Physics of Magmatic Processes

Physics of Magmatic Processes

by Robert Bero Hargraves


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ISBN-13: 9780691615752
Publisher: Princeton University Press
Publication date: 07/14/2014
Series: Princeton Legacy Library Series
Pages: 600
Product dimensions: 6.10(w) x 9.10(h) x 1.30(d)

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Physics of Magmatic Processes

By R. B. Hargraves


Copyright © 1980 Princeton University Press
All rights reserved.
ISBN: 978-0-691-08261-5




Department of Geological Sciences, Brown University


Attempts to quantify the physical and thermodynamic properties of silicate melts that influence such important igneous processes as diffusion, nucleation, crystal growth, major and trace-element crystal-liquid partitioning, or the formation of immiscible liquids, require at least an elementary understanding of the structure of these melts. It is clear, however, that the word structure has different implications for silicate minerals on the one hand and for melts on the other. Silicate minerals, in common with other crystalline solids, are characterized by systematic arrangement of atoms in a three-dimensional array. The structures of the most common silicate minerals reveal that the Si+4 ion occurs in tetrahedral coordination with oxygen over a wide range of temperatures and pressures. Each oxygen surrounding a central silicon ion has the potential of bonding to another silicate ion, thus forming chain, ring, sheet, or framework silicate structures. The linking by bridging oxygens of silicate tetrahedra is often referred to as polymerization; differing degrees of polymerization give rise to the great diversity of silicate structures. In general, a silicate mineral is monodisperse, in that it typically contains only one type of silicate group. For example, olivines contain only isolated SiO4 tetrahedra and pyroxenes only SiO3 chains. There are some exceptions, notably the fascinating biopyribole minerals that contain elements of both sheet and chain structures (Yeblen et al., 1977).

In contrast, there are no fixed lattice sites in a silicate melt, and the positions of the ionic groups change instantaneously and continuously in response to the random thermal motions of the atoms. However, the arrangement of atoms in the melt is not totally random. Radial distribution functions of silicate glasses obtained by the techniques of X-ray diffraction prove that the SiO4 tetrahedra persist in the melt (Warren and Biscoe, 1938; Mozzi and Warren, 1969). Interatomic distances out to 8 [Angstrom] correspond closely in length to the Si–O, Si–Si and O–O distances around a given silicon ion in silicate minerals. Recent X-ray and neutron-diffraction studies of SiO2 glass indicate that crystal-like "long-range" ordering may persist even to a distance of 20 [Angstrom] (Konnert and Karle, 1972).

These data demonstrate that the local structure around a central silicon ion is similar to that obtained in the crystalline state. However, any conclusions pertaining to the structure of the silicate melt on a larger scale remain speculative. The successful application of polymer theory to silicate melts of low SiO2 composition (Masson et al., 1970; Hess, 1971; among others) and the direct determination of the mass distributions of silicate ionic species by various chromatographic techniques (Baltã et al., 1976) reveal that silicate melts are polydisperse solutions containing a wide distribution of silicate ionic groups of various sizes and shapes. The structure of a given silicate anion is not necessarily fixed but may fluctuate between several related forms. However, the average structure of a melt at a given composition, pressure and temperature is a constant and reproducible function. The melt is therefore in a state of homogeneous equilibrium. As the silica content of a metal-rich liquid increases, the SiO4 units polymerize and progressively increase in size and complexity. At some composition, infinitely branched chains develop that eventually evolve into the continuous framework structure of pure silica.

Although this model of the silicate melt is widely accepted and is supported by measurements of such physical properties as viscosity, density, expansivity and ionic conductivity (Bockris et al., 1948, 1954, 1955, 1956), the polymerization path by which a silica-poor melt evolves into a silica-rich melt is not understood. Methods of classical polymer theory (Flory, 1953) can be adapted to calculate the size distributions of polymeric ions in a silicate melt (Hess, 1971). However, these methods have not been applied successfully for melts of SiO2-rich compositions, where silicate anionic polymers of high complexity and infinite size exist. A more general and less specific description of the polymerization reaction is required. This approach is considered in the following section.


