Earth and Planetary Science Letters, 64 (1983) 123-138 123 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

[51

Diffusion between olivine and spinel" application to geothermometry

J. Lehmann CRSCM, G.LS. CNRS-BRGM, 1A, rue de la F&ollerie, 45045 Orleans Cedex (France)

Received December 7, 1982 Revised version accepted March 21, 1983

Heating experiments were carried out, at 1100°C and 1200°C under controlled oxygen fugacity, on olivine-spinel assemblages from New Caledonia. This mineral pair constitutes a perfect experimental material for such studies. The result was a marked change in chemical composition of the minor phase, olivine: it becomes enriched in iron and chromium and the magnesium and nickel contents decrease. Careful studies of the influence of oxygen fugacity show that, though it has a strong effect on the rate of re-equilibration, it does not affect the equilibrium composition of the phases. The stability limits of the mineralogical assemblage used are also examined. Our results show the possibility of an important subsolidus re-equilibration in natural assemblages containing olivine and spinel. A new equation for the geothermometer based upon Fe2+-Mg 2+ partitioning between olivine and spinel is proposed and some applications discussed.

1. Introduction

The idea that significant subsolidus re-equilibration can occur between olivine and spinel originated from geothermometrical data. The temperatures derived from geothermometers based upon the partition- ing of Fe2+-Mg between olivine and spinel [1-6,21] are indeed often lower than those obtained from geothermometers based upon reactions involving one or two pyroxenes [6,7]. The assumption of a possible re-equilibration is supported by experimental works [5,7]. The problem deals not only with the simple interpretation of the data but also with the contents and the zonation observed in minerals. For example, we consider it hazardous to deduce the nickel content of a magma from the nickel content of the olivines crystallized from it only by using an experimentally determined partition coefficient. If nickel diffuses between olivine and spinel down to relatively low temperatures, the observed nickel content of the olivines will be completely different from what it was during crystallization.

The purpose of the present work is to study the Fe2+-Mg partitioning between olivine and spinel and the diffusion of nickel, chromium and magnesium between these two minerals. Our experiments enable us to propose a new olivine-spinel geothermometer using activity expressions different from those proposed by Irvine [8].

1.1. Notation

Ac/c AG R

(average content in the center - average content at the edge)/average content at the edge free enthalpy variation (in cal mol- l) gas constant (1.987 cal K tool-1)

0012-821X/83/$03.00 © 1983 Elsevier Science Publishers B.V.

124

Fo [A] (C)

forsterite content of the olivine: 100Mg/(EM 2+) activity of the component A for a given reference state mole fraction of component C

2. Experimental procedure

2.1. Sample used

High-temperature experiments were conducted on a natural olivine-spinel assemblage for various durations and under different oxygen fugacities. The sample used was a banded chromitite from the Alpha Mine located on the southwest side of the Ti6baghi Massif (New Caledonia) [9]. The chromite grains of this banded ore contain numerous olivine inclusions. Before any heating, the serpentine gangue was first dissolved in hydro-fluoric acid (the olivine inclusions, which were protected by their enclosing chromite host, were left unaffected) in order to get rid of all problems which may result from the presence of water in the system. Therefore, heating experiments were conducted on the pair olivine inclusion-host chromite. This mineralogical assemblage is considered to represent an exceptionally good experimental material because (a) the grain boundary between olivine and spinel was perfect: not the smallest impurity had been detected between these two minerals, either microscopically or by microprobe analysis; and (b) the lack of a third phase gives us a further degree of freedom which allows one to impose an oxygen fugacity without getting the paragenesis out of equilibrium.

The olivine inclusions are monocrystalline and show all the possible intermediate shapes between euhedral habit and a nearly perfectly spherical. Their size generally varies between 40 and 150 ~m (they can sometimes reach 200, even 300, /~m). The size of the chromite grains range from less than 1 mm to several millimeters.

Because of their small size, olivine inclusions were much more affected by reheating than the host chromite which only suffered a weak apparent transformation. That is why a few experiments were carried out on beads made of such chromite grains coated with synthetic forsterite powder in order to study the change in chromite composition.

The compositions of the starting material minerals are given in Tables 1, 2 and 3. Microprobe analyses were made every 10 ~tm throughout the olivine inclusions. These olivines have an unusual composition [10],

TABLE 1

Microprobe composition (wt.%) of host spinel before heating

Average Variations within content the whole sample

MgO 13.8 FeO * 15.5

Cr203 58.8 AI203 10.7 NiO 0.11 MnO 0.17 V203 0.11 ZnO 0.06 CaO < 0.01 SiO 2 < 0.05 TiO 2 0.13

13.5 -14.3 15.1 -16.2 58.3 -59.3 10.5 -11.0 0.08- 0.14

* A l l F e as F e O .

