diffusion gradients in an eclogite xenolith from the ... · from the roberts victor kimberlite...

Contrib Mineral Petrol (1990) 105:637-649 C o n t r i b u t i o n s t o Mineralogy and Petrology �9 Springer-Verlag 1990

Diffusion gradients in an eclogite xenolith from the Roberts Victor kimberlite pipe: (2) kinetics and implications for petrogenesis Violaine Sautter 1 and Ben Harte 2

1 Laboratoire de G~ophysique et G6odynamique Interne, Universit6 Paris-Sud, Batiment 510, F-91405 Orsay Cedex, France 2 Grant Institute of Geology, University of Edinburgh, West Mains Road, Edinburgh EH9 3JW, Scotland, UK

Received April 2, 1989 / Accepted June 14, 1990

Abstract. In a bimineralic eclogite xenolith (sample JJG41) from the Roberts Victor kimberlite, compositional gradients in clinopyroxene are related to garnet exsolution. Two principal reactions involving clinopyroxene and garnet occur: (i)The net-transfer A12Si-IMg -1 which is responsible for garnet growth according to the equation 2 Di + AlzSi- 1Mg- 1 = Grossular + MgCa- 1 (reaction 1). This has created substantial compositional gradients in A1, Si and Mg within clinopyroxene. (ii) The exchange of F e - Mg between garnet and clinopyroxene (reaction 2). During the stage of garnet growth (reaction 1) the larnellae crystallized sequentially as a result of a temperature decrease from around 1400 to 1200 ~ C. This exsolution growth-stage was under the control of A1 diffusion in clinopyroxene and at around 1200~ C further growth of garnet lamellae became impeded by the sluggishness of A1 diffusion in the clinopyroxene host. However, reaction 2 continued during further cooling down to about 1000 ~ C; this temperature being inferred from the constant F e - M g partitioning at clinopyroxene-garnet interfaces for the whole set of lamellae. The initial clinopyroxene in JJG41 was probably formed by crystallization from a melt in Archaean time. The cessation of F e - M g exchange between garnet and clinopyroxene at about 1000 ~ C may well predate the eruption of the eclogite in kimberlite at around 100 Ma. Kinetic models of reaction are examined for both reactions. Modelling of reaction 1, involving both diffusion and interface migration, allows several means of estimating the diffusion coefficient of A1 in clinopyroxene; the estimates are in the range 10-16-10 -20 cmZ/s at 1200 ~ C. These estimates bracket the experimentally determined data for A1 diffusion in clinopyroxene, and from these experimental data a preferred cooling rate of about 300 ~ C/Ma is obtained for the period of growth of garnet exsolution lamellae. A 'geospeedometry' approach (Lasaga 1983) suitable for a pure-exchange process (reaction 2) is used to estimate the cooling rate in the later stages of the thermal history (after garnet growth); values 4-40 ~ C/Ma

Offprint requests to: B. Harte

are consistent with the shape of the Fe-diffusion gradients in the clinopyroxene. The extensive thermal history recorded by JJG41, including probable melt involve- ment at ca. 1400 ~ C, demonstrates the complex evolution of rocks within the mantle. Whilst the notion of formation of mantle eclogites from subducted oceanic crust has become fashionable, it is clear that tracing eclogite geochemical and P - T characteristics backwards from their nature at the time of xenolith eruption, through high-temperature mantle events to the characteristics of the original subducted oceanic crust, will be very complex.

1 Introduction

This paper is concerned with the occurrence of compositional zoning in clinopyroxene showing garnet exsolution as found in an eclogite xenolith from the Roberts Victor kimberlite pipe. The xenolith has been extensively described and its evolution discussed by Harte and Gur- ney (1975) and Sautter and Harte (1988). In this paper we use the compositional-zoning profiles to estimate the diffusion coefficient for A1 in clinopyroxene and the cooling rate, and go on to note the general importance of thermal history in considering the petrogenesis of mantle xenoliths and their bearing on mantle constitution.

Variations in the chemical composition of minerals within a rock demonstrate a failure to maintain equilibrium, and provide a record of changing conditions during the rock's evolution. The changing conditions may be ones of temperature and/or pressure (e.g. mineral growth during prograde metamorphism, exsolution, or exchange of chemical components between minerals during cooling) or chemical changes (e.g. resulting from metasomatism) or both. The extent to which early mineral compositions are preserved within crystals will depend on diffusion rates and the periods of time over which particular P - T conditions operated. The occurrence of mineral compositional zoning considerably complicates attempts

638

to interpret the mineral compositions as expressions of thermodynamic equilibrium at a given T and P. However such zoned minerals potentially provide much greater petrogenetic information than those in an equilibrated rock, which reveals only one point of its P - T history.

In low-medium temperature metamorphic rocks from the crust chemical-zoning patterns in minerals may be interpreted as reflections of growth zoning and thereby reflect segments of P - T paths (Spear and Selverstone 1983). At high temperature under some crustal conditions diffusion may modify growth zoning and even elim- inate it (Yardley 1977; Tracy 1982). For mantle rocks it has been common practice to assume that the rocks formed well-equilibrated mineral assemblages under the ambient conditions of P and T at the point in the mantle from which they were plucked by eruption. Indeed this has been the whole basis of the construction of petrological geotherms (Boyd 1973), and general homogeneity of mineral compositions has been assumed to the extent that mineral analysis has sometimes aimed at character- ising average compositions or using hand-picked grains with little attention to spatial inhomogeneities (e.g. Boyd and Finger 1975; MacGregor and Manton 1986).

It may be argued that if rocks metamorphosed in the crust can form well-equilibrated assemblages, then surely this must be generally the case for rocks metamorphosed or metsomatised in the mantle. But this amounts to considering temperature and time to be the only significant variables where pre-existing minerals are re- equilibrating. Major distinctions must be recognised for such factors as: (1) whether the metamorphic event concerned was one of mineral recrystallisation or merely one of modification of existing mineral grains by diffusion; (2) the varying effects upon diffusion of factors such as deformation and fluid components.

Not only is the existence of mineral inhomogeneities important, but so also is the time of "freezing-in" of mineral compositions (Fraser and Lawless 1978). Harte et al. (1981) and Harte and Freer (1982) have noted the possibility that lower-temperature mantle xenoliths, with coarse grained and dry mineral assemblages, may well retain chemical compositions which became frozen some time prior to eruption. Until recently most evidence of significant variations in mineral composition within mantle xenoliths had come from eclogites and grosp- ydites (Chinner and Cornell 1974; Harte and Gurney 1975; Lappin and Dawson 1975; Lappin 1978; Hatton 1978; Hatton and Gurney 1977a, b, c), but there is increasing evidence of mineral chemistry variations from a variety of peridotite xenoliths from kimberlites and basalts (Fabrics et al. 1987; Harte et al. 1987; Smith and Boyd 1987; Witt and Seek 1987; Hops et al. 1989). Such rocks allow a much greater interpretation of thermal history and petrogenetic processes to be made for mantle rocks.

