Full text of DOI:10.1007/s004100000140

Contrib Mineral Petrol *2000) 140: 84±98
Ó Springer-Verlag 2000
Stephan Klemme á Hugh StC O'Neill
The effect of Cr on the solubility of Al in orthopyroxene:
experiments and thermodynamic modelling
Received: 9 August 1999 / Accepted: 18 February 2000
Abstract The partitioning of chromium and aluminium where nAl and nCr are the number of Al and Cr cations
between coexisting orthopyroxene and spinel in equi- per orthopyroxene formula unit of six oxygens. These
librium with forsterite in the system MgO±Al2O3±SiO2± expressions reduce to one-site mixing for Mg2Si2O6±
Cr2O3 *MAS±Cr) has been experimentally determined as MgAl2SiO6 orthopyroxenes in the Cr-free system, but
a function of temperature, pressure and Cr/*Cr + Al) are equivalent to two-site mixing for the exchange of Al
ratio. Experiments were conducted at temperatures be- and Cr between orthopyroxene and spinel, as required
opx
EM
opx
EC
tween 1300 and 1500 °C and at pressures from 5 to by the experimental data. We ®nd W
54 kbar. Previous experimental results on the *Al, Cr)2O3 20 kJ mol)1 and WMopCx ˆ 0.
and Mg*Al, Cr)2O4 solid solutions have been combined
ˆ W
ˆ
with the present results plus relevant data from the
CMAS system to derive a thermodynamic model for Al± Introduction
Cr-bearing orthopyroxenes, spinels and corundum±esk-
olaite solid solutions. The orthopyroxene solid solution More than 90% of the Earth's mantle is made up of the
can be modelled within the accuracy of all experimental four oxide components CaO, MgO, Al2O3 and SiO2 *e.g.
constraints as a ternary solid solution involving the O'Neill and Palme 1998), and therefore the simple sys-
components Mg2Si2O6 * E), MgAl2SiO6 *M) and tem CaO±MgO±Al2O3±SiO2 *CMAS) is often consid-
MgCr2SiO6 *C), in which the activities are related to ered to make an excellent starting point for modelling
composition through the equations:
mantle phase equilibria. However, many of the impor-
tant details of mantle processes depend on the behaviour
of the additional minor components, one of the most
signi®cant of which is Cr2O3.
opx
Mg2Si2O6
2
2
RT lnꢀa
† ˆ RT lnꢀXEopx† ‡ W opxꢀXEopx† ‡ W opxꢀXCopx
†
EM
EC
‡ ꢀW opx ‡ W opx À W opx†XMopxXCopx
EM
EC
MC
Natural spinel lherzolites and garnet lherzolites con-
tain on average about 2600 ppm chromium *O'Neill and
Palme 1998). At typical terrestrial oxygen fugacities,
nearly all of this chromium is in the trivalent oxidation
state. Cr3+ is known to partition strongly among the
major upper mantle phases, as illustrated by analyses of
coexisting phases in a ®ve-phase lherzolite xenolith
*Table 1). The spinel in this example contains ꢁ18 wt%
Cr2O3, while the coexisting pyroxenes contain 0.5 and
1.2 wt% Cr2O3. However, because the pyroxenes are
modally more abundant than the spinel, quite a large
percentage of the bulk-rock chromium is contained in
the pyroxenes. Clearly, an adequate thermodynamic
model for Cr in mantle rocks requires knowledge of the
properties of Cr-bearing pyroxenes.
ꢀ
ꢁ
opx
MgAl2SiO6
2
RT lnꢀa
† ˆ RT ln ꢀXMopx†2=ꢀXMopx ‡ XCopx
†
‡ W opxꢀXEopx
†
EM
‡ W opxꢀXCopx† ‡ ꢀW opx ‡ W opx À W opx†XEopxXCopx
2
MC
EM
MC
EC
ꢀ
ꢁ
opx
MgCr2SiO6
2
RT lnꢀa
† ˆRT ln ꢀXCopx†2=ꢀXMopx ‡ XCopx
†
‡ W opxꢀXMopx
†
MC
‡ W opxꢀXEopx† ‡ ꢀW opx ‡ W opx À W opx†XMopxXEopx
2
EM
EC
MC
EC
The mole fractions are de®ned as
XEopx ˆ ꢀ1 À nAl=2 À nCr=2†; Xopx ˆ ꢀnAl=2† and Xopx ˆ ꢀnCr=2†;
M
C
S. Klemme *&)1 á H. StC O'Neill
Research School of Earth Sciences, The Australian National
University, Canberra, ACT 0200, Australia
e-mail: Stephan.Klemme@Bristol.ac.uk
An example of this need is provided by the recent
work of Asimov et al. *1995) on melt productivity along
the solidus of mantle peridotite. Their results indicated
that melting may cease during adiabatic mantle upwel-
ling as the boundary between garnet lherzolite and spinel
Present address:
1 Department of Earth Sciences,
Wills Memorial Building, Queen's Road, Bristol, BS8 1RJ, UK
Editorial responsibility: J. Hoefs

85
Table 1 Spinel±garnet lherzolite
± Ming-Xi *China). Mineral
negligible *in olivine and spinel). The addition of Na2O
to the system similarly has negligible e€ect.
analyses of a garnet±spinel-bearing lherzolite from China *Ming-
Xi, province; Ai 1992) are depicted. Cr is concentrated in the spinel
phase, which is abundant in only minor modal amounts. Modal
amounts were calculated from bulk-rock analyses and mineral
analyses *Ai 1992)
Equilibrium *1) has been used as a geothermometer in
the spinel lherzolite facies *e.g. Gasparik and Newton
1984; Witt-Eickschen and Seck 1991). However, the re-
placement of Al by Cr in orthopyroxene probably exerts
a large in¯uence, and this has not been allowed for in the
calibrations of this equilibrium as a geothermometer.
From an experimental point of view, the e€ect of Cr
on the Al content of orthopyroxene should be most
obvious where the amount of Al in the orthopyroxene is
greatest, which is at high temperatures, and in the spinel
lherzolite facies, rather than in the garnet lherzolite
facies. For example, the solubility of Al2O3 in orthopy-
roxene in the Cr-free system CMAS is about 8 wt% at
15 kbar and 1200 °C in equilibrium with spinel, but only
about 1.5 wt% at 40 kbar at the same temperature, in
equilibrium with garnet. Hence we have concentrated
our experimental e€ort on reaction *1) rather than the
possible alternative reaction:
Spinel
Garnet
Olivine
opx
cpx
MgO
Al2O3
Cr2O3
FeO
SiO2
Modal
20.1
49.9
17.9
11.4
±
20.7
23.1
1.5
7.0
42.2
7.3
49.1
±
32.8
4.6
15.9
6.0
±
0.5
5.9
55.6
15.8
1.2
2.8
52.9
11.9
9.3
41.1
64.5
0.7
lherzolite is crossed. However, this result depends criti-
cally on the width of the garnet±spinel transition, which
cannot at present be modelled accurately for lack of data
on the partitioning of Cr into the pyroxenes.
In this study we investigate the e€ect of Cr on the
solubility of Al in orthopyroxene in equilibrium with
spinel and olivine in the system MgO±Al2O3±SiO2±
Cr2O3 *MAS±Cr) as a ®rst step towards a better un-
derstanding of the in¯uence of this element on upper
mantle phase relations. A series of subsolidus experi-
ments was conducted followed by thermodynamic
analysis of the experimental results. These data were
then combined with results in the system CaO±MgO±
Al2O3±SiO2 *CMAS) *Klemme 1998; Klemme and
O'Neill 2000), to produce an internally consistent ther-
modynamic model that enables calculation of phase re-
lations in Cr-bearing systems.
Mg3Al2Si3O12
garnet
ˆ
MgAl2SiO6
orthopyroxene orthopyroxene
‡
Mg2Si2O6
ꢀ3†
that controls the solubility of alumina in orthopyroxene
in equilibrium with garnet. However, the results of the
present study should be applicable to garnet-bearing
equilibria provided the thermodynamics of Cr-bearing
garnets are suciently well understood.
Experimental and analytical techniques and procedures
All high-pressure, high-temperature experiments but one were
performed in a conventional piston-cylinder apparatus *Boyd and
England 1960) at temperatures from 1300 to 1500 °C and pressures
between 0.5 and 4.0 GPa, using a 0.5-inch-diameter pressure as-
sembly. The assembly consists of two inner parts of MgO *66%
density) above and belowthe capsule, surrounded by three con-
centric shells: a graphite heater, a glass tube *Pyrex) and an out-
ermost sleeve of NaCl, pressed to >95% of the theoretical density.
Starting materials were sealed in platinum capsules, which were
insulated from the graphite heater by a small Al2O3 sleeve, and
separated from the thermocouple tip by a 0.5 mm Al2O3 disc. The
sample was placed in the hot spot of the assembly, the location of
which has been found in previous studies *W.O. Hibberson, per-
sonal communication).
Thermodynamic background
The solubility of Al and Cr in orthopyroxene in equi-
librium with olivine and spinel in the system MAS±Cr
may be described by two equilibria:
MgAl2O4
spinel
‡ Mg2Si2O6
orthopyroxene
ˆ
MgAl2SiO6
orthopyroxene
‡
Mg2SiO4
olivine
ꢀ1†
MgAl2O4
‡
MgCr2SiO6
spinel orthopyroxene
ˆ
MgCr2O4
spinel
‡
MgAl2SiO6
orthopyroxene
ꢀ2†
Equilibrium *1) describes the solubility of alumina in
orthopyroxene in equilibrium with spinel and olivine run pressure, temperatures did generally not exceed 750 °C to
while equilibrium *2) describes the exchange of Al and
Cr between coexisting spinel and orthopyroxene. Equi-
librium *1) has been experimentally investigated in the
Runs were performed using the ``piston-out'' routine. First, a
pressure of ꢁ2.5 kbar was applied. Then the sample was heated up
to 550 °C to soften the glass. During the compression to the ®nal
prevent deformation of the graphite heater. The pressure was then
raised to approximately 1 kbar higher than the ®nal run value, and
then lowered to run value when the ®nal run temperature was
achieved. Pressure was kept constant during runs to within
systems MgO±Al2O3±SiO2 *MAS) *e.g. Gasparik and
Newton 1984), CMAS *e.g. Fujii 1977; Gasparik 1984;
Sen 1985; Klemme 1998; Klemme and O'Neill 2000) and
Na2O±CMAS *NCMAS; Walter and Presnall 1994).
