##### i need to solve this home work? Ternary systems are, by-(Answered)

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i need to solve this home work??

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.

The University of Jordan

Igneous Petrology 931

Geology Department

Spring 2016

Dr. Ghaleb Jarrar

Problem set 2

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Three-Component Systems: Di-An-Fo

1. Derive the variance for composition a at 1800 C.

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2. As the system (a) cools, at what temperature will ? change? What occurs at this

temperature?

Derive the variance.

List all of the possible intensive variables that can be represented by F for the diagram

above at this point. Which are independent, and which are not?

3. As a general rule, how can you determine which phase forms first in the Figure? What

alternatives are there? What property of the melt determines which forms first?

4. As composition a cools further, draw the liquid line of descent in some color. What is

the meaning of this term? How can the LLD be determined? Determine the continuous

reaction.

5. What is the ratio of liquid to solid at 1500 C? Show your work with clear labels and

references to the diagram so that the source of your numbers is obvious.

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6. At what temperature will ? next change? What occurs at this temperature? What is the

name of the curve intersected? Describe the composition of each phase present. Derive

the variance. What does F imply?

7. Does cooling from this point represent a continuous or discontinuous reaction? Write

the reaction.

8. Determine the instantaneous bulk solid extract at 1300oC. What is the meaning of this

term? How does it differ from the total accumulated solids crystallized up to this point?

Show your work with clear labels and references to the diagram so that the source of your

numbers is obvious.

9. What can you say about the geometric relationship between the bulk composition and

the composition of the three phases that constitute that bulk as crystallization proceeds

along the cotectic?

10. Determine the ratio of the three phases present. Show your work with clear labels and

references to the diagram so that the source of your numbers is obvious.

11. At what temperature will ? next change? What occurs at this temperature? What is the

name of the point intersected? Describe the composition of each phase present. Derive

the variance. What does F imply?

12. Can you determine the ratios of the phases present under these conditions? Why or

why not? Does cooling from this point represent a continuous or discontinuous reaction?

Write the reaction.

13. Derive a geometric way to determine the reaction under these circumstances.

14. Given the value of F and the reaction that you determined, what must happen before

the system can be cooled further?

15. What is the final mineral assemblage in the rock (including %)? Show your work with

clear labels and references to the diagram so that the source of your numbers is obvious.

16. What will be the effect of fractional crystallization on the path of the liquid line of

descent? How will it differ from equilibrium crystallization?

17. How will the final rock composition differ between fractional crystallization and

equilibrium crystallization for composition a?

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18. Must all molten mixtures of Di, An, and Fo reach point M before solidifying

completely? Why or why not?

19. Summarize the sequence of minerals that formed as composition a crystallized. Using

different colors, illustrate bulk compositions and liquid lines of descent that represent all

six possible crystallization sequences of diopside, anorthite, and forsterite. Label each

with the sequence (e.g.An ? Di ? Fo).

20. What is the composition of the first melt formed by heating composition b?

21. What is the first solid phase to be consumed? How can you determine this?

22. At what point will the liquid line of descent leave the cotectic? How can you

determine this? What phase is consumed?

23. Assuming perfect fractional partial melting (each drop of liquid is removed as it is

generated), describe what happens when composition b is partially melted until the

system is completely molten. Will all the melt be produced at one temperature? Will melt

be produced along a continuous range of temperatures? Are the reaction(s) involved

continuous or discontinuous? Explain.

Paper#9210712 | Written in 27-Jul-2016

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