for the thermal state of the upper mantle. The curve is not valid below the lithenphete-asthenosphere boundary where heat transport by convection may become significant. Curves representing each of these constraints are presented for reference in each geotherm plot.

only one reaction is currently useful as a barometer, and only three have achieved popularity as thermometers. The aluminum content of enstatite coexisting with pyrope and the diopaide content of clinopyroxene coexisting with orthopyroxene (diopside-enstatite miscibility gap) constitute the most widely used ~o~orn~er for application to garnet Iherzolites (e.g.. BOYD, 1973). Partitions of Fer’ and Mg between garnet and clinopyroxene and between garnet and olivine have also been calibrated and are useful for estimating T, esp&ally in harxburgites and other ultramafic assemblages that hear only one pyroxene. Other equilibria have been partially calii and may become valuable thermometers after further study. All the thermometers and barometem evaluated in this work, with refances and codes that are used in the figures and text, are listed in Table i and some are discussed in the Appendix. MACGREGOR(1974) cabbrated the aluminum solubility of enstatite coexisting with pyrope in experiments on the

Code

EC79 CA79

simple system MgO-A&Or-SiQ, but did not reverse his determinations. The pmssure eI&t was found to be. large enough to be useful as a barometer, but the reaction is also subject to a strong temperature effect. AtLELU (1976) extended the experiments to C&earing compositions, achieving some revemk LANE and GANGULY (1980) mversed tbeirexperimeots on MgO-AlzOr-Si& and applied ~~~~ic constmints in their cahbratioo. None of these approaches deals directly with potentially serious effects of solution of Na, Fe, and Cr in garnet and pyroxene. WOOD (1974) has attempted semiempirical thermodynamic corrections. lo W074A (Table I), Cr in garnet and orthopymxene is $nored, whereas in W074B specific site assignments for Cr are assumed, and in WO74C the Cacr oonideal intetactioo parameter -bywoOD ( 1977) is incorporated (see Appendix). The diopside-enstatite miscibility gap was redeterminrxl by LINDSEY and DIXON ( 1976) in the system CaO-MgO-SiOr . They combined their experimental msults with those of previous workers to produce a miscibility gap at sevetal possums, defined solely by reversed runs. The data analyxed by LINDSLEY and DtXON appear to mnfvm the exi&OcC Ofa pressme e&t that can lead to errors of 3” to 4*C/kbar in temperature estimation. Their data have been fit to a nonlinear equation (Appendix) and programmed for use either with or without the pressure effect. The diopsideenstatite miscibility gap is influenced by solution of other components, especially F$‘. &3YD (1973) introduced the use of C#Ja + Mg) in natmal clinopyroxenes as an e%ctive way to calculate the diipside component while minimizing the inIIuence of Fe and other components. The Ca/(Ca + Mg) values for clinopyroxeoes in experiments on iron-bearing pyrolite III composition (MORI, 1976; Mo~l and GREEN, 1978) made at a variety of temperatures and pmssnms define a miscibility curve that is very similar to curves for the pure binary system (Fig. 2). The compositions of the pyrolite pyroxeoes am closely comparable to those found in natural garnet Ihetzolites, and agreement with experimental data on simple systems suggests that minor elements in the natural pyroxenes do not have much et&t in combination on the miscibility when properly projected. Hereaftar, Ca/ (Ca + Mg) is used for calculating model temperatures with

rw*crion

Reference

xA79 LO76 LD76 (20) LX81 HE76 (CPX)

Ellis and Green (1979) cangu1y (1979) Kawasaki (1979) Lindeley and Dixon (1976) Lindsley and Dixon (19,6) Llndslcy -sl, (i981) nercitr (1976)

NE76 WX)

nerefer

WC78 MC78 I4278 HGl8 MG76

(1976)

DIlEN GARICPX GAWOPX CARfOLV OPXfCPX

2:: oLv’cPx PO?8 OPXfcPx PO78 CAR/OF% RG74 SA?9 M71 Ml7

AK76 1680 Kc74 xl,‘* WJ741 WO74C

Lane and Gonguly “llccre*or 11974) WDod (1974)

(1980)