The addition of CaO to the MAS system should have
negligible e€ect on this reaction, since substitution of
CaO into the phases partaking in the reaction is either
minor *i.e. orthopyroxene, in which phase its e€ect tends
to cancel out across the reaction since orthopyroxene
‹0.2 kbar, by manual adjustment if necessary. In keeping with
usual practice for piston-cylinder assemblies with NaCl sleeves, no
correction for friction was applied *e.g. Johannes et al. 1971;
Mirwald et al. 1975; Bose and Ganguly 1995). A check on the
pressure calibration of our assembly, using the fayalite±ferrosilite±
quartz univariant equilibrium at 1050 °C, was reported in Klemme
and O'Neill *1997).
As regards friction corrections in piston-cylinder apparatus,
Bose and Ganguly *1995) have shown that friction decays with time
during an experiment. Moreover, these authors point out ``Since
the shear strength of the salts decreases with increasing tempera-
components occur on both sides of the reaction), or ture, the extent of friction correction should change with temper-

86
ature'' *Bose and Ganguly 1995, p. 233). Bose and Ganguly *1995) relative to Pt90Rh10 or Pt87Rh13 which is considerably greater than
also are of the opinion that friction may depend on the rate of the change of Pt94Rh6 relative to Pt70Rh30 *Brodowsky et al. 1998).
compression or decompression. At higher pressures, bulging of the
W±Re thermocouples have become increasingly popular for
piston may become important, a source of friction quite unrelated piston-cylinder experiments since Williams and Kennedy *1969)
to the nature of the pressure assembly used. Clearly the historical and Presnall et al. *1973) demonstrated their resistance to con-
practice of applying a simple percentage correction to nominal tamination in the piston-cylinder environment. Mao and Bell
pressures in piston-cylinder experiments is inappropriate. A more *1970), Mao et al. *1971), and Presnall et al. *1973) compared W±
realistic approach to the friction problem is to use a low-friction Re thermocouples with type S *Pt±Pt90Rh10) thermocouples, all
pressure medium, such as NaCl, while also running for sucient ®nding that the W±Re thermocouples su€ered less drift from
lengths of time that the friction decays. Bose and Ganguly *1995) contamination. It is important to note that even for the type S
have demonstrated decay of friction from 6.5% to zero in 30 h for thermocouples, signi®cant contamination e€ects *thermocouple
their 0.5-inch cell, at temperatures far belowthose of this study.
drift) were only observed at 1600 °C or above, provided that the
Consequently, because of the relatively long run times at high thermocouples were shielded by high-purity alumina, as used in this
temperatures used in this study, we believe that possible errors in study. For example, Presnall et al. *1973) report drift rates of
pressure due to friction are only very small. Finally we note that the 1 °C h)1 at 1600 °C. Thus, we would not have expected signi®cant
phase relations addressed in this study are not sensitive to pressure, drift by contamination in the experiments reported here even if we
and that quite large errors in pressure would have little e€ect on the had used type S thermocouples, since our highest temperature ex-
interpretation of our results.
periments are at 1500 °C, for 24 h *cf. Presnall et al. 1973, their
The run at 5.4 GPa was performed in a piston-cylinder appa- ®g. 5). Type B thermocouples have not, to our knowledge, been
ratus, which we have developed recently at the RSES to exploit similarly compared against W±Re thermocouples in the piston-
newly available grades of tungsten carbide with high compressional cylinder apparatus. At ambient pressure in an argon atmosphere,
strength. The pressure assembly was of similar design to those used Glawe and Szaniszlo *1972) found that the drift of type B ther-
in the conventional piston-cylinder runs, but with a CaF2 outer mocouples at 1327 °C was actually about half that of W±Re *or
sleeve, rather than NaCl. The length of the assemblage was tailored type S thermocouples).
carefully to ensure that only a small length of the piston remained
Although they may be more resistant to contamination, W±Re
unsupported outside the pressure vessel after ®nal compression. thermocouples su€er from several disadvantages, the most serious
The run was initially compressed to a nominal pressure of 6.0 GPa. of which is that their performance *i.e. emf vs. temperature char-
Decay of friction was then monitored by measuring the piston acteristics) is often far di€erent from the theoretical. We have tested
displacement using a transducer. Steady state conditions *i.e. both several batches of W97Re3±W75Re25 plus one batch of W95Re5±
no further piston displacement, and no change in oil pressure to the
piston), implying decay of most of the initial friction, was reached last 4 years, by comparing them from 800 to 1400 °C directly
at 5.4 GPa after about 72 h. against calibrated type S and type B thermocouples, at ambient
To check whether Cr2+ was present in the experiments at suf- pressure in a gas-mixing furnace, in argon and argon±10% hy-
®cient concentrations to in¯uence matters, a fewruns were con- drogen atmospheres. The W±Re thermocouples have been in error
W74Re26 thermocouple wire from various manufacturers over the
ducted with an internal Re±ReO2 bu€er to generate a high oxygen by up to 75 °C at 1400 °C, and no batch was closer to the theo-
fugacity environment, approximately midway between the Ni±NiO retical calibration than 10 °C at 1400 °C. Moreover, thermocou-
and the Fe3O4±Fe2O3 bu€ers *Pownceby and O'Neill 1994b). The ples made from the same spools of wire have been found to di€er
Re±ReO2 bu€er consisted of a ®ne-grained mixture of 50 mol% by up to 15 °C at 1400 °C. From switching legs from the various
Re-metal with 50 mol% ReO2. Neither Re nor ReO2 reacted with batches of wire, we deduce that it is the thermoelectric coecient of
the phases of interest in the experiments, hence the bu€er mixture the W97Re3 leg which is primarily to blame. The W97Re3 wire is
was mixed in with the starting materials. Results from the bu€ered manufactured with additions of alumina and silica plus other oxide
runs were indistinguishable from unbu€ered experiments, indicat- components that form an intergranular melt, to prevent recrystal-
ing no signi®cant Cr2+ in the experiments. Another item of evi- lization and grain growth, which would cause the wire to become
dence against the presence of signi®cant Cr2+ in all experiments is unusably brittle. However, this process can result in large compo-
the lack of detectable Cr in olivine *detection limit ꢁ600 ppm Cr sitional inhomogeneities in the W/Re ratio of the wire on the scale
with EDS and 150 ppm with WDS on the electron microprobe at of electron microprobe analysis. When a thermocouple is so far o€
RSES; Ware 1991).
its target performance, it is dicult to invest much trust in its
behaviour.
Temperature measurement
As an additional test of the performance of type B thermo-
couples, a number of piston-cylinder experiments have been un-
Temperatures were measured with Pt94Rh6±Pt70Rh30 thermocou- dertaken in our laboratory, at temperatures between 1350 and
ples *type B) inserted axially into the assembly inside two-bore
high-purity Al2O3 tubing. Possible pressure e€ects on the emf of W75Re25 thermocouples were used simultaneously *Klemme and
1400 °C and various pressures, in which both type B and W97Re3±
thermocouples were neglected. The temperature uncertainties are
estimated to be less than ‹15 °C in the temperature range of the thermocouples were inserted axially into the assembly as custom-
present experiments.
Several thermocouples made from the same spools of wire as the order of 10 °C during the ®rst fewhours, no drift of one
used in the piston-cylinder experiments were tested against the
melting point of Au at atmospheric pressure, returning an apparent to 400 h. The initial change we surmise is due to annealing of the
O'Neill 2000; U.H. Faul, personal communication, 1999). The
ary, using four-bore alumina. We ®nd that after an initial change of
thermocouple relative to the other is observable in runs lasting up
temperature of 1064 ‹ 1 °C, in good agreement with the recom-
mended ITS-90 ®xed point of 1064.2 °C *e.g. McGlashan 1990).
Type B thermocouples are much more resistant to the e€ects of
W97Re3±W75Re25 wires *Burns and Hurst 1972); we note that
Burns and Hurst *1972) recommend annealing of W±Re wires at
2400 K for 1 h in argon, a procedure admittedly not followed in
contamination at high temperature than the more commonly used our *or, we suspect most other) experimental petrology laborato-
Pt±Pt90Rh10 *type S) or Pt±Pt87Rh13 *type R) thermocouples, un-
der both oxidizing and reducing conditions *Metcalfe 1950; Walker
et al. 1962; Brodowsky et al. 1998), although they are somewhat
ries.
We have also found that the high-purity alumina used for the
thermocouple insulator in our experiments is suciently strong to
less sensitive. The reason for the superior performance under re- resist complete collapse even up to 10 kbar, resulting in signi®cant
ducing conditions of type B thermocouples compared to those with
a pure Pt leg is that the e€ect of impurities on the thermoelectric top of the assembly. Lastly, type B thermocouples possess the
oxidation of the W±Re wires in the vicinity of the steel plug at the
coecient of Pt±Rh alloys is a markedly non-linear function of Pt/
Rh composition. Therefore, a contaminating element such as Al or thermoelectric emf varies only between )2.5 and 2.5 lV, such that
B produces a change in the thermoelectric coecient of pure Pt
convenient characteristic that, over the range 0 to 50 °C, their
the temperature of the reference junction is unimportant.

87
In summary, we believe that type B thermocouples o€er the conducted by heating to 1700 °C for 5 min *to induce melting),
best prospect of accurate temperature measurement in piston-cyl- then cooling at 2 °C/min to 1550 °C, at which temperature the run
inder experiments in the range 1300 to 1500 °C, the range of the was held for 10 h. The sample was then cooled at a rate of 1 °C/min
present study. While W±Re thermocouples are clearly required at down to 1300 °C, resting at 1300 °C for 24 h before quenching.
temperatures in excess of 1800 °C *i.e. near to and above the
Preliminary experiments established that the Cr partitioning
melting point of Pt-rich alloys), whether they are preferable to reactions proceed sluggishly. To evaluate the run durations needed
type B thermocouples in the intermediate range 1500 to 1800 °C for attainment of equilibrium in the experiments, series of experi-
requires further study.
ments were conducted with di€erent run times. At 1400 °C run
The importance of the choice of thermocouple in the present durations of >120 h were found to be necessary to produce
experiments is that the reliability of the type B thermocouples per- homogenous mineral compositions *Table 3). Experiments at
mits long run times. For example, our run times of up to 400 h at 1300 °C had to be run for several weeks, but even then the mineral
1300 °C are nearly an order of magnitude longer than the times used analyses showed larger scatter than at higher temperatures
by Gasparik and Newton *1984) of 45.5 to 47 h at the same tem- *Table 4). Attempts at 1200 °C produced only inhomogeneous
perature in the Cr-free MAS system, and over two orders of mag- pyroxenes and are not reported.
nitude longer than the times used by Perkins et al. *1981) of 1 to 3 h.
