Thermodynamic Data for Phases in the FeO--MgO--SiO 2 System and Phase Relations in the Mantle Transition Zone

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1 Plays Chem Minerals (1995) 22: PHYSICS ]CHEMISTRY NMIHERAIS 9 Springer-Verlag 1995 Thermodynamic Data for Phases in the FeO--MgO--SiO 2 System and Phase Relations in the Mantle Transition Zone Olga B. Fabrichnaya * Theoretical Geochemistry Program, Department of Mineralogy and Petrology, Institute of Earth Sciences, Uppsala University, Norbyvfigen 18 B, S Uppsala, Sweden Received November 17, 1994/Revised, accepted February 21, 1995 Abstract. Based on the available experimental data on phase equilibria in the FeO-MgO-SiO2 system the mixing properties of the solid solutions (olivine, fl- and y-spinel, pyroxene, majorite, ilmenite and perovskite and magnesiowustite), the enthalpies of FeO and fictive FeSiO 3 phases with ilmenite and majorite structures have been assessed. The entropies, temperature dependance of heat capacities for fictive FeSiO 3 end-members were estimated from structural analogies. The calculated phase diagrams for Mg2SiO4-Fe2SiO 4 and MgSiO3-FeSiO 3 systems at pressures up to 30 GPa and temperatures between 1000 and 2100 K are quite consistent with the available experimental determinations except for the fine features of the phase diagram at 2073 K. Introduction The phases in the FeO- MgO- SiO z system olivine and pyroxene are the major constituents of Earth's mantle. The phase transitions in these minerals are assumed cause seismic discontinuities at depths of 400 and 650 km (Akimoto et al. 1972; Ringwood 1975; Liu 1975). The experiments on phase equilibria at high pressure (P) and temperature (T) supply the main information about stability of the phase assemblages of mantle transition zone and phase compositions. Recently new experimental data on phase relations in the Fe2SiO4-Mg2SiO 4 system were obtained by Katsura and Ito (1989) and Ito and Takahashi (1989). Phase equilibria including the phase majorite (Mg, Fe)SiO3 were studied by Kato (1986) and Ohtani et al. (1991). However, experiments do not cover all possible P - T- compositions in the mantle. To construct phase diagram of the FeO - MgO - SiO 2 system over wide P- T-composition condition thermodynamic modeling can be used. Given the solid solution model, combined with in- * Permanent address: V.I. Vernadsky Institute of Geochemistry and Analytical Chemistry, 19 Kosygin str., Moscow, Russia ternally consistent thermodynamic database for endmembers, it is possible to produce phase relations which have not been studied in experiments. Kuskov and Galimzyanov (1986), Fei and Saxena (1986), Bina and Wood (1987), Akaogi et al. (1989), Fabrichnaya and Kuskov (1991) and Fei et al. (1991) have used the available calorimetric measurement, data on thermal expansion and compressibility of phases together with experimental phase relations to calculate thermodynamic properties and phase diagrams of the FeO-MgO-SiO2 system. Most of recent experimental and theoretical studies of the FeO-MgO-SiO2 system are concentrated on phase relations in Fe2SiO4-Mg2SiOe join, phases ilmenite and majorite being not included. Fabrichnaya and Kuskov (1991) constructed phase diagrams of the FeSiO3-MgSiO3 system. However garnet was not considered there and some simplifications, such