The subject of this paper, bimineralic eclogite xenolith JJG41, is one of a large suite of eclogite and grospydite xenoliths collected from the Roberts Victor kimberlite pipe, South Africa (Hatton 1978). A number of these show variations in mineral chemistry which in some cases appear to be linked to layering and the pres-

ence of a third phase, especially kyanite (e.g. Lappin and Dawson 1975; Lappin 1978; Hatton and Gurney 1977a, b, c). In JJG41 the variations in mineral chemistry occur in clinopyroxene and are clearly associated with the development of garnet exsolution lamellae in the clinopyroxene. Data on textures, mineral chemistry and high P - T experiments were presented by Harte and Gurney (1975) and amplified by Sautter and Harte (1988), who also discussed the driving force of exsolution reaction and the role of net-transfer and cation-exchange reactions between clinopyroxene and garnet during the mantle cooling history of the rock, from ca. 1400~ to 1000 ~ C. The principal compositional gradients in the clinopyroxene are in A1, Mg and Si and relate to the growth of garnet lamellae. Diffusion of these cations, in association with net-transfer reaction causing growth of garnet, became arrested ('frozen') at higher temperatures than F e - Mg exchange at the C p x - G t interfaces; the latter exchange continued down to temperatures of ca. 1000 ~ C.

The major part of this paper is concerned with estimating the diffusion coefficient for A1 in clinopyroxene, which is the rate-determining process during the growth of garnet, and with estimating the cooling rate during F e - Mg exchange. In the discussion section of the paper, we note the importance of data on thermal history in assessing the petrogenesis of eclogite xenoliths and their bearing on mantle constitution.

2 Description of clinopyroxene and garnet lamellae in JJG41

The garnet exsolution lamellae occur parallel to six face orientations in clinopyroxene and are parallel to the c axis and perpendicu-

a ~ _ i

r

i . . . . . . . . . . . . . . .

4mm

110

Fig. 1 a, b. Schematic illustration of types and orientations of garnet lamellae in clinopyroxene after Sautter and Harte (1988): a crystallographic orientations in clinopyroxene; b garnet lamellae on a clinopyroxene section parallel to (001)*. The accompanying ray diagram has the same orientation as section b and shows traces paral- Icl to the faces as labelled. A are large garnet lamellae usually parallel to (010); B are intermediate lamellae and C are small lamellae, both of which occur parallel to all six directions {110}, {130}, {010}, {lOO}

639

lar to (001)* (Fig. 1). Composition gradients in clinopyroxene adjacent to the lamellae were determined in electron microprobe tra- verses on a section cut through the centre of a single clinopyroxene crystal (ca. 6 cm diameter) perpendicular to the c axis.

Three generations of garnet (Gt) lamellae have been defined (Sautter and Harte 1988) on the basis of size criteria, grossular content and the shape of diffusion gradients in adjacent clinopyroxenes (Cpx). Thick lamellae (> 500 gm: type A in Fig. lb) probably first nucleated with little overstepping, close to the transformation temperature of clinopyroxene to garnet as defined by thermodynamic calculation, which is expected to be close to the solidus temperature (1400 ~ C at 35 kbar) determined experimentally (Harte and Gurney 1975). These lamellae developed as discontinuous layers with an average spacing of 200 pm with the tow-energy face parallel to {010} of clinopyroxene. These garnets contain 0.44 mol.% grossular and 0.38 mol.% pyrope (Sautter and Harte 1988). Removal of garnet components from adjacent elinopyroxene produced a depletion halo alongside the garnet, where later garnet lamellae failed to nucleate (Fig. i b).

The lamellae of intermediate thickness (100-200 pm across; type B in Fig. 1 b) usually nucleated away from A lamellae where A1 concentrations in the clinopyroxene remained high. The same feature is observed in the later thin lamellae (around 10 gm across; type C) which tended to nucleate away from the A and B lamellae. Among the B and C lamellae sets, there is an increasing number of nuclei and therefore a decreasing spacing (around 100 gm for B lamellae, 10 gm for C lamellae, Fig. lb). Most commonly the B and C lamellae developed essentially parallel to (110) and (130) planes in the host pyroxene with a more and more regular narrow plate-like habit as the width of the lamellae decreases. This indicates slower growth in these two orientations. These characteristics are consistent with nucleation theory which predicts that nucleation rate increases as overstep increases. The Ca content of the lamellae increases as the width of the lamellae decreases with B having approximately 0.50 grossular and C approximately 0.60 grossular molecule (Harte and Gurney 1975; Sautter and Harte 1988). The temperatures at which B and C lamellae nucleated are not known accurately in the absence of the appropriate phase diagrams to estimate the amount of overstep. From experiments to determine equilibrium assemblages in the undersaturated part of the CMAS system with corundum buffer, (Gasparik 1984, Fig. 2), the temperatures of formation of C lamellae are probably lower than 1350 ~ C at 35 kbar, or lower than 1250 ~ C at 30 kbar (Sautter and Harte 1988).

In terms of compositional variations of the clinopyroxene host, the sequential development of A, B, and C, lamellae with decreasing temperature is supported by the shape of diffusion-controlled composition gradients adjacent to the garnet lamellae. The main gradients involve a major decrease of A1 and minor decrease of Fe, whilst Si and Mg increase towards the garnet contact (Fig. 2a and Table 1). The shape of these compositional profiles varies from broad and gentle adjacent to thick A lamellae, to narrow and steep adjacent to the thinner B and C lamellae (Fig. 2a). This correlation of profile shape with lamellar thickness shows the effect of falling temperature and reflects the timing of lamellar growth. Type A lamellae grew at high temperatures for a long time whereas type B and C lamellae grew at lower temperatures over a shorter period of time. If one compares the profiles adjacent to A lamellae (parallel to {010} direction) with those adjacent to B and C lamellae (parallel to {110} direction) definite differences are observed (Fig. 2b). The primary A1 and Si compositions of the clinopyroxene are clearly lost as far away from the A lamellae as can be determined without interference of any other lamellae; whereas they are approximately preserved at a distance (proportional to garnet width) for B and C lamellae. At the interface, A1 and Si values are fixed in the clinopyroxene adjacent to B and C lamellae; but the A1 and Si contents of the clinopyroxene adjacent to the A lamellar contacts are signifi- cantly lower and higher respectively by comparison with B and C lamellae (illustrated for A1 in Fig. 2b). With the assumption that during the growth stage interface equilibrium was observed for the whole set of lamellae, and the observation that a constant patti-

~ 1 . 5

IZ I-- Z fW) l.I]

o

0 .~

50 100 D I S T A N C E pm

150 200

b

At/60x CAI - 1 . 0

Cr

Go - G BJ I A

Ge

0.0 _ ~ X(pm)

Fig. 2a, b. Concentration-distance diagrams showing the different shape of diffusion gradients in Cpx as a function of the size of adjacent garnet lamellae: a Si, A1, Mg, Fe, Ca, Na profiles in Cpx adjacent to types B and C garnet lamellae parallel to (110) of Cpx. Garnet lamellae are shaded; the plane of the diagram is perpendicular Cpx c axis. b Al-concentration profiles in clinopyroxene adjacent to types A, B and C lamellae. X axis is the distance from garnet lamellae. Cr is the A1 concentration in garnet; Co is the estimated initial concentration of A1 in Cpx (Harte and Gurney 1975, Table 1, analysis cpx A); C e is the equilibrium concentration of A1 in Cpx obtained at the interfaces of types B and C lamellae. Note for A lamellae that the AI concentration at the interface is less than Ce

tioning of S i -A1 occurs only at contacts of B and C lamellae, it may be concluded that the B and C lamellae stopped growth at the same temperature (Fig. 3). This temperature was low enough for AI diffusion in the clinopyroxene to be frozen so that S i -A1 partitioning at the Gt-Cpx interface still reflects the growth equilibrium partitioning. On the other hand the A lamellae both started and stopped their growth at higher temperatures than B and C lamellae; the difference in stopping time being inferred from the different Si/A1 ratio at the pyroxene interface with A lamellae.