A A. Finnerty and F. R. Boyd

18

IS mmimized for reacttons wtth strong T and P effects (or both). utilizing elements that can be analyzed precisely. LJncertainty in Fe*‘/Fe” increases the width of the bands, as does propagation of analytical uncertainties in methods that incorporate analyses of many elements (e.g.. WOOD and BANNO. 1973). By companng P-T estimates for garnetiferous assemblages to appropriate stability curves (e.g.. diamond-graphite) certain combinations of thermometers and barometers can be identified as unacceptable, but the relative accuracy of thermobarometers that do not violate mineralogical constraints cannot be judged. Further appraisal may be based principally on the precision of each method. Inasmuch as analytical formulation of precision for each thermobarometer is a formidable task, we have taken an empirical approach. The individual point analyses (up to fifteen) for the minerals in each of the four rocks of the Lesotho suite (PHN 1569, PHN 1591. PHN 1611, and FRB 1) studied by BOYDand FINGER MOLE FRACTION (1975) were randomly combined and run with program TEMPEST to produce fifteen P-T estimates for each rock. I , for each combination of thermometer and barometer. These 0.30 0.40 0.50 four rocks cover the range of temperatures estimated for the +- Mg2Si206 CaMgSi206 Lesotho suite. Standard deviations for P and T estimation Cai(Ca + Mgl for all thermobarometers were calculated; examples for the barometers, paired with the LD76 (20 kbar) thermometer. FIG. 2. Ca/(Ca + Mg) of chnopyroxenes in experiments are presented in Table 2. Similar data for the thermometers, reported by MORI and GREEN(1978, Table 2). Analytical paired with MC74 barometer [except ME76 (CPX) and ME76 data are from MORI (1976, Appendix 3). Circular points are (OPX)], are given in Table 3. The data for several therrnofor runs at 30 kbar, and square points are for runs at 40 kbar. barometers are plotted in P-T projection in Figs. 3A-3F. Most of these runs were made with the composition pyrolite These data were selected to illustrate the effects of thermomIII minus 40% olivine. Curve A is the diopside limb of the eters based on different reactions and, in one example (Fig. diopsideznstatite miscibility gap of DAVISand BOYD(1966) 3B), the influence of a correction scheme on the barometer. determined at 30 kbar, curve E is the LINDSLEYand DIXON Two data points for the lowest-temperature rock. PHN (1976) determination at 20 kbar, curve C is the LINDSLEY 1569, plot far from the remaining thirteen points in ah these and DIXON limb corrected to 30 kbar with the equation in examples. The values for Ca/(Ca + Mg) of diopside for these the Appendix. outlying points are 4.20 and 18.80 from the mean of the other thirteen, and such data would normally be discarded during routine analysis by electron microprobe. The two uncorrected simple-system thermometers. More elaborate questionable points are not included in the calculation of corrections, based on thermodynamic theory, have been prostandard deviations for P-T estimates in Table 2. posed by WOOD and BANNO(1973) and WELLS(1977). Standard deviations for temperature estimates for all comThe exchange of Fe’+ and Mg between garnet and clinobinations of thermometers and barometers are generally less pyroxene- has been found to be strongly temperature dependent and slightly pressure dependent (ELLIS and GREEN, 1979: than 15°C for diopside-enstatite thermometers (see Table 3 for examples). For PHN 1569. standard deviations are about superseding the work of BAHEIM and GREEN, 1974). The a factor of two higher. The steepening of the diopside limb highly nonideal solution of Ca in garnet and thermodynamic of the miscibility is likely to be responsible: uncertainty in corrections for other components must be taken into account the Ca value of diopside is reflected in greater temperature (GANGULY, 1979; SAXENA, 1979). The most serious comuncertainty at low temperature. For this group of thermomplication in the use of this reaction, however. is the presence eters, standard deviations are greater when correction schemes of unknown amounts of Fe3+in the natural minerals. Gametolivine Fe’+-Mg partition (O’NEILL and WOOD, 1979; KA- are applied, as would be expected because uncertainties in analyses for a larger number of elements (e.g.. Fe, Na) are WASAKI,1979) is subject to the same uncertainty. Within the propagated through the equations used for temperature esnorthern Lesotho suite, Fe)+ may be relatively low (e.g.. MCCALLISTERet al., 1975) but may nevertheless cause sig- timates. For thermometers that are based on Fe/Mg exchange renificant errors in estimated equilibration temperatures. actions (e.g.. Figs. 3E and 3F), standard deviations for PHN 1569 are comparable to those for diopsideenstatite therACCURACY AND PRECISION mometers (e.g., Figs. 3A-3D). For higher-temperature xenoliths the comparison is less favorable, and for PHN 1611 A thermobarometer is a couple, composed of a thermometer (highest-temperature rock) the Fe/Mg thermometers display and a barometer. There is no fun&mental thermodynamic values of standard deviations about ten times higher than distinction between a thermometer and a barometer; either may be considered as an exchange reaction that may be rep resented in P-T space by isopleths or isopartition curves. Compositional analyses for the components involved in a particular exchange reaction define one curve in P-T space. The intersection of two such curves defines a P-T point that, ideally, signifies the conditions under which the rock was last equilibrated. Because of propagation of analytical errors,each of these should be thought of as a band. The precision of the P-T estimate is related to the area of the quadrilateral formed by the interaction of two such bands (e.g., POWELL, 1978). whereas the accuracy is related to the location of the central point. The precision is maximized for bands that intersect at right angles. The width of the bands, hence the uncertainty.

@4?

19

Garnet peridotite thermobarometers

Pm

1 (‘0 LD76(20 kbar) 879(20) La76 928(25) 881~28~ w77 WI73 1019C25) PO78 OPXlCPX 715(19)

RG74 EG7Y H678 GAR!CPS GA79 SA79

M678 HG78 MC78 PO78

GARlOPX OPX/CPX OLVICPX GAWOPX

1126(11) 952C11) .349(8, 1016C7) 899(14)

84YC16) 850(21) 851(14) 854CllI

FRB 1

1569

PIiN 1591 (kbar)

r

14.0(1.2) 17.1t1.51 14.lC1.7) 42.8C1.6) 24.9~1.1~ 15.4(2.1) 27.7CO.Y) 36.YCO.7)

56.OtO.4) 66.9C0.6) 50.1(0.6) 55.6CO.5) 61.1C1.6) 53.6CO.7,

1299(6)

49.5Cl.O) X3.6(0.9) 32.1tO.6) 4l.YCO.7) 15.1~1.1~

97.7C2.2) 61.8Cl.O) 56.9C1.0) 65.O(O.Y) 70.6C2.0)

p (kbar)

T (‘C)

e

(‘C,

p (kbar)

PHN 1611 (‘0

p (kbar)

1426(g)

62.2CO.5) 76.2CO.8) 55.1t0.6) 56.4CO.5)

r

1661C11) 1110(Y) 1128C7)

61.6CO.8)

59.8(0.7j

51.9CO.8)

1528C11) 1506(7)

51.7C1.0)

1816Cl2) 1114(14) 1210(15) 1367(H) 1155(24)

91.4C2.4) 62.Ot1.1, 64.OC1.0) 6l.lC1.7)

2018(117) 1411(56) 141OC59) 1465(45) 1321(86)

98.5C6.9) 62.5Cl.l) 61.lCl.4) 64.5C2.6) 56.OC5.1)

52.lcl.ij 53.1(1.0)

55.5cl.oj

18.6C1.8) 15.6(1.8) 11.9(1.7)

1107(24) 1227ClOI 1427(45)

61.lC1.6) 56.3C2.0) 68.YC2.9)

1165(25) 1111(U) 1471(58)

6l.YC1.7) 60.6C2.1) 70.70.5)

1470(110) 1449(202) 2027C420,

64.8C7.7) 61.6U2.0) Y7.8(24.9)

12.1(0.8) lZ.Z(l.5) 12.2~1.1~ 12.4Cl.O)

1201~21~ 127201) 1162C18) l&40(27)

54.6C1.4) 59.1C2.2) 52.1t1.2) 69.7C1.7)

122900) 1211~22) 1117C16) 1541(15)

55.4C2.0) 55.6t1.2) 49.7(1.1) 75.1C2.2)

1158(169) 1481(142) 1218(100) 1761(28)