as using ideal model of solid solutions and neglecting the Cp(T) dependences for all phases, was made. The aim of this study is to obtain the solid solution data on interaction energies and thermodynamic data on certain endmembers in the system of FeO-MgO- SiO a from the available data on experimental phase equilibria. Experimental Data on Phase Relations in the FeO - MgO-SiO2 System The phase equilibria in the FeO-MgO-SiO2 system at pressures and temperatures of mantle transition zone have been studied for many years and several phases such as (Mg, Fe)2SiO4 (olivine, O1; fi-spinel, fi; 7-spinel, 7), (Mg, Fe)SiO3 (pyroxene, Px; ilmenite, Ilm; perovskite, Pv; majorite, Mj), (Mg, Fe)O (magnesiowustite, Mw) and SiO2 (stishovite, St) are found to be stable at these P- T conditions. Ringwood and Major (1970) and Akimoto (1972) were the first who obtained phase diagrams of the Fe2SiO4-Mg2SiO4 system experimentally at temperatures 1273, 1473 K and pressures up to 18 GPa. The phase diagrams of the FeSiO3-MgSiO3 system were

2 324 determined by Ringwood and Major (1968) and Akimoto and Syono (1970), at pressures up to 10 GPa and temperatures of 1073 and 1273 K. Liu (1976) studied the system FeSiOz-MgSiO 3 and obtained solid solutions of perovskite at pressures higher than 20 GPa. Yagi et al. (1979) studied this system again in diamond anvil cell with laser heating at 1273 K and pressures up to 30 GPa. However the phase composition and temperature determination contained a large uncertainty. Ito and Yamada (1982) studied the FeSiO3-MgSiO 3 system in multiple anvil high pressure apparatus at 1373 K. They obtained the maximal solubility of FeSiO3 in perovskite equal to 9.5 mol%, while Yagi et al. (1979) got the value 20 mol%. The phase relations were not studied in detail for Mg-rich compositions, but the topologies of phase diagram suggested in those studies seem to be in contradiction with one and other, the univariant reactions were different in these studies. Yagi et al. (1979) supposed that two univariant assemblages? + St =Pv+ Mw and Ilm =? + Pv + St were stable at pressures GPa. According to Ito and Yamada (1982) the other two assemblages? + St = Ilm + Mw and Ilm = Pv + St + Mw were stable over narrow pressure range. Yagi et al. (1979) also studied phase diagram of the F%SiO~-Mg2SiO4 system. Recently Ito and Takahashi (1989) studied the phase relations in the F%SiO4-Mg2SiO 4 system at 1373 and 1873 K and confirmed the topology of phase diagram obtained by Yagi et al. (1979). Kato (1986) studied the FeSiO3-MgSiO z system at P = 20 GPa and temperatures up to 2473 K and obtained the stability fields of garnet phase with cubic and tetragonal structures. Ohtani et al. (1991) studied the phase relations in this system at T= 2073 K and pressures up to 25 GPa and only tetragonal garnet majorite was found. Ohtani et al. (1991) determined the phase compositions in equilibria of Mj St and Mj + Px. The univariant reaction Px +? + St = Mj was found to be stable at 16 GPa. Thermodynamic Relations The Gibbs free energy of a pure phase and end members of solid solution at P- T conditions equal to G(P, r)=h~ + ~CpdT-T(S~ - [~-dt) P + ~ VdP 1 where Cp is heat capacity expressed as Cp=a+bT+cT -2+dT 2+eT -3 +f T -~ Molar volume as the function of pressure and temperature was calculated using Murnaghan