640

Table 1. Changing composition of clinopyroxene adjacent to B garnet lamella

SiO2 = 52.25 50.59 49.48 48.06 47.39 47.18 47.08 46.90 TiO2 = 0.09 0.13 0.19 0.19 0.16 0.19 0.170 0.20 A120 3 = 6.15 8.56 10.05 11.55 12.24 12.55 12.68 13.29 Fe20 3 = 0.97 1.92 2.09 1.67 2.23 2.03 2.10 2.30 FeO = 2.04 1.52 1.50 2.17 1.58 1.84 1.81 1.72 MnO = 0.03 0.03 0.05 0.05 0.02 0.05 0.05 0.06 MgO = 13.71 12.69 11.96 11.09 10.90 10.75 10.72 10.81 CaO = 22.39 22.19 22.39 22.33 22.36 22.35 22.45 22.28 Cr203 = 0.06 0.11 0.11 0.06 0.12 0.10 0.09 0.09 Na20 = 1.59 1.73 1.68 1.52 1.54 1.49 1.45 1.44 K20 = 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Total 99.28 99.46 99.50 98.69 98.54 98.52 98.60 99.09

Structural formulaefor 6 oxygens

Si= 1.907 1.846 1.808 1.774 1.751 1.745 1.740 1.725 T i= 0.002 0.004 0.005 0.005 0.004 0.005 0.005 0.006 A1 Iv= 0.093 0.154 0.192 0.226 0.249 0.255 0.260 0.275 A1 v1= 0.172 0.214 0.240 0.276 0.284 0.292 0.293 0.301 Fe 3§ 0.027 0.053 0.057 0.046 0.062 0.056 0.058 0.064 Fe 2+ = 0.062 0.046 0.046 0.067 0.049 0.057 0.056 0.053 M n = 0.001 0.001 0.002 0.002 0.001 0.002 0.002 0.002 M g = 0.746 0.690 0.651 0.610 0.600 0.593 0.591 0.592 C a = 0.876 0.867 0.876 0.883 0.885 0.886 0.889 0.878 C r = 0.002 0.003 0.003 0.002 0.004 0.003 0.003 0.003 N a = 0.113 ~122 0.119 0.109 0.110 0.107 0.104 0.103 K = 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Total 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000

Clinopyroxene compositions measured at successively greater distances from a B garnet lamella (see Fig. 2a). All analyses by electron microprobe, see Sautter and Harte (1988) for further details

The Ko (partition coefficient) for F e - M g for the Cpx- -Gt interfaces yields roughly constant values for all lamellae types, de- spite differences in garnet Ca contents, and reflects the maintenance of F e - Mg exchange at the interface after the cessation of A1 diffusion and garnet growth, down to temperatures of about 1000 ~ C. This temperature appears to be the lowest recorded in the xenolith for any aspect of mineral reaction (Sautter and Harte 1988) and therefore represents the temperature at which mineral compositions became frozen in all respects (ignoring late-stage alteration which was probably associated with kimberlite emplacement).

-2500 100Ma ,

1400 1 3 0 0 1 2 0 0 1100 1000 T~ i i / i i

Although the sequential development of clinopyroxene and garnet compositions may be determined, it is not possible to place definite age constraints on this petrological history. Kramers (1979) tentatively suggests an age of 2500 Ma for the Roberts Victor eclogites, and a Precambrian age appears likely from other age constraints on the Kaapvaat Craton mantle lithosphere (Kramers 1979; Richardson et aL 1984). The eruption of the Roberts Victor eclogite was approximately 100 Ma ago (Kramers 1979), thus leaving a probable time span of approximately 2400 Ma for the evolution of JJG41 (Fig. 3) from its formation in a probable magmatic event (Harte and Gurney 1975; Hatton and Gurney 1977c, 1987).

3 Kinetics modelling

A I-- . . . . . . . . . ? . . . . . . . . . . . . . . . . . . . . . . . . . . .

g ? . . . . . . ~ . . . . . . . . . . . . . . . . . . . .

C ?--- -~ ....................

. . . . . ne t - t ran fer AI Si,Mg ............... exchange Fe Mg

Fig. 3. The sequential development of the 3 sets (A, B, C) of garnet lamellae with decreasing temperature, and the uncertainties of age relations. Initial formation (at 2500 Ma ago, see Kramers 1979) of the eclogite is postulated to have occurred by crystaUisation from a melt (1400 ~ C solidus, Harte and Gurney 1975). At 1150 ~ C, approximately, garnet growth ended with the cessation of A1 diffusion; the thick A lamellae possibly effectively stopped growing before thinner B and C lamellae. At 1000 ~ C F e - M g partitioning between all garnet lameltae and clinopyroxene became frozen. The dates of the 1150 and 1000~ C events are unknown. Eruption occurred approximately 100 Ma ago

Specimen JJG41 clearly preserves compositional gradients in cpx which are a product of diffusion-controlled reaction. The flux of the slowest-diffusing species will be a function of its diffusion coefficients (D) operating over some period of time (t) at certain physical conditions (especially temperature, T). Our objective is to estimate these variables, and thereby other quantities (e.g. cooling rate) from the JJG41 rock data.

Kinetic modelling of diffusion-controlled processes varies according to whether the type of reaction being considered is a net-transfer or a pure-exchange reaction. Net-transfer reactions, because of volume variations, re- quire kinetic modelling involving interface migration. Complex metamorphic reactions have been modelled by Loomis (1975, 1977). Mineral associations with simple geometry and mineral chemistry, as seen in exsolution in iron meteorites, have been used as cooling-rate indi-

641

cators (Wasson 1974). In exchange reactions, like the common geothermometers, there is no variation in the modal proportions of these phases and the interface between the coexisting phases is thus regarded as fixed. Diffusion gradients related to these reactions have been modelled for "geospeedometry" purposes (Lasaga 1983). This time-related extension of geothermometry allows interpretation of calculated temperatures in terms of equilibrium- and blocking-temperatures, and estimation of cooling rates. Such considerations have been applied to olivine-spinel (Ozawa 1984) and olivine-garnet pairs (Smith and Wilson 1985). Equivalent modelling for C p x - G t F e - M g exchanges is less advanced, partly because the appropriate diffusion coefficient in clinopyroxene is unknown. The kinetics of the net-transfer and exchange reactions are considered in turn below.

3.1 Kinetics of the net-transfer reaction

3.1.1 Assumptions. In sample JJG41, the large-scale A 1 - S i - M g diffusion gradients in the clinopyroxene are related to the net-transfer of A1 to the growing garnet and of Si and Mg, away from the moving interface with garnet. In the kinetic modelling of this net-transfer reaction we use the A1 profiles in clinopyroxene adjacent to type B and type C garnet lamellae, which are parallel to {110} in the host clinopyroxene. In this modelling we make various assumptions, which are partly based on textural, chemical and experimental features of the xenolith described by Harte and Gurney (1975), Sautter (1986) and Sautter and Harte (1988):

1. The layer-like habit of garnet exsolution makes it possible to apply a one-dimensional plane front model of growth in Cartesian coordinate space.