58.2C9.9) 65.5C8.4) 51.1C5.9) 82.2(1.7)

those of the diopside-enstatite thermometers. Inasmuch as the log of an equilibrium constant is proportional to inverse temperature, the Fe/Mg thermometers are expected to be less precise at higher temperatures. Greater uncertainty in F$‘/ Fe3+in the less depleted compositions of the higher-temperature xenoliths in the Lesotho suite may also enhance the scatter at higher temperatures. Some of the thermometers are pressure dependent, so that uncertainty in the analysis for A1203in enstatite somewhat increases the uncertainty in those temperature estimates [e.g., Table 3, LD76 (20 kbar) VS.LD76]. All versions of the A1203incnstatite barometer, on the other hand, are strongly temperature dependent, so that the scatter in pressure estimates is a strong function of the scatter in temperature estimates. The observed standard deviations are remarkably small, commonly less than 1 kbar, the majority less than 2 kbar. Where scatter is relatively great, there is a tendency to scatter along the direction of the geotherm (e.g., Figs. 3A3D at lower temperatures, Figs. 3E and 3F at higher temperatures), because the P-T slope of the AlSO3 isopleths for enstatite coexisting with pyrope is close to that of the ge.o&tm. FRASERand LAWLESS (1978) and O’NEILL(I 98 1) have suggested that paleogeotherms may lx artifacts arising from this effect, coupled perhaps with different “locking” temperatures for thermometers and barometers, and that the Lesotho xenolith suite is derived from a very restricted range of temperatures and depths. Inspection of Fig. 3 and Tables 2 and 3, in conjunction wi$ the chemical correlations in Fii I, re.veak that this is not the case; the scatter in P-T estimates for each xenolith is much smaller than the range covered by the entire suite. It is further apparent (Figs. 3E and 3F) that this type of scatter tends to define subparallel curves in P-T space. rather than a single “geothenn.” RESULTS The P-T estimates for the northern Lesotho suite made with the formulation of the LINDSLEY and DIXON (1976) diopside data at a constant pressure of 20 kbar as the geothermometer (Appendix) and six different formulations of the aluminous enstatite reaction as barometers are plotted in Fig. 4. In these and all subsequent geotherm plots, diamond-bearing BD 2 125 is represented by a diamond, graphite-bearing PHN 1569 by an open circle, primary-phlogopitebearing xenoliths by squares, sheared xenoliths by triangles, and eleven other xenoliths by crosses.

Only the barometer of MACGREGOR (1974) (Fig. 4A) satisfies the diamond-graphite constraint, whereas that of LANE and GANGULY( 1980) (Fig. 4FJ is closediamond plots less than 2 kbar into the graphite field. That of AKELJ_A(1976) (Fig. 4B) places graphite less than 2 kbar into the diamond field. The three formulations of the WOOD (1974) barometer (Figs. 4C4E) place diamond substantially into the graphite field, and the scatter between xenoliths is much larger. No other petrologic constraints are violated. The MC74 and LG80 barometers are both based on experimental calibration in the MgO-A1203-SO2 system, with no corrections applied for solution of other elements. Addition of calcium oxide in the experiments of AmLm ( 1976) results in shifting pressure estimates 5 to 8 kbar higher. The WOOD (1974) corrections shift estimates to lower pressures. The minimal corrections in the W074A formulation (Fig. 4C) increase scatter, whereas the more extensive corrections in the W074B version (Fig. 4D) increase scatter still more. The Ca-Cr cOrrection term added in the WO74C barometer decreases scatter and raises pressure estimates closer to those obtained by the uncorrected barometers (Fig. 4E). (In this context, “scatter” refers to increased departure of P, T estimates for individual rocks from best-fit curves through the data.) The same pattern is observed when these six barometers are applied against each of the thermometers. In every case MC74 is closest to satisfying the diamondgraphite constraint (usually in complete accord), whereas LG80 tends to be in slight disagreement, and the other four are in substantial conflict. Against several thermometers (e.g., ELLIS and GREEN, 1979), MC74 places phlogopite-bearing xenoliths up to 45°C above the ZIVC curve, whereas AK76 always meets the phlogopite constraint. Up to 100°C conflict is caused by LGSO, and the Wood barometers result in even greater violations. The phlogopite constraint is not strong, as discussed above, and contlicts of 50°C are not likely to be significant, given the uncertainty in the position of the phlogopite stability curve for the

20

A. A. Finnerty and F. R. Boyd DEPTH (kilometers) 200

150

100

! kllomoters)

DEPTH 250

LD76 iM kbarl vs MC74 60

40

PRESSURE

80

20

(ktlobors)

200

150

60

PRESSURE

DEPTH (kilomoterr) 100

40

DEPTH 250

100

80

(kIlobars)

(kliOtnQtQrS)

150

200

250

1600

- 1600 k!

14cxl ii E 1200 i t1000

1000 /

WB73 YS MC74

I

/’

800

800 40

PRESSURE

(kIlobars)

PRESSURE

60

80

(kilobars)

DEPTH (kllOmQtQrS) km<

g

1600

1600

1400

1400

1400

1200

1200

1200

1000

1000

1000

I600

1600

EG79 vs MC74 I’

800 20

800 4c

PRESSURE

60

(kilobars)

80

1’

800 20

800 40

PRESSURE

60

80

(kIlobars)

FIG. 3. Scatter plots for six thermobarometers, derived as described in the text. There are fifteen points for each of four rocks. In order of increasing temperature, the rocks are PHN 1569 (open circle), FRB 1 (X), PHN 1591 (diamond), and PHN 161 I (cross). Where data points are excessively crowded, a box is drawn to enclose them. The number next to the box refers to the number of data points within the box. The symbol within the box identifies the rock whose data are enclosed within the box. Reference curves are as follows: lherzolite dry solidus inferred by using the P-T slope of ITO and KENNEDY(1967) and KUSHIROet al. (I 968). constrained to pass through the P-T point of HARRISON(1979) at 1575°C. 55 kbar. ZIVC solidus extrapolated from ECCLERand WENDLANDT(1979) from experimental data obtained at 30 and 55 kbar, 40 mW/m* continental geotherm (dashed line) from POLLACK and CHAPMAN(1977), valid only at depths shallower than the lithosphere-asthenoaphere boundary where heat transport is dominated by conduction; graphitediamond stability curve from KENNEDY and KENNEDY(1976): unlabeled curve between 56 and 65 kbar and 1200” and I5OO”C is fit to the inflected portion of the northern Lesotho paleogeotherm as determined by the LD76 (20 kbar) vs. MC74 thermobarometer. (A) LD76 (20 kbar) vs MC74. (8) LD76 (20 kbar) vs. WO74C. (C) WE77 vs. MC74. (D) WB73 vs. MC74. (E) EC79 VS.MC74 (F) 0W79 vs. MC74.