The formation of a silicate melt is envisaged as a chemical reaction between liquid metal oxide and liquid silica. The reaction is described by the homogeneous equilibrium

Liquid Silica + Liquid Metal Oxide = Silicate Melt Si–O–Si + M–O–M = 2Si–O–M, (1)

where M represents a cation other than Si+4. This equilibrium is typically written in a shorthand notation (Toop and Samis, 1962a,b)

O0 + O2- = 2O-, (2)

where O0, O2- and O- are called bridging, free, and non-bridging oxygens, respectively. Although this shorthand terminology has the advantage of brevity, it is important to remember that these terms refer to certain bonding configurations and not to discrete oxygen ions in the melt. The bridging oxygen refers to the Si–O–Si complex, the free oxygen to the M–O–M complex and the non-bridging oxygen to the Si–O–M complex. In fact, Hess (1977) showed that in a binary system the chemical potentials of these oxygen species are directly related to the chemical potentials of the oxide and not to ionic components. Thus




As in all chemical reactions, the homogeneous equilibrium (1) is associated with an equilibrium constant, K, where

K = (O-)2/(O0)(O2-), (6)

and the bracketed terms refer to the activities of the oxygen species. If molar concentrations are substituted for the activities, then the concentrations of all oxygen species in a binary silicate can be calculated for a given equilibrium constant, K, and composition of the system (Toop and Samis, 1962a,b). The results of three sample calculations are illustrated in Figure 1. A melt for which K = 0 is one in which there is no reaction between liquid silica and liquid metal oxide to form non-bridging oxygen. The silicate melt is a solution of "molecules" of SiO2 and MO. A melt for which K = ∞ is one in which the reaction to form non-bridging oxygen is complete. Only free and non-bridging oxygen exist between 0 and 33 1/3 mole % SiO2 and only non-bridging and bridging oxygen exist between 33 1/3 and 100 mole % SiO2. Non-bridging oxygen are the sole oxygen species at 33 1/3 mole % SiO2. Melts characterized by K = 0 or K = ∞ are hypothetical and do not exist. Finally, a melt for which K is finite but non-zero is characterized by the occurrence of all three oxygen species throughout the compositional range from 0 to 100 mole % SiO2. As the SiO2 content of the silicate melt increases, the concentrations of free oxygen rapidly decrease to low values, the bridging oxygen gradually increase, and the non-bridging oxygen define a maximum at 33 1/3 mole % SiO2. The maximum is greater for melts characterized by larger K's. The trends reflect the polymerization reactions occurring in the melt as more and more SiO4 units share common oxygens to form larger silicate anionic complexes. For a given composition, a melt characterized by a smaller K contains more bridging oxygen and by definition is more polymerized than a melt characterized by a larger K.

The ability to calculate concentrations of oxygen species in a given system rests with the assumption that molar concentrations may be substituted for activities in Equation (6). This is possible only if the activity coefficients of the oxygen species are unity or if, by chance, they effectively cancel. Neither case is likely. Solution non-ideality in simple silicate melts is manifested by the occurrence of stable and/or metastable silicate liquid immiscibility in most SiO2-rich melts. For example, silicate liquid immiscibility occurs in FeO–, MgO– and CaO–SiO2 melts containing as little as 2 mole % metal oxide at temperatures as high as 1,700°C (Greig, 1927). In this region at least, it is not correct to substitute concentrations for activities. Nevertheless, it is instructive to describe the state of polymerization of a melt by the value of its "equilibrium constant," even though the true value of K, as expressed in terms of the activities of the oxygen species, is not known. The problem is to obtain an estimate of K for a given melt.