125

being very magnesian and rich in chromium and nickel. Moreover they are iron- and chromium-zoned: their iron content is higher in the center than at the edges; whereas it is the opposite for chromium. Determinations of chromium content for olivine inclusions were carefully performed: a secondary fluorescence effect was indeed to be expected during microprobe analysis because of the small size of the olivines and of their position as inclusions in the chromite grains. But a calculation of fluorescence intensity [l 1], as well as measurements at 7 kV (below the iron excitability level) have shown that the olivine chromium contents measured at 15 kV are fully significant.

The spinel host is a chromite with 58.8 wt.% Cr203 (Table l). The chemical composition of the chromite grains varies only slightly within a polished thin section as well as within the whole sample: this variation generally remains under 1 wt.%. There is sometimes a weak zonation in A1203 and in Cr203 but this zonation has not a clear direction. The ferric iron content, estimated by assuming a perfect stoichiometry, ranges from 4.4 to 5.5 mol.%.

2.2. Analytical procedure

Chemical analyses were obtained with a Camebax electron microprobe. The accelerating voltage was 15 kV (unless otherwise stated). Counting times (for the peak, but also for the background) were calculated in order to obtain the desired precision, which is shown by vertical lines in Figs. 1-4. Typical counting times are given in Table 4. Particular care was taken on the measurement of background (slope, counting time, distance from the peak).

2.3. Furnaces

Furnaces and samples are immersed in the same gaseous atmosphere. The run charges are about 250 mg, they are placed in aluminia containers (during experiments, these containers never reacted with run charges: after heating the charges were never stuck to the container which appeared unmodified after run). Temperature is measured by a Pt-Ptl0%Rh thermocouple, located close to the container, and regulated with an accuracy of I°C by a P.I.D. regulator. The oxygen fugacity was controlled by the gas mixture C O 2 / H z / A r . Preliminary experiments have shown that this method ensures a good reproducibility in imposing the oxygen fugacity: no thermodiffusion correction is necessary. The total gas pressure is 1 arm.

3. Results

Two different gas mixtures were used in order to study the influence of the oxygen fugacity on the re-equilibration between olivine and spinel. The first one imposed an fo2 of 10-10.02 at 1100°C and of 10 -8.94 at 1200°C, the second one an fo2 of 10-11.00 at 1200°C. Experimental results are summarized in Table 2. No new phases were detected at the end of the runs either inside the olivine, inside the chromite, or at grain boundaries.

3.1. Diffusion within the olivine

Iron and magnesium. The diffusion rate of the major elements Fe, Mg is high. After ten days of heating at 1200°C under fo2 = 1 0 - 8 9 4 (Fig. 2), the smallest olivines (whose size do not exceed 50 /~m) are already re-equilibrated (as far as iron is concerned); after 20 days of heating at 1200°C under the same oxygen fugacity, all iron zonation has disappeared: the olivines, which were Fo95 A before heating, are now Fo895 (Fig. 2). Magnesium zonations are more difficult to observe because of the absolute error in the measurement of high concentrations in this element.

126

TABLE 2

Composit ion of the olivines before and after experiments (AA, standard deviation, in wt.%)

Before heating 10 days 10 days 20 days 10 days 30 days at 1100°C at 1200°C at 1200°C at 1200°C at 1200°C

log(fo2) = - 10.02 - 8 . 9 4 -8 .94 - 11.00 - 11.00

center" edge a center edge a center edge a center edge a center edge a center edge a

FeO 4.1 3.8 4.1 5.6 8.2 9.2 z.n.o. 9.4 6.3 7.5 z.n.o. 9.3

A FeO 0.2 0.1 0.2 0.2 1.2 0.5 0.7 1.7 0.9 0.5

Fo 95. l 94.3 89.5 89.3 90.8 89.4

A Fo 0.2 0.3 0.6 0.6 1.2 0.2

%MnO x 100 z.n.o. 5.5 z.n.o. 10.5 z.n.o. 17.2 z.n.o. 17.2 6.9 n.d. n.d.

AMnOX 100 2.1 3.2 3.2 3.2 9.9

%NiO 0.44 0.44 z.n.o. 0.41 0.38 0.26 z.n.o. 0.26 0.39 0.31 0.26 A NiO 0.03 0.03 0.03 0.06 0.04 0.04 0.06 0.06 0.12

%Cr203 0.38 0.67 0.32 0.61 0.48 0.85 0.63 0.80 0.64 0.87 0.75 0.96 ACr203 0.14 0.16 0.14 0.19 0.25 0.29 0.22 0.35 0.35 0.24 0.08 0.25

Number of 10 8 8 9 6 4

grains

z.n.o. = zonation not observed; n.d. = not determined. a Edge: content measured at 10/~m from the edge of the inclusion.

9.

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0.4

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NiO

o o ftlf}t}} 0,4

O.2

0.(

Fig. 1. Content profiles (in wt.%) in two olivines before heating. (Analyses are performed every 10 #m; the vertical lines represent the absolute error.)

