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Formation of the Earth’s Core

  • Vsevolod N. AnfilogovEmail author
  • Yurij V. Khachay
Chapter
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Part of the SpringerBriefs in Earth Sciences book series (BRIEFSEARTH)

Abstract

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.

Keywords

Content 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

The possibility of the initial Earth’s pre-planetary bodies heating up to the melting temperature of CAI allowed us to propose a principally new mechanism of the Earth’s core formation [1]. The sense of it is as follows. In the initial stage of the Earth’s formation in the proto-planetary cloud, the initial pre-planetary bodies of the Earth were formed with sizes of few hundred kilometers, the central parts of which had been heated and melted. Together with the phases enriched with Al and Ca, iron was also melted, and was mainly located in the middle part of the pre-planetary bodies (Chap.  3, Fig. 3.4). According to our supposed model, the iron–nickel of the Earth’s core was formed by the collisions of the initial pre-planetary bodies. Due to the fact that the main volume of the initial pre-planetary bodies was in the melted state, their collisions were inelastic. From those inelastic collisions, the fusion of the pre-planetary bodies occurred, the fragments of iron resulting from the collisions were combined, and they then displaced from the central parts of the initial pre-planetary bodies the dense melted aluminum-silicate material, which together with the fragments of the solid cold envelope was thrown into the planetary supply zone. As a result of these collisions, new pre-planetary bodies were formed, in which the central parts were composed of the melted iron–nickel material (Fig. 4.1).
Fig. 4.1

Scheme of a secondary pre-planetary body with melted core formation by collision of two initial pre-planetary bodies. 1—the core of the pre-planetary body is composed of CAI minerals; 2—the middle part of the envelope is composed of iron; 3—the outer part of the solid envelope

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 [2]. 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 [2] and which exists in iron meteorites, formed in them later than iron, and it is not in an equilibrium state with the iron [3]. Therefore, the entry of considerable amounts of sulphur into the Earth’s core during the heterogeneous accumulation is problematical.

One of the problems that arise from discussion of the question about FeO entering into the core composition is the problem of the possibility of achieving in the proto-planetary cloud the value of partial oxygen pressure necessary for forming FeO. A priori that value is not known. In the literature there are many variants for obtaining the required value PO2, including the participation of water [2]. Actually, that problem is solved by nature itself. The existence in olivine pallasites up to 30 % of the fayalite molecule [4] is evidence that the iron oxide condensed from the gaseous phase in the form of olivine together with the metallic iron. From melting of the olivine in the melt, free iron oxide is formed, which is not linked with SiO2. It occurs as a result of partial decay of the fayalite component [5]:
$$ {\text{Fe}}_{ 2} {\text{SiO}}_{ 4} = {\text{ FeSiO}}_{ 3} + {\text{ FeO}} $$
The relation between the content of the free iron oxide FeO and the melt composition in the MgO-FeO-SiO2 system is shown in Fig. 4.2 [5]. If the olivine melt is in an equilibrium state with the melted iron, the part of free FeO will dissolve in the iron and the equilibrium of that reaction will shift to the right. The conditions of FeO dissolving in the melted iron were investigated in detail by Othani et al. [6]. According to their estimation, for the core density to correspond with the geophysical data, the content of the iron oxide in the core has to reach a value of 40 mol% FeO [6]. By the melting temperature of olivine and by low pressure, the solubility of FeO in the melt of Fe does not exceed 4.0 mol%, but that value sharply increases as the temperature increases [6]. The high solubility of iron oxide is achieved by the increase of pressure [6]. This is because the molecular volume of the FeO dissolved in the melted Fe is 3.8 cm3 less than in the melt of FeO [6]. Nevertheless, the possibility of dissolving 40 mol% FeO in the melted core is far from obvious. The problem lies in the fact that the main olivine mass, from which the iron oxide FeO enters into the core, is concentrated in the surface layer of initial pre-planetary bodies and as a result of these conditions it is impossible to provide the uniform distribution of FeO in the middle iron–nickel envelopes. It can be distinguished only in the formation of secondary pre-planetary bodies, when, as a result of collisions, mixing of the material of the initial pre-planetary bodies occurs. With the radius of the secondary pre-planetary bodies reaching more than 200 km, the necessary solubility of FeO in the core is achieved due to high internal pressure.
Fig. 4.2

