11/12) Phase Rule/Diagrams, Unary Binary, Eutectics, Solid Solutions

phase rule for unary system

F = C - P + 2

divariant field: F = 2, 1 phase, can change temp or pres and still be in the field
univariant curve: F = 1, 2 phases, increase pressure and temp to stay on the line
invarient point: F = 0, 3 phases, cannot change anything, the point is set

phase rule for binary system

F = C - P + 1

if there are 3 phases present, we have 0 df, this tells us the max number of phases that can co-exist in binary is 3

details on diopside and anorthite

mixture of the two, not solid solution, just proportions
eutectic temp is the melting temp of any mixture, 1274
eutectic composition is where both Di and An fully melt, and it happens at the eutectic temperature. it’s the first composition to melt, and the last liquid to cool
You could have a very An rich sample and it will still melt at the eutectic temp and comp. source melting may not produce liquid of the same composition

bulk composition never changes, just the liquid
liquid gets richer in Di because Di is melting

go through melting example (green dot)

starting at 20% An 80% Di
Binary: 2 components, 2 phases, so 1df, can increase temp and stay in field

at the eutectic temperature, the first composition is eutectic comp (42% An, 58% Di), this is 2 components, 3 phases, 0df, so a constant temperature is held until we get rid of 1 phase, this will be the solid An.
at the eutectic temp, the An completely melts until we have Di + L, and then the temp can increase again

after eutectic temp, the temp increases and the proportion of crystals decreases, and the liquid composition moves farther from the eutectic composition until everything reaches the liquidus, where the last bit of diopside melts, and the sample is all liquid, and the same as the starting composition

go through cooling example (red dot)

starts at 85% An, 15% Di
once it hits the liquidus, An starts crystallizing at about 1500°C
At this point it’s binary 2 components, 2 phases, 1 df so temp can change
through this, the proportion of crystals is increasing, and the composition of liquid is becoming less An rich (because it’s crystallizing)

at the eutectic temp, things hold, and Di starts crystallizing along with An, and Di completely crsytallizes until the temperature changes again (df rule)

A: at what temp does Di start crystallizing?
B: at what temp does the last drop of liquid solidify?
C: what is the comp of the last drop of liquid?
D: what is the composition of the final solid?

A: eutectic temp
B: eutectic temp
C: eutectic comp
D: bulk comp (unchanged)

explain solid solution details

solid changes its composition through heating/cooling
cooling: (blue dot): once you get to liquidus, read across to solidus for comp of solid (first solid to form is way more calcium rich
as T drops, the liquid composition moves along the liquidus, solid composition moves along the solidus

at 1280°C, liquid is 20%An and 80%Ab that is coexisting with a solid 55%An and 45% Ab, at this temp, there is more prop of crystals, liquid line gets smaller because liquid is solidifying

once it’s 100% solid, the composition of the solid is the same as the liquid we started with, no comp change happens anymore, only goes to where the comp is the same as start

explain plagioclase system

partial melting is the opposite of fractional crystallization, melt is removed from the system

pure fractional crystallization involves the physical separation of the solid from the melt as soon as it forms (melt can no longer react with the solids, crystals are removed from the system, the melt composition become the new bulk composition, comp of both final liquid and the solids that form from it will be more Ab-rich

what is peritectic point

point on phase diagram where mineral has precipitated and at some point it reacts with the liquid to form a new point (also called invariant point), temp cannot change while this is happening

explain forsterite quartz system

reaction between a previously precipitated phase and the liquid to produce a new solid phase

left side is Fo, right side Qtz, enstatite is an intermediate between them
solid rock can only be Fo+En or Qtz+En, not Fo and qtz

E and P are invariant points, meaning something has to get used up before you move on

incongruent melting: melting where a phase melts to a liquid with a comp diff from the solid and produces a solid of diff comp to the original solid

X composition in Fo and Qtz

temp crystals first crystalize at is 1800, first crsytals will be forsterite
at the peritectic temp, Fo reacts with the liquid to form En
at temps less than P, its solid rock, because temperature holds at P until all liquid has crystallized

Z composition in Fo and Qtz

At the liquidus, Fo starts crystallizing, then at P, Fo reacts with the liquid and it all converts to En +Liquid. holds until all Fo is gone

keeps cooling, then at E, Qtz starts crystallizing and completely crystallizes until solid rock is formed and then cools

example of melting in Fo-Qtz

first drop of liquid forms at eutectic temp and it is the eutectic comp
the eutectic comp is represented only by the Qtz-En box, not the whole bottom of the graph, all En melts here and temp holds

above eutectic temp, all En is melted, and Qtz begins melting here, the prop of crystals get smaller, and the liquid composition gets richer in Qtz (because its melting)

at the liquidus, last crystals of quartz melts, and liquid comp is what the solid started with

details on ternary systems

corners have highest composition
cotectic is the comp of ternary liquids that are in eqlm with the binary eutectic minerals
ternary eutectic is lower than the binary eutectic, lowest temp a liquid can exist is at this temp
isotherms are constant temp
everything above the diagram is liquid

ternary diagram example (cooling)

focus on one corner
450 is where it hits the surface
liquid comp slides down the liquidus surface
composition of the first crystals is 100% A

after, bc A is crystallizing from the liquid, the liquid gets poorer in A, therefore the liquid comp moves directly away from A, until it hits the cotectic (not directly to the meeting point)

when it hits the cotectic, B will start to crystalize because this is the cotectic between A and B. phase rule: 3 components, 3 phases, df = 1, temp can still change. A AND B are crystallizing together and liquid

when it hits the eutectic, A, B, C crystalize together, this is 4 phases so temp holds until all liquid is gone (invariant point)

comp of final solid is same as what we started with, just looking at journey of liquid

details on Di-An-Fo diagram

first crystals to form will be euhedral, nothing but liquid around them
as more crystals form, they will be less euhedral, the last to form will just fill in the spaces (very anhedral)

explain An-Fo-Qtz diagram

3 minerals in th efinal rock depends on which side of the dashed line the bulk comp is (between An and En)

liquid can end its journey at P or can end at E
from binary, after P it’s solid, doesn’t need to go past that

if you start at En, you’ll move away from En and end at E

starting left side (mostly), you’ll end at P, if on the right side you’ll end at E
exception: if you are to the right of dashed line but starting in Fo that’s peritectic situation: start crystalizing forsterite, reaches cotectic between Fo and En, then reaches P, not finished crystalizing, so it goes to E (forsterite dissolves, the final rock contains no Fo)