equation, V(P, T)= V(1, T)(1 +~-)K'Pp\-I/~q" where KT is isothermal bulk modulus expressed as KT = 1/(rio + fil T+ fi2 T2 + fi3 T3) and K~, is the pressure derivative of bulk modulus which in some cases has a temperature dependence: K'~ = K~T. + K'~T ( T- T 0 in (T/Tr) K'pr. is the pressure derivative of bulk modulus at T~ = K, K'pr is its temperature derivative. Molar volume at t bar is expressed as function of T V1, Tr exp ~(T) d \T~ / where V~rr is molar volume at 1 bar and T~= K, c~(t) is the thermal expansion depending on temperature ~(T)=~ TA-~2 T-1 q-~3 T-2" Note that in our thermodynamic treatment, we use the specific temperature dependence of bulk modulus as discussed by Saxena and Shen (1992). The Murnaghan equation is therefore used to generate a series of isotherms at different temperatures (Saxena et al. 1993). It was specially checked that using Murnaghan equation and Birch-Murnaghan one gave very close results in studied P, T range. The Gibbs free energy for solid solution G ss was expressed by G ss = X1 G, + X 2 G2 + RT(X1 in X 1 + X2 In X2) + G ex, where G1, z are the Gibbs free energy of solid solution end-members 1 and 2 (in this study 1 refers to Fe endmember, 2 - to Mg one), X1 is molar ratio Fe/(Fe + Mg) in a phase and Xz = 1 -X1 and G e~ is excess Gibbs flee energy of solid solution described by polynomial (Redlich-Kister model) G r =X 1 X2 [Ao +A1 (Xa --X2)], where Ao, At are the pressure and temperature depending parameters. Input Data and Method of Optimization Thermodynamic properties and equation of state parameters for phases stable at P- T conditions of the mantle were assessed by Saxena and Shen (1992) and Saxena et al. (1993). Phase equilibria data, calorimetric measurements and relationship between Cp, Cv, thermal expansion e and compressibitity fi (Cp=Cv+e 2 VT/~) were taken into into account. However the data on fictive phase FeSiO3 with the structure of ilmenite and majorite and data on mixing properties of solid solutions are not available in this database. The data on enthalpies, entropies, heat capacities, thermal expansion and compressibilities of end-members of solid solutions are presented in Tables 1-3.

3 Table 1. Enthalpies of formation from elements (J/tool), entropies at 1 bar, T= K and Cp=a+bT+cT-2+dTZ+eT-3+fT -~ +gt 1 (J/tool K) for minerals in the system MgO-FeO-SiO z Mineral H S a*10-2 b*10 2 c*10-6 d*10 5 e*10-8 f*10-3 g*10 -~ 325 Mg2SiO4 Forsterite ~-Forsterite y-forsterite F%SiO4 Fayalite ~-Fayalite y-fayalite MgSiO3 Orthoenstatite Ilmenite Perovskite M~orite FeSiO3 Ortho~rrosilite Ilmenite Perovskite t788 0 MNorite MgO FeO Periclase Wustite SiO 2 Stishovite Equation of state parameters and entropies of fictive phases were estimated from structural analogues and enthalpies values were assessed from phase equilibria in this study taking into account the restrictions to equation of state parameters and pressures of phase transitions in fictive end-members mentioned in Fabrichnaya and Kuskov (1991). The enthalpies of fictive phases and mixing properties of solid solution were optimized using the program Parrot (Jansson 1984), phase diagrams were calculated using Poly-3 program in THERMOCALC set (Sundman et al. 1985). The experimental data listed below were used in optimization to get mixing parameters of solid solutions and enthalpies of fictive phases.