2. The large clinopyroxene crystal was initially homoge- neous.

3. As exsolution proceeded the clinopyroxene and its exsolution lamellae showed closed-system behaviour. This is supported by the fact that the compositions of the various garnet lamellae and the shape of adjacent diffusion gradients in clinopyroxene differ from one mi- cro-domain to another.

4. The growth of garnet, which requires cross-migration of 2 A1 and Si+ Mg, was controlled by bulk diffusion of A1 as the slowest diffusive species in the clinopyroxene host. In high temperature and pressure experiments on JJG41 (Sautter 1986) it is found that resorption of the garnet lamellae is impeded by lack of A1 migration in the clinopyroxene. Therefore, it is likely that A1 mobility controls the exchange in the exchange A12Si-1Mg- 1

5. Interface equilibrium of the major components pre- vailed at all times during the growth of B and C lamellae because constant A1-Si partitioning at the C p x - G t interfaces survives for these lamellae.

6. There are no A1 gradients in the garnet.

7. A1 diffusion in the pyroxene is independent of the pyroxene composition.

8. There was negligible control of the A1 diffusion coefficient by crystallographic orientation in clinopyroxene for the garnet lamellae under consideration. In general, diffusion parallel to the c axis in clinopyroxene is probably a faster path compared to diffusion parallel to the a and b crystallographic directions. In this case we are concerned with diffusion perpendicular to the c axis towards the {hk0} garnet lamellae directions, and this will be assumed to be roughly the same in all these directions.

9. The garnet lamellae nucleated and grew within the temperature range 1400-1100 ~ C. For types B and C lamellae an overall range of 1300 ~ C-1150 ~ C is probable and average conditions of 1200 ~ C are assumed.

3.1.2 Geometrical reference frame and boundary conditions. For each individual garnet lamella the shape of the diffusion profiles in the adjacent clinopyroxene is symmetrical on both sides of the lamella (Fig. 4 a). There- fore, the garnet central plane will be taken as a fixed spatial reference plane. The garnet interface with the host pyroxene migrates with a velocity V as the garnet grows (Fig. 4b), and this will be termed the mobile reference plane (X'); the rate of movement of the coordinate system is tied to the garnet-clinopyroxene interface.

The expression of Fick's second law to be solved in this A1 diffusion-controlled reaction involving a moving phase boundary is as follows:

~CA1 D ~2 CA 1 . ~ ~C 1 ~t - ~ + v 0X

Where: 0CA~ refers to change in A1 concentration, 0t refers to change in time, ~X refers to change in distance, and D and V refer respectively to the diffusion coefficient for A1 in Cpx and the velocity of the Gt-Cpx interface. The flux of A1 in the direction perpendicular to the { 110} interfaces, therefore depends on the concentration gradient (diffusion term: - D 0 2 C/OX 2) and the rate of trans- lation of the spatial coordinate (transport or reaction term: V~C/~X) tied to the interface.

We wish to find an analytical solution to Eq. 1 which fits the natural-rock diffusion profiles and their evolution as illustrated in Fig. 4. Formally stating the boundary conditions illustrated in Fig. 4b we have the following:

For all t ~ 0: -

in garnet space where for 0 _< X _ X' (t) when X = 0 , then C=Cr when X = X' (t), then C = Cr

in clinopyroxene space where X _> X' (t) when X = X'(t), then C = Ce when X-~ ~ , then C = Co

where C o is the initial concentration of A1 (CM) in clinopyroxene, Cr is the CA~ in garnet and Ce is the equilibrium CA1 in clinopyroxene at the interface with garnet (Fig. 4b).

The flux of A1 within the clinopyroxene balances the growth of garnet. Thus if the interface moves a distance

642

(a)

(b)

(c)

C GT

d i s t a n c e

crib--, v Co

Ce i

0 X ' 0

C

1.0- Cr . . . . . . . 7

I ( i) I( i i ) I

C o

0.5

Ce.

0.0

Cx-

f

X

I i _ . . . . . . . . (ii)

I / I / i /

/

(iii)

i '

/ /

/ ' 5~0 1()0 150 /

X

- 0 . 5

Fig. 4a-c. Graphical illustration of boundary conditions for A1 diffusion and garnet growth (all graphs have distance, X, as horizontal axis, and concentration, C, as vertical axis): a Geometrical reference frame: the centre plane of a garnet lamella, which is fixed at (X = 0) during garnet growth, b Extent of reaction: (i), (ii), (iii) illustrate successive times or stages of garnet growth and diffusion in clinopyroxene; (i), (ii) illustrate the progressive evolution of the Al-concentration profile in the clinopyroxene as the garnet lamella increases in size; (iii) is the hypothetical final equilibrium stage, where all clinopyroxene attains the same composition (this stage is not reached in the JJG41 sample). C, is the garnet composition; Co is the initial Cpx composition; C e is the Cpx equilibrium interface composition for t>0; X' is the mobile Cpx-Gt interface; V is the interface velocity that decreases with reaction progress, c Illus- trates two thicknesses of garnet lamellae (straight lines) and associated clinopyroxene Al-concentration profiles (curved lines); similar to stages (i) and (ii) of diagram b. The clinopyroxene Al-concentration profiles are extrapolated beyond the real garnet interfaces through garnet to the garnet centre line (where distance X=0). C~, at -0.21, is the common point at X=0 to which the A1- concentration profiles (measured by electron microprobe) in elinopyroxene extrapolate

dX ' per unit o fd t , face will be equal to diffusion flux.

dX ot cp,, ( c . - c o ) . = -

since JA~t=0 then

(C.-C~). d X _ rCpx_nCw 8C d t ~AI - - i L e A l ' ~ X

nCvx 8 C dX ' "-'gl "~X

V - dt C r - - C e

the mass balance at the mobile inter-

2

As C, and Ce are assumed to remain constant while the reaction proceeds according to the model of irrevers- ible reaction developed previously, V is proport ional to the diffusional flux of A1 in Cpx and decreases as the OC/OX of the zoned clinopyroxene rim becomes smaller and the concentration gradient becomes smoother. Thus the interface velocity decreases as the garnet lamellar size increases. Because V is not constant, the solution of Eq. 1 is not theoretically straightforward.

3.1.3 Model solution. Because Ce is fixed at the interface and the shape of the diffusion gradients is proport ional to the width of the garnet lamellae it is possible to make a geometrical extrapolation. Examination of the natural- rock data (Sautter and Harte 1988, and this paper Figs. 2, 4c) shows that the diffusion gradients adjacent to the B and C lamellae extrapolate approximately to a common point Cx located on the fixed garnet central plane. This point, Cx, as determined from the compositional gradients measured on the specimen has a value close to -0 .21 (Fig. 4c).

The geometrical extrapolation to a constant Cx is only likely in the earlier stages (Fig. 4 b) of garnet growth and diffusion in clinopyroxene, whilst unmodified clinopyroxene concentrations survive at some distance from the garnet. For the specific garnet lamellae concerned (types B, C parallel to {110}), whose width is less than 100 gin, a sharp change in clinopyroxene compositional gradients between modified and unmodified is common. It is partly because of this that the geometrical extrapolation to constant Cx works empirically in JJG41. The geometrical extrapolation is also dependent on the fact that garnet thickness (and movement of the Gt-Cpx boundary) is also controlled by the characteristic diffusion length of A1 in clinopyroxene, whilst Ce is kept to a constant value because the reaction is diffusion controlled.