21

Garnet peridotite thermobarometen DEPTH (kilometers)

DEPTH (kilometers) loo

150

200

100

250

200

150

250

1600 LtiERZOLllE IRY SOLIDUS

, ,,/j8, 40

60

PRESSURE

20

60

40

1x1

200

60

80

PRESSURE (kilobars)

(kilobars)

DEPTH (kilometers) 100

LD76,@lkqar)vs,AK7

DEPTH (ktlometers) 100

250

1600

150

200

250

1600

1600

1200

1000

;<,$f

t”

(”

kbarj vs Wp74

800 40

20

60

PRESSURE

80

(kIlobars)

I50

200

40

60

PRESSURE

DEPTH (kilometers) 100

600 20

80

(kilobars)

DEPTH (kilometers) 250

150

100

200

250

I600

1600

1600

1400

1200

1000

LD76 (20 kbar) vs LG8D

LD76 (20 kbar) vs WO74C 800 20

40

PRESSURE

60

80

(kilobars)

40

60

80

PRESSURE(kilobars)

FIG.4. Geotherm plots for xenoliths from northern Lesotho in which six versions of the barometer based on aluminum content of enstatite coexisting with pyropc am used. The thermometer in all cases is LD76 (20 kbar). Reference curves as in Fig. 3. Symhots arc explained in the text. (A) MC74. (B) AK76. CC)

W074A. (D) W074B. (E) WO74C. (F) LGSO. natural phlogopites. Thermoharometers that result in 100°C disagreement may be suspect. The scatter between xenohths represented in these plots correfates roughly with the scatter tests on individual xenoliths listed in Tables 2 and 3 and Fig. 3. From these observations it is inferred that, on an empirical basis, the three Wood formulations are both

inaccurate and imprecise, whereas AK76 and LGSO are as precise as, but probably less accurate than, the MC74 barometer. The relative accuracy and precision of the MC74 barometer imply that nonideal sohrtion effkts in the compositional range of the Lesotho xenoliths are (fortuitously) compensating. As corrections are applied

4. 4. Finnerty and F. R. Boyd

for some interactions (e.g., W074A and W074B) the compensation is unbalanced, resulting in inaccuracy and increased scatter. Further correction (e.g.. for CaCr interaction in W074C) tends to bring the compensation back into balance, improving accuracy and reducing scatter. The Wood approach should match the performance of the MC74 barometer when extended and completed, and will then improve upon MC74 for com~sitions that depart from those of the Lesotho suite. Until further improvements in thermodynamic corrections are made, MC74 is the most accurate and precise barometer for garnet-bearing assemblages. The LGSO barometer is more carefully calibrated than MC74, and should probably be used as the data base for improved the~~ynamic correction schemes. The success of the MC74 barometer paired with other thermometers is illustrated in Fig. 5. Incorporation of a pressure effect into the LD76 diopsideenstatite thermometer (Fig. 5A) increases the pressure estimates of the hirer-tem~ratu~ xenoliths by up to 15 kbar, and the paleogeotherm is stretched to greater depths. Temperatures in excess of 1700°C for some xenoliths are estimated, but no petrologic constraints are violated and scatter remains low. The WWD and BANNO (1973) semi-empirical thermodynamic correction scheme (Fig. 5B) reduces the ag parent temperature range covered by the Lesotho suite, consequently compressing the pressure range. Scatter relative to the LD76 formulations is increased substantially, but no petrologic constraints are violated. The WELLS (1977) correction scheme also increases scatter (Fig. X), reduces the temperature range to a lesser extent than WB73, and tends to lower the estimated temperatures compared with LD76 (20 kbar) or LD76. As a consequence. diamond plots slightly into the graphite field. In view of the standard deviations in Table 2, this conflict is not significant at the 20 confidence level. No other petrologic constraints are violated. Garnet-ctinopyroxene Fe/Mg thermometry, as illustrated by the ELLIS and GREEN ( 1979) calibration (Fig. 5D), results in a large increase in scatter relative to the LD76 formulations. This increased scatter was anticipated because of the influence of unknown Fe2+/ Fe’+ in the Lesotho minerals. Two phlogopite-~a~ng rocks fall about 40°C above the estimated stabibty of the mica, but the stability estimate might be in error by this amount. The thermodynamic analysis ofGANGULY (1979) for this reaction compresses the temperature range and increases scatter over EG79, and two phl~opite-~~ng rocks plot 60”-70°C above the estimated mica stability (Fig. 5E). The O'NEILL and WOOD (1979) garnet-olivine Fe/Mg thermometer is in accord with petrologic constraints (Fig. 5F), with a moderate increase in scatter that is more evident in the higher-temperature rocks. A second calibration of this reaction by KAWASAKI ( 1979) (not illustrated) gives closely similar results.

The Fe/Mg thermometers as a group may be as accurate as diopside-enstatite thermometers but they tend to be less precise as a consequence of the Fc2’/ Fe3+ problem and the tendency for equilibrium constants to become less temperature dependent at higher temperatures. For those garnet peridotites that contain two pyroxenes, one of the diopside-enstatite thermometers is preferable. Solely on the basis of the criterion of minimum scatter (t.(* , closer fit to the shape of a theoretical temperature profile). the uncorrected diopside-limb thermometers as tit to the data discussed by LINDSLEY and DIXON ( 1976) are preferable. The magnitude of the pressure effect on the miscibility gap is still not well known, and the 20-kbar calibration is in better accord with geophysical predictions. so this calibration is preferred. Other thermometers that have been calibrated but have not been widely employed are potentially useful. MERCIER(1976) formulated the diopside-enstatite vs. aluminous enstatite thermobarometer in such a way that elemental analysis of one pyroxene (assumed to coexist with the other pyroxene and garnet) could be used to obtain both pressure and temperature estimates. Through this approach, garnet peridotites that have been altered by processes that destroy one or more minerals but leave one pyroxene can be used in the~obaromet~. The calibration of Mercier is unsuccessful; the orthopyroxene formulation places diamond 4 kbar into the graphite field with very high scatter within the Lesotho suite. whereas the clinopyroxene calibration results in diamond plotting IO kbar into the graphite field, with still greater scatter. SAXENA ( 1979) has developed a the~odynamic model for garnet~linopyroxene Fe’+/Mg exchange to account for nonideal solutions and substitution of other components, similar to the model of GANGlJL.\ t 1979). As was the case for such corrections in the diopsideenstatite system, scatter in P-p-7‘estimates among the Lesotho xenoliths about an expected geotherm is increased without notable improvement in accuracy compared with the simple-system calibrations. The thermodynamic model of POWELL (1978) for Ca/Mg exchange between two pyroxenes fails in the empirical test. The temperature estimates become very large for the higher-temperature xenoliths and eventually go negative. Diamond-~a~ng BD 2 I25 plots 6 kbar into the graphite fteid. Powell’s model for Cal Mg exchange between garnet and orthopyroxene. based on few experimental data, satisfies the petrologic constraints. A paleogeotherm is produced that extends to pressures and temperatures in excess of 80 kbar and 17OO”C, closely resembling that defined by the pressure-dependent fit to the data of LD76 (Appendix). Because of the potential for thermobarometry in the absence of clinopyroxene, this reaction should be further investigated. The thermodynamic model of LINDSLE~ ~1 ui. ( I98 I ) for exchange of CaMgSizOh component between diopside and enstatite is more successfuI than the Cai