4 326 Table 2. Molar volume V (cm3/mol) at 1 bar, 7" K and thermal expansion (l/k) c~=c~ o +~1T+c~z T- 1 +e3 T-2 for minerals in the MgO--FeO-SiO2 system Mineral V Co.105 ~1-10 s ~z.10 3 e3.101 Mg2SiO4 Forsterite /3-Forsterite y-forsterite FezSiO4 Fayalite /3-Fayalite ?,-Fayalite MgSiO3 Orthoenstatite Ilmenite Perovskite Majorite FeSiO3 Orthoferrosilite Ilmenite Perovskite Majorite MgO FeO Periclase Wustite SiO 2 Stishovite Table 3. Compressibility (1/bar) fl= 1/K r =flo-l-fll T + fl2 T2 + f13 T3, K'=(O K/c~ P)r and K"=(~K'/O T)e for minerals in the MgO--FeO--SiO2 system Mineral /30' 107 ill" 1010 f12" 101. / K' K" 104 MgzSiOr Forsterite p-forsterite Forsterite FezSiO4 Fayalite /3-Fayalite y-fayalite MgSiO3 Orthoenstatite Ilmenite Perovskite Majorite FeSiO3 Orthoferrosilite Ilmenite Perovskite Majorite MgO FeO SiO2 Periclase Wustite Stishovite l

5 The data on divariant phase equilibria: O1+/3,/3 + 7, Katsura and Ito (1989), O1+ 7, Nishizawa and Akimoto (1973); 2. The trivariant exchange equilibria data: on Px+7, Nishizawa and Akimoto (1973), Ol+Mw, /3+Mw, 7+Mw, Fei et al. (1991); 3. Divariant equilibria: Pv+Mw+St, Ito et al. (1984), Ito and Takahashi (1989), 7+Mw+St and Pv+Mw+7, Ito and Takahashi (1989); 4. Exchange equilibrium: Pv + Mw, studied by Ito and Takahashi (1989), Fei et al. (1991); 5. Divariant equilibria 7 + St + Mj, Px + Mj, Ohtani et al. (1991), 7 + St + Ilm, Ito and Yamada (1982). The equilibria are given in the sequence in which they were optimized. The mixing parameters for olivine and pyroxene were taken from Saxena et al. (1993). At the first step of optimization, the mixing parameters of/3 and y phases were obtained; they were used as the start values in optimization of mixing properties of/3, 7 and Mw phases. Equilibrium data (1-2) were considered simultaneously. The mixing parameters of Mw and Pv phases were optimized at the third step by including equilibrium data (1-4). Optimization of Mj and Ilm parameters was performed without changing the parameters of other phases, thus the thermodynamic properties of Ilm and Mj phases were obtained independently. The statistical error estimates for the thermodynamic data such as enthalpy, entropy and equation of state parameters can not be exclusively assigned because the optimization procedure involve several reactions simultaneously. A sensitivity test shows that in most cases error ~ 1 kj/mol in enthalpy of a phase might lead to considerable misfit of calculated and experimental phase relations (see also Fei and Saxena 1986). Results and Discussion The mixing parameters of solid solutions assessed in this study are presented in Table 4. The equilibria of olivine, pyroxene and other phases at pressures up to 5 GPa were calculated in Fabrichnaya and Kuskov (1994) using different databases and database of Saxena et al. (1993). It has been shown that the calculations are in a good agreement with experimental data on the olivine +pyroxene equilibrium (Matsui and Nishizawa 1974; Von Seckendorff and O'Neill 1993; Koch-Mfiller et al. 1992) and on the olivine + pyroxene + quartz equilibrium (Bohlen and Boettcher 1981; Koch-Miiller et al. 1992). The equilibria of olivine and pyroxene with other phases calculated with the database of Saxena et al. (1993) are in a good agreement with experimental data too. Equilibria of magnesiowustite and olivine experimentally studied at 1 atm and 1400 K by Wiser and Wood (1991) were not considered in Fabrichnaya and Kuskov (1994). Magnesiowustite was found to contain exess amount of oxygen in Fe-rich compositions. Fei and Saxena (1986) considered wustite as a solid solution FeO-FeOl.s and estimated its mixing parameters and thermodynamic properties of end-members using experimental data at 1 atm of Kubaschewski (1982). However, Table 4. Mixing parameters of solid solutions in FeO- MgO- SiO2 system