Subsolidus orthopyroxene-clinopyroxene systematics ...

Subsolidus orthopyroxene-clinopyroxene systematies in the system C a O - M g O - S i O 2 to 60 kb: a re-evaluation of the regular solution model Klaus G. Nickel and Gerhard Brey Max-Planck-lnstitut ffir Chemie, Mainz, Federal Republic of Germany

Abstract. On the basis of an increased set of experimental data, covering the miscibility gap between orthopyroxene and clinopyroxene from 2 to 60 kb with a temperature range of 850-1,500 ~ C, we present a new version of a regular solution model. The model with two independent regular solutions for opx and cpx is capable of reproducing experimental data in the system C a O - M g O - S i O 2 over a large range of temperatures and pressures. It is qualitatively in agreement with observed stability regions for an Fe-free low-Ca pyroxene, termed pigeonite. The model is constrained by and thus consistent with calorimetric measurements on pyroxenes. The simple form of equations provides a good starting point for the development of more reliable thermometers based on the miscibility gap.

Introduction

The miscibility gap between ortho- and clinopyroxene is the basis of widely used geothermometers for deep-seated rocks and its correct determination is thus of great importance for the estimation of P - T distributions in the earth's crust and mantle. Even though studies in simple systems cannot be extrapolated directly to natural rocks, the understanding of the very principle, the 'ideal' case of pure Ca, Mg-pyroxenes provides the foundation for all such thermometers, regardless whether they are strictly thermodynamic, semi- or purely empirical. Numerous studies in the simple system C a O - M g O SiO 2 (CMS) have been carried out since Davis and Boyd (1966) showed the temperature dependence of the miscibility gap. A number of studies and the models based upon those have been reviewed by Grover (1982), Lindsley (1982) and Lindsley et al. (1981). These authors pointed out that it is necessary to define equilibria for both reactions MgzSi20 6 ( O p x ) = M g 2 S i 2 0 6 (Cpx) CaMgSizO 6 (Opx) = CaMgSi20 6 (Cpx)

(A) (B)

Offprint requests to: G. Brey

Abbrevations used in the text cpx =clinopyroxene; di=diopside, CaMgSi206; en=enstatite, Mg2Si206 ; pig = pigeonite; opx = orthopyroxene; zIH (i) = molar enthalpy difference (of reaction i); AS (i)= molar entropy difference of reaction (i); A V (i)=molar volume difference of reaction (i); X[i]j= mole fraction of i in phase j

in order to construct phase diagrams and to understand the existence of an Fe-free low-Ca pyroxene termed pigeonite at low pressures. The effect of pressure on the miscibility gap in the CMS system has been noted by Lindsley and Dixon (1976) and Mori and Green (1975, 1976). However, the quantification of this pressure-effect suffered from the limited range of pressures under which bracketed data were available. Data at 1 atm (Boyd and Schairer 1964; Longhi and Boudreau 1980; Yang and Foster 1972) are mostly unreversed and suffer also from difficulties in correctly determining the existence of various polymorphs of low-Ca pyroxenes (Jenner and Green 1983; Longhi and Boudreau 1980). Very few experiments present data at low pressures (1-5 kb) and the pressure effect was therefore largely constrained by the bulk of bracketed experiments in the range 10-30 kb. Now more data are available covering the miscibility gap to higher pressures (Brey and Huth 1984), which allows a re-evaluation of models pertinent to the effect of both temperature and pressure on the miscibility gap. Choice of data

Like Holland et al. (1979) and Lindsley et al. (1981) we consider bracketed results as better constrained than unreversed experiments. Our data points are therefore the midpoints of brackets derived from the studies of Brey and Huth (1984), Mori and Green (1975, 1976), Lindsley and Dixon (1976), Nehru and Wyllie (1974), Perkins and Newton (1980) and Warner and Luth (1974) (Table 1). From this data set we excluded two brackets of Mori and Green (1975, 1976) at 900 ~ C, 10 kb and t,700 ~ C, 30 kb because of their inconsistency with the other data. One bracket of Brey and Huth (1984) (1,500 ~ C, 40 kb) also seemed to be inconsistent with the rest of their data. We have therefore repeated this experiment (Table 1, Fig. 1). The'result confirms the data points for orthopyroxene as given by Brey and Huth (1984), but shows some difference in clinopyroxene, indicating a more calcic composition. The two experiments are however in marginal agreement. We furthermore performed an experiment at 900 ~ C, 50 kb to check the behaviour of the miscibility gap at low-T/high P conditions (Table 1, Fig. 1). A further experiment was carried out at 1,500 ~ C and 30 kb. The composition of the clinopyroxene is however not well constrained and gives a very wide reversal bracket. This is attributed to the particu!arly difficult experimental condition: the diopside limb becomes very flat at around 1,500~ C on a 30 kb isobar and thus the cpx