FeO C rzO 3 NiO

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0 . 0 [ ~

tFttttt4tt tfttt

t t f

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Fig. 2. Content profiles (in wt.%) in olivines (and in their host spinels) after heating experiments conducted with the first gas mixture. (Analyses are performed every 10 #m; the vertical lines represent the absolute error.)

128

FeO 9.

Z

. OL 2161

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Fig. 3. Content profiles (in wt.%) in olivines (and in their host spinels) after heating experiments conducted with the second gas mixture. (Analyses are performed every 10/tm; the vertical lines represent the absolute error.)

Runs made with the second gaseous mixture show that the iron diffusion rate in the olivine decreases with decreasing oxygen fugacity. After 10 days of heating at 1200°C under fo~ = 10-ll.00 (Fig. 3), the iron content measured at 10 # m from the edge is 7.5 (_+0.9) wt.% FeO (Ac/c = 0.19), whereas it was 9.2 (_+0.5) wt.% FeO (Ac/c = 0.11) after a same durat ion run made at the same temperature but under fo2 = 10 8.94.

Yet the 30 days of heating at 1200°C and under fo 2 = 10-u.00 (Fig. 3), at the end of which the profiles are almost flat in most of the olivines, show that the olivine iron and magnesium contents at equilibrium are independent of oxygen fugacity.

Nickel. Nickel seems to diffuse as quickly as iron in olivine, at least at 1200°C and when the oxygen fugacity is sufficiently high. After the experiments made at 1100°C and under fo~ = 10-]0.02, most of the profiles of small inclusions are flat within the analytical error, but the little change of the observed average

129

contents (0.44 wt.% and 0.41 wt.%, respectively, before and after heating) does not allow us to say whether nickel has diffused or not. As in the case of iron, the diffusion rate clearly decreases with decreasing oxygen fugacity: after 30 days of heating at 1200°C under fo ~ = 10-ll.00 (Fig. 3), only one of the analyzed olivines is totally re-equilibrated for nickel. The nickel content of this olivine (0.27 wt.% NiO) is similar to the contents observed after the runs made with the first gaseous mixture. Here too, oxygen fugacity has an effect on the rate of re-equilibration but not on the equilibrium composition of the phases. Yet the evidence here is less convincing as far as nickel is concerned because of the important dispersion of the measured contents, which results from the low rate of re-equilibration under low fo2 (after 30 days of heating the NiO contents measured at 10 ~m from the edge range from 0.14 to 0.37 wt.%).

Chromium. The olivine, whether heated at 1100°C or at 1200°C, all show a chromium zonation similar to the zonation observed before heating, whatever the run duration and the fo2 employed: their chromium content is higher on the edge than at the center. The extent of this zonation varies according to run duration, temperature and fo2' Table 2 shows that:

(1) Chromium content of the included olivines increases with increasing temperature. The chromium profiles tend to become flat when the temperature and the run durations increase:

~c/c

l l00°C, 10 days; fo2 = 1 0 -1°'°2 -0 .90 1200°C, 10days ; fo = 10 8.94 -0 .77 1200°C, 20 days; fo 2 = 10 -1t°° -0 .27

Fig. 4, which gives the Cr203 contents at 10 /~m from the edge as a function of the inclusion size, corroborates the increase of the olivine chromium content after heating.

(2) The rate of chromium diffusion in olivine increases with decreasing oxygen fugacity. There is no convincing experimental evidence of the increase of chromium content of the olivine in

equilibrium with spinel with increasing temperature. But two facts argue for such an increase: (1) The olivine chromium content measured at 10/~m from the edges after heating at 1100°C was never

higher than the observed chromium content after heating at 1200°C. If the chromium diffusion coefficient in olivine was weak at 1100°C and if the chromium content of olivine in equilibrium with chromite

C rzO 3

1.5

I0

0.5

! ½

®

I I I I I

I 0 0 2 0 0 mic. in clu~ion's size

Fig. 4. Cr203 content (in wt.%) of the inc luded ol ivines as a funct ion of their size (© = Cr203 content before heat ing; • = Cr203 conten t after the 10- or 20-day runs at 1200°C and under f o ' = 10-9) .

130

decreased with increasing temperature, a very sharp concentration gradient should be observed at the edge of the inclusions. Such a gradient has never been observed.

(2) The second argument is a thermodynamic one. Chromium is a minor element in olivine and a major one in spinel. So the free enthalpy variation of the reaction which governs the distribution of chromium between olivine and spinel is very high. Because this is a reaction between solid phases, the entropy change is small and so the enthalpy variation is high and governs that of chromium in olivine and spinel with temperature.