With the above geometrical extrapolation, the reaction term in Eq. 1 becomes redundant and the clinopyroxene may be viewed as a semi-infinite medium with the fixed concentration Cx at an imaginary surface at X = 0 (Fig. 4c). The solution of Fick's second law may therefore be simplified (Philibert 1985, pp 7-8) to the form:

C-Co erfc ( ~ ) Cx- Co

The associated boundary conditions are:

For all t > 0:

when X = 0 , then C=Cx when X = X'(t), then C = C,

when X --, o% then C = Co.

Thus the concentration (C) at any point (X) in the clinopyroxene diffusion-profile, for a given time (t) is given by:

C=Co+(Cx-Co) e r f c ( ~ - ~ t ) . 4

A justification for the geometrical extrapolation for Cx may be made. The net-transfer problem involving a phase change from Cpx to Gt in the form of exsolution lamellae is equivalent to a heat-transfer problem involving a phase change from liquid to solid with interface migration as solidification proceeds (Fig. 5). This problem, namely the "Stefan problem" (see Turcotte and Schubert 1982, p 168) deals with the freezing of a layer of ice at the top of a lake. There is a temperature gradient within the ice but not within the water because of convec- tion. The horizontal ice layer solidifies downwards from its upper surface, maintained at a constant temperature (To), as a result of being cooled from above. The interface migrates with a velocity V and consumes latent heat (L) of solidification V=k(OT/~y)/pL (Turcotte and Schubert 1982). As the depth of the solidification boundary increases proportionately to the square root of time, it is possible to scale the depth of solidification, Ym, with

HEATtransfer MASS transfer

0 Y m ( t )

P . A S E C . . N G E INTERFACE

Liq

\

dYm

d t T

o x'(t)

\

Cpx

dX'

dt

Tm

To

O r -

G o -

G e -

l I 0

Ym~ Ym:, G x -

[ /"

/ t" �9 /

'x ; ' k' x; r X

Boundary condit ions Boundary condit ions

when t = O t h e n Y m = O w h e n t = O , t h e n C - C O where t > O and O < Y <__ Ym: where t > O and O ~ X < X'(t):

T = T o w h e n Y = O C = C x w h e n X = O T = T m when Y = Ym(t) C = C e when X = X' ( t )

Within the solid (hea t - t ransfer ) C = C O when X > X' ( t ) Within the Cpx (di f fus ion)

aT 0aT pCp - - = k OC 02D

0t Oy 2 3t 8 x z

At the in ter face , Ym(t) , latent heat is consumed by solidif icat ion. At the in ter face , X'(t) ,

a lumin ium (Cr-Ce) , is dY m 0T consumed for garnet growth.

L - - = k - - dt Oy dX ' OC

(Cr -Ce) = D Cpx AI

dt 8x

Fig. 5. Comparison between heat-transfer problem (Stefan problem) and the mass-transfer problem (garnet exsolution). The moving boundary X'(t) in the mass transfer problem is equivalent to the moving boundary Ym(t) in the heat-transfer problem, p is the den- sity, C v the heat capacity (at fixed pressure) and k the thermal conductivity for ice

643

~ ) . Similarly in the thermal diffusion length '~1-2

the mass transfer problem relating to the growth of garnet from the pyroxene, there are no concentration gradients in the garnet. The interface Cpx--Gt migrates with a velocity V and consumes (Cr- Ce) A1 for lamellar growth (for V see Eq. 2). Finally, as it is a diffusion- controlled process, one can scale diffusion length and

garnet lamellar width a = . In this problem, Cx

and a, are the main unknown factors in the two equations. The solution is given in the appendix and leads to a transcendental equation with the solution given graphically in Turcotte and Schubert (1982, p 170).

From analytical data (see Fig. 2 a), Ce at the pyroxene interface is 0.21, Co away from the interface is 0.59, and Cr, the garnet composition, is 0.95. Substituting these values into the left hand side of Eq. 9 (see appendix) gives:

3.45 = e-"2/a erfc a.

This yields a value for a of 0.5 (Turcotte and Schubert 1982, p 170). Substituting this value for a in Eq. 7 (see appendix) gives Cx = -0.21. This result is consistent with the graphical extrapolation made in Sect. 3.1.2 and Fig. 4 c.

3.1.4 Estimation of Al diffusion coefficient and cooling rate for the exsolved clinopyroxene. In the Fick's law solution given above (Eqs. 3, 4), we now have values for all parameters other than: DA1 and t (time). The time parameter represents the duration of growth of B and C lamellae and it is assumed that these lamellae nucleated and grew over a relatively small temperature range (1300 ~ C-1150 ~ C); thus estimation of time also gives a cooling rate. Clearly either the cooling rate or the Dht have to be estimated, if the other parameter is to be determined from the JJG41 clinopyroxene diffusion-profiles using Eq. 4. Determination of A1 diffusion coefficients in pyroxenes has been notoriously difficult (e.g. Freer et al. 1982), and only limited explicitly-determined experimental data are available (Sautter et al. 1988a, b). We therefore proceed by endeavouring to constrain the time (or cooling rate) parameter for JJG41 by other data, and then to calculate the DA1 by means of the clinopyroxene diffusion profiles and Eq. 4.

During the growth process, Ca saturation was reached in the clinopyroxene host (Sautter and Harte 1988). Therefore it is possible to approximate the minimum time of growth from the time required to homogenize the clinopyroxene host with respect to calcium for various garnet lamellar spacings using the interdiffusion coefficient D(ca_~tg ) in clinopyroxene from Brady and MacCallister (1983). The calculations have been made for an average temperature value of 1200 ~ C, with the equilibrium spacing of the garnet nuclei at the very earli- est stage of the exsolution process determined from their present spacing. Using an average temperature of 1200 ~ C, with a spacing of 200 pm for nuclei of type B lamellae, the time required to homogenize Ca in the

644

(a)

�9 M o d e l p ro f i l e : C=Co+(Cx-Co) erfc x _ 2,/55"

. ' " Measured prof i le

fo r t = ] .6x l011s

�9 DAI = 0 . 9 x ] 0 q 6 c m 2 ] s

, 6

/ u , Io

/

/

/

(b)

/ f

�9 DAI = 3.7xlO-17cm2[s t= 3 . 5 x l o n s

. q

o r

' 510 1(30 micron" Fig. 6a, b. Comparison of Al-concentration gradient in clinopyroxene determined by electron microprobe on sample (dashed lines), with concentration gradients calculated using Eq. 4 and estimates given of time and diffusion parameters (filled circles): a Calculated concentrations using t = 1.6 x 1011 s and DC~ x of 0.9 x 10-16 cm2/s, based on a minimum time estimate from C a - M g interdiffusion (see text), b Calculated concentrations using DA] = 3.7 x 10- t 7 cm2/s and t=3.5 x 10 I1 s, based on Al-diffusion data from Sautter et al. (1988a, b)

pyroxene is 1.6 x 1011 s. Similarly, for 150 gm, the spacing between B and C lamellae, a time of 2.5 x 1011s is obtained. Using these times the corresponding DA~ values that fit (using Eq. 4) the profiles in Fig. 4c are 1.3 x 10 -16 cm2/s and 0.8 x 10 -16 cmZ/s respectively (at 1200 ~ C). A comparison between the Al-concentration gradient measured adjacent to a B garnet lamella and the calculated gradient based on a DA1 value of 0.9 x 10 -16 cm2/s is given in Fig. 6a. Clearly the compari-

son can only be approximate, given that the calculated profile assumes a constant (1200 ~ C) temperature, rather than using a temperature range such as the 1300- 1150 ~ C suggested in Sect. 3.1.1.