Analytical procedures
Starting materials
Experimental run products were cut into halves using a low-speed
The starting mixtures *Table 2) consisted of mechanical mixes of
diamond sawand mounted in epoxy resin for electron microscopy
synthetic crystalline materials, mostly Mg*Cr,Al)2O4 spinel solid
and microprobe analysis. Mounts were polished in several steps
solutions, Mg2Si2O6 orthoenstatite and Mg2SiO4 forsterite. The
using sandpaper and diamond paste of di€erent grain sizes. The
starting mixture SM11, used for reversals, contained no forsterite.
Spinels were synthesized at 1500 °C at atmospheric pressure
under ¯owing CO2 which produces a slightly reduced environment
®nal polish was performed with 0.3 lm Linde B polishing powder.
to prevent any oxidation of Cr3+ to Cr4+. Mg2Si2O6 *clinoensta-
tite) was synthesized at 1100 °C at atmospheric pressure in air. This Table 3 Experimental runs in the system MgO±Al2O3±SiO2±
material transforms rapidly to orthoenstatite at high pressures. Cr2O3. Experimental run conditions and starting material are listed
These synthesis experiments were carried out for ꢁ24 h. Forsterite for each experiment. See text for details. P Pressure *kbar), T
*Mg2SiO4) was synthesized from MgO and SiO2 using a Li2WO4 temperature *°C), t run duration *h). spl spinel, ol olivine, opx or-
¯ux, with a ¯ux:oxide ratio of 4:1 by weight. The ¯ux:oxide mixture thopyroxene, gar garnet
was held for 6 days at 1050 °C in a Pt crucible, before cooling to
Run no.
P
T
t
*h)
Starting Phases
material present
room temperature and removing the ¯ux by dissolution in warm
water with the aid of ultrasonic agitation.
*kbar) *°C)
Most experiments approached equilibrium as regards ortho-
pyroxene compositions from the Cr- and Al-poor side, since the
orthopyroxene in the starting materials was pure Mg2Si2O6.
Equilibrium in such experiments is indicated if, ®rstly, a change in
orthopyroxene compositions is observable *which is sucient to
clarify that di€usion rates are fast enough to cause change), and,
secondly, if the ®nal orthopyroxenes and also the other solid so-
lution phases *here, spinel) are homogenous in composition. All
experiments reported here ful®l these dual criteria. Two quasi-re-
versal experiments were also performed to further con®rm the
achievement of equilibrium. These experiments contained a mixture
of two di€erent starting pyroxenes *SM47), one with high Al2O3
and Cr2O3 content, the other the pure Mg2Si2O6. Analyses of the
run products indicated that both types of pyroxenes converge
completely onto a single population in the run product. The high
Al/Cr orthopyroxene in SM 47 was crystallized from a melt at
19 kbar in a 5/8-inch piston-cylinder apparatus. The synthesis was
C 301-S 38
C 297-S 36
C 586-S 114 I
C 587-S 114-II 25
C 598-S 118-I 10
C 599-S 118-II 10
C 517-S101-I 10
UHP 28-S 126 54
C 543-S 104-I 40
C 544-S 104-II 40
C-545-S 104-III 40
C 299-S 37
C 576-S 111-I
C 577-S 111-II 35
C 623-S 123-I 35
C 624-S 123-II 35
C 233-S 22
C 587-S 115-I
C 588-S 115-II 24
C 591-S 116-I 20
C 592-S 116-II 20
C 724-S 130
C 730-S 131
C 326-S 50
C 577-S 112-I
C 578-S 112-II 10
C 618-S 122-I
C 689-S 127-I
C 690-S 127-III
C 329-S 51
C 596-S 117-I
C 597-S 117-II 35
C 323-S 47
C 578-S 113-I
C 579-S 113-II 25
40
25
25
1300 244 11
1300 260 11
1300 360 41
1300 360 42
1300 400 42
1300 400 41
1300 240 35
1400 120 50
1400 120 16
1400 120 34
1400 120 35
1400 144 11
1400 120 41
1400 120 42
1400 120 47
1400 120 50
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx, gar
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx, gar
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
spl, ol, opx
35
35
24
24
1400
24 11
1400 120 42
1400 120 41
1400 150 41
1400 150 42
1400 120 53
1400 120 53
1400 120 16
1400 120 42
1400 120 41
1400 120 41
1400 122 50
1400 122 47
Table 2 Starting materials. All starting material mixtures con-
tained synthetic Mg2SiO4 as well as Mg2Si2O6 with the exception of
SM 11 *no Mg2SiO4). SM 47 contained two starting pyroxenes:
pure enstatite as well as an orthopyroxene with ꢁ10 wt% Al2O3
and 0.8 wt% Cr2O3. See text for details and notes on the synthesis
of the starting materials
20
15
10
10
5
5
5
35
35
Mixture
Spinel
Bu€er
SM 11
SM 16
SM 34
SM 35
SM 41
SM 42
SM 47
SM 50
SM 53
Mg*Cr0.5Al0.5)2O4
Mg*Cr0.5Al0.5)2O4
Mg*Cr0.46Al0.54)2O4
Mg*Cr0.57Al0.43)2O4
Mg*Cr0.8Al0.2)2O4
Mg*Cr0.2Al0.8)2O4
Mg*Cr0.46Al0.54)2O4
Mg*Cr0.9Al0.1)2O4
Mg*Cr0.1Al0.9)2O4
±
±
±
±
1500
1500
1500
1500
1500
1500
1500
1500
24 11
24 42
24 41
24 11
24 41
24 42
24 50
24 11
25
25
±
±
Re±ReO2
±
±
C 685-S 124
C 325-S 49
15
10

88
Table 4 Analytical results. Cr # ꢀbulk) is Cr/*Cr+Al) in starting indicate uncertainties. For example, 1.759*18) must be read as
material. T temperature in *°C). P pressure in *kbar). Numbers 1.759‹0.018. At least ten analyses were done for each phase in
showaverage analyses for each phases, numbers in brackets
every experiment
P *kbar) 40
T *°C) 1300
Cr # *bulk) 50
25
1300
50
25
1300
80
25
1300
20
OPX
S 38
SPI
S 38
OPX
S 36
SPI
S 36
OPX
S 114-I
SPI
S 114-I
OPX
S 114-II
SPI
S 114-II
SiO2
57.1*4)
0.4*2)
57.7*4)
2.7*5)
1.6*2)
38.0*3)
100.0
0.5*4)
59.4*7)
0.9*1)
1.4*1)
39.1*6)
100.8
0.4*2)
56.6*7)
5.9*9)
1.2*3)
37.2*5)
100.9
0.6*1)
53.0*14)
20.5*17)
25.8*4)
99.9
Al2O3
Cr2O3
MgO
Totala
3.2*2)
1.9*1)
37.6*2)
99.8
28.1*6)
45.8*9)
22.8*3)
97.1
28.0*7)
45.9*8)
22.8*2)
97.2
10.2*8)
66.0*7)
20.9*3)
97.5
Si
Al
Cr
Mg
Total
1.923*4)
0.128*7)
0.051*1)
1.885*4)
3.987*1)
0.012*5)
0.954*19)
1.043*20)
0.981*9)
2.990*3)
1.937*14) 0.013*12)
0.106*21) 0.950*23)
0.043*6) 1.046*19)
1.902*14) 0.980*6)
3.988*2) 2.989*3)
1.976*4)
0.013*5)
0.374*28)
1.626*25)
0.974*7)
2.987*2)
1.881*21)
0.014*2)
1.584*34)
0.412*34)
0.977*6)
2.987*3)
0.037*5)
0.037*2)
1.938*5)
3.987*2)
0.232*37)
0.032*7)
1.842*24)
3.987*3)
P *kbar) 10
T *°C) 1300
Cr # *bulk) 20
10
1300
80
10
1300
57
54
1400
90
OPX
S 118-I
SPI
S 118-I
OPX
S 118-II
SPI
S 118-II
OPX
S101-I
SPI
S101-I
OPX
S 126
SPI
S 126
SiO2
57.2*10)
4.3*10)
1.1*3)
38.0*6)
100.6
0.5*1)
50.6*6)
21.4*7)
25.5*2)
98.0
59.6*7)
0.7*2)
1.3*2)
39.6*5)
101.2
0.4*0)
11.0*7)
64.6*5)
20.7*7)
96.7
58.3*6)
0.3*1)
59.3*6)
0.8*2)
1.3*1)
39.2*4)
100.6
0.6*1)
4.6*1)
72.1*6)
20.4*4)
97.7
Al2O3
Cr2O3
MgO
Total
1.3*4)
1.2*3)
38.5*6)
99.3
22.7*30)
50.5*28)
21.9*5)
95.4
Si
Al
Cr
Mg
Total
1.909*24) 0.013*1)
0.168*40) 1.549*14)
1.975*5) 0.012*2)
0.027*7) 0.407*21)
0.035*6) 1.598*30)
1.957*13) 0.967*21)
3.994*5) 2.985*7)
1.969*11)
0.053*16)
0.032*7)
1.936*16)
3.990*6)
0.010*2)
0.802*87)
1.199*86)
0.980*9)
2.990*3)
1.978*7)
0.020*2)
0.171*4)
1.820*17)
0.973*17)
2.984*5)
0.040*8)
0.035*4)
1.947*13)
3.990*6)
0.028*7)
1.887*27) 0.990*3)
3.992*7) 2.992*1)
0.440*14)
P *kbar)
T *°C)
Cr # *bulk) 50
40
1400
40
1400
46
OPX
S 104-II
40
1400
57
OPX
S 104-III
35
1400
50
OPX
S 37
OPX
S 104-I
SPI
S 104-I
SPI
S 104-II
SPI
S 104-III
SPI
S 37
SiO2
57.1*11)
4.6*4)
2.6*6)
38.1*6)
102.4
0.4*1)
29.8*16)
47.2*16)
23.9*2)
101.3
55.7*4)
4.9*2)
2.3*3)
36.9*8)
99.8
0.7*2)
33.8*66)
39.8*70)
23.9*10)
98.2
56.6*7)
3.8*2)
2.3*2)
37.7*4)
100.4
0.6*4)
22.9*17)
52.4*18)
22.3*6)
98.2
56.7*15)
3.9*1)
2.3*1)
37.5*4)
100.4
0.5*2)
28.0*8)
47.0*11)
23.2*3)
98.7
Al2O3
Cr2O3
MgO
Total
Si
Al
Cr
Mg
Total
1.878*21) 0.012*4)
0.180*15) 0.968*45)
0.068*15) 1.028*39)
1.879*8) 0.019*5)
0.193*6) 1.103*176)
0.063*8) 0.880*176)
1.859*19) 0.988*9)
3.994*9) 2.990*3)
1.896*7)
0.018*10)
1.901*15)
0.014*5)
0.937*26)
1.055*25)
0.984*7)
2.990*2)
0.151*7)
0.061*4)
1.890*9)
3.998*4)
0.788*47)
1.208*57)
0.970*12)
2.984*6)
0.154*8)
0.061*2)
1.876*20)
3.992*11)
1.871*6)
3.997*7)
0.981*5)
2.989*2)
P *kbar) 35
T *°C) 1400
Cr # *bulk) 80
35
1400
20
35
1400
46
35
1400
90
OPX
S 111-I
SPI
S 111-I
OPX
S 111-II
SPI
S 111-II
GAR
S 111-II
OPX
S 123-I
SPI
S 123-I
OPX
S 123-II
SPI
S 123-II
SiO2
59.3*2)
0.5*0)
9.7*4)
66.8*13)
20.4*4)
97.4
55.5*10)
0.6*1)
50.8*13)
20.7*13)
24.9*4)
97.0
43.9*12)
23.1*5)
4.0*8)
29.4*5)
100.4
55.9*7)
5.4*8)
2.0*3)
38.7*56)
101.9
0.6*1)
59.7*6)
0.7*1)
1.6*3)
39.8*5)
101.8
0.4*1)
5.6*3)
72.8*25)
21.7*13)
100.5
Al2O3
Cr2O3
MgO
Total
1.0*1)
1.5*3)
37.9*5)
99.7
6.6*7)
1.5*3)
36.1*8)
99.7
32.1*7)
42.2*6)
23.7*3)
98.6
Si
Al
Cr
Mg
Total
1.992*11) 0.014*1)
0.041*3)
0.040*7)
1.895*15) 0.951*11)
3.968*8) 2.978*4)
1.867*18) 0.016*2)
0.262*27) 1.567*27)
0.041*8) 0.429*27)
1.812*33) 0.973*2)
3.982*12) 2.985*1)
2.973*75)
1.853*74)
0.209*33)
0.052*8)
1.902*164)
4.016*79)
0.015*2)
1.057*15)
0.933*19)
0.985*8)
2.990*3)
1.969*9)
0.028*5)
0.042*8)
1.956*8)
3.995*4)
0.013*3)
0.358*15)
1.655*19)
1.842*33)
0.215*43)
2.968*66)
7.998*47)
0.203*16)
1.780*26)
1.001*34)
2.997*12)

89
Table 4 *Contd.)