23

Garnet peridotite thermobarometers DEPTH (kllomatars)

DEPTH (kilometers) 100

I50

200

100

250

I50

200

250

1600

1600 LHERZOLITE RY SOLIDUS

1200

LD76vs MC74 000 20

40

60

PRESSURE

00

20

(kilobars)

PRESSURE

DEPTH (kilomQtQrs) 150

100

60

40

60

(kilobars)

DEPTH (kilomotors) 100

200

I50

200

250

1600

1600

1400

1400

1200

1200

iti! t3 Q s

2 I-

1000

1000

EG79vs MC74 600 40

20

60

60

PRESSURE

20

(kilobars)

PRESSURE

DEPTH (kilOmQtQrS) 100

150

200

60

40

I30

(kilobars)

DEPTH CkiiOmQtQrS) 250

150

100

6

e

200

250

1600

1600 LHERIOLITE IRY SOLIDUS

1400

1200

/

/’

GA79vs MC14

/’ 40

PRESSURE

60

EO

(kilobars)

20

40

PRESSURE

60

60

(kIlobars)

FIG. 5. Geothezm plots for xenotiths from northern Lesotho in which six representative thermometers are used. The barometer in all cases is MC74. Reference curves as in Fig. 3. Symbols are explained in the text. (A) LD76. (B) WB73. (C) WE77. (0) EG79. (E) GA79. (F) OW79.

Mg exchange model of POWELL (1978). The L18 1 formulation was not intended to correct for effects of other components such as Fe, and it may be premature to apply it to natural rocks. NonetheIess, when diopside components in each pyroxene are calculated as atomic Ca/(Ca f Mg), and pressure is calculated with the MC74 barometer, a geotherm with minimal scatter

that placed diamond about 2 kbar within the graphite fiekI results. If diopside component is talcdated as Ca/(Ca + Mg + Fe), the diamond-bearing xenolith plots 5.5 kbar into the graphite field. A thermodynamic model such as that of WELLF (1977) that uses values of thermodynamic parameters for Ca/Mg exchange from LIND~LEY etal.(198 f ) would be very promising.

4. 4.

24

Finnerty and F. R. Bovd

MORI and GREEN (1978) ran experiments on complex compositions approximating natural garnet lherzolites, and six of the exchange equilibria measured by them exhibit temperature effects sufficiently strong to be useful as geothermometers. Pressure effects were not studied. All six of the thermometers (see Table I ) place diamond-bearing BD 2 125 no more than 3 kbar into the graphite field, with moderate to high scatter, The three. new Fe/Mg exchange reactions would appear to serve satisfactorily as thermometers if one could accept the increased uncertainty due to Fe’+/Fe’+, but they should be studied over a wider range of pressure and bulk composition. Several combinations ofthermometers with barometers other than MC74 yield adequate agreement with the petroiogic constraints (e.g., LD76 VS.WO74C, or WB73 vs. LG80), but for the most part one must beware of arbitrarily associating thermometers with barometers. Geothetm plots of WE77 vs. W074B and of LD76 vs. AK76 (Fig 6), for example, illustrate the range of variation in ~l~~t~e~s that can be ob-

DEPTH (kilometers) 100

150

200

250 I000

1600

DRY

SOLIDUS 1400

I200

1000

20

60

40

00

PRESSURE(ktlobars) DEPTH (kriometrrrs) 100

150

200

250 la00

1600

1600

1400

1200

1000

too0

600

600

20

40

PRESSURE

60

60

(kIlobars)

FIG. 6. Geothcrm plotr for xenoliths from northern Lesotho, in which two combinations of thermometers and barometers that ilustrate extreme shifts in the P-T locations of the paleogeotherms are used. Reference curves as in Fig. 3. Symbols are expIained in the text. (A) WE77 vs. W074B. (B) LD76 vs. AK76.

tamed. New thermometers and barometers should be tested against petrologic constraints before routine application. CONCLUSIONS In combination with the MC74 barometer, all thermometers that have been tested are in essential agreement with the petrologic constraints. T~e~ornete~ based on Fe’+/Mg exchange reactions show greater scatter about an expected curvilinear geotherm than do those based on Ca/Mg exchange reactions, probably because minerals were not analyzed and corrected for Fe3+. Corrections applied to thermometers based on the dio~ide~nstatite miscibility gap show greater scatter compared with uncorrected diopside-enstatite thermometers, because of propagation of analytical errors from more elemental analyses required for the corrections, or because some of the corrections may be inappropriate or incomplete. On an empirical basis, the uncorrected LD76 thermometers are preferred. with the pressure-independent version yieiding a fossil geotherm in better accord with geophysical models such as that of POLLACK and CHAPMAN (19771. Aluminum in orthopyroxene coexisting with garnet is clearly successful as a geobarometer for peridotites similar to the Lesotho rocks. Schemes that correct for su~titution of minor components in pyroxenes and garnets are inadequate because they decrease precision with no demonstrable increase in accuracy. Consequently, caution must be exercised when geobarometers based on this reaction are applied to garnet peridotites that differ in composition from the Mgrich Lesotho suite. The standard deviations and scatter in plots for P-T estimates from multiple analyses of minerals in single rocks are sufficiently small to counter criticism that paleogeotherms are the result of error propagation from analytical uncertainty or partial reequilibration. The range of aluminum contents in orthopyroxenes from the Lesotho suite is smaller than that seen in experimental calibrations because temperature and pressure effects on Al solubility along a typical geotherm partially compensate. The Lesotho suite xenoliths can definitely be ranked in order of in~re~ing depth or temperature along a geotherm. Regardless of the combination of thermometer and barometer, this ranking is always very similar, reflecting the high correlation between compositional pammeters for temperature-dependent reactions in the well-equilibrated Lesotho suite. The accuracy of the P-T estimates can be assessed within broad limits, but the petrofogic constraints are not strongly selective among thermometers. Precision of P-T estimates is best for those thermobarometers that require. the fewest compositional parameters for solution, and for those that are not strongly influenced by Fe3+. An in&e&on is readily apparent in the northern Lesotho ~~~othe~ for almost every combination of thermometer and barometer. If the kink is an artifact