The chromium distribution between olivine and spinel is described by the following equations [11]:

FezSiO 4 + MgCr204 ~ Cr2SiO 4 + FeCr204 AG ol sp ol sp

MgCr204 --~ MgCr204 AG' sp ol

SO:

{ (Cr)~p] /[ (FeZ+)2sp) k = e x p ( ~ T ) = k ( Cr)zo' ]/k (Fe) 2o' AG>>0

= e x p l - - ~ J = ~ ~ ]/1 ( Cr)2ol ]

the ratios k and k ' vary as exp(AH/RT) and exp(AH'/RT), so they decrease with increasing temperature: chromium diffuses from spinel to olivine when the temperature increases.

The similarity of chromium contents (within analytical errors) measured at 10 ~m from the edge of the inclusions that have been heated at 1200°C under fo 2 = 10 -8.94 or under f% = 10-H.00, seems to show that, here also, oxygen fugacity has an effect upon the diffusion rate but not upon the equilibrium chemical composition of phases.

3.2. Diffusion in spinel The previous experiments on olivine inclusions in chromite do not allow observation of clear chemical

composition gradients in spinel. At best, a decrease of the spinel iron content can be noticed close to the inclusions after ten days of heating at 1100°C and under f% = 10- ~0.02. The chromite composition appears not to have been altered during the runs at 1200°C. Two factors can explain this apparent inertia of the spinel chemical composition:

(1) The size differences between the chromite host (a few hundred microns to several millimeters) and the olivine inclusions (200-300/~m at the most).

(2) A cation diffusivity in chromite at least as high as in olivine. The conservation of matter requires the equality the grain boundary fluxes for each elements:

1 i = D i p

D;' t x=o+ l-g;-Z J x - o -

where D; is the diffusion coefficient of the element i. For a given value of this flux, the composition gradient will be small if the diffusion coefficient is sufficiently high. Since there is no noticeable composition gradient in the spinel, the diffusion coefficient of Fe, Mg, A1, Cr in the spinel are at least as high as they are in olivine.

The changes in the olivine chemical composition enable us to infer the effects of a temperature increase on the spinel chemical composition, i.e., an increase in Mg content, and a decrease in Fe z+ and Cr 3+ contents.

TABLE 3

Analyses of included olivines and of their host spinels before and after heating

131

JM411 a DIF009 DIF014 DIF017 before heating 10 days at 1100°C 20 days at 1200°C 30 days at 1200°C

log(fo2) = - 10.02 - 8.94 - 11.00

olivine olivine olivine olivine

ol 1 o15b ol 1221 o13221 ol 1931 o12931 o122971 o142971

size (/tm) d b (~tm)

Si Mg Cr Mn Fe Ni Z

90 160 240 70 60 60 120 60 10 10 10 10 10 10 10 10 0.4203 0.4179 0.4138 0.4165 0.4077 0.4086 0.4067 0.4084 0.5342 0.5320 0.5185 0.5271 0.4840 0.4868 0.4931 0.4970 0.0062 0.0041 0.0105 0.0060 0.0094 0.0085 0.0110 0.0099 0.0003 0.0005 0.0010 0.0007 0.0024 0.0019 0.0010 0.0012 0.0372 0.0390 0.0590 0.0513 0.1034 0.1012 0.0909 0.0936 0.0059 0.0046 0.0038 0.0042 0.0024 0.0021 0.0014 0.0021 1.0041 0.9981 1.0066 1.0058 1.0094 1.0092 1.0081 1.0026

spinel spinel spinel spinel

d(/Lm) 15 10 10 10 10 10 10 10 Mg 0.1361 0.1354 0.1469 0.1385 0.1365 0.1364 0.1441 0.1397 AI 0.1055 0.1054 0.1066 0.1048 0.1050 0.1046 0.1161 0.1058 Mn 0.1018 n.d. 0.0028 0.0035 0.0006 0.0008 n.d. n.d. Ni n.d. 0.0008 n.d. n.d. n.d. n.d. 0.0012 0.0012 Fe 0.1614 0.1621 0.1480 0.1574 0.1653 0.1638 0.1498 0.1641 Ti 0.0011 0.0011 0.0015 0.0009 0.0013 0.0012 0.0014 0.0013 Cr 0.5882 0.5876 0.5909 0.5883 0.5929 0.5909 0.5955 0.5907 "~ 0.9951 0.9924 0.9967 0.9934 1.0016 0.9977 1.0081 1.0026

a Experiment number. b d = distance from edge.

Experiments dealing with capsules made of chromite grains coated with forsterite powder (which was produced by electric arc fusion of natural olivine from Norway) corroborate these results. Heating runs were carried out at 1200°C and under fo2 = 10 -894 . Here too, no new phase has been detected. Equilibrium was never reached because of the great size of the chromite grains, and these experiments have delivered only qualitative results. This time, a clear re-equilibration of chromite can be observed: (a) the decrease of the FeO content, measured at 10 #m from the edge, ranges from 1.3 to 2.8 wt.%; (b) the increase in MgO content ranges from 0.8 to 1.3 wt.% (Fig. 5).