Phase A0 A1 Olivine fl-spinel V-spinel Pyroxene 0 0 Perovskite Ilmenite T T T T Majorite Magnesiowustite Mixing parameters for olivine, /Lspinel, 7-spinel are given for F%SiO4- MgzSiO4 molecule there is no data at high pressure which allow to estimate thermodynamic properties of wustite at high pressure. Using the model of nonstoichiometric wustite and thermodynamic properties from Fei and Saxena (1986) leads to the distortion of calculated phase diagram for the FeO--FeO1.5-SiO 2 system at T> 1800 K. The decomposition of fayalite to wustite and ferrosilite was obtained in the calculated phase diagram. This results in appearance of O1 + Px + Mw and 7 + Px + Mw assemblages in the calculated phase diagram of Fe2SiO 4- Mg2SiO~ system at 1873 K. These assemblages were not found in the experiments of Katsura and Ito (1989). Since the Px+Mw assemblage was obtained in the calculations for end-member system it can not be excluded by means of assessment of mixing parameters in the Fe2SiO4- Mg2SiO4 system. Thus, there is inconsistency between data obtained in the Fe-O system at 1 atm and data obtained in the Fe-Si-O system at 6-8 GPa and temperature above 1800 K. The Px + Mw phase assemblage was calculated to appear if FeO was considered as stoichiometric phase and enthalpy value for FeO was used from Fei et al. (1991). That is why the enthalpy of "FeO" was changed in comparison with Fei et al. (1991) and wustite was considered as stoichiometric phase in this study. The difference in the enthalpy of FeO formation assessed in this study and in Fei et al. (1991) is 3 kj. The uncertainties in the equation of state parameters provide 1 kj error in the Gibbs free energy of wustite at 6 8 GPa and 1873 K, which is not enough to get stable fayalite at these conditions. At pressure 1 atm the calculated Ko for olivine and magnesiowustite exchange reaction agrees with experimental values KD= of Wiser and Wood (1991) only in Mg-rich composition for Fe/ (Fe + Mg) < 0.25 where magnesiowustite is stoichiometric phase. The deviations from ideality in magnesiowustite obtained in this study are less than it was experimentally determined for nonstoichiometric magnesiowustite by Srecec et al. (1987). There errors in the mixing parameters and enthalpy and entropy values are related and can not be independently evaluated. Result of assessment depends on the thermodynamic properties of endmembers and used model of solid solution. The differences between calculated and experimental values of Ko

6 328 Table 5. Exchange reactions in FeO-MgO-SiO2 system used in optimization T, K P, GPa Composition KFD e OVMw Fe/(Fe+Mg) xsio2 calc exp , p/mw ) /Mw px/~ Pv/Mw I Ref References: 1 Fei et al. (1991), 2 - Nishizawa and Akimoto (1973), 3 Ito and Takahashi(1989) for O1/Mw equilibrium in Fe-rich composition might be caused by uncertainty of FeO enthalpy. There are experimental evidences that wustite become more stoichiometric phase with a pressure increase (Simons 1980). However stoichiometric wustite was not obtained and the "FeO" end-member should be considered as a fictive phase. Its thermodynamic properties and magnesiowustite mixing parameters are the fit constants providing plausible agreement of calculated and experimental phase equilibria at high pressures. However the model used in this study does not take into account the nonstoichiometry of wustite and magnesiowustite and does not describe the O1/Mw exchange equilibrium properly if Fe/ (Fe + Mg) ratio is higher than The uncertainty of thermodynamic data for magnesiowustite effects to the mixing parameters of other phases being in equilibria with magnesiowustite. The calculated and experimental values of K, for exchange equilibria used to assess mixing parameters of solid solutions are presented in the Table 5. The phase diagrams of Fe2SiO,-Mg2SiO4 system at temperatures 1473 and 1873 K and at pressures up to 20 GPa calculated in this study along with the experimental data of Katsura and Ito (1989) are shown in Fig. 1 a, b. The phase diagrams at temperatures 1473 and 1873 K and pressures GPa along with experimental data of Ito and Takahashi (1989) are presented in Fig. 2 a, b. The calculated phase diagrams of F%SiO4- Mg2SiO 4 are in agreement with the experimental data within experimental uncertainty. In spite of some fine compositional featues of Fe/Mg distribution between olivine and magnesiowustite (Fei et al. 1991),?