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Chemical Phase Equilibrium and Physical Structure Within the Earth's Mantle

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Chemical Phase Equilibrium and Physical Structure Within the Earth's Mantle JOURNAL OF PHYSICS OF THE EARTH, VOL. 4, No. 1, 1956 1 Chemical Phase Equilibrium and Physical Structure Within the Earth's Mantle. By Yasuo SHIMAZU Institute of Earth Sciences, Nagoya University, Nagoya. Abstract Phase equilibrium of Fe-Si-O system within the earth is discussed. Due to the action of gravitational differentiation, there is chemical squeezing of the lighter material out of the earth. Then the silicate or oxide phase is decompose below certain depths even if the temperature is low. It is concluded that Fe2SiO4 layer is decomposed at 1,000 km from the earth's surface. This result suggests the origin and the physical properties of Jeffrey's 20° discontinuity. §1. Introduction in the combination, so that the mol ratio cannot In my previous paper (Y. SHIMAZU[1955]), we diverge from some definite ratios. FeO and SiO2 studied the chemical equilibrium condition can exist either in the form of 2FeO・SiO2 (faya- within the earth. Our discussions were based lite) or in the form of FeO・SiO2 (ferrosilite). In a upon an assumption that a mixed crystal can system of components which can combine into be chemically stable with any mixing ratio of its different compounds, gravity will obviously components. For instance, FeO and SiO2 were tend to develop a mechanically stable arrange- assumed to be able to combine with any mol ment of different layers of different chemical ratio. There is, however, a very narrow area Phases and of different densities. If the Fig. 1. Phase equilibrium of H2O-system in the gravitational field. gravitational differentiation proceeds far equal. enough, as was discussed in my previous It is interesting to note that ordinary GIBBS paper (Yasuo SHIMAZU [1955]),then the system phase rule cannot be applied to the phase becomes saturated at the lower end with one equilibrium in the gravitational field as compound phase, and further transport of W. SWIETOSLAWSKY[1947] pointed out. He dis- material will form another compound. We cussed one-component system (H2O) under the then have two phases of different compound action of gravitational force. According to concentration ratios. There will be a concent- the ordinary GIBBS phase rule, the maximum ration discontinuity at the point where the number of co-existing phases for H2O-system chemical potentials of the two phases are is three. In fact, at the so-called triple point 2 Yasuo SHIMAZU in the phase diagram we have solid ice, liquid is due to W. EITEL [1951]. Experimental water, and water vapor. values are obtained from the works of Let us assume thatlarge amounts of water, F. BIRCH et. al. [1942]. We calculated ΔG0 (=ΔG ice, and water vapor are put in a closed at ordinary pressure) from the integration of container. In Figure 1, the initial state (a) (2) and final state (b) are schematically shown. First, the block of ice is partly in the vapor Results of calculations are as follows and partly immersed into the liquid. The immersed part is subjected to the action of hydrostatic pressure, which changes from the top vapor pressure p0(=0.006 atm. in this system)to p0+Δp and thus the equilibrium temperature between the solid and liquid phases (3) changes from T° (triple point=0.0078℃) to T°-ΔT as seen in the phase diagram. In Figure 1 (a), there is only one line along which T° can actually be found. As is easily understood, the ice below the surface of the (4) water undergoes melting. On the other hand, the ice surrounded by vaporous space is covered by ice formed. Thus the movement of ice toward the surface takes place. The balance of heat requires that the heat used (5) in melting the ice must be compensated by Table I. Heat of formation ΔH at several that in the formation of the corresponding amount of ice. As we see in Figure 1 (b), temperatures (kcal/mol) three phases have no mutual contact with each other in the final state. We may also note that the order of layering of the three phases is governed by their density differences. §2. Calculation of free energy of oxidation Along the general line in section 1, we shall discuss the chemical equilibrium of three- component system (Fe-Si-O) within the gravi- Table II. Free energy change ΔG0 at tational field of the earth. For this purpose several temperatures (kcal/mol) we must get as a function of temperature the heat of formation ΔH and GIBBS free energy change ΔG during the chemical reaction. We can obtain ΔH from the change of specific heat ΔCp (1) Since the specific heat Cp of each component Since no experimental value is available, is known experimentally as a function of another reaction temperature, ΔCp, can be obtained from the difference between the Cp of each