TABLE 4

Microprobe analysis typical counting times (in seconds) for the different elements in olivine and spinel

Olivine Spinel

Si 20 Mg 20 Mg 20 AI 20 Cr 120 Mn 20 Mn 120 Fe 60 Fe 120 Ti 20 Ni 120 Cr 20

Ni 300

132

T A B L E 5

Some dif fus ion coefficients in ol ivine and spinel (Fe 3+ conten t of the spinel is ca lcu la ted assuming a perfect s to ichiometry)

Minera l Ele- t log(fo2 ) Compos i t i on Dif fus ion coeff icient ment (°C) (a tm) × 1016 (m 2 S- I)

Ol iv ine Fe 1200 - 8.94 F°s9.3 19.1

- - 1100 - 10.01 Fo94 1.34

- Cr 1200 - 8.94 1:7089.3 3.96

Spinel Fe 2+ 1200 - 8 . 9 4 F e 2 + / 5 ' M 2+ = 5 -12% 31.9 - Fe 3+ 1200 - 8 . 9 4 F e 3 + / y . M 3+ = 5 -8% 8.12

- Mg 1200 - 8.94 Mg/Y~M 2+ = 75-80% 9.78

The chromium diffusion into olivine is not sufficiently important to permit the observation of a clear chemical change in the spinel: the chromium content decrease can be hidden by a primitive zonation. Structural formulae calculations show that the decrease of the total iron content on the edge of the

FeO MgO CrzO 3 AIzO $ 15 20 61 12

14

13

12

t t t t t t

t t "t I

SP2811

18 ! I

16

14

i O l l p l t D t l

60

59

58

I t t t l l t t f i t

11

10

9

t I

15

14

13

12

t l t t l t l t

t

SP181t

20

18

16

14

I

!

t t l O l t l t

60

59

58,

57

i t t t t l t I t

12

11

10

9

t l ° l O i ~ q g I

14,

13

12

11

t t t l l t t

t t 20

18

16

SP31221 14

t t t

F | t t t ~ g

62

61

6 0

59

t tt t t t l l tt

12

11

10

9

Fig. 5. FeO, MgO, Cr203, A1203 content (in wt.%) of chromi te gra ins coated wi th forster i te powder as a funct ion of the d i s tance from the edge after a 10-day run at 1200°C and under f o 2 = 10 -9. Before heat ing, the content profi les were a lmost flat; yet, a weak zona t ion in A1203 and in Cr203 somet imes exists but have not a def in i te direct ion. These zonat ions are found again after heat ing. (Mic roprobe analyses are per formed every 10 #m.)

133

chromite grains brings both a decrease in ferrous iron and an increase in ferric iron (Fig. 6). Since there are no other phases apart from olivine and spinel, this increase of the spinel ferric iron content is the condition required for chromium entering in olivine: it has been shown [ l l ] that chromium, when abundant, is

F e 3 + l

030

0.05

i L

0 20{ff#

Fe 2+

O:IG

• I I [ 100

0.05

O t I I I - - loo 2oo~

Fig. 6, Ca l cu l a t ed c o n c e n t r a t i o n s in Fe 3+ a n d Fe 2+ of a

c h r o m i t e g ra in (which was r e -hea ted 10 days a t 1200°C a n d

u n d e r fo~ = 1 0 - 9 in c o n t a c t wi th fors ter i te p o w d e r ) as a func-

t ion of the d i s t ance f r o m the edge.

present in olivine mainly in a bivalent oxidation state. Chromium entering olivine can be described by the reaction:

Mg2SiO 4 + 2 FeCr204 --* Cr2SiO 4 + MgCr204 + MgFe204 ol sp ol sp sp

So, the transformation of trivalent chromium of the spinel into divalent chromium requires the transforma- tion of spinel ferrous iron into ferric iron.

4. Discussion

4.1. Influence of oxygen fugacity

The change of the diffusion coefficients with oxygen fugacity has been shown by the use of two different gas mixtures. Our experiments are in agreement with those of Buening and Buseck [12], who have shown that the iron diffusion coefficient of olivine increases with increasing oxygen fugacity (the range of oxygen fugacity used in their experiments was wider than ours). However, while oxygen fugacity has an effect on diffusion rate, it does not seem to have any effect on the equilibrium chemical composition, since contents measured at 10 # m from the edge are the same for long run durations whatever the gaseous mixtures used.

This can be easily demonstrated if olivine and spinel stoichiometries are supposed to be nearly perfect, this assumption is based on the following considerations:

(1) Deviations from stoichiometry in olivine are at the most in the range of analytical error [13]. So they are very weak in natural systems.

(2) In spinel, deviations from stoichiometry at temperatures not exceeding 1300°C, could only come

134

from an excess of A1203 and of Fe203 [14]. However, activities of these two components (whose values reflect deviations from stoichiometry) are weak in natural spinels.

