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You will need to print out the phase diagram in order to measure quantities accurately on the phase diagram (you will want to use a ruler so you can be accurate)

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You will need to print out the phase diagram in order to measure quantities accurately on the phase diagram (you will want to use a ruler so you can be accurate).

Please show your working on the phase diagrams and any basic arithmetic e.g. calculating the lever rule. You need to show your working to receive full credit.

 

The Phase Rule can be modified for restricted variance by subtracting 1 degree of freedom (F) for each such restriction e.g. for an isobaric system we only need to add 1 intensive variable to represent temperature (instead of +2 at the end we have +1):

           

F = C - Φ + 1 (isobaric)           (also applies to isothermal, isochoric, isentropic, etc.)

 

Where F is the number of degrees of freedom (variance), C is the number of components that define the system (in the case of binary phase diagrams this number is 2) and Φ is the number of phases present. Normally the last integer for geological problems is 2 (pressure and temperature), but for these problems we will deal with isobaric conditions i.e. only temperature is an intensive variable. We will only deal with systems as isobaric in this assignment.

 

*When calculating phase compositions and proportions use a ruler with mm markings to be as precise as possible. Do not simply estimate. This is a quantitative exercise. You should be able to easily determine phase compositions to within a couple % and lever rule calculations to within 5% or better.

 

Binary Eutectic Systems:

 

The Di-An (Diopside-Anorthite) Binary Eutectic system can be considered an isobaric system (fixed pressure) for the purposes of calculating variance.

 

Using the Di-An Binary Eutectic System phase diagram given, please answer the following questions:

 

1.    Calculate the variance (F) for composition X (An₈₀-Di₂₀) at 1600°C.

 

 

 

 

2.    As the An₈₀ system cools, at what temperature will Φ change? What is the variance at this temperature? 

 

 

 

 

3.    What is point E called? What is the variance at point E?

 

 

 

 

4.    Please describe the sequence of equilibrium crystallization for composition X (An₈₀) using the example format provided above.

 

 

 

 

5.    Please describe the sequence of equilibrium crystallization for composition Y (An₂₀-Di₈₀) as it cools from 1550°C to 1200°C (mark "Y" on diagram at 1550°C). Include the temperature(s) at which the phases present change.

 

 

 

 

6.    For bulk composition Y at 1300°C, what will the system consist of? Detail all phases present, their compositions, and their proportions. 

 

 

 

 

7.    Suppose that bulk composition X at 1200°C is warmed up until it begins to melt and then more heat is added until it eventually reaches its liquidus temperature. Describe the sequence of events from 1200°C as heating and melting proceeds all the way to the liquidus (consider only equilibrium conditions)?

 

 

 

 

8.    How will the system composition for composition Z (An₆₀-Di₄₀) change as it cools from the liquidus to the solidus temperature while undergoing perfect fractional crystallization (Mark "Z" on diagram at this system comp). What will the final bulk composition of the system be at 1270°C? You can assume that this is an open system and the crystals that have crystallized prior to reaching 1270°C have been removed from the system.

 

 

 

 

9.    Predict what a series of lavas would look like if a magma chamber containing a liquid of bulk composition Z (An₆₀-Di₄₀) erupted lava flows at 1600°C and 1300°C. Assume the lavas rapidly quenched upon eruption). Detail phases present and their proportions. 

 

 

 

 

10. Please provide your annotated (marked up) binary eutectic phase diagram showing your work.