how to build a binary phase diagram: simple eutectic systems · tutorial on binary phase diagrams...

TUTORIAL ON BINARY PHASE DIAGRAMS

How to Build a Binary Phase Diagram:Simple Eutectic Systems

Problem:

Solution:

A binary phase diagram shows thephases formed in differing mixturesof two elements over a range oftemperatures.

Compositions run from 100%Element A on the left of the diagram,through all possible mixtures, to100% Element B on the right.

How to represent themicrostructure of an alloygiven a particulartemperature and composition

Weight percentages are often used to specifythe proportions of the alloying elements, butatomic percent is also used. The type ofpercentage is specified:

Cu - 20 wt% Al for weight percentages andCu - 20 at% Al for atomic percentages.

The composition of an alloy is givenin the form A - x%B.

For example, Cu - 20%Al is 80%copper and 20% aluminium



Observation:Alloys tend to solidify over atemperature range, rather than at aspecific temperature like pureelements.

At each end of the phase diagramonly one of the elements is present(100% A or 100% B) and thereforea specific melting point exists.

The phase diagrams for some simplebinary alloys do not have eutectic points,such as the Cu-Ni system discussedpreviously

Systems:

Construction:

Sometimes there is a mixture of the constituent elementswhich produces solidification at a single temperature like apure element. This is called the eutectic point. The eutecticpoint can be found experimentally by plotting cooling ratesover ranges of alloy composition.



Eutectic liquidus:By cooling alloys from the liquidstate and recording their coolingrates, the temperature at whichthey begin to freeze can bedetermined and then plotted on thephase diagram.

. Construction:

If a sufficient number of experiments areperformed over a range of compositions, astart of solidification curve can be plottedonto the phase diagram.

This curve will join the three singlesolidification points and is called theliquidus line.



Solubility limits:In the same way that sugardissolves in water, it is possible forone element to dissolve in another,while both remain in a solid state.This is called solid solubility, anddepends on crystal structure,electronegativity, valence, andatomic radius. For most solids, thesolubility limit is a few percent byweight. This solubility limitnormally depends on temperature.

Construction: The extent of the solid solubility region isplotted on phase diagram and appropriatelylabeled. A solid solution of B in A (i.e. mostlyA) is called alpha and a solid solution of A inB (i.e. mostly B) is called beta.

It is worthwhile to note that somepairs of elements have zero solidsolubility;a good example is Al - Si alloys, wherealuminium has zero solid solubility insilicon. We say Al is insoluble in Si:



Eutectic isotherm:If an alloy's composition does notplace it within the small solidsolution regions at either side of thephase diagram, the alloy willbecome fully solid at the eutectictemperature, shown as the eutecticisotherm on the phase diagram.

Construction:The region below the eutecticisotherm, and outside the solidsolution region, will be a solid mixtureof alpha and beta, that is, a two phaseregion, and the diagram is labeled toreflect this.

At alloy compositions and temperatures betweenthe start of solidification and the point at which itbecomes fully solid (the eutectic temperature) amushy mix of either alpha or beta will co-exist assolid lumps within a liquid mixture of A and B.These two phase partially solid regions are markedon the phase diagram.


Binary Phase Diagrams: Simple Eutectic Systems

Eutectic solidification:Consider a mixture of elements Aand B at the eutectic composition ata high enough temperature so thatthe mixture is fully liquid.

Microstructure:

Eutectic reaction:L(CE) α(CαE) + β(CβE)



Eutectic solidification:The mixture is slowly cooled,(maintaining equilibriumconditions) undergoing no phasechange until it reaches temperatureT2, where it starts to solidify at anynucleation site. This is termedheterogeneous nucleation.

The alloy freezes into "stripes" which are alternatelayers of alpha and beta. These layers are very thin,often on the order of 1 micron and the reason thatthe eutectic forms in this way can be understood byconsidering diffusion times required to form thesolid. This microstructure is known as lamellar.

Microstructure:



Eutectic solidification:As the alloy cools below the eutectictemperature, T2, the existing nucleationsites will grow, adding alpha to alpha andbeta to beta.

These nucleating and growing regions ofsolid alloy will form grains. Grainboundaries are formed where growinggrains, which will be of differingorientations meet.

The eutectic composition solidifies, like a pureelement, at a single temperature, not over atemperature range.