Assuming that there is nearly no silicon in the spinel lattice and that the tetrahedral sites of olivines are occupied almost entirely by the cations Si n+ (the concentrations of A1, Cr, Mg [11] in the tetrahedral sites are very weak), the conservation of silicon and oxygen atoms numbers implies that oxygen fugacity has no effect on the chemical composition of olivine and spinel at equilibrium as long as no other mineralogical phase appears.

The demonstration is the following: If oxygen fugacity had an effect on the chemical compositions of the two phases at equilibrium, one would be allowed to write a reaction of the following kind:

y O 2 At- E x l X i y j o 4 -1- E xJZJSiO4 ~ ExI 'X i ' y~ '04 .-t- Y~ x~'Z~'SiO 4 (1) i j i ' .1'

- -conservat ion of silicon number:

Ex =Zx j j '

- -conservat ion of the oxygen atoms number:

2y + 4 E x I + 4 E x ~ = 4 E x i ' + 4 E x ~' i j i ' j '

- - f r o m these two relations:

i ' i

i.e. the number of moles of spinel would increase, which is possible only if the number of moles of olivines decreases. But this number remains constant (conservation of Si number), so a reaction such as (1) is impossible.

Nevertheless, oxygen fugacity cannot be imposed upon the employed mineralogical assemblage olivine- spinel in a totally arbitrary way otherwise equilibrium may not be preserved. Preliminary experimental runs under oxygen fugacity (fo2 = 10-45 at 1200°C) have indeed shown that our assemblage's stability field is restricted by the formation of a pyroxene under high oxygen fugacity, according to the following reaction:

02 + 6MgzSiO 4 + 6FeCr204 ~ 6MgCr204 + 6MgSiO 3 + 2Fe304 ol sp sp opx sp

and by the formation of metallic alloy Fe-Ni-Cr under low oxygen fugacity according to the following reaction:

Fe304 ~ 3Fe + 202 sp

4.2. Evaluation of some diffusion coefficients

Rates of re-equilibration reaction between two minerals for a given element A depend on the diffusion coefficients of the element A of each of the two minerals, which participate to the reaction. The diffusion coefficient of an element is characteristic of the mineral in which diffusion occurs. It depends on the composition of the mineral and on the temperature and pressure.

Some of these experiments give us some data on diffusion coefficients in the olivine and in the spinel. Two methods have been used for these calculations [20]:

(1) A method based on the solution of Fick's equation to the plane-sheet or cylindar problem. In this method, which is only applicable to small crystals, the diffusion coefficient is supposed to be independent

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of the concentration of diffusing substance (which is rarely the case). (2) The Bolzmann-Matano method which is applicable only to crystals which are sufficiently wide to

suppose that diffusion occurs only through one crystal face. The computation results are indicated in Table 3. Because of the imprecision of these methods [15], the

reported values are only indicative. They show that Fe diffusivities in olivine and in spinel are in the same range.

4.3. Geothermometry

After Irvine [8], several authors [1,5,6] proposed a geothermometer based on Fe2+-Mg partitioning between coexisting olivine and spinel. All these geothermometers present two noteworthy weaknesses:

(1) The activity expressions for the solid-solution components are far too simple to be realistic. Deviations from ideality of olivine solution [16] and spinel solution are not taken into account.

(2) Calibration of geothermometers is sometimes questionable. The determination of free-energy variation of the reaction, on which geothermometer is based, often comes from results delivered by other geothermometers. Roeder et al. [5] used their experiments to test the best value of the free energy of formation of FeCr204 but they also used Irvine's formulation.

Recently, Sack [21] gives some activity-composition relations for the spinel solid solution and uses these relations to deliver a new olivine-spinel geothermometer. But, his solid-solution model is different from the model we use [17]: for example, the problem of the existence of inversed structures is solved only by expressing spinel composition with five given end-members.

In the two geothermometric expressions proposed here, deviation from ideality is described by using Nafziger and Muan's results [16] for olivine solid solution, which yields to the following expression:

(Mg)2expl, (914 + 3.16p)[1T - (Mg)]2 } [Mg2Si04]ol

(Fe)2exp(. (914 + 3.16p)[1T - (Fe)]2 } [Fe2SiO,]ol

( p in kbar, T in kelvin) and Vannier's model for spinel solid solution, which yields for MgCr204 and FeCr204 activity ratios:

[MgCr204] (Mg) exp{[AG,I(Fe3+)_AG~(A1)] [ (Mg)+(Fe2+) ] 1636[(Fe2+)2- (Mg)2] } [FeCr204 ] (Fe 2+ ) RT + T

where AG] and AG~ are the free-enthalpy variations of the reaction:

FeFe204 + Mger204 ~ FeerzO 4 + MgFe204 aG',/R = 633 - 4.07p (kbar)

FeCr204 + MgA1204 --* FeA1204 + MgCr204 aGJR = 1126 + 6.57p (kbar)

