EAS 4550: Geochemistry Problem Set 4 Solutions Due Sept. 27, 2017

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Marjorie Sparks
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1 1. Interaction parameters for the enstatite diopside solid solution have been determined as follows: WH-En = 34.0 kj/mol, WH-Di = kj/mol (assume WV and WS are 0). (a) Use the asymmetric solution model to calculate Greal as a function of X2 (let diopside be component 2) curves for this system at 100 K temperature intervals from 1000 K to 1500 K. Label your curves. The key equation is: Gex = (W G1 + W G2 X 1 )X To express this as a function of, we need only note that X 1 = 1-. Making this substitution, we have: G ex = (W G1 +W G2 (1 ))(1 ) Expanding this: Gex = (W G2 W G1 ) (W G1 2W G2 ) + W G 2 Since we may assume W S is 0, then W G = W H. We also note that DG real = DG ideal + DG ex where DG ideal = RT (X 1 ln X 1 + ln ) = RT ((1- )ln (1- ) + ln )). As an example, the calculation for 1000K is shown in the spreadsheet below: The G-bar-X diagram is shown below. 1

2 2000! 1500! 1000! 1000 K! 1100 K! 1200 K! 1300 K! 1400 K! 1500 K! Greal (J)! 500! 0! -500! -1000! -1500! -2000! 0.0! 0.1! 0.2! 0.3! 0.4! 0.5! 0.6! 0.7! 0.8! 0.9! 1.0! X2 (Di)! (b) What is the maximum mole fraction of diopside that can dissolve in enstatite in this temperature range? The composition of the two partial solid solutions are found by drawing a line that is tangent to the G-bar-X curve. These points will be near the two minima. For example, at 1500 K, we would draw a line tangent at about X Di = 0.2 and 0.9. Thus the enstatite s.s. (solid solution) phase would have about 20% Di and the diopside s.s. would have about 10% En. The maximum would be about 20% at 1500K. At higher mole fractions of diopside, two solids would be stable, each of which would be a limited solid solution. The minimum, at 1000 K would be about 10%. Notice that at 1000 K there is no line we can draw that is tangent in two places as there is no real minimum at high X2. In this case, we have nearly pure Diopside and about 10% diopside in the enstatite s.s. (c) Sketch the corresponding T X phase diagram. To sketch the phase diagram, we use these estimates of the fraction of the component Di in the two phases (the enstatite s.s. and the diopside s.s.) and plot them as a function of temperature: 2

3 2. Suppose you conduct a 1 atm melting experiment on a plagioclase crystal. Predict the mole fractions of anorthite in the liquid and solid phases at a temperature of 1425 C. Assume both the liquid and solid behave as ideal solutions. Albite melts at 1118 C, anorthite at 1553 C. Hm for albite is kj/mol; Hm for anorthite is kj/mol. The equations we need to answer this problem are 4.36 and 4.34: s X An = X l An e ΔG m An RT l 1 e ΔG m An RT 4.34 X Ab = 4.36 e ΔG m Ab RT e ΔG m An RT (actually, we use the anorthite equivalent of 4.36) 3

4 One cannot use equation That equation, which comes from equation 3.66 was derived under the assumption that the solid was a pure phase, i.e., X s = a s = 1. This is not the case here, because albite and anorthite form both liquid and solid solutions. The only other thing we need to know is DG m for albite and anorthite. DG = DH - TDS. At the melting temperature of the pure phase, DG is 0, so DS m = DH m /T m. In this way, we estimate DS m for albite of 39.4J and DS m for anorthite of 67.4J. After that, it is just a matter of calculating the two DG m s, then calculating the mole fraction in the liquid with 4.36 and finally, the mole fraction in the solid with The spreadsheet is shown below. albite anorthite H H Tm 1391 Tm 1826 S S = 1425 C 1698 Gan Gab Xan(liq) Xan(sol) Given the following two analyses of basaltic glass and coexisting olivine phenocrysts, determine the KD for the MgO FeO exchange reaction, and calculate the temperatures at which the olivine crystallized using both MgO and FeO. Assume Fe2O3 to be 10 mole % of total iron (the analysis below includes only the total iron, calculated as FeO; you need to calculate from this the amount of FeO by subtracting an appropriate amount to be assigned as Fe2O3). Note that the mole % Fo in olivine is equivalent to the mole % Mg or MgO. (HINT: you will need to calculate the mole fraction of MgO and FeO in the liquid 4