Garnet peridotite thermobarometem

of the method of P-T estimation, the problem must lie in the barometer, because independent thermometers lead to inflected geotherms. The lower-temperature limb of the northern Lesotho paleogeotherm as determined with thermobarometers that satisfy petroiogic constraints is very close to the geotherm caIculated for 40 mW/m’ surface heat flow above a conductive continental iithosphere (POLLACK and CHAPMAN, 1977). Such a surface heat flow is typical of cratonic areas, and agreement with the geophysical model is supportive of the belief that thermobarometry of garnet Iherzolites is reasonably accurate as well as precise. The important question of the reality of fine structure in paleogeotherms must still be resolved, but the ability to constrain thermal and geophysical models for the earth’s interior by thermobarometric determination of thermal gradients in the future now seems assured.

25

W. J. (1979) Partitioningof REE hetweeagarnet peridotite minerals and coexisting melts during partial

HARRISON

melting. Carnegie Inst. Wash. Yearb. 7&562-568. HAR’~EB. and FREER R. (1982) Diliusion data and their

bearingon the interpmtation of mantle nodules and the evolution of the mantle lithosphere. Terra Cognifa f273275.

KENNEDYG. C. ( 1967) Melting and phaser&ions in a natuml peridotite to 40 kb. Amer. f. sci. 265, 519538. KAWASAKIT. ( 1979) ~e~~ynamic analyses on the FeMg exchange~uiii~urn betweenolivine and garnet: an

ITO K. and

application to the estimation of P-T relations of ultramafic rocks. J. Jpn. Assoc. Mfnerai. Petrol. Econ. Geoi. 74,395405. KENNEDY C. S. and KENNEDYG. C. (1976) The equilibrium boundary between graphite and diamond. J. Geophys. Res. 81.2467-2470. KUSHIROI., SYONOY. and AKIMOTOS. (1968) Melting of

a peridotite nodule at high piessums and high water piessums. J. Geophys. Res. 73,6023-6029. LANE D. L. and GANGULYJ. (1980) A&O3 solubility of orthopymxene in the system MgGAl&-Si02: a reevahnion, Acknowledgements-We thank Dm. R. F. Wendlandt, J. V. and mantle geotherm. J. Geophys. Res. 85.6963-6972. Smith, and H. S. Yoder, Jr., for helpful reviews. This work LINDSLEYD. and DIXON S. A. (i976) Coexisting diopside was initiated when the first author was a postdoctoral fellow and enstatite at 20 kbar and 900”-12iKl”C. Amer. J. Sci. at the Geophysical Laboratory, Carnegie institution of Wash276, 1285-1301. ington, and was completedat the Jet PropulsionLaboratory LINDSLEYD. Ii., &OVER 1. E. and DAVIDSONP. M. (1981) under NASA contract NAS 7-100. The thermodynamics of the MgtSi206-CaMgSix4join: a REFERENCES

AKELLAJ. (1976) Garnet pyroxene equilibria in the system CaSiO~-MgSiOJ-A&O, and in a natural mineral mixture. Amer. Mineral. 61, 589-598. BOYD F. R. (1973) A pyroxene geothenn. Geochim. Cosmochim. Acta 37,2533-2546. _

BOYDF. R. and FINGERL. W. (I 975) Homoaeneitv of minerals in mantle rocks from I&o&. Carnegie I&. Wash. Yearb. 74, 5 19-525. BOYD F. R. and NIXON P. H. (1975) Origins of ultramaiic

noduies from some kimberlites of northern Lesotho and the Monastery mine, South Africa. Phys. Chem. Earth 9, 43 I-454.

CARSWELLD. A. and GIBB F. G. F. ( 1980) Geothemtometry of garnet lherzolite nodules with special reference to those from the kimberlites of northern Lesotho. Contrib. Mineral. Petrol. 74, 403-4 16.

DAWSONJ. B. and SMITHJ. V. (1975) Occurrence ofdiamond in a mica-garnet lhemolite xenolith from kimberlite. Nature 254, 580-58 I. DAVISB. T. C. and BOYD F. R. (1966) The join Mg2Si206CaMgSi206 at 30 kilobars pressure and its application to pyroxenes from kimberlites. J. Geophys. Res. 71, 35673576. EGGLERD. H. and WEND~NDT R. F. f 1979) Experimental studies on the ~lation~ip

between kimberlite magmas

and partial melting of peridotite. In The Mu&e S&p/e IProc. 2d Int. Kimberiite Conf. Vol. 1). (eds. F. R. BOYD and H. 0. A. MEYER),pp. 336338. Ame&an Geophysical Union. ELLISD. J. and GREEN D. H. (1979) An experimental study of the effect of Ca upon garnet-clinopyroxene Fe-Mg exchange equilibria. Contrib. Mineral. Petrol. 71, 13-22. FINNERTVA. A. and B~YD F. R. (1978) Pressure.dependent solubility of calcium in forsterite coexisting with diooside and enstatite. Carnegie inst. Wash. Yeurbr 77, 7 13-j 17. FRASERD. G. and LAWLESSP. J. (1978) Paleoaeotherms: implications ofdisequilibrium in garnet lherzolite xenohths. Nattrrc 273, 220-223. GANGULYJ. ( 1979) Garnet and cIinopy~xene solid solutions, and ~othe~ometry based on Fe-Mg di~~but~on coefficient. Geochim. Cosmochim. Acta 43, 102 I - 1029.

review and an improved model. In Thermo&tamics of Minerab and Melts (eds. R. C. NEWTON,A. NAVROTSKY and B. J. WOOD), pp. 149-175. Springer-Verlag. MACGREGOR1. D. (1974) The system MgO-A120&i02: soiubility of A120, in enstatite for spinet and garnet peridot&e compositions. Amer. Mineral. 59, 1IO-1 19. MCCALLISTERR. H., FINGERL. W. and OHASHIY. (1975) The equilibrium cation distribution in Ca-rich clinopyroxenes. Carnegie Inst. Wash. Yearb. 74, 539-542. MERCIERJ.-C. C. (1976) Single-pyroxene geothermometry and geobarometry. Amer. Mineral. 61, 603-6 15. MORST. (1976) Pyroxene equilibria in ultmm~c rocks. Ph.D. thesis, Australian National Univ. MORI T. and GREEND. H. (I 975) Pymxenes in the system Mg&O&aMgSi,06 at high pressure. Earth Planet. Sci. Lett. 26, 277-286. MORIT. and GREEND. H. (1978) Laboratory duplication of phase equilibria observed in natural garnet Iherzolites. J. Geol. 86, 83-97. NEHRU C. E. and WYLLIEP. J. (1974) Electron microprobe measurement of pyroxenes coexisting with HsG-undersaturated liquid on the join CaMgSiz06-MgsSi,0s at 30 kilobars, with applications to geothermometry. Contrib. Mineral. Petrol. 48, 22 I-228.

