1. Mineral Surface Reactions(cont.); Trace Element Geochemistry Lecture 23

2. Review: Surfaces in Water Oxygen and metal atoms at an oxide surface are incompletely coordinated hence have partial charge. Consequently, mineral surfaces immersed in water attract and bind water molecules. The water molecules then dissociate, leaving a hydroxyl group bound to the surface metal ions: ≡M + + H 2 O ⇄ ≡MOH + H + Similarly, unbound oxygens react with water to leave a surface hydroxyl group: ≡O – + H 2 O ⇄ ≡OH + OH – The surface quickly becomes covered with hydroxyls (≡SOH), considered part of the surface rather than the solution.

3. Adsorption of Metals and Ligands Solutes in water can then be adsorbed to the surface as well.

4. Development of Surface Charge Mineral surfaces develop electrical charge for three reasons: o Complexation reactions between the surface and dissolved species, such as those we just discussed. Most important among these are protonation and deprotonation. This aspect of surface charge is pH- dependent. o Lattice imperfections at the solid surface as well as substitutions within the crystal lattice (e.g., Al 3+ for Si 4+ ). Because the ions in interlayer sites of clays are readily exchangeable, this mechanism is particularly important in the development of surface charge in clays. o Hydrophobic adsorption, primarily of organic compounds, and “surfactants” in particular (discussed in Chapter 12).

5. Surface Charge We define σ net as the net density of electric charge on the solid surface, and express it as: σ net = σ 0 + σ H + σ SC where σ 0 is the intrinsic surface charge due to lattice imperfections, etc., σ H is the net proton charge (i.e., the net of binding H + and OH – ), σ SC is the charge due to other surface complexes. σ is usually measured in coulombs per square meter (C/m 2 ). σ H is given by: σ H = F (Γ H - Γ OH ) where F is the Faraday constant and Γ H and Γ OH are the adsorption densities (mol/m 2 ) of H + and OH – respectively. In a similar way, the charge due to other surface complexes is given by σ SC = F (z M Γ M + z A Γ A ) where the subscripts M and A refer to metals and anions respectively, and z is the charge of the ion. Thus net charge on the mineral surface is: σ net = σ 0 + F (Γ H –Γ OH + z M Γ M + z A Γ A )

6. Charge as a function of pH At some value of pH the surface charge, σ net, will be zero. The pH at which this occurs is known as the isoelectric point, or zero point of charge (ZPC). The ZPC is the pH at which the charge on the surface of the solid caused by binding of all ions is 0, which occurs when the charge due to adsorption of cations is balanced by charge due to adsorption of anions. A related concept is the point of zero net proton charge (pznpc), which is the point of zero charge when the charge due to the binding of H + and OH – is 0; that is, pH where σ H = 0. Surface charge depends upon the nature of the surface, the nature of the solution, and the ionic strength of the latter. o ZPC, however does not depend on ionic strength.

7. Determining Surface Charge The surface charge due to binding of protons and hydroxyls is readily determined by titrating a solution containing a suspension of the material of interest with strong acid or base. The idea is that any deficit in H + or OH – in the solution is due to binding with the surface.

8. Surface Potential The charge on a surface exerts a force on ions in the adjacent solution and gives rise to an electric potential, Ψ (measured in volts), which in turn depends upon the nature and distribution of ions in solution, as well as intervening water molecules. The surface charge, σ, and potential at the surface, Ψ 0, can be related by Gouy-Chapman theory, which is similar to Debye–Hückel theory. The relationship between surface charge and the electric potential is: where z is the valence of a symmetrical background electrolyte (e.g., 1 for NaCl), Ψ 0 is the potential at the surface, F is the Faraday constant, T is temperature, R is the gas constant, I is ionic strength of the solution in contact with the surface, ε r is the dielectric constant of water, and ε 0 is the permittivity of a vacuum. Most terms are constants, so at constant temperature, this reduces to: where α and β are constants with values of 0.1174 and 19.5, respectively, at 25˚C.

9. Surface Potential Where the potential is small, the potential drops off with distance from the surface as: where κ has units of inverse length and is called the Debye length: o The one variable, other than temperature, is I. The inverse of κ is the distance at which the electrostatic potential will decrease by 1/e. o We also see the potential will drop off more rapidly at high ionic strength. (Atom diameters are ~10 -1 nm)

10. Development of the ‘Double Layer’ The surface charge results in an excess concentration of oppositely charged ions Na + in this case, and a deficit of like charged ions, Cl - in this case, in the immediately adjacent solution. Thus an electric double layer develops adjacent to the mineral surface.

11. The Double Layer The inner layer, or Stern Layer, consists of charges fixed the the surface. The outer diffuse layer, or Gouy Layer, consists of dissolved ions that retain some freedom of thermal movement. The Stern Layer is sometimes further subdivided into an inner layer of specifically adsorbed ions (inner sphere complexes) and an outer layer of ions that retain their solvation shell (outer sphere complexes), called the inner and outer Helmholtz planes respectively. o Hydrogens adsorbed to the surface are generally considered to be part of the solid rather than the Stern Layer. The thickness of the Gouy (outer) Layer is considered to be the Debye length, 1/κ and will vary inversely with the square root of ionic strength. Thus the Gouy Layer will collapse in high ionic strength solutions and expand in low ionic strength ones.

