Research Statement 

S. K. Saxena

The following are the high lights of his research (the numbers in brackets correspond to the the number of the publication in the bibliography):

 1. From solar gas to terrestrial planets

        Since the Earth’s interior is inaccessible, the only information on the composition of the deep Earth is indirect. Therefore, it is necessary to consider the cosmochemical constraints on planetary chemistry. The basic tenet is that if it is not in the solar gas, it cannot be in the terrestrial planets. The concentration of a chemical species in the Earth, depending on the accretion history, should have some proportional relationship to its solar abundance. During the 1980’s, we developed programs and data bases to compute equilibrium condensation of solids from solar gas. This was a substantial improvement over previous studies because the technique of Gibbs free energy minimization was used (52) and solid solutions were included in the data base (63,64). These studies clearly mapped the pressure-temperature stability of several solids found in different classes of meteorites. For the first time, the study covered the condensation of both hydrous and anhydrous species (63). The data bases and the calculations have acquired a new significance because of the current interest in the formation and composition of the asteroidal bodies and their exploration for space resources. Using the density data on various terrestrial planets, the possibility of the formation of planetary bodies, entirely by condensation from the solar gas, was explored and it was demonstrated that this could have happened in the primitive solar cloud (71). In these models, the Earth continues to remain chondrititc in composition which has been the geochemical consensus for several decades.  

2. Computation of phase equilibrium

        Computation of phase equilibrium to understand the chemical composition of the Earth’s core and mantle has always remained as one of our important goals. Earth’s outer core has liquid properties and its density is substantially less than that of iron. Several dilutents have been proposed to explain this property. One early study (51),  showed that it was thermodynamically possible to dissolve sufficient Si in iron to lower the density to an appropriate level.

        Computation of multicomponent phase equilibrium by using the minimization of Gibbs free energy in a given chemical system (62) has been one of the mainstays of our work. In these studies, the chondritic model composition has been used to simulate the mantle (65,113) and core densities both under hydrous  and anhydrous conditions. These studies have led to various interesting results. The mantle density can be modeled in the ternary system (MgO-FeO-SiO2) for a chondritic mantle but the iron content has a strong influence on the density variation (113). The mineralogical model, while not requiring any seismic data for its construction, reproduces the seismic discontinuities and the density variation in the mantle which are almost exact replica of those produced by the Preliminary Earth Reference Model (PREM). Calculated adiabatic geothermal gradient starting at 6 GPa and 1500 K reaches a temperature of 2046 K at the core/mantle pressure (135 GPa) in a pyrolite mantle. The model Earth parameters in the lower mantle are (PREM parameters in bracket): Ks = 308 (306)  to 687 (656) GPa; f = 70 (69) to 121 (118) km2s-2.

3. Fluids in the Earth’s interior

        The question whether there is any significant amount of fluid phase in the deep mantle has always occupied our minds. It is quite evident that a certain amount of trapped primitive fluid in the mantle  would facilitate the geodynamical processes. With this view in mind and particularly for modeling processes in the proto-planetary bodies, we have worked on a program to model high pressure fluids. This work started with formal thermodynamic applications (76-80,99) and then continued with calculations using molecular dynamics methods (90,91,96,98) at ultra-high pressures. The models have now been incorporated in the Gibbs free energy program (Chemsage) and can be used for systems of as many as 13 different fluids in the system (C-H-O-S-N-Ar) (100). With such multicomponent non-ideal fluid models, it is possible to study the role that fluids must have played in the early history of the planet forming processes. Our work (81,82) showed that the fluid in growing primitive mantle of carbonaceous chondritic composition was dominantly methane with subordinate amounts of hydrogen and water. Such a composition is stable over a broad range of pressure and temperature. The solids in equilibrium with such fluids would be olivine and pyroxene (or their high pressure equivalents), graphite or diamond and iron.  This mixture is quite appropriate for an undifferentiated Earth. At upper mantle pressures, the fluid composition is strongly influenced by presence or absence of free iron. A fluid with as much as 75% methane could be in equilibrium with olivine (13% fayalite) without metallic Fe as a coexisting phase. The oxygen fugacity of the primitive mantle with such fluid composition would be several log units below that of the quartz-fayalite-magnetite buffer.