side of (6) reaction equation. The procedure of calculation is not discussed here. Tables 1 and 2 give Chemical Phase Equilibrium and Physical Structure Within the Earth's Mantle 3 ΔH and ΔG0 at several temperatures. The migration of solid ice occurs. The melting of quantity ΔG0 is nothing but the chemical ice at the bottom has a compensated formation potential at the standard pressure. We have at the top. In a multi-component system, on also the following general relation between the other hand, there must be the migration chemical potential ΔG and the vapor pressure of any one phase through others. This is (7) nothing but the diffusion phenomena. Even in crystalline solid system, there will always The equilibrium condition is given by ΔG=0. be some diffusion effect. Thus, the chemical We get the temperatures T0=4,200°K, 5,200°K and 4,400°K at which the equilibrium condi- potential gradient will always cause a diffusioin through the system if sufficient time is allowed. tion are realized at room for the reactions (3), We do not concern ourselves with the mecha- (4) and (5), respectively. At these tempera- tures the corresponding oxides or silicates are nism of diffusion. The final equilibrium state decomposed. At higher temperatures, oxides is assumed apriori. or silicates are unstable. Migration is controlled by gravitational differentiation in which the lighter material Pressure dependence of the decomposing temperature T0 is given by the CLAPEYRON moves upward and the relatively heavier equatlon material moves downward. If the lighter material is in the fluid form, diffusion through (8) the solid phase will effectively realized. Equi- librium of hydrous minerals, such as mica, where ΔV is the volume change between the has already been discussed by several authors left-hand and right-hand sides of the reaction based on this concept of migration (cf. J. B, equation. In (3) and (4), ΔV are equal to the THOMPSON [1955]). Of these studies the most volume changes in gaseous oxygen phases, or famous is that on calcite (CaCO3)→wollastonite -1/2×22 .4×103cc/mol and -22.4×103cc/mol, (CaSiO3) reaction. (cf."Theoretical Petrology" respectively. In (5), ΔV is the difference in by T.F.W. BARTH [1948] (p. 286)). As this molar volume between both sides of the reaction proceeds to the right, gas phase CO2 equation, viz. is produced and the equilibrium temperature will therefore increase with increasing pressure. This is given by equation (8). At one atmo- In conclusion, we get spheric pressure, the formation of wollastonite requires a temperature of about 450℃. for (3) (9) However, the rock is usually semipermeable to CO2 gas which thus escaping from the for (4) (10) locale of the reaction will percolate to the for (5) (11) surface, If the gas escapes as soon as it is These equations show that an exceedingly produced, the molecular volume of the gas can high temperature is necessary to decompose be neglected and the change in the temperature oxides within the earth's interior. Then we of the reaction with pressure can be calculated may infer that oxides and silicates are stable from (8), taking into consideration only the within the earth's mantle if the abundance of molar volumes of the solid Phases. The elements concerned is appropriate. molar volumes in c.c. are as follows: §3. Phase equilibrium within the gravita- tional field. (12) As we see in §1, the phase equilibrium within the gravitational field has a particular (13) character, that is, the ordinary GIBBS phase rule cannot be applied. In one-component the latter showing that the differential pressure system, as stated in §1, the movement or squeezes CO2 gas out of calcite at a lower 4 Yasuo SHIMAZU temperature than is otherwise possible. The thick layer of A is unstable in the gravitational formation of wollastonite is facilitated with field even if the temperature is below T0 increasing pressure. In this case gas escapes in (8). A more stable state exists if the through the fissure rather than by diffusion. reaction proceeds to the right below a certain As is shown later, however, the above discus- depth h, so that the dense phase B is formed , sion is not rigorous since the chemical poten- while the liberated phase C is displaced tial gradient of CO2 is neglected. to the top of layer A. The top of layer A The idea of chemical squeezing of some is the zero level surface. This state is shown light materials out of deeper parts of the schematically in Figure 2. The migration of earth has also been presented by several C phase is shown by a pipe line (fissure) authors. Decrease in the degree of oxidation which passes through A layer. or decrease in the ratio of oxygen to metallic GIBBS free energy G per mol is a function ions at different levels in the earth's crust of pressure P, temperature T, and the depth shows the squeezing of oxygen.
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