(the ratio AG/R is in kelvin). Our thermometrical relations are based on the following reactions:

Mg2SiO 4 + 2FeCr204 --. Fe2SiO 4 + 2MgCrzO 4 AG 1 ol sp ol sp

Mg2SiO 4 + 2FeAlzO 4 --. Fe2SiO 4 + 2MgAlzO 4 A G 2

ol sp ol sp

(2a)

(2b)

Our experimental runs at 1100°C and 1200°C are considered accurate (after 20 days of heating at 1200°C, all inclusions have reached equilibrium), the calculation at l l00°C is more questionable: all olivine

136

inclusions heated at 1 i00°C are zoned indicating that complete equilibrium was not achieved. Hence, the indicated values are obtained by extrapolation from microprobe profiles. Nevertheless the range of values of the entropy variations is correct for reactions between solid solutions:

AG,/R (K) = 7242 - 1.37T AGJR (K) = 5171 - 1.49T

(The difference between the values of the two entropy changes results from the imprecision in the determination of the free enthalpy variations.)

These two relations associated with the expressions of activities in olivine and in spinel solid solutions yield two geothermometrical equations:

T(K) = {3621 + ([1 - (Fe)o,] 2 - [1 - (Mg)o,]2)(457 + 1.83p) + [AG'l(Fe3+)sp - AG~(al)sp]

X [(Mg)sp + (Fe z+)sp] /R + 1636[(Fe 2+)2sp- (Mg)2p])

x (0.685 + ln([ ( M g ) o , / ( F e ) o , ] / [ (Mg)sp/ (Fe z + )sp ] ) ) - '

T(K) = {2585.5 +( [1 - (Fe)o,] 2 - [1 - (Mg)o,]2)(457 + 1 .83p)+ [AG~(Cr)~p - AG~(Fe3+)sp]

x [(Mg)sp + (Fe 2+)~p]/R + 1636[(Fe 2+)2 _ (Mg)2p]}

× (0.745 + ln([ (Mg)o,/(Fe)o, ] / [ (Mg)~p / (Fe 2 + )sp ] } ) - '

AG~ = - ( A G ' l + AG~) corresponds to FeAlzO 4 + MgFe204 ~ FeFezO 4 + MgA1204. These two equations might give the same temperature for the same minerals pair. Yet the imprecision in

the determination of the free-enthalpy variations will give two different calculated temperatures. One may choose between these equations, for example if the A1203 content of the spinel is known with a better accuracy than the Cr203 content.

4.4. Application

This geothermometer has been applied to some ore samples collected by Moutte [9] from the Ti6baghi Massif. The average temperature, calculated on some pairs included olivines--host chromites, is low: 800°C. So if we assume that the podiform chromitites of the ophiolitic complexes are generated by a magmatic crystallization, a simple interpretation can be given to the low calculated temperature and to the low FeO and high NiO content of the included olivines: they are the result of a subsolidus re-equilibration between olivine and spinel. This hypothesis explains also very well the observed FeO zonation of the included olivines.

The interpretation of the included olivines-chromium zonation is more difficult, assuming a magmatic crystallization. We have seen that there are two arguments--an experimental and a thermodynamic o n e - - t o say that the chromium content of the olivines in equilibrium with chromite increases with increasing temperature. So the explanation of the initial Cr zonation of the included olivines--olivines are enriched in chromium at the edges--cannot be a simple subsolidus re-equilibration. Indeed, if we assume that the podiform chromitites had been produced by a simple magmatic crystallization and that this crystallization was followed by a simple cooling, the chromium content of the olivines included in chromites should decrease at the edges of the inclusions because of the value diffusion coefficient of chromium in olivine (after only 10 days of heating at 1200°C, a change in Cr content of olivines in equilibrium with chromites is clearly observed).

The observed increase of the chromium content cannot be due to a later stage of re-heating because of the low content of the olivines in iron and nickel. Indeed, these two elements diffuse faster than chromium.

137

So the observed Fe and Ni content and iron and chromium zonat ion argues for a model of format ion of

the podiform chromiti te more complicated than a magmatic crystallization followed by a cooling down to low temperature. A later stage of relatively low temperature probably exists in the history of the chromitites

of ophiolitic complexes.

5. Conclusion

Our experiments have shown that Fe, Mg, Ni diffuse in olivine and in spinel down to relatively low temperatures. The chromium diffusion rate in olivine seems to be lower. A geothermometer based upon Fe-Ni par t i t ioning between olivine and spinel would probably record thermal episodes at least as short as those recorded by the geothermometer based upon Fe2÷-Mg part i t ioning.