The above calculations provide an estimate of the Al-diffusion rate in pyroxene that controls the net- transfer reaction responsible for garnet growth at high T (calculations at 1200 ~ C). This estimate gives a maximum possible value for A1 diffusion as it has been determined with a limited time-scale based on a faster diffusive process ( C a - M g exchange in pyroxene). This minimum time of approximately 1011 s or 4000 years implies

an extremely fast T decrease with a cooling rate averag- ing 4 x 104 ~ C/Ma.

The above cooling rate is extremely high for the growth of the comparatively thick B and C garnet exsolution lamellae seen in JJG 41 (cf. Huebner et al. 1975). Moreover, this temperature cooling rate is very much greater than that calculated in the following section from the "geospeedometry" analysis of the pure exchange ( F e - Mg-1) reaction down to 1000 ~ C. The cooling rates suggested by this F e - M g diffusion are between 4 and 40 ~ C/Ma. For the rock represented by the JJG41 nodule to follow two such different cooling stages is possible, but necessarily involves complex initial conditions and boundary conditions. The nodule could have been derived from an initially high-temperature and very thin basic layer that approached thermal equilibrium very quickly within mantle peridotite 'country rock', and then followed a slower cooling path which was the same P - T path as the 'country rock' peridotite. However, the idea of very thin basic layers in peridotite as possible proto- liths for eclogite nodules is questionable, in view of the scarcity of composite xenoliths (peridotite wall rock + eclogite) in the Roberts Victor pipe (see also Discussion, Sect. 4).

A very different approach to estimating the ,-'A]ncvx is to apply the low-temperature cooling rate from F e - M g exchange (Sect. 3.2) to the whole history of the sample. Applying the minimum cooling rate from F e - Mg "geospeedometry" of 4 ~ C/Ma to the high temperature (1300-1150~ history involving A1Si-IMg -1 net transfer gives a cooling duration of 37.5 Ma. Using this timescale to recalculate the A1 diffusion in pyroxene (with Eq. 4) gives DA1 in clinopyroxene of 5 • 10 -20 cm2/s .

The last calculation almost certainly underestimates the coefficient of A1 diffusion in pyroxene. The implied linear cooling rate must overerstimate the cooling time at high temperatures, because cooling often follows a negative exponential law since the driving force (i.e. the thermal contrast) decreases with time. Thus this second calculation is diametrically opposite to the first calculation using a cooling rate based on C a - M g diffusion, in that the second calculation should yield a minimum possible value for DA~.

The maximum (1.1x10-16cm2/s) and minimum (5 x 10 -z~ cruZ/s) values for A1 diffusion in pyroxene at 1200~ C given by the above calculations, bracket the value of DA] of 3.7 x 10 - iv cmZ/s (Sautter et al. 1988a) obtained experimentally at 1180 ~ C for diopside, and are therefore in accord with experimental data. A comparison of the Al-concentration gradient with one calculated using the experimental DA1 is given in Fig. 6 b. As before the calculated gradient carries the simplification of constant temperature (1180 ~ C) rather than a range of cooling temperatures. At this constant temperature the time for diffusion is calculated as 3.5 x 1011 s.

If this time estimate is used to provide a guide to cooling rate for the diffusion process, actually occurring over a temperature range 1300~1150 ~ C, then a relatively rapid cooling rate is obtained of 1.35 x 104 o C/Ma (see above discussion). However, another approach to esti-

mating cooling rate may be adopted. Further experimental work by Sautter et al. (1988b and in preparation) gave a first estimation of the activation energy (E, =65+5 Kcal/mol) and of the pre-exponential factor (D o = 0.4 x 10-7 cma/s) for A1 diffusion in clinopyroxene. Using these quantitative experimental data, it is possible to make another estimate of the cooling rate of JJG 41 during the high-temperature stage when the garnet exsolution lamellae grew.

Dodson (1973) defined a relation between the closure temperature (T~) for volume diffusion and the time (t') beyond which diffusion is frozen. In the relation derived,

E,/R T~ = in (A t' Do a 2)

E, is the activation energy, and R the gas constant. A is a numerical constant depending on geometry (taken as A = 8.7 for planar sheet) and Do/a 2 the frequency factor for the diffusing component in a system with the characteristic dimension a (in our case a is approximately 100 pro, corresponding to the half width of garnet lamellae spacing). Assuming that the closure temperature for A1 diffusion in JJG 41 was 1150 ~ C, then different values of t' may be calculated depending on the value chosen for activation energy (E,). For E, equal to 60 Kcal/mole, t' is 0.015 Ma; whereas for E, of 70 Kcal/mole one ob- tains t' of 0.54 Ma.

With these t' values relating to cooling times from 1300~ to 1150~ (time B and C garnet lamellae growth), the corresponding cooling rates are: 104o C/Ma for t' =0.015 Ma and 278 ~ C/Ma for t' =0.54 Ma. Clearly the data are extremely sensitive to the Ea value, but the

645

value of 278 ~ C/Ma for the average cooling rate is rea- sonable by comparison with the lower-temperature geospeedometry F e - M g interdiffusion estimates of 4~ 40 ~ C/Ma (following Sect. 3.2), given that the cooling rate may be expected to decrease as the temperature becomes lower (see above).

3.2 Kinetics of the pure exchange process ( G t - C p x ; Fe - Mg)

During subsolidus cooling of sample JJG 41 the Fe - Mg exchange was first coupled to the 2 A1Si- 1Mg- 1 transfer across the moving C p x - Gt interface and then continued through the simple-exchange reaction (the C p x - G t , F e - M g geothermometer) down to about 1000 ~ C. The final concentration-distance profiles in Cpx and Gt show that the clinopyroxene is the mineral with the slower F e - Mg diffusion, and it is the pyroxene therefore which controls the behaviour of the geothermometer with time (Lasaga 1983). In this section the shape of the Fe-compositional gradients in the pyroxene are discussed with respect to the geospeedometry method that allows estimation of the cooling rate (Lasaga 1983). As this method strictly applies to pure-exchange reactions (fixed interface), the cooling-rate estimation concerns the last stage of the cooling, from about 1150 ~ C down to 1000 ~ C.

The geospeedometry analysis gives a set of theoretical "frozen" profiles which are the graphical solution of Fick's second law.