P *kbar) 24
T *°C) 1400
Cr # *bulk) 50
24
1400
20
24
1400
80
20
1400
80
OPX
S 22
SPI
S 22
OPX
S 115-I
SPI
S 115-I
OPX
S 115-II
SPI
S 115-II
OPX
S 116-I
SPI
S 116-I
SiO2
58.0*8)
3.2*7)
2.0*3)
37.9*4)
101.1
0.7*3)
56.0*8) 0.7*1)
6.5*10) 51.8*15)
59.9*5)
0.9*2)
1.5*2)
38.8*6)
101.1
0.4*1)
9.4*4)
67.7*9)
20.6*5)
98.1
59.0*3)
1.1*2)
1.6*2)
38.6*3)
100.3
0.4*0)
Al2O3
Cr2O3
MgO
Total
28.0*3)
46.4*3)
23.2*3)
98.3
10.1*2)
65.7*1)
21.0*0)
97.2
1.6*3)
36.5*4)
100.6
20.9*18)
25.4*3)
98.8
Si
Al
Cr
Mg
Total
1.926*20) 0.021*10)
0.127*26) 0.939*12)
1.869*26) 0.017*1)
0.255*38) 1.569*38)
0.043*7) 0.426*37)
1.814*19) 0.974*4)
3.981*5) 2.986*1)
1.985*8)
0.012*3)
1.973*4)
0.013*1)
0.373*6)
1.624*5)
0.978*4)
2.988*2)
0.034*6)
0.039*6)
1.920*14)
3.978*6)
0.345*13)
1.667*14)
0.958*9)
2.982*2)
0.042*9)
0.042*4)
1.927*11)
3.984*2)
0.052*9)
1.879*17) 0.984*8)
3.984*6) 2.988*3)
1.044*9)
P *kbar) 20
T *°C) 1400
Cr # *bulk) 20
15
1400
10
20
1400
10
10
1400
50
OPX
S 116-II
SPI
S 116-II
OPX
S 131
SPI
S 131
OPX
S 130
SPI
S 130
OPX
S 50
SPI
S 50
SiO2
56.1*7)
5.7*9)
1.3*1)
36.7*3)
99.8
0.6*1)
50.4*11)
22.2*17)
25.4*2)
98.6
55.5*8)
1.2*6)
58.7*4)
10.4*1)
26.5*2)
96.8
55.0*5)
0.8*3)
58.7*7)
2.2*3)
1.4*4)
38.6*2)
100.9
0.5*3)
Al2O3
Cr2O3
MgO
Total
6.6*8)
0.8*1)
36.5*6)
99.4
7.7*8)
0.9*1)
36.2*3)
99.8
58.1*6)
10.5*5)
26.3*5)
95.7
27.6*7)
46.9*7)
23.1*2)
98.1
Si
Al
Cr
Mg
Total
1.885*20) 0.016*2)
0.227*34) 1.539*32)
1.870*16) 0.030*15)
0.261*33) 1.753*11)
0.022*4) 0.208*5)
1.835*22) 1.000*8)
3.988*12) 2.991*4)
1.848*18)
0.304*30)
0.024*4)
1.812*15)
3.988*11)
0.021*8)
1.755*11)
0.213*7)
1.006*5)
2.995*3)
1.950*14)
0.015*8)
0.929*20)
1.061*20)
0.984*4)
2.989*3)
0.088*11)
0.036*11)
1.914*16)
3.988*8)
0.035*3)
1.836*11) 0.979*3)
3.983*3) 2.988*1)
0.454*35)
P *kbar)
T *°C)
Cr # *bulk) 20
10
1400
10
1400
80
OPX
S 112-II
5
1400
80
OPX
S 122-I
5
1400
90
OPX
S 127-I
OPX
S 112-I
SPI
S 112-I
SPI
S 112-II
SPI
S 122-I
SPI
S 127-I
SiO2
56.4*13)
4.8*12)
1.3*3)
37.0*10)
99.3
0.5*1)
51.3*39)
19.4*43)
24.5*6)
95.7
57.6*7)
0.5*2)
1.1*1)
37.7*5)
96.9
0.3*0)
9.7*2)
65.3*5)
19.9*1)
95.2
59.2*8)
0.7*2)
1.4*2)
39.2*5)
100.5
0.4*0)
60.2*9)
0.2*0)
1.1*1)
39.8*6)
101.3
0.4*1)
Al2O3
Cr2O3
MgO
Total
10.7*2)
65.3*5)
21.0*4)
97.4
5.7*3)
72.3*6)
20.9*5)
99.3
Si
Al
Cr
Mg
Total
1.901*32) 0.014*3)
0.192*50) 1.597*93)
1.990*7) 0.010*1)
0.021*6) 0.367*4)
0.029*4) 1.653*3)
1.945*25) 0.950*6)
3.985*10) 2.980*2)
1.978*9)
0.012*1)
0.391*6)
1.609*10)
0.976*8)
2.988*0)
1.992*4)
0.013*4)
0.210*6)
1.788*18)
0.977*15)
2.988*5)
0.026*9)
0.037*6)
1.949*7)
3.990*4)
0.005*5)
0.029*3)
1.964*5)
3.990*2)
0.034*9)
0.407*94)
1.860*38) 0.966*7)
3.987*13) 2.984*3)
P *kbar) 5
T *°C) 1400
Cr # *bulk) 46
35
1500
50
35
1500
20
35
1500
80
OPX
S 127-III
SPI
S 127-III
OPX
S 51
SPI
S 51
OPX
S 117-I
SPI
S 117-I
GAR
S 117-I
OPX
S 117-II
SPI
S 117-II
SiO2
59.1*2)
1.9*1)
1.3*2)
39.3*3)
101.6
0.4*1)
28.7*13)
45.6*18)
23.0*1)
97.7
55.0*4)
5.3*3)
2.9*2)
36.9*1)
100.1
0.5*1)
55.4*7)
6.9*7)
1.8*3)
36.0*3)
100.1
0.8*1)
43.7*1)
58.4*6)
1.2*3)
2.0*5)
38.2*7)
99.8
0.6*1)
10.0*1)
65.3*3)
21.0*2)
96.9
Al2O3
Cr2O3
MgO
Total
29.4*7)
44.9*8)
23.4*1)
98.2
47.0*34)
24.9*38)
24.9*5)
97.6
21.3*4)
4.5*8)
29.6*8)
99.1
Si
Al
Cr
Mg
Total
1.952*8)
0.012*2)
0.967*43)
1.030*39)
0.980*5)
2.989*1)
1.857*12) 0.015*2)
0.211*12) 0.983*20)
0.076*6) 1.005*20)
1.856*8) 0.988*3)
4.000*5) 2.991*1)
1.859*19)
0.021*2)
1.463*84)
0.522*86)
0.982*3)
2.988*1)
3.004*17)
1.728*20)
0.245*43)
3.034*56)
8.011*23)
1.966*11) 0.019*2)
0.047*11) 0.368*4)
0.053*13) 1.618*5)
1.918*26) 0.982*6)
3.984*10) 2.987*2)
0.075*4)
0.033*6)
1.934*8)
3.994*5)
0.271*28)
0.048*8)
1.803*14)
3.981*5)

90
Table 4 *Contd.)