Toop and Samis (1962a,b) have approximated the free energy of mixing of a binary silicate melt by the equation

Δ[bar.G] = -(O-/2 RT ln K), (7)

where O- equals the concentrations of non-bridging oxygen and K is expressed in terms of the concentrations of the oxygen species. With temperature and pressure fixed, RT ln K is a constant characteristic of the system. The shape of the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] curve, where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] = mole fraction SiO2, is therefore similar (but with a negative sign) to that of the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] curve. Two important conclusions are deduced from this equation of state. First, the minimum in the free energy of mixing curve should correspond to the maximum in the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] curve. Thus, as discussed in the previous section, the minimum in the free energy of mixing curve should occur near 33 1/3 mole % SiO2. Second, for two melts of the same SiO2 content but containing different metal oxides, the free energy of mixing is most negative for the melt with the greatest concentration of nonbridging oxygen. Such melts are characterized by a large value for the equilibrium constant, K.

Although this equation of state is not applicable to regions where silicate liquid immiscibility is encountered, it does mimic the basic features of the free energy of mixing curves for binary silicate melts. Some free energy of mixing curves for various binary systems are shown in Figure 2. All the curves have minima near [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], in good agreement with theory. The free-energy curves for the systems FeO–, MnO–, CaO–, Li2O–, and Na2O–SiO2 are ordered from least to most negative. According to the equation of state (7), these systems should also be ordered from those characterized by small K to those characterized by large K, and from most polymerized to least polymerized melt. Thus, for a given [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], a FeO–SiO2 melt contains more bridging — and less non-bridging — oxygen than a Na2O–SiO2 melt. By definition, it is the more polymerized melt.


The equilibrium structure of a silicate melt is obtained at constant P, T, and composition when the distribution of oxygen species minimizes the free energy of the solution. If the standard states are the liquids MO and SiO2 at the same P and T, then the free energy of the solution is

Δ[bar.G] = Δ[bar.H] - T Δ[bar.S] = -(O-/2) RT ln K, (8)

where Δ[bar.H] and Δ[bar.S] are the molar enthalpy and molar entropy respectively. In order to predict the state of polymerization of a silicate melt, one must be able to correlate the magnitude of this free energy, and therefore the value of K, with some measurable property of the metal cation. Concepts borrowed from acid-base theory have proven very useful. The definition of basicity when applied to molten silicates is open to a number of interpretations and is subject to some controversy. In this paper, basicity refers to the state of the oxygen atom and its ability to donate some of its negative charge to a metal ion (Duffy and Ingram, 1976). The oxygens are then bases, and the cations acids, in the Lewis sense. The ability of oxygen to donate its negative charge to a given cation depends upon the influence of the surrounding cations. The basicity is at a maximum when the oxygen exists as a free oxygen ion removed from the influence of neighboring cations. Such a state is not stable (Cotton and Wilkinson, 1966), but is approached when the coordinating cations are of a low electronegativity, i.e., they have only a weak affinity for electrons in the particular bond. When oxygen is coordinated to cations of low electronegativity, such as Rb+1 K+1 or Ca+2, the basicity of the oxygen and therefore that of the molten oxide is high. When the oxygen is coordinated with Si, a cation of high electronegativity, its basicity is much less because more of the charge is drawn towards the silicon (i.e. covalent bond formation). In this sense, a bridging oxygen is less basic than a non-bridging oxygen, provided that the latter is associated with a cation of low electronegativity.

