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Chapter 07 Ans

# Chapter 07 Ans - Answers for Chapter 11 Diversification of...

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Answers for Chapter 7: Ternary Systems. Ternary systems are, by definition, 3-component systems. The addition of another component to a 2- component system requires 3-dimensions to illustrate the T-X variables for an isobaric system, but we cannot further simplify our diagrams by ignoring T or a component, so we construct isobaric T-X diagrams by contouring the liquidus surface for temperature, as illustrated in the ternary Fo-An-Di system below. The inset shows the system in 3-D perspective, showing the three binary eutectic systems. 1. Begin with composition a at 1800 o C. What is the weight fraction of An in the liquid ( Liq An X )? What about Liq Di X ? Liq Fo X ? Liq An X = ~ 0.21, Liq Di X = ~0.16, Liq Fo X = ~0.63 2. What is the variance at 1800 o C? Show your work. List the intensive variables that are relevant to this diagram and could contribute to F. Which variables in your list, if any, are not independent? Above the liquidus, so only liquid present. F = C – φ + 1 (isobaric) = 3 – 1 + 1 = 3. 3. What mineral begins to crystallize as a liquid of composition a is cooled to 1700 o C? What is the variance? Show your work. Forsterite begins to crystallize. F = 3 – 2 + 1 = 2. 1 4 6 8 9 : Bulk solid extract c d e f

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4. Illustrate with a dashed line labeled “4” the “liquid line of descent” as the liquid continues to cool below 1700 o C. Why does it move in the direction you have indicated? It must move directly away from Fo because forsterite is being extracted from it. 5. What is the “continuous reaction” involved that permits the liquid composition to change? Liquid A = Forsterite + Liquid B 6. Indicate with an “6” the point along the liquid line of descent where a new phase begins to crystallize. What phase is it? Anorthite 7. Derive the variance at this point and show your work. F = 3 – 3 + 1 = 1 8. Show with a heavy line and an “8” the liquid line of descent from the point at which the new phase in part (6) formed. Write the new continuous reaction responsible for the change in liquid composition. Liquid A = Forsterite + Anorthite + Liquid B 9. Choose a point along the cotectic between (6) and point M and show how you derive the bulk solid extract crystallized from the liquid at that point. How does that bulk solid extract differ from the total amount of solid crystallized? Extrapolate a tangent to the cotectic from the point in question and extend it back to the Fo – An side of the triangle to get the bulk solid extract. This is the instantaneous solid proportions crystallizing from the melt at any particular point, whereas the total amount crystallized must include all the prior Fo and An that has crystallized since 1700 o C. 10. Determine a general geometric rule relating the bulk composition to the compositions of the three phases that compose it (liquid, forsterite, and anorthite).
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