~ C 0 2 C 1 0 ~ - - D 0 ~X 2

10-

8-

6-

4-

2--

0

o ,~ 10-

6-

2-

In i t ia l

~('_- 0.01

/~/~/: 0.15

b

c CPx Fe Atoms / 6 Oxygen

~ - - ~ . . . . - _ _ _ - _ _ _ : ~ _ - - - - : - ~ . . . . ~i ~ |

0.1t ." �9 . �9 ~ �9 �9 Tf / [ . . . . dr

012 0~4 ' 0.'6 018 1 0.0 0.2 0.4 0.6 0.8 1 a

f ~ " 0,1

,(:0.15

o o12 o.'4 ole 0'.8 D i s t a n c e from edge of crystals

Fig. 7a, b. F e - M g exchange and cooling rate (Geospeedometry): a Theoretical profiles from Lasaga (1983). b Fe profiles in JJG41 clinopyroxene adjacent to garnet lamellae with dimensionless unit plotted along the abscissa (see text), dr/a is diffusion distance di- vided by crystal radius. T I are the measured Fe-concentration pro-

Cpx C Fe

0.2] i . . . . . i . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ti . . . . TO

0.1 . ,,.. o . " " " ' " T f

d r 0.0 o!, o14 o'.e o'.8 ~ a

files frozen into the clinopyroxene, and may be compared with the theoretical profiles, T~ is the initial concentration of Fe in clinopyroxene at 1300-1400 ~ C, whilst T o is the estimated Fe concentration at the cessation of garnet growth

646

where D O is the value of D at T o (the peak temperature) and t' is the time in compressed time-scale units. The transformation of t to t' diminishes the original diffusion problem where diffusion depends on temperature (and thus varies with time during cooling) to a problem where diffusion becomes a constant (Do) at constant temperature. For a linear temperature decrease (T= To -~ t), t' is equal to t '= 1/?(1 - e -'~) where ? =E~a/RTo 2" When t -.o% t '= 1/7 i.e. it reaches a final value beyond which the diffusion profiles are "frozen". The shape of these profiles will depend on the cooling rate and the diffusion coefficients for F e - M g in the minerals. Lasaga (1983) thus defines two dimensionless parameters which are suffi- cient to characterize the behaviour of the geothermometer with time: 7 is related to the sample cooling rate s (7' =E~ s~/Do RT~ Eq. 10); ill? depends on the diffusion properties in the mineral (slow diffusion fi/7=0.15 in Cpx; fast diffusion fi/7=0.01 in Gt). For each value of 7' and ill? there will be a final profile (t +oo).

To evaluate the cooling history of the sample, Fe profiles in clinopyroxene adjacent to garnet are compared to the theoretical profiles established by Lasaga (1983) in Cpx (fi/?=0.15) for different values of ?' (Fig. 7a). Two questions however, must first be ad- dressed:

1. What graphical modifications are required to compare the theoretical and natural profiles (Fig. 7)?

2. What part of the F e - Cpx profiles (Fig. 2 a) are related to changes following garnet growth and down to 1000 ~ C?

To compare the JJG 41 F e - Cpx profiles to the theoretical ones, a transformation has been done in terms of distance units. The natural profiles are redrawn in Fig. 7 b using the dimensionless value dr/a (dr = diffusion distance; a = crystal radius).

The Fe concentration C(oo, t'), measured within Cpx has fallen from the initial concentration C(oe, 0), corresponding to the initial temperature (T~) of 1300-1400 ~ C. As the present shape of Fe profiles are not fiat, C(oo, t) is different from C(0, t) and thus reflects an intermediate temperature. Mass-balance calculation of A 1 - F e elements vs S i - Mg in Cpx gives the Fe contribution during garnet growth from T~ to To (ca. 1150 ~ C). Subtracting the corresponding C v e - X surface from the CFe-X in the unexsolved Cpx shows that Fe concentration at To was superior to Fe concentration C(oo, t) at Ty (1000 ~ C) (Fig. 7b).

The result of the comparison between the natural and the theoretical profiles (Fig. 7) is a "best fit" for a value of 0.01. From this may be calculated cooling rate values for different values of To (temperature at start of exchange reaction without net-transfer reaction). For T o of 1100 ~ C and of 1200 ~ C the cooling rates are respectively 4 ~ C/Ma and 40 ~ C/Ma. These cooling rates are slower than the best estimate (ca. 300 ~ C/Ma) determined for the earlier stages of garnet exsolution in Sect. 3.4.1, but such a change of cooling rate with time is expected because the thermal contrast decreases with time (see Sect. 3.1.4).

4 Discussion

Considerations of the manner of formation of the mantle rock bodies represented by eclogite xenoliths, have given rise to three major categories of hypotheses:

1. The eclogite xenoliths represent a component of the upper mantle formed during the early evolution of the Earth (e.g. Anderson 1981). 2. The eclogites were formed within the mantle as a consequence of crystallisation of melts (e.g. O'Hara and Yoder 1967; MacGregor and Carter 1970; Anderson 1981; Hatton and Gurney 1977c, 1987). Within this group there are a variety of opinions as to the extent the eclogites might represent actual melt compositions or 'cumulates'; where 'cumulates' may be interpreted to mean a crystal aggregate formed by melt crystallisation but from which part of the melt constituents (e.g. residual liquid) have been removed by any process.

3. The mantle eclogites represent metamorphosed subducted oceanic crust. Hypotheses under this heading may vary from ones in which the eclogites are reasonably direct products of the subducted crust (e.g. Helmstaedt and Doig 1975; MacGregor and Manton 1986), to ones in which the eclogites are very complex products of metamorphism, melting and metasomatism, perhaps with a relation to regolith bodies (e.g. Ringwood 1982; Hatton and Gurney 1987).

Some hypotheses of mantle eclogite formation fall into more than one of the above categories, such as those involving both subduction and mantle-melting events (e.g. Ringwood 1982; Hatton and Gurney 1987). In re- cent years the third group of hypotheses have gained much ground on the basis of a variety of evidence involving texture, mineralogy, bulk-chemical compositions, and radiogenic and stable-isotope data (e.g. Helmstaedt and Schulze 1979; Exley et al. 1983; Ater et al. 1984; Jagoutz et al. 1984; Jagoutz 1988; Kyser 1986; MacGre- gor and Manton 1986), in addition to the basic facts that subducted oceanic lithosphere must be going some- where (Ringwood 1982) and that it offers a source of distinctive isotope signatures in the deeper mantle (Hofo mann and White 1982). Much of the evidence is partly circumstantial, and the extent to which eclogites may have a high-temperature evolution in the mantle, possibly involving melts, must be important in considering the preservation of signatures of a potential oceanic crustal origin.

The features described in JJG 41 (Harte and Gurney 1975; Sautter and Harte 1988; this paper) establish the following general points concerning its evolution:

1. Textural and chemical features show a progressive evolution by exsolution from a high-temperture rock with much clinopyroxene and little garnet to a lower temperature state with a much higher proportion of garnet to clinopyroxene.

2. During its cooling history the diffusional mobility of elements became restricted, and the effective blocking temperatures to diffusion of different elements were passed successively. In particular A1 diffusion in clinopy-

647

roxene became severely curtailed at higher temperatures than F e - M g diffusion. At clinopyroxene-garnet interfaces, but not within clinopyroxene, F e - M g interdiffusion continued down to temperatures of about 1000 ~ C.

3. Many geochemical and textural features of the eclogite were clearly developed during the high-temperature, probably melt-related, event involving the formation of the Al-rich clinopyroxene and its subsequent cooling. The P - T characteristics of the high-temperature event are clearly within the mantle domain and there can be few features of the rock that unambiguously provide information concerning the evolution of the rock prior to this time.