12. Importance of the Double Layer When clays are strongly compacted, the Gouy layers of individual particles overlap and ions are virtually excluded from the pore space. This results in retardation of diffusion of ions, but not of water. As a result, clays can act as semi-permeable membranes. Because some ions will diffuse more easily than others, a chemical fractionation of the diffusing fluid can result. At low ionic strength, the charged layer surrounding a particle can be strong enough to repel similar particles with their associated Gouy layers. This will prevent particles from approaching closely and hence prevent coagulation. Instead, the particles form a relatively stable colloidal suspension. As the ionic strength of the solution increases, the Gouy layer is compressed and the repulsion between particles decreases. This allows particles to approach closely enough that they are bound together by attractive van der Waals forces between them. When this happens, they form larger aggregates and settle out of the solution. For this reason, clay particles suspended in river water will flocculate and settle out when river water mixes with seawater in an estuary.

13. Effect of the surface potential on adsorption The electrostatic forces also affect complexation reactions at the surface, as we noted at the beginning of this section. An ion must overcome the electrostatic forces associated with the electric double layer before it can participate in surface reactions. We can account for this effect by including it in the Gibbs free energy of reaction: ∆G ads =∆G intr +∆G coul where ∆G ads is the total free energy of the adsorption reaction, ∆G int is the intrinsic free energy of the reaction (i.e., the value the reaction would have in the absence of electrostatic forces; e.g., the same reaction taking place in solution), and ∆G coul is the free energy due to the electrostatic forces and is given by: ∆G coul = F ∆ZΨ 0 where ∆z is the change in molar charge of the surface species due to the adsorption reaction. For example, in the reaction: ≡SOH+Pb 2+ ⇄ ≡SOPb + +H + the value of ∆z is +1 and ∆G coul = F Ψ 0

14. Effect on Equilibrium Thus if we can calculate ∆G coul, this term can be added to the intrinsic ∆G for the adsorption reaction (∆G intr ) to obtain the effective value of ∆G (∆G ads ). From ∆G ads it is a simple and straightforward matter to calculate K ads : o (note equation 6.128 in the book has typos. Should be the above.) Since K intr = e -∆G intr /RT and ∆G coul = F ∆zΨ 0, we have: Thus we need only find the value of Ψ 0, which we can calculate from σ.

15. Effect of potential on adsorption The effect of surface potential on a given adsorbate will be to shift the adsorption curves to higher pH for cations and to lower pH for anions. The figure illustrates the example of adsorption of Pb on hydrous ferric oxide. When surface potential is considered, adsorption of a given fraction of Pb occurs at roughly 1 pH unit higher than in the case where surface potential is not considered. In addition, the adsorption curves become steeper.

16. Introduction to Trace Element Geochemistry Chapter 7

17. Importance Though trace elements, by definition, constitute only a small fraction of a system of interest, they provide geochemical and geological information out of proportion to their abundance. There are several reasons for this. First, variations in the concentrations of many trace elements are much larger than variations in the concentrations of major components, often by many orders of magnitude. Second, in any system there are far more trace elements than major elements. In most geochemical systems, there are ten or fewer major components that together account for 99% or more of the system. This leaves 80 trace elements. Each element has chemical properties that are to some degree unique, hence there is unique geochemical information contained in the variation of concentration for each element. Thus the 80 trace elements always contain information not available from the variations in the concentrations of major elements. Third, the range in behavior of trace elements is large, and collectively they are sensitive to processes to which major elements are insensitive.

18. What is a Trace Element? For most silicate rocks, O, Si, Al, Na, Mg, Ca, and Fe are “major elements”. An operational definition might be as follows: trace elements are those elements that are not stoichiometric constituents of phases in the system of interest. o This definition is a bit fuzzy: a trace element in one system is not one in another. For example, K never forms its own phase in mid-ocean ridge basalts (MORB) but K is certainly not a trace element in granites. o Of course this definition breaks down for fluid solutions such as water and magma. Trace elements in seawater and in rocks do have one thing in common: neither affect the chemical or physical properties of the system as a whole to a significant extent. o But some components do influence properties even at very low conc.; e.g. trace elements can influence color of minerals. Perhaps the best definition of a trace element is: an element whose activity obeys Henry’s Law in the system of interest. o This implies sufficiently dilute concentrations that, for trace element A and major component B, A–A interactions are not significant compared to A–B interactions, simply because A–A interactions will be rare.