NIXON P. H. and BOYD F. R. (1973) Petrogenesis of the granularand sheared uhrabasic nodule suite in kimberlites. In Lesotho Kim~~ites (ed. P. H. NIXON); pp. 48-56. Lesotho National Development Corporation.

O’NEILLH. ST. C. ( I98 1) The transition between spine1 iherzolite and garnet Ihenolite, and its use as a geobarometer. Contrib. Mineral. Petrol. 77, 185-194.

O’NEILLH. ST. C. and WOOD B. J. (I 979) An experimental study of Fe-Mg partitioning between garnet and olivine and its calibration as a geothermometer. Contrib. Mineral. Petrol. 70, 59-70.

POKHILENKON. P., SOBLEVN. V. and LARENT’EVYu. G, ( 1977) Xenoliths of diamondiferous ultramafic rocks from Yakutian kimberlites. Extended Abstracts. Second International Kimberlite Conference, Santa Fe, New Mexico, October 1977. POLLACK H. N. and CHAPMAN D. S. (1977) On the regional variation of heat Bow, w and li&spheric thickness. T~tonophysi~s 3S, 279-296, POWELLR. f 1978) The thermodynamics of pyroxene ge+

26

therms.

4 A. Fmnerty and F. R. Boyd Philos.

Trans.

R. Sot. London,

Ser .4, 288, 457-

469.

RAHEIMA. and GREEN D. H. (1974) Experimental determination of the temperature and pressure dependence of the Fe-Mg partition coefficient for coexisting garnet and clinopyroxene. Conwib. Mineral. Petrol. 48, 179-203. SAXENAS. K. (1979) Gamet-clinopyroxene geothermometer. Contrib.

Mineral. Pewol. 70, 229-235.

WARNER R. D. and LUTH W. C. (1974) The diopside-orthoenstatite two-phase region in the system CaMg&O,Mg&06. Amer. Mineral. 59, 98- 109. WELLSP. R. A. (1977) Pyroxene thermometry in simple and complex systems. Contrib. Mineral. Petrol. 62, 129- 139. WOODB. J. ( 1974) The solubility of alumina in orthopyroxene coexisting with garnet. Confrib. Mineral. Petrol. 46, I - 15. WOODB. J. (1977) The influence of Cr203 on the relationships between spinel- and garnet-peridotites. Extended Abstracts. Second lnrernational Kimberlite Conference. Santa Fe. New Mexico, October 1977. WOODB. J. and BANNOS. (1973) Garnet-orthopyroxene and orthopyroxene-clinopyroxene relationships in simple and complex systems. Conlrib. Mineral. Pevol. 42, 109-124.

APPENDIX Several of the thermometers and barometers evaluated in this paper were not presented in analytic form in the original publications, and the published data were fit to equations for inclusion in program TEMPEST. In other cases, errors or obscurities in presentation caused difficulties in implementing the thermobarometers or required special computation techniques. In order to avoid ambiguity, specific equations and techniques are discussed below. LD76 and LD?6(20

kbar)

The data for the diopside limb of the diopside-enstatite miscibility gap, discussed in LINDSLEYand DIXON (1976), were fit by nonlinear least-squares techniques to an equation of the form _Uz =

[T/(a

+ bP)]<.

(Al)

where Xg is the mole fraction of Mg$i20, in the diopside ( = I - [ZCa/(Ca + Mg)] ), Tis temperature in K, P is pressure in kilobats. and a, b, and c are the constants that were evaluated. There is no thermodynamic basis for this equation beyond the fact that it meets the limiting conditions for describing a limb of a miscibilty gap; at zero temperature there is no solubility of enstatite component in the clinopyroxene, and with increasing temperature, solubility can only increase. With this equation, temperature is estimated by a technique equivalent to the graphical technique of BCIYD(1973). In the fitting procedure, only those data that constitute a reversal bracket were used. These include data points from NEHRUand WYLLIE(1974), WARNERand LUTH (1974), and MORI and GREEN (l975), as discussed by LINDSEY and WXON. The latter authors emphasize that “there is no a priori reason to choose a ‘best’ value at a particular point within the limits imposed by the brackets.” Yet such a value must be selected in o&r to fit the data, so we used the value midway between the extremes of each reversal bracket. Each observation was then weighted according to the inverse of the square of the width of the reversal bracket. Parameter estimatesare a = 1941(18), b = 5.04(0.61), and c = 5.37(0.16), wheru the quantities in parentheses are the 1~ uncertainties conventionally derived from the residuals matrix. LINLSLEYand DIXON evaluated their data and those of previous workers for a pressure effect, attempting to account also for the uncertainties in the data. They concluded that the CaSiO, content of diopside increases with pressure by 0.10 to 0.12 mole %&bar at 12oO”C, and by 0.17 to 0.35 mole %/kbar at 1400°C. From Eqn. (Al) the pressure effect

IS 0.1 I4 mole Yo/kbar at 1200°C and 0.225 mole %/kbar ar 14OO”C, in close agreement. The relatively small uncertainty in the coefficient of pressure of 12.1% from the nonlinear le;ist-squares fit to the LINDSLEYand DIXON data suggests that such a pressure effect is real. As this is still somewhat controversial, however, the LINDSLEYand DIXONthermometer has also been evaluated with no pressure effect [LD76(20 kbar)] with Eqn. (A I) and an assumed pressure of 20 kbar.