P *kbar) 25
T *°C) 1500
Cr # *bulk) 50
25
1500
80
25
1500
20
15
1500
90
OPX
S 47
SPI
S 47
OPX
S 113-I
SPI
S 113-I
OPX
S 113-II
SPI
S 113-II
OPX
S 124
SPI
S 124
SiO2
56.5*1)
3.9*2)
2.3*1)
38.2*2)
100.9
0.7*1)
59.3*5)
0.5*1)
9.4*2)
67.2*12)
20.3*8)
97.4
55.0*6)
8.0*7)
1.7*2)
35.1*5)
99.8
0.7*1)
49.6*7)
22.1*2)
24.8*4)
97.2
60.2*4)
0.4*2)
1.6*2)
39.5*2)
101.7
0.4*0)
Al2O3
Cr2O3
MgO
Total
26.8*2)
47.2*4)
23.4*1)
98.1
1.2*4)
1.8*3)
37.5*3)
99.8
5.2*4)
72.8*4)
20.6*2)
99.0
Si
Al
Cr
Mg
Total
1.889*4)
0.020*3)
0.904*10)
1.070*5)
0.999*1)
2.993*1)
1.991*11) 0.016*3)
0.046*14) 0.349*7)
0.049*8) 1.665*14)
1.877*13) 0.948*21)
3.963*3) 2.978*8)
1.849*15)
0.019*2)
1.986*7)
0.014*1)
0.191*14)
1.813*16)
0.966*5)
2.984*1)
0.152*8)
0.061*2)
1.902*7)
4.004*3)
0.316*27)
0.045*5)
1.759*18)
3.969*4)
1.536*4)
0.459*6)
0.971*4)
2.985*1)
0.014*7)
0.041*5)
1.946*7)
3.987*3)
P *kbar) 10
T *°C) 1500
Cr # *bulk) 50
OPX
S 49
SPI
S 49
SiO2
57.3*8)
2.8*8)
2.0*4)
38.5*5)
100.6
0.6*1)
Al2O3
Cr2O3
MgO
Total
27.4*13)
46.5*11)
23.1*2)
97.6
Si
Al
Cr
Mg
Total
1.918*22) 0.017*4)
0.111*32) 0.929*38)
0.052*10) 1.056*33)
1.919*21) 0.988*4)
4.000*4)
2.990*2)
a Analyses of spinels yielded totals systematically lower than 100, di€ering hardness of spinel, opx and olivine, polishing of the
although the structural values indicate high-quality analyses. Low experimental specimens often resulted in proud spinel slightly
totals can be caused by beam current ¯uctuations during the sticking out of the surface. Proud minerals usually yield higher
analyses. Another possibility to explain lowtotals in spinels might
totals, as exited X-rays are less subject to attenuation on the way
be lower conductivity of Mg*Cr,Al)2O4 spinels relative to out of the sample into the detector. However, lower conductivity of
orthopyroxene *N.G. Ware, personal communication), the latter of the spinel would, in fact, counteract this e€ect, thus resulting in
which yielded higher totals on average. Because of the strongly lower totals
Energy and wavelength dispersive analyses were obtained with
a JEOL 6400 scanning electron microscope at the Electron
Microscopy Unit *EMU) and with a Cameca ``Microbeam'' elec-
tron microprobe at the Research School of Earth Sciences, both at
Figure 2 shows results from experiments at 1400 °C
at pressures between 5 and 54 kbar. The alumina solu-
bility in orthopyroxene seems also to depend slightly on
pressure in the middle range of Al/*Al + Cr) ratios,
with higher pressure, correlating with more alumina in
the orthopyroxene at a given spinel composition.
Equilibrium *2) describes the partitioning of Cr and
Al between spinel and orthopyroxene in MAS±Cr.
Figure 3 depicts the partitioning as a function of tem-
perature at a constant pressure of 24 kbar. The results
indicate the temperature e€ect on equilibrium *2) is
the Australian National University. All analyses were performed
with a spot size of ꢁ1 lm. Special care was taken in selecting areas
of orthopyroxene to analyse, so as to avoid small spinel inclusions
within the orthopyroxene.
Experimental results
As expected from equilibrium *1), the addition of Cr to negligible. Figure 4 shows the results at a constant
the MAS system lowers the amount of alumina dissolved temperature *1400 °C), and pressures between 5 and
in the orthopyroxene solid solution at a speci®ed pres- 54 kbar. Within the error margins, no signi®cant pres-
sure and temperature, as illustrated in Fig. 1 for runs at sure e€ect on equilibrium *2) is observed either.
24 kbar. A similar trend is observed at other pressures.
Two experiments in relatively low bulk Cr/*Cr + Al)
The experimental and thermodynamic results in the Cr- compositions yielded garnet as an additional phase
free system *e.g. Gasparik and Newton 1984) indicate *S-117-I and S-111-II at 35 kbar, 1500 °C and 1400 °C
that the solubility of alumina in orthopyroxene depends respectively). The garnet compositions exhibit a relative
on temperature, increasing temperature resulting in in- large scatter. Taking the uncertainties into account, the
creasing alumina in orthopyroxene. The same trend is garnet composition in both experiments is constant with
observed in the Cr-bearing system MAS±Cr *e.g. Fig. 1). a Cr/*Cr + Al) in the garnet of 0.12 ‹ 0.03.

91
Fig. 1 The solubility of alumina in orthopyroxene in equilibrium
with spinel and olivine. Experimental results at 24 kbar are depicted;
experiments at other pressures showsimilar trends. The bars indicate
maximum and minimum alumina contents in orthopyroxene
*Table 4); uncertainties in spinel compositions are relatively small
*Table 4) and are, for clarity, not shown here. Experiments between
1300 and 1500 °C are depicted. Note that experiments at 1300 and
1500 °C were performed at 25 kbar *cf. Table 3). The box in the
right upper corner indicates experiments in the Cr-free system *MAS)
by Gasparik and Newton *1984). The lines are hand-drawn to
illustrate the observed trends of the experimental results. *N Alopx
*pfu) ˆ alumina content in orthopyroxene per formula unit of six
oxygens.) At 1300 °C and 24 kbar garnet is stable in the Cr-free
system MAS
Fig. 3 Experimental results at 24 kbar and di€erent temperatures.
Note that experiments at 1300 and 1500 °C were performed at
25 kbar *cf. Table 3). The cross in the upper right corner depicts
compositions in the Cr-free systems. For clarity, only uncertainties for
the 1400 °C experiments *Table 4) are shown; other experiments show
similar uncertainties. The line is hand-drawn
Fig. 4 Experimental results in MAS±Cr at 1400 °C and pressures
ranging from 5 to 54 kbar. For clarity, only uncertainties are shown
for the orthopyroxenes, especially as the errors in spinel compositions
are comparatively small *Table 4). Compositions in the Cr-free system
*MAS) lie in the upper right corner. All experiments but two *at 5 and
54 kbar) fall onto the curve
Thermodynamic evaluation of results
Fig. 2 Experiments in the system MAS±Cr at 1400 °C and pressures
between 5 and 54 kbar. Bars indicate maximum and minimum
alumina contents in orthopyroxene as determined by electron
microprobe *cf. Table 4). Experiments at other temperatures exhibit
similar trends. The amount of alumina solved in orthopyroxene is a
function of the coexisting spinel composition and perhaps also of
pressure. The depicted lines are hand-drawn to illustrate the possible
pressure trends. *N Alopx pfu ˆ number of cations of Al in
orthopyroxene per formula unit of six oxygens). The slight pressure
e€ect on the solubility of alumina in orthopyroxene in the Cr-free
system MAS is actually opposite to that observed in MAS±Cr. This
results in an inversion of the slightly positive slope of the alumina
isopleths in orthopyroxene in MAS to a slightly negative slope of the
isopleths in relatively Cr-rich compositions
A number of solution models have been proposed to
describe the mixing of Mg2Si2O6±MgAl2SiO6 orthopy-
roxenes in the system MAS *e.g. Wood and Banno 1973;
Ganguly and Ghose 1979; Lane and Ganguly 1980). In
the most widely used model, Wood and Banno *1973)
assumed that half the Al in the orthopyroxene formula
unit of six oxygens substitutes for Mg on the M1 octa-
hedral site, with the other half of the Al occupying an
adjacent tetrahedral site. Since the position of the Al
onto the tetrahedral site is completely speci®ed by the

92
XEopx ˆ ꢀ1 À XMopx À XCopx† ˆ ꢀ1 À nAl=2 À nCr=2†
XMopx ˆ nAl=2
position in the crystal structure of the octahedral Al, the
tetrahedral Al contributes nothing to the con®gurational
entropy of mixing, which therefore corresponds to
XCopx ˆ nCr=2
one-site mixing. Hence
opx
a
ˆ 1 À ꢀnAl=2†
spinel
Al±Cr
ꢀMg2Si2O6†
Moreover, if W
is allowed to vary as a parameter
in the regression, we ®nd Wspinel » 10 kJ mol)1 *on a
opx
ꢀMgAl2SiO6†
a
ˆ ꢀnAl=2†
Al±Cr
one-site basis), which is in very good agreement with the
value experimentally determined by Oka et al. *1984;
and re-evaluated here in the Appendix), from completely
independent measurements on the partitioning of Al and
Cr between Mg*Al, Cr)2O4 spinel and *Al, Cr)2O3 solid
solutions. This agreement is surely indicative that the
simple two-site model, unlikely though it may appear
from a crystal-chemical perspective, has real validity in a
thermodynamic sense.
The next stage of the model-building process is to ®t
the experimental data of this study along with literature
data in the systems MAS, CMAS and NCMAS to a
thermodynamic expression for reaction *1). However,
here a paradox is encountered. The simple two-site
model used so successfully for reaction *2) is not able to
®t these data satisfactorily, even if we use more com-
plicated excess mixing models. If only the data from the
Cr-free systems are considered, then although a fair ®t,
statistically speaking, can be obtained with the two-site
where nAl is the number of Al cations per formula unit of
six oxygens.
In the context of crystal-®eld theory, Cr3+ has the
largest excess octahedral site preference energy of any
®rst-rowtransition cation *Burns 1970, 1975), and is
found exclusively in octahedral co-ordination in oxides
and silicates *Burns and Burns 1975). Moreover, its
ionic radius is considerably larger than that of Al3+
,
hence much larger than that of Si4+. Both these simple
crystal-chemical considerations argue that Cr3+ should
not substitute for Si on the tetrahedral sites of the
orthopyroxene structure. Accordingly, a suitable end
member to describe the thermodynamics of Cr3+ in
orthopyroxenes might, one would suppose, be
MgCrAlSiO6, and not MgCr2SiO6 *e.g. Chatterjee and
Terhart 1985).
The results presented here, however, confound this
expectation. The most obvious point is that in several
runs nAl < nCr is observed, hence the hypothetical end
model, this is only with an exceptionally large excess
member MgCrAlSiO6 cannot account for all the Cr3+
.
opx
EM
mixing term *W
ꢁ 200 kJ mol)1). Such a large value
Similarly, Canil and O'Neill *1996) have found
nAl < *nCr+nFe3‡ ) in natural orthopyroxenes.
Even more unexpected is that an extremely good ®t to
the partitioning of Cr3+ and Al between orthopyroxene
and spinel is obtained if the partitioning reaction is
written as:
is physically unreasonable; more tangibly, it is also
grossly inconsistent with the calorimetrically measured
heats of mixing in the clinopyroxene join CaMgSi2O6±
CaAl2SiO6 *Newton et al. 1977), expected to be some-
what similar to the Mg2Si2O6±MgAl2SiO6 orthopyrox-
enes of interest here. This analogy implies that W
opx
EM
should be ꢁ20 kJ mol)1.