-spinel and pyroxene (Nishizawa and Akimoto 1973) are not reproduced by the calculations the discrepancies with all set of di- and trivariant equilibria is minimum. The experimental uncertainties are discussed in detail by Katsura and Ito (1989). The errors in pressure calibration at room temperature were GPa at pressure ~ 15 GPa and 1 GPa at pressure ~ 23 GPa. Pressure calibration at high temperature was carried out using coesite-stishovite transformation, which slope dp/dt is still uncertain (Kuskov et al. 1992; Swamy et al. 1994). Thus the error of pressure measurement might exceed _+1 GPa at 1873 K and GPa. The precision of temperature measurement was _+ 10 K. The phase compositions were determined by electron probe microanalysis with uncertainty of _+0.7mo1%. The calculated pressure of Ol+7=fl univariant reaction at 1873 K is 1 GPa lower than in the experiments of Katsura and Ito (1989). There arc some inconsistencies between calculated phase compositions of 7 + Mw + St assemblage and the experimental data of Ito and Takahashi (1989). The calculated pressure of?+st=pv+mw univariant reaction at 1373 K is 1 GPa higher than obtained in the experiments of Ito and Takahashi (1989). This inconsistency is caused by the differences between calculated and experimental curves Ilm=Pv and 7=Pv+MgO in the MgO--SiO2 system. It should be noticed that the uncertainty in experiments is quite high. For example, the uncertainy of pressure measurement might reach GPa. These features are within the uncertainty limits of experiments.

7 329 c~ 13. (5 20 I l I I I I T=1473 K 13_ ( O L I I I. I! I T=1873 K \ \ ~:- ol(on3) X ~ '~-!a(~ \,\,-(ol+,~) a 8 OI Egf 4 i... i i J J 'l Fig. 1. Phase diagrams of the Fe2SiO4-Mg2SiO 4 at pressures up 20GPa and temperatures 1473 K (a) and 1873 K (b). X(FeO) is molar fraction of FeO in the bulk composition of the system. The solid curves are calculated. The experimental data are from Katsura and Ito (1989). Phase assemblages obtained in the experiments are b 10 8 E.C 6 I 1 I J I I given in brackets. If the phase composition was measured in experiments this phase or two phases are indicated before brackets and symbol refers to this phase composition or bulk composition of two phases 28 ~ i J i i I I I 27 Pv+ M T=1373 K Pv + Mw 26 1 V x T=1873 K <~ X Mw + St 25 ~- +, 25 -~.. V v 13_ (9 a ~-(Pv+Mw) O- Mw+St(~+Mw+St) ~ '~ 21,",-("r) _ +-'YmP~+u~ ~ \ 20 ~.~- Pv+Mw(Pv+Mw+St) ~- Pv+Mw(~+Pv+Mw) ~ "~ o Mw+St(F~+Mw+St) X" (Mw+St) ~ \ rrl-~(~/+mw+st) 19 i I L i i l Fig. 2. Phase diagrams of the FezSiO~- MgzSiO,~ at pressures up 28 GPa and temperatures 1373 K (a) and 1873 K (b). X(FeO) is molar fraction of FeO in the bulk composition of the system. The c6 02 b O \ 19 E.C calculated curves are given by solid lines. The experimental data are from Ito and Takahashi (1989) and Ito et al, (1984) X The pressure and phase composition of 7 + St = Pv + Mw univariant equilibrium at 1873 K are in a good agreement with the experiments of Ito and Takahashi (1989). The calculated phase diagrams are in agreement with calculations of Fei et al. (1991), though the mixing properties of solid solutions obtained in this study differ from Fei et al. (1991). For/~- and y-spinel the deviations from ideality are not high according to both studies, but the mixing parameter values for y-spinel were obtained negative in this study and positive in Fei et al. (1991), The reason is the difference in enthalpies, entropies, Cp data and equations of state for pure phases adopted in this study and in Fei et al. (1991). The differences in MgSiO3 (Pv) enthalpy, entropy and equation of state parameters