36

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Fig. 1. a Composition of orthopyroxenes and clinopyroxenes in an experiment at 900~ C, 50 kb (water added). Triangles pointing outward are for analyses of unmixing (from glassy starting material), triangles pointing inward for mixing (crystalline pure en+di starting material) experiment. Connection lines represent core-rim measurements (open symbols: rim). Region of overlap (bracket) indicated by the solid line on top. h Plot of ('dry') experiments at 1,500~ C, 30 and 40 kb analogous to I a. Fine grained character of run products precluded core-rim determinations

Table 1. Run conditions and composition of the reversal brackets used in the modelling procedure P(kb) T(~ 2 5 5 10 10 I5 15 15 15 15 15 20 20 20 20 20 20 20 20 20 25 25 25 30 30 30 30 30 30 30 30 40 40 40 40 50 50 50 50 50 50 60

1,200 1,200 1,200 1,100 1,200 850 1,000 1,100 1,200 1,300 1,400 900 900 1,000 1,000 1,100 1,200 1,300 1,400 1,400 900 1,000 1,100 900 900 1,000 1,100 1,200 1,400 1,500 1,500 1,200 1,300 1,500 1;500 900 1,100 1,200 1,300 1,400 1,500 t ,300

t(h)

3

2 9 3 2.5 2.5 335 22.5 9 4.8 3 2.5 2.5

X[di]cpx

X[di]opx

Source

0.792-0.805 0.803-0.843 0.770-0.790 0.877-0.880 0.823-0.825 0.930-0.940 0.900--0.910 0.850-0.880 0.840-0.850 0.740--0.770 0.590-0.650 0.930-0.940 0,930-0.946 0.900-0.920 0.9t0-0.9t4 0.860-0.900 0.820-0.840 0.750-0.800 0.610-0.680 0.608-0.646 0.938-0.946 0.910-0.916 0.870-0.884 0.923-0.932 0.940 0.904-0.916 0.866-0.892 0.833-0.884 0.665-0.720 0,574-0.584 0.456-0.654 0.842-0,872 0.780-0.794 0.478-0.520 0.524-0.574 0,914-0.948 0,872-0.894 0.842-0.880 0,784-0.816 0.724-0.752 0.586-0.608 0.788-0.828

0.077-0.086 0.056-0.082 0.070-0.080 0.045-0.050 0.061-0.071 0.010 0.030 0.040-0.050 0.060 0.080-0.090 0.110 0.012--0.025 0.012-0.030 0.030 0.030 0.035-0.050 0.050-0.060 0.060-0.080 0.080-0.110 0.102-0.103 0.016-0.020 0.024-0.030 0.022-0.028 0.019-0.029 0,010-0.012 0.0t8-0.032 0.026-0.028 0.042-0.051 0.080-0.082 0.090-0.I03 0.108-0.110 0.034-0.038 0.052 0.100 0.092-0.098 0.006-0.008 0.023-0.032 0.032 0.046-0.048 0.063 0.086 0.036-0.038

WL WL - MG LD LD-WL M G - WL LD LD LD LD LD LD LD PN LD PN LD LD LD LD BH PN PN PN MG PN PN PN MG LD-NW MG NB BH BH BH NB NB BH BH BH BH BH BH

Sources: BH: Brey and Huth (1984); LD: Lindsley and Dixon 1976; MG: Mori and Green 1975, 1976; NB: Nickel and Brey, this work; NW: Nehru and Wyllie 1974; PN: Perkins and Newton 1980; WL: Warner and Luth I974. Run times are quoted only for those experiments performed at this laboratory

