Lecture 4: Thermodynamics continued Flashcards
How would you find the mole fraction of a component B in a B+L phase?
lever rule
In a plot of ΔGmix vs. composition, how would you find the chemical potentials @ at specific composition for single phase (alpha)?
- draw a tangent line where the comp meets alpha
- the intercepts at 0 and 1 comp are the chemical potentials of compo
Does chemical potential change with composition?
yes
What is the notation for chemical potential?
𝜇
sub - component
exponent - phase its in
In a plot of ΔGmix vs. composition 2, how would you find the chemical potentials for the phases (for two phase equilibrium)?
draw the common tangent line between the two phases and extended it to the ends
at 0,
a. μ 1α = μ 1β
b. μ 2α = μ 2β
**so the chem potentials of the same COMPONENT (not phase) are equal
For single phase ΔGmix, how many chemical potentials are there?
2
if phase is alpha–
𝜇 sub 1 ^alpha
𝜇 sub 2 ^alpha
What are four conditions of two-phase equilibrium?
- thermal equilibrium T α = T β
- mechanical equilibrium P α = P β
- chemical equilibrium
a. μ 1α = μ 1β
b. μ 2α = μ 2β - the system energy in α +β region is the common tangent segment (red line)
For an ideal solution phase diagram, explain how to draw the gibbs free energy at temperatures 1 2 and 3
think about putting the phase present at each composition on the bottom on the CURRENT Point of the gibbs diagram
How are gibbs free energy and phase diagrams related?
the system with lowest free energy will be adopted
What is a eutectic phase diagram?
phase diagram where there’s a point where a L transforms into to two solid phases
Which lines are the liquidous, solidus, and solvus?
What is the lowest melting temp at any comp on a eutectic phase diagram?
eutectic temp
What coexists at a eutectic point?
3 phases
What is the degrees of freedom for binary phase diagram?
f = c - p +1 (usually it’s 2),
this is because P is fixed at 1 atm
What are the degrees of freedom at a Eutectic point? Can this change?
f = 2-3+1 = 0
No, it’s fixed for the sysem
At any point in the alpha + beta region of a eutectic phase diagram, what is the composition of each phase?
it’s the same as the solvus boundary @ the temp (the composition of phases are unique and a property of the phase itself, nothing overall)
What happens to the compositions of alpha and beta if your X2 is between the two solvus lines?
The COMPOSITIONS of alpha and beta don’t individually change, but the OVERALL composition changes (phase fraction)
What rule do you use to determine phase fractions?
Lever Rule
How do you find the total Gibb’s free energy at P (a point on a phase diagram @ a temperature T)? How is this denoted?
A weighted sum of the two phases (their phase fractions and individual Gibbs free energies of mixing)
Where is the total Gibbs Free energy at P located?
on the common tangent line
How do you find the phase fractions of alpha and beta?
What does the lever rule determine?
The relative amounts of two phases when the coexist in equlibrium
What is the composition at P denoted by?
What would the material drawing (box with alpha and beta background or circles) look like when P is close to A?
beta circles in alpha background – since the phase fraction of alpha is bigger
What would the material drawing (box with alpha and beta background or circles) look like when P is close to B?
alpha particles in beta background
What happens if we cool a Pb-Sn system slowly at the eutectic composition?
lamellar microstructure
How can you control microstructure?
by changing composition
What is a peritectic phase diagram?
phase diagram where there’s a transition from a solid + L phase to a DIFFERENT solid phase
What are two elements that form a peritectic phase diagram?
Ag-Pt
When is it common for peritectic phase diagrams to form?
When the melting temp of one pure component is much higher than the other
What is a way to get different microstructures for peritectic phase diagram?
cool the system at dif compositions
What is an intermediate/intermediated phase? How is it shown in a graph? Why?
A phase made from the 2 pure components but with a different crystal structure
ex: Mg2Si (from Mg and Si)
In a graph they’re shown as a vertical line because they have a fixed stoichiometry (ex Mg2Si Mg2:Si1)
What is a property of an intermetallic phase?
they’re typically brittle
What are the different behaviors exhibited by the these different alloys:
1. Pb-Sn
2. Ag-Pt
3. Mg-Si
4. Cu-Zn
5. Fe-C
- eutectic
- Peritectic
- Intermediate phase
- Diffusion couple
- form steels - eutectoid point
What is a diffusion couple?
When you put 2 materials next to each other at a certain temp and then they diffuse into each other
What is a eutectoid point?
when a single solid phase turns into dif two solid one
How can you determine the solubility of the alpha phase for C?
check how far it goes into the C wt% on the x-axis. so for this it’s very low
What are the three Hume-Rothery rules for substitutional solid solutions?
- Atomic size factor
- Electrochemical effect
- Relative valency effect 4
What is the Atomic size factor Hume-Rothery rule for substitutional solid solutions?
“If the atomic diameter size of the solute atom differs by more than 15% from that of the solvent atom, the extent of the primary solid solutions is small”
What kind of solutions do the Hume-Rothery rules deal with? What are those?
substitutional solid solutions
solid solutions where solute atoms “substitute” so replace the solvent atoms in the crystal lattice
To form an idea solution for substitutional solids, what is needed?
A and B have to have the same crystal structure
What is an example of an ideal solution with atomic-size factor? non-ideal?
ideal : Cu-Ni, they have a similar atomic radius size (continuous alpha phase throughout all concentrations)
non-ideal : Au-Ni, 1.74 and 1.49 – very dif atomic radius sizes (non-continuous phase)
What would an ideal phase diagram look like? non-ideal?
ideal has one phase throughout the whole thing
What is the Hume-Rothery electrochemical effect rule?
The more electropositive the one component and the more electronegative the other (larger the dif in electronegativity), the greater the tendency for the two elements to form compounds rather than extensive solid solutions
more dif in electroneg = more likely to NOT be a single-phase (non-ideal) and form compounds
What are extensive solid solutions?
they can form a single-phase structure across a wide range of compositions
How would Mg (group 2) behave comparing to group IV and V elements?
The group 4 will have BETTER solubility because there’s a smaller electrochemical difference. Thus, the phase diagram (left) has a larger solid alpha region than the one on the right
How does Gibbs free energy relate to solubility and formation of compounds?
If the compound is much more stable than the individual phases, then the solubility of B in A is going to be limited
Explain the relative valency effect?
a metal of higher valency is more likely to dissolve to a large extent in one of lower valency
- large valency metals will disappear more into the low valency ones (dissolve into it), so the phase diagram will have a large solid low valency region and then opposite one will be small
Why does the relative valency effect happen?
higher valency electrons have more electrons to contribute, and also they’re often smaller than low-valency electrons so there’s less room to dissolve
For a Zn-Cu system which dissolves more? Zn-2 VE, Cu-1VE
Zn dissolves into Cu, so large Cu region
How does a ternary phase diagram work?
**right side is the horizontal line, bottom is up and right, left is down and right
- It’s at a fixed T & P
- each corner is a pure component
- each side is a binary system and the component at the opposite corner is 0
- X1+X2+X3 = 1