1=2MgAl2SiO6 ‡ 1=2MgCr2O4 ˆ 1=2MgCr2SiO6 ‡ 1=2MgAl2O4
opx
spinel
opx
spinel
In any case, no satisfactory ®t with two-site mixing at
all could be found when the MAS±Cr data were
included. Our conclusion is that reaction *1) clearly
requires a coupled-substitution for the orthopyroxene
mixing model *equivalent to one-site mixing), of the type
used by Wood and Banno *1973); yet, reaction *2)
requires the two-site mixing model.
ꢀ4†
and activities are modelled making the simplest possible
assumption, that
opx
ꢀMgAl2SiO6†
2
a
ˆ ꢀnAl=2†
and
The solution to this paradox is to invoke a model in
which there is random mixing of Mg, Al and Cr3+ on
the M1 site, with complete coupling of *Al + Cr3+) on
M1 with *Al + Cr3+) on the tetrahedral sites *i.e. as
postulated for one-site mixing in the MAS system), but
with random mixing of Al with Cr3+ on the ``associat-
ed'' tetrahedral site.
opx
ꢀMgCr2SiO6†
2
a
ˆ ꢀnCr=2†
*i.e. ideal two-site mixing of Al and Cr). Assuming ap-
propriate activity±composition relations for the spinel
solid solution from previous work in the literature, the
37 data points from this study *Table 4) can be ®tted
very well to this model *the ®tting procedure and results
are described fully below). Including non-ideal terms for
the orthopyroxene solid solution in the form of a ternary
regular solution between Mg2Si2O6, MgAl2SiO6 and
MgCr2SiO6 did not improve the ®t at all, implying
The con®gurational entropy of mixing in this model
is:
"
À
Á
À
Á
Sconfig ˆ À R 1 À XMopx À XCopx ln 1 À XMopx À XCopx
opx
MC
opx
EM
opx
EC
W
ˆ 0, and W
ˆ W . The components used here
XMopx
XMopx ‡ XCopx
‡ XMopx ln XMopx ‡ XCopx ln XCopx ‡ XMopx ln
are de®ned as M ˆ MgAl2SiO6, E ˆ Mg2Si2O6,
C ˆ MgCr2SiO6, and the mole fractions of these com-
ponents can be de®ned without ambiguity in terms of
the number of Al and Cr cations per formula unit of six
oxygens *nAl and nCr) as:
À
Á
#
XCopx
‡ XCopx ln
À
Á
XMopx ‡ XCopx

93
The ®rst three terms on the right hand side of this and Wood 1998). Incorporation of such order±disorder
equation are due to the mixing of Mg, Al and Cr3+ on e€ects into the model would introduce tremendous
the octahedral *M1) site; the last two terms are due to the complexity that is in no way justi®ed by any practical
mixing of Al and Cr on the ``associated'' tetrahedral site. need as regards data ®tting.
Since the form of these last two terms is slightly dif-
ferent from that normally obtained for the con®gura-
tional entropy of mixing on sites, we give their
derivation explicitly, as follows: The permutability W of
Al and Cr on the ``associated'' tetrahedral sites is
Details of the ®tting procedure
Accurate activity±composition relations may in principle
be determined from the analysis of coexisting solid so-
lutions, but only if the activity±composition relations of
one of the phases are known independently. Hence, the
evaluation of the orthopyroxene solid solution depends
on the spinel solid-solution model. Activity±composition
relations in the Mg*Al, Cr)2O4 spinel solid solution have
been calibrated from the partitioning of Al and Cr be-
tween this phase and *Al, Cr)2O3, studied by Oka et al.
*1984). Interpretation of Oka et al.'s data in turn de-
pends on the mixing properties of the *Al, Cr)2O3 solid
solution, which were evaluated by Chatterjee et al.
*1982) from the experimental work of Jacob *1978). The
Appendix presents a critical re-evaluation of this chain
of investigation. We ®nd that while both the *Al, Cr)2O3
and the Mg*Al, Cr)2O4 solid solution are obviously non-
ideal, it is dicult to decide whether the non-ideality can
be modelled with symmetrical excess mixing models *the
simplest possible representation of non-ideality in a solid
solution), or whether the more complicated asymmetric
mixing models are warranted. Accordingly, both possi-
ble models have been investigated here. In summary,
these models are:
X ˆ ꢀNAl ‡ NCr†!=ꢀNAl! ‡ NCr!†
where NAl and NCr are the numbers of Al and Cr cations
on those sites, per mole *six oxygen formula basis). The
con®gurational entropy of mixing on these sites is:
Sconfig ˆ k ln X
ˆ k‰lnꢀNAl ‡ NCr†! À ln NAl! À ln Ncr!Š
where k is the Boltzmann constant. Using Stirling's
approximation for large numbers *i.e. if x is a large
number, ln x! ˆ x ln x ± x):
S ˆ Àk‰ꢀNAl ‡ NCr† lnꢀNAl ‡ NCr† À NAl ln NAl À NCr ln NCr
Š
ꢂ
ꢃ
NAl
NCr
ˆ Àk NAl ln
‡ NCr ln
ꢀNAl ‡ NCr
†
ꢀNAl ‡ NCr†
Hence, since NAl ˆ NXopx and NCr ˆ NXopx, where N
M
C
is Avogadro's number,
ꢂ
ꢃ
XM
XM ‡ XC
XC
XM ‡ XC
S ˆ ÀR XM ln
‡ XC ln
;
where R ˆ kN:
Di€erentiation of the equation for the con®gura-
tional entropy of mixing gives the following expressions
for the ideal part of the activities of each component:
opx
Mg2Si2O6
A: a symmetric model for both the Mg*Al, Cr)2O4 and
the *Al, Cr)2O3 solid solutions
B: an asymmetric model for both the Mg*Al, Cr)2O4 and
the *Al, Cr)2O3 solid solutions
a
a
a
ˆ ꢀ1 À XMopx À XCopx
ˆ ꢀXMopx†2=ꢀXMopx ‡ XCopx
ˆ ꢀXCopx†2=ꢀXMopx ‡ XCopx
†
opx
MgAl2SiO6
†
†
opx
MgCr2SiO6
With these models for the spinel solid solution, the 37
data of the present study were then ®tted by non-linear
least squares regression to equations of the form:
This formulation is equivalent to two-site mixing for
the ratio aMgAl SiO =aMgCr SiO in modelling equilibrium
2
6
2
6
"
#
*2), but reduces to one-site mixing between Mg2Si2O6
and MgAl2SiO6 in the Cr-free system, as required by the
data for equilibrium *1). With this model it was possible
to ®t 97 data from this study and from the literature in
the systems MAS, CMAS, NCMAS and MAS±Cr sat-
isfactory to equilibrium *1), while also ®tting the MAS±
Cr data to equilibrium *2).
spinel
Al
X
XCopx
spinel
Cr
spinel
Al
0 ˆ DH2 À TDS2P ‡ RT ln
‡ RT ln c
À RT ln c
spinel XMopx
XCr
The compositional data were weighted according to the
uncertainties given in Table 4, and the uncertainties on
P were assumed to be ‹1 kbar and on T ‹15 K
*1 SD).
In formulating the above model, we have implicitly
assumed that the partitioning of Al and Cr between the
octahedral M1 site and our hypothetical ``associated''
tetrahedral site is random. It is to be understood that the
site assignments used here are only meant as a heuristic
guide to formulating the algebra: we do not expect that
an XRD experiment, for example, would reveal the
presence of tetrahedral Cr3+ in these orthopyroxenes. In
actuality, tetrahedral Cr3+ could be avoided if it is
Mg2+ that occupies the tetrahedral site, with the Cr3+
replacing this Mg on the octahedral site. A similar
substitution mechanism has been proposed for the Cr3+
substitution into the wadsleyite structure *Gud®nnsson
For model A *symmetric spinel mixing model) we
obtain:
A : DGꢀ2† ˆ 19; 065 ꢀ10; 351† À 17:06 ꢀ5:90† T
À 0:154 ꢀ0:047† P J molÀ1
with a reduced chi-squared *v2m) of 0.76, while model B
*asymmetric spinel model) yields
B : DGꢀ2† ˆ 21; 443 ꢀ10; 501† À 18:67 ꢀ5:99† T
À 0:161 ꢀ0:048† P J molÀ1
with v2m ˆ 0.72. P is in bars. The numbers in parentheses
indicate the uncertainties of the individual parameters as

94
determined by the regressions. The lowvalues of v2m in-
Again, the same two data *S 126 at 54 kbar, and
dicate that both models ®t the data well. Only two runs S 127-III at 5 kbar) which were poorly ®t to equilibrium
are not ®tted within two standard deviations of their *2) were also poorly ®t to equilibrium *1). One datum of
observed uncertainties *S 126 ± 54 kbar, S 127-III ± Sen *1985) in the system CMAS does not ®t well either
5 kbar, see Fig. 4).
*15 kbar, 1200 °C). Also, the recent experimental results
We then ®tted equilibrium *1) using both the sym- of Gud®nnsson and Presnall *1996) in the system CMAS
metric and the asymmetric model for the spinel solid could not be ®tted within their stated uncertainties and
solution. We used 60 data from the literature for the Cr- were therefore excluded from the ®tting procedure.
free systems MAS *Dankwerth and Newton 1978; Gas- These data di€er from the earlier data from the same
parik and Newton 1984), CMAS *Gasparik 1984; Sen laboratory of Walter and Presnall *1994), which agree
1985; Klemme 1998; Klemme and O'Neill 2000) and well with the other studies.