The dependence of free iron oxide content in MgO-FeO-SiO2 system melt on the mole fraction of FeO. Melt composition: 1—(0.5MgO-0.5SiO2) – 1.0FeO; 2—(0.2MgO-0.8SiO2) − 1.0FeO; 2173К—black, 1873К—open symbols

Additional information about the possible composition of the Earth’s core can be obtained from the density distribution in the present core. From the curve of the core’s radial distribution density (Fig. 4.3), three intervals can be distinguished.
Fig. 4.3

Radial density distribution in the modern earth’s core. I—the central part of the inner core, composed of Fe-Ni alloy without FeO; II—outer part of the inner core, which consists of a different quantity of FeO; III—outer melted core area

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 [1]. 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.

Mathematical modelling of the thermal evolution of the growing planet is based on the above scheme of the process. For the velocity of the growth of the planet’s pre-planetary body, from the model of Safronov in variant [9], the following equation is used:
$$ \frac{\partial m}{\partial t} = 2(1 + 2\theta )r^{2} \omega (1 - \frac{m}{M})\sigma $$
(4.1)
where: ω—angular velocity of the orbital motion, σ—surface density of the matter in the “supply” area of the planet, M—modern mass of the planet, r—the radius of the growing pre-planetary body, q—statistical parameter which takes into account the distribution of particle masses and velocities in the supply zone. The temperature distribution in the body, whose radius is increasing, was discovered from numerical solution of the boundary problem for the heat equation, with consideration of the possibility of melt occurring, but without taking into account the crystallization front position and parametric counting of the convective heat transport in the melt [10, 11]:
$$ c_{ef} \rho \frac{\partial T}{\partial t} = \nabla (\lambda_{ef} \nabla T) + Q $$
(4.2)
where: \( c_{ef} ,\lambda_{ef} \)—the effective values of the heat capacity and thermal conductivity, T—temperature at the desired point in time t, Q—volumetric capacity of internal heat sources. On the surface of a growing body of given conditions, to ensure the balance between the incoming part of the potential energy of the gravitational interaction of bodies, loss of heat to heating of the sediment material, and radiated heat into space with the transparency of the environment:
$$ k\rho \frac{GM}{r}\frac{dr}{dt} = \varepsilon \sigma [T^{4} - T_{1}^{4} ] + \rho \,c_{P} [T - T_{1} ]\frac{dr}{dt} $$
(4.3)
where: ρ—density of the matter, G—gravitational constant, M—mass of the growing planet, r—its radius. T and T 1 —correspondingly, the temperature of the body boundary and outer space, ε—coefficient of medium transparency, c p —specific heat capacity, k—the part of the potential energy transformed into heat. The velocity of change of the radius according to the chosen density model is defined from (4.1). At present, the more perfect expressions are suggested for the Earth’s accumulation time [12]. They provide a qualitative similarity with (4.1) and give the best correspondence with the given data, but the calculation of ∆r leads to additional technical complexity, which is why we use (4.1) at each step. The problem is solved by use of the constant step for the space grid ∆r = 100 m, and not a uniform step for the time grid, which is defined from (4.1) for given ∆r. We used the implicit, conservative, stable scheme, with the second approximation order for the space coordinate and with the first order for the time coordinate. For the successive time moments, at which the planet radius grows in the step ∆r, we define the distributions of temperature, lithostatic pressure, adiabatic temperature, melting temperature, viscosity, and effective thermal conductivity, linked with the solid state value through the Nusselt number. It is assumed that in the area with a developed convection there are realized not very critical flows, for which Nu ≤ 2. That corresponds to the variant in which the temperature distributions in convective areas give their upper estimation.
Some possible variants of the temperature distribution in the core, when the Earth’s size is equal to 3500 km, are shown in Fig. 4.4.
Fig. 4.4

Variants of the temperature distributions in the growing earth’s core [7]. 1—k = 0.3 for iron proto-core; k = 0.01 in silicate mantle. k is varied linear for the interval 2500–3500 km. 2—k = 0.4 for iron proto-core; k = 0.02 in silicate mantle. 3—k = 0.4 for iron proto-core; k = 0.03 in silicate mantle. 4—Dependence of the melting temperature on pressure in the modern core

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.