Whereas WOODand BANNO(1973) assumed equipartmon of Fe and Mg between M sites in pyroxenes for their semiempirical thermometer, MORI and GREEN (1978) made site assignments according to an experimentally determined temperature-dependent intersite partition. In program TEMPEST, the MORI and GREEN equation is solved with the initial assumption that

The initial temperature estimate is then used to calculate the intersite partition in the pyroxenes; then a new temperature estimate is made. This procedure is iterated until the temperature estimate is constant to within 1“C. ow79 Typographical errors in the thermometric equation are present in O’NEILLand WOOD(1979). The corrected equation (O’NEILL, 1981) is used in program TEMPEST. Because it is quadratic in P and r, an iterative technique is used for its solution in TEMPEST. Temperature is first estimated with the assumption that P = 30 kbar: then pressure is estimated with the chosen barometer. Temperature and pressure are then reestimated, and the process is repeated until T converges to within 1“C and P to within 0. I kbar. GA79

GANGULY(1979) recommended that his Eqn. (lOa) be used at T r 1333“C, and Eqn. (lob) be used at T < 1333°C. TEMPEST was programmed to use both equations. then to select the P-T estimate that was in accord with GANCULY’S recommendation for print-out. MC74 Tbe temperature and pressure dependence of an equilibrium constant may be expressed by an equation of the form a + bP

In & = 7

+ c,

where a, b, and c are constants related to iyj”, A V’”and Us0 of the reaction, respectively. Inasmuch as the concentration of aluminum in pyrope remains sensibly constant over a considerable P-T range in which aluminum in enstatite varies widely, it was deemed appropriate to fit the data of MACGREGOR(1974) to Eqn. (A3), with the weight fraction of A1203 in enstatite substituted for &. An unweighted linear least-squares solution gives a = -3736(307), b = -97.1(4.5), and c = 1.46(0.2 I), where pressure is in kilobars, temperature in K, and the quantities in parentheses a la uncertainties derived conventionally from the residuals matrix. The MACGREGOR data are reproduced within experimental uncertainties by this equation. AK76

The experimental data of AKELLA(I 976) for aluminum in enstatite coexisting with pyrope in a Ca-bearing synthetic

27

Garnet peridotite thermobarometers system were fitto thesameequation asthe MACGREGOR (i974) data, yielding the following parameter estimates: a = -2042(215). b = -73.8(3.4). and c = -0.22(0.12). The observations were equally weighted for the linear least-squares solution, and as for MC74, the experimental data are reproduced within satisfactory limits by the equation.

is the same as that at 1 atm and 298 K. Because difficulties were encountered in substituting constants into the equation, the form utilized in TEMPEST is listed below: P = -236.87 - [ 1.I7067 + 0.0085628 In (4X_&,)]T + 0.10675TIn T+ 1.935. 10-57’2 + 1.250 X IO’T-’ + 20.1373T”2.

WO74A, B, C Equation (12) of Woo0 (1974) is the basis for ah three versions of the W074 barometer we have evaluated. Care is necessary when this equation is used because the gas constant, R, is used in two different systems of units. In order to formulate Wood’s equation for solution on the computer, it was necessary to derive an analytical expression for the dependence of AV, on the fraction of Al in the Ml site of enstatite. The data used by WOOD and BANNO(1973) were fit graphically to a linear equation, with the result v, = -7.85 - 4.43XE’,

(A4)

where V, is in cm3/mole and Xy’ is the fraction of Ml sites occupied by Al atoms. The composite equation used for barometry in TEMPEST is P = ({0.1623 - 0.0831448 In [X$‘(l - Xz’)/(l

- y,)‘]}/

(7.85 + 4.43Xz’))T - 293.4/(7.85 + 4.43X:‘) - 10.45Xp(e 1 - 2X:‘).

(A5)

All quantities are as defined by WOOD, and the WG74A and W074B versions tested in this paper correspond to site assignments of assumptions (a) and (b), respectively, in WOOD (1974, p. 7). In assumption (b) of WOOD(1974), no allowance was made for the case where atomic Na exceeds Cr in orthopyroxene. Because some orthopyroxenes in the Lesotho suite~contain Na in excess of Cr. assumntion (b) is modified in TEMPEST so that the excess Na is as&red to NaAlSi,O,, and the amount of Al thus “consumed” is subtracted from the total available for a Tschermak-type substitution. The WO74C version of the barometer was suggested by D. H. E~ZLER (Penn. State Univ., private commun., 1979). The activity-composition relation for Ca-Cr interaction in garnet (WOOD, 1977) was used in n&riving Eq. ( 12)Of WOOD (1974) with the result that Eq. (A5) is modified by adding the term 2092X&X&/(7.85 + 4.43Xr). Superscripts c and o refer to the cubic and octahedral sites in garnet, respectively. LG80 Equation (9a) of LANEand GANGULY(I 980) is the expression they have calculated under a simplifying assumption that A Ve for the reaction at the tempemturc and pmsure of interest

(A6)

This equation was difficult to implement directly in TEMPEST, so a technique of successive approximations was employed. The sum of the last four terms in Eq. (A6) is nearly linear in T and was fit by linear least-squares to the equation Z=aT+c,

(A7

where a and c are constants. The parameter estimates are a = 1.1974(0.00 14) and b = 208.02( 1.92),where the quantities in parentheses are IS uncertainties derived conventionally from the residuals matrix. The linearized equation approximates the full equation (A2) to within 1.7 kbar over the range 900”-1400°C. By comparison of the linearized equation with the full equation, it is possible to calculate a residuals equation: R = -208.02 - 1.19747+

0.106757’ln T+

X IO-?f’ + 1.250 X IO?’

1.935

+ 20.1373T”‘.

(AS)

This residuals equation is used in TEMPEST to refine an initial pressure estimate made with the linearized equation. The temperature estimate is then refined, and the process is repeated until convergence to within 1°C and 0.1 kbar is attained. Note added in proof: PERKINSer al. (198 I) present forty-six reversed determinations of the AIrOr content of enstatite in equilibrium with garnet. Their very carefully obtained results are comparable to the earlier data of MACGREGOR(1974).We have not fit the data Of&RKJNS elal.to an equation for use in TEMPEST, but expect pressure estimates very similar to those obtained using the data of MACGREGOR. LINDSLEYand ANDERREN( 1983) have experimentally determined the effects of iron on exchange of Ca and Mg between ortho- and clinopyroxene, and introduced a graphical method to estimate temperatures in two-pyroxene assemblages. Ag plication of these data in TEMPEST awaits formulation of thermodynamic models. References PERKINS D. III, HOLLANDT. J. B. and NEWTONR. C. (1981)

The Al20, contents of enstatite in equilibrium with garnet in the system MgG-A1203-Si02 at 15-40 kbar and 9001,600 C. Contrib. Mineral. Petrol. 78, 99-109. LINDSLEYD. H. and ANDERSEND. J. (1983) A two-pyroxene thermometer. Proc. Lunar Planet. 13th Sci. Co& Par/ 2. J. Geophys. Res. 88, A887-A906.