NCMAS *Walter and Presnall 1994), plus the 37 data
for the system MAS±Cr from this study. All data were
®tted simultaneously to the equation:
Discussion and implications
0ˆDH1 ÀTDS1 ‡DV1P
h
i
Previous work
‡RT lnꢀ1ÀXMopx ÀXEopx†À2lnXMopx ‡lnꢀXMopx ‡XCopx†‡2lnXspinel
Al
spinel
‡W opxꢀÀ1‡2XMopx ‡XCopx†‡W opxXCopx
In an early experimental study, Dickey and Yoder
*1971) investigated the distribution of Cr and Al be-
tween coexisting clinopyroxene and spinel in the system
CMAS-Cr, focusing on the spinel compositions as a
function of temperature above the solidus. Perhaps due
to short run times spinels were only small *<3 lm), and
the clinopyroxene was reported to host numerous spinel
inclusions. Wood *1978) investigated the in¯uence of Cr
on the transition from spinel to garnet peridotite in the
system MAS±Cr. Evaluation of his experiments led him
to the assumption of ideal two-site mixing of the
MgAl2O4±MgCr2O4 solid solution. In a subsequent
study on the transition in the system CMAS±Cr, O'Neill
*1981) postulated a positive deviation from ideality on
the binary MgAl2O4±MgCr2O4 join. Oka et al. *1984)
investigated the partitioning between Cr and Al between
the *Al, Cr)2O3 and the Mg*Al, Cr)2O4 solid solutions in
detail, and showed that the spinel solution does indeed
deviate positively from ideality, in agreement with
O'Neill's *1981) prediction. Carroll-Webb and Wood
*1986) studied the partitioning of Cr and Al between
coexisting spinel and sodic clinopyroxene of formula
Na*Al, Cr)Si2O6. They performed reversal piston-cylin-
der experiments at 25 kbar and 1100 °C *two experi-
ments at 1000 °C) on the partitioning equilibrium:
‡2RT lnc
EM
EC
Al
Where possible, the data were weighted according to the
published uncertainties in mineral compositions *Danc-
kwerth and Newton 1978; Sen 1985; Walter and Presnall
1994; Klemme 1998). However, the uncertainties were
not given by Gasparik *1984) and Gasparik and Newton
opx
Al
*1984), so that uncertainties for n of ‹0.005 *Al at-
oms per formula unit of six oxygens) were assumed.
Note that from the modelling of reaction *2) above, we
opx
EC
constrain W
In performing the non-linear least-squares regression,
ˆ WEoMpx, W opx ˆ 0.
MC
we found that allowing the value of WEoMpx*=W opx ) to
EC
vary in the usual way resulted in lack of convergence,
probably because this parameter is highly correlated
with others over the relatively limited range of Mg±Al
compositional space which is accessible in orthopyrox-
ene solid solutions. Hence we constrained the value of
opx
EM
opx
EC
this parameter to be W
ˆ W
ˆ 20 kJ mol)1, by
analogy with the calorimetric data for CaMgSi2O6±
CaAl2SiO6 clinopyroxenes *Newton et al. 1977). Manual
opx
adjustment of W
to higher or lower values increases
EM
reduced chi-squared for model A, indicating that the
chosen value of 20 kJ mol)1 was appropriate to a sur-
prising degree of precision. The results for the two
models are as follows. Model A [symmetric model for
Mg*Al, Cr)2O4 spinels]:
NaCrSi2O6 ‡1=2 MgAl2O4 ˆ 1=2 MgCr2O4 ‡ NaAlSi2O6
clinopyroxene
spinel
spinel
clinopyroxene
DG ꢀ1† ˆ 188 ꢀ312† À 4:518 ꢀ0:216† T À 0:018 ꢀ0:007† P J molÀ1
with a reduced chi-squared of 1.93. P is in bars; and
model B [asymmetric model for Mg*Al, Cr)2O4 spinels]
DG ꢀ1† ˆ 1363 ꢀ300† À 4:890 ꢀ0:206† T À 0:014 ꢀ0:0006† P J molÀ1
Caroll-Webb and Wood *1986) found that mixing in
Na*Cr,Al)Si2O6 clinopyroxene was approximately ideal,
which agrees well with the ideal mixing of the
MgAl2SiO6 and MgCr2SiO6 components postulated in
this study. Nickel *1986) investigated phase relations in
the system CaO±MgO±Al2O3±SiO2±Cr2O3. He found a
with a reduced chi-squared of 2.21. For this model B we good positive correlation of the Al/*Al + Cr) ratios of
used W
opx
EM
ˆ 21 kJ mol)1 since this value gave a slightly orthopyroxene and spinel *Nickel 1983), with no sig-
better ®t. Nevertheless, the value of v2m is clearly greater ni®cant pressure or temperature e€ect, in good agree-
than for model A.
Since model A is also the simpler model, it seems on
ment with results of this study.
The only other experiments that can be directly
balance preferable, although it does give a poorer ®t to compared with the results of this study are those re-
some of the Mg*Al, Cr)2O4 and *Al, Cr)2O3 data *see ported in a recent paper by Doroshev et al. *1997). They
Appendix).
investigated the partitioning of Cr and Al between

95
but also on the thermodynamics of Cr in pyroxenes
*Asimov et al. 1995; Klemme 1998). The present study
sets the stage for further investigations of phase relations
in Cr-bearing systems relevant for the Earth's upper
mantle.
Acknowledgments SK would like to acknowledge funding by an
ANU PhD scholarship. The authors would also like to thank Drs
C. Shaw and B. J. Wood for careful reviews which helped con-
siderably to improve the manuscript. We would also like to thank
members of the Petrochemistry and Experimental Petrology group
at the Research School of Earth Sciences, especially Alan Major,
Paul Willis, Dean R. Scott and William O. Hibberson.
Appendix
Fig. 5 Calculated temperature using the empirical geothermometer of
Witt-Eickschen and Seck *1991) for experiments at 1400 °C in MAS±
Cr of the present study. Witt-Eickschen and Seck's *1991) thermom-
eter does not reproduce experiments in MAS *Gasparik and Newton
1984), it also cannot reproduce the present experimental results.
Especially at high Cr/*Cr + Al) ratios, Witt-Eickschen and Seck's
geothermometer *1991) systematically underestimates the experimen-
tal temperatures by several hundred degrees
Activity±composition relations
in Al±Cr solid solutions
Cr3+ can replace Al in octahedral co-ordination in many minerals,
and complete solid solution exists between, for example, the oxides
Al2O3±Cr2O3 [albeit with a solvus below ꢁ950 °C *Roy and Barks
1972)]; spinels M Al2O4±M Cr2O4, where M is Mg, Fe2+, Zn etc.
*O'Neill and Navrotsky 1984); garnets Ca3Al2Si3O12±Ca3Cr2Si3O12
*Huckenholz and Knittel 1975) and Mg3Al2Si3O12±Mg3Cr2Si3O12
*Irifune and Hariya 1983; Doroshev et al. 1997); and clinopyrox-
enes NaAlSi2O6±NaCrSi2O6 *Carroll-Webb and Wood 1986).
However, Cr3+ generally does not replace Al on tetrahedral sites.
For example, the amounts of Cr substituting in CaAl2Si2O8
*anorthite) are generally too small to be reported even when the
anorthite-rich plagioclase is in equilibrium with Cr-rich spinel *e.g.
Deer et al. 1992).
coexisting spinel, orthopyroxene, olivine and garnet in
the divariant ®eld of the system MgO±Al2O3±SiO2±
Cr2O3 where garnet and spinel coexist with orthopy-
roxene and olivine. An attempt to ®t Doroshev et al.'s
*1997) data in conjunction with the present experimental
results was not successful, indicating that their results
are not compatible with ours. The large scatter in the
orthopyroxene compositions as indicated by Doroshev
et al. *see their comments on p 570 of their paper), may
indicate failure to reach equilibrium, probably due to
short run durations *e.g. only 24 h at 1400 °C as op-
posed to ꢁ120 h at 1400 °C in the present study).
Approximate activity±composition relations in Ca3Al2Si3O12
Ca3Cr2Si3O12 garnet solutions were determined by Mattioli and
Bishop *1984), by displacement of the univariant reaction:
±
Ca3Al2Si3O12 ‡ SiO2 ˆ CaAl2Si3O8 ‡ 2CaSiO3
They found the solution to be nearly ideal, in agreement with
the almost negligible excess enthalpies of solution found by Wood
and Kleppa *1984) from oxide melt solution calorimetry.
More precise activity±composition relations in Al±Cr oxide and
silicate solid solutions may in principle be determined from analysis
of coexisting solid solutions. However, as has been shown for
Fe2+±Mg solid solutions, such measurements can only accurately
yield the di€erence in the activity±composition relations of the two
phases *e.g. Matsui and Nishizawa 1974; von Seckendor€ and
O'Neill 1993): it is necessary for absolute values of one of the
phases to be known independently. Fortunately, such measure-
ments exist for the Al2O3±Cr2O3 solid solution. Jacob *1978) de-
termined the mixing properties of this solution from the
displacement of the reaction:
Geothermometry based on the solubility
of alumina in orthopyroxene
Equilibrium *1) has been calibrated empirically by Witt-
Eickschen and Seck *1991) as a geothermometer, using
data for coexisting phases in spinel lherzolite xenoliths
from West Eifel, Germany, with temperatures of equil-
ibration of the xenoliths derived from the two-pyroxene
geothermometer of Brey and Kohler *1990).
2 Cr ‡ 1:5 O2 ˆ Cr2O3
in fO2±T space, using an electromotive force *emf) method with
YDT *yttria-doped thoria) solid oxygen-speci®c electrolytes. The
low fO2 of the Cr±Cr2O3 equilibrium is beyond the useful range of
zirconia-based electrolytes. The thoria-based electrolytes are di-
cult to obtain *they appear to be no longer manufactured com-
mercially), and are also extremely expensive. Consequently, it is
unlikely that Jacob's *1978) experiments will be repeated.
Jacob's experimental results were reinterpreted by Chatterjee
et al. *1982), who ®tted them to a subregular *asymmetric) solution
model. Chatterjee et al. *1982) also reported molar volumes for the
*Al, Cr)2O3 solution. This modelling was then used by Oka et al.
*1984) in conjunction with their experimental partitioning data on
coexisting *Al, Cr)2O3±Mg*Al, Cr)2O4 solid solutions at 25 kbar,
to derive activity±composition relations for the latter solution.
They found that the Mg*Al, Cr)2O4 spinel solid solution shows
Here, we can use our experimental data to test this
calibration. The temperatures calculated using the geo-
thermometer of Witt-Eickschen and Seck *1991) for
experiments at 1400 °C are plotted against the Cr/
*Cr + Al) ratio of the spinel in Fig. 5. There is obvi-
ously poor agreement, especially at high Cr/*Cr + Al)
ratios. This illustrates well the importance of including
the e€ect of Cr in modelling any equilibrium involving
aluminous pyroxenes.
Calculations of the position of the transition from
garnet lherzolite to spinel lherzolite, for example, depend
not only on the thermodynamics of Cr-garnets and Cr-
spinels *Klemme and O'Neill 1997; Klemme et al. 2000), slightly asymmetric positive deviations from ideality. However, the

96
uncertainties *i.e. standard deviations) were not given by Chatterjee being sampled by a set of analyses is really completely homoge-
et al. *1982) or by Oka et al. *1984); indeed, nor were the details of nous. It is therefore preferable to use standard deviations, which
the regression method they used. In viewof the importance of the were assumed to be three times the reported standard errors of the
solution properties of Mg*Al, Cr)2O4 spinels to the interpretation mean *as would be the case if the latter were based on ten analyses).
of the experimental data of this study, the data ®tting of these
studies have been reexamined in detail.