The loss of textural-structural and geochemical characteristics which closely relate to any earlier history, pre- dating the high-temperature mantle event, in JJG41, must apply to other Roberts Victor eclogite-grospydite xenoliths which show both petrographic and geochemical evidence of development during a high P - T mantle event involving melt (e.g. Lappin and Dawson 1975; Lappin 1978; Hatton and Gurney 1977a, b, c, 1987). In some cases oxygen isotope ratios may provide an exception to this and maintain oceanic crustal signatures (though these may not be particularly distinctive); but radiogenic isotopes must be affected by redistribution of trace elements during a melting event which is probably of Archaean age (Kramers 1979; Jagoutz et al. 1984).

For the Roberts Victor xenoliths as a whole, Mac- Gregor and Manton (1986) endeavour to use textural- structural and geochemical data to establish relationships which date from an initial origin in the oceanic crust. It is evident that they have to make many assumptions in doing this, and the validity of these assumptions must be questioned given the evidence of high P - T mantle-melt histories. It is an important part of MacGre- gor and Manton's (1986) viewpoint that possible correla- tions in geochemical and textural features point to an oceanic-crustal origin, but for the case concerned different geochemical features may retain memories of different events, just as P - T and textural signatures may refer to different events. We do not imply that an ulti- mate derivation of mantle eclogites from oceanic crust is necessarily wrong, but that some of the types of evidence used so far in this debate are not cogent.

The data provided by JJG41, and other Roberts Vic- tor eclogites showing high-temperature histories and compositional inhomogeneities (Lappin and Dawson 1975; Lappin 1978; Hatton and Gurney 1977a, b, c), also demands some attention from the viewpoint of inter- preting temperature and pressure assignments to mantle xenoliths. It is usually assumed that the temperature estimates obtained from xenoliths refer to their temperature just prior to entrainment by the kimberlite, and can be used simultaneously to estimate their position of origin within the mantle and to provide estimates of mantle P - T conditions (petrologic geotherms).

In JJG41, there is a general lack of equilibrium amongst all elements in the clinopyroxene, and the only compositions in garnet and clinopyroxene that may have been in equilibrium at the time of kimberlite eruption are those of Fe and Mg at the immediate C p x - Gt inter-

faces. Even in this case, given the evidence in JJG41 of progressive 'freezing' of atomic mobility, it is impossi- ble to say whether the temperature of about 10000 C obtained from these F e - M g compositions, pertains to the time just prior to kimberlite eruption or much older freezing of the mineral compositions as the rock cooled below the blocking temperatures for mineral thermome- ters. It is not clear, therefore, whether JJG41 and similar xenoliths were entrained from mantle at about 1000 ~ or some lower temperature. It is also unclear to what extent this problem of ascertaining the time and temperature of freezing of mineral compositions, applies generally to the interpretation of many mantle xenoliths (Harte et al. 1981; Harte and Freer 1982; Jagoutz 1988).

Caution is therefore necessary, in erecting models of thermal and petrologic structure of the mantle on the basis of xenolith temperature (with or without pressure) estimates, especially where there is clear evidence of a history of changing P - T conditions. MacGregor and Manton (1986) erect a model of mantle-eclogite derivation from oceanic crust and its emplacement and distri- bution in the mantle involving a series of assumptions. They use temperature estimates for the xenoliths in con- junction with Boyd and Nixon's (1975) xenolith-derived geotherm to provide depth estimates, and thereby sug- gest that the eclogites are concentrated along a zone in the mantle closely related to the lithosphere-asthen- osphere boundary. The validity of this assignation is questionable simply on the basis of the wide variety of mantle petrologic geotherms that have been erected using the same mineral data (e.g. see Sautter and Harte 1988).

Another uncertainty in the matter determining the position of origin of mantle eclogites, is that the age of the temperature-pressure/depth estimates may not relate to the time of eruptions, as discussed above. But, MacGregor and Manton's (1986) hypothesis involves even greater assumption. In their adoption of a model of derivation of the eclogites from oceanic crust, Mac- Gregor and Manton (1986) assume both that the principal eclogite mineralogical characteristics are the product of metamorphism of crust during subduction, and that the temperature estimates gathered from the xenoliths not only refer to their position of sampling by kimberlite but also to the position of their emplacement in the mantle as a consequence of subduction. Such a suggestion not only ignores the evident high-termperature thermal history of some Roberts Victor eclogites, but also takes no account of the fact that the thermal and tectonic characteristics of the subduction regime would surely be different from those of the cratonic lithosphere sam- pled by the kimberlite.

5 Conclusions

1. Diffusion profiles in eclogite xenolith JJG41 (from the Roberts Victor kimberlite) may be fitted by a variety of constraints with the diffusion coefficient of A1 in clinopyroxene determined experimentally as 3.7 x 10 -17 cm2/s (at 1180 ~ C).

648

2. A preferred est imated average cool ing rate of approximately 300 ~ C / M a is obta ined for the high temperature (1300-1150 ~ C) cooling period dur ing which A1 diffusion occurred and garnet grew. The profile of Fe concentra- t ion in e l inopyroxene indicates a slower cool ing rate for the lower temperature (ca. 1150-1000 ~ C) cooling history, with average estimates of 4 4 0 ~ C/Ma.

3. The evidence of h igh- tempera ture mant le histories provided by xenoliths like JJG41, with melt being in- volved in these histories in some cases, indicates tha t textural and composi t ional features definitive of an earlier oceanic crustal origin m a y be very hard to ascertain. Where there is evidence of a high P - T mant le melt history, different textural and geochemical da ta may refer to different events. A simple history, involving a single mant le event of limited P - T characteristics, cannot be assumed.

4. The preservat ion of disequil ibrium mineral composi - tions in JJG41, some of which clearly predate the time of kimberlite entrainment , urges caut ion in assuming that temperature-pressure da ta f rom mant le xenoliths necesarily relate to the time immediately preceding eruption. Using available radiometr ic da ta and the cool ing rate evidence, J J G 4 I mineral composi t ions were p robab- ly frozen in the Archaean.

Appendix

Solution of a semi-infinite medium with fixed Cx concentration

X C = Co + (Cx- Co) e r f c - - 4

X t a ~

Two equations, two unknowns Cx and a.

0C C C 2 1 I x ~ AtX=X'

C=Cr Cr

so C C Ce- Co x - o - er~cca

from Eqs. 5 and 2 (see text) respectively:

dX' a ~ and dX'=D OC/OX dt ~tt dt Cr--Ce

OC a]/-D C,-Ce SO

~X 1~ D

substituting from 6 and 7 into 8 gives

( C - - C e ) ~ - e -a2

Ce- Co a erfc a '

The graphical solution of this transcendental equation is given by Turcotte and Schubert (1982, Fig. 4-31).

Acknowledgements. We wish to thank the British Council for a grant enabling V. Sautter to study in Edinburgh in 1984-85. We are indebted to J.J. Gurney, O. Jaoul and L. Fleitout for much helpful discussion; and to J.R. Ashworth for a helpful review of the initial paper. Heather Hooker and Helena Jack are thanked for their patient and careful typing of the manuscripts. This work was supported by CNRS: INSU-DB, Th6me Fluids et Cin6tique, Contribution No. 163.

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