The heat effect Δ[bar.H], associated with the formation of non-bridging oxygen, is believed to result from the closer association of the nonbridging oxygen to silicon (Charles, 1969). Non-bridging Si–O (nbr) bonds in crystalline silicates are, in fact, typically shorter than the Si–O (br) bridging bond (Gibbs et al., 1972). According to the acid-base theory, the shortening of the Si–O non-bridging bond is due to the polarization of the electron cloud of oxygen towards, and the oxygen nucleus away from, the silicon (Weyl and Marboe, 1962). The Si–O bond is thus strengthened and the M–O (nbr) is weakened relative to the Si–O (br) and M–O (fr) bonds respectively. In the case for which the total enthalpy change is exothermic, the increased strength of the Si–O (nbr) bond more than compensates for the weak M–O (nbr) bond. The non-bridging oxygens should be most stable in a bond where the coordinating cation has a low electronegativity. Therefore, the addition of oxides of "weak" cations to a SiO2 melt introduces polarizable oxygens that by reaction (2) form non-bridging oxygens, and thus stabilize the melt phase.

This hypothesis is tested by comparing the heats of formation of crystalline metasilicates (MsiO3) and orthosilicates (M2SiO4), for which the crystalline oxides MO and SiO2 are the standard states. The heat of formation of a metasilicate, Δ[bar.H]f for example, is


and is the enthalpy change of converting one bridging and one free oxygen to two non-bridging oxygen, i.e.,

O0 + O2- [right arrow] 2O-. (10)

The heat of formation of the orthosilicate is that obtained by converting two O0 and two O2- to four O-. According to the model, the heats of formation of each isostructural series should be related to the ability of the cation to draw electrons from the oxygen, that is, its electronegativity.

Several electronegativity scales have been proposed (Cotton and Wilkinson, 1966). Unfortunately, the correlation of electronegativities with the enthalpies of formation of the silicates is generally poor. One reason for this is that the electronegativity scales are not very sensitive, that is, the electronegativities of Fe+2, Ni+2, Si+4 and Pb+2 are all 1.8 (Pauling, 1960). A direct measure of the ability of a cation to attract electrons is its ionization potential. This is the minimum energy required to detach one or more electrons from an atom or ion (Cotton and Wilkinson, 1966). Unfortunately, the ionization energies are obtained for atoms in the gaseous state and are not equal to the electron-drawing power of the cation in a bond. However, Mulligan (Pauling, 1960) proposed that the average of the ionization potential and the electron affinity (the energy of the reaction X + e- [right arrow] X- where e- is an electron) was a property closely related to the electronegativity. Thus, although the ionization potential is not a true measure of the electronegativity, it probably is related to it. Consequently, it will be assumed that an ordering of cations according to their ionization potentials should be the same as an ordering obtained from their true electronegativities.


Excerpted from Physics of Magmatic Processes by R. B. Hargraves. Copyright © 1980 Princeton University Press. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
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Table of Contents

  • FrontMatter, pg. i
  • Contents, pg. v
  • Preface, pg. ix
  • Chapter 1. Polymerization Model for Silicate Melts, pg. 1
  • Chapter 2 The Igneous System CaMgSi2O6-CaAl2Si2O8-NaAlSi3O8: Variations on A Classic Theme by Bowen, pg. 49
  • Chapter 3. Viscosity, Density, and Structure of Silicate Melts at High Pressures, and Their Petrological Applications, pg. 93
  • Chapter 4. Trace-Element Constraints on Magma Genesis, pg. 121
  • Chapter 5. Heat Flow and Magma Genesis, pg. 161
  • Chapter 6. The Fracture Mechanisms of Magma Transport From The Mantle to The Surface, pg. 201
  • Chapter 7. Aspects of Magma Transport, pg. 265
  • Chapter 8. Magmatic Infiltration Metasomatism, Double-Diffusive Fractional Crystallization, and Adcumulus Growth in the Muskox Intrusion and other Layered Intrusions, pg. 325
  • Chapter 9. Diffusion in Natural Silicate Melts: A Critical Review, pg. 385
  • Chapter 10. Crystal Growth and Nucleation Theory and the Numerical Simulation of Igneous Crystallization, pg. 419
  • Chapter 11. Experimental Studies on the Dynamic Crystallization of Silicate Melts, pg. 487
  • Author Index, pg. 553
  • Subject Index, pg. 565

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