composition is very sensitive to slight variations in temperature. This problem is also demonstrated by the results o f Mori and Green (1975) who report two different results for two runs at 30 kb and 1,500 ~ C. All experiments were carried out as described by Brey and H u t h (1984). Pressures are estimated to be accurate to 4-1 kb and temperatures to + 7 ~ C. Lindsley et al. (1981) changed the values o f the data within the brackets for their fitting procedure to get a better statistical solution (low sum of least squares) for the numerous parameters fitted. They argued that this method is valid, because any point within the bracket is equally likely to be the equilibrium value. While this is certainly true for any single experiment, the " b e s t " points should be statistically distributed around the midpoints of the brackets for a larger set of experiments, if reaction rates of mixing and unmixing are not greatly different. Published experimental investigations of reaction rates with differing starting material are fairly inconclusive (cp. Howells and O ' H a r a 1978) and certainly extensive time-studies are needed to resolve the problem. However, if one accepts the idea o f greatly different reaction rates within bracketing experiments, we in fact loose all bracketing constraint, because it is then entirely possible that for a given set one halfbracket represents a strong overshoot over equilibrium values, while the other half-bracket may not have reached those values. The correct equilibrium value would then lie outside the " b r a c k e t " . Being aware o f this possibility (and the discrepancy between some experimental brackets, e.g. the Warner and Luth (1974) - Mori and Green (1975) and the Lindsley and Dixon (1976) brackets at 1,200 ~ C, 5 kb points in this direction), we prefer to base our fitting procedure on the assumption of similar reaction rates and thus take the mid-points o f experimental brackets as the best approach:

The pressure dependency problem The reason for the pressure dependence of the miscibility gap in the CMS-system (Lindsley and Dixon 1976; Mori and Green 1975, 1976) is not obvious. Newton et al. (1979) showed in a calorimetric study the volume decrease o f diopside with increasing en-component. The most magnesian diopside contained some 80% o f en and a quadratic regression yielded nearly identical molar volumes of ortho-enstarite and the fictive en-endmember with diopside structure. In fact the A V (Ve,(Cpx)- Ve,(Opx)) came out to be slightly negative ( - 0 . 1 cm3), a value certainly too small and with

37

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Fig. 2, Molar volume of Ca,Mg-diopside with differing en-content.

Data points from Newton et al. (1979). Scale on the left side indicates A V for reaction (A) in cm 3. The molar volume of the pure en-endmember is likely to be in the range of the shaded area (bottom line: quadratic fit of Newton et al. (1979), top line: fitted by eye in analogy to volume behaviour of other binary silicate solid solutions (Newton and Wood 1980). Lines within the shaded area indicate the predicted path of volume behaviour from the model of LindsIey et al. (1981) and this work a wrong sign in order to explain the observed dependency. However, it is known that binary silicate solutions do show S-shaped molar volume curves with negative deviation from linearity near the small-volume end-member, which can not be described by quadratic or cubic equations (Newton and Wood 1980). Figure 2 shows the likely range of molar volumes for the "en in diopside-endmember'" and hence the likely range of A V for reaction (A) based on a volume behaviour similar to those observed in binary silicate solutions by Newton and Wood (1980). The range indicated is from - 0 . 1 to about -t-0.7 cm ~. Because of this uncertainty a A V value for reaction (A) can not be taken from measurements, but has to be fitted. The widening of the miscibility gap is not a linear function of pressure. Therefore the pressure dependence is not only due to the difference in molar volumes of the endmembers. A second pressure dependency can be expressed by applying a Margules parameter model, because the interaction parameter W principally contains a P-term: W= W~- r*Ws+P*W V

(I)

The pigeonite problem and the question of the model The existence of Fe-free pigeonite at low (1 arm) to moderate (ca. 15 kb) pressures has been documented in experimental studies (Longhi and Boudreau 1980; Schweitzer 1982), while it most probably does not exist at higher pressures despite Kushiro's (1969) experiments (Howells and O ' H a r a 1975; Mort and Green 1975, 1976). It is very likely that Fe-free pigeonite has at high temperatures C2/c symmetry (Prewitt et al. 1971), the diopside structure. Lindsley et al. (1981) pointed out that any model for pyroxenes in the CMS-system has to be able to explain the existence of pigeonite. However, this constraint is insufficient to distinguish