With this weighting,
V =cm3 ˆ 25:578 ‡ 3:634 XCr À 0:158 XC2r; v2m ˆ 2:16
or
Activity±compositions in *Al, Cr)2O3 solid solutions
V =cm3 ˆ 25:578 ‡ 3:795 XCr À 0:629 XC2r À 0:311 XC3r; v2m ˆ 1:13
Jacob *1978) studied seven compositions *nominal XCr from 0.1 to
0.9 using cells of the type:
Hence, for each g-atom of Al, Cr mixing, AV0 ˆ
0.0079 J bar)1 *symmetric model) or AV0 ˆ 0.0081 and
AV1 ˆ )0.0078 J bar)1. These numbers are slightly di€erent from
those given by Chatterjee et al. *1982), because the latter used a
simpli®ed regression method with unweighted data.
In summary: for a one-term, regular *symmetric) solution
model:
Pt; ꢀAl; Cr†2O3 ‡ CrjYDTjCr2O3 ‡ Cr; Pt
The temperature range was 800 to 1320 °C. Results were given
only in the form of an equation for the emf of the cell, E *in
millivolts). Here, we have re®tted Jacob's results as follows. The
emf at 1173 K *a temperature near the middle of the range stud-
ied, and close to the optimum for this type of experiment, ac-
cording to Pownceby and O'Neill 1994a) was ®tted to an equation
AG0ꢀˆ W sp † ˆ 17; 300 ‡ 1:53 T ‡ 7:9 P
AlÀCr
with an uncertainty of ꢁ700 J mol)1
.
For a two-term, subregular *asymmetric) model:
ꢀ
of the form 3 FE ˆ DGmix ˆ RT ln XCr ‡ ‰AG0 ‡ AG1 ꢀ4 Xcr À 1† . . .Š
where the terms in AG0 etc. are the terms in the Redlich±Kister
expansion, F is the Faraday constant *96,484.56 J C)1) and R the
gas constant. The data were weighted assuming an uncertainty,
one standard deviation, of 0.4 to 0.7 mV in E *Jacob 1978, his
Table 1), and of ‹0.01 in XCr. The latter is assumed, as no un-
certainty in composition is given by Jacob *1978). This is unfor-
tunate, as in these type of experiments it is the uncertainties in
composition which generally predominate.
AG0 ˆ 17; 320 ‡ 2:10 T ‡ 8:1 P
AG1 ˆ À1380 À 1:09 T À 7:8 P
where P is in kbar. The e€ect of pressure is obviously quite minor.
For a one-term model *i.e. a symmetric or regular solution),
AG0 ˆ 19,390 ‹ 690 J mol)1 with a reduced chi-squared *v2m) of
2.57. For the two-term model *asymmetric or subregular),
AG0 ˆ 20,200 ‹ 700 and AG1 ˆ )2880 ‹ 1100 J mol)1, with
v2m ˆ 1.48, i.e. seemingly a signi®cantly better ®t. Calculated values of
XCr from these two ®ts are compared to their nominal values in
Table A.1. It may be seen that the better ®t of the two-term *sub-
regular) model is entirely due to one composition, that at XCr ˆ 0.64
*nominal), and even for the asymmetric model, the ®t to this datum is
relatively poor.
Activity±compositions in Mg*Al, Cr)2O4
spinel solutions
Oka et al. *1984) measured the partitioning of Al and Cr between
*Al, Cr)2O3 and Mg*Al, Cr)2O4 solutions at 796, 1050 and
1250 °C. Compositions were determined from lattice parameters
*see below). The uncertainties in XCr for the Mg*Al, Cr)2O4 solid
solutions are quoted as 0.0091, 0.0022 and 0.0015 at 796, 1050 and
1250 °C respectively, while those for XCr in the *Al, Cr)2O3 solu-
tion are 0.0200, 0.0172 and 0.0028. Thus the composition of the
*Al, Cr)2O3 oxide solution is quoted as being nearly an order of
magnitude more precise at 1250 °C than at the other two temper-
atures. The scatter of the data at 1250 °C shows that this level of
precision is over-optimistic. Therefore, to lessen the domination of
these data in the regression analysis, their uncertainty in XCr was
doubled to 0.0056.
The calculated values of XCr for each model were then used as
the input values in the regression to determine the temperature
dependence of the mixing parameters AG0 *‹AG1), i.e. the excess
entropies of mixing, from the slopes dE/dT of the emf of the cells.
The uncertainty in the slopes was assumed to be the uncertainty in
the emf for each cell as given by Jacob *1978), divided by 400 K,
the typical temperature range over which the cells were studied.
For the one-term model, AS0 ˆ 1.53 ‹ 0.4 J mol)1 K)1, while
for the two-term model, AS0 ˆ 2.10 ‹ 0.39 and AS1 ˆ 1.09 ‹
With these uncertainties, the results of Oka et al. *1984) were ®t
by least squares regression in two ways, according to which model
*symmetric or asymmetric) was assumed for the *Al, Cr)2O3 solu-
tion. For the asymmetric model, the regression gives:
0.60 J mol)1 K)1
.
The molar volumes of *Al, Cr)2O3 solutions measured by
Chatterjee et al. *1982) were ®tted to quadratic and cubic expres-
sions in XCr, corresponding to the symmetric *regular) and asym-
metric *subregular) solution models respectively, weighting the data
according to the uncertainties in volume given by Chatterjee et al.
*1982, their Table 1). However, Chatterjee et al. *1982) report their
uncertainties in composition as standard errors of the mean, rather
than as standard deviations. Standard errors of the mean tend to
underestimate the true uncertainties in composition, probably be-
cause it is doubtful whether the parent population of compositions
DH ˆ 1015 Æ 710 J molÀ1
DS ˆ 0:341 Æ 0:460 J molÀ1
AG0 ˆ 12; 400 Æ 260 J molÀ1
AG1 ˆ À4963 Æ 450 J molÀ1
with v2m ˆ 1.72. The entropy of the exchange reaction is thus pre-
dicted to be approximately zero. No improvement to the ®t was
observed if the excess mixing parameters were allowed to vary as a
function of temperature. For the symmetric model:
Table A.1
DH ˆ À6992 Æ 1524 J molÀ1
DS ˆ À4:101 Æ 0:985 J molÀ1
AG0 ˆ 9980 Æ 275 J molÀ1
XCr nom
XCr calc 1-term
XCr calc 2-term
0.1
0.1132
0.2463
0.3707
0.4982
0.6057
0.7707
0.9017
0.0968
0.2386
0.3751
0.5094
0.6181
0.7774
0.9032
0.24
0.37
0.5
0.64
0.77
0.9
with v2m ˆ 1.07, i.e. a signi®cantly better ®t to the data. In princi-
ple, the di€erence in standard entropies of the exchange reaction
between the two models could also be used to discriminate between
them, but at the moment the uncertainty in the entropy of Mg-
Al2O4 is too large for this to be practical, due to the uncertainty in

97
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Oka et al. *1984) also measured the lattice parameters across the
MgAl2O4±MgCr2O4 solid solution, and hence derived molar vol-
umes of mixing at room temperature. The interpretation of their
data is complicated by the fact that the lattice parameter of
MgAl2O4 depends on the amount of Mg/Al order±disorder, as well
as the exact stoichiometry *i.e. bulk Mg/Al ratio), which can vary
widely in this spinel. [By contrast, MgCr2O4 spinel shows negligible
Mg/Cr order±disorder, and does not deviate signi®cantly from the
ideal stoichiometry, provided that the sample is synthesized
somewhere within the broad range of oxygen fugacities where
neither Cr2+ or Cr4+ is stable *O'Neill and Dollase 1994).] Oka
et al. *1984) thus found that samples quenched from di€erent
temperatures have slightly di€erent lattice parameters, which they
ascribed to di€ering degrees of Mg/Al order. However, it is
doubtful whether the di€erence between the equilibrium cation
distributions at 1250 °C or 1050 °C and 796 °C would be preserved
during the quench *O'Neill 1997), since rates of Mg±Al exchange
appear to be fast on typical quenching time scales. It is therefore
probable that the lowvalue of the lattice parameter that they ob-
served is instead due to the Mg/Al ratio in their MgAl2O4-rich
spinels being slightly less than unity. This asymmetry appears to be
largely due to a slightly lowvalue for the lattice parameter of
Ê
MgAl2O4, e.g. 8.0810 *1) A at 1250 °C, as compared to that given
by O'Neill *1997):
ao=A ˆ 7:9829 ‡ 0:1052ꢀXMgO=XAl O † À 4:01  10À6 T=K
Ê
2
3
where T is the temperature from which the sample was quenched,
and all values refer to room temperature measurements. The value
of the lattice parameter of MgCr2O4 measured by Chatterjee et al.
*1982) is identical to that given by O'Neill and Dollase *1994), so
there seems to be no interlaboratory bias. Hence stoichiometric
MgAl2O4 quenched from 1250 °C should have a lattice parameter
Ê
of 8.0820 A. However, as mentioned above, slightly non-stoichio-
metric MgAl2O4 re-orders extremely rapidly on quenching, such
that it is likely that the sample synthesized by Chatterjee et al.
*1982) at 1250 °C has a cation distribution corresponding to an
equilibration temperature of ꢁ800 °C. The lattice parameter of
Ê
stoichiometric MgAl2O4 at 800 °C is 8.0837 A.
Because of these problems, the molar volume data of Chatterjee
et al. *1982) were ®tted without the datum for pure MgAl2O4.
*Although we acknowledge that Mg±Al cation ordering may also
be important in the more Al-rich members of the solid solution
series, thermodynamic modelling indicates that it becomes rapidly
less so as Cr replaces Al, hence all other data were accepted.)
A satisfactory ®t to a quadratic equation was obtained, with:
2
V ꢀJ barÀ1† ˆ 3:9780 ‡ 0:3983 XCr À 0:01919ꢀXCr
†
with chi-squared ˆ 2.31. Hence WV Al±Cr ꢀsp) ˆ 0.0096 J bar)1
per mole of Al±Cr. A slightly better ®t is obtained using a cubic *i.e.
asymmetric ®t), with chi-squared ˆ 1.95. However, examination of
the ®t shows that this is probably an artefact of the slightly lower
lattice parameters of the most Al-rich data, as discussed above.
Hence W
Gasparik T, Newton RC *1984) The reversed alumina contents of
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Glawe G, Szaniszlo A *1972) Long term drift of some noble- and
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sp
AlÀCr
ˆ 9739 + 9.6 P J mol)1, where P is in kbar.
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