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Binary PD Problems

This document contains questions about binary phase diagrams. It asks the student to use phase diagrams to: 1) Determine degrees of freedom at different points and fields. 2) Draw schematics showing the evolution of phases during cooling of magmas with different compositions. 3) Describe the final textures after complete equilibration during cooling. 4) Label phases on simplified diagrams and determine degrees of freedom. 5) Predict products of melting a solid with a given composition.

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Shin Naira
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© Attribution Non-Commercial (BY-NC)
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171 views5 pages

Binary PD Problems

This document contains questions about binary phase diagrams. It asks the student to use phase diagrams to: 1) Determine degrees of freedom at different points and fields. 2) Draw schematics showing the evolution of phases during cooling of magmas with different compositions. 3) Describe the final textures after complete equilibration during cooling. 4) Label phases on simplified diagrams and determine degrees of freedom. 5) Predict products of melting a solid with a given composition.

Uploaded by

Shin Naira
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Hirsch - Binary phase diagrams problems

Name _______________________

Question 1.

1A. Using the phase rule, determine the degrees of freedom:


a. at point e
b. within the field A + B
c. within the field A + L
1B. Envision this system as a slowly cooling magma chamber. Start with a liquid of bulk composition d at
T0. In the circles below, show schematically the appearance of the system at temperatures T0, T1, T2,+
0.01C (i.e., just above T2) and T3. When drawing, think about the crystallization process, not just the
numbers! Also, try to portray the proportions of phases somewhat correctly. In the blanks, list the phases
present, and the amount & composition of each. Not every text line will be needed.
Temperature = T0
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Temperature = T1
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________

Hirsch - Binary phase diagrams problems

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Temperature = T2 + 0.01C
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Temperature = T3
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________

1C. For a given pressure, why cant the temperature of the system be lowered beyond T2 until all of L has
crystallized? (hint: use the phase rule)

1D. Follow the instructions for 1B. above for a liquid of bulk composition c and temperatures T1, T2,+ 1 C
and T3
Temperature = T1
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Temperature = T2 + 0.01C
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Temperature = T3
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________

Hirsch - Binary phase diagrams problems

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QUESTION 2

2A. Follow the instructions in question 1B for a liquid of bulk composition d at T0, T1, T2, and T3. Assume
complete equilibration during cooling (relatively slow cooling). Describe the texture of the final product.
Temperature = T0
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Temperature = T1
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Temperature = T2
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________

Hirsch - Binary phase diagrams problems

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QUESTION 3
3A. Label each of the fields in this simplified phase diagram, except for the tiny one at the right. You may
wish to use your text (Ch. 6) for help.

3B. Use the Phase Rule to determine the degrees of freedom at points P, E, and L

3C. Follow the instructions in question 1B for composition c at temperatures T1, T2, T3 + 0.01C, and T4.
Assume slow (equilibrium) cooling.
Temperature = T1
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Temperature = T2
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________

Hirsch - Binary phase diagrams problems

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Temperature = T3 + 1 C
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Temperature = T4
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________

3D. Follow the instructions in question 1B for composition d at temperatures T3,+ 0.01C, T3 - 0.01C, T4
and T5. Assume slow (equilibrium) cooling.
Temperature = T3 + 1 C
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Temperature = T3 - 1 C
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Temperature = T4
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Temperature = T5
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
Phase _______: Volume % = _________________ . Composition= _________
3E. Given a solid of composition Mg2Si2O6, at what temperature will the solid first melt? What will be the
product(s) of melting? What are their compositions?

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