19. Concentrations in the Silicate Earth

20. Goldschmidt’s Classification Atmophile elements are generally extremely volatile (i.e., they form gases or liquids at the surface of the Earth) and are concentrated in the atmosphere and hydrosphere. Lithophile, siderophile and chalcophile refer to the tendency of the element to partition into a silicate, metal, or sulfide liquid respectively. o Goldschmidt classified them based on the minerals in which they were concentrated in meteorites. Lithophile elements are those showing an affinity for silicate phases and are concentrated in the silicate portion (crust and mantle) of the Earth. Siderophile elements have an affinity for a metallic liquid phase. Concentrated in Earth’s core. Chalcophile elements have an affinity for a sulfide liquid phase. They are also depleted in the silicate earth and may be concentrated in the core. o Most elements that are siderophile are usually also somewhat chalcophile and vice versa.

21. Goldschmidt’s Classification

22. Distribution of the Elements Atmophile in the atmosphere. Siderophile (and perhaps chalcophile) in the core. Lithophile in the mantle and crust. o Incompatible elements, those not accepted in mantle minerals, are concentrated in the crust. o Compatible elements concentration in the mantle.

23. Geochemical Classification

24. The volatile elements: Noble gases, nitrogen The semi-volatiles o they partition readily into a fluid or gas phase (e.g., Cl, Br) or form compounds that are volatile (e.g., SO 2, CO 2 ). Not all are volatile in a strict sense (volatile in a strict sense means having a high vapor pressure or low boiling point; indeed, carbon is highly refractory in the elemental form). The alkali and alkaline earth elements o The alkali and alkaline earth elements have a single valence state (+1 for the alkalis, +2 for the alkaline earths). The bonds these elements form are strongly ionic in character (Be is an exception, as it forms bonds with a more covalent character)These elements relatively soluble in aqueous solution. The atoms of these elements behave approximately as hard charged spheres; size and charge dictate their behavior in igneous processes. o The heavier alkalis and alkaline earths have ionic radii too large to fit in many minerals (mantle ones in particular). As a consequence, they are said to be incompatible. High field strength (HFS) elements o So called because of their high ionic charge: Zr and Hf have +4 valence states and Ta and Nb have +5 valence states. Th (+4) and U (+4, +6) are sometimes included in this group. Because of their high charge, all are relatively small cations but because of their high charge they are excluded from most minerals and hence are also incompatible. The first series transition metals o Chemistry is considerably more complex: many of the transition elements have two or more valence states; covalent bonding is more important (bonding with oxygen in oxides and silicates is predominantly ionic, but bonding with other non-metals, such as sulfur, can be largely covalent) A final complicating factor is the geometry of the d-orbitals, which are highly directional and thus bestow upon the transition metals specific preferences for the geometry of coordinating ligands. They range from moderately incompatible (e.g., Ti, Cu, Zn) to very compatible (e.g., Cr, Ni, Co). The noble metals o The platinum group elements (Rh, Ru, Pd, Os, Ir, Pt) plus gold (and Re) are often collectively called the noble metals. These metals are so called for two reasons: first, they are rare, and second, they are unreactive and quite stable in metallic form. Their rarity is in part a consequence of their highly siderophilic character. These elements are all also to varying degrees. These elements exist in multiple valence states, ranging from 0 to +8, and have bonding behavior influenced by the d-orbitals. o Au Pt, Re, and Pd are moderately incompatible elements, while Rh. Ru, Os, and Ir are highly compatible

25. The Rare Earth Elements The rare earths and Y are strongly electropositive. As a result, they form predominantly ionic bonds, and behave as hard charged spheres. The lanthanide rare earths are in the +3 valence state over a wide range of oxygen fugacities. In the transition metals, the s orbital of the outermost shell is filled before filling of lower electron shells is complete so the configuration of the valence electrons is similar in all the rare earth, hence all exhibit similar chemical behavior. Ionic radius, which decreases progressively from La 3 to Lu 3+ (93 pm) governs their relative behavior. Because of their high charge and large radii, the rare earths are incompatible elements. o The degree of incompatibility of the lanthanides varies with atomic number. Highly charged U and Th are highly incompatible elements, as are the lightest rare earths. o However, the heavy rare earths have sufficiently small radii that they can be accommodated to some degree in many common minerals such as Lu for Al in garnet. Eu 2+ can substitute for Ca in plagioclase.

26. Rare Earth Diagrams The systematic variation in lathanide rare earth behavior is best illustrated by plotting the log of the relative abundances as a function of atomic. Relative abundances are calculated by dividing the concentration of each rare earth by its concentration in a set of normalizing values, such as the concentrations of rare earths in chondritic meteorites. o Rare earths are also refractory elements, so that their relative abundances are the same in most primitive meteorites - and presumably (to a first approximation) in the Earth. Why do we use relative abundances? The abundances of even-numbered elements in the solar system are greater than those of neighboring odd-numbered elements and abundances generally decrease with increasing atomic number, leading to a saw-toothed abundance pattern. Normalizing eliminates this. Abundances in chondritic meteorites are generally used for normalization. However, other normalizations are possible: sediments (and waters) are often normalized to average shale.