Microstructure:



Eutectic solidification:The entire mixture rapidly solidifies into aeutectic solid.

Looking at the phase diagram, it can be seenthat the compositions of alpha and beta changewith temperature.

By considering tie lines and the phase diagram,it can be seen that beta has a decreasingproportion of A in it as the temperaturedecreases. Similarly the proportion of B inalpha decreases.

Even though the alloy is now solid, the compositionof the alpha and beta lamella must continue tochange as it cools (to room temperature forexample).

Atoms of A and B will diffuse across these lamellaeto produce the equilibrium compositions of alphaand beta at a given temperature.

Microstructure:


Simple Eutectic Systems: Hypo-eutectic compositions

Solidification:Consider a mixture of A and B so that theoverall composition of the alloy places itto the left of the eutectic point. Initiallythe alloy is at a high enough temperatureto ensure that the mixture is fully liquid.

When the composition of an alloy places it at alower composition than that of the eutectic point itis called hypo-eutectic.

If the phase diagram had been drawn the other wayaround, with 100%A on the right and 100%B onthe left, then the same alloy would be called hyper-eutectic, since it would have a composition greaterthan that of the eutectic.

Microstructure:



Solidification:The hypo-eutectic mixture is slowlycooled, undergoing no change in stateuntil it reaches temperature T1, when itreaches the liquidus. Here, alpha phasestarts to solidify at any nucleation site,such as a defect on the container wall oron an impurity particle.

Microstructure:

The alpha solidifies as dendrites, which grow tobecome grains of alpha.

The first solid to form is called the primarysolid, and in this example, would be calledprimary alpha.



Solidification:As the alloy continues to cool the existingnuclei grow (coarsen) and additional siteswill continue to form within the liquidparts of the mixture.

These nucleating and growing regions ofsolid alloy form grains, and when thesemeet grain boundaries are formed. Theprimary alpha dendrites grow, whichaccounts for the shapes the alpha formsin cross sectional samples.

Microstructure: As the remaining liquid cools its composition becomesricher in B (following the liquidus). The composition ofsolid alpha also becomes richer in B, as indicated bythe phase diagram. If cooling is not sufficiently slow(i.e. non-equilibrium) then B atoms will not be able todiffuse into the grains of alpha. If this is the case thenmicrostructural “coring” will occur.



Solidification:As alpha solidifies it removes A and Batoms from the remaining liquid. Alphais mostly A (with a small amount of B)and so the remaining liquid becomesenriched in B. This continues untilenough A has been removed so that theremaining liquid, following the liquidus,is of eutectic composition.

This composition will be achieved attemperature T2, at the point where thetemperature crosses the eutectic line.

Microstructure:At this point alpha stops forming as a discrete solidand the remaining liquid solidifies into the lamellareutectic composition of alpha and beta. Therefore,solid eutectic forms.



Solidification:The existing eutectic nucleation siteswill grow, adding alpha to thelamellae of alpha, and beta to thelamellae of beta in the eutecticregions. New sites will continue toform.

Microstructure: Note that, unlike the alpha solidification, it is notnecessary to continue decreasing the temperature toachieve full solidification. The eutectic liquid solidifiesin the same way as a pure solid, at a specifictemperature.



Solidification:The entire alloy has now solidifiedinto a mixture comprising grains ofalpha and grains of eutectic (alphaand beta in a lamellararrangement).

Microstructure: The diffusion processes through the solid, which occuras the alloy cools, are more complex than those of theeutectic case. As with a eutectic alloy, the amount of Bin the alpha phase changes with temperature, and so Bwill have to diffuse through the alpha. This diffusionmust also occur in the grains of pure alpha, as thecomposition of alpha also changes. This can be seen byexamining the diagram.

.


Eutectic Systems: Hyper-eutectic compositions

Solidification:Now consider a mixture of A and Bsuch that the overall composition ofthe alloy places it to the right of theeutectic. Initially the alloy is at ahigh enough temperature to ensurethat the mixture is fully liquid.

Microstructure: Then the composition of an alloy places it to the rightof the eutectic point it is called hyper-eutectic. If thephase diagram had been drawn the other way around,with 100%A on the right and 100%B on the left, thenthe same alloy would be called hypo-eutectic, since itwould fall to the left of the eutectic point.



