Lecture 2/3: Phases Equilibria Thermodynamics (Phase and Stability) Flashcards
What is a system (thermo)?
a material with one or more phases (ex: Fe-C alloy)
What is a phase (thermo)?
portion of the system whose properties are homogenous (typically atomic structure is the same, such as fcc, bcc, solid/liquid/vapor)
what is a component (thermo)?
chemical elements or compounds which make up the system (ex: Fe and C in the Fe-C system)
what is a composition (thermo)?
concentration of components in a phase (ex: 99.5 at %Fe and 0.5 %C or wt%)
What is U?
U-internal energy
includes both kinetic and potential energy
What is H?
H - enthalpy
note the heat absorbed or released under constant pressure is the change of enthalpy
What is S?
S- entropy
A measure of the “disorder” of a system. For example, S (gas) > S(liquid) > S (solid) for the same material
What is G?
G - gibbs free energy
At constant P and T, the equilibrium state has the lowest G
G = H - TS
What must be required with G for a spontaneous change? what is the driving force?
the change of G from the initial state to the final state the change must be negative (initial greater),
change of G is the “driving force”
What does a graph of G vs. system configurations look like?
According to G = H-TS, what do you need to have the lowest G? Why would you want it?
small H (enthalpy) and high S (entropy)
highest stability
How can you calculate G?
calculate H and S from Cp
What is the 3rd law of thermodynamics?
S is zero for single element in its perfect stable form at 0K (e: FCC Cu)
What reference condition do we use for H and G and why?
they don’t have an absolute 0 value so we need a reference, usually standard condition
298 K
1 atm
At constant T & P, which phase is the most stable?
phase with the lowest G
How does G behave at transition temperatures?
it’s continuous bc ΔH = TΔS
so they cancel out at the transition temperatures
What is the Gibbs Phase Rule?
In Gibbs Phase Rule, what does f stand for?
degrees of freedom
In Gibbs Phase Rule, what does c stand for
components
In Gibbs Phase Rule, what does p stand for?
of phases
In Gibbs Phase Rule, what does the 2 represent
P and T
At any one point in a one-phase area, what is f?
At a point along a two-phase coexistence line, what is f?
At a triple point (3-point coexistence), what is f?
what is a critical point (f=0)?
beyond which liquid and gas are indistinguishable
What is a multi-component system?
related to mixing several components together
If mixed completely, what is the product of a multi-component system?
a solution (solid or liquid solution, gas mixture)
Can you determine solution properties from the pure components?
NO. they are NOT the sum of the pure components
What is G sub i? what is it called?
“the effective Gibbs free energy per mole”
the partial molar gibbs free energy of component i
called the “chemical potential”
What does the bar represent?
a partial molar property
How do you calculate the new Gibbs free energy after mixing?
the weighted sum of the partial molar Gibbs free energy/chemical potentials
what is ai for pure materials?
ai = 1
what is ai for ideal solution?
ai = Xi
what is ai for non-ideal solution?
ai = yi*Xi (yi is the activity coefficient)
How would you find the total Gibbs after mixing?
adding G unmix + G mix
what is the gibbs free energy before mixing
weighted sum of pure components
what is the gibbs free energy of mixing?
additional energy due to mixing
How would you find the enthalpy of mixing?
delta H is enthalpy of mixing
What does it mean if ΔH = 0? ΔH < 0? ΔH >0?
ΔH = 0
- ideal solution
- spontaneous random mixing bc ΔG mix <0
ΔH < 0
- non-ideal solution
- non-random mixing bc ΔGmix<0
ΔH >0
- non-ideal solution
- phase separation below a certain T
For an ideal solution, do enthalpy and volume change after mixing?
no. ΔH mix = 0, ΔV mix =0
What is mixing driven by for an ideal solution? spontaneous or not?
driven by entropy of mixing
it is spontaneous
What is the entropy of mixing for an ideal solution? Independent of dependent of T?
independent of T
What is the Gibbs free energy of mixing? Independent or dependent of T?
dependent of T
What do the graphs of ΔSmix, ΔGmix, ΔVmix, and ΔHmix look like for an ideal solution?
What does the phase diagram look like for an ideal solution (ex: Ni-Cu binary system)?
Determine the ΔGmix & phase boundaries at T1, T2, and T3.
*closer is more stable = lower
* middle is split
What is the eutectic temperature?
the lowest melting temperature at any composition – lower than both pure components
At the eutectic point, what happens?
3 phrases coexist
f = 0 (for binary system), so it’s fixed for the system
What doe a eutectic phase diagram look like? where are the liquidus, solidus, and solvus lines?
