Redox in Magmatic Systems Activities in NonIdeal Solutions

Redox in Magmatic Systems Activities in Non-Ideal Solutions Lecture 10

Line 5 has a slope of -1 and an intercept of log K. We can also use pe-p. H diagrams to illustrate stability of solid phases in presence of solution. In this case, we must choose concentration.

More about pe-p. H diagrams • pe-p. H diagrams are a kind of stability or predominance diagram. • They differ from phase diagrams because lines indicate not phase boundaries, but equal concentrations. o There is only 1 phase in this diagram – an aqueous solution. • Regions are regions of predominance. o The aqueous species continue to exist beyond their fields, but their concentrations drop off exponentially.

Environmental Interpretation of pe-p. H

Redox in Magmas

Oxygen Fugacity • Igneous geochemists use oxygen fugacity ƒO 2 to represent the redox state of the system. Hence, the oxidation of ferrous to ferric iron would be written as: 2 Fe. O + O 2(g) = Fe 2 O 3 • For example, oxidation of magnetite to hematite: 2 Fe 3 O 4+ ½O 2(g) = 3 Fe 2 O 3 • (Actually, there isn’t much O 2 gas in magmas. Reaction more likely mediated by water and hydrogen).

Redox in Magmatic Systems • For magnetite-hematite • 2 Fe 3 O 4+ ½O 2(g) = 3 Fe 2 O 3 • assuming the two are pure solids • At a temperature such as 1000 K

Oxygen Fugacity Buffers • The log ƒO 2 – T diagram is a phase diagram illustrating boundaries of phase stability. The two phases coexist only at the line. • Reactions such as magnetitehematite (or iron-wüstite or fayalite-magnetite-quartz) are buffers. • For example, if we bleed O 2 into a magma containing magnetite, the ƒO 2 cannot rise above the line until all magnetite is converted to hematite (assuming equilibrium!)

Real Solutions: Minerals and Magmas Chapter 4

We will cover Chapter 4 only through section 4. 6 (page 144). You will not be responsible for the remaining material in the chapter.

Power of Solutions • Our thermodynamics would be so much simpler if all solutions behaved ideally! Even simpler if there were no solutions at all! • But, once we learn how to handle them, we’ll see that we can use solution behavior to do some real geochemistry and learn things about the Earth. o Because the distribution of Mg and Fe between olivine and a magma depends on temperature, we can use the observed distribution to determine magma temperatures. o We can predict the temperature at which K- and Na-feldspar will exsolve and use this to determine metamorphic temperatures. o We can actually predict the plagioclase-spinel peridotite phase transition o We can determine equilibration temperatures of garnet peridotites.

In This Chapter • We’ll learn how to handle non-ideal solutions • Learn how to construct phase diagrams from thermodynamic data • Learn how thermodynamics is used for geothermometry and geobarometry • See how thermodynamics can be used to predict the sequence of minerals precipitating from magma.

Non-Ideality • We found a useful approach to non-ideality in electrolyte solutions (Debye-Hückel), but there are many other kinds of non-ideal solutions, including solids, liquid silicates, etc. • Some substances undergo spontaneous exsolution (oil and water; K- and Na-feldspar; clino- and orthopyroxene; silicate and sulfide magmas). When that happens, we know the solution is quite non-ideal (ideal solutions should always be more stable than corresponding physical mixtures).

Margules Equations • When you need to fit an empirical function to an observation and don’t fully understand the underlying phenomena, a power series is a good approach because it of its versatility. • So, for example, we can express the excess volume of a solution (e. g. , alcohol and water) as: • where X 2 is the mole fraction of component 2 and A, B, C, … are constants, Margules parameters, to be determined empirically (e. g. , by curve fitting).

Symmetric Solutions • Let’s first look at some simple cases. One such case would be where we need only the first and second order terms. • The excess volume (and other excesses) should be entirely functions of mole fraction, so for a binary solution where X 1 = 1 - X 2, A= 0 and our equation should reduce to: • The simplest such case would be symmetric about the midpoint X 1 = X 2. • In that case, • Substituting X 1 = 1 – X 2, we find that B = -C

Interaction Parameters or • Let WV = B • W is known as an interaction parameter (volume interaction parameter in this case) because non-ideal behavior results from interactions between dissimilar species. • The interaction parameter is a function of T, P, and the nature of the solution, but not of X. • We can define similar interaction parameters for free energy, enthalpy, and entropy.

Regular Solutions • Since ∆G = ∆H-T∆S • The free energy interaction parameter is: WG = WH – TWS • Regular solutions are the special case where WS = 0 and therefore WG = WH and WG is independent of T. o what does this imply about ∆Sexcess?

Interaction Parameters and Activity Coefficients • For a binary symmetric solution, λ 1 must equal λ 2 at X 1 = X 2. • From this we can derive: • For X 2 ≈ 1 (very dilute solution of X 1), then • and WG = RT ln h • What happens when X 1 ≈ 1?

Asymmetric Solutions • More complex situation where expansion carried out to third order. • Excess free energy given by: • Activity coefficient: Calculated Free Energy at 600˚C in the Orthoclase-Albite System as a function of Albite mole fraction.

Albite-Orthoclase Free Energy at various T A 3 -D version

G-bar–X and Exsolution • We can use G-bar–X diagrams to predict when exsolution will occur. • Our rule is the stable configuration is the one with the lowest free energy. • A solution is stable so long as its free energy is lower than that of a physical mixture. • Gets tricky because the phases in the mixture can be solutions themselves.

Inflection Points • At 800˚C, ∆Greal defines a continuously concave upward path, while at lower temperatures, such as 600˚C (Figure 4. 1), inflections occur and there is a region where ∆Greal is concave downward. All this suggests we can use calculus to predict exsolution. • Inflection points occur when curves go from convex to concave (and visa versa). • What property does a function have at these points? • Second derivative is 0. Albite-Orthoclase

Inflection Points • Second derivative is: • First term on r. h. s. is always positive (concave up). • Inflection will occur when

Spinodal Actual solubility gap can be less than predicted because an increase is free energy is required to begin the exsolution process.