Solidification:The mixture is slowly cooled,undergoing no phase change until itreaches temperature T1, when itreaches the liquidus. Here primarybeta starts to nucleate at anynucleation site.

Microstructure: The beta solidifies as dendrites, which coarsen, orgrow, to become grains of beta phase. The first solid toform is called the primary solid and so, in this case,primary beta is formed.



Solidification:As the alloy cools, the existingnucleation sites will grow and furthernucleation sites will form within theliquid.

These nucleating and growing regionsof solid beta alloy form grains, andwhen these meet, grain boundaries areformed. The primary beta dendritesgrow, which accounts for the shape ofbeta in cross sectional samples.

Microstructure: As the remaining liquid cools, its composition becomesenriched A (effectively following the liquidus). Thecomposition of the solid beta also becomes richer in A,as shown by the phase diagram. If cooling is relativelyfast (i.e. non-equilibrium) then A atoms will not beable to diffuse into the centres of the grains of beta. Ifthis is the case then microstructural “coring” willoccur.



Solidification:As beta solidifies, A and B atoms areremoved from the remaining liquid.Beta is mostly B (with a small amountof A) and so the remaining liquidbecomes enriched in A. This continuesuntil enough B has been removed sothat the remaining liquid - followingthe liquidus - is of eutectic composition.

This composition will be achieved attemperature T2, at the point where thetemperature crosses the eutectic line.

Microstructure: At this point beta stops forming as a discrete solid andthe remaining liquid starts to solidify into the lamellareutectic composition of alpha and beta. Therefore,solid eutectic forms.



Solidification:The existing eutectic nucleationsites will grow, adding alpha tothe lamellae of alpha, and beta tothe lamellae of beta in theeutectic regions. New sites willcontinue to form.

Microstructure: Note that, unlike the beta solidification process, it isnot necessary to decrease the temperature to achievefull solidification. The eutectic solidifies in the sameway as a pure solid, at a specific temperature.



Solidification:The entire alloy has nowsolidified into a mixtureconsisting of grains of beta andgrains of eutectic mixture (alphaand beta). Thus, themicrostructure of the solidifiedalloy contains two phases; onephase is beta (primary beta), theother phase is the eutectic(consisting of alternating layersof alpha and beta).

Microstructure: The diffusion processes through the solid, which occuras the alloy cools, are more complex than those of theeutectic case. As with a eutectic alloy, the amount of Ain the beta phase changes with temperature, and so Awill have to diffuse through the beta. This diffusionmust also occur in the grains of pure beta, as thecomposition of beta also changes. This can be seen byexamining the diagram.


The Fe-C system

Background:In their simplest form, steels aresimply alloys of Iron (Fe) andCarbon (C). (C is an interstitialsubstitutional solute in Fe) TheFe-C phase diagram is shown onthe right, up to around 7%Carbon.

This is a fairly complex phase diagram; fortunately,most of the technologically interesting materials existnear the lower left-hand corner of the diagram.


Binary systems: Ag-Cu


Binary systems: Pb-Sn


Binary systems: Pb-Sn microstructures

A eutectic microstructurenote the alternating light and dark bands in each grain.


Binary systems: eutectic solidification

Eutectic microstructure


Binary systems: hypo-eutectic microstructures

Photomicrograph of a hypo-eutectic microstructure


Binary systems: other invariant points

eutectoid:δ γ + ε

peritectic:γ + L δ

peritectic:δ + L ε

Eutectoid: one solid phase transforms into two other solid phases upon coolingPeritectic: one solid and one liquid phase transform into another solid phase upon cooling


Intermediate phases: the Cu-Zn system


The Fe-C system


The Fe-C system: eutectoid microstructure

This microstructure is called “pearlite,” which is a mixture of ferrite (α-Fe) + cementite (Fe3C)(ferrite = light phase, cementite = dark phase)


The Fe-C system: hypo-eutectoid microstructure

This microstructure shows proeutectoid ferriteand pearlite

fraction of pearlite, Wp = T/(T+U)fraction of proeutectoid ferrite, Wα = U/(T+U)


The Fe-C system: hyper-eutectoid microstructure

fraction of pearlite, Wp = X/(V+X)fraction of Cementite, WFe3C = V/(V+X)

Thismicrostructureshowsferrite andproeutecticcementite

how to build a binary phase diagram: simple eutectic systems · tutorial on binary phase diagrams...

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