The possible variants of the temperature distribution up to the moment when the planet size reaches 6300 km are shown in Fig. 4.5.
Fig. 4.5

Possible variants of the temperature distributions up to the moment when the earth is 6300 km in size [8]. 1—The accumulation from small particles. The generation of heat by short-living radioactive elements is not taken into account. k = 0.001 for growing core; k = 0.001 for mantle; 2 and 3—the generation of heat by short-living radioactive elements is taken into account; 2—k = 0.3 for growing core; k = 0.02 for mantle; 3—k = 0.4 for growing core; k = 0.01 for mantle; 4—k = 04 for growing core; k = 0.02 for mantle; 5—k = 0.5 for growing core; k = 0.05; 6—The distribution of the core’s melting temperature with depth by lithostatic pressure [13]

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 [14], support the melting state of the outer core and the solid state of the inner core.

References

  1. 1.
    Anfilogov V, Khachay Y (2005) A possible scenario of material differentiation at initial stage of the Earth formation. Dokl Earth Sci 403A:954–947 (in Russian) Google Scholar
  2. 2.
    Ringwood A (1982) Origin of the earth and moon. Nedra, Moscow (in Russian)Google Scholar
  3. 3.
    Park F, Bunch T, Masalski T (1966) A study of the silicate and other phases in Campo del Cielo meteorite. Geochim Cosmochim Acta 30:399–414CrossRefGoogle Scholar
  4. 4.
    Mason B (1962) Meteorites. Wiley, New York (in Russian)Google Scholar
  5. 5.
    Bobylev I, Anfilogov V (1986) The calculation of the free form metal oxide concentration and the structural parameters of poly component silicate melts. Izv USSR Ser Met 2:23–27 (in Russian) Google Scholar
  6. 6.
    Othani E, Ringwood A, Hibberson W (1984) Composition of core 3, II. Effect of high pressure on solubility of FeO in melted iron. Earth Planet Sci Lett 71:94–103CrossRefGoogle Scholar
  7. 7.
    Khachay Y, Anfilogov V (2009) The temperature distribution numerical models for the Earth envelopes at its accumulation stages. In: Geodynamics. Deep structure. The earth’s thermal field. Geophysical fields interpretation. Proceedings 5th conference on behalf of Bulashevich, Ekaterinburg, pp 520–522 (in Russian)Google Scholar
  8. 8.
    Khachay Y, Anfilogov V (2009) Variant of temperature distributions in the Earth on its accumulation. In: The study of the earth as planet by methods of geophysics, geodesy and astronomy. Proceedings 6th Orlov conference, Kiev, pp 197–202 (in Russian)Google Scholar
  9. 9.
    Safronov V (1969) Evolution of the protoplanetary cloud and formation of the earth and the planets. Nauka, Moscow (in Russian)Google Scholar
  10. 10.
    Samarsky A, Moiseenko B (1965) The economic scheme of transparent account Stefan problem. J Calculating Math 5:816–827 (in Russian)Google Scholar
  11. 11.
    Tikhonov A, Liubimova E, Vlasov V (1969) About the evolution of fusion zones in the thermal history of the earth. Dokl Acad Sci USSR 188:338–342 (in Russian)Google Scholar
  12. 12.
    Pechernikova G, Vitjasev A (2005) The impacts and the early earth evolution by catastrophic action of cosmic bodies. In: Adushkin V (ed) Academkniga Press, Moscow, pp 251–265 (in Russian) Google Scholar
  13. 13.
    Stacey F (1969) Physics of the Earth. Wiley, New YorkGoogle Scholar
  14. 14.
    Boehler R, Chopelas A, Zerr A (1995) Temperature and chemistry of the core-mantle boundary. Chem Geol 120:199–205CrossRefGoogle Scholar

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© The Author(s) 2015

Authors and Affiliations

  1. 1.Institute of MineralogyRussian Academy of SciencesMiassRussia
  2. 2.Institute of GeophysicsRussian Academy of SciencesEkaterinburgRussia

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