between models assuming independent c p x - o p x regular solutions (Saxena and Nehru 1975; Powell 1978; Holland et al. 1979), assymmetric solutions (Lindsley et al. 1981), convergent disordering [Navrotsky and Loucks (1977)] or non-convergent site-disorder models (Davidson et al. 1982), while it excludes models treating cpx and opx as part of one solution. More constraints are therefore needed to evaluate the differing models. Lindsley et al. (1981) and Grover (1982) argued for a regular solution model for opx and an assymmetric solution model for cpx, because the pigeonite-diopside solvus appears to be assymmetric. As mentioned before, one atmosphere experiments rest upon exact recognition of a number of polymorphs of tow-Ca pyroxenes [Longhi and Boudreau (1980)] and are unreversed. While these experiments do indicate an assymmetric pigeonite-diopside behaviour (relative to 50 mol%), the results of Schweitzer (t982) at 15 kb are consistent with a symmetric solution model (within bracket). For a clarification more reversed data are needed for pigeonite-diopside equilibria at pressures < 15 kb. The more sophisticated models of Navrotsky and Loucks (1977) and Davidson et at. (1982) are difficult to evaluate, because a verification requires high-temperature X-ray studies. The presently available data (Newton et al. 1979) do not confirm the expected disorder of the Navrotsky and Loucks (1977) model, where Ca should strongly partition into the M1 site at high temperatures. Davidson et at.'s (t982) model requires only a very small degree of Ca partitioning into the M1 site (too small to be detected by X-ray methods) and is supported by their experimental data at very high temperatures. It remains however unclear, if the excess Ca in those experiments was present as intrastructural layers of wollastonite or indeed represents incorporation of Ca in the MI site of diopsidic clinopyroxene (Appendix I of Davidson et al. 1982). These authors argue for the latter because of the coexistence of pure diopside and wollastonite. Data for such pairs were given by Kushiro (1964) and Schairer and Bowen (1942). In view of the limited analytical techniques available for these studies at their time one may argue that the diopsides of the wollastonitediopside pairs were in fact impure to a degree undetectable by X-ray methods (just like the supposed Ca-excess would have to be). In this case pure diopside may in fact not coexist with wollastonite and pure diopside may still be considered a true end-member. A method to resolve this problem would be to study the wotlastonite-diopside pairs extensively with microprobe methods and to check the ' C a excess' experiments by means of high-resolution transmission electron microscopy. At this stage we thus cannot positively verify the one or the other model. Our approach is to use the simplest model that describes the known hard-core data. In order to evaluate the simple models we have tested the published models of Holland et al. 1979; Lindsley et al. 1981 and, as a comparison, an empirical model without any pressuredependent term (Wells 1977) for reproduction of data to 60 kb, taking midpoint-of-bracket values (Fig. 3). We define the midpoints of brackets for cpx as (X[di]max(unmixing)+X[di]mln(mixing))/2 and vice versa for opx, which gives for some published experiments values not identical to those given in Table 1 of Holland et al. (1979). This test is not for the purpose of looking at the absolute accuracy of reproduction but to demonstrate systematic deviations of estimates from experimental conditions. We estimate the

38

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Fig. 3. Plot of A T= T(estimated)- T(experiment) vs. T(experiment) for various pressures, using midpoint-of-bracket values from Brey and Huth (1984), Lindsley and Dixon (1976), Marl and Green (1975, 1976), Nehru and Wyllie (1974), Perkins and Newton (1980), Warner and Luth (1974) and this study. T were estimated by the methods of (a) Wells (1977), (b) Holland et al. (1979), (c, d) Lindsley et al. (1981) reactions (A) and (B) respectively and (e, t) this work for reactions (A) and (B) respectively

combined error of the experimental procedure (calibration, accuracy and precision of P, T control) and the analytical uncertainty to be in the order of +_20-30 ~ C; therefore it is not envisaged to have a better absolute reproduction of temperatures. Because the Wells (1977) model does not take into account any observed non-ideality nor a pressure-dependency it is not expected to work very well. Nonetheless the averaging method of calibration of this thermometer gives quite good results over a range of temperatures and pressures (1,000-1,300 ~ C, 5-30 kb, Fig. 3 a). Thus, despite its incapability to explain a number of known systematics and its thermodynamic invalidity, this thermometer may still be

seen as a useful tool for the empirical estimation of temperatures within certain limits. Figure 3a shows those limitations in the CMS-system, where temperatures are strongly overestimated at low and high temperatures, combined with a tendency to give lower estimates at higher pressures. Figure 3b shows the same plot using the parameters and equations of Holland et al. (1979). These authors have used a restricted data set to derive their parameters and their model reproduces this set very well. Using in addition the now available high-pressure (Brey and Huth 1984) and low-temperature data O00-1,100 ~ C, 20-30 kb of Perkins and Newton 1980) as well as some more of previously published data (900, 1,500 and 1,600 ~ C at 30 kb of Moil and