These observations have many geological implications and must be kept in mind when dealing with the significance of chemical composi t ion of olivine and spinel. For instance, the magnesian composi t ion of

ophiolitic complexes is sometimes explained [22] by the differentiat ion of a basaltic magma conta in ing Mg-rich olivines. But olivines have a high Fe diffusivity and re-equilibrate quickly with spinels (for example

after 10 days of heating at 1200°C). They would re-equilibrate more rapidly with liquids which have a much higher diffusivity and so, very magnesian olivines cannot coexist for a long time with a basaltic

liquid. A n other example is given by the applicat ion to the genesis of podiform chromitite. The olivine-spinel

geothermometer here proposed delivers a low temperature, 800°C, when applied to the ore minerals. But the observed chromium zonat ion of the olivines included in the chromites implies that the genesis of the chromiti tes was not a simple magmatic crystallization followed by a cooling down to low temperatures.

References

1 E.D. Jackson, Chemical variations in coexisting chromite and olivine in the chromitite zones of the Stillwater complex, Econ. Geol., Monogr. 4, 41-71, 1969.

2 B.W. Evans and T.L. Wright, Composition of the chromite of the 1959 (Kilauea Ki) and 1965 (Malaopuki) eruptions of the Kilauea volcano (Hawai), Am. Mineral. 57, 217-230, 1972.

3 B.W. Evans and B.R. Frost, Chrome-spinel in progressive metamorphism: a preliminary analysis, Geochim. Cosmochim. Acta 39, 959-972, 1975.

4 T. Fujii, Fe-Mg partitioning between olivine and spinel, Carnegie Inst. Washington, Geophys. Lab. Yearb. 76, 563-569, 1976. 5 P.L. Roeder, I.H. Campbell and H.E. Jamieson, A re-evaluation of the olivine-spinel geothermometer, Contrib. Mineral. Petrol. 68,

325-334, 1979. 6 J. FabriCs, Spinel-olivine geothermometry in peridotites from ultramafic complexes, Contrib. Mineral. Petrol. 69, 329-336, 1979. 7 E.T. Berger, Enclaves ultramafiques, m~gacristaux et leurs basaltes h6tes en contextes oc6anique (Pacifique Sud) et continental

(Massif Central fran~ais), Th~se h rUniversit~ de Paris-Sud, Centre d'Orsay, 1981. 8 I.N. Irvine, Chromian spinel as a petrogenetic indicator, I. Theory, Can. J. Earth Sci. 2, 648-672, 1965. 9 J. Moutte, Le massif de Ti6baghi, Nouvelle Cal~donie, et ses gites de chromites, Th~se Docteur-lng~nieur, Ecole des Mines, Paris,

1979. 10 Z. Johan and L. Le Bel, Sur la gen~se des couches et des podes de chromite dans les complexes ophiolitiques, R~sum~ des

principaux r6sultats scientifiques et techniques du S.G.N. pour 1978, pp. 96-99, B.R.G.M., Paris, 1978. 11 J. Lehmann, Equilibrage en subsolidus du couple olivine-spinelle. Application aux chromitites de Nouvelle Cal~donie, Th~se

Docteur-Ing~nieur, Ecole des Mines, Paris, 1981. 12 D.K. Buening and P.R. Buseck, The pO 2 dependence of vacancy formation in olivine, EOS, Trans. Am. Geophys. Union 54, 498,

1973. 13 T. Mori and D.H. Green, Subsolidus equilibria between pyroxenes in the CaO-MgO-SiO 2 system at high pressures and

temperatures, Am. Mineral. 61,616-625, 1976. 14 G.C. Ulmer, Experimental investigation of chromite spinels, Econ. Geol., Monogr. 4, 114-131, 1969. 15 A. Jambon, Diffusion cationique dans les silicates fondus: ~tude exp6rimentale et modules p6trologiques, Th~se h l'Universit~

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d'Orl6ans, U.E.R. des Sciences Fondamentales et Appliqu~es, 1980. 16 R.H. Nafziger and A. Muan, Equilibrium phase compositions and thermodynamic properties of olivines and orthopyroxenes in the

system MgO-"FeO"-SiO 2, Am. Mineral. 52, 1364-1385, 1967. 17 M. Vannier, Mod61isation de la solution spinelle naturelle, Bull. Soc. Fr. Min6ral. Cristallogr. 100, 239-245, 1977. 18 B.J. Wood and S. Banno, Garnet-orthopyroxene-clinopyroxene relationships in simple and complex systems, Contrib. Mineral.

Petrol. 42, 109-124, 1973. 19 Y. Adda and J. Philibert, La Diffusion dans les Solides, I, P.U.F., Paris, 1966. 20 B.J. Wood and J. Nicholls, The thermodynamic properties of reciprocal solid solutions, Contrib. Mineral. Petrol. 66, 389-400,

1978. 21 R.O. Sack, Spinels as petrogenetic indicators: activity-composition relations at low pressures, Contrib. Mineral. Petrol. 79,

169-186, 1982. 22 J. Moutte, Chromite deposits of the Ti~baghi ultramafic massif, New Caledonia, Econ. Geol. 77, 576-591, 1982.