Formation of the Earth’s Core
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This chapter describes the physical model that is used for numerical solution of the problem of temperature distribution in the forming core of the growing Earth. It defines the composition of the Earth’s core, on which depends, in particular, the changes during the process of accumulation and the melting temperature distribution from the pressure. There is discussion of the conditions that describe the energy balance on the surface of the growing planet. The obtained variants of the numerical temperature distribution in dependence on the values of the model parameters are presented. All variants of the solution are described for the moment when the core ceases to grow, the formation of the inner solid core and melted outer core. It is shown that different conditions ensure either the solid state or the melted state of the layer that forms at the bottom of the forming mantle.
KeywordsContent of the initial core matter Numerical modelling Variants of the temperature distribution Temperature in the core
4.1 Mechanism of the Earth’s Core Formation and Its Possible Composition
According to geophysical data, the modern distribution of the density of the Earth’s core requires that, besides iron, it must also include a considerable amount of light components. In our variant, in the initial stage of the process of heterogenic accumulation, core growth occurred from the materials which arrived on the surface of the growing Earth from the supply zone at low pressure. Therefore in the core composition there can be only those components that were by that time present in the supply zone and that were dissolved in substantial amounts in the melted iron by low pressure. The main light component in the core is FeO, according to the assumption of . In the initial stage, when the initial pre-planetary Earth’s bodies are formed, the composition of the iron–nickel material corresponds to the composition of iron meteorites, in which the composition of FeO is negligibly low. Troilite, which is considered as a possible light component of the core  and which exists in iron meteorites, formed in them later than iron, and it is not in an equilibrium state with the iron . Therefore, the entry of considerable amounts of sulphur into the Earth’s core during the heterogeneous accumulation is problematical.
For the interval from 6370 to 5600 km, the density gradient is equal to 0.0002 g/cm3 per km. For the interval from 5600 to 4800 km, it increases to 0.43 g/cm3 per km and finally, for the interval from 4800 to 3000 km, it increases to 1.04 g/cm3 per km. The subsequent density distribution allows us to propose that the core for the interval from 6370 to 5600 km has a constant composition and contains the iron–nickel melt without light components. The density change for that interval is stipulated by the dependence of the specific volume of Fe-Ni alloy on pressure. In the interval from 5600 to 4800 km, iron oxide can appear in the composition of the inner core. The compressibility of this material increases with increasing FeO content. The strong increase of the density gradient in the third interval is brought about because in that interval the material is in the melted state and its compressibility is significantly greater than that of solid matter. This interpretation of the radial distribution of density agrees well with the given mechanism of the formation of the Earth’s core.
Thus, the process of the formation of the Earth’s core can be divided into three stages: 1—formation of the initial pre-planetary bodies, in which the middle envelope is mainly composed of melted iron; 2—formation of the secondary pre-planetary bodies, in which the Fe–Ni melt is located in the central part of the new pre-planetary bodies; 3—combination of the secondary pre-planetary bodies into one growing planet. At the third stage, the core continues to increase due to the iron melting, which reaches the Earth’s surface as meteorite content and sinks to the core’s surface as melted iron. Based on the average iron composition in meteorites H, L and LL, at that stage about 30 % of the present core mass passed into the core. The role of the meteorite material will be considered in more detail in the Chap. 5.
4.2 The Temperature Regime During the Process of the Earth’s Core Growing
Further evolution of the growing Earth depends on the temperature that was reached in the core. We can estimate it by the following. The temperature distribution in the body of the increasing radius is obtained from the numerical solution of the boundary value problem for the system of heat equation with a convective term, the balance equation of impulse, mass, gravitation potential, and the equation of the Stefan problem for phases of boundary shifting . In this stage the solution can be derived using the 1-D model taking account of the possibility of melting appearing without explicit location of the crystallization of the front boundary, and taking parametrical account of convective heat transfer in the melting zone [7, 8]. On the surface of the growing body we assign the conditions that provide the balance between the incoming part of potential energy of gravitational bodies interaction, heat expenditure for heating of the falling matter, and thermal energy radiating to space, taking account of the transparency of outer space. The separation of the proto-planetary material into the metallic and silicate components that occurred in the stage of core growth must be taken into account in the mathematical modelling of the core’s thermal regime. The concentration of short-living isotopes decreases at the final stage of core formation and the energy contribution from their decay becomes minor.
The main difference between these variants and the variants given before consists in the existence of the minimum values of T corresponding to 400–500 km. By that time, the value of energy being released decreases significantly with 26Al decay. At the same time, as the mass of the proto-planet increases, the amount of the kinetic energy of falling accumulated bodies and particles also increases. In the final stage of the core accumulation, account is taken of the decrease of the part of the energy transformed into thermal energy, which is due to the part of the solid silicate component of the collision bodies, which leads to the significant decrease in temperature of the forming layers.
As seen from the results presented in Fig. 4.1, the temperature distribution is determined by the heat output caused by the decay of short-living radioactive isotopes only in the initial stage, and up to the moment when the radius reaches 300 km. The further energy balance depends on the part of the potential gravitation energy that results from collisions of the accumulated bodies, on the heat, and on the other part, which is lost by radiation. According to the mechanism described above in the presented variants, the differentiation is explicitly on account of the fact that, in the growing stage of the greater part of the iron core, the collisions that occur are practically inelastic and most of the potential energy is transformed into thermal energy. In the final stage of the core’s growth, the pre-planetary body can already retain the outer brittle envelope of the collision bodies. The impact becomes more elastic, which is explained by the decrease in the part of the potential energy used for heating. The presented results show that, by the end of core formation, the temperature distribution in the variants obtained in accordance with the experimental relation of the iron’s melting temperature, the Fe–FeO mixture, and the pressure , support the melting state of the outer core and the solid state of the inner core.
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