39 Green 1975, 1976;) and thus doubling the data base shows two things: a) temperatures are systematically overestimated with increasing pressure and b) the negative slope of the lines connecting experiments at one pressure indicates a systematic error with temperature. Furthermore the fit, when expanded to include both reaction (A) and (B) fails to predict stable pigeonite-diopside assemblages at any P, T condition (Lindsley and Davidson 1980, p 303). Figures 3c and d show the estimates calculated by the method of Lindsley et al. (1981) for the same data set (note that the equations used have been taken from Grover (1982), because of a number of typing errors in the original). Lindstey et al.'s (1981) (assymmetric cpx - symmetric opx) and Holland's (1979) (symmetric cpx - symmetric opx) models are approximately equal in reproducing experimental data. Lindsley et al. (1981) cautioned against the use of their equations for conditions > 4 0 kb and the figures confirm that the model is inadequate for high pressures, yielding strong over- and underestimations with increasing pressure for reaction A and B respectively. In addition to this drawback the model of Lindsley et al. (1981) is not very satisfactory with respect to the fitted value of A H of reaction (A), which is only in very poor, marginal agreement with the calorimetric determinations of Newton et al. (1979). We have tried to modify the assymmetric-symmetric model, using the increased data set, but were unable to obtain a more satisfactory agreement with calorimetric values. We thus opted for a modification of the regular solution model based on Newton et al.'s (1979) data. Despite its formal simplicity it was found to be capable of reproducing data well and explain the existence of Fe-free pigeonite. Figures 3e and f show the corresponding plots using equations (4) and (5) of the modified regular solution model outlined below.

Re-evaluation of the regular solution model The regular solution model for coexisting ortho- and clinopyroxenes in the system C a O - M g O - S i O 2 (CMS) assuming two independent regular solutions for opx and cpx has been outlined and discussed by Holland et al. (1979, 1980), Lindsley et al. (1981), Lindsley and Davidson (1980), Powell (1978) and Saxena and Nehru (1975). The most recent regular solution model presented by Holland et al. (1979) was intended as an empirical tool for the estimation of temperatures, based on the fact that this type of model describes a number of solid solutions over a range of compositions. As pointed out by Lindsley and Davidson (1980), this model has potentially much more thermodynamic validity then Holland et al. (1979) envisaged. We present here an expansion of the regular solution model to pressures up to 60 kb and demonstrate its capability to reconstruct the o p x - c p x phase diagram and the qualitative agreement with the current knowledge about pigeonite-stability. Within the concept of the regular solution model the conditions for equilibrium of reactions (A) and (B) are - - A H + T A S - P A V = R T In KD(A) + W~px (X[di]cpx) 2 - Wop,(Xtdi]opx) 2 - - A H + T A S - P A V = R T In KD(B) + 14~p~ (X[en]cpx) 2 - Wop~(X[en]opx) =

(2) (3)

respectively (KD(A) = (X[en]cpx/X[en]opx); K D(B) = (X[di]cpx/XIdi]opx])). For the fitting procedure we used the following assumptions and methods:

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Fig. 4. Effect of pressure on the miscibility gap between opx and cpx in the CMS-system and on pigeonite stability. Shown are isotherms of mole fraction di in opx, cpx vs. pressure as calculated from the regular solution model of this study. Numbers inside the pigeonite+diopside field are for closing temperatures at 50 mol% and for begin of stability relative to cpx-opx assemblages at 10 kb, Pressure dependence of the miscibility gap becomes stronger with decreasing pressure and increasing temperature (a) The values of the fitted parameters for reaction (A) are fairly insensitive to the choice of Wop, within the range of 20-50kJ [Saxena and Nehru (1975)], Holland etal. (1979)), and so we adopted their value Wop~= 34 kJ. (b) The AH of reaction (A) was set to A H ( A ) = 7 kJ in order to satisfy.' the enthalpy of solution measurements of Newton et al. (I 979). (c) Reaction (A) is better constrained then reaction (B) because KD(B) is very sensitive to small changes in X[di]opx and this quantity has a high relative error in experiments. Therefore Wcpx was fitted taking only equation (2) into account. Subsequently we fitted AH, AS and d V of reaction (B), using the previously defined W's. This method has the advantage that for the first fit the number of free parameters is reduced to 5 (AS, A V, W n, W s, Wv) based on 42 data, hereby ensuring a reasonable statistical significance (standard errors of estimate for AS, Wn, Ws