Sample TR3D-1 DS-D8A glass (liquid) composition (wt % oxide) (wt % oxide) SiO 2 50.32 49.83 Al 2 O 3 14.05 14.09 SFe as FeO 11.49 11.42 MgO 7.27 7.74 CaO 11.49 10.96 Na2O 2.3 2.38 K2O 0.10 0.13 MnO 0.

5 Sample TR3D-1 DS-D8A glass (liquid) composition (wt % oxide) (wt % oxide) SiO Al 2 O SFe as FeO MgO CaO Na2O K2O MnO TiO Olivine Mole % Fo (= mole % Mg) The solution to this problem follows Example a. Determine the temperature and oxygen fugacity of equilibration for the following set of coexisting iron-titanium oxides in lavas from the Azores using the Spencer and Lindsley oxide geothermobarommeter described in the book. Titanomagnetite s.s. phase mole % magnetite Ilmenite s.s. phase mole % hematite G-4 groundmass

6 SJ-8 phenocrysts SM-28 microphenocrysts T-8 groundmass F-29 microphenocrysts Make a plot of ƒo2 vs. temperature using your results and compare with Figure What buffer do the data fall near? The solution to this problem follows Example 4.4. XUsp XIlm G Interaction Parameters SJ WHU WSU SM WHM WSM T WHI WSI F WHH WSH H S R G-4 SJ-8 SM-28 T-8 F-29 A B C D K T= (A*WHU-B*WHM-C*WHI+D*WHH+ H) (A*WSU-B*WSM C*WSI+D*WSH+ S-R*ln(K)) Temperature C G-4 SJ-8 SM-28 T-8 F-29 T <800 C T>800 C T K T C WG=WH-T*WS WGU WGM WGI WGH Log MH Log ƒo2 (<800) Log ƒo2 (>800) b. Compare your results with those using the Ghiroso and Evans (2008) oxide geothermobarommeter using either the online calculator or spreadsheet (Windows only) at 5. Use one of the MELTS tools ( to calculate to following. 6

For a Mid-Ocean Ridge Basalt of the following composition: a. What is the liquidus temperature (± 5K) at 0.1 MPa the MORB (Mid-Ocean Ridge Basalt) composition in the Table?

7 For a Mid-Ocean Ridge Basalt of the following composition: a. What is the liquidus temperature (± 5K) at 0.1 MPa the MORB (Mid-Ocean Ridge Basalt) composition in the Table? What is the first solid phase to precipitate and what it it s composition? 1215 C, plagioclase AN 82.6 b. What is the liquidus temperature (± 5K) at 500 MPa? What is the first solid phase to precipitate and what it it s composition? 1288 spinel ~75% spinel, 25% chromite What phases are present and what is there relative abundance at 900 C and 1 MPa? 27 g augite 14.7 %olivine 3% orthopyroxene 1.6 %spinel 53.4%plagioclase 0.19% liquid c. What is the liquid temperature for the ankaratirite at 0.1 MPa? What is the liquidus phase? 1308 C, olivine wt. percent MORB Ankaratrite SiO TiO Al2O Fe2O Cr2O FeO MnO 0 0 MgO CaO Na2O K2O P2O H2O

Problem Set Four Solution Due October 3, 2007

Problem Set Four Solution Due October, 007 1. Construct G-bar X diagrams for a regular solution with W= 1 kj (W is the interaction parameter in a non-ideal solution) at 100 temperature intervals from 00