4. Thermodynamic data bases

        Thermodynamic data bases are crucial to all our applications requiring the calculation of the planetary processes. We have devoted considerable efforts to systematize and maintain a thermodynamic data base which is both geological as well as metallurgical. Our early efforts were in the field of solid solution modeling which resulted in the publication of two monographs (1,3). The question of the choice and implementation of the solid solution models has now reached a stage that we do not have to worry about the details which are all computerized. The Chemsage (GTT,Aachen) and Thermocalc (Stockholm) programs permit the use of a variety of solutions and we are happy to have contributed to these programs which can be used for all types of geophysical and geochemical computations. The improvements in solution models followed the attempt to obtain internally systematized data bases. We worked on improving the analytical expressions for heat capacity (4,78), thermal expansion and bulk modulus (4,85-97) and making all these internally consistent (4,72,89,125). Since all individual parameters, e.g. heat capacity, thermal expansion and compressibility are constrained to vary with one another and with temperature, our data base can be used with confidence for extrapolations (113,125). The use of the data base permits the calculations on the variations of planetary densities, thermal gradients  and the nature of the Earth’s core and its interaction with the lower mantle.


5. High pressure and high temperature experiments

        Iron Phase Diagrams and Earth’s Core: Earth has a large core reaching to a depth of nearly 2900 km from its center; this core stores a substantial part of the planet's energy and, therefore, exercises significant influence on the dynamic processes. Iron has always been considered as well-suited to form a major part of the core; it is sufficiently abundant and seems to have the right density. Seismic data require that the core contain a solid inner core and a liquid outer core. The study of iron at Uppsala has been focused on three aspects. The first one concerns melting to ultra-high pressures (103,104,105), the second with finding new iron phases (104, 105, 108, 110, 117, 121) and the third with systematizing a thermodynamics data base (104, 113, 114) with which to calculate the phase equilibrium relations in the proto-Earth, the deep mantle and the core.  Iron melting has been done to a pressure of 140 GPa (1.4 megabar) reaching the outer core of the Earth (104). These data along with those of  R. Boehler’s to 195 GPa have been used to calculate the melting curve of iron to pressures reaching the center of the Earth for which a temperature of 6150 K is estimated (104). We have generated a considerable debate after proposing that iron may occur as a new polymorph beta, now recognized to be a double layer DHCP structure. We have confirmed this structure to pressures as high as 130 GPa or 1.3 megabar. Several other interesting polymorphic transitions are possible at high pressure and temperature. Our latest result have reached pressures as high as 200 GPa .

        Stability of perovskite in the deep Earth: Perovskite (MgSiO3) has always been regarded as the stable phase in the mantle. It is generally considered as occurring with magnesiowustite and the iron is distributed between the two solid solutions. We asked the question: what if the silicate was not stable with respect to the oxide mixture MgO + SiO2. While it may or may not make a major difference in the density profile of the deep Earth, it would surely constrain all the iron to be contained in the magnesiowustite causing important redistribution of species in the deep mantle. We followed this research both experimentally (119) and theoretically (121,122). It was discovered that pure MgSiO3 perovskite broke down to MgO+SiO2 between 60 and 70 GPa in the diamond-anvil cell. Such a reaction could be stress related. Therefore, we studied the problem theoretically and found that an oxide mixture does become more stable than perovskite at pressures between 115 (15) GPa. Finally, we have repeated the experiment again with a differently designed diamond-anvil cell with electrical heating and and studied the dissociation reaction: MgSiO3 (perovskite) = MgO (periclase) + SiO2 (high pressure silica phase) at 82 (3) GPa by in-situ heating to temperatures between 300 and 1780 (50) kelvin and x-ray diffraction. The orthorhombic perovskite changed to a pseudo-cubic phase between 1280 to 1485 kelvin. The oxide mixture was observed to grow at  temperatures between 1600 to 1700 kelvin and orthorhombic perovskite was recovered upon cooling at 1140 K. Compositionally, the instability of perovskite makes the oxide mixture as the most probable mantle material which can provide a variety of possible mantle compositions. Dynamically, the lighter SiO2 component would facilitate differentiation of the lower mantle.

         The new mineral physics data has some very important consequences for modeling Earth’s early history. Hot condensing material in a nebular setting, where differentiated planetesimals with their iron cores are plentiful, forms the solid protocore (Fe-Ni-S-C) which reacts with FeO available in magnesiowustite and due to dissociation of perovskite at the core-mantle interface. The interface grows to form  the liquid core at the expense of the solid proto-core. The model is consistent with geochemical data and has important implications for the dynamo and for the rotation of the inner core.  

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