8 I i I T=1273 K lira 1 I T=1873 K 15- +St 18 "~ +St 14-13_ (.9 o_ ( Px Px a 9 I I I / L 1 b 10 I f I I (5 a_" [] Arm "Y+St T=1373 K 9 0 Mw + St P~ 2O r T=1873 K Mw + St " E9; c 19-i ' ' ]~[- Pv(Pv+Mw+St) 9 ~ ~ I- <~- Mw+St(Pv+Mw+St) A- ('y+st) I-q- "/+St(7+Mw+St) 4-- (Mw+St) O- Mw+St(~+Mw+St) 0- ~+St(llm+y+St) ~7- IIm(llm+Pv) y- (Pv) z~,- IIm(llm+7+St) "~- Pv(llm+Pv) f T [ I I I T=2073 K ]_.! /** / 18 +~ E.C 16 0 I I [ I ~ ilml (.9 18-~ a_" E Px " ~ ~ \,-.~- Px (Mj+Px) :~- Mj (Mj+~+St) ~ - ~- MI (Mj+Px) ~-?+St (Mj+y+St) l I I I Fig. 3. Phase diagram of the FeSiO3- MgSiO3 system at pressures up to 20 GPa and T-1273 K (a), T= 1873 K (b), at pressures up to 28GPa and T=1373K (c), T=1873 K (d), T=2073 K (e). Solid lines are the calculated ones. The experimental data are from Ito and Yamada (1982c), Ito et al. (1984) (d) and Ohtani eta]. (1991) (e)

9 331 (Belonoshko 1994; Saxena, person, commun.) and FeO enthalpy result in significant differences in mixing parameters for Pv and Mw assessed in this work and in Fei et al. (1991). The thermodynamic properties of endmembers have a greater influence on calculated phase diagram than the mixing parameters of solid solutions. The difference between the mixing energies is more important than their absolute values. The result of optimization is also affected by amount of experimental points and different equilibria considered simultaneously. The more data are included the more stable result is obtained. Where it was possible the symmetric model of solid solution have been used. The asymmetric solid solution model with mixing parameters dependent on temperature have been used if it was impossible to describe experimental data by simplier models. The maximum solubility of FeSiO3 in perovskite is important for understanding of nature of 650 km seismic discontinuity and was discussed by Fei et al. (1991) and Kuskov and Panferov (1991a, 1993). The thermodynamic data optimized in this study describe experimentally obtained maximum of iron solubility in the perovskite phase quite well. As mentioned above, the fine structure of phase diagrams of the FeSiO3--MgSiO3 system is not resolved in experiments at temperatures 1273 and 1373 K. The calculated phase diagrams at pressures up to 28 GPa are presented in Figs. 3 a-e along with experimental data of Ito and Yamada (1982), Ito et al. (1984) and Ohtani et al. (1991). The topology of phase diagram of the FeSiO3-MgSiO3 system at T= 1373, 1873 K is similar to that obtained in Yagi et al. (1979). The calculated pressure of univariant reactions 7 + St = Pv+ Mw and Ilm=7+St+Pv almost coincides at 1373 K and equal to 25.6 GPa. Ito and Yamada (1991) indicated univariant equilibria at the same pressure. Due to a very narrow pressure range where these equilibria take place at 1373 K they were not distinguished in experiments of Ito and Yamada (1982). The phase diagram of the FeSiO3-MgSiO 3 system calculated at T= 2073 K along with experimental data of Ohtani et al. (1991) is shown in Fig. 3e. There are some inconsistencies between experimental and calculated phase diagrams. The loop ofpx + Mj is wider in experiments than in the calculation; the univariant reaction Px St = Mj appears to be 2 GPa lower. The phase equilibrium Mj St is not stable at P = 23 GPa, as obtained in the experiments by Ohtani et al. (1991). At a pressure of --~ 20 GPa the di- and univariant equilibria including/?-phase become stable in the calculation, but they were not found by Ohtani et al. (1991). Kato (1986) studied exchange equilibria between/?-phase and tetragonal garnet majorite. He found that the composition of/?-phase and majorite almost coincide, as obtained in our calculations. The reasons of some disagreement might be due to both inconsistencies in experiments and data assessment the MgO-SiO2 system. At these high temperature and high pressures the uncertainty of experiments and calculation is quite high. For pressure calibration at high temperature Ohtani et al. (1991) used phase transformation of O1 = fl, Px = Mj, Mj = Ilm and Ilm = Pv in MgO -- SiO L o d g 18 a_ I I I I I I m ~ / P v + Mw / S t +! ~ ~ Px+ + jji px+ 1g:::7// / Ol+Px / r+0 I I I I Temperoture (K) Fig. 4. Phase diagram of the FeO - MgO - SiO 2 system for the composition close to pyrolie XSiO2 = 0.4 mol%, Fe/(Fe + Mg) = The next phase assemblages are indicated by numbers: 1 - Ol+7+Px, 2 - Ol+/~+Px, 3 - /~+Px+St, 4 /7+Px+Mj, 5 - #+St+Mj, 6 - #+7+Mj, 7 - ~+Mj, 8-7+St+Mj, 9-7+Pv+Mj, 10-7+Px+St, 11 - fl+7+pv, I2 - ~+Pv, I3 - ]?+Pv+Mj, 14-/~+Pv+Mw, 15 7+Pv+Mw, 16-7+St+Ilm. Dash lines restrict the range of possible geotherms system. The uncertainty of pressure measurement at P ~ GPa and T= 2073 K might reach 4-2 GPa. There is not enough data on phase equilibria which include majorite in the FeO-MgO-SiO2 system to reassess thermodynamic data of the end-member MgO- SiO2 system. Therefore the data obtained should be considered as preliminary results and further experimental investigations of phase relations between majorite and other phases are necessary. Hopefully these results will be useful in designing new experiments. To understand the fine mineral structure of mantle transition zone the P- Tdiagram for the mantle composition is necessary. Complete phase relations in the FeO-MgO-SiO2 system can be constructed in pressure-temperature-composition space by means of presented thermodynamic model. Such computation can provide information on bulk chemical composition, stable mineral assemblages, geotherm and density profile. Phase diagram for the bulk composition close to pyrolite (Ringwood, 1975) is given on Fig. 4. The conclusion can be made that two narrow divariant zones olivine-/?-spinel-pyroxene and p.spinel-magnesiowustite-perovskite might be assign to 400 and 650 km discontinuities correspondently. Temperature distribution is quite uncertain in the mantle. If temperature at the depth km is higher than K, the assemblages including majorite might be stable at these depths. If temperature in the mantle transition zone is less than 1900 K the majorite phase appears to be unstable. Kuskov et al. (1991) and Kuskov and Panferov (1991a, b, 1993) showed that a topology of (P- T)x diagram is strongly dependent on the SiO2 and FeO content in bulk composition. Phase diagram presented in Fig. 4 is not adequate

10 332 enough to make the final conclusion about consequence of phase assemblages at the depths between 400 and 650 kin. However Fig. 4 shows that the mantle transition zone might consists from sequence of tri-, di- and univariant assemblages. In order to understand the detailed mineralogy of the Earth mantle the phase diagrams of more complicated systems such as MgO-FeO-CaO -A1203-SiO2 should be constructed. Acknowledgments. I am greatful to S.K. Saxena and O.L. Kuskov for useful comments and discussions. The constructive criticism of anonymous reviewers helped to improve the manuscript. This study was supported by grants from Royal Swedish Academy of Sciences, CAMPADA project, the Swedish Natural Science Research Council (NFR) and International Science Foundation. References Akaogi M, Ito E, Navrotsky A (1989) The olivine-modified spinelspinel transformations in the system Mg2SiO~-Fe2SiO~: Calorimetric measurements, thermochemical calculation and geophysical application. 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